APPROVED:

Angela K. Wilson, Major Professor Martin Schwartz,Committee Member Paul Marshall, Committee Member William E. Acree, Chair of the Department of

Chemistry Costas Tsatsoulis, Interim Dean of the Toulouse

Graduate School

TRANSITION METAL CATALYZED OXIDATIVE CLEAVAGE OF C-O BOND

Jiaqi Wang

Thesis Prepared for the Degree of

MASTER OF SCIENCE

UNIVERSITY OF NORTH TEXAS

May 2015

Jiaqi, Wang. Transition Metal Catalyzed Oxidative Cleavage of C-O Bond. Master of

Science (Chemistry-Physical Chemistry), May 2015, 96 pp., 25 tables, 16 figures, chapter

references

The focus of this thesis is on C-O bonds activation by transition metal atoms. Lignin is a

potential alternative energy resource, but currently is an underused biomass species because of

its highly branched structure. To aid in better understanding this species, the oxidative cleavage

of the Cβ-O bond in an archetypal arylglycerol β-aryl ether (β–O–4 Linkage) model compound

of lignin with late 3d, 4d, and 5d metals was investigated. Methoxyethane was utilized as a

model molecule to study the activation of the C-O bond. Binding enthalpies (∆Hb), enthalpy

formations (∆H) and activation enthalpies (∆H‡) have been studied at 298K to learn the energetic

properties in the C-O bond cleavage in methoxyethane.

Density functional theory (DFT) has become a common choice for the transition metal

containing systems. It is important to select suitable functionals for the target reactions,

especially for systems with degeneracies that lead to static correlation effects. A set of 26 density

functionals including eight GGA, six meta-GGA, six hybrid-GGA, and six hybrid-meta-GGA

were applied in order to investigate the performance of different types of density functionals for

transition metal catalyzed C-O bond cleavage. A CR-CCSD(T)/aug-cc-pVTZ was used to

calibrate the performance of different density functionals.

Copyright 2015

by

Jiaqi Wang

ii

TABLE OF CONTENTS

Page

LIST OF TABLES .......................................................................................................................... v

LIST OF FIGURES ...................................................................................................................... vii

CHAPTER 1 INTRODUCTION .................................................................................................... 1

CHAPTER 2 THEORETICAL BACKGROUND.......................................................................... 4

2.1 Schrödinger Equation ................................................................................................... 4

2.2 Electronic Structure Theory .......................................................................................... 7

2.3 Basis Sets .................................................................................................................... 14

2.4 References .................................................................................................................. 15

CHAPTER 3 TRANSITION METAL CATALYZED OXIDATIVE CLEAVAGE OF C-O BOND OF β–O–4 LINKAGE OF LIGNIN ................................................................................. 19

3.1 Abstract ....................................................................................................................... 19

3.2 Introduction ................................................................................................................ 19

3.3 Computational Details ................................................................................................ 22

3.4 Results and Discussions.............................................................................................. 23

3.5 Conclusion .................................................................................................................. 34

3.6 References .................................................................................................................. 35

3.7 Figures and Tables ...................................................................................................... 38

CHAPTER 4 PERFORMANCE OF DENSITY FUNCTIONALS FOR MODELING GAS PHASE REACTIONS OF LATE TRANSITION METAL ATOMS WITH METHANOL ....... 55

4.1 Abstract ....................................................................................................................... 55

4.2 Introduction ................................................................................................................ 56

4.3 Computational Details ................................................................................................ 59

4.4 Results and Discussion ............................................................................................... 60

iii

4.5 Conclusion .................................................................................................................. 72

4.6 References .................................................................................................................. 73

4.7 Figures and Tables ...................................................................................................... 76

CHAPTER 5 SUMMARY OF PERFORMANCE OF DENSITY FUNCTIONALS FOR C-O BOND INSERTION REACTIONS OF SMALL MOLECULES WITH TRANSITION METAL ATOMS .......................................................................................................................... 96

5.1 References .................................................................................................................. 96

iv

LIST OF TABLES

Page

Table 3.1. Ground State Multiplicities at CR-CCSD(T)/cc-pVTZ Level of Theory4 ............47

Table 3.2. RMSDs of Each Functional for Binding Enthalpies, Activation Enthalpies and Enthalpy Formations of 3d Species .......................................................................48

Table 3.3. RMSDs of Different Types of Functionals ............................................................48

Table 3.4. RMSDs of Each Functional for Activation Enthalpies and Enthalpy Formations of 4d Species .......................................................................................49

Table 3.5. RMSDs of Different Types of Functionals for Activation Enthalpies and Enthalpy of Formations of 4d Species ..................................................................49

Table 3.6. RMSDs of Each Functional for Activation Enthalpies and Enthalpy Formations of 5d Species .......................................................................................50

Table 3.7. RMSDs of Different Types of Functionals for Activation Enthalpies and Enthalpy Formations of 5d Species .......................................................................50

Table 3.8. MSDs of Each Metal and Overall 3d, 4d, and 5d Species for Each Functional ....51

Table 3.9. MSDs of Each Metal and Overall 3d, 4d, and 5d Species of Different Types of Functionals .............................................................................................................52

Table 3.10. RMSDs of Each Metal and Overall 3d, 4d, and 5d Species of Different Types of Functionals.........................................................................................................53

Table 3.11. RMSDs of Each Metal and Overall 3d, 4d, and 5d Species of Different Types of Functionals.........................................................................................................54

Table 4.1. Summary of the Density Functionals Applied in This Study ................................86

Table 4.2. Ground State Multiplicities Calculated at CR-CCSD(T)/aug-cc-pVTZ Level .....87

Table 4.3. MSDs and RMSDs of Each Metal and Overall 3d and 4d Species of Each Functional for Binding Enthalpies .........................................................................88

Table 4.4. MSDs of Different Types of Functionals of Each Metal and Overall 3d and 4d Species for Binding Enthalpies ..............................................................................89

Table 4.5. RMSDs of Different Types of Functionals of Each Metal and Overall 3d and 4d Species for Binding Enthalpies ..................................................................89

v

Table 4.6. MSDs and RMSDs of Each Metal and Overall 3d and 4d Species of Each Functional for Activation Enthalpies ....................................................................90

Table 4.7. MSDs of Different Types of Functionals of Each Metal and Overall 3d and 4d Species Activation Enthalpies...........................................................................91

Table 4.8. RMSDs of Different Types of Functionals of Each Metal and Overall 3d and 4d Species for Activation Enthalpies ..............................................................91

Table 4.9. MSDs and RMSDs of Each Metal and Overall 3d and 4d Species of Each Functional for Enthalpies Formation ....................................................................92

Table 4.10. MSDs of Different Types of Functionals of Each Metal and Overall 3d and 4d Species for Enthalpies Formation .....................................................................93

Table 4.11. RMSDs of Different Types of Functionals of Each Metal and Overall 3d and 4d Species for Enthalpies Formation ..............................................................93

Table 4.12. Difference between S2 and S(S+1) for Different Types of Calculations ...............94

Table 4.13. Comparison between RODFT and UDFT of Different Types of Functionals of Each Metal and Overall 3d and 4d Species ...........................................................94

Table 4.14. Comparison between RODFT and UDFT of Different Types of Functionals of Different Types of Reactions .................................................................................95

vi

LIST OF FIGURES

Page

Figure 3.1. Phenylpropane units, sinapyl, conyferyl and p-coumaryl alcohol .........................38

Figure 3.2. Reaction mechanism of TM atoms oxidative cleavage of C-O bond of methoxyethane .......................................................................................................39

Figure 3.3. Binding enthalpies of each metal species with different density functionals ........39

Figure 3.4. Activation enthalpies of each metal species with different density functionals ....39

Figure 3.5. Enthalpy formations of each metal species with different density functionals ....40

Figure 3.6. Optimized geometries and structural parameters at the B3LYP/cc-pVTZ ............41

Figure 3.7. Optimized geometries and structural parameters at the B3LYP/cc-pVTZ ............42

Figure 3.8. Optimized geometries and structural parameters at the B3LYP/cc-pVTZ ............44

Figure 4.1. Reaction pathway of TM atom-based C-O bond activation of methanol ..............76

Figure 4.2. The energy diagram of the reactions with spin inversion ......................................77

Figure 4.3. Binding enthalpies of the C-O bond cleavage of methanol for each transition metal atom ..............................................................................................................78

Figure 4.4. Activation enthalpies of the C-O bond cleavage of methanol for each transition metal atom ..............................................................................................................79

Figure 4.5. Enthalpies formation of the C-O bond cleavage of methanol for each transition metal atom ..............................................................................................................80

Figure 4.6. Optimized geometries and structural parameters at the B3LYP/aug-cc-pVTZ .....81

Figure 4.7. Optimized geometries and structural parameters at the B3LYP/aug-cc-pVTZ .....83

Figure 4.8. Optimized geometries and structural parameters at the B3LYP/aug-cc-pVTZ ....85

vii

CHAPTER 1

INTRODUCTION

Computational chemistry is an important branch of theoretical chemistry in which

chemical, mathematical, and computing skills are applied to model the structures, energies,

physical and chemical properties, and reactivates of atomic and molecular systems.

Computational methods have been employed in many fields, such as physics, chemistry, biology,

and geophysics, and are more favorable than traditional laboratory experiments when the

materials of interest are too difficult to obtain, too dangerous, or too expensive. Computational

chemistry helps chemists gain in-depth understanding about compounds. For instance, molecular

bonding information that may not be obtained from experimental methods can be obtained from

computational methods. Computational chemistry also assists in experimental chemistry as it

can help make predictions beforehand.

Ab initio methods are based on the Schrödinger equation. They solve the many-body

Schrödinger equation and give the energy and wave function of the system. The wave function

is a mathematical function that can be used to calculate the electron distribution. The

Schrödinger equation can only be solved exactly for molecules with one electron. Therefore,

several approximations can be made to deal with electron correlation. The Hartree-Fock method

generally accounts for 99% of the total energy, and to account for electron correlation, the

reference wave function must be expanded to more advanced calculations, such as Many-Body

perturbation theory, configuration interaction theory, and coupled cluster theory.

Semi-empirical techniques use parameters from experimental data to provide the input

into the mathematical models. Although semi-empirical calculations are faster than the ab initio

calculations, their results can be erratic.

1

The main methods used in this thesis are DFT methods that can be used for large systems

(hundreds or even thousands of atoms) at a modest computational cost. The total energy

calculated by DFT methods is expressed in terms of the total electron density rather than a wave

function.

The focus of this thesis is on C-O bonds activation by transition metal atoms. Because of

the depletion and environmentally unfriendly properties of fossil fuels, renewable resources are

needed to replace fossil fuels. Biomass, such as lignin, has been of great interest. Catalytic

conversions of biomass to useful chemicals and energies include activation of C-O bonds,

hydrogenation, and hydrodeoxygenation. Studies of the intrinsic properties of catalysts that

control the reactions would help better elucidate and improve the reaction mechanisms. Since

metal centers play important roles in the performance of the TM-based catalysts (both

homogenous and heterogeneous), the reactivity of neutral metal atoms can provide a starting

point to investigate the intrinsic behavior of TMs in catalysis and guide the design of novel

catalysts.

In Chapter 2, a brief review of the theoretical methods most often used in computational

studies is given. The Schrödinger equation, Hartree-Fock methods, post Hartree-Fock methods,

and density functional theory are described. Basis sets associated with the use of these methods

are also included in this chapter.

Chapter 3 presents the computational investigation of the C-O bond cleavage of β–O–4

linkage of lignin by late 3d (Fe, Co, and Ni), 4d (Ru, Rh, and Pd), and 5d (Re, Os, and Ir)

transition metal atoms. Methoxyethane was used as the representative module molecule to study

the performance of several DFT methods (BLYP, B97D, TPSS, M06L, PBE0, M06, TPSSh, and

B2PLYP). As shown by early work, TM atoms tend to catalyze C-O bond activation reactions

2

that have lower activation enthalpies and form more stable products than later TM atoms when

breaking the C-O bond. 3d and 4d TMs tended to have lower binding enthalpies and higher

activation enthalpies than 5d TMs. PBE0 performed better than other considered DFT methods

with RMSDs of 3.5 kcal/mol, 6.2 kcal/mol, and 4.4 kcal/mol for 3d, 4d, and 5d species

respectively.

In Chapter 4, the performance of density functionals for modeling gas phase reactions of

late TM atoms (Fe, Co, Ni, Cu, Ru, Rh, Pd, and Ag) with methanol is discussed. DFT has

become a common choice for the transition metal containing systems. It is important to select a

suitable functional for the target reactions. A set of 26 DFT methods including eight GGAs, six

meta-GGAs, six hybrid-GGAs, and six hybrid-metal-GGAs were applied in order to study the

performance of different types of density functionals for transition-metal-catalyzed bond

cleavage. The results showed that hybrid-GGAs and hybrid-meta-GGAs performed similarly and

that both types of functionals had lower root mean squared deviations than GGAs and Meta-

GGAs with respect to CR-CCSD(T) calculations. Earlier metals also tended to have more

exothermic reactions than later metals.

3

CHAPTER 2

THEORETICAL BACKGROUND

2.1 Schrödinger Equation

Computational chemistry is a rapidly growing branch of chemistry that investigates

chemical problems using various mathematical approximations and computer programs. One of

the foundations of computational quantum chemistry is to solve the time independent

Schrödinger equation1-7 (Eqn. 1) which describes the relationship between the structure and the

energy of a system.

(1)

In this expression, is the wave function (eigenfunction for a given Hamiltonian) of a

chemical system, which describes the electronic and nuclear structure of a giving system, and

is the Hamiltonian operator, which operates on the wave function, Ψ, to return the total energy

(E) of the system as an eigenvalue. The Hamiltonian operator includes five contributions to the

total energy of a system with N electrons and M nuclei: the kinetic energies of electrons and

nuclei ( ), the attraction between electrons and nuclei ( ), and the inter-electronic

and inter-nuclear repulsions ( and ) (Eqn. 2).

(2)

The different terms of this equation are shown as following (Eqn. 3):

(3)

4

where is the mass of the nucleus, is the charge of nucleus, is the distance between

electron i and nucleus A, is the distance between electron i and electron j, and is the

distance between the nucleus A and nucleus B.

2.1.1 Born-Oppenheimer Approximation

Since nucleus is much heavier than an electron, its velocity as compared to that of the

electron is negligible. Therefore, the motion of electrons and nuclei can be separated, so the

wave function can be divided into the electronic wave function and the nuclear wave function.

This is the Born Oppenheimer approximation,8 which considers electrons to be moving in a field

of fixed nuclei. The Hamiltonian operator can be reduced to the electronic Hamiltonian. Thus,

the wave function Ψ is only dependent on the kinetic energy of the electron (Te), the electron-

nuclear attrction (VNe) and the inter-electronic repulsion (Vee). The electronic Hamiltonian is

defined according to Eqn. 4.

(4)

Application of the electronic Hamiltonian to the wave function results in the electronic

Schrödinger equation described in Eqn. 5.

(5)

2.1.2 Slater Determinant

The wave function Ψelec is described by both the electrons’ spatial coordinates and their

spin quantum number, , where is the spatial component and is the spin component.

5

Each electron has two possible orthonormal spin states, α (spin up) and β (spin down), under

magnetic conditions (Eqn. 6&7):

< α|α >= < β|β >= 1 (6)

< α|β >= < β|α >= 0 (7)

Since electrons are indistinguishable, the total wave function must be anti-symmetric

with respect to interchange of spatial or spin coordinates. This demonstrates Pauli’s exclusion

principle (‘no two electrons can occupy the same [quantum] state’).9-10 To meet this mentioned

restriction, the electronic wave function is expressed as an anti-symmetric product of an N-

electron system with N spin orbitals, referred to as the Slater determinant (Eqn. 8). 11

(8)

The Slater determinant is normalized with factor 1/ √ N!. The single-electronic wave

functions are described by the columns and the electron coordinates are described by the rows.

2.1.3 Variational Method

The variational principle states that any approximate wave function will yield an energy

that is greater than or equal to the ground state energy, E0 (Eqn. 9).

(9)

Thus, by varying and adjusting Ψ until the energy is minimized, the “best” solution to the

Schrödinger equation can be found using the variational principle.

6

2.2 Electronic Structure Theory

The term “ab initio” translated from Latin means “from the beginning.” This refers to the

fact that computations using ab initio methods depend solely on quantum mechanics without any

experimental data.12-13 However, even with the Born-Oppenheimer approximation, an ab initio

calculation of a many-body system is complex, and may not always be computationally feasible.

In Paul Dirac’s 1929 paper,14 he said that “The underlying physical laws necessary for the

mathematical theory of a large part of physics and the whole of chemistry are completely known,

and the difficulty is only that the exact application of these laws leads to equations much too

complicated to be soluble. It therefore becomes desirable that approximate practical methods of

quantum mechanics should be developed, which can lead to an explanation of the main features

of the complex atomic systems without too much computation." Different types of ab initio

calculations require different approximations including: Hartree-Fock (HF)15-19 and electron

correlation methods or post-Hartree-Fock theories. Density functional theory (DFT) is another

electronic structure method, but it is not strictly ab initio due to the common use of fitted

parameters in the functionals.

2.2.1 Hartree-Fock Approximation

Hartree-Fock (HF) theory15-19 provides a good starting point for theoretical methods and

is fundamental to many electronic structure theories. The electronic Hamiltonian can be divided

into a one-electron operator, (Eqn. 10), which describes the kinetic energy and the electron-

nuclei attraction potential and a two-electron operator, (Eqn.11) that describes the inter-

electronic repulsion:

7

(10)

(11)

In HF method, the one-electron part can be solved exactly, while the two-electron part

can be approximated by assuming that each electron moves independently of the others in an

average field created by the rest of N-1 electrons. The HF equation can be written as (Eqn. 12),

(12)

where is an eigenfunction of the Fock operator, is the corresponding energy. The Fock

operator is an effective one-electron operator which has the form20 (Eqn. 13).

(13)

In this expression, the HF potential, replaces the more complex inter-electronic repulsion

1/rij operator by representing the average repulsion potential created by the other N-1 electrons.

It is composed of two terms, the Coulomb operator and the exchange operator .

(14)

(15)

(16)

The Coulomb term gives the average local potential at point due to the charge

distribution from the electrons in spin orbital . The exchange term switches spin orbitals

and .

8

2.2.2 Electron Correlation

Since HF theory makes the approximation that each electron only experiences the

average repulsion of the remaining electrons, the correlation between electron motions is

effectively ignored. Therefore, HF wave functions typically only recover ~99% of the total

electronic energy. The remaining ~1% energy can have a large influence on the properties

calculated for the system. The energy difference between the exact electronic energy (Eexact) and

the HF-calculated energy (EHF) is the electron correlation energy (Ecorr), shown in Eqn. 17.

(17)

Electron correlation methods account for the neglected instantaneous electron-electron

interactions from the HF method. The HF method uses a single Slater determinant to describe the

molecular wave function. The main problem caused by the lack of electron correlation is that the

total energy obtained is always higher than the actual value because of the overestimated inter-

electron repulsion. The usual way to introduce the correlation is to take into account the excited

states of a given system by adding additional Slater determinants using the HF wave function as

the starting point (Eqn. 18). The combination of which gives the new trial function that should be

closer to the real system than the original determinant.

(18)

is the coefficient defining the contribution of each exited state to the wave function.

Electron correlation can be divided into two parts with different physical concepts21: non-

dynamical correlation and dynamical correlation. Non-dynamical correlation energy is caused by

degeneracy or near degeneracy and is responsible for bond cleavage or formation and most

excited states. The major part of the correlation energy is associated to a few extra configurations

9

besides the HF configuration. The dynamical correlation energy, on the other hand, is related to

the motion of the electrons.

2.2.2.1 Coupled Cluster (CC) Methods

Coupled cluster (CC) theory22-25 is one of the most commonly used post-HF quantum

chemistry methods to account for electron correlation and essentially includes electron

correlation by using the exponential cluster operator to act on the reference wave function to

generate excited determinants. The CC wave function is written in the form (Eqn. 19),

(19)

and the cluster operator is written in the form (Eqn. 21),

…

(20)

where , , …, are the operators for single, double, ..., infinite order excitations, i, j, …

represent occupied states, and a, b, … represent unoccupied states, and t is the amplitude

determined by the constraint that Eqn. 20 be satisfied.

When used with large basis sets, singles and doubles couple cluster with perturbative

treatment of triple excitations, CCSD(T), has been used in accurate quantum-chemical

10

calculations.57,58 Unfortunately, CCSD(T) is inadequate to describe the potential energy surfaces

(PESs) involving bond breaking. However, the completely renormalized couple cluster method

[CR-CCSD(T)] can be used to study PESs involving a breaking of single chemical bonds with

the results of nearly spectroscopic accuracy. The computational cost of the CR-CCSD(T)

calculations are comparable to the costs of the standard CCSD(T) calculations. Therefore, CR-

CCSD(T) method is a useful alternative to the standard CCSD(T) methods when single bonds are

broken. 59,60

2.2.3 Density Functional (DFT) Theory

Density functional theory (DFT), built on the Hohenberg-Kohn theorem27 and Kohn-

Sham equations28, has been used quite extensively in the last few decades because of its

reliability and capability to deal with relatively large systems at relatively low computational

costs.29 The basic concept of DFT is that the ground state energy of a system depends only on the

electron density.30 Therefore, the electronic states of atoms, molecules, and materials are

described in terms of the three-dimensional electronic density, which is a great simplification

over wave function theory, which describes electronic properties by calculating or making

approximations upon the 3N-dimensional anti-symmetric wave function a system with N

electrons. According to the Hohenberg-Kohn theorem, 27 the energy of the ground state is a

unique functional of the electronic density, ρ(r). Although Hohenberg-Kohn theorem marked the

beginning of modern DFT, it yields a poor representation of the kinetic energy of a system;

however, the Kohn-Sham density functional theory28, the most widely used theory in quantum

chemistry, resolves the problem by introducing an approximate form of kinetic energy by

building a fictitious non-interacting system from a set of one-electron functions, where each

11

electron moves in an average repulsion field due to surrounding electrons.31 The total energy of

system is divided in the following parts (Eqn. 21),

(21)

where is the kinetic energy of the hypothetical non-interacting electron system. is the

Coulomb interaction of electrons (or Hartree energy). is an external potential arising from

the nuclei, and is the energy which is omitted from the previous terms because of using the

idea of a non-interacting electron system, such as electron exchange, correlation energy, the

portion of the kinetic energy referring to the differences between the non-interacting and the real

system, and self-interaction caused by replacing the exact HF exchange. In practice, because the

exact form of is unknown, the functional described in the following represent different

approximations to the . Here, we will only introduce local density approximation (LDA) (first

rung), generalized gradient approximation (GGA) (second rung), meta-GGA (third rung), and

hybrid-GGA (fourth rung)

2.2.3.1 LDA: Local Density Approximation

LDA 33depends only on density of a uniform electron gas and is the base of the exchange-

correlation functionals. The form of its exchange-correlation functionals are known exactly or to

a very high accuracy. In the case of open shell systems, the local spin density approximation

(LSDA) considering spin polarization was developed, where the electron density, ρ, is replaced

by the spin electronic densities, ρα and ρβ. LDAs generally describe molecular properties, such as

structures and vibrational frequencies, more accurately than the HF method but poorly

characterize chemical reaction energetics, such as bond energies and energy barriers.

12

2.2.3.2 GGA: Generalized Gradient Approximation

The generalized gradient approximation (GGA)34-39 considers how electron density

changes, in other words the gradient of the electron density (∇ρ), as well as the density itself.

GGAs are usually divided into exchange and correlation terms that can be solved individually.

For example, B is an exchange functional developed by Becke, 39 P86 is a correlation functional

developed by Perdew, 37 and LYP is a correlation functional developed by Lee, Yang, and Parr. 35

Combinations of exchange and correlation functionals result in more complete descriptions of

systems. The most widely used combinations include BLYP, 35,39PBE, 40,41 and B97D. 42

2.2.3.3 Meta-GGA

Meta-GGA functionals are expansions of the pure GGA functionals by including the

second derivative of the electron densities and/or local kinetic energy densities, ∇2ρ, in the

exchange-correlation functional. Common meta-GGA functionals include TPSS,43 M06L,44 and

BB95.45 In gas phase studies of molecular properties, these functionals have been shown to offer

more accurate results than LDA functionals and GGA functionals with similar computational

cost as GGA functionals.

2.2.3.4 Hybrid-GGA

The self-interaction problem, i.e., the spurious interaction of an electron with itself poorly

describes the exchange parts of density functional. On the other hand, the exchange parts in HF

are defined exactly so the self-interaction is cancelled. Thus, hybrid-GGA functionals combine

the “exact exchange” from HF theory with some conventional treatment of DFT exchange and

correlation, such as GGA, to improve the performance of density functional. The most widely

13

used hybrid-GGA is the B3LYP35, 39 functional. Sousa et al.46 found that 80% of the references

included B3LYP in the Web of Science over the year 1999-2006 by analyzing the number of

different functional names in article titles and abstract. In B3LYP, three empirical parameters are

used to control the combination of the HF exchange and density functional exchange and

correlation, as shown below (Eqn. 22):

(22)

where a0 = 0.20, ax = 0.72, and ac = 0.8. This functional has shown great success in predicting

geometries and thermochemical properties of organic molecules in gas phase.47

2.3 Basis Sets

Correlation consistent basis sets, developed by Dunning and coworkers,48-52 aim to

systematically recover the correlation energy by increasing the size of the basis set. In this

design, the basis sets with similar contributions to correlation energy independent of the function

type are included in the same shell. For example, 2d and 1f functions are added together to a core

set of atomic HF function. Commonly employed correlation consistent basis sets are designated

as cc-pVnZ, where p for polarization functions, V for Valence, n stands for the number of shells

the valence functions are split into (n= D (3s2p1d), T (4s3p2d1f), Q (5s4p3d2f1g), 5

(6s5p4d3f2g1h), …), and Z for zeta level. The addition of diffusion function with a smaller

exponent to every angular momentum is indicted by a prefix “aug”. For instance, aug-cc-pVDZ

has diffuse s, p, d functions for the C atom. With the systematic improvement of the total

correlation energy with increasing basis set size, correlation consistent basis sets provide

opportunities to extrapolate energy to the CBS limit using several different methods. For

14

instance, Peterson53 proposed a three-point mixed Gaussian exponential extrapolation with aug-

cc-pVnZ (n=D, T, Q) basis sets (Eqn. 23):

( ) ))1(()1( 2−−−− ++= nnCBSn CeBeEE (23)

where B and C are parameterization constants and n is the ζ –level of the basis set.

The properties of transition metal-containing systems are computationally expensive to

calculate because a large number of basis functions is needed to describe the electrons. The cost

can be reduced by using effective core potentials (ECPs) that describe the potential of the nuclei

and core electrons as an average effect.54 In this way, not only is the computational cost reduced,

but some relativistic effects can also be included without carrying out the relativistic calculations

because these basis functions are generated from relativistic atomic calculations.55

2.4 References

[1] Schrödinger, E. Phys. Rev. 1926, 28, 1049.

[2] Schrödinger, E. Ann. Phys. 1926, 79, 361.

[3] Schrödinger, E. Ann. Phys. 1926, 79, 489.

[4] Schrödinger, E. Ann. Phys. 1926, 79, 734.

[5] Schrödinger, E. Ann. Phys. 1926, 80, 437.

[6] Schrödinger, E. Ann. Phys. 1926, 81, 109.

[7] Schrödinger, E. Die Naturwissenschaften, 1926, 14, 664.

[8] Born, M.; Oppenheimer, R. Ann. Phys. 1927, 84, 457.

[9] Pauli, W. Z. Phys. 1925, 31, 765.

[10] Pauli, W. "Exclusion principle and quantum mechanics." (Nobel Prize Lecture) Geneva, Switzerland, 1945.

[11] Slater, J. C. Phys. Rev. 1929, 34, 1923.

15

[12] Jensen, F. Introduction to Computational Chemistry; John Wiley & Sons Ltd.: Chichester, West Sussex, 1999.

[13] Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital

Theory; John Wiley & Sons, Inc.: New York, NY, 1986. [14] Dirac, P. A. M. Proc. R. Soc. A. 1929, 123, 714.

[15] Hartree, D. R. Proc. Cambridge Philos. Soc. 1928, 24, 89.

[16] Hartree, D. R. Proc. Cambridge Philos. Soc. 1928, 24, 111.

[17] Hartree, D. R. Proc. Cambridge Philos. Soc. 1928, 24, 426.

[18] Fock, V. Z. Phys. 1930, 61, 126.

[19] Fock, V. Z. Phys. 1930, 62, 795

[20] Löwdin, P.O. Adv. Chem. Phys. 1959, 2, 207.

[21] Siegbahn, P. E. M. The direct CI method, in Methods in Computational Molecular Physics, edited by G. H. F. Diercksen and S. Wilson, pages 189-207, D. Reidel, Dordrecht, 1983.

[22] Paldus, J. "Coupled Cluster Theory." In Methods in Computational Molecular Physics;

Wilson, S., Diercksen, H. F., Eds.; Plenum Press: New York, NY, 1992.

[23] Paldus, J.; Li, X. "A Critical Assessment of Coupled Cluster Method in Quantum Chemistry." In Advances in Chemical Physics; Prigogine, I., Rice, S., Eds.; John Wiley and Sons, Inc., 1999; Vol. 110; pp 1.

[24] Bartlett, R. J. Ann. Rev. Phys. Chem. 1981, 32, 359.

[25] Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head‐Gordon, M. Chem. Phys. Lett. 1989, 157, 479.

[26] Butt, D. A. E. J. Anal. Appl. Pyrolysis, 2006, 76, 38.

[27] Hohenberg, P.; Kohn, W. Phys. Rev. 1964, 136, B864.

[28] Kohn, W.; Sham, L. J. Phys. Rev. 1965, 140, A1133.

[29] Parr, R.G.; Yang, W. 1989. Density-functional theory of atoms and molecules, Oxford University Press, New York.

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[30] Szabo, A.; Ostlund, N. S. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory; McGraw‐Hill, Inc.: New York, NY, 1989.

[31] Geerlings, P.; DeProft, F.; Langenaeker, W. Density Functional Theory: A Bridge Between Chemistry and Physics. Eds.; VUB University Press: Brussels, 1999.

[32] Perdew, J. P.; Schmidt, K. AIP Conference; 2001, 577, 1-20.

[33] Slater, J. C. Phys. Rev. 1951, 81, 385.

[34] Becke, A. D. Phys. Rev. B. 1988, 38, 3098.

[35] Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B. 1988, 37, 785.

[36] Miehlich, B.; Savin, A.; Stoll, H.; Preuss, H. Chem. Phys. Lett. 1989, 157, 200.

[37] Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865.

[38] Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1997, 78, 1396.

[39] Becke, A. D. Phys. Rev. A 1988, 38, 3098.

[40] Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865.

[41] Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1997, 78, 1396.

[42] Grimme, S. J. Comp. Chem. 2006, 27, 1787

[43] Tao, J. M.; Perdew, J. P.; Staroverov, V. N.; Scuseria, G. E. Phys. Rev. Lett. 2003, 91, 146401.

[44] Zhao, Y.; Truhlar, D. G. J. Chem. Phys. 2006, 125, 194101.

[45] Becke, A. D. J. Chem. Phys. 1996, 104, 1040.

[46] Sousa, S. F.; Fernandes, P. A.; Ramos, M. J. J. Phys. Chem. A. 2007, 111, 10439.

[47] Miehlich, B.; Savin, A.; Stoll, H.; Preuss, H. Chem. Phys. Lett. 1989, 157, 200.

[48] Dunning, Jr., T. H. J. Chem. Phys. 1989, 90, 1007-1023.

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17

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18

CHAPTER 3

TRANSITION METAL CATALYZED OXIDATIVE CLEAVAGE OF C-O BOND OF β–O–4

LINKAGE OF LIGNIN

3.1 Abstract

Lignin is a potential alternative energy resource, but currently is an underused biomass

species because of its highly branched structure. To aid in better understanding this species, the

oxidative cleavage of the Cβ-O bond in an archetypal arylglycerol β-aryl ether (β–O–4 Linkage)

model compound of lignin with late 3d, 4d, and 5d metals was investigated. Methoxyethane was

utilized as a model molecule to study the activation of the C-O bond. Binding enthalpies (∆Hb),

enthalpy formations (∆H) and activation enthalpies (∆H‡) have been studied at 298K to learn the

energetic properties in the C-O bond cleavage in methoxyethane. A set of density functional

(DFT) methods (BLYP, B97D, TPSS, M06L, PBE0, M06, TPSSh, and B2PLYP) with a cc-

pVTZ basis has been applied in this study. A CR-CCSD(T)/cc-pVTZ was used to calibrate the

performance of different density functionals. PBE0 gave the lowest root mean squared

deviations (RMSDs) for both 4d and 5d species and second lowest RMSDs for 3d species, which

means that PBE0 described the most accurate properties of the considered reaction systems. The

energetic trend in terms of TMs showed that earlier TM systems tend to have lower activation

enthalpies and form more stable products.

3.2 Introduction

Biomass, a resource that can be processed into fuels, energy, and chemicals, has been of

great interest for replacing environmentally-unfriend fossil fuels. Lignocellulosic biomass has

three main advantages over fossil fuels: it is a sustainable resource, it is produced through a

19

closed carbon cycle, and it produces smaller amounts of other damaging gases, such as carbon

dioxide, when degraded.1 The conversion of cellulose to ethanol and other biofuels has been

extensively studied; however, research on lignin, which is 15-30% by weight and 40% by energy

of lignocellulosic biomass, is very scarce. In fact, although lignin is one of the largest sources of

organic raw material, it is primarily used to provide heat or is treated as a by-product of the paper

industry instead of being converted to useful chemicals.2

One reason that lignin is not currently used as a chemical feedstock is that lignin is very

difficult to convert into high commercial value chemicals due to its complicated chemical

structure, which is a highly branched three-dimensional phenolic polymer formed from three

main types of phenylpropane units [sinapyl alcohol, conyferyl alcohol, and p-coumaryl alcohol

(Figure 1)] connected by various types of ether and C-C linkages.3

Because of the complex structure, model compounds, rather than lignin itself, are

commonly employed in lignin decomposition and conversion studies to help illustrate the

intricate reaction properties. The β-O-4 linkage, 1-(4-hydroxy-3-methoxyphenyl)-2-(2-

methoxyphenoxy)-1,3-propanediol, comprises 50-60% of lignin linkages in both softwood and

hardwood lignin, and thus is commonly used to represent the structure of lignin.4

Three major experimental processes have been used to study the thermal decomposition

of lignin model compounds. Gasification converts lignin to synthesis gases including H2, CO,

CO2, and CH4.5, 6 Hydrolysis uses water to break lignin to monomeric or oligomeric units.7,8

Pyrolysis converts lignin to bio-oil in the absence of air at various temperatures and heating

rates.9 Among these three thermal degeneration methods, pyrolysis, which lacks selectivity of

specific products, is studied the most extensively.10,11 Many experimental and theoretical

investigations showed that lignin pyrolysis is a radical process that starts with a homolytic

20

cleavage of the weak Cβ-O bond, while the stronger Cα-Cβ bond is cleaved less frequently, but

only at temperatures higher than 200°C.12-16 Lignin degeneration using ligninolytic enzymes has

low efficiency and high cost because the fungus that produces the enzymes is slow-growing and

hard to remove.17 C-C and C-O bonds were broken in various ratios with different oxidative

enzymes. For instance, Kirk and coworkers18 discovered that the oxidative cleavage of the Cα-Cβ

bond by the fungus phanerochaete chrysosporium was the primary reaction during lignin

degradation, while the cleavage of the O-C4 bond occurred less frequently. In contrast, Vicuna

and coworkers19 found that Cβ-O bond cleavage was more important for lignin decomposition by

pseudomonas acidovoran.

Compared to traditional thermal decomposition and biodegradation, chemical

decomposition of lignin by catalysis has many advantages, such as high selectivity and easily

controlled processes.20 Heterogeneous catalysts in particular have easier separation processes, are

less expensive, and have longer lifetimes than other types of catalysts.21 Therefore, the atomic-

level investigation of the intrinsic catalytic properties of different transition metals provides a

crucial foundation for heterogeneous metal catalyst design for lignin decomposition. Before

considering more complex catalysis reactions involving solid state surfaces/nanoparticles and

entire β-O-4 linkages, it is more reasonable to examine simpler representative models, such as

methoxyethane and neutral transition metal atoms with accurate high-level quantum mechanical

methods to understand why certain transition metals can activate C-O bonds more effectively

than others. This study investigated the fundamental energetics of the oxidative cleavage of the

β-O-4 linkage in a lignin model compound. Many intrinsic properties of transition metal

catalysts that affect the activation of the C-O bond were investigated by the study of reactions

21

between several bare, late 3d, 4d, and 5d transition metal (TM) atoms (Fe, Co, Ni, Ru, Rh, Pd,

Os, Ir, and Pt) and methoxyethane.

Despite the development of cost-efficient theoretical methods and the availability of

super computing resources in recent decades, the application of wave functional methods are still

typically limited to small systems. Density functional theory (DFT) is a more computationally

affordable alternative because of its excellent cost-to-performance ratio.22 B3LYP is an

especially popular method in computational chemistry because it predicts ground-state geometric

parameters of molecules accurately. Over the past decades years, several different types of

density functionals have been developed and applied in the field of transition metal chemistry.22

Therefore, this paper applied a set of generalized gradient approximation (GGA) functionals,

including pure-GGA (BLYP23 and B97D24), meta-GGA (TPSS25 and M06L26), hybrid-GGA

(B3LYP23,27,28 and PBE029-31), hybrid-meta-GGA (M0626 and TPSSh25,32), and double-hybrid-

GGA (B2PLYP), to choose a suitable DFT method to treat TM atom-based bond activation

reactions.

3.3 Computational Details

All the stationary points studied in this work were optimized using the Becke’s three-

parameter Lee-Yang-Parr (B3LYP) exchange-correlation functional, which has shown to give

reliable geometries and vibrational frequencies for many 3d transition metal compounds.33,34 All

values were calculated with the correlation consistent polarized triple-ζ quality (cc-pVTZ35) basis

set for main group and 3d transition metal atoms and a small-core relativistic pseudopotential

basis set (cc-pVTZ-PP36,37) for the 4d and 5d transition metal atoms. Harmonic frequency

calculations following the equilibrium geometry calculations also using B3LYP obtained the

22

thermal corrections. Single point calculations were performed on the optimized structures using

the following set of density functional methods: BLYP23 and B97D24 (pure-GGA), TPSS25 and

M06L26 (meta-GGA), B3LYP23,27,28 and PBE029-31 (hybrid-GGA), M0626 and TPSSh25,32 (hybrid-

meta-GGA), and B2PLYP38 (double-hybrid-GGA) to study the enthalpy formations. Thermal

corrections were added to single point calculations for the enthalpy changes. The performance of

these methods were evaluated by comparing their results to the more accurate enthalpies

obtained by completely renormalized (CR)-CCSD(T) calculations. All of DFT calculations in

this paper were carried out with the Gaussian 09 program package39, while the NWChem

computational chemistry software suite40 was applied for the CR-CCSD(T) calculations.

3.4 Results and Discussions

Several previous experimental and theoretical studies have shown that for reactions

between ethers and transition metal ions or neutral transition metal atoms: the metal center binds

to the oxygen of the ether to form the adducted complex, which then rearranges to form the

intermediate structure by C-O oxidative addition and ends with H migration.41-45 This paper will

focus on C-O bond cleavage that plays an important role in lignin decomposition so H migration

was not studied. The reaction pathway is shown in Figure 3.2. The metal center binds to the

oxygen atom of methoxyethane to form the adduct [MO(CH3)(CH3CH2)], which then goes

through the transition state ([CH3CH2MOCH3] ‡) by oxidative insertion to form the complex

(CH3CH2MOCH3 ), which is referred as the final product later in this paper. Three reaction

terms, binding enthalpies (enthalpy difference between reactants and adduct), activation enthalpy

(enthalpy difference between adduct and transition state) and enthalpy formations (enthalpy

23

difference between final complex and reactants) will be discussed to make comparisons of the

catalytic abilities of TMs.

3.4.1 Ground State Multiplicities

The CR-CCSD(T)/cc-pVTZ level of theory was used to determine the ground state

multiplicities for the transition metals and the transition metal complexes (Table 3.1). The

multiplicity of the ground state was used in calculating the thermodynamics, specifically

considering three enthalpy formations: binding enthalpies (∆Hb), activation enthalpies (∆H‡), and

enthalpy formations (∆H). As shown in Table 1, Fe, Co, and Pd had spin allowed reactions while

the rest of considered TM did not. All density functionals, carried out with a triple ζ basis set cc-

pVTZ(PP), predicted the correct ground state multiplicities for all compounds of the spin

allowed reactions. However, even with this high level of basis set, only the Ir and Pt systems

showed the correct spin multiplicities from all the DFT methods except for B2PLYP which

failed to predict the corrected spin multiplicities of transition states for all metal systems. BLYP

and B97D predicted NiO(CH3)(CH3CH2)) to be a singlet instead of triplet and PBE0 and

B2PLYP predicted the triplet as more stable than singlet for ([CH3CH2MOCH3] ‡). For Ru

system, all DFT methods failed to predict the singlet as the ground state for transition state

complexes except BLYP and TPSS. BLYP, B97D, and M06 predicted a doublet as the ground

state multiplicity instead of the actual quartet state for Rh, while TPSS, B3LYP, and B2PLYP

fail to predict doublet as the ground state multiplicity for adduct complexes. All DFT methods

failed to predict triplet state to be more stable than the real ground state quintet for

CH3CH2OsOCH3. Among these considered density functionals, M06L is the only one that

predicted the correct ground state multiplicities successfully throughout all the reaction steps. In

24

previous studies,26-46 M06L gave considerably better results for non-covalent bond systems.

Marom and coworkers47 found that M06L offered a reduction of error for systems with

dispersion interactions and for mixed binding complexes. On the other hand, B2PLYP, has the

drawback of giving unreliable indications of long-range dispersion interactions, and performed

worse than other considered DFT methods in predicting the ground state multiplicities.26

Therefore, long range interactions were expected to have an important effect on the

thermodynamics of the studied system. The same situation was also found in previous studies of

the activation of heteroatom bonds by transition metals.48-50 For instance, Feng and coworkers,50

reported that long range interactions should be considered in order to get accurate results in the

study of the activation of CO by single gold atom.

3.4.2 Reaction Energetics of the Activation of C-O Bond of Methoxyethane

3.4.2.1 Binding Enthalpies: M + CH3OCH2CH3 = MO(CH2CH3)CH3

The binding enthalpies shown in Figure 3.5 are the enthalpy difference between the

reactants and the adducts. The transition metals first approached the oxygen atom of

methoxyethane and formed an adduct MO(CH2CH3)CH3. The orbital overlap between the metal

atom center and the O oxygen atom accompanies with the electron donation. Therefore, the

metal atom centers need to have vacancies on either the nd or (n+1)s orbitals in order to accept

incoming electron(s) from the oxygen atoms. The electron configurations of the TM atoms

ground state multiplicities (Table 3.1) are: Fe: [Ar] 3d7 4s1, Co: [Ar] 3d8 4s1, Ni: [Ar] 3d9 4s1,

Ru: [Ar] 4d7 5s1, Rh: [Ar] 4d8 5s1, Pd: [Ar] 4d10 5s0, Os: [Ar] 4f14 5d6 6s2, Ir: [Ar] 4f14 5d8 6s1,

Pt: [Xe] 4f14 5d9 6s1. Thus all the TM atoms can accept extra electron(s) and have an exothermic

binding reaction varying from -4.1 to -16.0 kcal/mol (CR-CCSD(T)/cc-pVTZ, Figure 3.3). The

25

binding enthalpies of 3d species is in the decreasing order of Co, Fe, and Ni, that of 4d species is

Rh, Pd, and Ru, and that of 5d species is Pt, Ir and Os. Most of the 3d and 4d species had lower

binding enthalpies than the 5d species. Group 9 TM atoms showed the strongest bonding with

methoxyethane except for Ir (-13.6kcal/mol) which had a slightly lower binding enthalpy than Pt

(-15.7kcal/mol) in CR-CCSD(T)/cc-pVTZ level of theory.

Most of the density functionals underestimated the binding enthalpies for group 10 TM

species but overestimated the binding enthalpies for group 9 TM species when compared to the

CR-CCSD(T)/cc-pVTZ results. B97D showed large deviations for Ru and Rh, and especially for

Pt with a binding enthalpy value 27.4kcal/mol lower than the CR-CCSD(T)/cc-pVTZ result.

BLYP, TPSS, and TPSSH underestimated the binding enthalpy of Pt-containing systems with the

corresponding deviations of 14.2, 18.5, and 16.1 kcal/mol. B2PLYP overestimate the binding

enthalpies for all TM species except Fe. It showed large deviations for Co and Ir, with 11.3 and

13.2 kcal/mol higher binding enthalpies than the CR-CCSD(T)/cc-pVTZ results respectively.

3.4.2.2 Activation Enthalpies: MO(CH2CH3)CH3 = [H3COMCH2CH3]‡

The activation enthalpies (∆H‡) shown in Figure 3.4 are the enthalpy differences between

the adducts and the transition states [H3CMOCH2CH3] ‡. The reactions catalyzed by all TM

atoms gave positive activation enthalpies based on the CR-CCSD(T)/CBS results. The ∆H‡ of 3d

species for the oxidative addition of the C-O bond of methoxyethane to the TM atoms followed

the trend Fe < Co < Ni, 4d species followed the trend Ru < Rh < Pd, and 5d species followed the

trend Os < Pt < Ir. These trends show that earlier TM species tend to have lower ∆H‡ than later

TM species for both 3d and 4d species. Most of the 3d and 5d TM species had higher activation

enthalpy than the 4d species. It is worth mentioning that the height of global reaction barrier,

26

which is the enthalpy difference between the reactants and the transition state, showed the same

trend as the ∆H‡ for 3d and 5d TM species.

All the considered density functionals, except B2PLYP, predicted lower values of ∆H‡

than that of CR-CCSD(T)/cc-pVTZ calculations, indicating that most of the density functionals

underestimated ∆H‡. For the Ni system, B97D and B2PLYP showed large deviations of 31.3

kcal/mol and 30.8 kcal/mol, respectively.

3.4.2.3 Enthalpy Formations: M + CH3OCH2CH3 = CH3CH2MOCH3

The enthalpy formations shown in Figure 3.5 are the enthalpy differences between the

reactants and the products. All TM-based C-O bond oxidative additions are exothermic with CR-

CCSD(T)/cc-pVTZ calculations, except Pd. The reactions catalyzed by earlier TM atoms had

more exothermic reactions than those catalyzed by later TM atoms for 3d and 4d species, while

5d TM atoms had similar enthalpy formations. Most of 3d and 5d species formed more stable

products than 4d species. Fe and Ru showed the most exothermic among 3d and 4d species. Os,

belonging to the same group as Fe and Ru, had similar enthalpy formations as Ir and Pt. This

trend can be explained by the electronic configurations of the TM atoms that have been shown to

have large effects on determination of enthalpy formations.53 The electron configurations of the

ground state multiplicities (Table 3.1) of the Os atoms is Os: [Ar] 4f14 5d6 6s2. The unexpected

situation on Os, may be caused by greater repulsion from the doubly occupied s orbital, which is

more diffuse than the d orbitals.

All considered density functionals predicted exothermic reactions by all the TM atoms,

except for Pd. Only M06 and B2PLYP correctly predicted the oxidative reaction by Pd to be

endothermic, while the other density functionals treated this reaction as an exothermic reaction.

27

Although B2PLYP predicted the enthalpy of formation of Pd in the correct trend, it had a large

deviation (14.7 kcal/mol) with respect to CR-CCSD(T)/cc-pVTZ. Again, most of the density

functionals underestimated the enthalpy formations for group 9 and group 10 TM species.

B2PLYP predicted the enthalpy formations to be less exothermic for all TM species, except for

Fe. Overall, density functionals performed more poorly at calculating the enthalpy formations

than the binding enthalpies and activation enthalpies because of the large deviations for several

species.

3.4.3 Performance of Density Functionals

The performance of each density functionals and different types of density functionals

will be reported in terms of the mean signed deviations (MSDs) for the extent of systematic error

and root mean squared deviations (RMSDs) for the average magnitude of errors within the metal

species and reaction types, comparing with the results from CR-CCSD(T)/cc-pVTZ calculations.

3.4.3.1 The Performance of Density Functionals in Terms of Different Reaction Terms

The performance of the density functionals with respect to reaction terms was considered,

which in this study are binding enthalpies, activation enthalpies, and enthalpy formations. For 3d

TM species (Table 3.2), all considered density functionals performed well in reproducing the

accuracy of CR-CCSD(T)/cc-pVTZ for the binding enthalpies with most of the RMSD values

less than 5 kcal/mol. Notably, BLYP, TPSS and B2PLYP had the lowest RMSD values of 2.8

kcal/mol, 2.7 kcal/mol and 4.8 kcal/mol, respectively, for activation enthalpies. All of the

considered density functionals performed poorly in predicting the enthalpy formations

accurately, except for M06L and M06 that resulted in the lowest RMSD values for enthalpy

28

formations. Although B97D had no significant error in predicting the binding enthalpies with an

acceptable RMSD value of 2.9 kcal/mol, it failed to predict activation enthalpies and enthalpy

formations accurately with large RMSD values of 12.9 kcal/mol and 15.9 kcal/mol, respectively.

M06L and M06, on the other hand, performed the best in producing the enthalpy formations

close to the CR-CCSD(T)/cc-pVTZ results but had slightly larger RMSD values than most of

other density functionals for binding enthalpies and activation enthalpies. When considering all

three enthalpy terms, PBE0 and B3LYP, which are hybrid-GGA functionals, performed the best.

For the performance of different types of density functionals (Table 3.3), hybrid-GGAs resulted

in the most accurate binding enthalpies, activation enthalpies and enthalpy formations with

lowest RMSD values of 1.8 kcal/mol, 3.5 kcal/mol, and 4.3 kcal/mol respectively.

For 4d TM species (Table 3.4), the RMSD values of the binding enthalpies were not

always the lowest of all three enthalpy terms. All the functionals without Hartree-Fock exchange

predicted the activation enthalpies more accurately than the other two enthalpy terms, followed

by the enthalpy formations. B2PLYP and none of the functionals without Hartree-Fock exchange

had acceptable RMSD values in predicting all three reaction terms, except M06L which was

designed to describe long-range dispersion interactions.26 TPSSh performed the worst in

predicting all three reaction terms among the functionals with Hartree-Fock exchange. PBE0

performed the best in predicting the most accurate values of binding enthalpies, activation

enthalpies, and enthalpy formations with RMSD values of 2.6 kcal/mol, 3.7 kcal/mol, and 5.2

kcal/mol respectively. M06L, B3LYP, and M06 also had acceptable RMSD values. For the

performance of different types of density functionals (Table 3.5), the results of hybrid-GGAs for

all three reaction terms were still in the best agreement with those of the CR-CCSD(T)/cc-pVTZ

calculations, with RMSD values of 1.9 kcal/mol, 10.6 kcal/mol, and 3.5 kcal/mol for binding

29

enthalpies, activation enthalpies, and enthalpy formations. Compared to the performance of

different types of density functionals for the 3d species, all types of density functionals

performed worse in predicting the thermodynamic properties for the 4d species accurately,

except for hybrid-GGAs, which had a lower RMSD value indicating more accurate enthalpy

formations for the 4d species than for the 3d species.

For 5d TM species (Table 3.6), most of the density functionals predicted the binding

enthalpies fairly accurately, followed by enthalpy of formation. Although B97D and B2PLYP

had acceptable RMSD values of 6.6 kcal/mol and 3.3 kcal/mol for binding enthalpies, they

performed worse in predicting the activation enthalpies and enthalpy formations correctly; most

notably B97D, which had an extremely large RMSD value of 33.9 kcal/mol for activation

enthalpies. B3LYP gave the most accurate values of binding enthalpy and enthalpy of formation,

while PBE0 had the lowest RMSD value of 9.8 kcal/mol for activation enthalpy (followed by

B3LYP) and acceptable RMSD values (less than 5 kcal/mol) for binding enthalpy and enthalpy

of formation. M06 gave relatively low RMSD values for all three reaction terms among all the

density functionals excluding PBE0 and B3LYP. In considering the performance of different

types of density functionals in terms of the three types of enthalpies examined in this study,

hybrid-GGA still perform best in predicting the enthalpies of all three reaction terms. None of

the density functionals gave acceptable RMSD values for activation enthalpies and enthalpy

formations expect hybrid-GGAs.

Overall, most of the density functionals perform best for 3d species in predicting the

enthalpies of all reaction terms, which considered in this study are binding enthalpies, activation

enthalpies, and enthalpy formations. PBE0 had the most accurate enthalpy values for all reaction

terms with respect to the results from CR-(CCSDT)/cc-pVTZ, which means that PBE0

30

performed the best among all considered density functionals. M06L, B3LYP and M06 also

performed well for all TM species, however M06L failed to predict binding enthalpies and

activation enthalpies for 5d species. All functionals with Hartree-Fock exchange performed well,

except for TPSSh, which had lower amount of Hartree-Fock exchange. Thus, increasing the

percent of Hartree-Fock exchange may improve the performance of functionals. B97D and

B2LYP, although they had a few acceptable RMSD values, had significant error in predicting

most of reaction terms, which mean they perform the worst. Hybrid-GGAs performed better than

the other types of density functionals in predicting accurate enthalpy values.

3.4.3.2 The Performance of Density Functionals in Term of the Metals

Both MSDs and RMSDs are considered to gauge the performance of the density

functionals in terms of each metal and the overall 3d, 4d, and 5d species. All the density

functionals except B2PLYP had negative MSD values (Table 3.8) for the overall 3d, 4d, and 5d

species, which show that most of density functionals generally underestimated the enthalpy

formations. For the 3d and 5d species, most density functionals predicted higher enthalpy

formations for earlier TM systems than for later TM systems. The enthalpies of Os were

overestimated by several density functionals (M06L, B3LYP, PBE0, and M06). For the 4d

species, most of the density performed similar and underestimated the enthalpies for Rh and Pd

systems. M06 had the lowest deviations for both overall 3d (-0.3 kcal/mol) and 5d (-0.1

kcal/mol) species, while PBE0 had the lowest deviation for 4d species (-3.9 kcal/mol). TPSS

gave the most negative MSD value of -7.4 kcal/mol for the 3d species, while B97D gave the

most negative MSD values of -14.9 kcal/mol and -13.9 kcal/mol for the 4d and 5d species. All

types of density functionals underestimated the enthalpies of the overall 3d, 4d, and 5d species

31

(Table 3.9), except B2PLYP which only had a negative MSD value for Fe system. Hybrid-GGAs

gave the lowest deviation of 1.9 kcal/mol, 4.2 kcal/mol, and 0.8 kcal/mol for 3d, 4d, and 5d

species respectively.

For RMSDs (Table 3.10), most of the earlier TM systems tend to have relatively lower

RMSD values than later TM systems for 3d and 5d metals. B97D performed worst of all the

considered density functionals, with the highest RMSD values of 12.0 kcal/mol, 21.5 kcal/mol,

and 17.1 kcal/mol for 3d, 4d, and 5d species respectively. Although BLYP, TPSS, and B2PLYP

did not gave the highest RMSD values and have some acceptable RMSD values for Fe and Os

systems, they all performed poorly in predicting the accurate enthalpies of the overall metal

species. PBE0 performed best for 4d and 5d species with the respective RMSD values of 6.2

kcal/mol and 4.4 kcal/mol and the second lowest RMSD value of 3.5 kcal/mol for 3d species.

B3LYP predicted the enthalpies of the overall 3d species most accurately with the lowest RMSD

value of 3.1 kcal/mol. M06 and M06L showed better performance than all other considered

density functionals except PBE0 and B3LYP. For different types of density functionals (Table

3.11), hybrid-GGA gave the most accurate values of enthalpies for each TM systems and the

overall 3d, 4d, and 5d species. Because of the failure of TPSSh, hybrid-meta-GGA did not show

improvement upon hybrid-GGA. Thus, the same conclusion can be made here as mentioned in

the last section: the percentage of Hartree-Fock exchange has an effect on the accuracy of

functionals for predicting the enthalpies of these kinds of systems.

32

3.4.3.3 Comparison between Transition Metal Atom Catalysts and Transition Metal Ion Catalysts

Previous research by Cong and coworkers52 focused on utilizing transition metal ions

including late 3d and 4d TMs ions (3d: Fe+, Co+, Ni+ and Cu+; 4d: Ru+, Rh+, Pd+ and Ag+) as

catalysts to activate C-O bond in dimethyl ether. In this study of oxidative cleavage of C-O bond

of methoxyethane, several late 3d and 4d neutral TMs were applied. It is of interest to compare

the abilities of TM ions and neutral TMs to active the C-O bond. Although different ethers were

applied in both studies, different properties of TM ions and neutral TM atoms can be discussed

qualitatively. The TM ions showed stronger binding with O atoms, lower height of reaction

barriers, and formed more stable products than neutral TM atoms. Both the neutral TM atom-

based insertion reaction and TM ion-based oxidative cleavage reaction had a lower height of the

reaction barriers for 4d species than 3d species. Neutral TM atoms had the more stable adducts

and products for 3d than for 4d, and vice versa for TM ions. The earlier TM systems tended to

form more stable products and have lower height of reaction barriers than later TM systems in

both cases. The analysis of density functionals showed that PBE0 gave the most accurate results

in both studies. This phenomenon in which the percentage of Hartree-Fock exchange affected the

performance of density functionals was found in both studies.

3.4.3.4 The Reaction Mechanism of the β–O–4 Linkage of Lignin

As mentioned before, this study was also interested in finding out selectivity of C-C and

C-O bond cleavage by TM atoms, because cleavages of these two bonds are most important steps

in decomposition of lignin, and compete with each other. Therefore, before studying the reaction

mechanism of the β–O–4 linkage of lignin, it is important to find a TM that has high selectivity

of C-C and C-O bond cleavage. The previous study by Oyedepo and coworkers53 was focused on

33

the Cα-Cβ bond cleavage of the β–O–4 linkage of lignin using Ni, Cu, Pd, and Pt neutral atoms in

gas phase. They started by using the representative model compound, ethane, to study the

properties of the four considered TM atoms. For comparison on the performance of Ni, Pd, and

Pt as catalysts, the C-O bond activation of methoxyethane had much higher activation enthalpies

than the C-C bond activation of ethane did by all considered TM atoms. The bond activation

reactions using Pt and Pd formed more stable products in the C-C bond activation than in the C-

O bond activation, while the enthalpy formations for Ni atom-catalyzed reaction were similar in

both bond activation reactions. Thus, the C-C bond cleavage can be expected to be more

favorable than the C-O bond cleavage in decomposition of the β–O–4 linkage of lignin with TM

atoms, which were therefore predicted to start with the Cα-Cβ bond cleavage.

3.5 Conclusion

The purpose of this study was to determine whether the transition metal atoms considered

can activate the C-O bond of methoxyethane effectively, in consideration of different density

functionals. The main findings in present study are shown below:

In terms of the enthalpy formations of breaking the C-O bond of methoxyethane, 3d and

4d TM species tend to have lower binding and enthalpy formations and higher activation

enthalpies than 5d TM species. Earlier TM systems tend to have lower activation enthalpies and

form more stable products. These trends, which indicate the intrinsic properties of catalysts in

breaking C-O bonds, can show guidance in the rational design of novel transition metal catalysts.

Comparing with the previous study of activation C-O bond of dimethyl ether by late 3d and 4d

transition metal ions,52 neutral TM atoms showed weaker binding with O atoms, higher height

of reaction barriers, and formed less stable products than the TM ions. For lignin decomposition

34

by TMs, the C-C bond cleavage can be predicted to be more favorable than its competitor, C-O

bond cleavage, based on the comparison between the C-O bond activation of methoxyethane and

C-C bond activation of ethane.

A series of density functionals, including generalized gradient approximation-GGAs

(BLYP and B97D), metal-GGAs (M06L and TPSS), hybrid-GGAs (B3LYP and PBE0), hybrid-

meta-GGAs (M06 and TPSSh), and a double-hybrid-GGA (B2PLYP) with cc-pVTZ basis set

were compared against CR-CCSD(T)/cc-pVTZ. To determine the performance of density

functionals, the comparisons were made for each considered TM atoms and also different

reaction terms. Among the density functionals employed in the present study, PBE0 gave the

lowest RMSDs for both 4d (6.2 kcal/mol) and 5d (4.4 kcal/mol) species and the second lowest

RMSD for 3d (3.5kcal/mol) species. It also performed the best in indicating all the reaction terms

accurately. Although, GGAs without Hartree-Fock exchange perform worse than hybrid-GGAs,

M06L gave competitive performance for 3d and 4d species. Hybrid-GGA described the

considered reactions most accurately than other types of density functionals. Because of the poor

performance of TPSSh, which has relatively small amount of Hartree-Fock exchange, the hybrid-

meta-GGAs gave larger RMSD values than hybrid-GGAs, but still performed better than GGAs

and meta-GGAs. Thus, the percentage of Hartree-Fock exchange is expected to strongly affect

the performance of density functionals.

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3.7 Figures and Tables

sinapyl alcohol conyferyl alcohol p-coumaryl alcohol

Figure 3.1. The phenylpropane units, sinapyl, conyferyl and p-coumaryl alcohol, are depicted in blue, green and red, respectively.

38

M +

CH3CH2OCH3 CH3

CH2

O

CH3

M

CH3

CH3 O

MCH3

CH3

CH2

M

O

CH3

Figure 3.2. Reaction mechanism of TM atoms oxidative cleavage of C-O bond of methoxyethane.

Figure 3.3. Binding enthalpies of each metal species with different density functionals using cc-pVTZ basis set and with CR-CCSD(T)/cc-pVTZ.

Figure 3.4. Activation enthalpies of each metal species with different density functionals using cc-pVTZ basis set and with CR-CCSD(T)/cc-pVTZ.

39

Figure 3.5. Enthalpy formations of each metal species with different density functionals using cc-pVTZ basis set and with CR-CCSD(T)/cc-pVTZ

40

41

Figure 3.6. Optimized geometries and selected structural parameters at the B3LYP/cc-pVTZ for the adducts in the C-O bond activation of methoxyethane with TM atoms. Bond lengths are in angstroms and bond angles in degrees.

42

Figure 3.7. Optimized geometries and selected structural parameters at the B3LYP/cc-pVTZ for the transition states in the C-O bond activation of methoxyethane with TM atoms. Bond lengths are in angstroms and bond angles in degrees.

43

44

45

Figure 3.8. Optimized geometries and selected structural parameters at the B3LYP/cc-pVTZ for the products in the C-O bond activation of methoxyethane with TM atoms. Bond lengths are in angstroms and bond angles in degrees.

46

Table 3.1

Ground State Multiplicities at the CR-CCSD(T)/cc-pVTZ Level of Theory

Atom Ground State Multiplicity

M MO(CH3CH2)CH3 TS CH3CH2MOCH3

Fe 5 5 5 5

Co 4 4 4 4

Ni 3 3 1 3

Ru 5 5 1 3

Rh 4 2 2 2

Pd 1 1 1 1

Os 5 5 3 5

Ir 4 4 2 2

Pt 3 1 1 1

47

Table 3.2

RMSDs of Each Functional for Binding Enthalpies, Activation Enthalpies and Enthalpy Formations of 3d Species, with Respect to CR-CCSD(T)/cc-pVTZ in kcal/mol

Method Binding

Enthalpies

Activation

Enthalpies

Enthalpy

Formations

BLYP 4.5 2.8 8.9

B97D 2.9 12.9 15.9

TPSS 3.3 2.7 11.0

M06L 5.2 5.5 1.3

B3LYP 1.6 1.8 5.1

PBE0 2.0 2.1 3.3

M06 4.6 6.8 4.6

TPSSh 1.6 2.4 9.7

B2PLYP 7.9 4.8 9.0

Table 3.3

RMSDs of Different Types of Functionals for Activation Enthalpies and Enthalpy Formations of 3d Species, with Respect to CR-CCSD(T)/ cc-pVTZ in kcal/mol

Functional Type Binding

Enthalpies

Activation

Enthalpies

Enthalpy

Formations

GGA 3.8 18.5 8.1

Meta-GGA 4.4 13.3 11.0

Hybrid-GGA 1.8 3.5 4.3

Hybrid-meta-GGA 3.5 8.3 7.4

Double-hybrid-GGA 7.9 4.8 9.0

48

Table 3.4

RMSDs of Each Functional for Activation Enthalpies and Enthalpy Formations of 4d Species, with Respect to CR-CCSD(T)/ cc-pVTZ in kcal/mol

Method Binding

Enthalpies

Activation

Enthalpies

Enthalpy

Formations

BLYP 17.6 9.7 17.2

B97D 19.5 8.6 14.2

TPSS 16.9 11.7 15.9

M06L 8.3 5.8 6.3

B3LYP 4.1 6.1 7.1

PBE0 2.6 3.7 5.2

M06 5.9 4.0 7.2

TPSSh 10.1 11.3 10.9

B2PLYP 18.5 22.5 12.0

Table 3.5

RMSDs of Different Types of Functionals for Activation Enthalpies and Enthalpy Formations of 4d Species, with Respect to CR-CCSD(T)/ cc-pVTZ in kcal/mol

Functional Type Binding

Enthalpies

Activation

Enthalpies Enthalpy Formations

GGA 9.3 29.4 18.6

Meta-GGA 4.3 21.1 15.5

Hybrid-GGA 1.9 10.6 3.5

Hybrid-meta-GGA 5.1 15.1 11.8

Double-hybrid-GGA 18.5 22.5 12.0

49

Table 3.6

RMSDs of Each Functional for Activation Enthalpies and Enthalpy Formations of 5d Species, with Respect to CR-CCSD(T)/ cc-pVTZ in kcal/mol

Method Binding Enthalpies Activation Enthalpies Enthalpy Formations

BLYP 9.3 24.1 16.4

B97D 6.6 33.9 20.6

TPSS 10.5 24.2 21.4

M06L 11.5 17.3 5.0

B3LYP 3.1 11.3 2.4

PBE0 5.2 9.8 4.3

M06 7.0 12.5 3.6

TPSSh 7.9 17.3 16.4

B2PLYP 3.3 14.0 17.8

Table 3.7

RMSDs of Different Types of Functionals for Bind Enthalpies, Activation Enthalpies and Enthalpy Formations of 5d Species, with Respect to CR-CCSD(T)/ cc-pVTZ in kcal/mol

Functional Type Binding

Enthalpies

Activation

Enthalpies

Enthalpy

Formations

GGA 12.9 15.8 18.6

Meta-GGA 7.8 12.1 15.5

Hybrid-GGA 4.3 6.2 3.5

Hybrid-meta-GGA 7.6 9.2 11.8

Double-hybrid-GGA 3.3 14.0 17.8

50

Table 3.8

MSDs of Each Metal and Overall 3d, 4d, and 5d Species for Each Functional, with Respect to CR-CCSD(T)/ cc-pVTZ in kcal/mol

Fe Co Ni 3d-MSD

Ru Rh Pd 4d-MSD

Os Ir Pt 5d-MSD

BLYP -0.4 -5.2 -13.7 -6.4 -4.4 -12.4 -10.9 -9.2 -5.4 -10.1 -17.4 -11.0 B97D -0.8 -6.1 -13.3 -6.7 -17.9 -16.7 -10.1 -14.9 -6.0 -12.4 -23.2 -13.9 TPSS -2.4 -4.9 -15.1 -7.4 -4.3 -12.8 -13.5 -10.2 -7.1 -12.3 -21.2 -13.6 M06L -1.5 -9.5 -10.4 -7.1 -9.1 -9.1 -9.4 -9.2 0.1 -4.5 -5.3 -3.2 B3LYP -0.5 -1.6 -3.3 -1.8 -6.7 -3.4 -3.3 -4.5 1.0 -2.2 0.4 -0.3 PBE0 -1.2 -2.8 -2.0 -2.0 -4.7 -3.7 -3.3 -3.9 0.5 -3.9 -0.5 -1.3 M06 7.2 -4.0 -4.0 -0.3 -7.7 -7.7 1.2 -4.7 4.0 -2.1 -1.7 -0.1 TPSSh -1.8 -4.6 -9.5 -5.3 -10.2 -8.0 -9.2 -9.2 -3.8 -7.9 -17.1 -9.6 B2PLYP -1.3 4.3 11.1 4.7 14.7 15.3 9.6 13.2 13.5 15.7 6.4 11.9

51

Table 3.9

MSDs of Each Metal and Overall 3d, 4d, and 5d Species of Different Types of Functionals, with Respect to CR-CCSD(T)/ cc-pVTZ in kcal/mol

Fe Co Ni 3d-

MSD

Ru Rh Pd 4d-

MSD

Os Ir Pt 5d-

MSD

GGA -0.6 -5.6 -13.5 -6.6 -11.2 -14.6 -10.5 -12.1 -5.7 -11.3 -20.3 -12.4

Meta-GGA -1.9 -7.2 -12.8 -7.3 -6.7 -11.0 -11.5 -9.7 -3.5 -8.4 -13.3 -8.4

Hybrid-GGA -0.8 -2.2 -2.6 -1.9 -5.7 -3.6 -3.3 -4.2 0.7 -3.0 0.0 -0.8

Hybrid-meta-GGA 2.7 -4.3 -6.7 -2.8 -8.9 -7.8 -4.0 -6.9 0.1 -5.0 -9.4 -4.7

Double-hybrid-GGA -1.3 4.3 11.1 4.7 14.7 15.3 9.6 13.2 13.5 15.7 6.4 11.9

52

Table 3.10

RMSDs of Each Metal and Overall 3d, 4d, and 5d Species of Different Types of Functionals, with Respect to CR-CCSD(T)/ cc-pVTZ in kcal/mol

Fe Co Ni 3d-

RMSD

Ru Rh Pd 4d-

RMSD

Os Ir Pt 5d-

RMSD

BLYP 4.5 9.7 17.3 11.8 15.5 17.0 12.3 15.1 8.6 15.4 18.1 14.6

B97D 3.0 9.0 18.4 12.0 29.2 20.5 10.7 21.5 6.9 14.7 24.8 17.1

TPSS 4.4 8.7 17.7 11.7 13.8 17.6 15.2 15.6 7.7 16.3 22.4 16.6

M06L 1.9 10.0 11.1 8.7 10.2 12.8 9.9 11.0 1.1 5.5 5.9 4.7

B3LYP 1.6 3.4 3.9 3.1 8.7 8.8 3.6 7.5 2.0 7.7 4.4 5.2

PBE0 3.2 4.7 2.4 3.5 6.0 8.1 3.5 6.2 1.5 6.7 3.2 4.4

M06 7.5 4.8 5.1 5.9 8.5 11.3 4.3 8.5 5.2 6.9 3.4 5.4

TPSSh 3.0 6.4 10.8 7.5 12.7 12.8 10.4 12.0 3.8 11.6 18.2 12.7

B2PLYP 7.4 6.6 17.8 11.8 17.6 17.4 10.7 15.5 14.1 17.1 7.3 13.5

53

Table 3.11

RMSDs of Each Metal and Overall 3d, 4d, and 5d Species of Different Types of Functionals, with Respect to CR-CCSD(T)/ cc-pVTZ in kcal/mol

Fe Co Ni 3d-

RMSD

Ru Rh Pd 4d-

RMSD

Os Ir Pt 5d-

RMSD

GGA 3.8 9.4 17.9 11.9 23.4 18.8 11.5 18.6 7.8 15.1 21.7 15.9

meta-GGA 3.4 9.4 14.7 10.3 12.1 15.4 12.8 13.5 5.5 12.2 16.4 12.2

hybrid-GGA 2.5 4.1 3.2 3.3 7.5 8.5 3.6 6.9 1.8 7.2 3.8 4.8

hybrid-meta-GGA 5.7 5.6 8.5 6.7 10.8 12.1 7.9 10.4 4.6 9.5 13.1 9.7

double-hybrid-GGA 7.4 6.6 17.8 11.8 17.6 17.4 10.7 15.5 14.1 17.1 7.3 13.5

54

CHAPTER 4

PERFORMANCE OF DENSITY FUNCTIONALS FOR MODELING GAS PHASE

REACTIONS OF LATE TRANSITION METAL ATOMS WITH METHANOL

4.1 Abstract

The transition metal-based carbon-oxygen bond activation of methanol by late 3d and 4d

transition metal atoms was investigated. A set of 26 density functionals including eight GGA, six

meta-GGA, six hybrid-GGA, and six hybrid-meta-GGA were applied in order to investigate the

performance of different types of density functionals for transition metal catalyzed C-O bond

cleavage. Binding enthalpies, activation enthalpies, and reaction enthalpies were considered in

this study. The results from high-spin and low-spin potential energy surfaces calculations

showed that a crossing between the high-spin and the low-spin potential energy surfaces helps to

decrease the barrier heights of transition states and stabilize the final complexes. Furthermore, 3d

metal species tend to have lower activation enthalpies and more exothermic reactions than 4d

metal species. For the performance of density functionals, hybrid-GGA and hybrid-meta-GGA

functionals performed similarly, and both of them had lower root mean squared deviations

(RMSDs) than GGA and Meta-GGA. In general, PEB0 and B972 are recommended as they

afford a reasonable balance between cost and accuracy. For the comparison between restricted

open shell DFT and unrestricted DFT, RO-GGA and UGGA performed similarly for all metals

and all considered types of reactions, RO-meta-GGA and RO-hybrid-meta-GGA performed

similar to or even better than U-meta-GGA and U-hybrid-meta-GGA, U-hybrid-GGA performed

better than RO-hybrid-GGA. Therefore, the better choice of restricted open shelled DFT or

unrestricted DFT depends on which type of functional will be applied in certain studies.

55

4.2 Introduction

The gas-phase study of transition metal-based reactions is of fundamental importance in

predicting the reaction mechanisms of several chemical and catalytic processes.1 Additionally,

chemical bonds activation plays an important role in various areas of chemical researches, such

as organic chemistry, biochemistry, and catalysis. The oxidative addition of covalent bonds to

transition metal centers is a widespread type of chemical bond activation reaction induced by the

valence electron configurations of transition metals.2 In the gas phase studies, bond activation

reactions by a number of transition metal cations have been studied in detail for both mechanistic

and thermochemical information.3-5 For instance, Cao and coworkers 6 reported an experimental

and theoretical investigation of reactions between M+ and methanol using B3LYP, and the

combination of ECP and valence basis set as LANL2DZ basis7 on the metal atom and 6-31g* for

the main group atoms. The results showed that the reaction enthalpies of the transition states

decreased by a crossing between the high-spin and low-spin potential energy surfaces, and the

main products of these reactions were MO+ and MOH+ after passing through two transition

states. These reactions are commonly caused by the presence of long-range ion-induced dipole

forces.8 However, the properties of metal cation-catalyzed bond activation reactions cannot

represent the behavior of most homogeneous transition metal catalysts which are neutral without

the long-range attraction force. Furthermore, heterogeneous catalysts are widely used in industry

with good tolerance of high temperature.9,10 Consequently, neutral atoms were applied in this

study not only because of their ability to be better models for homogeneous catalysis, but also

because of their ability to be more realistic models for condensed phase systems. The C-O bond

activation of alcohols, compounds that widely exist in nature, plays an important role in

industries.11 Thus, investigation of the ability of different transition metal atoms to activate the

56

C-O bond of alcohol could provide significant breakthroughs for catalysis design. This study is

focused on modeling the activation of small molecules, methanol, by neutral transition metal

atoms to get a fundamental insight into the intrinsic catalytic properties of transition metals,

which plays a significant role in catalysis of C-O bond activation.

Although effective electronic structure methods have been developed in recent decades,

there are still several challenges that must be met. For instance, the size of the studied system is

often limited due to the non-linear dependence of system size with computational cost.12 Density

functional theory (DFT) has become a common choice for the transition metal containing

systems because of its favorable cost-to-size scales and its competitive accuracy compared with

correlated high level electronic structure methods.13 Several challenges of density functionals for

transition metal containing systems include accurately calculating the ground-state structures,

electron distributions, and enthalpies with large non-dynamical correlation effects caused by

partially filled d subshells and nearly degenerate (n+1)s and nd subshells.14 As density

functionals have become so widely used, it is important to select suitable functionals for the

target reactions, especially for systems with degeneracies that lead to static correlation effects.

Most previous computational studies have applied B3LYP to predict the reaction enthalpies of

C-O bond activations.6,15 While the B3LYP functional, a hybrid GGA, is one of the most

popular density functionals in computational chemistry, it exhibits unsatisfactory performance in

predicting reaction barrier heights, non-covalent interactions, and transition metal chemistry

because of the non-dynamical correlation effects,16 while several other density functionals have

provided acceptable accuracy in certain transition metal containing systems17. Therefore,

evaluating the performances of density functionals by comparing to high level electronic

structure methods or experimental results is a crucial step in computational studies. In this study,

57

a set of different types of DFT have been applied, including generalized gradient approximation

(GGA), meta-GGA, hybrid-GGA, and hybrid-meta-GGA functionals. Transition metal

containing systems tend to have open-shell electronic configurations because of the partially

filled d subshells, which may be described by either restricted open shell (RO) or unrestricted

(U) DFT. A disadvantage of any unrestricted method is spin contamination, which may play an

important role in systems exhibiting more than one multiplicity. The problem caused by spin

contamination is that the predicted potential energy surface can be significantly distorted towards

the high-spin state, a situation that is recognized to affect energy in some studies.18,19 On the

other hand, RODFT has no spin contamination, but it requests an additional cost in term of CPU

time for correctly description of both singly occupied and doubly occupied orbitals and the

interaction between them. In order to reduce computational cost without sacrificing accuracy, it

is of interest to examine the performance of RODFT and UDFT in presenting the reaction

enthalpies in this study, by comparing the calculations to completely renormalized CR-CCSD(T)

calculations.

The proposed reaction pathway (Figure 4.1) started with the metal center directly

approaching to the O atom of methanol. The reactants then form a reaction complex,

M(OH)(CH3), that went through a transition state, [CH3MOH]‡, to break the C-O bond,

ultimately forming the final complex (CH3MOH) in this study. As shown in previous

investigation by Cao and coworkers,6 this reaction may proceed to another transition state by C-

H bond activation and proton transfer to form CH4 and MO. However, this study is focused on

the C-O bond activation, so the reactions occurring after CH3MOH were not studied.

58

4.3 Computational Details

All of the calculations of unrestricted density functional theory (UDFT) in this paper

were performed with the Gaussian 09 program package,20 while the NWChem21 computational

chemistry software suite was utilized for CR-CCSD(T) calculations and the restricted open shell

density functional theory (RODFT) calculations. Based on the previous study by Piecuch and

coworkers,22 CR-CCSD(T) obtained results similar to those from spectroscopic studies for

breaking single bonds, which are described poorly with standard CCSD(T) methods. A total of

26 density functionals in both restricted open shell and unrestricted forms were considered from

four different categories of DFT methods as shown in Table 4.1. The eight GGA functionals

include both the gradient of electron density and the density itself, and six meta-GGA functionals

also include the kinetic energy density as well. The six hybrid-GGA functionals depend on the

Hartree-Fock exchange, the electron density, and the electron density gradient, while six Hybrid-

meta-GGA functionals also contain kinetic energy density as well. Among the functionals, the

B97D functional accounts for the dispersion effect. M06L and M06 functionals account for non-

covalent attractions and dispersion effect, and the LC-BLYP and LC-wPBE functionals account

for long-rang corrections. Post-HF calculations using CR-CCSD(T) were used to gauge the

performance of the considered density functionals.

Both the geometry optimizations and the frequency calculations were performed with

B3LYP, a functional that offers enthalpy thermochemical corrections to the single point

enthalpies calculated by each method. Long-range interactions play important roles in these

transition metal based insertion systems; therefore, diffuse augmented functions were added to

the correlation consistent basis sets23 (cc-pVnZ, n=D, T, Q, etc.) to account for this, denoted as

aug-ccpVnZ.24-26 Geometries were optimized for different spin states with the aug-cc-pVTZ

59

basis on the 3d metal atoms and main group elements. For 4d metal atoms, small-core effective

core potential (ECP) of the Stuttgart-Dresden type and their valence basis sets were applied,

which replaces 28 core electrons with a fully relativistic multi-electron fitted potential, denoted

as the aug-cc-pVTZ-PP basis set.25,27

4.4 Results and Discussion

4.4.1 Prediction of Ground State Multiplicities

The ground state multiplicities (Table 4.2) were determined at the CR-CCSD(T)/aug-cc-

pVTZ level of theory and were then used throughout the rest of the project. The ground state spin

multiplicities of the Co, Ni, Ru, and Rh complexes changed at various steps throughout the

reaction pathway, which demonstrated as spin-forbidden reactions. The reaction energy profiles

shown in Figure 4.2 show that a crossing between the high multiplicity and low multiplicity

potential energy surfaces played an important role in decreasing the activation enthalpies and

stabilizing the products for several considered transition metals. Among the 26 density

functionals considered, only UPBE0, UB1B95, and UTPSS predicted the same ground state

multiplicities as the CR-CCSD(T) method did for the 3d and 4d TM atoms. Although UPBE0

gave correct ground state multiplicities for TM atom, UPBE0 failed to predict the reaction

complex Ni(OH)(CH3) and final complex CH3NiOH as triplets, instead determining the singlet

states as the most stable. UPBE0 also treated the triplet to be more stable than quintet for the

final complex CH3RuOH. UB1B95 and UTPSS predicted the correct ground state multiplicity

for the reaction complex and transition state but failed to indicate the correct ground state

multiplicity for CH3RuOH. UM06L and UO3LYP were the only two functionals that predicted

the ground state multiplicities for all reaction states of all the metals besides Rh to be the same as

60

the ground state multiplicities calculated by CR-CCSD(T). Pd was the only TM species that all

functionals correctly predicted the same multiplicities that CR-CCSD(T) predicted.

Overall, functionals that do not contain some amount of Hartree-Fock exchange tended to

prefer the low-spin, which may be caused by the self-interaction error. Unrestricted hybrid-GGA

functionals, on the other hand, favored high multiplicities, especially the ones including high

percent of Hartree-Fock exchange.

4.4.2 Comparison between Different Metals

The binding enthalpies, reaction enthalpies, and reaction enthalpies calculated at the CR-

CCSD(T)/aug-cc-pVTZ level of theory are shown in Figure 4.3-4.5.

4.4.2.1 Binding Enthalpies: M+CH3OH → M(OH)(CH3)

The metal atoms approached to the O atom of methanol and formed the reaction complex

M(OH)(CH3). Based on the ground state multiplicities shown in Table 4.2, the electron

configurations of the considered late 3d and 4d TM atoms were Fe ([Ar] 3d74s1), Co ([Ar]

3d84s1), Ni ([Ar] 3d94s1), Cu ([Ar] 3d104s1), Ru ([Kr] 4d75s1), Rh ([Kr] 4d85s1), Pd ([Kr]

4d10), Ag ([Kr] 4d105s1), indicating that all TM atoms had the ability to accept electrons from

methanol. In other words, the metal acceptor orbitals of σ-symmetry could accept electron

density from the O atom of methanol. Therefore, the binding reactions were expected to be

exothermic for the TM atoms, later verified by the CR-CCSD(T)/aug-cc-pVTZ level

calculations. The differences between the binding enthalpies of different TM atoms were small,

varying between -10.9 kcal/mol (for Co) and -0.6 kcal/mol (for Ag), as shown in Figure 4.3, The

magnitudes of binding enthalpies in decreasing order are Co > Ni > Cu ~ Fe for 3d systems and

61

Pd > Ru ~ Rh > Ag for 4d systems. Two TM atoms belonging to the same group, Ni and Pd,

bonded with methanol relatively stronger because of their completely filled nd and (n+1)s

orbitals, Ni [Ar] 3d104s2 and Pd [Kr] 4d105s2, after gaining two electrons from methanol. As a

result, the completely filled d and s orbitals helped stabilize the reaction complex.

4.4.2.2 Activation Enthalpies: M(OH)(CH3)→[CH3MOH]‡

The activation enthalpies (Figure 4.4), calculated by the CR-CCSD(T)/aug-cc-pVTZ

level of theory, were decreasing in the order of Cu > Co > Ni > Fe for 3d systems and Ag > Ru >

Rh > Pd for 4d systems. The height of reaction barriers varied from 9.4 kcal/mol (of Fe) to 41.5

kcal/mol (of Cu) for 3d TM systems and 30.4 kcal/mol (of Pd) to 51.0 kcal/mol (of Ag) for 4d

TM systems. The 4d TM systems tended to have larger reaction enthalpies than the 3d TM

systems.

The C-O bond activation was induced by donating electrons from the σ-orbital of the C-O

bond to the s-orbital of the metal, and back-donating electrons from the d-orbital of the metal to

the anti-bonding orbital of the C-O bond. Based on this reaction mechanism, three possible

factors could have caused the 4d TM atoms to have larger reaction enthalpies. The energy

differences between the d-orbitals of 4d TM atoms and the anti-bonding orbital of the C-O bond

is larger than those of the 3d TM atoms and the anti-bonding orbital of the C-O bond, making the

back donation of electrons from metals to C-O bonds harder for 4d TM atoms. Furthermore, the

methyl group needs more energy to rotate into a position that is optimal for methanol to bind

with metals with larger atomic radii. The last reason was caused by low-lying atomic states.

Because of the similar enthalpies of nd and (n+1)s orbitals, the lowest atomic state dns2of TM

can mix with the nearly degenerate excited state dn+1s1, allowing the 3d metals to have a dn+1s1

62

atomic state that decreases the activation enthalpies. However, because the 3d orbital becomes

more stable to the 4s orbital from left to right in the row, the nearly degenerate effect should

decrease across the 3d TM row. These factors together explain the reasons that 4d TM atoms

with the s1 state, the state that has the smallest repulsion towards the C-O bond and allows the

metals to approach sufficiently close to the C-O bond, still have similar or even higher activation

enthalpies than 3d TM atoms with these s2 state. The factors also explain the reason why the Fe

system has the lowest activation enthalpies. Moreover, due to the second factor, Cu and Ag have

larger reaction enthalpies compared to the other TM atoms in their row. Pd and Ni, which have

stronger binding enthalpies, have relatively low reaction enthalpies.

4.4.2.3 Reaction Enthalpies: M+CH3OH→CH3MOH

All of the reaction enthalpies, as shown in Figure 4.5, were exothermic, with the

exception of the reaction catalyzed by Ag which had a large positive enthalpy of 22.6 kcal/mol.

The reaction catalyzed by Cu was nearly endothermic, with an enthalpy of -0.6 kcal/mol. Both of

these TM atoms have fully filled nd orbitals and half-filled (n+1)s orbitals, making them less

likely to accept electrons from methanol and more likely to have less exothermic reactions. Fe

and Ru, which belong to the same group, formed least stable final complexes. Overall, the earlier

TM atoms tended to have more exothermic reactions than the later TM atoms. This could be due

to the difference in geometry; earlier TM atoms formed highly symmetric complexes. Two H

atoms, one connected to the C atom and another to the O atom, lie on the same plane as the non-

hydrogen atoms. However, later TM atoms did not form symmetric complexes. Based on the

results, it was also concluded that 3d TM atoms have more exothermic reactions than 4d TM

atoms. Moreover, the calculated Mulliken population analysis showed that 4d metal centers had

63

positive atomic charges but 3d metal centers had negative atomic charges. This indicates the

concurrent back-donating from occupied d orbitals of metals into the anti-bonding orbitals of

methanol was more effective for 3d TM atoms, allowing the 3d TM atoms to form more stable

complexes.

4.4.3 Overall Performance of Density Functionals

Twenty-six functionals were applied in this study. The performance of the functionals

were determined in terms of the mean signed deviations (MSDs) and the root mean squared

deviations (RMSDs) of each functional. The performance of different types of functionals was

also studied in terms of each metal and the 3d and 4d species for the different types of reactions

with respect to CR-CCSD(T)/aug-cc-pVTZ level of theory. The comparison between the

performance of UDFT and RODFT in relation with the metals was also considered in this study.

4.4.3.1 Performance of Density Functionals with Respect to Binding Enthalpies

For both 3d and 4d TM species, most of the MSD values were negative for binding

enthalpies, showing that density functionals usually underestimated the binding enthalpies,

shown in Table 4.3. However, two special cases that overestimated the binding enthalpies for

both 3d and 4d TM species were the UG96LYP and UO3LYP functionals. Among all the

considered functionals, UVSXC produced the most negative MSD values for both 3d (-10.0

kcal/mol) and 4d (-9.4 kcal/mol) species. On the other hand, UB972 gave the least negative MSD

values for 3d (-0.1 kcal/mol) species, while UB1B95 gave the least negative values for 4d (-0.1

kcal/mol) species. As shown in Table 4.4, all types of functionals underestimated the binding

enthalpies. The performance of U-GGA, U-meta-GGA, and U-hybrid-meta-GGA functionals

64

were similar, with respective MSDs of -3.5, -4.8, -4.0 kcal/mol for the 3d species. As for the 4d

species, U-meta-GGA functionals gave the most negative MSD value of -4.0 kcal/mol. The U-

hybrid-GGA functionals performed well and gave the least negative values of MSD for both 3d

(-2.0 kcal/mol) and 4d (-0.5 kcal/mol) species.

RMSDs were also considered in this study to gauge the performance of each functional.

For the binding enthalpies, as shown in Table 4.3, O3LYP produced the highest RMSD value for

3d species (14.7 kcal/mol) because of the extremely high deviation of Fe (MSD=-27.8 kcal/mol).

Likewise, VSXC gave the highest RMSD values for 4d species because the RMSD value for Rh

was especially high. In contrast, the U-hybrid-GGA UB972 performed the best for the 3d species

with a RMSD of 1.6 kcal/mol, while UPBE0 performed best for the 4d species with a RMSD of

2.3 kcal/mol. M06, M06L and B97D, which are designed to account for dispersion effect, also

had acceptable RMSDs for the 3d (6.2kcal/mol, 8.2kcal/mol, and 5.5 kcal/mol) and 4d species

(6.6kcal/mol, 4.2kcal/mol, and 9.8kcal/mol). As shown in Table 4.5, earlier metal species tended

to have relatively higher RMSDs than later metal species for all types of functionals, especially

Fe in 3d species and Rh in 4d species. Overall, similar performances were seen for both 3d and

4d species for each type of functional. In particular, the U-GGA and meta-GGA functionals had

similar accuracies for both 3d and 4d species. Likewise, the performance of the U-hybrid-GGA

and the U-hybrid-meta-GGA were similar for both 3d and 4d species and improved upon the U-

GGA and U-meta-GGA. Thus, the inclusion of Hartree-Fock exchange helped improve the

accuracy of density functionals for calculating binding enthalpies. One interesting phenomena

shown here is that the RMSD values for the U-GGA functionals with long-range correction is

lower than those of U-GGA functionals and even the same as that of the U-hybrid-GGA for 3d

65

species, showing that long-range correction plays an important role in the determination of

binding enthalpies.

4.4.3.2 Performance of Density Functionals with Respect to Activation enthalpies

As shown by the MSD values in Table 4.6, the U-meta-GGA functionals UBB95 and

UmPWB95 gave the most negative MSDs values of -13.2 and -13.4 kcal/mol for the 3d species,

respectively. They also underestimated the activation enthalpies more than the other functionals

for 4d species, providing respective MSDs values of -18.3 and -18.6 kcal/mol. UB971 and BMK,

both of which include Hartree-Fock exchange, gave the least negative MSD values for 3d (-0.6

kcal/mol) and 4d (-1.7 kcal/mol) species. The MSDs in Table 4.7 show that the U-hybrid-meta-

GGA functionals overestimated the activation enthalpies for Fe, Ni and Pd systems. U-hybrid-

GGA and U-hybrid-meta-GGA functionals both had extremely high positive MSD values, but

this can be attributed to the overestimation of the activation enthalpies for reactions containing

Fe. However, U-GGA and U-meta-GGA functionals produced negative MSD values for overall

3d species because of the large negative MSD values for other 3d species except Fe. For 4d

species, U-hybrid-GGA and hybrid-metal-GGA functionals underestimated the activation

enthalpies less than the other types of functionals with MSD values of -6.5 kcal/mol and -4.2

kcal/mol respectively.

The data in Table 4.6 demonstrates that UmPWB95 had the largest RMSD values for

both 3d and 4d species, in other words, UmPWB95 gave less accurate results. UM05 gave the

lowest RMSD value of 2.6 kcal/mol, indicating the most accurate activation enthalpies for 3d

species, while UPBE0 performed the best for the 4d species with a RMSD value of 3.6 kcal/mol.

Most functionals with Hartree-Fock exchange gave lower RMSD values for both 3d and 4d

66

species than other types of functionals did. Table 4.8 includes the performance of different types

of functionals for 3d and 4d species based on the RMSDs. The Pd species, which is the only

closed-shell species, had the most accurate activation enthalpies calculated by all considered

types of functionals compared to other metal systems. Ru had the highest RMSD values

compared to the other metal systems in the same row, while Fe had the highest RMSD values by

all types of functionals except GGA and meta-GGA functionals. Overall, with the exception of

U-meta-GGA functionals, all types of functionals produced more accurate results for 4d species

than 3d species. The U-GGA and meta-GGA functionals provided similar accuracy for both 3d

and 4d species. Likewise, the U-hybrid-GGA and hybrid-meta-GGA functional performed

similarly for 3d and 4d species, giving RMSD values about 6 kcal/mol less than that of U-GGA

and meta-GGA functionals respectively. Therefore, the inclusion of the Hartree-Fock exchange

improved the accuracy of the density functionals for calculating the activation enthalpies as well

as the binding enthalpies of the reactions. The RMSD values for U-GGA functionals with long-

range corrections are still lower than those for U-GGA functionals and are the same as those for

U-hybrid-meta-GGA functionals for both 3d and 4d species. This indicates long-range correction

played an important role in predicting the activation enthalpies.

4.4.3.3 Performance of Density Functionals with Respect to Reaction Enthalpies

Most density functionals underestimated the reaction enthalpies with negative MSD

values for almost all 3d species as shown in Table 4.9. The exception was Fe whose reaction

enthalpies were overestimated by almost all functionals. UM05 and UO3LYP overestimated the

reaction enthalpies for the overall 3d species because of the extremely high positive deviations of

the Fe species. For the 4d species, all U-hybrid-meta-GGA functionals except UBMK gave high

67

positive MSD values for the Ru and Pd species, which indicated that these types of functional

overestimated the reaction enthalpies. In addition to giving the most negative value for binding

enthalpies of 3d species, UVSXC also gave the most negative MSDs value of -15.4 kcal/mol for

reaction enthalpies of 3d species. Furthermore, the functional gave a very negative MSD value of

-19.9 kcal/mol for the 4d species. However, UB97D underestimated reaction enthalpies the most

for the 4d species (-22.6kcal/mol). The U-hybrid-GGA B972 gave the least negative MSD value

for the 3d (-0.1 kcal/mol) species. Although all types of functionals in Table 4.10 give positive

MSD values for the Fe and Pd species, all of them underestimated the reaction enthalpies for the

overall 3d and 4d species.

Based on the data shown in Table 4.9, UVSXC performed the worst in calculating the

reaction enthalpies of the reactions, providing the largest RMSD value of 22.7 kcal/mol for the

3d species. For the 4d species, UB97D had the poorest performance in predicting the reaction

enthalpies with a RMSD value of 32.8 kcal/mol. UM062X gave the most accurate reaction

enthalpies for 3d species with the lowest RMSD value of 7.0 kcal/mol. UO3LYP performed the

best for 4d species with a RMSD value of 5.0 kcal/mol. Most hybrid-GGA functionals gave

acceptable RMSD values (around 6 kcal/mol) for 4d species. The performance of different types

of DFT based on the results of RMSDs is shown in Table 4.11. U-metal-GGA and hybrid-GGA

functionals performed better for 4d species, while U-GGA and U-hybrid-meta-GGA performed

better for 3d species. U-GGA and U-meta-GGA functionals had similar accuracies for both 3d

and 4d species, while U-hybrid-GGA and U-hybrid-meta-GGA functionals had similar

accuracies for both 3d and 4d species and performed much better than U-GGA and U-meta-GGA

functionals. Thus, reaction enthalpies calculations by density functionals benefited from

including the Hartree-Fock exchange. The RMSD values for U-GGA functionals with long-range

68

correction were lower than those of U-GGA functionals and even better than those of U-hybrid-

meta-GGA functionals for both 3d and 4d species, indicating that long-range correction also

plays an important role in the indication of reaction enthalpies.

Overall, unrestricted hybrid-GGA functionals always showed better performance for 4d

species compared to 3d species for all considered types of reaction enthalpies, including binding

enthalpies, activation enthalpies, and reaction enthalpies. Moreover, the functionals with Hartree-

Fock exchange performed better for both 3d and 4d species. One special case was functionals

with long-range correction. They provided accuracies similar to the accuracies of the hybrid

types of functionals. Therefore, the long-range exchange effect was predicted to be important in

the analysis of transition metal-containing insertion reactions. Since U-hybrid-GGA functionals

performed similarly to U-hybrid-meta-GGA functionals but offered a good balance between cost

and accuracy, certain U-hybrid-GGA functionals, such as UPBE0 and UB972, are recommended

for the investigation of transition metal-containing bond activation reactions.

4.4.4 Comparison of RODFT Functionals and UDFT Functionals

As mentioned above, open shell systems can be calculated with either restricted

(RODFT) and unrestricted (UDFT) methods. Since some studies indicated that restricted

calculations failed to describe bond dissociations correctly, UDFT may be the better choice for

the considered reaction systems. However, restricted open-shell calculations can overcome spin

contamination encountered in unrestricted calculations of open-shell systems.28-30 Because spin-

polarized Slater determinant is no longer an eigenfunction of spin operator in unrestricted

methods, the average value of S2 is not the same as the correct value of S(S+1).56 The spin

contaminations of the considered reactions were measured by the value of S2. The common rule

69

is that spin contamination can be neglected if S2 differs from S(S+1) by less than 10%.57 Thus,

the spin contamination may affect the enthalpies of the considered systems since the differences

between S2 and S(S+1) are more than 10%, shown in Table 4.12 for different types of

functionals. To our best knowledge, no research had been focused on comparing the

performances of RODFT and UDFT for transition metal-based C-O bond insertion reactions, and

the quantum chemical calculations on open-shell electronic configurations are far from

accurately predicting which type of DFT is the better choice. The comparison of RODFT and

UDFT functionals was considered in this study.

4.4.4.1 Comparison as a Function of the Metals

The accuracy of RODFT and UDFT is demonstrated, in comparison to CR-CCSD(T), by

the RMSD values in Table 4.13. RO-GGA and U-GGA performed similarly for all metals;

however, RO-GGA produced much less accuracy for Fe than U-GGA and U-GGA did for Pd

than RO-GGA. Both RO-GGA and U-GGA gave relatively low accurate results for earlier

metals in the 3d and 4d species. For meta-GGA functionals that included the second-derivative

of the electron density and kinetic energy density in the exchange correlation functionals,

RODFT performed better than UDFT for all metals except Rh and overall 3d and 4d species. On

the other hand, when the Hartree-Fock exchange was taken into account for the exchange energy,

the RMSDs values of U-hybrid-GGA were much lower than those of RO-hybrid-GGA. Earlier

metals also had relatively high RMSDs values. However, for hybrid-meta-GGA, which includes

Hartree-Fock exchange, second-derivative of the density, and kinetic energy density, UDFT and

RODFT performed similarly for the overall 3d and 4d species. However, for Co and Ru, RO-

70

hybrid-meta-GGA performed better than U-hybrid-meta-GGA, and for Fe, U-hybrid-meta-GGA

indicated the reactions more accurately than RO-hybrid-meta-GGA.

4.4.4.2 Comparison with Respect to Reaction Types

In addition to comparing the performances of the different types of DFT in terms of each

metal, how different types of DFT performed for different types of reactions (binding enthalpies,

activation enthalpies, and reaction enthalpies) was also of interest in this study (Table 4.14). For

3d species, the RMSDs decreased in the order of binding enthalpies, activation enthalpies, and

reaction enthalpies for all types of UDFT and RODFT except RO-GGA and RO-hybrid-GGA,

for which reaction enthalpies had the largest RMSD and for which activation enthalpies had the

lowest RMSD respectively. For the two types of functionals, meta-GGA and hybrid-meta-GGA,

which include the kinetic energy density, RODFT performed similarly to UDFT or even better

than UDFT for binding enthalpies. On the other hand, for the other two types of functionals,

GGA and hybrid-GGA, UDFT had lower RMSD values and performed better than RODFT for

all three types of reactions enthalpies except for RO-GGA for reaction enthalpies. The 4d species

showed a similar trend to the 3d species. The RMSDs also decreased in the order of binding

enthalpies, activation enthalpies, and reaction enthalpies for all types for UDFT and RODFT

except for RO-hybrid-GGA, in which activation enthalpies had the lowest RMSD. By taking the

kinetic energy density into account, RODFT showed a similar performance to UDFT or

performed even better than UDFT for reaction enthalpies. U-hybrid-GGA produced more

accurate results than RO-hybrid-GGA did for both binding enthalpies and reaction enthalpies,

but they had similar accuracies for indicating the activation enthalpies. For GGA functionals,

RO-GGA and U-GGA perform similarly for all types of reactions enthalpies.

71

4.5 Conclusion

This study focused on the performance of 26 different types of density functionals on

transition metal-based insertion reactions and the catalytic properties of the activation of the

carbon-oxygen bond in methanol by late 3d and 4d transition metal atoms. Several interesting

findings are summarized as followed.

The energetic trends of C-O bond activation of methanol by transition metals, the 3d

metal species had more thermodynamically favorable reactions because they tended to have

relatively lower activation enthalpies and form more stable complexes than 4d metals. Earlier

metals also had more thermodynamically favorable reactions because they tended to have lower

activation enthalpies and more exothermic reactions than later metals. Among the considered

metals, Ni and Pd, which belong to the same group, had relatively stronger binding with

methanol which led to a relatively low activation enthalpies, while Fe and Ru, which belong to

the same group, had the lowest reaction enthalpies. Like mentioned before, these intrinsic

catalytic trends of metal atom-catalyzed C-O bond insertion reactions can provide guides for the

rational design of novel transition metal contained catalysts. Based on the results, Pd is the best

choice as a catalyst for C-O bond cleavages because of its low activation enthalpies and

moderate exothermic reaction.

Another important objective of the present study was to compare the performance of

different types of DFT on the C-O bond activation of alcohols by transition metals using

methanol as an example. A set of DFT methods including GGA, meta-GGA, hybrid-GGA and

hybrid-meta-GGA with the aug-cc-pVTZ basis set was applied with respect to the results of CR-

CCSD(T)/aug-cc-pVTZ level of theory for the reaction energetics. The functionals with Hartree-

Fock exchange always performed better for both 3d and 4d species. However, no significant

72

improvement was found when hybrid-meta-GGA was applied instead of hybrid-GGA. Therefore,

some hybrid-GGA functionals, such as PBE0 and B972, can be recommended for the

investigation of transition metal-based bond activation reactions. One special case was

functionals with long-range correction, which had accuracies similar to hybrid-GGA functionals.

This study also compared the performance of 17 restricted open-shell DFT and 17 respective

unrestricted DFT for different metals and different reaction types. When functionals included the

kinetic energy density, such as meta-GGA and hybrid-meta-GGA, RODFT had similar or even

better performances in terms of metals and for all types of reactions compared to UDFT. For

GGA functionals, RO-GGA and U-GGA performed similarly for all metals and all types of

reactions. In general, the U-hybrid-GGA functionals indicated the reactions more accurately than

did the RO-hybrid-GGA functionals. Therefore, choosing between restricted open-shell DFT or

unrestricted DFT depends on the type of functional that will be applied in certain studies.

4.6 References

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4.7 Figures and Tables

M + CH3OH C

M

OHH3C

OH

M

H3CM

OH

Figure 4.1. Reaction pathway of TM at atom-based C-O bond activation of methanol.

76

Co+CH3OH

doublet

quartet

R RC TS P

-10.9

10.922.8

13.2

40.5

-21.8

Ni+CH3OH

singlet

triplet

-2.7

24.1

-25.4

0

0

50.5

40.5

-5.7

34.8

-39.8

R RC TS P

Ru+CH3OH

triplet

quintet

R RC TS P

-6.1

11.2

41.2

41.8

30.8

-30.8

Rh+CH3OHsinglet

triplet

5.9

28.0

-29.0

0

0

32.1

13.8-4.0

37.4

-19.4

R RC TS P

Figure 4.2. The energy diagram of the reactions with spin inversion, in the high-spin and the low-spin states with CR-CCSD(T)/aug-cc-pVTZ in kcal/mol.

77

Figure 4.3. Binding enthalpies of the C-O bond cleavage of methanol for each transition metal atom with density functionals using aug-cc-pVTZ basis set and with CR-CCSD(T)/aug-cc-pVTZ in kcal/mol.

78

Figure 4.4. Activation enthalpies of the C-O bond cleavage of methanol for each transition metal atom with density functionals using aug-cc-pVTZ basis set and with CR-CCSD(T)/aug-cc-pVTZ in kcal/mol.

79

Figure 4.5. Enthalpy formations of the C-O bond cleavage of methanol for each transition metal atom with density functionals using aug-cc-pVTZ basis set and with CR-CCSD(T)/aug-cc-pVTZ in kcal/mol.

80

81

Figure 4.6. Optimized geometries and selected structural parameters at the B3LYP/aug-cc-pVTZ for the reaction complexes in the C-O bond activation of methanol with TM atoms. Bond lengths are in angstroms and bond angles in degrees.

82

83

Figure 4.7. Optimized geometries and selected structural parameters at the B3LYP/aug-cc-pVTZ for the transition states in the C-O bond activation of methanol with TM. Bond lengths are in angstroms and bond angles in degrees.

84

Figure 4.8. Optimized geometries and selected structural parameters at the B3LYP/aug-cc-pVTZ level of theory for the transition states in the C-O bond activation of methanol with TM atoms on the ground state electronic configuration. Bond lengths are in angstroms and bond angles in degrees.

85

Table 4.1

Summary of Density Functionals Applied in This Study

Functional Xa Type Exchange Functional

Correlation Functional

(RO)BLYP31,48 0 GGAb Becke88 Lee-Yang-Parr (RO)B97D32 0 GGA B97-D B97-D G96LYP33,31 0 GGA Gill96 Lee-Yang-Parr (RO)HCTH37 0 GGA Hamprecht-Cohen-Tozer-

Handy Hamprecht-Cohen-Tozer-Handy

(RO)OLYP31,51 0 GGA OptX Lee-Yang-Parr (RO)PEB36 0 GGA Perdew-Burke-Ernzerhof Perdew-Burke-Ernzerhof LC-BLYP31,48 0 GGA Becke88 Lee-Yang-Parr LC-wPBE36,45 0 GGA Perdew-Burke-Ernzerhof Perdew-Burke-Ernzerhof (RO)TPSS40 0 M-GGAc Tao-Perdew-Staroverov-

Scuseria Tao-Perdew-Staroverov-Scuseria

(RO)M06L41 0 M-GGA M06L M06L (RO)VSXC42 0 M-GGA van Voorhis-Scuseria van Voorhis-Scuseria TPSSKCIS40,43 0 M-GGA Tao-Perdew-Staroverov-

Scuseria Krieger-Chen-Iafrate-Savin

BB9540 0 M-GGA Tao-Perdew-Staroverov-Scuseria

Tao-Perdew-Staroverov-Scuseria

mPWB9544,32 0 M-GGA Modified Perdew-Wang91 Becke95 (RO)B97150 21 H-GGAd B97-1 B97-1 (RO)B3LYP31,47,48 20 H-GGA Becke88 Lee-Yang-Parr (RO)PBE044,45,49 25 H-GGA Perdew-Burke-Ernzerhof Perdew-Burke-Ernzerhof (RO)B97250 21 H-GGA B97-2 B97-2 O3LYP51 11.61 H-GGA Optx Lee-Yang-Parr B9852 21.98 H-GGA B98 B98 (RO)M0641 27 HM-

GGAe M06 M06

(RO)TPSSh40 10 HM-GGA Tao-Perdew-Staroverov-Scuseria

Tao-Perdew-Staroverov-Scuseria

(RO)B1B9544 28 HM-GGA Becke88 Becke95 (RO)M0554 28 HM-GGA M05 M05 (RO)M062X41 54 HM-GGA M062X M062X BMK55 42 HM-GGA BMK BMK a. X presents the percentage of Hartree-Fock exchange, b. GGA = generalized gradient approximation, c. M-GGA = Meta-GGA, d. H-GGA = Hybrid-GGA, e. HM-GGA = Hybrid-meta-GGA.

86

Table 4.2

Ground State Multiplicities Calculated at CR-CCSD(T)/aug-cc-pVTZ Level of Theory

Metal Species

Ground State Multiplicity M M(OH)(CH3) TS CH3MOH

Fe 5 5 5 5 Co 4 4 4 2 Ni 3 3 1 3 Cu 2 2 2 2 Ru 5 5 3 5 Rh 4 2 2 2 Pd 1 1 1 1 Ag 2 2 2 2

87

Table 4.3

MSDs and RMSDs of Each Metal and Overall 3d and 4d Species of Each Functional for Binding Enthalpies, with Respect to CR-CCSD(T)/aug-cc-pVTZ in kcal/mol

%HF Method Fe Co Ni Cu 3d-MSD 3d-RMSD

Ru Rh Pd Ag 4d-MSD

4d-RMSD

GGA

0 BLYP -6.3 -8.4 -1.6 -1.7 -4.5 5.4 3.0 -8.9 -2.2 -0.4 -2.1 4.8 0 B97D -6.7 -6.1 -5.3 -2.9 -5.3 5.5 -13.6 -13.8 -2.2 -2.1 -7.9 9.8 0 G96LYP -3.0 1.8 0.7 0.8 0.1 1.8 5.6 -5.9 0.1 1.7 0.4 4.2 0 HCTH -4.3 1.1 -1.1 0.7 -0.9 2.3 1.4 -8.1 2.6 -0.1 -1.1 4.3 0 OLYP -27.8 -7.9 3.5 3.4 -7.2 14.7 7.1 -4.0 5.0 2.5 2.6 5.0 0 PBE -8.2 -3.3 -3.9 -3.5 -4.7 5.1 1.2 -9.9 -4.0 -1.6 -3.6 5.4 0 LC-BLYP -8.4 -5.6 -5.1 -4.5 -5.9 6.1 -15.2 -5.4 -3.2 -2.2 -6.5 8.3 0 LC-WPBE 1.0 4.2 -1.7 -1.5 0.5 2.4 -9.1 -4.2 1.0 -0.3 -3.2 5.0

meta-GGA

0 TPSS -7.5 1.7 -3.8 -2.7 -3.1 4.5 2.2 -6.7 -3.2 -0.8 -2.1 3.9 0 M06L -9.3 -12.1 -4.4 -4.0 -7.4 8.2 -2.3 -6.9 -3.6 -2.2 -3.7 4.2 0 VSXC -12.6 -9.5 -10.1 -7.6 -10.0 10.1 -5.0 -20.3 -8.3 -4.0 -9.4 11.4 0 TPSSKCIS -10.4 2.3 -3.1 -2.4 -3.4 5.7 2.3 -7.4 -2.5 -0.8 -2.1 4.1 0 BB95 -5.9 3.2 -2.1 -1.6 -1.6 3.6 2.9 -11.2 -2.2 -0.1 -2.6 5.9 0 mPWB95 -7.8 1.2 -3.6 -3.1 -3.3 4.6 1.4 -13.1 -3.7 -1.3 -4.2 6.8

hybrid-GGA

21 B971 -4.2 -5.1 -2.6 -1.7 -3.4 3.7 1.3 -8.9 -0.2 -1.2 -2.2 4.5 20 B3LYP -11.5 -4.0 -0.5 -0.8 -4.2 6.1 3.1 -5.4 0.0 -0.3 -0.7 3.1 25 PBE0 -12.2 -4.2 -1.9 -1.4 -4.9 6.6 2.3 -3.9 -0.3 -0.8 -0.7 2.3 21 B972 -2.8 1.1 1.2 0.1 -0.1 1.6 2.8 -9.4 2.4 0.2 -1.0 5.1 11.6 O3LYP 1.2 7.4 4.0 2.9 3.9 4.5 9.2 -2.6 4.9 1.9 3.4 5.5 21.98 B98 -4.0 -5.5 -1.2 -1.2 -3.0 3.5 1.9 -7.6 0.2 -0.8 -1.6 3.9

hybrid-meta-GGA

27 M06 -7.9 -9.2 -2.0 -2.0 -5.3 6.2 -0.6 -13.0 -0.3 -1.5 -3.9 6.6 10 TPSSh 2.8 -5.1 -2.8 -1.9 -1.7 3.4 2.5 -4.6 -1.6 -0.6 -1.1 2.8 28 B1B95 -11.3 -1.8 -0.6 0.0 -3.4 5.7 3.3 -4.9 1.2 0.2 -0.1 3.0 52 M05 -7.2 -2.7 -1.5 -0.2 -2.9 3.9 0.6 -11.6 3.2 -1.2 -2.2 6.0 54 M062X -7.3 -5.5 -2.3 -2.8 -4.5 4.9 -1.1 -6.9 0.7 -2.4 -2.4 3.7 42 BMK -17.7 -4.5 -1.3 -1.6 -6.3 9.2 -8.4 -4.0 -2.9 -1.0 -4.1 4.9

88

Table 4.4

MSDs of Different Types of Functionals of Each Metal and Overall 3d and 4d Species for Binding Enthalpies, with Respect to CR-CCSD(T)/aug-cc-pVTZ in kcal/mol Fe Co Ni Cu 3d-

MSD Ru Rh Pd Ag 4d-

MSD GGA -8.0 -3.0 -1.8 -1.2 -3.5 -2.5 -7.5 -0.3 -0.3 -2.7 Meta-GGA -8.9 -2.2 -4.5 -3.6 -4.8 0.2 -10.9 -3.9 -1.5 -4.0 Hybrid-GGA -5.6 -1.7 -0.2 -0.3 -2.0 3.4 -6.3 1.2 -0.2 -0.5 Hybrid-meta-GGA -8.1 -4.8 -1.8 -1.4 -4.0 -0.6 -7.5 0.0 -1.1 -2.3

Table 4.5

RMSDs of Different Types of Functionals of Each Metal and Overall 3d and 4d Species for Binding Enthalpies, with Respect to CR-CCSD(T)/aug-cc-pVTZ in kcal/mol Fe Co Ni Cu 3d-

RMSD Ru Rh Pd Ag 4d-

RMSD GGA 11.3 5.4 3.3 2.7 6.6 8.6 8.1 2.9 1.6 6.2 Meta-GGA 9.2 6.5 5.2 4.1 6.5 2.9 11.9 4.4 2.0 6.6 Hybrid-GGA 7.4 4.9 2.2 1.6 4.6 4.3 6.8 2.2 1.1 4.2 Hybrid-meta-GGA 10.1 5.4 1.9 1.7 5.9 3.9 8.3 2.0 1.3 4.7 LC-GGA 6.0 4.9 3.8 3.4 4.6 12.5 4.8 2.3 1.6 6.9

89

Table 4.6

MSDs and RMSDs of Each Metal and Overall 3d and 4d Species of Each Functional for Activation Enthalpies, with Respect to CR-CCSD(T)/aug-cc-pVTZ in kcal/mol

%HF Method Fe Co Ni Cu 3d-MSD

3d-RMSD Ru Rh Pd Ag 4d-

MSD 4d-RMSD

GGA

0 BLYP 8.8 -12.5 -19.8 -16.8 -10.1 15.0 -24.6 -13.3 -9.2 -14.7 -15.5 16.5 0 B97D 8.3 -12.3 -24.2 -15.9 -11.0 16.2 -29.9 -12.5 -6.9 -15.5 -16.2 18.3 0 G96LYP 9.1 -12.5 -20.0 -16.2 -9.9 15.0 -22.8 -14.7 -9.5 -13.4 -15.1 15.9 0 HCTH 11.8 -8.7 -20.0 -11.2 -7.0 13.6 -19.9 -11.2 -4.9 -8.7 -11.2 12.4 0 OLYP 12.2 -9.6 -18.4 -12.2 -7.0 13.5 -17.6 -12.9 -6.8 -8.1 -11.4 12.1 0 PBE 7.6 -13.1 -21.8 -16.5 -11.0 15.6 -22.4 -16.6 -12.3 -13.5 -16.2 16.6 0 LC-BLYP 23.8 6.0 2.8 0.2 8.2 12.3 -4.2 2.6 6.0 0.1 1.1 3.9 0 LC-WPBE 20.9 4.6 -0.3 -1.8 5.8 10.7 -19.8 -1.6 2.5 -1.8 -5.2 10.1

Meta-GGA

0 TPSS 7.7 -13.3 -18.5 -17.1 -10.3 14.7 -19.9 -16.3 -12.2 -14.5 -15.7 16.0 0 M06L 13.5 -6.7 -6.1 -13.4 -3.2 10.5 -12.1 -10.0 -5.7 -11.3 -9.8 10.1 0 VSXC 7.9 -12.4 -21.0 -19.8 -11.3 16.2 -28.9 -13.1 -9.2 -19.9 -17.8 19.3 0 TPSSKCIS 9.2 -12.6 -18.5 -16.4 -9.6 14.6 -20.3 -13.4 -11.0 -13.7 -14.6 15.0 0 BB95 6.6 -14.9 -26.3 -18.1 -13.2 17.9 -26.6 -18.0 -13.4 -15.0 -18.3 19.0 0 mPWB95 6.5 -14.8 -26.9 -18.3 -13.4 18.2 -27.5 -17.9 -13.7 -15.5 -18.6 19.4

Hybrid-GGA

21 B971 16.0 -6.4 -3.1 -9.0 -0.6 9.8 -18.2 -7.0 -2.2 -7.2 -8.6 10.4 20 B3LYP 15.7 -4.1 -0.8 -8.2 0.7 9.1 -11.6 -5.8 -1.3 -6.1 -6.2 7.2 25 PBE0 15.6 -4.7 4.0 -5.9 2.2 8.9 2.1 -5.8 -1.9 -3.4 -2.2 3.6 21 B972 17.3 4.6 -5.6 -7.7 2.1 10.1 -18.0 -6.1 -0.6 -5.7 -7.6 9.9 11.6 O3LYP 11.4 -5.7 -8.3 -7.9 -2.6 8.6 -14.6 -5.8 -2.5 -4.3 -6.8 8.3 21.98 B98 16.2 -4.6 -2.2 -8.3 0.3 9.5 -16.6 -6.5 -1.6 -6.5 -7.8 9.5

Hybrid-meta-GGA

27 M06 -3.5 0.0 -4.0 -5.0 -3.1 3.7 -16.8 -4.8 2.0 -3.6 -5.8 9.0 10 TPSSh 0.9 -9.2 -8.7 -12.6 -7.4 8.9 -14.2 -11.8 -8.0 -10.3 -11.1 11.3 28 B1B95 16.6 -4.4 2.3 -6.4 2.1 9.2 -10.1 -6.0 -1.9 -3.7 -5.4 6.2 52 M05 -2.0 1.0 -2.8 -3.7 -1.9 2.6 -16.5 -1.4 4.8 -4.1 -4.3 8.9 54 M062X 25.4 0.0 25.8 -0.4 12.7 18.1 -0.2 3.0 8.6 0.3 2.9 4.5 42 BMK 22.1 6.2 11.5 -3.3 9.1 12.9 -10.2 3.1 1.2 -0.8 -1.7 5.4

90

Table 4.7

MSDs of Different Types of Functionals of Each Metal and Overall 3d and 4d Species for Activation Enthalpies, with Respect to CR-CCSD(T)/aug-cc-pVTZ in kcal/mol

Fe Co Ni Cu 3d-MSD Ru Rh Pd Ag 4d-

MSD GGA 12.8 -7.3 -15.2 -11.3 -5.2 -20.2 -10.0 -5.1 -9.4 -11.2 Meta-GGA 8.6 -12.5 -19.6 -17.2 -10.2 -22.6 -14.8 -10.9 -15.0 -15.8 Hybrid-GGA 15.3 -3.5 -2.7 -7.8 0.3 -12.8 -6.2 -1.7 -5.5 -6.5 Hybrid-meta-GGA 9.9 -1.1 4.0 -5.2 1.9 -11.3 -3.0 1.1 -3.7 -4.2

Table 4.8

RMSDs of Different Types of Functionals of Each Metal and Overall 3d and 4d Species for Activation Enthalpies, with Respect to CR-CCSD(T)/aug-cc-pVTZ in kcal/mol

Fe Co Ni Cu 3d-RMSD

Ru Rh Pd Ag 4d-RMSD

GGA 14.0 10.4 18.0 13.0 14.1 21.3 11.9 7.8 11.0 13.9

Meta-GGA 8.9 12.8 20.7 17.3 15.6 23.3 15.1 11.2 15.2 16.8

Hybrid-GGA 15.5 5.1 4.7 7.9 9.3 14.6 6.2 1.8 5.7 8.5

Hybrid-meta-GGA 15.4 4.9 12.3 6.4 10.6 12.7 6.1 5.3 5.0 7.9

LC-GGA 22.4 5.4 2.0 1.3 11.6 14.3 2.1 4.6 1.3 7.6

91

Table 4.9

MSDs and RMSDs of Each Metal and Overall 3d and 4d Species of Each Functional for Enthalpy Formation, with Respect to CR-CCSD(T)/aug-cc-pVTZ in kcal/mol

%HF Method Fe Co Ni Cu 3d-MSD

3d-RMSD Ru Rh Pd Ag 4d-

MSD 4d-RMSD

GGA

0 BLYP 17.2 -31.8 -2.5 -21.8 -9.7 21.1 -4.6 -19.8 31.5 -15.7 -2.2 20.3 0 B97D 16.8 -22.7 -7.5 -21.7 -8.8 18.2 -23.9 -57.7 8.9 -17.7 -22.6 32.8 0 G96LYP 19.1 -22.2 -0.7 -19.4 -5.8 17.6 -2.6 -18.3 -10.8 -13.6 -11.3 12.7 0 HCTH 20.2 -15.7 -0.5 -13.9 -2.5 14.6 -6.0 -16.5 -1.0 -9.7 -8.3 10.0 0 OLYP -5.5 -23.8 3.5 -12.6 -9.6 13.8 0.4 -14.6 -1.8 -7.0 -5.7 8.1 0 PBE 13.2 -27.3 -6.3 -24.4 -11.2 19.7 -8.5 -24.2 35.1 -17.6 -3.8 23.5 0 LC-BLYP 7.9 -17.6 -2.2 -16.2 -7.0 12.6 -4.8 -3.0 16.4 -7.0 0.4 9.4 0 LC-WPBE 6.9 -10.0 -1.2 -15.5 -5.0 9.9 -10.8 -5.8 15.1 -5.8 -1.9 10.1

Meta-GGA

0 TPSS 13.0 -21.7 -7.7 -25.4 -10.5 18.4 -5.3 -20.7 35.7 -18.0 -2.1 22.7 0 M06L 12.3 -24.7 -7.2 -26.7 -11.6 19.5 -5.1 -13.8 26.9 -15.1 -1.8 17.1 0 VSXC 11.5 -28.1 -14.3 -30.7 -15.4 22.7 -14.9 -27.5 -15.3 -21.7 -19.9 20.5 0 TPSSKCIS 15.7 -20.4 -4.9 -23.0 -8.2 17.4 -4.0 -19.7 -13.8 -16.0 -13.4 14.6 0 BB95 15.6 -24.1 -4.8 -22.7 -9.0 18.5 -7.4 -25.8 -14.1 -16.8 -16.0 17.3 0 mPWB95 14.1 -26.0 -6.2 -24.1 -10.6 19.3 -9.0 -27.5 -15.5 -18.1 -17.5 18.8

Hybrid-GGA

21 B971 18.5 -19.2 -1.9 -17.0 -4.9 15.8 -3.3 -13.6 22.5 -9.9 -1.1 14.2 20 B3LYP 12.5 -10.5 2.8 -13.7 -2.2 10.7 1.5 -7.8 -1.5 -7.0 -3.7 5.3 25 PBE0 9.2 -13.1 0.3 -13.8 -4.3 10.6 20.9 -7.1 20.6 -5.9 7.1 15.4 21 B972 19.6 -8.2 1.5 -13.4 -0.1 12.6 -2.8 -13.2 3.0 -6.8 -5.0 7.7 11.61 O3LYP 33.1 -3.0 6.2 -9.4 6.8 17.5 3.2 -8.3 2.7 -3.5 -1.5 5.0 21.98 B98 18.5 -14.2 -0.2 -15.6 -2.9 14.0 -2.1 -12.0 -2.3 -9.0 -6.3 7.6

Hybrid-meta-GGA

27 M06 -3.1 -14.0 6.4 -10.7 -5.3 9.5 12.2 -8.4 7.8 -3.4 2.1 8.6 10 TPSSh 13.3 -22.3 -4.7 -21.0 -8.7 16.9 20.8 -14.2 29.7 -13.3 5.8 20.6 28 B1B95 11.0 -10.7 3.2 -11.2 -1.9 9.6 21.2 -7.3 1.5 -4.3 2.8 11.4 52 M05 25.0 -11.1 4.2 -8.8 2.3 14.5 17.1 -6.0 16.1 -1.9 6.3 12.2

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54 M062X -10.6 6.0 3.4 -6.0 -1.8 7.0 20.9 4.7 17.6 3.8 11.8 14.0 42 BMK 3.8 -9.8 -4.3 -16.9 -6.8 10.2 -5.6 -8.4 -17.3 -9.2 -10.1 11.0

Table 4.10

MSDs of Different Types of Functionals of Each Metal and Overall 3d and 4d Species for Enthalpy Formations, with Respect to CR-CCSD(T)/aug-cc-pVTZ in kcal/mol

Table 4.11

RMSDs of Different Types of Functionals of Each Metal and Overall 3d and 4d Species for Enthalpy Formations, with Respect to CR-CCSD(T)/aug-cc-pVTZ in kcal/mol

Fe Co Ni Cu 3d-MSD Ru Rh Pd Ag 4d-

MSD GGA 12.0 -21.4 -2.2 -18.2 -7.4 -7.6 -20.0 11.7 -11.8 -6.9 Meta-GGA 13.7 -24.2 -7.5 -25.4 -10.9 -7.6 -22.5 0.7 -17.6 -11.8 Hybrid-GGA 18.6 -11.4 1.5 -13.8 -1.3 2.9 -10.3 7.5 -7.0 -1.7 Hybrid-meta-GGA 6.6 -10.3 1.4 -12.4 -3.7 14.5 -6.6 9.3 -4.7 3.1

Fe Co Ni Cu 3d-RMSD Ru Rh Pd Ag 4d-

RMSD GGA 14.4 22.3 3.9 18.6 16.3 10.3 25.4 19.1 12.7 17.9 Meta-GGA 13.8 24.3 8.2 25.6 19.4 8.5 23.0 21.9 17.8 18.7 Hybrid-GGA 20.0 12.4 3.0 14.0 13.8 8.9 10.7 12.6 7.3 10.1 Hybrid-meta-GGA 13.3 13.3 4.5 13.4 11.8 17.3 8.7 17.4 7.2 13.5 LC-GGA 7.4 14.3 1.8 15.9 11.3 8.3 4.6 15.8 6.5 9.8

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Table 4.12

The Difference between S2 and S(S+1) for Different Types of UDFT Calculations

S2-S(S+1) ∆/S(S+1)%

U-GGA 0.1288 10.65 U-meta-GGA 0.1581 12.90 U-hybrid-GGA 0.1868 15.12 U-hybrid-meta-GGA 0.1433 11.67 ∆=S2-S(S+1)

Table 4.13

Comparison between RODFT and UDFT of Different Types of Functionals of Each Metal and Overall 3d and 4d Species, with Respect to CR-CCSD(T)/aug-cc-pVTZ in kcal/mol

Fe Co Ni Cu 3d-RMSD

Ru Rh Pd Ag 4d-RMSD

RO-GGA 22.9 17.1 14.9 14.1 17.3 16.8 20.7 7.7 14.6 15.6 U-GGA 11.7 16.1 12.6 14.2 13.8 15.8 20.2 13.5 11.0 15.5 RO-meta-GGA 9.3 12.8 11.9 18.6 13.7 13.4 20.4 10.1 13.5 14.9 U-meta-GGA 11.2 16.6 11.9 19.0 15.1 14.8 16.4 17.0 14.1 15.7 RO-hybrid-GGA 18.5 14.7 16.6 19.0 17.3 14.9 21.6 14.6 16.1 17.1 U-hybrid-GGA 13.9 8.5 2.6 9.5 9.5 10.3 8.3 8.9 5.5 8.5 RO-hybrid-meta-GGA 17.9 5.0 7.8 7.9 10.8 5.2 10.8 8.1 4.7 7.6 U-hybrid-meta-GGA 12.3 9.0 7.7 8.4 9.5 13.3 8.1 10.6 5.1 9.8

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Table 4.14

Comparison between RODFT and UDFT of Different Types of Functionals of Different Types of Reactions (Binding Enthalpy, Activation Enthalpy, and Enthalpy Formation), with Respect to CR-CCSD(T)/aug-cc-pVTZ in kcal/mol

3d-RMSD 4d-RMSD

∆Hb ∆H‡ ∆H ∆Hb ∆H‡ ∆H RO-GGA 15.6 20.6 15.4 9.2 17.0 18.9 U-GGA 4.9 15.3 17.7 6.3 15.1 21.0 RO-meta-GGA 5.8 14.7 17.7 8.1 16.0 18.3 U-meta-GGA 8.0 14.5 20.3 7.7 15.9 20.2 RO-hybrid-GGA 17.7 12.9 20.4 19.0 8.1 21.2 U-hybrid-GGA 4.9 9.5 12.6 3.9 8.3 11.5 RO-hybrid-meta-GGA 2.8 12.9 13.4 4.7 7.8 9.5 U-hybrid-meta-GGA 4.9 10.1 12.1 4.7 8.3 13.9

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CHAPTER 5

SUMMARY OF PERFORMANCE OF DENSITY FUNCTIONALS FOR C-O BOND

INSERTION REACTIONS OF SMALL MOLECULES WITH

TRANSITION METAL ATOMS

Density functional theory (DFT) has become popular to investigate the thermochemistry

properties of transition metal containing systems because DFT has more favorite size-to-cost

scales than the correlated wave function theory dose for these systems.1 As I mentioned before,

there was a relatively small number of investigates have been done in the field of transition metal

chemistry and different bond activations by transition-metal catalysts have been of great interest

in experimental and theoretical studies. Both of projects included in this thesis were focused on

investigating the C-O bond activations of small organic molecules, methoxyethane and

methanol, by several late transition metal atoms, and gauging the performance of several density

functionals with accurate ab initio method, CR-CCSD(T). The conclusion based on the results

from these two projects provides practical information about the choice of more suitable density

functionals and the more effective TMs for the future works on C-O bond activations. The

energetic trends of both projects showed that earlier TM atoms tend to have lower activation

enthalpies and form more stable products. Among the considered density functionals (nine

functionals in the first project in Chapter 3 and 26 functionals in the second project in chapter 4),

hybrid-GGA functionals had lower RMSD gave more accurate description of the energetic

properties of these kinds of systems. PBE0 was recommended by both projects as the most

reliable functional to investigate C-O bond activations by transition metals.

5.1 References

[1] Christopher J. C.; Donald G. T. Phys. Chem. Chem. Phys. 2009, 11, 10757-10816

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