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Correlations between Density-Based Bond Orders and Orbital-Based Bond Energies for Chemical Bonding AnalysisCitation for published version (APA):Rohling, R. Y., Tranca, I. C., Hensen, E. J. M., & Pidko, E. A. (2019). Correlations between Density-Based BondOrders and Orbital-Based Bond Energies for Chemical Bonding Analysis. Journal of Physical Chemistry C,123(5), 2843-2854. https://doi.org/10.1021/acs.jpcc.8b08934

DOI:10.1021/acs.jpcc.8b08934

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https://doi.org/10.1021/acs.jpcc.8b08934https://doi.org/10.1021/acs.jpcc.8b08934https://research.tue.nl/en/publications/correlations-between-densitybased-bond-orders-and-orbitalbased-bond-energies-for-chemical-bonding-analysis(7a531605-3578-4219-8d21-9881d2a30364).html

Correlations between Density-Based Bond Orders and Orbital-BasedBond Energies for Chemical Bonding AnalysisRoderigh Y. Rohling,,§ Ionut C. Tranca,,§ Emiel J. M. Hensen,*, and Evgeny A. Pidko*,,�

Inorganic Materials Chemistry Group, Department of Chemical Engineering, and Energy Technology, Department of MechanicalEngineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

*S Supporting Information

ABSTRACT: Quantum chemistry-based codes and methodsprovide valuable computational tools to estimate reactionenergetics and elucidate reaction mechanisms. Electronicstructure methods allow directly studying the chemical trans-formations in molecular systems involving breaking and makingof chemical bonds and the associated changes in the electronicstructure. The link between the electronic structure and chemicalbonding can be provided through the crystal orbital Hamiltonpopulation (COHP) analysis that allows quantifying the bondstrength by computing Hamilton-weighted populations oflocalized atomic orbitals. Another important parameter reflectingthe nature and strength of a chemical bond is the bond orderthat can be assessed by the density derived electrostatic andchemical (DDEC6) method which relies on an electron and spindensity-partitioning scheme. Herein, we describe a linear correlation that can be established between the DDEC6-derived bondorders and the bond strengths computed with the COHP formalism. We demonstrate that within defined boundaries, theCOHP-derived bond strengths can be consistently compared among each other and linked to the DDEC6-derived bond ordersindependent of the used model. The validity of these correlations and the effective model independence of the electronicdescriptors are demonstrated for a variety of gas-phase chemical systems, featuring different types of chemical bonds.Furthermore, the applicability of the derived correlations to the description of complex reaction paths in periodic systems isdemonstrated by considering the zeolite-catalyzed DielsAlder cycloaddition reaction between 2,5-dimethylfuran and ethylene.

1. INTRODUCTION

Modern computational chemistry provides a powerful toolboxfor studying the fundamental aspects of chemical bonding andchemical reactivity.14 A wide range of practical methodologieshas been developed so far to investigate the electronic aspectsof chemical bonding, making use of electron densitypartitioning schemes or based on the direct analysis of theelectronic wavefunctions. For example, the quantum theory ofatoms in molecules (QTAIM) provides a framework for thetopological analysis of the electron density.5 Local descriptorssuch as the electron, Laplacian, and energy densities can becomputed in the framework of QTAIM and utilized for thequalitative and quantitative analysis of chemical bonds.6,7 Thepotential electron density has been shown recently to beparticularly useful for estimating the effective force constants ofa chemical bond as a measure of the bond strength.8,9 Analternative partitioning scheme is the density derived electro-static and chemical (DDEC6) method1012 which involvesspherical averaging of the atomic electron densities. In thismethod, the dressed exchange hole approach is employed tocompute the DDEC6-based bond orders (BOs) that can beregarded as quantitative descriptors, reflecting the strength ofthe chemical bonds. The energy decomposition analysis

(EDA) partitions the interaction between a pair of atomsinto energy components, namely, the electrostatic, polarization,charge transfer, exchange, and correlation contributions byreferencing the wavefunction and electron density of thechemical system to those of the isolated reference ions.13,14

The crystal orbital overlap population (COOP) analysis putforward by Hofmann15 and the crystal orbital Hamiltonpopulation (COHP) analysis introduced by Dronskowski andco-workers16 utilize the electronic wavefunction to derive thebonding information. The COOP and COHP schemes enabledirect quantification of the (anti)bonding orbital overlap andthe strength of interatomic bonds, respectively.

Among the different available bonding analysis formalisms,the COHP and DDEC6 methods are particularly attractive forpractical applications in computational chemistry, given thechemically intuitive nature of the respective bond quantifiers.Recent studies demonstrate the power of these approaches forthe theoretical analysis of catalytic reactions and scaling laws

Received: September 12, 2018Revised: December 19, 2018Published: January 7, 2019

Article

pubs.acs.org/JPCCCite This: J. Phys. Chem. C 2019, 123, 2843−2854

© 2019 American Chemical Society 2843 DOI: 10.1021/acs.jpcc.8b08934J. Phys. Chem. C 2019, 123, 28432854

This is an open access article published under a Creative Commons Non-Commercial NoDerivative Works (CC-BY-NC-ND) Attribution License, which permits copying andredistribution of the article, and creation of adaptations, all for non-commercial purposes.

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on transition-metal surfaces,17,18 transition-metal oxides,19 andzeolites.20

The DDEC6 charge partitioning yields consistently accurateresults for a wide range of materials and bonding types. TheDDEC6 methodology assigns atomic electron and spindistributions to each atom in a chemical system.12 Thisapproach provides a number of important advantages overother available methods because (1) it avoids the assumptionof a constant BO to electron density overlap,21,22 (2) does notrequire the use of the method-dependent first-order densitymatrix,2326 (3) does not use the bonding/antibonding orbitaloccupancies which fail for longer bonds,27 and (4) avoids thecomputationally expensive exchangecorrelation hole parti-tioning approach.28 The COHP yields complementaryinformation to the density of states (DOS). Although theDOS provides insight into the probability of finding anelectron in a particular atomic orbital as a function of electronenergy, the COHP enables one to identify whether therespective electron contributes to a bonding, antibonding, ornonbonding interaction.16 The COHP formalism enables adirect quantification of these energy-partitioned contributionsby using the Hamiltonian.

Recently, we thoroughly investigated the DielsAldercycloaddition (DAC) between 2,5-dimethylfuran (DMF) andethylene over third-row d-block-29 and alkali-exchanged30faujasite models using both the DDEC6 and COHP methods.In the former study,29 we found a qualitative correlationbetween the integrated COHP (ICOHP) and BO valuescomputed for the interaction between the various d-blockcations and the carbon atoms of either DMF or ethylene. Inthe latter study,30 we found a qualitative trend between theICOHP-computed interaction strength between the active sitesand the carbon atoms of DMF in line with the Lewis acidity ofthe alkali cations, albeit these interactions were ionic for whichthe COHP analysis is less well suited.16 Furthermore, it hasbeen demonstrated that the variation of the ICOHP values andthe DDEC6-derived BOs with interatomic distances generallyfollows the trend of the heuristic Pauling BOs.12,31,32Therefore, the observed trends and the notion that onecould potentially correlate chemical intuitive BOs withchemical bond strength, make an exploration of the correlationbetween the ICOHP-computed bond strength and DDEC6-derived BO (ICOHPBO correlation) appealing.

However, such an effort is hampered by the fundamentalproblem in which periodic models share no absolute energyreference point when using the COHP formalism.16,33,34 Thelack of an absolute energy reference makes the COHP methodmodel dependent and thus prohibits a comparison of bondstrengths computed for pairs of atoms in different structuralmodels. On the other hand, the DDEC6-derived BOs arerelatively insensitive to the choice of basis sets and exchangecorrelation functionals and can directly be compared betweenthe different systems.12 Considering these notions, it is thusimportant to investigate methodological and chemicallimitations of a possible ICOHPBO correlation.

Herein, we report on a theoretical and quantum chemicalinvestigation which aimed at establishing the ICOHPBOcorrelation and exploring the framework in which such acorrelation is possible. The ultimate goal is to use thiscorrelation to describe and compare the changes to interatomicbonds in catalytic reactions. To this end, we will first introducethe COHP- and DDEC6-derived BO formalisms. Then, gas-phase molecules will be studied to explore the boundaries

within which the correlation remains valid. Finally, the validityof such correlation is evaluated for the case of the zeolite-catalyzed DAC between DMF and ethylene in periodic zeolitemodels of different chemical compositions.

2. INTRODUCTION TO THE METHODS2.1. COHP Analysis. The COOP and COHP analyses

allow the description of bonding in molecules and solids. Theyallow for the deconvolution of the band structure into atomicorbitals, quantify the degree of net orbital overlap, and they canalso be used to determine the bond strength.

In order to apply methods3539 using localized basis sets toanalyze material properties for plane wave-based calculations,projection schemes were introduced.40,41 Also, within theCOHP method employed in this work, the plane-wave (PW)wavefunction is transformed into a wavefunction based on acombination of localized atomic orbitals (LCAOs):16,36,37,42,43

cJ Ji n

m

ni J ni JPW, LCAO, , ,� � �� = � =(1)

where in eq 1, n is the nth basis function in a set with m totalbasis functions that all make up the wavefunction, J is the bandnumber, and cni,J is the the orbital coefficient matrix of theorbital �ni,J. Consequently, the energy-partitioned bandstructure can be transformed into orbital pair contributionsto obtain a localized DOS for atoms i and j, Figure 1a. This isalso called the projected DOS (pDOS):

E c E EpDOS ( ) ( )in

in

n2� �= | |

(2)

Using the overlap population (Pij):

P S c cij ijn

m

ni nj�= *(3)

one obtains an overlap population-weighted pDOS. Here, Sij =��i|�j� is the overlap of atomic orbitals �i and �j.

Because the DOS is an energy-partitioned property, theoverlap population-weighted pDOS shares this property. Usingthis and Pij, one can define regions where the atomic orbitaloverlap is bonding, antibonding, and nonbonding in nature.

Figure 1. The pDOS of N2 split into pDOSs of every individual N-atom (red = 2s and black = 2p) in (a). The total pCOOP andpCOHP of the nitrogen molecule are shown in (b,c), respectively.

The Journal of Physical Chemistry C Article

DOI: 10.1021/acs.jpcc.8b08934J. Phys. Chem. C 2019, 123, 28432854

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http://dx.doi.org/10.1021/acs.jpcc.8b08934

The resulting function is called the COOP (COOPij(E)) asintroduced by Hoffmann15 (Figure 1b):

E S f c c E ECOOP ( ) ( )ij ijn

J ni nj n� �= * (4)

in which f J is the occupation number of each band J.Integration of the COOPij(E)-function up to the Fermi levelwill yield the net orbital overlap between atoms i and j. As Pij isused, the COOP(E) function is basis-set dependent.34

The COOP function can be rewritten by replacing theoverlap matrix with the Hamiltonian matrix. By convention,the COHP function is defined as COHPij(E) and can becomputed according to:

E H f c c E ECOHP ( ) ( )ij ijn

J ni nj n� �= * (5)

where Hij represents the Hamiltonian matrix element betweenatomic orbitals �i and �j, and ci and cj are the coefficients ofthese atomic orbitals in the molecular orbital �n (�n =�icin�i). A positive value for COHPij(E) symbolizes abonding electronic interaction between the atomic orbitals iand j, whereas a negative value describes an antibondinginteraction. A value of zero is associated with a nonbondinginteraction (see for instance Figure 1c). The integrated valueof COHPij(E), ICOHP, is a measure for the bond strength.This formulation provides a good approximation of the bondenergy as long as the repulsive energy of the nuclei is canceledby the double-counted electrostatic interactions.44 Note,though, that the energy computed with eq 5, accounts forpair-wise interactions but does not account for many-particleinteractions, which may also influence the strength of theinteratomic bond under study.

Within the COHP formalism, the lack of an absolute zeroenergy reference prohibits one to compare ICOHP valuesobtained in different structural models directly with each other.This can be appreciated by examining eq 6, which is anexpression for the crystal’s total cohesive energy (Ecoh),obtained by subtracting the total energy of the atoms fromthe total energy of the crystal. The equation is adopted fromref 16, which also contains the full derivation:

E f c c H f c c H

f E n r E n r

ZZ

r r

d d

( ) ( )

ni njJ ni nj ij

niJ ni ni ii

i JJi

Ji

i j

i j

coh

el xc

F F� ��

� �

�

�

= � * + � *

+ � { � } + � { � }

+| � �|

� �

(6)

In the above equation, �J refers to occupied one-electroneigenvalues. In combination with f J, summation over all J(third term) yields the band structure energy. The first term isthe off-site COHP. The second term is the on-site COHP andthe third term is the band structure energy of the atom. Thefourth, fifth, and sixth relate to the charge density difference,exchangecorrelation difference, and Madelung term, respec-tively. Note that the third term arises from the summation ofthe total energy of a single reference atom whose energy isdetermined by the occupation of J bands each with energy �J.The fourth and fifth terms are the differences in Coulomb andexchangecorrelation energies between the separate referenceatoms and that of the actual crystal under study, respectively.

The sixth term is the nucleusnucleus repulsion term arisingfrom the Schro�dinger equation used for the crystal.

The importance of eq 6 is that it tells us that the bondenergies (off-site COHP) are only the real bond energies if thesecond and third lines in eq 6 cancel out exactly. Additionally,the second, third, and fourth terms carry undeterminedconstants. We can, therefore, rewrite eq 6 essentially as:

E f H Cd c cni nj

J ni nj ijcoh F� � �= � * +

�

(7)

where C is the total sum of the errors that not exactly cancelout each other and the undetermined constants.

2.2. Density-Derived Electrostatic and ChemicalMethod. Molecular bonding can be studied in terms of thechemically intuitive BOs. The density-derived electrostatic andchemical method was introduced by Manz and Limas in 2016(DDEC6)10 and is a revised version of its predecessors45,46(e.g. DDEC3). The DDEC6-based BOs can provide one abinitio BOs without the assumption of constant BOs to atomiccharge-density overlap ratios.12 The exact derivation of theequations necessary to both compute the BOs and execute theunderlying density derived electrostatic and chemical(DDEC6) charge partitioning is explained elsewhere.1012Fundamentally, formation of a bond is assumed to arise fromelectron exchange between two atoms close enough to exhibitoverlapping electron densities.

Manz defined the BO of an atom pair A (in the unit cell)and j (atoms in both unit cell and periodic images):12

B CEA j A j A j, , ,= + � (8)

where BA,j is the BO between atom A and j, CEA,j is the contactexchange, and �A,j is the dressed exchange hole delocalizationterm. The term CEA,j describes the electron exchange betweenatoms A and j in a material, formulated in:

r r

r rr rCE 2

( ) ( )

( ) ( )( )dA j

A A j j,

avg avg

avg avg3

� �

� ��=

� � • � �

� � • � ��

(9)

where any ��iavg is the average spherical electron density of atomi as a function of the atomic electron distribution and atomicspin magnetization density vector obtained through DDEC6-based partitioning of the electron density. The term ��avg is thesum of all ��iavg found in the material (unit cell + periodicimages). Note that, this equation deals with the dressedexchange hole, which is an adjusted (either more contracted ormore diffuse) exchange hole to obtain more accurate BOs. Thesecond term in eq 8 is the dressed exchange hole delocalizationterm, defined according to eq 10:

CEA j A j A j A j A j, ,coord. nr.

,pairwise

,con.

,� = � (10)

where �A,jcoord.nr. accounts for coordination number effects,�A,jpairwise for pair-wise interactions, and �A,jcon. is a constraint onthe density-derived localization index, BA,A. The latter is amatrix that equals the total number of the dressed exchangeelectrons in the material (unit cell + periodic images). Theseterms are constraints and scaling relationships to keep the BOswell behaved.

3. COMPUTATIONAL DETAILS3.1. Models. The first model was a box with cell edges of

20 × 20 × 20 Å3. The molecules were located in the center ofthe periodic box. An N2 molecule was always located on one of



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the cell edges as a reference. The studied molecules were:ethane (1), ethylene (2), acetylene (3), propylene (4),cyclooctyne (5), 1,3,5-hexatriene (6), hexa-1,5-dien-3-yne(7), benzene (8), toluene (9), para-xylene (10), benzoicacid (11), terephthalic acid (12), benzodithioic acid (13),benzene-1,4-bis(carbodithioic) acid (14), furan (15), 2-methylfuran (16), DMF (17), furan-2-carboxylic acid (18),furan-2,5-dicarboxylicacid (19), furan-2-carbodithioic acid(20), furan-2,5-bis(carbodithioic) acid (21), acetonitrile(22), hydrogen cyanide (23), cyanogen fluoride (24),cyanogen chloride (25), cyanogen bromide (26), cyanogeniodide (27), cyanogen (28), acrylonitrile (29), acetic acid(30), oxaclic acid (internal H-bond) (31), ethanedithioic acid(32), ethanebis(dithioic) acid (33), and pyridine-2,5-dicarbox-ylic acid (34), pyridine (35), pyrazine (36), piperidine (37),piperazine (38), benzamidine (39), terephthalamidine (40),aniline (41), and dihydropyrazine (42). Atom indices can befound in Figure 2.

Different groups of bonds were defined on the basis of theclass of molecules (e.g. furanics vs aromatics) and the presenceof heteroatoms (e.g. oxygen vs sulfur). The former accounts fordifferent stoichiometries, for example, the carbon-to-oxygen

ratio changes the number of valence electrons on a per elementbasis. The second accounts for a variation in the valenceprinciple quantum number of the atoms involved in theICOHP analysis. The groups were (I) CC bonds inhydrocarbon molecules including aromatic compounds con-taining only carbon and hydrogen atom groups (110). Thisgroup is referred to as the H,C-only hydrocarbon group. (II)CC bonds in molecules containing carboxylic acid function-alities (11, 12, 30, and 31), (III) CC bonds in molecules (13,14, 32, and 33) containing dithioic acid functions, (IV) CObonds in furanic compounds (1521), (V) CO bonds inaromatic compounds containing carboxylic acid functionalities(11, 12, and 34), (VI) CC bonds in furanic compoundscontaining carboxylic acid functionalities (1519), (VII) CCbonds in furanic compounds having dithioic acid functions (20and 21), (VIII) CS bonds in aromatic compounds containingdithioic acid functionalities (13 and 14), (IX) CS bonds infuranic compounds containing dithioic acid functionalities (20and 21), (X) CN bonds in halogen cyanides, acrylonitrile, andacetonitrile (2229), (XI) CC bonds in N-heterocyclic cycles,cyanogen, and acrylonitrile (28, 29, 3442), and (XII) CNbonds in N-heterocyclic cycles, cyanogen, and acrylonitrile

Figure 2. Molecular library including 42 molecules (part I) and the DielsAlder reactive system (part II) represented by the intermediates and TSsinvolved in the DAC reaction between DMF and C2H4 analyzed in this work. Black Arabic numbers between brackets are the molecular indices.Gray, blue, red, and pink Arabic numbers are the carbon, nitrogen, oxygen, and sulfur atom indices, respectively. For obvious cases, the atomindices are omitted. Red or Blue Roman numerals indicate the various groups as used in this work. Some groups are used twice to analyze carbonheteroelement/carboncarbon bonds, that is, IX/VII and XI/XII.



2846


(28, 29, 3442). The members of each group can be lookedup in Figure 2 and the Supporting Information, Tables S1S12.

The NN bond in the dinitrogen molecule placed at a largedistance from the investigated molecule in the same periodicbox served as a reference for the COHP-computed bondstrengths. We hypothesized that for an adiabatic system ofnoninteracting molecules, the strength of the NN bond in anoninteracting N2 molecule should always be the same,irrespective of the chemical composition of the system.

The second and third types of models were adopted fromprevious work.29,30 These were periodic rhombohedral low-silica alkali-exchanged faujasite30 and the high-silica third-rowd-block cation-exchanged faujasite29 models, respectively.Briefly, the low-silica alkali-exchanged zeolites (Si/Al = 2.4,Si34Al14O96M14, M = Li+, Na+, K+, Rb+, Cs+) are characterizedby a high accessible active site density in the faujasitesupercage and are referred to as MY. The high-silica third-row d-block cation-exchanged faujasites hold a single active siteand an appropriate amount of framework aluminumsubstitutions to compensate for the charge of the d-blockcation. These models are referred to as TMFAU (TM = Cu(I),Cu(II), Zn(II), Ni(II), Cr(III), Sc(III), and V(V)).

3.2. DielsAlder Cycloaddition. The DAC reactionbetween DMF and ethylene in both TMFAU and MY hasbeen studied in previous studies using periodic DFTcalculations.29,30,47,48 We directly used these models in ourcurrent work. Briefly, the initial state (IS) consists of DMF andethylene both coadsorbed in either TMFAU or MY. The IS isreferred to as 1DAC. The DAC transition state (TS) is referredto as TS and the adsorbed cycloadduct (FS) as 2DAC. Duringthe DAC reaction, three �-bonds are converted into two �-bonds and one �-bond. The two �-bonds are completely newbonds, which do not exist in 1DAC. As this reaction has beenanalyzed in different chemical environments and involvesseveral bonds undergoing significant changes, it provides ampleopportunity to investigate both the scaling and reproducibilityof the ICOHP and BO analyses. Examples of some of theevaluated structures are given in Figure 3. The IS (1DAC/Cu(I)FAU) and TS (TS/Cu(I)FAU) of the synchronousconcerted DAC reaction over Cu(I)FAU are shown in panels(a) and (b), respectively. Panel (c) displays the first TS of thetwo-step DAC reaction over Cu(II)FAU (TS1/Cu(II)FAU).1DAC/LiY and 1DAC/KY are shown in panels (d,e), respectivelyand the DAC TS in KY in panel (f).

3.3. Electronic Structure Calculations. Periodic DFTcalculations were performed with the Vienna Ab initioSimulation Package (VASP).4951 For all the systems, the k-point mesh was set to the Gamma point. The cut-off energywas 500 eV, employing a plane-wave basis set. To approximatethe exchange and correlation energy, the PBE-functional wasused.52 This was complemented by the projected augmentedwave scheme to describe the electronion interactions.53 TheDFT-D3 method with BeckeJohnson damping was used toaccount for long-range dispersive interactions.54,55 The gas-phase models were optimized from scratch. The root-mean-square force convergence criterion was set to 0.015 eV/Å. TheTMFAU and MY zeolite models were adopted from previouswork29,30 and subjected to a single-point calculation only toobtain the wavefunction and the electron density.

3.4. COHP-Analysis. The COHP analysis was performedwith the Lobster 2.2.1 code, upon a transformation of the(plane) wave functions from VASP into a localized basis set(STO).16,36,37,42,43 In addition, an automatic rotation of thebasis set was applied. The pair-wise interatomic interactionstrength was computed by integrating the COHP up to theFermi level (ICOHP). For a proper COHP analysis, thenumber of bands was set to the total number of orbitalspresent in the model in each calculation.

3.5. BO Analysis. BOs were analyzed using the Chargemolcode.56 To obtain accurate electron densities, the VASPcalculations were performed using a 2.5 times increased fastFourier transform (FFT) grid density. This grid is more thansufficient for accurate BO analysis. The effects of plane-waveenergy cutoff, k-point mesh, and FFT grid spacing oncomputed DDEC6 properties have been studied in detail byLimas and Manz.57

4. RESULTS

4.1. Bond Strength Quanti�cation in Gas-PhaseMolecules. The first part of the study focused solely on themolecular library including 42 gas-phase molecules. Here, wespecifically targeted the possible ICOHPBO correlation. Thedependency of the ICOHPBO correlation on the chemicalcomposition of the evaluated molecules was also investigated.The results are shown in Figure 4. The fitted parameters arereported in Table 1.

The residuals from Figure 4 imply that a linear fit isappropriate to describe the data. The standard errors of the fitsof groups I, II, V, VIII, IX, and XII are found to be smallestwith values of 0.13, 0.16, 0.12, 0.04, 0.13, and 0.12 eV/BO,

Figure 3. Example geometries for 1DAC/Cu(I)FAU and TS/Cu(I)FAU shown in (a,b), respectively. The first TS of the two-step DAC pathwayover Cu(II)FAU is shown in panel (c). Selected cuts from the periodic unit cell from 1DAC/LiY and 1DAC/KY in (d,e), respectively. The DAC TS inKY is shown in (f).



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respectively (Table 1). In contrast, groups III, IV, VI, VII, X,and XI exhibit lower R2-adjusted values accompanied by thelarger errors, being 0.40, 0.3, 0.91, 0.78, 0.53, and 0.39 eV/BO,respectively.

The good fit of group I is attributed to the fact that themolecules of this group only contain carbon and hydrogenwithout the presence of functional groups that couldpotentially affect the CC bond strength via electrondelocalization or ionic interactions. Interestingly, the largerange of the H/C ratio (3 in 1 and 1 in 8) has no significantinfluence on the ICOHPBO correlation. This is possiblybecause hydrogen atoms cannot induce too significant changesto the electronic structure of CC bonds. The poor fits forgroups VI and VII indicate that their ICOHPBO correlationsare sensitive to changes in the stoichiometry. For instance, ingroup VI, the O/C ratio in 15 is 1/4 and increases to 0.83 in19. Additionally, group VI contains molecules with andwithout functional side groups, that is, methyl and carboxylicacid site groups. The inductive effect of these functional groupsis different and will affect the electronic structure of the CCbonds significantly, thus reducing the quality of the ICOHPBO correlation. Another example is group VII. Similar S/Cratios are found for group VII as compared to those in groupVI, but a third-row element is also present within themolecules. The addition of a carbodithioic acid side group

(20 � 21) increases the sulfur content significantly. This addsextra orbitals with a principal quantum number of 3 (3s and3p), potentially shifting the reference energy and/or theunknown constant C. Because of this, the CC bond ICOHPBO correlation does not hold well anymore. Therefore,although the aforementioned O/C ratios in groups VI andVII are smaller than the H/C ratio in group I, it ishypothesized that the introduction of a third element andthe presence of functional side groups affect the electronicstructure of the molecules and thus reduces the quality of theICOHPBO correlation. The above observations mightexplain why group II exhibits such a surprisingly good fit. Allits members contain carboxylic acid groups and only theelements C and O.

Furthermore, fits of the ICOHPBO correlations for groupsIV, V, VIII, and IX are good. We note that these groups onlyconsist of a limited set of CS and CO bonds such that each ofthese fits essentially interpolates two points. However, the datain these groups illustrate the reproducibility of the BO andICOHP analyses and with all other groups indicating linearcorrelations; we are confident that a linear interpolation isacceptable.

The poor fit for group X, as illustrated by the large errorvalue, is caused by the presence of group 17 elements (denotedas Hal). Although the various CHal bonds in the cyanogenhalides exhibit a trend by themselves as a function of theirvalence shell principle quantum number (data not shown), thecyanogen halides cannot be used to fit CN bonds. Rather, agood correlation could have been obtained when usingacrylonitrile or cyanide derivatives as members of group X.This statement is supported by the good fit of group XII forwhich only small standard deviations are found for the slopeand intercept (0.12 and 0.25 eV/BO, respectively, with an R2-adjusted of 0.99). We note that the poor fit for group XI isexplained along the same lines as those for groups VI and VII.The nitrogen atoms are present at different positions withinthe cyclic molecules and are sometimes part of a functionalgroup. Therefore, although the ICOHPBO correlation forCN bonds in XII holds well, that for CC bonds in XI breaksbecause of inductive effects. From these data, we infer thatinductive effects of functional side groups reduce the ICOHPBO correlations for CC bonds involving � and � carbon atoms.The ICOHP values for CN, CO, and CS bonds canconsistently be correlated to BO values.

We also note that none of the ICOHPBO slopes (Figure4) intersect with the point (0, 0). This is an unexpectedobservation. We expected the BO and ICOHP values to reachzero when the interatomic distance is infinitely large. Moreresearch is necessary to elucidate the meaning of this nonzerointercept.

In an attempt to increase the quality of the fits, the N2reference molecule was used. We took one ICOHP value ofthe NN bond in N2 within each group against which wereferenced all other members of the respective group. Thereference compounds are marked with an asterisk in TablesS1S12 in the Supporting Information. The results are shownin Table S13. Scaling within each group was performed bycomputing the deviation (in percentage) of each NN bondwith respect to the NN reference bond. Subsequently, the CC/CN/CS/CO bonds were scaled with the same percentage.This procedure yielded hardly any changes to the fittingparameters.

Figure 4. ICOHPBO correlation for groups I to XII. The insetshows the residuals of each fit. The lines represent the linear fits.

Table 1. Linear Fits a × BO + b of Each Group

id. no. a (eV/BO) aerror (eV/BO) b (eV) berror (eV) R2-adj

I 5.04 0.13 1.12 0.21 0.98II 2.6 0.16 5.39 0.22 0.94III 2.81 0.40 5.08 0.57 0.75IV 5.89 0.3 2.95 0.43 0.95V 6.67 0.12 1.72 0.22 0.99VI 3.24 0.91 4.52 1.29 0.37VII 2.5 0.78 6.03 1.1 0.54VIII 5.01 0.04 1.87 0.05 0.99IX 4.93 0.13 1.81 0.19 0.99X 5.43 0.53 3.10 1.42 0.86XI 4.72 0.39 2.09 0.56 0.79XII 7.27 0.14 1.26 0.25 0.99



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The established correlations allow either the ICOHP or BOvalue to be estimated when the other quantity is known. Forinstance, ethane (1), ethylene (2), and acetylene (3) have BOs(ICOHP values) of 1.224 (6.64 eV), 1.706 (8.86 eV), and2.993 (15.45 eV) respectively. Propylene (4) has a BO of1.968 (10.6 eV) for the C1C2 bond. In benzene (8), eachCC bond has a BO of ca. 1.552 (9.1 eV). Other H,C-onlymolecules with conjugated bonds involve hexatriene (6) andhexa-1,5-dien-3-yne (7). The C1C2 and C3C4 bonds in 6are characterized by BO values of 2.594 and 2.364 and ICOHPvalues of 14.59 and 14.19 eV, respectively. The C1C2bond in 7 has a BO of 1.945 and an ICOHP of 10.54 eV. Onthe basis of these findings, we can define regimes within theICOHPBO correlation of H,C-only hydrocarbons. Namely, aBO of 11.5 is characterized by an ICOHP of ca. 6 to 9eV; CC bonds with a strength of 9 to 12 eV have BOs of ca.1.52; and the CC bonds with BOs of 2.5 and 3 arecharacterized by ICOHP values of 14 and 16 eV,respectively. Such regimes can also be defined for all of theother studied chemical bonds.

Minor changes to carboncarbon BOs via the addition ofsubstituents are more challenging to probe with the ICOHPmethod (or vice versa). Adding a methyl side group to benzene(8) changes it into toluene (9). The result is that the C1C2/C1C6 bonds in 9 have a BO 0.14 lower than those in 8 (BO8= 1.55). Addition of the second methyl group at the paraposition yields para-xylene (10) and results in the same effectfor the C3C4/C4C5 bonds. Lowering of the BO valuesresults in a consistent and concomitant bond weakening; theabsolute ICOHP bond strength becomes 0.20.3 eV smaller.Additionally, the BOs of the C2C3/C5C6 bonds increasemarginally but consistently with ca. 0.01 per added methylsubstituents. However, the changes to these BO values are toosmall to provide reliable changes in ICOHP values.

As the fits in Figure 4 illustrated, the ICOHPBOcorrelation changes upon varying the stoichiometry. Forinstance, replacing the methyl substituents by carboxylic acidfunctionalities shifts the ICOHPCC values to more negativevalues. The C2C3/C5C6 bonds have BO values ofapproximately 1.569/1.565 in benzoic acid (11) and 1.571each in terephthalic acid (12), ca. 0.01 higher than in benzene.However, ICOHP values shift to 9.38/9.36 and 9.55/9.54 eV. The respective ICOHP values change with ca. 0.34and 0.53 eV with respect to the ICOHP values found inbenzene. Replacement of the carboxylic acid groups by dithioicacid functionalities hardly shifts the bond energies for the sameBO. Replacement of oxygen by sulfur results in C2C3/C5C6 BOs of 1.578/1.577 with the corresponding ICOHP valuesof 9.42/9.42 eV in benzodithioic acid (13). These BOs are0.01 higher than in 11 and equal to those in 12. ICOHP valueshave changed with only 0.06 and +0.1 eV. Yet, inbenzene(bis)carbodithoic acid (14), the C2C3/C5C6BOs increase with only approximately 0.02 whilst theICOHP values increase with ca. 0.16/0.22 to 9.58/9.66eV. Furthermore, the CC bonds in ethanedithioic acid (35)and ethane(bis)dithioic acid (36) are 1.233 (7.78 eV) and1.169 (8.66 eV), respectively. These seem to be best relatedto the C1C7 and C4C8 bonds in 13 and 14 of which theBOs are 1.164 (8.19) and 1.167 (8.39 eV). However, 32and 33 differ clearly from the correlation found in 13 and 14.The relative amount of sulfur increased from C/S = 0.5 in 33to C/S = 3.5 and 2 in 13 and 14.

Summarizing, the change in the ICOHP value as a functionof increasing BO can be studied between different modelsdirectly, provided the stoichiometry remains relatively similar.CC and CO bonds can be compared when originating fromthe same compound as they come from the same model withthe same unknown total constant C. Inductive effects offunctional side groups reduce the ICOHPBO correlations forCC bonds involving � and � carbon atoms. The ICOHP valuesfor CN, CO, and CS bonds can consistently be correlated toBO values. Importantly, the trends displayed in Figure 4 allowone to distinguish between bonds with different BOs, once theICOHP value is known. In addition to these findings, wedefine four prerequisites:

1. An ICOHPBO correlation of good quality can only beestablished when the stoichiometry of the evaluatedmolecules does not vary significantly. For instance, CCbonds in H,C-only hydrocarbons and furanic com-pounds should not be compared directly. The presenceof the oxygen atom changes the ICOHPBOcorrelation.

2. ICOHPBO correlation of CC bonds involving � and �carbon atoms can only be constructed when the numberof functional groups or the stoichiometry within thefunctional group remains similar. The functional sidegroups cause inductive effects which negatively affect thequality of the ICOHPBO correlation for the CC bondsinvolving � and � carbon atoms.

3. ICOHPBO trends are approximately linear for aspecies containing CHet bonds with Het being aheteroelement whose principle quantum numberchanges (i.e., going down a group). However, there isnot necessarily a strong ICOHPBO correlation for theother bond types in these molecules. For instance, thereis an ICOHPBO correlation for carbonhalide bondsin cyanogen halides, but the CN bonds in thesecyanogen halides do not exhibit a strong ICOHPBOcorrelation.

4. The changes in ICOHP /BO values have to besufficiently large (�BO � 0.25). In the evaluated trendspresented here, CC bonds in H,C-only hydrocarbonscan be studied with greater accuracy and with smallerBO-margins (in the order of �BO � 0.2) than mostother evaluated trends.

4.2. Studying Bond Evolution in Chemical Reactions.The second part of the study was dedicated to the investigationof the reproducibility and BOICOHP correlation on a morepractical example of the DAC reaction between DMF andC2H4 in periodic models of cation-exchanged faujasite zeolites.

The mechanism of the DAC/D reaction between 2,5-DMFand ethylene in alkali (Li, Na, K, Rb, and Cs)-exchangedfaujasite catalysts was investigated in previous work.47 Twomodels were used, namely, the isolated-site high-silica and low-silica faujasite model containing a high density of accessibleactive sites representative of the as-synthesized catalyst. Theresults indicated that the DAC reactivity trend was inverted inthe second more realistic model as compared to the single-sitemodel.47 These reactivity differences were rationalized in afollow-up work based on an in-depth electronic structureanalysis.30 The results indicated that there are only ionicinteractions because of the absence of effective alkali cation···reactant orbital overlap. The effects associated with thesubstratecatalyst orbital interaction become important when



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the reaction is carried out using first-row d-block (Cu(I),Cu(II), Zn(II), Ni(II), Cr(III), Sc(III), and V(V)) cation-exchanged faujasites.29 The overlap between the d-orbitals ofthe active site and the MOs of the substrate strongly affect thereaction energetics and can even alter the mechanism of thechemical transformation.

In this work, we studied the variations in ICOHP and BO asa function of the CC bond lengths in 1DAC, TS, and 2DAC percatalyst. This results in ICOHPBO correlations for everyevaluated catalyst model. Selected results of the ICOHP andBO analyses focused on the CC bonds that are plotted versusthe interatomic distance in Figure 5a,b. Note that these plotsalso include the C1C6 and C4C5 interactions present in1DAC, TS, and 2DAC. Thus, the resulting ICOHP and BO valuesfor the C1C6 and C4C5 bonds are correlated to distanceslonger than the equilibrium CC bond length.

The results in Figure 5a,b show that we reproduced the sameasymptotic ICOHP and BO curves for the CC bonds in allevaluated models. The trends for the CC bond are thusindependent of the chemical composition of the periodicfaujasite model. On the one hand, the qualitatively similar CCbond length�ICOHP correlation seems logical as we onlymeasured the CC bonds originating from DMF and C2H4. Onthe other hand, the chemical surrounding is drastically

changed. TMFAU catalysts hold d-block cations with differentd-shell fillings and exhibit zeolite matrices with different Alcontents. Similarly, MY catalysts hold different alkali cationswith different principle quantum numbers for the valence shellsand exhibit different degrees of framework basicity.58 Theorigin of this behavior requires further investigation.

Additionally, the gas-phase models yield slightly higherICOHP values for the same bond length as compared to theTMFAU and MY models. Meanwhile, the BObond lengthcorrelation does not vary upon changing from the gas phase toperiodic faujasite models. This is a feature that has to bestudied in greater depth also. Nevertheless, we anticipate thatthe change in the ICOHP versus CC bond distance trendresults in a change in ICOHPBO correlation.

With the ICOHP versus CC bond length trend establishedto be similar for all evaluated zeolite models in this work, twoof the CC bonds in the DMF + C2H4 DAC reactions canreliably be compared. Inspection of Figure 5c shows that theICOHP values in 1DAC for the ethylene (C5C6) bond areordered as CsY < NaY � LiY < KY < RbY. This is well in linewith the ethylene adsorption geometries and the properties ofthe MY models, discussed elsewhere.30,47 Briefly, because ofthe large size of the Cs+ cations, ethylene establishes multiplenoncovalent interactions with the accessible sites in the

Figure 5. Plots of ICOHP (a) and BO values (b) for CC pair-wise interactions relevant to 1DAC, TS, and 2DAC in various cation-exchangedfaujasites and the molecular library. CC pair-wise interactions exceeding 1.6 Å relate to the C1···C6 and C4···C5 interactions in 1DAC and TS. Thechanges to the ICOHP values for the C2C3 and C5C6 bonds during the DAC reaction in MY models are shown in (c).

Figure 6. ICOHPBO correlation for CC bonds during the DAC reaction between DMF and C2H4 over cation-exchanged faujasite MY andTMFAU periodic models. In panels (a,b) the green and gray lines demarcate the 95% confidence interval and prediction limit, respectively. Panels(c,d) show all ICOHPBO correlations obtained for all evaluated cation-exchanged faujasites, without 95% confidence intervals and predictionlimits. Panel (e) shows the studentized residuals of the linear and polynomial fits using the data of all TMFAU models.



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faujasite supercage. This results in polarization of the C5C6bond and a reduction of electron density in between thecarbon atoms. In LiY and NaY, ethylene is adsorbed on oneactive site only. The Li and Na cations are both relativelystrong Lewis acids as compared to the other alkali cations. Incontrast, potassium and rubidium cations are relatively weakerLewis acids, which polarize the C5C6 bond less, whichresults in the highest C5C6 bond energies found for thesesystems. However, while 1DAC can be analyzed in a chemicalmeaningful way, investigations aimed at the other states inFigure 5c become uncertain because of the relatively smalldifferences between the ICOHP values and the inherentnumerical inaccuracies in the employed ab initio method.

The difficulty of discussing relatively small variations of theICOHP values per state in depth is illustrated by the weakICOHPBO correlation. For instance, the C5C6 bond in1DAC,RbY has a BO of 2.13 and an ICOHP of 12.87 eV,whereas 1DAC,CsY has a BO of 2.18 and an ICOHP of 12.22eV. Still, these BOs are significantly higher than those in theTS for which the computed BOs (ICOHP values) are ca. 1.8(about 10.7 to 11 eV). Continuing along the reactioncoordinate toward 2DAC, the C5C6 ICOHP and BO valuesdecrease to values between 8.12 to 8.38 and 1.081.09,respectively. For C2C3, BOs range from 1.414 to 1.432 in1DAC and from 1.79 to 1.81 in 2DAC. The respective ICOHPsrange from 9.55 to 9.78 eV in 1DAC and from 12.01 to12.22 in 2DAC. The C2C3 bond reaches approximatelysimilar values as C5C6 in state TS.

In summary, the zeolite-based ICOHP interatomic distancetrends show significant reproducibility. The formation andcleavage of the CC bonds during the DAC reaction betweenDMF and ethylene can be studied which involves differentmodels (e.g. 1DAC, TS, 2DAC). Additionally, a reactivity trendon the basis of the catalyst stoichiometry can be established.

4.3. Statistical Analysis. The third part of the study wasdevoted to the investigation of the ICOHPBO correlation forCC bonds in more chemically complex zeolite-based systems.This additional analysis was required as we observed a changein the gradient of the ICOHP bond length correlation. Plots ofthe ICOHPBO correlation in Cu(II)FAU and KY can befound in Figure 6a,b, respectively. These panels also show the95% confidence interval and the prediction limit (green andgray lines). The ICOHPBO correlations of all TMFAU areplotted together in Figure 6c. The correlations of all MYmodels can be found in Figure 6d. Plots showing the linearICOHPBO correlation and the associated 95% confidenceintervals and prediction limits for every cation individually canbe found in the Supporting Information, Figures S1 and S2,respectively. We have also attempted to fit the ICOHPBOcorrelations with a polynomial fit. These results can be foundin Figures S3 and S4. The resulting studentized residualsobtained by fitting the ICOHPBO correlation with linear andpolynomial plots, are shown in Figure 6e. The resulting linearfitted parameters are displayed in Table 2. Parameters for apolynomial fit can be found in Table S14.

Both the linear and polynomial fits exhibit R2-adjusted valuesof ca. 0.98. In Figure 6e, the large residuals (>3) for data pointsabove a BO of 2 indicate that such points are outliers withinthe framework of a linear fit. Although the polynomial fit seemsto be the best as indicated by a distribution of residuals arounda value of zero in panel (e) of Figure 6, we opted for the linearfit. Such a linear fit allows for a chemical intuitive andchemically relevant interpretation of the ICOHPBO

correlations. The data points related to BO > 2 were,therefore, removed from the datasets to obtain the linear fit.The linear fit was deemed reasonably because (1) the DACreaction (and many other reactions) does not exceed CCdouble bonds and (2) the standard errors of the linear fits aresmall. Furthermore, all parameters of the polynomial fits arecharacterized by large standard errors. Apart from suchcorrelation being difficult to interpret chemically, these largestandard errors make predictions dubious.

The obtained nonlinearity of the ICOHPBO correlationsin cation-exchanged faujasites when compared to thecorrelations obtained with the gas-phase library is rathersurprising. The exact reason for the change in ICOHPBOcorrelation is unknown and further research into this matter isrequired. Yet, we note that the COHP analysis treats chemicalbonds as pair-wise interactions with no consideration for theeffects of the chemical surrounding on the bond beingevaluated.16 Therefore, we hypothesize that the increasedchemical complexity of the cation-exchanged faujasites mightbe the cause of the nonlinear ICOHPBO correlation ascompared to the molecular gas-phase models involving isolatedentities. For instance, donoracceptor interactions of theexchangeable cations with the substrates will affect the bondsin the substrates and are thus suspected to be at the origin ofthe nonlinear ICOHPBO correlation. This hypothesis isfurther strengthened by the second prerequisite defined afterevaluating the ICOHPBO correlations using the molecularlibrary. This prerequisite involved the inductive effect offunctional groups on the CC bonds involving � and � carbonatoms.

Limiting our discussion to the linear fits, the obtained resultsindicate that the values for a2 are very similar for the differentmodels. The smallest slope is found for KY with a2 = 7.28 ±0.15 eV/BO. The largest slope is found for V(V)FAU with a2 =8.13 ± 0.15 eV/BO. In spirit of our hypothesis, the ICOHPvalues in V(V)FAU might be significantly affected by thepolarizing power of the pentavalent V(V) cation. If this systemis omitted from the series, one obtains a maximum slope forCu(II)FAU with an a2 of 7.79 ± 0.07 eV/BO. The ICOHPBO correlations in TMFAU models are characterized by astandard error of less than 0.1 eV/BO (V(V)FAU excluded).The trends in MY have standard errors below 0.15 eV/BO.The result is thus an error of 0.20.3 eV maximum uponchanging the CC BO from 1 to 2. The total ICOHP changesfrom 7.3 to 7.8 eV. Note that although we constraint the linearfit to intersect the y-axis at the point (0, 0), unconstraint fitting

Table 2. Fitted Parameters for the Linear Fits

ICOHP = a2 × x (BO < 2)

system a2 (eV/BO)

Cu(I)FAU 7.3 ± 0.10Cu(II)FAU 7.79 ± 0.07Zn(II)FAU 7.44 ± 0.08Ni(II)FAU 7.53 ± 0.09Cr(III)FAU 7.63 ± 0.09Sc(III)FAU 7.39 ± 0.09V(V)FAU 8.13 ± 0.15LiY 7.44 ± 0.16NaY 7.29 ± 0.14KY 7.28 ± 0.15RbY 7.34 ± 0.14CsY 7.35 ± 0.15



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yielded only minor values for the intercept (intercept < 0.5 eV,data not shown). This is markedly different from the gas phasecorrelations for which significant values for the intercepts werefound. The underlying reason for this difference is in need offurther research.

Summarizing, the changes to the ICOHP trends with respectto the interatomic distance in TMFAU and MY models ascompared to gas-phase systems resulted in a polynomialICOHPBO trend instead of a linear one. As a first-orderapproximation, the ICOHPBO correlation can be describedwith a linear fit up to a BO of 2. The resulting fits arepractically equivalent. For the models evaluated herein, the fitsallow for a description of CC and CO bond strength changesin the DAC reaction along the reaction coordinate both withinthe same system and across different systems. The practicalrelevance of this finding is in the fact that it provides us with anew descriptor that can be used directly to compare thereactivity of different catalysts for the same type of reaction as afunction of their chemical properties. Such propertyactivityrelationships are of great interest to the catalysis community.

5. CONCLUSIONSIn this work, we investigated the possibility and limitations ofcorrelating DDEC6-derived BOs and COHP-computed bondstrengths to quantify chemical bonding in gas-phase moleculesand periodic zeolite models. We show that the ICOHP analysisallows obtaining reproducible results when limiting the analysisto one reaction class, albeit in chemical systems withsubstantially different chemical compositions. Our studyimplies that the strengths of chemical bonds estimated usingthe COHP approach can be successfully employed toquantitatively analyze the changes in bonding patterns alongchemical conversion routes.

When applied to gas-phase molecules, the ICOHPBOcorrelations can be established for different types of chemicalbonds and these correlations exhibit a pronounced sensitivityto the stoichiometry of the chemical system and valence shellprinciple quantum number of the involved atoms. Further-more, the ICOHPBO correlations for the same class ofsubstances are affected by the presence of functional groups,reflecting the inductive effects and short-range electrostaticinteractions. We identify four key prerequisites for establishingthe ICOHPBO correlations, namely: (1) the individualcorrelations may be constructed for molecules with similarchemical composition; (2) ICOHPBO correlations of CCbonds involving � and � carbon atoms can only be constructedwhen the number of functional groups or the stoichiometrywithin the functional group remains similar; (3) for moleculescontaining CHet bonds with Het being an heteroelementdown a group (i.e., different valence principle quantumnumbers), an ICOHPBO correlation may only be establishedfor the CHet bonds, but not for the other bonds in themolecules; (4) only for substantially large variations in theBO/ICOHP values, their direct comparison among thedifferent molecules is possible. The exact threshold dependson the particular system investigated and the accuracy of thecorrelation (�BO � 0.20.25).

Despite these promising findings, our study reveals a numberof phenomena that require additional theoretical analysis. Inparticular, it is not clear why for the ICOHPBO correlationsof chemical bonds in gaseous molecules, the extrapolation ofBO to zero gives rise to finite values of ICOHP, whereas theICOHP value vanishes in periodic models. Furthermore, the

fundamental origin for the different ICOHP bond distancetrends obtained for the periodic and gaseous systems requiresfurther in-depth theoretical analysis beyond the scope of thisinitial work.

Significantly, the presented results on the ICOHPBOcorrelations demonstrate the applicability of the ICOHPanalysis method beyond a single structural model. Thetransferability of the ICOHP parameters is illustrated byconsidering the DAC of DMF and ethylene catalyzed byfaujasite-type zeolite catalysts as a model chemical process.When applied to intermediates belonging to the same reactionclass, the ICOHP analysis yields consistent results for differentperiodic zeolites with varied chemical compositions. Impor-tantly, our study demonstrates the possibility of the directbond strength quantification using the ICOHP analysis and itsapplicability to study the formation and cleavage of chemicalbonds during the catalytic reactions. These data together withthe computed BOs can provide detailed quantifiable bondinginformation on the reacting chemical systems necessary forconstructing quantitative structureactivity relations in com-plex chemical systems.

� ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.jpcc.8b08934.

Tables S1S12 listing the members of group one totwelve; Table S12 summarizing the linear fits afterscaling of the COHP values; Table S14 summarizingpolynomial fits; Figures S1 and S2 displaying linear fitsof the ICOHPBO correlations in alkali- and first-rowd-block cation-exchanged faujasites, respectively; FiguresS3 and S4 displaying polynomial fits of the ICOHPBOcorrelations in alkali- and first row d-block cation-exchanged faujasites, respectively (PDF)

� AUTHOR INFORMATIONCorresponding Authors*E-mail: [email protected] (E.J.M.H.).*E-mail: [email protected] (E.A.P.).ORCIDEmiel J. M. Hensen: 0000-0002-9754-2417Evgeny A. Pidko: 0000-0001-9242-9901Present Address�Inorganic Systems Engineering group, Department ofChemical Engineering, Faculty of Applied Sciences, DelftUniversity of Technology, Van der Maasweg 9, 2629 HZ Delft,The Netherlands.Author Contributions§R.Y.R. and I.C.T. contributed equally to the manuscript.NotesThe authors declare no competing financial interest.

� ACKNOWLEDGMENTSThis work was supported by the Netherlands Center forMultiscale Catalytic Energy Conversion (MCEC), an NWOGravitation programme funded by the Ministry of Education,Culture and Science of the government of the Netherlands.The authors also thank The Netherlands Organization forScientific Research (NWO) for access to the national high-performance computing facilities.



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� REFERENCES(1) Van Speybroeck, V.; Hemelsoet, K.; Joos, L.; Waroquier, M.;

Bell, R. G.; Catlow, C. R. A. Advances in Theory and TheirApplication within the Field of Zeolite Chemistry. Chem. Soc. Rev.2015, 44, 70447111.(2) Sperger, T.; Sanhueza, I. A.; Kalvet, I.; Schoenebeck, F.

Computational Studies of Synthetically Relevant HomogeneousOrganometallic Catalysis Involving Ni, Pd, Ir, and Rh: An Overviewof Commonly Employed DFT Methods and Mechanistic Insights.Chem. Rev. 2015, 115, 95329586.(3) Cheng, G.-J.; Zhang, X.; Chung, L. W.; Xu, L.; Wu, Y.-D.

Computational Organic Chemistry: Bridging Theory and Experimentin Establishing the Mechanisms of Chemical Reactions. J. Am. Chem.Soc. 2015, 137, 17061725.(4) Klippenstein, S. J.; Pande, V. S.; Truhlar, D. G. Chemical

Kinetics and Mechanisms of Complex Systems: A Perspective onRecent Theoretical Advances. J. Am. Chem. Soc. 2014, 136, 528546.(5) Bader, R. F. W. Atoms in Molecules: A Quantum Theory. Atoms

in Molecules: A Quantum Theory; Clarendon Press, 1994.(6) The Quantum Theory of Atoms in Molecules; Matta, C. F., Boyd,

R. J., Eds.; Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim,Germany, 2007.(7) The Chemical Bond; Frenking, G., Shaik, S., Eds.; Wiley-VCH

Verlag GmbH & Co. KGaA: Weinheim, Germany, 2014.(8) Ananyev, I. V.; Karnoukhova, V. A.; Dmitrienko, A. O.;

Lyssenko, K. A. Toward a Rigorous Definition of a Strength of AnyInteraction Between Bader’s Atomic Basins. J. Phys. Chem. A 2017,121, 45174522.(9) Romanova, A.; Lyssenko, K.; Ananyev, I. Estimations of Energy

of Noncovalent Bonding from Integrals over Interatomic Zero-FluxSurfaces: Correlation Trends and beyond. J. Comput. Chem. 2018, 39,16071616.(10) Manz, T. A.; Limas, N. G. Introducing DDEC6 Atomic

Population Analysis: Part 1. Charge Partitioning Theory andMethodology. RSC Adv. 2016, 6, 4777147801.(11) Limas, N. G.; Manz, T. A. Introducing DDEC6 Atomic

Population Analysis: Part 2. Computed Results for a Wide Range ofPeriodic and Nonperiodic Materials. RSC Adv. 2016, 6, 4572745747.(12) Manz, T. A. Introducing DDEC6 Atomic Population Analysis:

Part 3. Comprehensive Method to Compute Bond Orders. RSC Adv.2017, 7, 4555245581.(13) Morokuma, K. Molecular Orbital Studies of Hydrogen Bonds.

III. C=O···HO Hydrogen Bond in H2CO···H2O and H2CO···2H2O.J. Chem. Phys. 1971, 55, 12361244.(14) Zhao, L.; von Hopffgarten, M.; Andrada, D. M.; Frenking, G.

Energy Decomposition Analysis. Wiley Interdiscip. Rev.: Comput. Mol.Sci. 2018, 8, e1345.(15) Hoffmann, R. Interaction of Orbitals through Space and

through Bonds. Acc. Chem. Res. 1971, 4, 19.(16) Dronskowski, R.; Bloechl, P. E. Crystal Orbital Hamilton

Populations (COHP): Energy-Resolved Visualization of ChemicalBonding in Solids Based on Density-Functional Calculations. J. Phys.Chem. 1993, 97, 86178624.(17) van Santen, R. A.; Tranca, I. How Molecular Is the

Chemisorptive Bond? Phys. Chem. Chem. Phys. 2016, 18, 2086820894.(18) Van Santen, R. A. Modern Heterogeneous Catalysis: An

Introduction; Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim,Germany, 2017.(19) van Santen, R. A.; Tranca, I.; Hensen, E. J. M. Theory of

Surface Chemistry and Reactivity of Reducible Oxides. Catal. Today2015, 244, 6384.(20) Liu, C.; Tranca, I.; van Santen, R. A.; Hensen, E. J. M.; Pidko,

E. A. Scaling Relations for Acidity and Reactivity of Zeolites. J. Phys.Chem. C 2017, 121, 2352023530.(21) Lu, T.; Chen, F. Bond Order Analysis Based on the Laplacian

of Electron Density in Fuzzy Overlap Space. J. Phys. Chem. A 2013,117, 31003108.

(22) Wheatley, R. J.; Gopal, A. A. Covalent Bond Orders andAtomic Anisotropies from Iterated Stockholder Atoms. Phys. Chem.Chem. Phys. 2012, 14, 20872091.(23) Mayer, I.; Salvador, P. Overlap populations, bond orders and

valences for “fuzzy” atoms. Chem. Phys. Lett. 2004, 383, 368375.(24) Fulton, R. L. Sharing of Electrons in Molecules. J. Phys. Chem.

1993, 97, 75167529.(25) Mayer, I. On Bond Orders and Valences in the Ab Initio

Quantum Chemical Theory. Int. J. Quantum Chem. 1986, 29, 7384.(26) Matito, E.; Sola�, M.; Salvador, P.; Duran, M. Electron Sharing

Indexes at the Correlated Level. Application to AromaticityCalculations. Faraday Discuss. 2007, 135, 325345.(27) Cioslowski, J.; Mixon, S. T. Covalent Bond Orders in the

Topological Theory of Atoms in Molecules. J. Am. Chem. Soc. 1991,113, 41424145.(28) Francisco, E.; Penda�s, A. M.; García-Revilla, M.; A�lvarez Boto,

R. A Hierarchy of Chemical Bonding Indices in Real Space fromReduced Density Matrices and Cumulants. Comput. Theor. Chem.2013, 1003, 7178.(29) Rohling, R. Y.; Tranca, I. C.; Hensen, E. J. M.; Pidko, E. A.

Mechanistic Insight into the [4 + 2] Diels-Alder Cycloaddition overFirst Row d-Block Cation-Exchanged Faujasites. ACS Catal. 2019, 9,376391.(30) Rohling, R. Y.; Tranca, I. C.; Hensen, E. J. M.; Pidko, E. A.

Electronic Structure Analysis of the Diels-Alder CycloadditionCatalyzed by Alkali-Exchanged Faujasites. J. Phys. Chem. C 2018,122, 1473314743.(31) Deringer, V. L.; Stoffel, R. P.; Wuttig, M.; Dronskowski, R.

Vibrational properties and bonding nature of Sb2Se3 and theirimplications for chalcogenide materials. Chem. Sci. 2015, 6, 52555262.(32) Pauling, L. Atomic Radii and Interatomic Distances in Metals. J.

Am. Chem. Soc. 1947, 69, 542553.(33) Bo�rnsen, N.; Meyer, B.; Grotheer, O.; Fa �hnle, M. Ecov- a new

tool for the analysis of electronic structure data in a chemicallanguage. J. Phys. Condens. Matter 1999, 11, L287L293.(34) Grechnev, A.; Ahuja, R.; Eriksson, O. Balanced crystal orbital

overlap population-a tool for analysing chemical bonds in solids. J.Phys. Condens. Matter 2003, 15, 77517761.(35) Segall, M. D.; Pickard, C. J.; Shah, R.; Payne, M. C. Population

Analysis in Plane Wave Electronic Structure Calculations. Mol. Phys.1996, 89, 571577.(36) Deringer, V. L.; Tchougre�eff, A. L.; Dronskowski, R. Crystal

Orbital Hamilton Population (COHP) Analysis as Projected fromPlane-Wave Basis Sets. J. Phys. Chem. A 2011, 115, 54615466.(37) Maintz, S.; Deringer, V. L.; Tchougre�eff, A. L.; Dronskowski, R.

Analytic Projection from Plane-Wave and PAW Wavefunctions andApplication to Chemical-Bonding Analysis in Solids. J. Comput. Chem.2013, 34, 25572567.(38) Dunnington, B. D.; Schmidt, J. R. Generalization of Natural

Bond Orbital Analysis to Periodic Systems: Applications to Solids andSurfaces via Plane-Wave Density Functional Theory. J. Chem. TheoryComput. 2012, 8, 19021911.(39) Galeev, T. R.; Dunnington, B. D.; Schmidt, J. R.; Boldyrev, A. I.

Solid State Adaptive Natural Density Partitioning: A Tool forDeciphering Multi-Center Bonding in Periodic Systems. Phys. Chem.Chem. Phys. 2013, 15, 50225029.(40) Sanchez-Portal, D.; Artacho, E.; Soler, J. M. Projection of

Plane-Wave Calculations into Atomic Orbitals. Solid State Commun.1995, 95, 685690.(41) Sa�nchez-Portal, D.; Artacho, E.; Soler, J. M. Analysis of Atomic

Orbital Basis Sets from the Projection of Plane-Wave Results. J. Phys.Condens. Matter 1996, 8, 38593880.(42) Maintz, S.; Deringer, V. L.; Tchougre�eff, A. L.; Dronskowski, R.

LOBSTER: A Tool to Extract Chemical Bonding from Plane-WaveBased DFT. J. Comput. Chem. 2016, 37, 10301035.(43) Maintz, S.; Esser, M.; Dronskowski, R. Efficient Rotation of

Local Basis Functions Using Real Spherical Harmonics. Acta Phys. Pol.B Proc. Suppl. 2016, 47, 1165.



2853


(44) Landrum, G. A.; Dronskowski, R. The Orbital Origins ofMagnetism: From Atoms to Molecules to Ferromagnetic Alloys.Angew. Chem., Int. Ed. 2000, 39, 15601585.(45) Manz, T. A.; Sholl, D. S. Improved Atoms-in-Molecule Charge

Partitioning Functional for Simultaneously Reproducing the Electro-static Potential and Chemical States in Periodic and NonperiodicMaterials. J. Chem. Theory Comput. 2012, 8, 28442867.(46) Manz, T. A.; Sholl, D. S. Chemically Meaningful Atomic

Charges That Reproduce the Electrostatic Potential in Periodic andNonperiodic Materials. J. Chem. Theory Comput. 2010, 6, 24552468.(47) Rohling, R. Y.; Uslamin, E.; Zijlstra, B.; Tranca, I. C.; Filot, I. A.

W.; Hensen, E. J. M.; Pidko, E. A. An Active Alkali-ExchangedFaujasite Catalyst for p-Xylene Production via the One-Pot Diels-Alder Cycloaddition/Dehydration Reaction of 2,5-Dimethylfuranwith Ethylene. ACS Catal. 2018, 8, 760769.(48) Rohling, R. Y.; Hensen, E. J. M.; Pidko, E. A. Multi-Site

Cooperativity in Alkali-Metal-Exchanged Faujasites for the Produc-tion of Biomass-Derived Aromatics. ChemPhysChem 2018, 19, 446458.(49) Kresse, G.; Hafner, J. Ab initiomolecular dynamics for liquid

metals. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 47, 558561.(50) Kresse, G.; Furthmu�ller, J. Efficiency of Ab-Initio Total Energy

Calculations for Metals and Semiconductors Using a Plane-WaveBasis Set. Comput. Mater. Sci. 1996, 6, 1550.(51) Kresse, G.; Furthmu�ller, J. Efficient Iterative Schemes for Ab

Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys.Rev. B: Condens. Matter Mater. Phys. 1996, 54, 1116911186.(52) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient

Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 38653868.(53) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the

Projector Augmented-Wave Method. Phys. Rev. B: Condens. MatterMater. Phys. 1999, 59, 17581775.(54) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and

Accurate Ab Initio Parametrization of Density Functional DispersionCorrection (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010,132, 154104.(55) Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the Damping

Function in Dispersion Corrected Density Functional Theory. J.Comput. Chem. 2011, 32, 14561465.(56) Manz, T. A.; Limas, N. G. Chargemol program for performing

DDEC analysis. http://ddec.sourceforge.net/ (obtained Oct 27,2016).(57) Limas, N. G.; Manz, T. A. Introducing DDEC6 Atomic

Population Analysis: Part 4. Efficient Parallel Computation of NetAtomic Charges, Atomic Spin Moments, Bond Orders, and More.RSC Adv. 2018, 8, 26782707.(58) Schoonheydt, R. A.; Geerlings, P.; Pidko, E. A.; van Santen, R.

A. The Framework Basicity of Zeolites. J. Mater. Chem. 2012, 22,18705.



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