theoretical chemistry molecular orbital (mo) calculations

"Everything You Always Wanted to Know about Computational Chemistry, But Were Afraid Would Be Answered by 27 Pages of Integrals in a Nomenclature That You've Never Seen Before." or “How to Understand MO Calculations, for the Theoretically-Challenged." web.utk.edu/~bartmess/comptalk.html John Bartmess Dept. of Chemistry University of Tennessee

Theoretical Chemistry Molecular Orbital (MO) Calculations Quantum Mechanics Calculations Computational Chemistry

"In theory, there is no difference between theory and practice. In practice, there is."

"Man's gotta know his limitations" - Dirty Harry Callahan (John Milius)

- Jan L. A. van de Snepscheut (computer scientist)

But often attributed to Yogi Berra

Goal of this Talk:

-To give you an understanding of the basics of computational work in the literature

-Information on which methods are really good, and which are either inappropriate or flat-out garbage for a given problem

- The Alphabet Soup of Computation

Goals of Computational Chemistry:

Gas-phase molecules (molecules in solution take extra work, and involve major approximations)

Geometries: Closed shell (= octets around all heavy (non-H) atoms):

well-met even at low level calculations Open shell (= radicals, sextet cations):

problematic, but solvable with knowledge

Energies: relative versus absolute accuracy and precision 

Other Quantities: Dipole Moments Orbital energies and occupations (eigenvalues and eigenvectors) Charge distributions (atomic and orbital) Mulliken populations (atomic charges) Spin matrices, total spin states Bond orders Ionization energy & electron affinity (vertical and adiabatic): Koopmans Physica 1934 1, 104) Polarizabilities, hyperpolarizability Vibrational frequencies/force constants (intensities) Rotational constants/moments of inertia Entropy, Heat capacity, Partition functions Zero point energies

UnitsBohr - One atomic unit of distance = 0.5292 Angstrom (archaic now)Hartree - One atomic unit of energy = 2 x IE(H.) 2625.500 kJ/mol 627.5095 kcal/mol 27.2114 eV 219474.6 cm-1

 Energetic Data (ab initio) - absolute energy, as negative value: cleavage of all bonds to form free atoms, then ionization of atoms to bare ionic nuclei plus free electrons at infinite distance (E = 0) benzene: -231.820 hartrees = -145,469 kcal/mol  - atomization energy to atoms: benzene -2.1099 hartrees (-1324 kcal/mol); expt: -1323 kcal/mol  - heat of formation semi-empirical: close (± 2 kcal/mol, average organics) ab initio: usually too unstable, unless very high level calculation (variational principle)

Practicalities  speed ("cost" to computationalists): scales as as a high power of the number of electrons (typically n4 to n8) known failure modes of method (certain structures known to be wrong energy or geometry)  cost of hardware 3.3GHz duo hex-core processor PC, 12 GB RAM, 1 TB hard drive : $3000 (Feb 2012) : 100x speed of a 1969 Cray I ($30M in current $) : 330,000x speed of Osborne (1979; $6K current) 10,000,000x media storage 200,000,000x RAM  = 3 x1020 better, at ½ cost cost of software Gaussian 03 $1500 (site license) MOPAC (QCPE $400?) MNDO: free  Linux (Red Hat or Fedora) for ab initio

Hierarchy of 4 Methods  - Molecular Mechanics: Not a quantum mechanical method.  - Empirical: Hückel, Extended Hückel  - Semi-empirical archaic: INDO, PPP, CNDO/n, MINDO/n current: MNDO, AM1, PM3

- ab initio e.g. Gaussian, GAMES, MOLPRO (programs) Hartree/Fock Electron Correlation Configuration Interaction Extrapolation  Density Functional Theory

Input name, method, time limits charge, multiplicity geometry: - Cartesian coordinates - Z matrix, or internal coordinates:

bond lengths planar angles dihedral (torsional) angles connectivity

sometimes called “Natural Coordinates”

AM1 precise acetone OC 1.22 1 1 C 1.54 1 120. 1 2 1 C 1.53 1 120. 1 180. 1 2 1 3H 1.11 1 110. 1 180. 1 4 2 1H 1.11 1 110. 1 60. 1 4 2 1H 1.11 1 110. 1 -60. 1 4 2 1H 1.11 1 110. 1 180. 1 3 2 1H 1.11 1 110. 1 60. 1 3 2 1H 1.11 1 110. 1 -60. 1 3 2 10 0 0 0 0 0 0 0 0 0 0

Semi-empirical input

%mem=256MB%nosave # g3mp2b3 Opt=Maxcyc=100 Me2C(.)CH2NH3+ +1 2N C 1 1.5283C 2 1.5050 1 115.9692C 3 1.5022 2 115.2106 1 182.2808C 3 1.4956 2 124.5590 1 2.8544H 4 1.1100 3 110.6428 2 60.1046H 4 1.1100 3 110.6213 2 -239.9345H 4 1.1077 3 112.2541 2 180.0153H 5 1.1104 3 111.0735 2 61.1423H 5 1.1108 3 111.3159 2 -239.8219H 5 1.1085 3 111.9526 2 180.4718H 2 1.1190 1 105.8385 3 122.4183H 2 1.1192 1 105.6916 3 -122.5352H 1 1.0250 2 110.0652 3 179.7632H 1 1.0245 2 112.2413 14 119.2315H 1 1.0246 2 112.1792 14 -119.2190

Common to all: - Input of starting geometry - Trial orbital set (Extended Hückel) - Self Consistent Field (modify orbitals to reflect  reality) - Geometry Optimization (modify nuclear geometry to find minimum energy) Method of Steepest Descent – derivatives of E vs. geom.  Problems Local minima: benzene with 1 H inside = +156 kcal/mol above reality Oscillation - Final output: Total energy, other properties Vibrational Frequencies, other Statistical Mechanics properties 

Global vs. local minima: anti vs gauche butane

Benzene, with H in center: ΔfH = 131 vs. 19.4 kcal/mol normal

←1/2hυ

Negative freq↓

Thermochemistry (non-0K)

From statistical mechanics: Etot = E0 + Etrans + Erot + Evib + Eelec

mass geometry (moments of inertia) vibrational frequencies orbital energiesallow calculation of: zero point energy = h/2· E0 = E0 + ZPE heat capacity: E298 H298 (=E298 + RT) entropies: S298 G298

Frequencies

-Lowest ones (<300 cm-1) most important to stat. mech. entropy, yet worst known Internal rotors, free vs. hindered Ring breathing modes

- Harmonic approximation (parabola), yet real ones anharmonic

- Scaling: 0.896 HF/6-31G* 0.96 B3LYP

Heats of Formation

Absolute:ΔfHo(molecule) = E0 (molecule) - E0(atoms) + ΔfHo

exptl(atoms)

Relative:A + B = C + DEA EB EC ED

ΔfH(A) = EA+ EB - EC – ED

+ ΔfH(C) + ΔfH(D) - ΔfH(B)

EXACT THEORY: the Schrödinger Equation H(Ψ) = E·Ψwhere Ψ is a "full molecule" wave function.H = Hamiltonian function (general case: Hermetian operator)E = eigenvalue

H = T (kinetic part) + V (potential part)

M M M

H = - h2/82 MA-12

A + e2ZAZBrAB-1

A=1 A=1 B>A

N

N M N N

- h2/(8m) i2 - 2ZArAi

-1 + e2rij-1

i=1 i=1 A=1 i=1 j>i

Hamiltonian divides up into:

1. Kinetic energy of nuclei2. Nuclear-nuclear repulsion3. Kinetic energy of electrons4. Nuclear-electron attraction5. Electron-electron repulsion

Born-Oppenheimer approximation:Nuclei don’t move, on electron motion timeframe1. = 02. Static calculation: Coulomb’s Law

MORE APPROXIMATIONS: 1. Ψ = ψ1 . ψ2 . ψ3 ...., where ψi are one electron molecular orbitals. Separate the Schrödinger equation: H(ψi) = Ei· ψi

2 = probability of electron position All physical observables relate to 2, because has imaginary parts.

Normalized:aa* = 1 <a|a*> = 1

Orthogonal:ab = 0 <a|b> = 0 no overlap

1 electron orbitals so far

Spin: and

= spatial·

Pauli Principle: is antisymmetric wrt exchange of 2 electrons(1,2) = -(2,1)

If every electron has its own , “unrestricted”If paired s, “restricted” (faster calculation)

2. Represent each ψi as a Linear Combination of Atomic Orbitals (LCAO):

ψi = ci,1· φ1 + ci,2· φ2 + ..... where φj are basis orbitals (usually atomic)

3. Variational Principle: For any approximate (one e-) ψi, Ei from the Schrödinger Equation is greater than the true Ei for the exact ψi. Thus ψi and cij are varied so as to minimize Ei, or δEi/δci,j = 0. The true value of the variational principle is that one knows when the calculation is getting closer to reality, because the energy is going down. There are other methods, such as Density Functional Theory, or certain types of electron Correlation, that are not variational.

4. Self Consistent Field (SCF) approximation. “Three Body Problem” ψi is calculated for one given electron interacting with the field of the nuclei plus an average smeared-out charge distribution of all other electrons. This ψi is then used as part of the average distribution as the next electron's ψi is found, and so on. After successive iterations result in an energy change of less than a given amount (ca. 1 cal), the Self Consistent Field is said to have converged, and that set of ψis is used as a valid wave function.

5. Hartree-Fock Limit. - Approximations 2 and 4 (LCAO and SCF) lead to Eo always too high. - If a small number of terms [limited number of basis orbitals] is used in (2), then the ψi will not be as good as with a larger number of terms. - As a sufficiently large number of terms (j>20, typically) is used, E approaches the "Hartree-Fock limit".

This Hartree-Fock limit still is only 90-95% of the way to the true energy, since the SCF approximation ignores :

(1) "electron correlation", or the fact that the other electrons are not a statistical average, but moving, when calculating the SCF.

(2) "configuration interaction" or "CI", because empty orbitals mix into filled MOs.

(3) relativistic speed of the core electrons, which can still contribute a 0.1% error in total energy (especially important for atoms low in the Periodic Table)

RHF (Restricted Hartree-Fock) Every spatial orbital has an exactly equal orbital, i.e. every spin up electron has a spatially equivalent spin down electron. This generally implies a closed-shell wavefunction, though restricted open-shell SCF can be done. UHF (Unrestricted Hartree-Fock) Every spin-orbital has different spatial forms. Drawback: time, spin contamination. spin-contamination: calculations with UHF wavefunctions that are not eigenfunctions of spin, and are contaminated by states of higher spin multiplicity (which usually raises the energy).

ECP = Effective Core Potential. The core electrons have been replaced by an effective potential. Saves computational expense. May sacrifice some accuracy, but can include some relativistic effects for heavy elements. isodesmic: a chemical reaction that conserves types of chemical bond. MeO- + EtOH → MeOH + EtO-

isogyric: a chemical reaction that conserves net spin. Lower-level calculations of such relative energetics can be asaccurate as much higher(slower) ones of absolute energetics

____________________________

------------------------ 0 E______________ LUMO

_____↑↓______ HOMO

_____↑↓ _____

Koopman's Theorem:

IE = energy of the HOMO (Highest Occupied Molecular Orbital). This is a vertical IE, not adiabatic. Errors from no e- correlation plus geometry relaxation tend to cancel for IEs.EA = energy of the LUMO (Lowest Unoccupied Molecular Orbital). These errors compound for trying to approximate EA

MERP (Minimum Energy Reaction Path) or IRC (Intrinsic Reaction Coordinate): An optimized reaction path that is followed downhill, starting from a transition state, to approximate the course (mechanism) of an elementary reaction step. (Ignores tunneling, contribution of vibrationally excited modes/partition function, etc.) Transition States: saddle points (one negative frequency), sometimes found as minima. Search routines exist. scaling: Multiplying calculated results by an empirical fudge factor in the hope of getting a more accurate prediction. Very often done for vibrational frequencies computed at the HF/6-31G* level, for which the accepted scaling factor is 0.893.

Molecular Mechanics Methods "Balls and Springs"  MM2 - Allinger Force Field version 2 MM3 - MMX - PCModel Sybyl - Amber - CHARMn -  All ΔfH ca.±1 kcal/mol 

μD ±0.1  Limit: only parameterized functional groups  Advantage: fast, up to proteins

Empirical Methods 

Hückel Calculation Many integrals pre-calculated or equated to measured data Pros: orbital symmetry resonance energy back of envelope Cons: flat geometry, π orbitals only polar bonds poor 

EHT - Extended Hückel Theory (Roald Hoffman)Hückel with sigma bonds as wellIgnores e- e- repulsionUses expt’l IEs for certain integrals Pros: Ethane rotational barrier Woodward-Hoffman rules includes AO overlap terms Frontier orbitals All elements Cons: valence only (not hypervalents) geometry poor (Me-Me = 1.92Å) partial charges high singlet & triplet same (no e- spin) Used as first guess for higher level methods

Semi-Empirical Methods Approximation: many computationally expensive (= slow)integrals replaced by adjustable parameters, determined by fitting experimental atomic and molecular data. Non-nearest-neighbor interactions neglected

Different choices of parameterization lead to different specific theories (e.g., MNDO, AM1, PM3). Archaic: CNDO - Complete Neglect of Differential Overlap PPP - Pariser-Parr-Pople INDO/1 - Intermediate NDO MINDO/3 – Modified Intermediate Neglect..

MNDO: Minimal Neglect of Differential Overlap

Atoms: H, Li-F, Al-Cl, Cr, Zn, Ge, Br, Sn, I, Hg, Pb  Basis: 32 molecule parameterization  Developed by M.J.S. Dewar Problems (geometries): -O-O- bond ~0.17Å short C-O-C angle 9o large amides pyramidal Aniline, nitrobenzene: NH2, NO2 group perpendicular

to ring, due to nuclear repulsion

MNDO Problems (energies): no H-bonds, no H2O dimer S, Cl, & Br Ionization Energies high activation barriers high bond dissociation enthalpies too weak conjugation too stable 3-center B bonds too stable no Van der Waals attraction: Sterically crowded hydrocarbons too unstable (Me4C: -24. kcal/mol, exp -40.3 kcal/mol) N-O bonds poorly parameterized - heats way off (MeNO2: calc ΔfH = +5.1, exp -17.9 kcal/mol) 4 membered rings too stable (cyclobutane: -11.9, exp +6.8 kcal/mol) (cubane: + 108 , exp 148.7 kcal/mol) Underestimates polarizability interactions (aliphatic alcohol acidities all the same) hypervalent unstable 3rd,4th row elements: only low valent cases have good absolute heats though relative heats of same oxidation state okay

AM1 - Austin Model 1 (Dewar) Atoms: H, Li, B - F, Al - Cl, Zn, Ge, Br, I, Hg Basis: 100 molecule parameterization Pros: H-bond energies, lengths better proton affinities good better activation barriers Heat of Formation 40% better 2-Cl-THP axial (anomeric effect) Aniline, nitrobenzene now planar

AM1: Problems: poor on hypervalent compounds (none in parameterization set) conjugate interactions low -CH2- ΔfH ~ 0.2 kcal/mole low each Heat of Hydrogenation low bond dissociation enthalpies too weak activation enthalpies high -NO2 energies high -O-O- bond ~ 0.17Å short H-bond angles, H2O H-bond geometry wrong C-C-O-H gauche in ethanol proton transfer barrier high 

PM3 – Parameterized Model 3 (Stewart: student of Dewar’s) Program: MOPAC Atoms: H, Li, Be, C-F, Mg-Cl, Zn-Br, Cd-I, Hg-Bi Basis: 657 molecule parameterization   Pros: hypervalent included in parameterization set ΔfH 40% better -NO2 better ground state geometries better H2O H-bonds: lengths & angles   

PM3: Cons: partial charges on N unreliable bond dissociation enthalpies low amides pyramidal, barrier low no barrier to formamide rotation spurious minima D2d symmetry for CBr4

IEs poor proton transfer barrier high wrong glucose geometry: H-bonds 0.1A short C-C-O-H gauche in ethanol Van der Waals attraction high/H-H core repulsion low (MeNO2: calc -15.9, exp -17.9 kcal/mol) (cyclobutane: -3.8, exp +6.8 kcal/mol) (cubane: 114, exp 148.7 kcal/mol) (Me4C: -35.8, exp -40.3 kcal/mol) (MeOH..-OMe: bond strength 19, exp 28.8 kcal/mol Hypervalents good energy

Ab initio Methods

Hartree-Fock methods Basis Set: math functions that describle orbitals STO (Slater-Type Orbital) Minimal Basis Set

Basis function with an exponential radial function, i.e., e –αr or

a fit to such a function using other functions, such as Gaussians: e-ar2 (Gaussians are computationally faster)

STO-3G “stodgy” (1969, Pople) is a MBS that uses 3 Gaussians to fit an exponential. Exponentials are better basis functions than Gaussians, but are expensive computationally.

Split Valence: a basis set that is more than minimal for the valence orbitals. Much better for polar bonds than MBS.

DZ (Double-Zeta): A basis set for which there are twice as many basis functions as are minimally necessary. "Zeta" (Greek letter ζ) is the usual name for the exponent that characterizes a Gaussian function. (Dunning, 1970)TZ: (triple zeta)

3-21G Basis set: 3 Gaussian function primitives for core electrons Split Valence: 2 Gaussians with linked coefficients for inner valence electrons 1 Gaussian for each outer valence electron- Polar bonds better described than minimal basis set- Atoms: H – Xe

6-31G Basis set: 6 Gaussian functions for core 3 Gaussian (linked coefficients) for inner valence electrons 1 Gaussian for each outer- Atoms: H - Ar

6-31G* = 6-31G(d)

6-31G plus a set of polarizing d-functions (6D) added to heavy atoms- most popular, widely used/validated- Atoms: H - Ar- Polarization functions help to account for the fact that atoms within molecules are not spherical. Even better for polar bonds. 6-31+G diffuse (large) s orbitals added (in essence opposite of *)- negative ions bound- slower 6-31+G* = 6-31+G(d) - Augmented 6-31G*6-31++G* = 6-31++G(d) - Augmented 6-31+G set of diffuse s-functions added to H, too6-31+G* = 6-31+G(d,p)-6-31++G* = 6-31++G(d,p)-

cc-pVDZ - Correlation Consistent, polarized Valence Double Zeta Basis: correlation consistent basis set Valence Double Zeta set of polarizing d-functions (5D) added to heavy atoms Pros: use with correlated methods series converges exponentially to complete basis set limit Atoms: H-Ne, B-Ne, Al-Ar cc-pVDZ+ - Augmented cc-pVDZ Basis: add diffuse functions Atoms: H, C-F, Si-Cl cc-pVDZ++ cc-pVTZ - Correlation Consistent Valence, polarized Triple Zeta

Post-Hartree-Fock Methods

Electron Correlation:

Explicitly considering the effect of the interactions of specific electron pairs, rather than the effect each electron feels from the average of all the other electrons. (the latter is the SCF approximation).

Large correlation effects occur for:- electron rich systems - transition states - "unusual” coordination numbers- no unique Lewis structure- conjugated multiple bonds - radicals and biradicals

MP2 - 2nd Order Møller Plesset ( = Many Body Perturbation Theory) Basis: Taylor Series expansion, truncated at 2nd order Pros: dynamic correlation for Van der Waals forces: CH4 - CH4 binding π-π stacking interaction bond breaking consistent with diradical formation (without correlation, heterolytic cleavage is seen) anomeric effect Cons: not variational (MP3, MP4, etc.) transition metals not parametrized overbinds CO2, PO free radicals too stable O3 frequencies way off bonds too long scales as n5 (slow)

CI (Configuration Interaction) The simplest variational approach to incorporate dynamic electron correlation. Combination of the Hartree-Fock configuration plus many other configurations of electrons in excited states

MRCI (Multi-Reference Configuration Interaction) CISD (Configuration Interaction, Singles and Doubles substitution only) Comparable to MP2. QCISD(T) Quadratic Configuration Interaction, all Single and double excitations and perturbative inclusion of Triple excitations. Scales as n7. MCSCF (MultiConfiguration Self-Consistent Field) CASSCF (Complete Active Space Self-Consistent Field

CC (Coupled Cluster) CCD (Coupled Cluster, Doubles only.) CCSD (Coupled Cluster, Singles and Doubles only.) CCSD(T) (Coupled Cluster, Singles and Doubles with Triples treated approximately.) CCSDT (Coupled Cluster, Singles, Doubles and Triples)

Extrapolation (to complete basis set (CBS)) methods G1, G2, G3 (Pople: Nobel 1998) (Gaussian 1(2,3,4) theory): empirical algorithm to extrapolate to complete basis set and full correlation from combination of lower level calculations: G2: HF/6-31G(d) frequencies; MP2/6-311G(dp) geometries; single point energies of MP4SDTQ w/ 6-311G**, 6-311+G** 6-311G**(2df) QCISD(T)/6-311G**. Practical up to ~7 heavy atoms. Cons: Cl, F BDE's poor ΔfH ±1.93 kcal/mol Atoms: H-Ca,Ga-Br

G3 (Gaussian 3 "slightly empirical" theory) extension of G2, adding systematic correction for each paired e- (3.3 milliHa = 2 kcal/mol) & each unpaired e- (3.1 milliHa). ΔfH ±1.45 kcal/mol Atoms: H-Ar G3(MP2) G3(MP2)/B3LYP (Geometries and Frequencies at DFT B3LYP) CBS-xxx (Peterson) CBS-QCI (Complete Basis Set Quadratic Configuration Interaction) alternative extrapolation algorithm to complete basis set. W1/W2 (Martin)

Density Functional Theory - DFT ab initio electronic method from solid state physics. Tries to find best approximate “functional” to calculate energy from e- density. Static correlation built in. Not variational. Believed to be size consistent. SVWN LYP P86 B88 BP - Becke-Perdew BLYP - Becke Lee-Yang-Parr GGA91 B3LYP (most commonly used one!) B3P86 Scales as n5 or less. Houk et al. J. Phys. Chem. A 2003 107, 11445. "Benchmarking Computational Methods.."

AIM (Atoms In Molecule) An analysis method based upon the shape of the total electron density; used to define bonds, atoms, etc. Atomic charges computed using this theory are probably the most justifiable theoretically, but are often quite different from those from older analyses, such as Mulliken populations. The latter uses LCAO coefficients, and overestimates charge separation.

Books: Tim Clark, "Molecular Orbital Calculations." No math! Written in English! Deals with actual input to the programs. Highly recommended, if currently dated (1985). Szabo and Ostlund, "Modern Quantum Chemistry," MacMillan 1982. Good explanations between the 42 pages of integrals. For Michael Dewar's (somewhat biased, but amusing) history of MO Calculations: J. Molec. Struc. 100 (1983) 41.

Solvation COSMO (Conductor-Like Screening Model) implicit solvation model. Considers macroscopic dielectric continuum around solvent accessible surface of solute. TIP3P Molecular Mechanics model of water with charge, Van der Waals, and angle terms.  

Timings (Different Methods) (2.8 GHz PC) Gaussian 98, benzene starting at 1.40Å hexagon, units of seconds no freqs with freqs E ΔfH exptl: 19.8 AM1 1.5 3.1 22.0 STO-3G 4.9 8.6 -227.8914 HF/6-31G 8.1 9.4 -230.6245 1234. HF/6-31G* 17.4 116 -230.7031 HF/6-31+G* 61 321 -230.7111 MP2/6-31G* 71 752 -231.4872 MP2/6-31+G* 161 1747 -231.5020 G2 4231 -231.7815 23.6 G3 2702 -232.0522 20.4 G2(MP2) 1278 -231.7708 24.8 G3(MP2) 681 704 -231.8297 18.6 G3(MP2)B3 685 -231.8406 18.4 B3LYP/6-31G* 132 -232.2486 MNDO on a 8088 PC: 1100 sec.

Timing: size (cation, 2007) G3(MP2), all anti conformation molecule #e- minutes MeOH 14 2. EtOH 20 18. nPrOH 26 64. nBuOH 32 195. nPnOH 38 569. nHxOH 44 736. nHpOH 50 1734. (72 min 2012)- scales as n7, n = # valence e-

- more elaborate geometry optimizations take longer

Conformations: nHxO-4 rotatable bonds: anti, +gauche(g), -gauche(f) ΔfH agfg -61.75 aagg -64.14 ggag -65.76 aggf -61.95 gffg -64.22 gfag -65.77 aagf -62.33 aaga -64.25 gafa -65.78 agfa -62.67 agaa -64.25 gfgg -65.87 agff -63.04 aaaa -64.55 gfga -65.91 gggf -63.19 gfgf -64.61 gfff -65.91 agag -63.28 gfaf -64.83 gaaa -66.06 agaf -63.30 gaga -65.48 ggga -66.08 gagf -63.54 ggaf -65.50 gagg -66.17 aggg -63.59 gaag -65.51 ggff -66.28 gafg -63.77 gaff -65.58 ggaa -66.29 agga -63.84 gaaf -65.62 gffa -66.46 aaag -63.98 gggg -65.74 ggfa -66.58 ggfg -66.59 weighted average: -66.24

Cations [G3(MP2)] ΔfH298 S E0 ΔfG298

Me2CHCH2NH2+.178.41±0.41 84.12 186.24 213.00

Me2C(.)CH2NH3+ 168.49±0.41 90.02 176.02 201.33

CH3CHO+. 198.27±0.20 61.88 201.14 206.57 CH2=CHOH+. 184.13±0.20 62.61 186.80 192.21 NH4

+ 152.67±0.10 44.35 155.37 165.90 NH3 -10.00±0.10 48.08 -8.32 -3.54 PA: 203.0 22.3 H2NNH2

+. 211.64±0.20 59.10 214.81 226.29 H2NNH2 27.82±0.20 58.70 31.04 42.59 Neutral pyramidal: θ = 106.5º, ion θ = 157º Relaxation Energy of cation ca. 17 kcal/mol

%mem=256MB %rwf=a,1900MB,b,1900MB,c,1900MB,d,1900MB,e,1900MB,f,1900MB,g,1900MB,h,-1 %nosave -------------------- # g3mp2 maxdisk=15GB -------------------- H2O --- Symbolic Z-matrix: Charge = 0 Multiplicity = 1 H O 1 0.95 H 2 0.95 1 107. Job cpu time: 0 days 0 hours 0 minutes 44.6 seconds. Exact polarizability: 2.778 0.000 6.679 0.000 0.000 4.808 Approx polarizability: 2.363 0.000 5.340 0.000 0.000 4.005 Full mass-weighted force constant matrix: Low frequencies --- 0.0010 0.0017 0.0021 7.3489 8.3093 9.9159 Low frequencies --- 1826.5724 4070.4025 4188.6410 Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering activities (A**4/AMU), Raman depolarization ratios, reduced masses (AMU), force constants (mDyne/A) and normal coordinates: 1 2 3 A1 A1 B2 Frequencies -- 1826.5724 4070.4025 4188.6410 Red. masses -- 1.0823 1.0455 1.0828 Frc consts -- 2.1275 10.2061 11.1935 IR Inten -- 107.2699 18.2084 58.1069 Raman Activ -- 5.7238 75.5382 39.0879 Depolar -- 0.5300 0.1830 0.7500 Atom AN X Y Z X Y Z X Y Z 1 1 0.00 0.43 0.56 0.00 0.58 -0.40 0.00 -0.56 0.43 2 8 0.00 0.00 -0.07 0.00 0.00 0.05 0.00 0.07 0.00 3 1 0.00 -0.43 0.56 0.00 -0.58 -0.40 0.00 -0.56 -0.43

E (Thermal) CV S TOTAL 16.196 5.985 44.987 Job cpu time: 0 days 0 hours 0 minutes 28.5 seconds. Job cpu time: 0 days 0 hours 0 minutes 50.6 seconds. Time for triples= 0.30 seconds. Job cpu time: 0 days 0 hours 0 minutes 14.8 seconds. Population analysis using the SCF density. ********************************************************************** Orbital Symmetries: Occupied (A1) (A1) (B2) (A1) (B1) Virtual (A1) (B2) (A1) (B1) (A1) (B2) (B2) (A1) (B2) (A1) (A1) (A2) (B1) (A1) (B2) (B2) (B1) (A1) (B2) (A1) (B1) (A2) (A1) (B2) (A1) (A1) (B2) (A2) (B2) (B1) (A1) (B2) (A1) (B1) (B1) (A1) (B2) (A1) (B1) (A2) The electronic state is 1-A1. Alpha occ. eigenvalues -- -20.56872 -1.34865 -0.71169 -0.58430 -0.51016 Alpha virt. eigenvalues -- 0.04343 0.07176 0.23737 0.24590 0.24670 Alpha virt. eigenvalues -- 0.25723 0.31315 0.32565 0.66568 0.71047 Alpha virt. eigenvalues -- 0.78527 0.83837 0.91676 1.05684 1.08545 Alpha virt. eigenvalues -- 1.17607 1.26297 1.49508 1.59397 1.65944 Alpha virt. eigenvalues -- 2.04137 2.05832 2.16884 2.42432 2.51212 Alpha virt. eigenvalues -- 2.75287 3.17403 3.92773 3.96741 3.98654 Alpha virt. eigenvalues -- 4.20632 4.44500 4.57676 5.44010 5.51822 Alpha virt. eigenvalues -- 5.57238 5.67011 5.83662 5.91657 6.05253 Alpha virt. eigenvalues -- 6.15622 7.41580 7.44458 7.46822 7.56939 Alpha virt. eigenvalues -- 7.82945 7.84240 8.06737 51.59303

Condensed to atoms (all electrons): 1 2 3 1 H 0.484816 0.269298 -0.009496 2 O 0.269298 7.972169 0.269298 3 H -0.009496 0.269298 0.484816 Total atomic charges: 1 1 H 0.255382 2 O -0.510764 3 H 0.255382 Sum of Mulliken charges= 0.00000 Atomic charges with hydrogens summed into heavy atoms: 1 1 H 0.000000 2 O 0.000000 3 H 0.000000 Sum of Mulliken charges= 0.00000 Electronic spatial extent (au): <R**2>= 19.6152 Charge= 0.0000 electrons

Dipole moment (Debye): X= 0.0000 Y= 0.0000 Z= -2.0828 Tot= 2.0828 Quadrupole moment (Debye-Ang): XX= -7.5928 YY= -4.2259 ZZ= -6.2360 XY= 0.0000 XZ= 0.0000 YZ= 0.0000 Octapole moment (Debye-Ang**2): XXX= 0.0000 YYY= 0.0000 ZZZ= -1.3274 XYY= 0.0000 XXY= 0.0000 XXZ= -0.3419 XZZ= 0.0000 YZZ= 0.0000 YYZ= -1.4746 XYZ= 0.0000 Hexadecapole moment (Debye-Ang**3): XXXX= -6.6121 YYYY= -5.9400 ZZZZ= -7.2496 XXXY= 0.0000 XXXZ= 0.0000 YYYX= 0.0000 YYYZ= 0.0000 ZZZX= 0.0000 ZZZY= 0.0000 XXYY= -2.4331 XXZZ= -2.3735 YYZZ= -1.8084 XXYZ= 0.0000 YYXZ= 0.0000 ZZXY= 0.0000 N-N= 9.088303640043D+00 E-N=-1.987824085983D+02 KE= 7.594119614980D+01 Symmetry A1 KE= 6.791617182163D+01 Symmetry A2 KE= 1.406616952546D-34 Symmetry B1 KE= 4.473677327000D+00 Symmetry B2 KE= 3.551347001170D+00

1\1\GINC-THERMO\SP\RMP2-FC\GTMP2Large\H2O1\JB\14-Nov-2001\0\\#N GEOM=A LLCHECK GUESS=TCHECK MP2/GTMP2LARGE\\H2O\\0,1\H,-0.070384131,0.,-0.897 2787415\O,-0.0958886836,0.,0.0709538934\H,0.8374935995,0.,0.3296475945 \\Version=x86-Linux-G98RevA.7\State=1-A1\HF=-76.0558204\MP2=-76.314758 5\RMSD=9.212e-09\PG=C02V [C2(O1),SGV(H2)]\\@   PICNIC: A SNACK IN THE GRASS. Temperature= 298.150000 Pressure= 1.000000 E(ZPE)= 0.020515 E(Thermal)= 0.023350 E(QCISD(T))= -76.207892 E(Empiric)= -0.037116 DE(MP2)= -0.117911 G3MP2(0 K)= -76.342404 G3MP2 Energy= -76.339568 G3MP2 Enthalpy= -76.338624 G3MP2 Free Energy= -76.360001 1\1\GINC-THERMO\Mixed\G3MP2\G3MP2\H2O1\JB\14-Nov-2001\0\\# G3MP2 MAXDI SK=15GB\\H2O\\0,1\H,-0.070384131,0.,-0.8972787415\O,-0.0958886836,0.,0 .0709538934\H,0.8374935995,0.,0.3296475945\\Version=x86-Linux-G98RevA. 7\State=1-A1\MP2/6-31G(d)=-76.1968478\QCISD(T)/6-31G(d)=-76.2078917\MP 2/GTMP2Large=-76.3147585\G3MP2=-76.3424035\FreqCoord=-0.1507632936,0., -1.6611179585,-0.1742115986,0.,0.1289098018,1.5444560828,0.,0.62983954 4\PG=C02V [C2(O1),SGV(H2)]\NImag=0\\0.05943423,0.,0.00000270,0.0086474 6,0.,0.61314791,-0.06074901,0.,-0.01968431,0.62304397,0.,-0.00000333,0 .,0.,0.00000666,0.05298665,0.,-0.59899355,0.12003565,0.,0.69644113,0.0 0131478,0.,0.01103685,-0.56229497,0.,-0.17302230,0.56098019,0.,0.00000 064,0.,0.,-0.00000333,0.,0.,0.00000270,-0.06163412,0.,-0.01415436,-0.1 0035133,0.,-0.09744759,0.16198545,0.,0.11160194\\0.00000116,0.,-0.0000 0451,-0.00000580,0.,0.00000429,0.00000465,0.,0.00000021\\\@ Job cpu time: 0 days 0 hours 0 minutes 18.3 seconds.

File lengths (MBytes): RWF= 263 Int= 0 D2E= 0 Chk= 3 Scr= 1 Normal termination of Gaussian 98. # g3mp2 maxdisk=15GB H2O 0 1 H O 1 .9686 H 2 .9686 1 103.9822 _dHf(298)= -57.41+/-0.02 S= 44.99 E0= -56.72 dGf(298)= -54.20 Time: 2.6 min. Polarizability = 1.23 Ang^3

Bottom line:Molecular Mechanics: proteins/DNA above oligimer (>10)

Semi-empirical: front end for ab initio

Ab initio: at least MP2 Gn up to 20 heavies

DFT: most common these days (speed), but hard to find “best” functionals, sometimes strange errors