"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."
- Jan L. A. van de Snepscheut
(computer scientist)
But often attributed to Yogi Berra
"Man's gotta know his limitations"
- Dirty Harry Callahan (John Milius)

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

Units
Bohr - One atomic unit of distance = 0.5292 Angstrom (archaic now)
Hartree - One atomic unit of energy = 2 x IE(H .
)
2625.500 kJ/mol
27.2114 eV
627.5095 kcal/mol
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 n 4 to n 8 ) 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 x10 20 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”

Semi-empirical input
AM1 precise acetone
O
C 1.22 1 1
C 1.54 1 120. 1 2 1
C 1.53 1 120. 1 180. 1 2 1 3
H 1.11 1 110. 1 180. 1 4 2 1
H 1.11 1 110. 1 60. 1 4 2 1
H 1.11 1 110. 1 -60. 1 4 2 1
H 1.11 1 110. 1 180. 1 3 2 1
H 1.11 1 110. 1 60. 1 3 2 1
H 1.11 1 110. 1 -60. 1 3 2 1
0 0 0 0 0 0 0 0 0 0 0

%mem=256MB
%nosave
# g3mp2b3 Opt=Maxcyc=100
Me2C(.)CH2NH3+
+1 2
N
C 1 1.5283
C 2 1.5050 1 115.9692
C 3 1.5022 2 115.2106 1 182.2808
C 3 1.4956 2 124.5590 1 2.8544
H 4 1.1100 3 110.6428 2 60.1046
H 4 1.1100 3 110.6213 2 -239.9345
H 4 1.1077 3 112.2541 2 180.0153
H 5 1.1104 3 111.0735 2 61.1423
H 5 1.1108 3 111.3159 2 -239.8219
H 5 1.1085 3 111.9526 2 180.4718
H 2 1.1190 1 105.8385 3 122.4183
H 2 1.1192 1 105.6916 3 -122.5352
H 1 1.0250 2 110.0652 3 179.7632
H 1 1.0245 2 112.2413 14 119.2315
H 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: Δ f
H = 131 vs. 19.4 kcal/mol normal

←1/2hυ
Negative freq
↓

From statistical mechanics:
E tot
= E
0 mass
+ E trans
+ E rot
+ E vib
+ E elec geometry (moments of inertia) vibrational frequencies orbital energies allow calculation of: zero point energy = h/2·

E 0 = E
0
+ ZPE heat capacity: E 298 H 298 (=E 298 + RT) entropies: S 298 G 298

- Scaling: 0.896 HF/6-31G*
0.96 B3LYP
- Harmonic approximation (parabola), yet real ones anharmonic
-Lowest ones (<300 cm -1 ) most important to stat. mech. entropy, yet worst known
Internal rotors, free vs. hindered
Ring breathing modes

Absolute:
Δ f
H o (molecule) = E 0 (molecule)
-

E 0 (atoms)
+
 Δ f
H o exptl
(atoms)
Relative:
A + B = C + D
E
A
E
B
E
C
E
D
Δ f
H(A) = E
A
+ E
B
- E
C
– E
D
+ Δ f
H(C) + Δ f
H(D) - Δ f
H(B)

EXACT THEORY: the Schrödinger Equation
H(Ψ) = E·Ψ where 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 = - h 2 /8
 2 
M
A
-1

2
A
+
  e 2 Z
A
Z
B r
AB
-1
A=1 A=1 B>A
N
- h 2 /(8  m)  i=1
 i
2
N M N N
 2Z
A r
Ai
-1 +  e i=1 A=1 i=1 j>i
2 r ij
-1

Hamiltonian divides up into:
1. Kinetic energy of nuclei
2. Nuclear-nuclear repulsion
3. Kinetic energy of electrons
4. Nuclear-electron attraction
5. Electron-electron repulsion
Born-Oppenheimer approximation:
Nuclei don’t move, on electron motion timeframe
1. = 0
2. Static calculation: Coulomb’s Law

MORE APPROXIMATIONS:
1. Ψ =
ψ
1
.
ψ
2
.
ψ
3
...., where
ψ i are one electron molecular orbitals.
Separate the Schrödinger equation: H( ψ i
) = E i
· ψ i
 2 = probability of electron position
All physical observables relate to
 2 , because
 has imaginary parts.
Normalized:
 a
 a
* = 1 <
 a
|
 a
*> = 1
Orthogonal:
 a
 b
= 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 ψ i as a Linear Combination of
Atomic Orbitals (LCAO):
ψ i
= c i,1
· φ
1
+ c i,2
· φ
2
+ ..... where φ j are basis orbitals (usually atomic)

3. Variational Principle:
For any approximate (one e )
ψ i
Equation is greater than the true E i
, E i from the Schrödinger for the exact ψ i
. Thus ψ i and c ij are varied so as to minimize E i
, or δE i
/δc i,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”
ψ i 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
ψ i is then used as part of the average distribution as the next electron's
ψ i found, and so on. After successive iterations is 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
ψ i s is used as a valid wave function.

5. Hartree-Fock Limit.
- Approximations 2 and 4 (LCAO and SCF) lead to E o always too high.
- If a small number of terms [limited number of basis orbitals] is used in (2), then the ψ i 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 as accurate as much higher(slower) ones of absolute energetics

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
______________
______________
-----------------------0 E
______________ LUMO
_____
______ HOMO
_____
_____

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.

"Balls and Springs"
MM2 - Allinger Force Field version 2
MM3 -
MMX - PCModel
Sybyl -
Amber -
CHARMn -
All Δ f
H ca.
± 1 kcal/mol
μ
D
± 0.1
Limit: only parameterized functional groups
Advantage: fast, up to proteins

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 well
Ignores e e repulsion
Uses 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

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 9 o large amides pyramidal
Aniline, nitrobenzene: NH
2
, NO
2 group perpendicular to ring, due to nuclear repulsion

MNDO Problems (energies): no H-bonds, no H
2
O 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
(Me
4
C: -24. kcal/mol, exp -40.3 kcal/mol)
N-O bonds poorly parameterized - heats way off
(MeNO
2
: calc Δ f
H = +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
-CH
2
- Δ f
H ~ 0.2 kcal/mole low each
Heat of Hydrogenation low bond dissociation enthalpies too weak activation enthalpies high
-NO
2 energies high
-O-O- bond ~ 0.17Å short
H-bond angles, H
2
O 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
Δ f
H 40% better
-NO
2 better ground state geometries better
H
2
O 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
D
2 d symmetry for CBr
4
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
(MeNO
2
: calc -15.9, exp -17.9 kcal/mol)
(cyclobutane: -3.8, exp +6.8 kcal/mol)
(cubane: 114, exp 148.7 kcal/mol)
(Me
4
C: -35.8, exp -40.3 kcal/mol)
(MeOH..-OMe: bond strength 19, exp 28.8 kcal/mol
Hypervalents good energy

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, too
6-31+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:
CH
4
- CH
4 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 CO
2
, PO free radicals too stable
O
3 frequencies way off bonds too long scales as n 5 (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 n 7 .
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
Δ f
H ± 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).
Δ f
H ± 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)

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 n 5 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)
B3LYP/6-31G* 132
MNDO on a 8088 PC: 1100 sec.
(2.8 GHz PC)
Gaussian 98, benzene starting at 1.40Å hexagon, units of seconds no freqs with freqs E Δ f
H exptl: 19.8
AM1
HF/6-31G
HF/6-31G* 17.4 116
HF/6-31+G*
MP2/6-31G* 71 752
MP2/6-31+G* 161 1747
G2
G3
G2(MP2)
G3(MP2)
G3(MP2)B3
1.5
3.1
STO-3G 4.9 8.6
8.1 9.4
61 321
4231
2702
1278
681 704
685
-227.8914
-230.7031
-230.7111
-231.4872
-231.5020
-231.7815
-232.0522
-231.7708
-231.8297
-231.8406
-232.2486
22.0
-230.6245 1234.
23.6
20.4
24.8
18.6
18.4

Timing: size (cation, 2007)
G3(MP2), all anti conformation molecule #e minutes
MeOH
EtOH
14 2.
20 18.
nPrOH 26 64.
nBuOH 32 195.
nPnOH 38 569.
nHxOH 44 736.
nHpOH 50 1734.
(72 min 2012)
- scales as n 7 , n = # valence e -
- more elaborate geometry optimizations take longer

Conformations: nHxO-
4 rotatable bonds: anti, +gauche(g), -gauche(f)
Δ f
H 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)]
Me
2
CHCH
2
NH
2
+.
Me
2
C(.)CH
2
NH
3
+
CH
3
CHO +.
CH
2
=CHOH +.
Δ f
H 298
178.41
168.49
198.27
184.13
±
±
±
±
0.41
0.41
0.20
0.20
S E
0
Δ f
G 298
84.12 186.24 213.00
90.02 176.02 201.33
61.88 201.14 206.57
62.61 186.80 192.21
NH
4
+
NH
3
PA:
152.67
-10.00
±
±
0.10
0.10
203.0
44.35 155.37 165.90
48.08 -8.32 -3.54
22.3
H
2
NNH
2
+.
H
2
NNH
2
211.64
27.82
±
±
0.20
0.20
Neutral pyramidal: θ = 106.5º, ion θ = 157º
59.10 214.81 226.29
58.70 31.04 42.59
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 --
Frc consts --
1.0823 1.0455 1.0828
2.1275 10.2061 11.1935
IR Inten -107.2699 18.2084 58.1069
Raman Activ --
Depolar --
5.7238 75.5382 39.0879
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 --
Alpha virt. eigenvalues --
Alpha virt. eigenvalues --
0.04343 0.07176 0.23737 0.24590 0.24670
0.25723 0.31315 0.32565 0.66568 0.71047
0.78527 0.83837 0.91676 1.05684 1.08545
Alpha virt. eigenvalues --
Alpha virt. eigenvalues --
Alpha virt. eigenvalues --
Alpha virt. eigenvalues --
Alpha virt. eigenvalues --
Alpha virt. eigenvalues --
Alpha virt. eigenvalues --
1.17607 1.26297 1.49508 1.59397 1.65944
2.04137 2.05832 2.16884 2.42432 2.51212
2.75287 3.17403 3.92773 3.96741 3.98654
4.20632 4.44500 4.57676 5.44010 5.51822
5.57238 5.67011 5.83662 5.91657 6.05253
6.15622 7.41580 7.44458 7.46822 7.56939
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