MOLECULAR MODELING QUICK REFERENCE GUIDE
Parameters & Basis Sets
Optimization Methods
Acronyms & Definitions
Compliments of:
CHAMOT LABS, INC.
Chemical Research and Consulting
http://www.chamotlabs.com/
6/2/2000
------------
PARAMETERS & BASIS SETS
(Accuracy: 食fｰ, 食r, 食ﾝ kcal/mole;
D Debye; IP eV; l ﾅ; a,d ｰ; v cm-1)
Molecular Mechanics Methods
MM2 - Molecular Mechanics, Allinger Force Field version 2
Basis:
XRD & ND Structures
75 parameters
3rd Order Dihedral term
bond dipoles vs electrostatic
Pros:
covalent
organic
Ground States
Cons:
metal bonding
excited states
transition states
Atoms:
H, D
B - F
Si - Cl
Ca, Cr, Co, Cu - Br
Sr, Rh, Pd, Cd, Sn, Te, I
Pb
Accｹy:
食fｰｱ0.5, 食rｱ0.4, 食ﾝｱ2
Dｱ0.1
lｱ0.01, aｱ1, dｱ8
vｱ80
MM3 -
Basis: added 4th order dihedral
Atoms:
H
Li, C - O
Na, Mg, P, S
K, Ca
Rb, Sr, I
Cs, Ba
Pros:
accuracy
cyclohexylamine conformation
entropy by vibrational analysis
F-C-C-F hyperconjugation
anomeric effect
Bohlmann effect
Accｹy:
食fｰｱ0.6, 食rｱ0.4, 食ﾝｱ1
Dｱ0.07
lｱ0.01, aｱ1, dｱ5
vｱ40
ChemX -
Basis:
organics
inorganics
peptides
Accｹy: 食rｱ1, 食ﾝｱ2
Sybyl -
Basis:
biomolecules
atomic
general purpose
harmonic force field
Pros:
biomolecules
saturated HCs
Cons:
inorganics
unsaturations
nonbond attractions high
2-Cl-THP eq. (no anomeric)
Accｹy: 食rｱ1, 食ﾝｱ1
Amber -
Basis:
biomolecules
harmonic force field
25 parameters
united atom charges from HF 6-31G*
(CH as united atom in old version)
electrostatic ("disappearing" L-J) H-bond
Pros:
proteins/DNA
aqueous
Cons:
inorganic
no general atom types
Atoms:
H
C - F
Na, Mg, P - Cl
K, Ca, Fe, Cu, Br
Rb, I
Cs
Accｹy: 食rｱ0.7
CHARMm -
Basis:
18 parameter force field
(CH as united atom in old version)
Pros:
biopolymers
QM-MD
GAMESS or AMPAC QM
Atoms:
H
C - O
Na - S
K - Fe
Rb
Eu
Accｹy:
食ﾝｱ0.9
lｱ0.01, aｱ1
OPLS - Optimized Potentials for Liquid Simulation
Basis:
electrostatic ("disappearing" L-J) H-bond
protein/DNA
liquids, solutions
ab initio calc'ns on 100 organics
CH as united atom
Pros: condensed phase
Born Model -
Atoms:
H
Li, Be, O
Na - Si, Cl
K - Ni, Zn, Ge, Br
Rb - Nb, Cd, Sn, I
Cs- La, Nd, Eu-Tb, Ho, Yb-Hf
Pu
Dreiding -
Basis:
Bonds from atomic radii
angles from hydrides
harmonic force field
Pros: General organic & main group
Cons:
Accuracy
nonphysical charges
2-MeO-THP equilibrium
Atoms:
H
B - F
Na, Al - Cl
Ca, Fe, Zn - Br
In - I
Accｹy:
食ﾝｱ2, 食rｱ1
lｱ0.03, aｱ3, dｱ8
UFF - Universal Force Field
Basis:
Organic
Inorganic
parms calcｹd from basic props
Pros: full periodic table
Cons:
needs charge equilibration
2-MeO -THP equatorial
Acc'y: 食rｱ0.9
CFF - Consistent Force Field
Basis:
Class II Force Field
based on ab initio/QM data
nondiagonal force field
crossterms
generalized parameters
Atoms:
H
C-F
Na, Si-S, Ar
Ca, Br
I
Cons:
2-MeO-THP equatorial
nonbond anomaly expands condensed phase
Accｹy:
食rｱ0.5, 食ﾝｱ0.8
lｱ0.01, aｱ1
solubility parameterｱ0.2
sorption energyｱ5
PCFF -
Basis:
derived from CFF, QM based FF
optimized for polymer properties
COMPASS - Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies
Basis:
derived from CFF, QM based FF
optimized for condensed phase MD
ESP from 6-31G*
integral for cutoff tail sums
6-9 L-J term
Pros:
long range/nonbonded interaction
condensed phase properties
Accｹy:
食rｱ0.4
aｱ1.8
Xtal densities +6%
CVFF -
Basis:
general purpose
Morse function stretch term
nondiagonal force field
crossterms
empirical parametrization
Cons: anomeric effect w/ 2-MeOTHP
Acc'y: 食rｱ1
ESFF ｭ
Basis:
diagonal valence
rule based:
electronegativity
atomic radii
hardness
scaling
d-p ｼ bonding
organics, inorganic, organometallic & biomolecules
Pros:
any element
organometallic complexes
Cons: accuracy
Atoms:
H
Li - F
Na - Cl
K - Br
Rb - I
Cs - At
MMFF94 ｭ Merck Molecular Force Field
Basis:
small molecule
ab initio & experimental
Pros: ions
Semiempirical Quantum Mechanics
(1-Electron MO Methods)
Hckel -
Basis:
"Tight Binding Approximation"
ｼ-orbitals only
Hｵｵ= alpha
Hｵv = beta, adjacent atoms only
Sｵv = 0
Pros:
orbital symmetry
resonance energy
back of envelope
Cons:
flat, ｼ orbitals only
polars poor
EHT -
Basis:
valence s & pｹs
Hｵｵ= -IPｵ (ionization potential)
Hｵv = 1.75(IPｵ + IPv)Sｵv
Sｵv computed
Pros:
C2H6 rotational barrier
Woodward-Hoffman rules
includes AO overlap terms
Fock matrix diagonalized once
Frontier orbitals
Walsh Diagrams
All elements
Cons:
valence only
geometry poor
partial charges high
singlet & triplet same (no e- spin)
no e-/e- or nuclear repulsions
IEHT -
Basis:
Iterate to consistent charge
Hｵｵ= -IPｵ - Qa(IPa-EAa)
Pros:
reasonable, but low charges
better dipoles
better orbital order
Cons:
valence only
convergence poor
benzene asymmetric
Fenske-Hall -
Basis:
parameter free
minimal basis
all electron
spectroscopic Slater terms
(2-Electron MO Methods)
CNDO - Complete Neglect of Differential Overlap
Basis:
all 2 e- overlap Orbitals
IP & EA
XｵXvdt = 0
Hｵv ﾟabSｵv fit to minimum basis set
Pros:
bond lengths
bond angles
Cons: dissociation energies poor
Accｹy: 食fｰｱ200
PPP -
Basis:
one 2pｼ STO per conjugation
single CI
valence ｼ & sigma separate
Pros: aromatic species
Cons:
valence only
ignores many e-/e- repulsions
INDO/1 -
Basis:
minimal basis set
valence s, p, & d orbitals
2-center integrals 0
includes 1-center exchange integrals
Hｵｵ= -(IPｵ - EAｵ/2 + . . .
Hｵv from STO-3G SCF
Pros:
transition metals
bond lengths
bond angles
singlet-triplet splitting
better electron spin
SCRF
Cons:
small rings favored
dye absorbances low
no double excitations
dissociation energies poor
no SCRF for spectra
Atoms:
H
Li - F
Na - Cl
K - Zn
Y - Cd
Accｹy:
食fｰｱ100
lｱ0.08
INDO/S -
Basis:
parameterized for spectra
single CI
Pros: UV spectra
Cons: metals w/ unpaired e-
Atoms:
Li, B - F
P, S
Sc - Zn
(2 Electron NDDO Methods)
MINDO/3 -
Basis:
32 molecule parameterization
1-center integral parameters
3 & 4-center integrals on same
resonance integral from exp.
Pros:
carbocations
amides flat
Cons:
valence s & p only
small rings favored
resonance energy low
no H-bonds
lone pair repulsion low
rings flat
transition states poor
Atoms:
H
B - F
Si - Cl
Accｹy:
食fｰｱ5, 食rｱ13
Dｱ0.5, IPｱ0.7
lｱ0.02
MNDO - Minimal Neglect of Differential Overlap
Basis: 32 molecule parameterization
Pros:
multiple bonds
EAｹs for ions
better lone pair repulsion
better angles
Cons:
valence s & p only
no H-bonds, no H2O dimer
spurious H-H interaction
S, Cl, & Br IP high
activation barriers high
bond dissociation enthalpies low
conjugation low
3-center B bonds low
-O-O- bond ~ 0.17ﾅ short
C-O-C angle 9ｰ large
Ar-NO2 out of plane
amides pyramidal
no Van der Waals attraction
steric crowding disfavored:
neopentane unstable
4-membered rings too stable
hypervalent unstable
Atoms:
H
Li - F
Al - Cl
Cr, Zn, Ge, Br
Sn, I
Hg, Pb
Accｹy:
食fｰｱ11, 食rｱ13, 食diss-20, 食ﾝｱ16
Dｱ0.5, IPｱ0.8
lｱ0.07, aｱ5, dｱ17
v+11%
MNDO/d -
Basis:
adding d-orbitals to MNDO
split valence
11 parameters for sp elements
15 parameter for spd elements
d orbitals for 2nd row main group
Atoms:
Na - Cl
Ti, Fe, Ni, Cu, Zn, Ge - Br
Zr, Pd, Ag, Cd, Sn - I
Hf, Hg
Pros:
Heat of formation
hypervalent shape
Cons:
IP
dipole moment
overpredicts agostic interaction
metal-ethylene short
no insertion barrier
Accｹy:
食fｰｱ6
Dｱ0.5, IPｱ0.6
lｱ0.06, aｱ2
AM1 - Austin Model 1
Basis:
100 molecule parameterization
1-center from spectroscopy
minimal basis set
Gaussian patches
7-21 parameters per element
theoretical consistency
Pros:
H-bond energies
H-bond lengths
proton affinities
better activation barriers
hypervalent P
Heat of Formation 40% better
2-Cl-THP axial (anomeric)
Cons:
valence s & p only
no hypervalent compounds
P orbitals irregular @ 3ﾅ:
P4O6 asymmetric
P-O bonds
conjugate interactions low
-CH2- 食f ~ 2 kcal low each
Heat of Hydrogenation low
bond dissociation enthalpies low
activation enthalpies high
-NO2 energies high
-O-O- bond ~ 0.17ﾅ short
H-bond angles, H2O H-bond geometry wrong
C-C-O-H gauche in ethanol
H+ transfer barrier high
acrolein, glyoxal
Atoms:
H
Li, B - F
Al - Cl
Zn, Ge, Br
I
Hg
Accｹy:
食fｰｱ8, 食rｱ5, 食diss-20, 食ﾝｱ7
Dｱ0.5 ,IPｱ0.6
lｱ0.06, aｱ4, dｱ13
v+4.7%
SAM1 -
Basis: AM1 w/ d-orbitals
Pros:
theoretical consistency
transition metals
Atoms:
H
C - F
Si - Cl
Fe, Cu, Br
I
Accｹy:
食fｰｱ8, 食rｱ5
Dｱ0.4, IPｱ0.4
lｱ0.04, aｱ3
vｱ13%
PM3 -
Basis:
657 molecule parameterization
minimal basis set
18 parameters per element
2 Gaussians for each element
all 2 e- integral parameters optimized
Pros:
hypervalent included
HOF 40% better
-NO2 better
ground state geometries better
reproducing experimental data
H2O H-bonds: lengths & angles
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
CH4 LUMO symmetry A1
IPｹs poor
Proton Affinity
H+ transfer barrier high
wrong glucose geometry:
H-bonds 0.1ﾅ short
C-C-O-H gauche in ethanol
VdW attraction high/H-H core repulsion low, H-H 1.7 vs 2.0 ﾅ
Atoms:
H
Li, Be, C - F
Mg - Cl
Zn - Br
Cd - I
Hg - Bi
Accｹy:
食fｰｱ9, 食rｱ7, 食diss-20, 食ﾝｱ9
Dｱ0.6, IPｱ0.7
lｱ0.05, aｱ9, dｱ15
vｱ20%
PM3(tm) -
Basis:
PM3 with d-orbitals
minimal basis set
optimized for geometries
Pros:
transition metals
geometries
Cons: energies
Atoms:
H
Li - F
Mg - Cl
Ca, Ti, Cr - Br
Zr, Mo, Ru - Pd, Cd - I
Hf - W, Hg
Gd
Density Functional
Basis: Kohn-Sham theory
Pros:
static correlation included
less basis set sensitivity
less spin contamination
Cons:
no dynamic correlation
quasiparticle functions, not true MOs
overstabilizes low spin state of metal complexes
Xalpha ｭ
Basis:
Local Spin Density/functionals
Slater style exchange
alpha ~ 0.7
Pros:
geometries
EA's
Cons:
no dynamic correlation: VdW/dispersion
H-bonds
N2 orbital order
bond energies high
IP's low
bandgap low
delocalized 3e- bonds too stable
exchange functional only
Acc'y:
lｱ0.02, aｱ3
vｱ35
SVWN -
Basis:
Local Spin Density functionals
Slater exchange
Vosko-Wilk-Nusair correlation
Pros:
scales as big x n^2
no parameters
Cons:
bonds short
bond energies high
proton affinities
H-bonds
H-abstractions poor
radical Rxn barriers low
long range dispersion
band gap low
spurious e- self interaction
overstablizes lo spin states of metal complexes
Accｹy:
食f+90, 食rｱ9, 食diss+16, 食atom+80, 食ﾝｱ7
Dｱ0.1
lｱ0.02, aｱ2
vｱ7%
LYP ｭ
Basis:
Lee-Yang-Parr gradient correction
correlation functional from He atom
Cons:
charge transfer complexes
excited states
1 e- correlation 0
nonuniform e- gas limit
parallel = opposite spin e- pairs
P86 ｭ
Basis:
Perdew gradient correction
correlation functional
parameter free
Pros:
uniform e- gas limit
parallel opposite spin pairs
Cons: 1 e- correlation 0
B88 ｭ
Basis:
Becke gradient correction
exchange functional
1 parameter fitted to calculated atomic data
Pros:
1 e- correlation =0
parallel opposite spin pairs
Cons:
nonuniform e- gas limit
inhomogeneity limits interpolation
BP - Becke-Perdew
Basis:
nonlocal/Generalized Gradient Approximation method
B88 exchange w/ P86 correlation
scales as n^3
Pros:
transition metals
better metal spin state preference
Cons: overstablizes high spin state of metal complexes
Acc'y:
食f+16, 食rｱ5, 食diss+5, 食atom+20
Dｱ0.2
lｱ0.02, aｱ0.9
BLYP - Becke Lee-Yang-Parr
Basis:
nonlocal/Generalized Gradient Approximation method
B88 exchange w/ LYP correlation
scales as n^3
Pros:
heavy atom BDE's
IR scaling
better metal spin state preference
Cons:
popular, well tested/validated
overstablizes high spin state of metal complexes
transition states for: F + H2, N + O2, O + HCl
Acc'y:
食fｱ7, 食rｱ5, 食dissｱ5, 食atomｱ9, 食ﾝｱ6
Dｱ0.2
l+0.03, aｱ1
vｱ6%
GGA91 ｭ
Pros:
parallel opposite spin pairs
uniform e- gas limit
no fit parameters
H-bonds
Cons: 1 e- correlation 0
ACM ｭ Adiabatic Correction Method
Basis:
nonlocal gradient corrections
hybrid HF exchange for part of DFT
Pros:
transition states
H-bonds
B3LYP -
Basis:
hybrid nonlocal method
3-parameter exchange fitted to G2 thermochemistry data:
Becke exchange
HF exchange
LYP correlation
favors greater density
favors greater inhomogeneity
Pros:
good rxn barriers
nondynamic correlation
radical hyperfine coupling
eliminates overbinding
agostic interactions
transition metal geometries
transition metal complex spin preferences
naphthalene cation geometry
O3 frequencies
popular, well tested/validated
Cons:
bonds slightly long
no dynamic correlation: dispersion interactions
transition state for: F + H2
harder to converge for transition metals
scales as n^4
Accｹy:
食fｰｱ3 , 食rｱ4, 食dissｱ5, 食atomｱ3, 食ﾝｱ4
Dｱ0.2, IPｱ0.1
lｱ0.007, aｱ0.9
v+4.0%
B3P86 -
Basis:
B3 hybrid exchange w/ P86 correlation
Accｹy: v+4.6%
ab initio
Standard (uncorrelated) HF
Basis:
Hartree-Fock
Self Consistent Field
single Slater determinant/e- configuration
Pros:
isodesmic energies
relative activation enthalpies
Cons:
homolysis & atomization enthalpies low
食ﾝs high w/o correlation
acrolein isomers
naphthalene cation symmetry
O3, F-O-O-F
radical hyperfine coupling too high x2
organic bonds short
M - ｼ bonds long
favors metal s over d
wrong N2 orbitals order
overstablizes hi spin states of metal complexes
no e- correlation:
no static correlation: singlet methylene
no dynamic correlation: dispersion energy (ｼ - ｼ stacking) low
scales as n^2.7
MP2 - 2nd Order Moller Plesset ( = Many Body Perturbation Theory)
Basis:
Rayleigh-Schrodinger perturbation theory
Taylor Series expansion, truncated at 2nd order
Pros:
size consistent
dynamic correlation for dispersion forces:
CH4 - CH4 binding
ｼ - ｼ stacking interaction
bond breaking
anomeric effect
Cons:
not variational
transition metals
overbinds CO2, PO
free radicals too stable
O3 frequencies
bonds long
greater BSSE
diverges for e- gas
diffuse orbitals, extended system
scales as n^5
Acc'y:
食fｰｱ3, 食rｱ4, 食dissｱ7, 食atom-22, 食ﾝｱ11
l+0.01, aｱ1
v+6.0% w/ 6-31G*, +6.7% w/ 6-31G**, +5.3% w/ 6-311G**
MP4 - 4th order Moller-Plesset
Cons: scales as n^7
CCD - Coupled Cluster, doubles
Basis: double excitations "coupled" to reference configuration
Pros:
includes correlation
complete to order for double excitations
CCSD - Coupled Cluster, singles, doubles
Basis: single & double excitations "coupled" to reference configuration
Pros:
includes correlation
complete to order for single and double excitations
includes most quadruple & hextuple excitation effects
scales as n^6
CCSD(T) - Coupled Cluster, singles, doubles with approximate triples
Basis:
single & double excitations "coupled" to reference configuration
triples contributions perturbatively
Pros:
includes correlation
size consistent
popular for high level method
less spin contamination
transition metals
O3 frequencies
Cons:
overbinds CO2
not variational
greater BSSE
scales as n^5-7
CCSDT - Coupled Cluster, singles, doubles, & triples
Basis: single, double, & triple excitations "coupled" to reference configuration
Cons: scales as n^8
CI - Configuration Interaction
Basis:
HF reference determinant/e- configuration
expand reference configuration into series of excited configurations
interaction with excited configurations used as many e- basis set
Pros:
dynamic correlation
more flexible wavefunctions
Cons: truncated forms not size consistent
CIS -
Basis:
CI w/ single excitation configurations only
HF reference determinant
Pros: electronic spectra
Cons:
no e- correlation
not size consistent
excited state properties
potential energy surfaces
CID -
Basis:
CI w/ double excitation configurations only
HF reference determinant
Cons: not size consistent
CISD = SDCI -
Basis:
CI w/ single and double excitation configurations
HF reference determinant
Pros:
includes correlation
single & double excitations
variational
Cons:
not size consistent
scales as n^6
QCISD(T) - Quadratic Configuration Interaction, singles, doubles, approximate triples
Basis:
CI w/ single and double excitation configurations
HF reference determinant
terms added to CI to make size consistent
Pros: size consistent
Cons: scales as n^7
Acc'y:
l+0.01, aｱ1
v+5%
MRCI - Multi-Reference Configuration Interaction
Basis:
more than 1 reference determinant/e- configuration
interaction w/ excited configurations used as many e- basis set
Pros:
a multireference method
biradicals
Cons: scales as n^8
MR-CISD -
Basis:
more than 1 reference determinant/e- configurations
CI w/ single & double excited configurations
Pros: a multireference method
Cons: not dissociation consistent
MCSCF - Multi-Configuration SCF
Basis:
more than 1 reference determinant/e- configurations
both, configuration and orbital, coefficients optimized
a limited type of CI
Pros: a multireference method
CASSCF - Complete Active Space SCF
Basis:
full CI "in active space"
select # of e- and orbitals
Pros:
includes correlation
a multireference method
Cons: selection of active space
GVB - Generalized Valence Bond
Basis:
limited type of MCSCF/a multireference method
use excitations w/i e- pairs
Pros: dissociation consistent
GVB-PP - GVB, Perfect Pairs
Basis:
GVB
CI restricted to doubles
GVB-RCI - GVB Restricted Configuration Interaction
Basis:
GVB
CI w/ singles and doubles
QMC - Quantum Monte Carlo
Basis:
correlated basis functions
evaluate integrals numerically numerical via Monte Carlo
Pros:
includes correlation
most accurate
Cons: long calculation
Basis Sets
STO-3G -
Basis:
minimal basis set
Slater type orbitals
3 Gaussian to fit exponential
Pros: Pauling point
Atoms:
H, He
Li - Ne
Na - Ar
K - Kr
Rb - Xe
Accｹy:
食dissｱ3, 食ﾝｱ5
Dｱ0.5
lｱ0.09, aｱ5, dｱ8
STO-3G* -
Basis:
STO-3G
set of polarizing d-functions (5D) added to heavy atoms
Atoms:
Na - Ar
K - Kr
Rb - Xe
Accｹy:
3-21G -
Basis:
Pople style (Gaussian Type Orbital) basis set
Valence Double Zeta:
3 Gaussians function primitives for each core basis functions
Split Valence:
2 Gaussians with linked coefficients for each inner valence e-
1 "uncontracted" (variable) primitive for each outer valence e-
Pros: Gaussians reduce 4-body mathematical problem to 2-body problem
Cons:
cis vs trans acrolein
amine N too flat
M-O short
adsorption energy high
Atoms:
H, He
Li - Ne
Na - Ar
K - Kr
Rb - Xe
Accｹy:
食fｰｱ7, 食rｱ15, 食diss-30, 食ﾝｱ4
Dｱ0.4
lｱ0.06, aｱ3, dｱ20
v+10.9%
3-21G* = 3-21G(d) -
Basis:
3-21G
set of polarizing d-functions (6D) added to atoms past 1st row
Atoms:
Na - Ar
K - Kr
Rb - Xe
Accｹy:
3-21+G -
Atoms:
Li - Ne
Na - Ar
K - Kr
Rb - Xe
3-21++G* -
Atoms:
H, He
Li - Ne
Na - Ar
K - Kr
Rb - Xe
4-21G -
Atoms:
H, He
Li - Ne
4-21G* -
Basis:
4-21G
set of polarized d-functions (6D) added to heavy atoms
4-21G** -
4-31G -
Atoms:
H - He
Li - Ne
P - Cl
Accｹy: lｱ0.04
4-31G* -
Basis:
4-31G
set of polarizing d-functions (6D) added to heavy atoms
4-31G** -
6-21G -
Atoms:
H - He
Li - Ne
Na - Ar
6-21G* -
6-21G** -
6-31G -
Basis:
Pople style (GTO) basis set
Valence Double Zeta:
6 Gaussian function primitives for each core basis function
Split-valence:
3 Gaussian primitives (linked coefficients) for each inner valence basis function
1 "uncontracted" (variable) primitive for each outer
Pros:
Gaussians reduce 4-body mathematical problem to 2-body problem
popular
Atoms:
H - He
Li - Ne
Na - Ar
6-31+G -
Pros:
negative ions
Rydberg states
less BSSE w/ diffuse (3rd) primitive Gaussian
Cons: convergence difficult w/ diffuse
6-31++G -
6-31G* = 6-31G(d) -
Basis:
6-31G
set of polarizing d-functions (6D) added to heavy atoms
Pros:
anomeric effect
accuracy
most popular, widely used/validated
Atoms:
H, He
Li - Ne
Na - Ar
Accｹy:
食fｰｱ4, 食rｱ7, 食diss-20, 食atom-120, 食ﾝｱ7
Dｱ0.5
lｱ0.03, aｱ1
v+11.7%
6-31G** = 6-31G(d,p) -
Basis:
6-31G*
set of polarizing p-functions added to H, too
Pros: less BSSE w/ diffuse (3rd) primitive Gaussians
Cons: convergence w/ diffuse (3rd) primitive Gaussians
Accｹy: v+11.2%
6-31+G* = 6-31+G(d) - Augmented 6-31G*
Basis:
6-31G*
set of diffuse s- and diffuse p-functions added to heavy atoms
6-31++G* = 6-31++G(d) - Augmented 6-31+G*
Basis:
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)-
6-311G -
Basis:
Pople style (GTO) basis set
Valence Triple Zeta:
6 Gaussian primitives for each core basis functions
Triple split valence:
3 primitives (linked coefficients) for each inner valence basis function
1 uncontracted primitive for 2nd layer of valence
1 uncontracted primitive for outer layer of valence
Cons: less flexible than real triple-zeta
Accｹy: v+10.5%
6-311G* = 6-311G(d) -
Basis:
6-311G
set of polarizing d-functions (5D) added to heavy atoms
Atoms:
H - He
Li - Ne
Na - Ar
6-311G** = 6-311G(d,p) -
Basis:
6-311G*
set of polarizing p-functions added to H, too
Accｹy: v+10.5%
6-311+G** -
6-311+G(3df,2p) -
Basis:
6-311G
diffuse s- and p-functions added to heavy atoms
3 d- and 1 polarizing f-function added to heavy atoms
2 polarizing p-functions added to H
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
Basis:
correlation consistent basis set
Valence Triple Zeta
set of polarizing d-functions (5D) and f-functions added to heavy atoms
Pros: CH4 - CH4 binding
Atoms:
H-He
B-Ne
Al-Ar
cc-pVTZ+ -
Basis: add diffuse functions
Atoms:
H
C-F
Si-Cl
cc-pVTZ++ -
cc-pVQZ - Correlation Consistent, polarized Valence Quadruple Zeta
Basis:
correlation consistent basis set
Valence Quadruple Zeta
cc-pV5Z - Correlation Consistent, polarized Valence Quintuple Zeta
Basis:
correlation consistent basis set
Valence Quintuple Zeta
MIN -
Basis:
minimal basis set
numeric
Pros: DFT
Atoms: not limited to set
DN - Double Numeric
Basis:
Double Zeta
numeric basis set
exact numerical function from spherical atom
DND -
Basis:
Double Zeta
numeric basis set
set of polarizing functions (p- and d-) on heavy atoms
Pros: more accurate than 6-31G*
Atoms: not limited
DNP - Double Numeric with Polarization
Basis:
Double Zeta
numeric basis set
set of polarizing functions (s-, p-, d-) on all atoms
Pros:
DFT
more accurate than 6-31G**
speed
Cons: sensitive to orientation
Atoms: not limited
DZ94 - Double Zeta
Basis:
Double Zeta
contracted Gaussians, optimized for (local) DFT
Atoms:
H - He
Li - Ne
Na - Ar
K - Kr
Rb - Xe
DZ94P - Double Zeta with Polarization
Basis:
DZ94
polarization functions (1 angular momentum # higher than valence) added
Atoms:
H - He
Li - Ne
Na - Ar
K - Kr
Rb - Xe
DZV - Double Zeta Valence
Basis:
Dunning/Hay & Binning/Curtiss
Valence Double Zeta
Atoms:
H - He
Li - Ne
Al - Ar
Ga - Kr
DZVP - Double Zeta Valence with Polarization
Basis:
Valence Double Zeta
contracted Gaussians, optimized for (local) DFT
(~ 6-41G* ?)
polarization d-functions added to heavy atoms
Atoms:
H - He
Li - Ne
Na - Ar
K - Kr
Rb - Xe
DZVP2 -
Basis:
DZVP
polarization functions added to H, too
Atoms:
H - He
Li - Ne
Al -Ar
Sc - Zn
D95 -
Atoms:
H
Li - Ne
Al - Cl
D95* -
Basis:
D95
set of polarizing functions (6D) added to heavies
D95V -
Atoms:
H
Li - Ne
D95V* -
Basis:
D95V
set of polarizing functions (6D) added to heavies
TZ94 - Triple Zeta
Basis:
Triple Zeta
contracted Gaussians, optimized for (local) DFT
Atoms:
H - He
Li - Ne
Na - Ar
K - Kr
Rb - Xe
TZ94P - Triple Zeta with Polarization
Atoms:
H - He
Li - Ne
Na - Ar
K - Kr
Rb - Xe
TZV -
Basis:
Triple Zeta Valence
6-311G & McLean/Chandler
Gaussian primitives
Atoms:
Li - Ne
Na - Ar
K - Zn
TZVP - Triple Zeta Valence with Polarization
Basis:
Triple Zeta Valence
(~ 6-311G* ?)
optimized for (local) DFT
Atoms:
H - He
B - Ne
Al - Ar
LAV1S ( = LANL1MB ?) -
Basis:
Los Alamos (Hay-Wadt) Effective Core Potentials
Minimal basis set: Valence only
STO-3G for non ECP atoms
Atoms:
Na - Ar
K - Kr
Rb - Xe
Cs - La, Hf - Bi
LAV2D (= LANL1DZ ? LANL2DZ ?) -
Basis:
Los Alamos (Hay-Wadt) ECP's
Double Zeta: Valence only
D95V basis for non ECP's
Atoms:
Na - Ar
K - Kr
Rb - Xe
Cs - La, Hf - Bi
LAV2P -
Basis:
Los Alamos Effective Core Potentials
Double Zeta: Valence only
6-31G basis for non ECP's
Atoms:
Na - Ar
K - Kr
Rb - Xe
Cs - La, Hf - Bi
LAV3D -
Basis:
Los Alamos Effective Core Potentials
Triple Zeta: Valence only
D95 basis for non ECP's
Atoms:
Na - Ar
K - Kr
Rb - Xe
Cs - La, Hf - Bi
LAV3P -
Basis:
Los Alamos Effective Core Potentials
Triple Zeta: Valence only
pseudospectral
6-31G for non ECP's
Atoms:
Na - Ar
K - Kr
Rb - Xe
Cs - La, Hf - Bi
LACVD -
Basis:
Los Alamos Effective Core Potentials
Double Zeta: Valence and outermost core
D95 basis for non ECP's
Atoms:
K - Cu
Rb - Ag
Cs - La, Hf - Au
LACVP -
Basis:
Los Alamos Effective Core Potentials
Double Zeta: Valence and outermost core
6-31G basis for non ECP's
pseudospectral
Pros:
correlated wavefunctions
charge transfer effects
3rd row & higher elements
d(0) metals
Atoms:
K - Cu
Rb - Ag
Cs - La, Hf - Au
LACV3P -
Basis:
Los Alamos Effective Core Potentials
Triple Zeta: Valence & outermost core
6-311G for non ECP's
pseudospectral
Pros:
atomic state splittings
correlated wavefunctions
3rd row & higher elements
d(0) metals
charge transfer
Atoms:
K - Cu
Rb - Ag
Cs - La, Hf - Au
LACV3P++ -
Basis:
LACV3P
diffuse added to all atoms, including H & He
Pros:
low spin M(0), late 1st row transition metal complexes
anions
CEP = SBK - Stevens-Bash-Krauss-Jasien-Cundari
Basis:
Effective Core Potentials
Double Zeta: valence only
-31G splits
Atoms:
Li - Ne
Na - Ar
K - Kr
Rb - Xe
Cs - Rn
CEP-4 -
CEP-31 -
CEP-121 -
HW - Hay - Wadt ECP's
Basis:
Double Zeta: valence only
-21 splits
Atoms:
Na - Ar
K - Kr
Rb - Xe
MSV -
Atoms:
H - He
Li - Ne
Na - Ar
K - Ru, Pd - Xe
MSV* -
Basis:
MSV
set of polarizing d-functions (5D) added
******************************************************
OPTIMIZATION METHODS
Energy Minimizations
Simplest
Consistently moves downhill
Rapid at first, can oscillate near minimum
No test for convergence
Simplex method
Sequential Univariate
Change one coordinate at a time
Fit parabola to initial point plus 2 displacements
Adjust individual coordinate to minimum of parabola
Problem with long narrow valley
1 + 3N x m evaluations
1st Derivative/Gradient Methods
Order of magnitude faster
Convergence to stationary points (minima, saddle, maxima)
Steepest Descent
Consistently moves downhill
Can oscillate near minimum
In effect approximates Hessian w/ unit matrix
Conjugate Gradient/Fletcher-Reeves
Faster than Steepest Descent (& BDNR for PP)
Uses gradients as if updating Hessian
Fast convergence when far from stationary point
Slow to converge for floppy
May oscillate near minimum
NLLSQ (NonLinear Least Squares)
Nearest stationary point
Not on shoulder
Modified Fletcher-Powell
Two displacements along each coordinate
Fit quadratic surface w/ interactions (in effect calculating g & elements of H numerically)
Two displacements along downhill direction
Fit parabola to downhill direction
Displace atoms
2N + 4 + m x (N + 3) evaluations
Second Derivative/Hessian Methods
Assume quadratic gradient surface: f(E, g, H)
Newton-Raphson
Calculate Hessian matrix directly at each step
Augmented Hessian for transition state
Quasi-Newton
Estimate Hessian (Inverse Hessian/Greenｹs Function)
Calculate E, g
Update Hessian
Move to stationary point of model surface
N+1 steps, but each one longer
Block Diagonal Newton-Raphson
Guesses Hessian
Unit matrix for cartesian, better for internal coordinate
Better convergence near minimum
DFP (Davidson-Fletcher-Powell)
Better for transition states
Murtagh-Sargent
BFGS (Broyden-Fletcher-Goldfarb-Shanno)
Faster than N-R
Better for optimizations
EF (Eigenvector Following)
Faster than NLLSQ, Sigma, BFGS
May fail with dummy atoms
Analytical Gradients
Analytical rather than finite differences
More accurate
Single Hessian Calculation
Hessian not recomputed after 1st step
Rapid for nearest stationary point
Fails if initial gradient large
Sigma
Gradient Norm Squared/Powell
Refine N-R geometry
Stationary point including shoulder
**********************************************
ACRONYMS & DEFINITIONS
AIM ｭ (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.
AO ｭ (Atomic Orbital) An orbital described by wavefunction for a single electron centered on a single atom.
AOM ｭ (Angular Overlap Model)
AM1 ｭ (Austin Model 1) Dewar's NDDO semiempirical parameterization.
ASE ｭ (Aromatic Stabilization Energy)
BAC-MP4 ｭ (Bond Additive Corrections to energies from Mller-Plesset 4th order perturbation theory) empirical corrections to calculated energy based (exponentially) on bond lengths.
Bader's analysis ｭ see AIM
Basis Set ｭ finite set of functions used to approximately express the Molecular Orbital wavefunction(s) of system, normally atom centered, consisting of AOs differing in local angular momentum for each atom.
BCUT ｭ (Burden CAS University of Texas) topological molecular similarity index of Burden.
BDE ｭ (Bond Dissociation Energy)
BSSE ｭ (Basis Set Superposition Error) error introduced when the energy of two molecules modeled together is lower than the sum of the energies when modeled separately, because more basis sets are available for each fragment (more degrees of freedom) during the calculation. Minimal basis sets can have less BSSE because only diffuse functions can span a to b. A particular problem for binding energies of weakly bonded molecular complexes, less with more complete basis sets.
BLYP ｭ (Becke-Lee-Yang-Parr)
bohr - One atomic unit of distance, equal to 0.5292 ﾅ.
CADPAC ｭ (Cambridge Analytical Derivatives PACkage)
CAS ｭ (Complete Active Space)
CASPT ｭ (Complete Active Space Perturbation Theory)
CASSCF ｭ (Complete Active Space Self-Consistent Field) popular variant of the MCSCF method, using a specific choice of configurations. One selects a set of active orbitals and active electrons, then forms all of the configurations possible by placing the active electrons in the active orbitals, consistent with the proper spin and space symmetry requirements. Essentially equivalent to the FORS method.
CBS-QCI ｭ (Complete Basis Set Quadratic Configuration Interaction) alternative extrapolation algorithm to complete basis set.
CC ｭ (Coupled Cluster) A perturbation theory of electron correlation with an excited configuration that is "coupled" to the reference configuration. Complete to infinite order, but only for a subset of possible excitations (doubles, for CCD). Newer than CI.
CCD ｭ (Coupled Cluster, Doubles only.) Complete to infinite order for doubles excitations.
CCSD ｭ (Coupled Cluster, Singles and Doubles only.) Complete to order for singles & doubles excitations.
CCSD(T) ｭ (Coupled Cluster, Singles and Doubles with Triples treated approximately.) Size consistent. 食diss ｱ 1.0 kcal/mol
CCSDT ｭ (Coupled Cluster, Singles, Doubles and Triples)
CCSS ｭ (Correlated Capped Small Systems) Special case of IMOMO. See Truhlar's and Hass's work.
CEPA ｭ (Coupled Electron Pair Approximation)
CFF ｭ (Consistent Force Field) Class II force field based on ab initio data developed by Biosym Consortium/MSI.
CFMM ｭ (Continuous Fast Multipole Method) linear scaling method for matrix formation for DFT.
CFSE ｭ (Crystal Field Stabilization Energy)
CHA ｭ (Chemical Hamiltonian Approach) excludes BSSE effects from wavefunction w/ BSSE free Hamiltonian.
CHF ｭ (Coupled Hartree-Fock method)
CHELP ｭ (CHarges from Electrostatic Potential) an attempt to obtain atomic charges by fitting the electrostatic potential to a set of atomic point charges. The key component to the CHELP method is that it is non-iterative, rather using a Lagrangian multiplier method.
chemical shift tensor ｭ representation of the chemical shift. 3x3 matrix field felt in a direction induced by current due to applied field in b direction.
CI ｭ (Configuration Interaction) The simplest variational approach to incorporate dynamic electron correlation. Combination of the Hartree-Fock configuration (Slater determinant) and a large set of other configurations is used as a many e- basis set. The expansion coefficients are determined (in principal) by diagonalizing the Hamiltonian matrix and variationally minimizing the total energy of the CI wavefunction. Not size consistent.
CID ｭ (Configuration Interaction, Doubles substitution only) post-Hartree-Fock method that involves configuration interaction where the included configurations are the Hartree-Fock configuration and all configurations derived from doubles substitution.
CIDEP ｭ (Chemically Induced Dynamic Electron Polarization)
CIDNP ｭ (Chemically Induced Dynamic Nuclear Polarization)
CIS ｭ (Configuration Interaction with Singles excitations) simplest method for calculating electronically excited states; limited to singly-excited states. Contains no e- correlation and has no effect on the ground state (Hartree-Fock) energy.
CISD ｭ (Configuration Interaction, Singles and Doubles substitution only) post-Hartree-Fock method that involves configuration interaction where the included configurations are the Hartree-Fock configuration and all configuration derived from singles and doubles substitution. Comparable to MP2.
CKFF ｭ (Cotton-Kraihanzel Force Field)
CNDO ｭ (Complete Neglect of Differential Overlap) The simplest of the semi-empirical methods. The principle feature is the total neglect of overlap between different orbitals. In other words, the overlap matrix S is the unit matrix. The only two-electron integrals kept are those where electron 1 is in just one orbital and electron 2 is in just one orbital. Like all semiempirical methods the integrals are evaluated empirically.
Combinatorial Chemistry ｭ testing a large number of related compounds (as a mixture?) to find a compound that is active.
CoMFA ｭ (Comparative Molecular Field Analysis) technique used to establish 3-D similarity of molecular structure in relation to a target property.
COMPASS ｭ (Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies) Molecular Mechanics force field derived from Class II force field, but optimized for condensed phase properties.
contraction ｭ the particular choice of scheme for generating the linear combinations of Gaussian functions that constitute a contracted basis set. A "generally-contracted" basis set is one in which each primitive is used in many basis functions. A "segmented" basis set, in contrast, is one in which each primitive is used in only one (or maybe two) contracted function.
COOP ｭ (Crystal Overlap pOPulation)
Correspondence Principle ｭ classical mechanics becomes a special case of quantum mechanics at larger masses/scale.
COSMO ｭ (Conductor-Like Screening Model) implicit solvation model of Andreas Klamt. Considers macroscopic dielectric continuum around solvent accessible surface of solute. Less sensitive to outlying charges then PCM.
COSMO-RS ｭ (COSMO for Realistic Solvents) describes solute and solvent on the same footing. Allows for realistic calculations of fluid thermodynamics: partition coefficients, solubilities, activity coefficients, vapor pressures, & phase diagrams.
Coulomb integral ｭ 1-center, 2 electron integral in Hamiltonian. Represents localized contribution of e- pair (in A+B- or A-B+) to bonding.
CP ｭ (Counter Poise) correction method for BSSE based on assumption of additivity of effects caused by BSSE on intermolecular interactions. The BSSE is approximated as the energy difference between (1) an isolated fragment and (2) t fragment accompanied by the basis functions, but not the atoms, of its companion fragment(s).
CPHF ｭ (Coupled Perturbed Hartree-Fock )
CVFF ｭ (Consistent Valence Force Field)
Density Matrix ｭ
DFT ｭ (Density Functional Theory) ab initio electronic method from solid state physics. Tries to find best approximate functional to calculate energy from e- density. Scales as 2nd power times a large number. Static correlation built in. Not variational. Believed to be size consistent.
diffuse ｭ refers to basis functions that are typically of low angular momentum (unlike polarization functions) but with much smaller exponents, so that they spread more thinly over space. Usually essential for calculations involving negative ions or Rydberg states.
DIIS ｭ (Direct Inversion in the Iterative Space) Pulay's extremely efficient, extrapolation procedure, to accelerate the convergence of the SCF in Hartree-Fock calculations.
DISCO ｭ
DOS ｭ (Density Of States)
dynamic correlation ｭ All the correlation energy or correlation effect that is not considered "nondynamic" or "static." Essential for dispersion interactions.
DZ ｭ (Double-Zeta) A basis set for which there are twice as many basis functions as are minimally necessary. "Zeta" (Greek letter z) is the usual name for the exponent that characterizes a Gaussian function.
DZP ｭ (Double-Zeta with Polarization functions added) A polarization set generally has an angular momentum one unit higher than the highest valence function. So a polarization set on carbon is a set of d-functions.
ECP = pseudopotential ｭ (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.
EFFF ｭ (Energy Factored Force Field)
EHT ｭ (Extended Hckel Theory)
electron correlation ｭ explicitly considering the effect of the interactions of specific e- pairs, rather than the effect each e- feels from the average of all the other e-. High correlation effects for e- rich systems, transition states, "unusual" coordination numbers, no unique Lewis structure, condensed multiple bonds, radicals, & biradicals.
Embedded Cluster ｭ Sauer's (and Teunissen's and others) approach to modeling large/extended systems, using a high accuracy (QM) method for the important site, and a less accurate (MM) method for the environment. Subtract out duplicated overlap term, in case of extended system. See also IMOMM, and CCSS.
ESFF ｭ (Extensible & Systematic Force Field) Rule based force field designed for generality rather than accuracy by Biosym/MSI.
ESP ｭ (ElectroStatic Potential) The electrical potential due to the nuclei and electrons in the molecule, as experienced by a test charge.
exchange energy ｭ Also called "exchange correlation energy." The energy associated with the correlation among the positions of electrons of like spin. This is included in Hartree-Fock calculations.
Exchange integral ｭ integral in Hamiltonian centered on 2 atoms. Corresponds to covalent bond term.
FMO ｭ (Frontier Molecular Orbital Theory) reaction controlled by interaction and overlap (energy, symmetry, accessibility) of frontier MO. Fukui calculation of weighted contributions, but dominated by HOMO for electrophilic, LUMO for nucleophilic susceptibility, closest energy for free radical superdelocalizability.
Fock Matrix ｭ 1 particle/e- Hamiltonian; matrix of 1 e-, 2 e- Coulomb, & 2 e- Exchange integrals in total energy
Fock Operator ｭ replaces the Hamiltonian Operator in the Schrdinger equation for a spin orbital/single electron in a mean field of the other electrons
FORS ｭ (Fully Optimized Reaction Space) The FORS method, first proposed by Ruedenberg and coworkers, is essentially equivalent to the CASSCF method, except for the implementation of the MCSCF.
G1, G2 ｭ (Gaussian 1 theory, Gaussian 2 theory) empirical algorithm to extrapolate to complete basis set and full correlation (beyond MP2/6-31G**) from combination of lower level calculations: HF/6-31G(d) frequencies; MP2/6-311G(dp) geometries; single point energies of MP4SDTQ w/ 6-311G**, 6-311+G** & 6-311G**(2df) and QCISD(T)/6-311G**. Practical up to ~7 heavy atoms. Cons: Cl, F BDE's. 食f ｱ 1.93 kcal/mol
G3 ｭ (Gaussian 3 "slightly empirical" theory) extension of G2, add systematic correction for each paired e- (3.3 mHa) & each unpaired e- (3.1 mHa). 食f ｱ 1.45 kcal/mol
Gaussians ｭ functions frequently used as primitive functions to expand total wave function. Typically defined with Cartesian coordinates w/ respect to a point in space.
GAPT ｭ (Generalized Atomic Polar Tensor) A method for determining atomic charge on the basis of dipole moment derivatives.
GGA ｭ (Generalized Gradient Approximation) Corrects local density approximation by including a functional of the density gradient (i.e., f[grad rho]) in addition to the local functional. Favors greater densities and inhomogeneity, overcomes LDA tendency to overbind. Uses scale factors from density & 1st derivative of density. Adds ~20% to compute time.
ghost function ｭ A basis function that is not accompanied by an atomic nucleus, usually for counterpoise corrections for BSSE.
GIAO ｭ (Gauge Independent Atomic Orbitals) Ditchfield's method for canceling out the arbitrariness of the choice of origin & form (gauge) of the vector potential used to introduce the magnetic field in the Hamiltonian when calculating chemical shielding and chemical shift tensor. An exponential term containing the vector potential is included with each atomic orbital. Originally developed based on Hartree-Fock, improved by Pulay w/ DFT to be faster, also used w/MP2 & CCSD. Pros: less basis set dependence than IGAIM
Green's Function ｭ inverse of the Hessian Matrix.
GTO ｭ (Gaussian-Type Orbital) Basis function consisting of a Gaussian function, i.e., exp(-r2), multiplied by an angular function. If the angular function is "Cartesian", there are six d-functions, ten f-functions, etc. (6d, 10f). If the angular function is spherical, there will the usual number of functions (5d, 7f).
GUGA ｭ (Graphical Unitary Group Approximation)
GVB ｭ (Generalized Valence Bond) Bill Goddard's "laid back Southern California wavefunctions." Equivalent to MCSCF correlation treatment: 2 configurations used to represent each e- pair and solved for 2 associated orthogonal functions. Excitations are taken within an electron pair but not between orbitals in different pairs Dissociation-consistent. If restricted to doubles, is called "perfect pairing" (GVB-PP). If includes both singles and doubles, is called "restricted configuration interaction" (GVB-RCI).
Hamiltonian ｭ Matrix of bare nucleus, 0 e- Fock Matrix. Matrix that operates on wavefunction to calculate the energy in Schrdingers equation.
hartree ｭ One atomic unit of energy, equal to 2625.5 kJ/mol, 627.5 kcal/mol, 27.211 eV, and 219474.6 cm-1.
Hessian ｭ Matrix of mass normalized 2nd derivatives of energy with respect to nuclear displacement in Cartesian coordinates. Diagonalized to determine normal modes & calculate vibrational frequencies.
HF ｭ (Hartree-Fock) Named after the developers of the most widely practiced method for solving the Schrdinger Equation for multi-electronic systems. The Hartree-Fock approximation (sometimes called the Self-Consistent Field Approximation) assumes a single (Slater) determinant wavefunction, or in other terms, the standard molecular orbital model. Approximates the molecular, all e- wavefunction as product of single e- wavefunctions, and approximate molecular wavefunctions as LCAO. Orbitals that contain e- are occupied, those that are vacant are called "virtual." The orbital for each electron is determined in the average field of the other electrons, and iterated until self-consistency is achieved. Uses exact form of the (electronic) Hamiltonian Operator in Schrdingerｹs equation, and tries to find the best approximate wavefunction. Scales as n^3-4.
HMO ｭ (Hckel Molecular Orbital theory)
HOMO ｭ (Highest Occupied Molecular Orbital) The occupied molecular orbital having the greatest energy. In Frontier Molecular Orbital theory the HOMO plays a significant role in determining the course and barrier to reactions. The energy of this orbital approximates the ionization energy of the molecule by Koopman's Theorem.
HONDO ｭ
IEHT ｭ (Iterative Extended Hckel Theory)
IEPA ｭ (Independent Electron Pair Approximation) An alternative method to the CI approach for obtaining electron correlation. Assumes the correlation energy is pair-wise additive: the correlation energy for each pair of electrons is obtained independently of all other electrons and then summed up. The method was developed by Sinanoglu (who called it Many-Electron Theory or MET) and Nesbet (who called it Bethe-Goldstone Theory).
IGLO ｭ (Individual Gauge for Localized Orbitals) Kutzelnigg & Schiendler's method for canceling out the arbitrariness of the choice of origin & form (gauge) of the vector potential used to introduce the magnetic field in the Hamiltonian when calculating chemical shielding & chemical shift tensors at nuclei. An exponential term containing the vector potential premultiplies MOs that have been localized in real space. Faster than HF based GIAO
IMOMM ｭ (Integrated Molecular Orbital & Molecular Mechanics) Morokuma's method to extrapolate to high level calculation on large systems by integrating addition of 職 between large system and small model systems calculated at low level (MM), to the energy of the small model calculated at a high level (MO).
IMOMO ｭ (Integrated Molecular Orbital & Molecular Orbital) same as IMOMM with high (ab initio) and low level (semiempirical) MO calculations.
INDO ｭ (Intermediate Neglect of Differential Overlap) A semiempirical method closely related to the CNDO method, where all terms of the Fock matrix used in CNDO are included, but the restriction that the monocentric two-electron integrals all be equal is lifted.
internal coordinates ｭ Bond lengths, bond angles, and dihedral (torsional) angles; sometimes called "natural coordinates."
IRC ｭ (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.)
isodesmic ｭ a chemical reaction that conserves types of chemical bond. Due to better cancellation of systematic errors, energy changes computed using such reactions are expected to be more accurate than those computed using reactions that do not conserve bond types.
isogyric ｭ a chemical reaction that conserves net spin. Due to better cancellation of systematic errors, energy changes computed using such reactions are expected to be more accurate than those computed using reactions that do not conserve spin.
Koopman's Theorem ｭ the ionization potential can be approximated by the energy of the HOMO. Errors from neglect of e- correlation & e- relaxation tend to cancel for IP, but compound for trying to approximate EA from LUMO energy.
LCAO ｭ (Linear Combination of Atomic Orbitals) Molecular orbitals are usually constructed as a linear combination of atomic orbitals. The coefficients in this expansion are determined by solving the Schrdinger equation, typically in the Hartree-Fock approximation.
LDA = LSDA ｭ (Local Density/Spin-Density Approximation) A DFT method involving only local functionals: those that depend only upon the value of the density, f[rho]: no dependence upon the gradient of the electron density.
level shifting ｭ method to avoid oscillations during SCF convergence by artificially raising the energies of the virtual orbitals to separate the different states.
LFER ｭ (Linear Free Energy Relationship)
LNDO ｭ (Local Neglect of Differential Overlap)
LORG ｭ (Localized Orbitals, Local Origin) Hansen & Bouman Gauge invariant method for calculating chemical shielding & chemical shift tensors: expanding angular momentum terms relative to local origin for each orbital so no reference to gauge origin. Similar to IGLO.
LST ｭ (Linear Synchronous Transit) An interpolative method to provide an initial guess for a transition state. Assumes each atom position in the transition state is in a direct line between its position in the reactants and its position in the products.
LUMO ｭ (Lowest Unoccupied Molecular Orbital) The unoccupied molecular orbital having the lowest energy. In Frontier Molecular Orbital theory the LUMO plays a significant role in determining the course and barrier to reactions. The energy of the LUMO is a poor approximation of the EA.
Madelung Potential ｭ a set of point charges used to represent a solid continuum.
MBPT = Mller-Plesset Perturbation Theory ｭ (Many Body Perturbation Theory)
MC ｭ (Monte Carlo) method of sampling based on generating random numbers.
MCCM ｭ (Multi Coefficient Correction Method) Truhlar's method to scale each component of the correlation energy to extrapolate to full correlation: HF, MP2, and MP4 terms.
MCPF ｭ (Modified Couple Pair Functional)
MCSCF ｭ (MultiConfiguration Self-Consistent Field) A limited type of CI. A simple extension of the SCF approach to include non-dynamic electron correlation, with the added feature of orbital optimization. A number of configurations are chosen in some manner, then both the expansion coefficients and the orbital coefficients are optimized.
MD ｭ (Molecular Dynamics) method of sampling geometries based on Newtonian laws of motion.
MEP ｭ (Molecular Electrostatic Potential)
MERP ｭ (Minimum Energy Reaction Path)
MINDO ｭ (Modified Intermediate Neglect of Differential Overlap) Refers to the parametrization set (and computer code) developed by the Dewar group for performing INDO calculations. The most useful of the MINDO series is MINDO/3.
Minimal Basis Set ｭ The smallest # of functions needed to hold all electrons and still be spherical. Commonly refers to STO-3G.
MM ｭ (Molecular Mechanics) classical description of molecules as atoms held together by spring-like bonds. Chemical "Hamiltonian" based on force constants.
MM2 ｭ (Molecular Mechanics, Allinger Force Field version 2) one of the earliest, and probably the best known and tested Molecular Mechanics force field for organic molecules.
MMFF ｭ (Merck Molecular Force Field)
MMP2 ｭ (Molecular Mechanics, Allinger Force Field version 2 with Pi electrons handled quantum mechanically). Pi bond stretch calculated on the fly based on simple SCF bond order.
MM3 ｭ (Molecular Mechanics, Allinger Force Field version 3)
MNDO ｭ (Modified Neglect of Diatomic Overlap) Dewarｹs first parametrization of the NDDO semiempirical method. First incorporated into the MOPAC program.
MNDOC ｭ (Modified Neglect of Diatomic Overlap Correlated) Thielｹs version of MNDO which includes limited configuration interaction.
MNDO/d ｭ (MNDO with d-orbitals) Thiel's version of MNDO with extra set of orbitals for second row transition and main group elements.
MO ｭ (Molecular Orbital) An orbital described by the wavefunction for a single electron in a molecule, usually delocalized across the entire molecule. Usually, molecular orbitals are constructed as combinations of atomic orbitals.
MP2 ｭ (Mller-Plesset theory, 2nd order) Mller-Plesset developed the perturbative approximation to include electron correlation, using the Hartree-Fock wavefunction as the zeroth order wavefunction. MP2 refers to the second order energy correction. Comparable to CISD.
MP3 ｭ (Mller-Plesset Theory, 3rd order) A perturbative approximation for including electron correlation, using the Hartree-Fock wavefunction as the zeroth order wavefunction. MP3 refers to the third-order energy correction.
MP4 ｭ(Mller-Plesset Theory, 4th order) A perturbative approximation for including electron correlation, using the Hartree-Fock wavefunction as the zeroth order wavefunction. MP4 refers to the fourth order energy correction. MP4 as implemented in GAUSSIAN can be calculated using various configurations. For example, MP4SDQ means that all terms involving singles, doubles and quadruples configurations are included through fourth order.
MPA ｭ ( Mulliken Population Analysis)
MR ｭ (Multi-Reference)
MRCI ｭ (Multi-Reference Configuration Interaction) CI using more that one reference determinant, instead of the usual single Hartree-Fock reference (ie. the ground state wavefunction). Among multi-reference theories, MR-CISD (singles and doubles CI) is popular and high-level (but not dissociation consistent).
Mulliken Charges ｭ Charges are assigned to each atom from an electronic calculation, by arbitrarily attributing the e- density of the diagonal terms (single atom terms) to each atom, plus half of the e- density of each off-diagonal term for that atom. Very sensitive (<100%) to basis set.
NAO ｭ (Natural Atomic Orbital)
natural orbital ｭ those orbitals for which the first-order density matrix is diagonal; each will contain some non-integer number of electrons between 0 and 2. Usually discussed in the context of a correlated calculation. RHF calculations give molecular orbitals that are also natural orbitals. The NOs are the orbitals for which the CI expansion converges fastest. Particularly valuable in modeling organometallic complexes.
NEMD ｭ (Non Equilibrium Molecular Dynamics) MD w/ applied forces, such as shear.
NBO ｭ
NDDO ｭ (Neglect of Differential Diatomic Overlap) This semiempirical method that keeps all terms of the Fock matrix except those involving diatomic differential overlap: the only two-electron terms, are those where e- 1 is in one orbital on atom A and e- 2 is in one orbital on atom B.
NPA ｭ (Natural Population Analysis) A method for determining atomic charge distributions in a molecule. Based on creating atomic natural orbitals from the molecular orbitals, by finding eigenfunctions of atomic sub-blocks of the molecular density matrix, based on chemical concepts of bonds, lone pairs, etc. Fairly independent of basis set.
OPLS ｭ (Optimized Potentials for Liquid Simulations) force field for condensed (aqueous) simulations. Electrostatic only for H-bond, "Disappearing L-J" H-bond.
ONIOM ｭ (Our own N-layered Integrated molecular Orbital molecular Mechanics method) Morokuma's generalized method for modeling large/condensed systems. Model critical part of chemical system with a high accurate/level method, intermediate region with a less expensive method, outer region approximately.
orbital ｭ the wavefunction describing where an e- is in an atom or molecules. Usually an eigenfunction of a one-electron Hamiltonian, e.g., from Hartree-Fock theory. A spin orbital has an explicit spin and a spatial orbital does not. Orbitals are probably the most useful concept from quantum chemistry: one can think of an atom or molecule as having a set of orbitals that are filled with electrons (occupied) or vacant (unoccupied or "virtual").
Pauling point ｭ calculation that gives a good result because systematic, but opposed errors cancel out.
PCI ｭ (Parameterized Configuration Interaction) empirical scaling of contribution of dynamic correlation to bond strengths. See Siegbahn, Blomberg, et. al.
PCM ｭ (Polar Continuum Model) implicit solvation model of Tomasi.
PES ｭ (Potential Energy Surface) The 3N-6 (or 3N-5, for linear molecules) dimensional function that indicates how the molecule's energy depends upon its geometry.
Perturbation Theory ｭ approximation to include electron correlation, based on Taylor Series expansion of the Hartree-Fock wavefunction (1 e- Hamiltonian) as the 0th order wavefunction, for E in Schrdinger equation, truncated after n terms.
PM3 ｭ (Parametric Method number 3) A re-parameterized version of AM1 by Stewart.
PMO ｭ (Perturbation Molecular Orbital theory)
PNDO ｭ (Partial Neglect of Differential Overlap)
polarized ｭ basis set that includes functions that are of higher angular momentum than is minimally required. (Combination of p-orbitals added to the valence s-orbitals, or d-orbitals in addition to valence p-orbitals on carbon, for instance.) The added functions are often called "polarization functions." Polarization functions help to account for the fact that atoms within molecules are not spherical.
PPP ｭ (Pariser-Parr-Pople)
PRDDO ｭ (Partial Retention of Diatomic Differential Overlap)
primitive ｭ individual Gaussian functions used singly to produce a contracted basis function: a set of p-functions is three basis functions, but may be many primitives (3n, where there are n primitives in the cGTO).
PRISM ｭ (Polymer Reference Interaction Site Model) Adaptation of RISM theory for liquid polymers by Schweizer & Curro. Based on single chain conformational statistics and interaction potentials.
PUHF ｭ (spin-Projected UHF) An approximation to provide the energy that would result from a UHF calculation, if it did not suffer spin-contamination. The PUHF energy is usually lower than the UHF energy because the contributions of higher-multiplicity states, which usually have high energies, have been (approximately) subtracted.
QCI ｭ (Quadratic Configuration Interaction) CI method with terms added to confer size-consistency. An approximation to coupled-cluster theory.
QCISD(T) ｭ (Quadratic Configuration Interaction with all Single and Double excitations and perturbative inclusion of Triple excitations) post Hartree-Fock method. Similar results to QCISDT, used in G2. Scales as n^7.
QCPE ｭ (Quantum Chemistry Program Exchange) The Quantum Chemistry Program Exchange is a warehouse of chemistry computer codes. They have operated since 1962, providing a depository of what is now well over 600 different programs. QCPE can be contacted at QCPE Creative Arts Building 181 Indiana University Bloomington, IN 47405 USA telephone: (812)855-4784 fax: (812)855-5539 E-mail: qcpe@ucs.indiana.edu anonymous ftp access: qcpe6.hem.indiana.edu
QMC ｭ (Quantum Monte Carlo) ab initio method using explicitly correlated wave functions, and evaluating integrals numerically via Monte Carlo integration.
QSAR ｭ (Quantitative Structure-Activity Relationship) correlation developed between chemical structure and (biological) activity. Typically used to design drugs & predict activity.
QSPR ｭ (Quantitative Structure-Activity Relationship) correlation developed between chemical structure and (physical) properties. Typically used to design materials and predict properties.
RECP ｭ (Relativistic Effective Core Potential) Core electrons have been replaced by an effective potential that is based upon relativistic quantum calculations of the free atoms. Saves cost because of fewer explicit electrons and also includes some relativistic effects, especially the contraction of core s- and p-orbitals.
reference ｭ As in "single-reference" or "multi-reference," refers to the number of configurations (or Slater determinants) in the 0th-order description of the wavefunction. Most methods that don't begin with "MR," "MC," or "CAS" are single-reference methods
RHF ｭ (Restricted Hartree-Fock) The standard HF-SCF method where every spatial orbital is doubly occupied, 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.
RIS ｭ (Rotational Isomeric State) Build representative polymer models by sequentially considering rotational isomers of next bond along backbone to add each monomer. Statistical weights fitted to experiment.
RISM ｭ (Reference Interaction Site Model) Chandler & Anderson's theory of small molecule liquids based on interaction potentials.
ROHF ｭ (Restricted Open-shell Hartree-Fock) Restricted Hartree-Fock theory for open shell systems. a electron of spin up and b electron of spin down with a>b, and for electrons 1,2...b use the identical spatial form of the orbitals for the up and down spins. No spin contamination, but singly occupied orbital energies don't obey Koopman's Theorem.
RRKM ｭ (Rice-Ramsperger-Kassel-Marcus) kinetic theory for reaction rates
SAC ｭ (Scaling All-Correlation) empirical scaling of contribution of dynamic correlation to bond strengths. See Truhlar, Gordon, et. al.
SALC ｭ (Symmetry Adapted Linear Combinations)
SAM1 ｭ (Semiempirical Ab initio Method version 1) Andy Holderｹs extension of AM1 in Ampac by the addition of d-orbitals in the Hamiltonian. More theoretically consistent.
scaling ｭ 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.
SCEP ｭ (Self-Consistent Electron Pairs)
SCF ｭ (Self Consistent Field) The most widely practiced method for solving the Schrdinger Equation for multi-electron systems. The Self-Consistent Field Approximation (typically referred to as the Hartree-Fock Approximation, but also applies to most DFT and all MCSCF calculations) assumes a single determinant wavefunction, or in other terms, the standard molecular orbital model. The orbital (ie. the coefficients of the atomic basis functions in each molecular orbital) for each electron is adjusted in the average field of the other electrons, and iterated until self-consistency is achieved.
SCI-PCM ｭ (Self Consistent Isodensity surface Polar Continuum Model) enhanced solvation method of Tomasi.
SCREEP ｭ (Surface Charge Representation of the Electrostatic Embedding Potential) Truong's representation of effect of surrounding charge on closed surface around a cluster.
SCRF ｭ (Self-Consistent Reaction Field) an implicit solvation model.
semiempirical ｭ An approximate version of Hartree-Fock theory in which the more computationally expensive integrals are replaced by adjustable parameters, which are determined by fitting experimental atomic and molecular data. Different choices of parameterization lead to different specific theories (e.g., MNDO, AM1, PM3).
secular equation ｭ
SINDO ｭ (Symmetrically orthogonalized INDO method)
size-consistent ｭ a calculation that gives the same energy for two atoms (or molecular fragments) separated by a large distance as is obtained from summing the energies for the atoms (or molecular fragments) computed separately. So for a size-consistent method, the bond energy in N2 is 職diss = 2E(N) - E(N2). For a method that is not size-consistent, a "supermolecule" calculation with a big distance (e.g., 100 ﾅ) is required: 職diss = E(N......N) - E(N2).
Slater Determinant ｭ a trial guess for the electronic wavefunction in the form of a determinant describing the Hartree-Fock configuration
SOMO ｭ (Singly Occupied Molecular Orbital) for radicals
SOS-DFPT ｭ (Sum Over States Density Functional Perturbation Theory)
SPCA ｭ (Single Point Charge Extended) model of water.
SPC water ｭ (Simple Point Charge) MM model of water with charge, Van der Waals, and angle terms.
spin-contamination ｭ calculations with UHF wavefunctions that are not eigenfunctions of spin, and are contaminated by states of higher spin multiplicity (which usually raises the energy).
spin density ｭ The amount of excess alpha (over beta) spin. Identifies the location of unpaired electrons in radicals and for interpreting ESR experiments.
Spin Orbital ｭ single electron/particle function: eigenfunction to 1 particle Hamiltonian
Split Valence ｭ basis set that is more than minimal for the valence orbitals. At least VDZ. In Gaussian nomenclature, 3-21G is a split valence basis, and 6-311G is a triple-split-valence basis.
static correlation = nondynamic correlation ｭ The part of the correlation that is ascribed to the "multireference" nature of the problem at hand, i.e., to the qualitative failure of Hartree-Fock theory to describe the dissociation of a system into fragments. The best-known stable molecule with important nondynamic correlation is singlet methylene, CH2 ( 1A1), for which two configurations are important: (a1)2(b1)0 and (a1)0(b1)2. In many cases, the distinction between nondynamic and dynamic correlation is rather arbitrary. When nondynamic correlation is important, single-reference theories may be unreliable.
STO ｭ (Slater-Type Orbital) Basis function with an exponential radial function, i.e., exp(- zeta r). Also used to denote a fit to such a function using other functions, such as Gaussians. For example, STO-3G is an MBS that uses 3 Gaussians to fit an exponential. Exponentials are probably better basis functions than Gaussian, but are so much more difficult computationally that they were abandoned by most people a long time ago.
TCSCF ｭ (Two-Configuration Self-Consistent Field)
TIP3P ｭ MM model of water with charge, Van der Waals, and angle terms.
Transition State Theory ｭ the transition state is a maximum along the vibrationless potential energy surface. The activation energy is taken as the difference between the energies of the ground state and the transition state.
TZ ｭ (Triple Zeta)
UFF ｭ (Universal Force Field) Force field of Rappe & Landis to include all elements.
UGA ｭ ( Unitary Group Approach)
UHF ｭ (Unrestricted Hartree-Fock) The self-consistent field method without the restriction of pairing up and down electrons. Unlike the restricted case, where the spin-orbitals are defined such that each spin up and spin down pair have the same spatial form, in the unrestricted space every spin-orbital has different spatial forms. The drawback to this approach is that the UHF wavefunction does not have to be an eigenfunction of the S^2 operator, while the RHF will always be an eigenfunction of the S^2 operator.
Variational Transition State Theory ｭ transition state is at the maximum in free energy along the reaction path. Takes into account the shape of the PES in kinetic calculations. An essential definition for bond cleavage.
VB ｭ (Valence Bond)
VDZ ｭ (Valence double-zeta) A minimal basis is used to describe core electrons, but the valence electrons have twice the minimum number of functions.
VSEPR ｭ (Valence Shell Electron Pair Repulsion)
Wigner correction ｭ approximate correction to transition state theory for tunneling, based on the imaginary frequency at the transition state.
ZDO ｭ (Zero Differential Overlap)
Z-matrix ｭ common format for specifying molecular geometry in terms of internal coordinates. Each atom is described in terms of its distance from some other atom (normally one it is bonded to), the angle it makes with that atom and a previously defined atom, and the dihedral angle between those 3 atoms and a 4th atom.
ZPVE ｭ (Zero-Point Vibrational Energy, also ZPE)
-----------
Cl - Na
/ | /|
Na - Cl |
| Na | Cl
| / |/
Cl - Na
(Grain of Salt)
The information above has been collected from various published results, documentation, and personal experience. (Accuracies are averages of typical literature comparisons.) This list is updated as information comes to my attention and as time allows, but as rapidly as methods evolve (and companies merge), some info is no doubt out of date and/or incomplete. Consequently, this compilation is meant more as an aid to jog oneｹs memory on keywords and capabilities, rather than as a complete and authoritative reference.
Ernest Chamot