Methods: Parameters & Basis Sets

Method Groupings

Mechanics
Semiempirical
Density Functional
ab initio (Hartree Fock)
Basis Sets

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’y:

ΔHf°±0.5, ΔH_r±0.4, ΔH^†±2
D±0.1
l±0.01, a±1, d±8
v±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’y:

ΔHf°±0.6, ΔH_r±0.4, ΔH^†±1
D±0.07
l±0.01, a±1, d±5
v±40

ChemX -

Basis:

organics
inorganics
peptides

Acc’y: ΔH_r±1, ΔH^†±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’y: ΔH_r±1, ΔH^†±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’y: ΔH_r±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’y:

ΔH^†±0.9
l±0.01, a±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’y:

ΔH^†±2, ΔH_r±1
l±0.03, a±3, d±8

Basis:

Organic
Inorganic
parms calc’d from basic props

Pros: full periodic table
Cons:

needs charge equilibration
2-MeO -THP equatorial

Acc'y: ΔH_r±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’y:

ΔH_r±0.5, ΔH^†±0.8
l±0.01, a±1
solubility parameter±0.2
sorption energy±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’y:

ΔH_r±0.4
a±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: ΔH_r±1

• ESFF –
  

Basis:

diagonal valence
rule based:
electronegativity
atomic radii
hardness
scaling
d-p π 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 – Merck Molecular Force Field

Basis:

small molecule
ab initio & experimental

Pros: ions

Semiempirical Quantum Mechanics

• Hückel -
  

Basis:

"Tight Binding Approximation"
π-orbitals only
H_µµ= alpha
H_µv = beta, adjacent atoms only
S_µv = 0

Pros:

orbital symmetry
resonance energy
back of envelope

Cons:

flat, π orbitals only
polars poor

EHT -

Basis:

valence s & p’s
H_µµ= -IPµ (ionization potential)
H_µv = 1.75(IPµ + IPv)Sµv
S_µv 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_µµ= -IP_µ - Q_a(IP_a-EA_a)

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
XµXvdt = 0
H_µv ƒ ßabSµv fit to minimum basis set

Pros:

bond lengths
bond angles

Cons: dissociation energies poor
Acc’y: ΔH_f°±200

• PPP -
  

Basis:

one 2pπ STO per conjugation
single CI
valence π & 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_µµ= -(IP_µ - EA_µ/2 + . . .
H_µv 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’y:

ΔH_f°±100
l±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’y:

ΔH_f°±5, ΔH_r±13
D±0.5, IP±0.7
l±0.02

MNDO - Minimal Neglect of Differential Overlap

Basis: 32 molecule parameterization
Pros:

multiple bonds
EA’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 ~ 0.17Å short
C-O-C angle 9° 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’y:

ΔH_f°±11, ΔH_r±13, ΔH_diss-20, ΔH^†±16
D±0.5, IP±0.8
l±0.07, a±5, d±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’y:

ΔH_f°±6
D±0.5, IP±0.6
l±0.06, a±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 @ 3Å:
P4O6 asymmetric
P-O bonds
conjugate interactions low
-CH2- ΔHf ~ 2 kcal low each
Heat of Hydrogenation low
bond dissociation enthalpies low
activation enthalpies high
-NO2 energies high
-O-O- bond ~ 0.17Å short
H-bond angles, H2O H-bond geometry wrong
C-C-O-H gauche in ethanol
H⁺ transfer barrier high
acrolein, glyoxal

Atoms:

H
Li, B - F
Al - Cl
Zn, Ge, Br
I
Hg

Acc’y:

ΔH_f°±8, ΔH_r±5, ΔH_diss-20, ΔH^†±7
D±0.5 ,IP±0.6
l±0.06, a±4, d±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’y:

ΔH_f°±8, ΔH_r±5
D±0.4, IP±0.4
l±0.04, a±3
v±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’s poor
Proton Affinity
H⁺ transfer barrier high
wrong glucose geometry:
H-bonds 0.1Å short
C-C-O-H gauche in ethanol
VdW attraction high/H-H core repulsion low, H-H 1.7 vs 2.0 Å

Atoms:

H
Li, Be, C - F
Mg - Cl
Zn - Br
Cd - I
Hg - Bi

Acc’y:

ΔH_f°±9, ΔH_r±7, ΔH_diss-20, ΔH^†±9
D±0.6, IP±0.7
l±0.05, a±9, d±15
v±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 Theory

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 –
  

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±0.02, a±3
v±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’y:

ΔH_f+90, ΔH_r±9, ΔH_diss+16, ΔH_atom+80, ΔH^†±7
D±0.1
l±0.02, a±2
v±7%

LYP –

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 –

Basis:

Perdew gradient correction
correlation functional
parameter free

Pros:

uniform e^- gas limit
parallel ‚ opposite spin pairs

Cons: 1 e^- correlation ‚ 0

• B88 –
  

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:

ΔH_f+16, ΔH_r±5, ΔH_diss+5, ΔHatom+20
D±0.2
l±0.02, a±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:

ΔH_f±7, ΔH_r±5, ΔH_diss±5, ΔH_atom±9, ΔH†±6
D±0.2
l+0.03, a±1
v±6%

GGA91 –

Pros:

parallel ‚ opposite spin pairs
uniform e^- gas limit
no fit parameters
H-bonds

Cons: 1 e^- correlation ‚ 0

• ACM – 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’y:

ΔH_f°±3 , ΔH_r±4, ΔH_diss±5, ΔH_atom±3, ΔH^†±4
D±0.2, IP±0.1
l±0.007, a±0.9
v+4.0%

B3P86 -

Basis:

B3 hybrid exchange w/ P86 correlation

Acc’y: v+4.6%

ab initio Quantum Mechanics

• 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
ΔH†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 - π 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 (π - π 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
π - π 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:

ΔH_f°±3, ΔH_r±4, ΔH_diss±7, ΔH_atom-22, ΔH†±11
l+0.01, a±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 ƒ order for double excitations

CCSD - Coupled Cluster, singles, doubles

Basis: single & double excitations "coupled" to reference configuration
Pros:

includes correlation
complete to ƒ 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±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

Quantum Mechanics 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’y:

ΔH_diss±3, ΔH^†±5
D±0.5
l±0.09, a±5, d±8

STO-3G* -

Basis:

STO-3G
set of polarizing d-functions (5D) added to heavy atoms

Atoms:

Na - Ar
K - Kr
Rb - Xe

Acc’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’y:

ΔH_f°±7, ΔH_r±15, ΔH_diss-30, ΔH^†±4
D±0.4
l±0.06, a±3, d±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’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’y: l±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’y:

ΔH_f°±4, ΔH_r±7, ΔH_diss-20, ΔH_atom-120, ΔH^†±7
D±0.5
l±0.03, a±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’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’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’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

(Grain of Salt)

The information above has been collected from various published results, documentation, and personal experience. This list is updated as information comes to my attention and as time allows, but as rapidly as methods evolve, some info is no doubt out of date and/or incomplete. (Accuracies are averages of typical literature comparisons, for instance, which, of course, is dependent on the systems included in the published study.) Consequently, this compilation is meant more as an aid to help remember the strengths and limitations of each method, rather than as a complete and authoritative reference.

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6/11/00 Ernie Chamot / Chamot Labs / / echamot@chamotlabs.com