Molecular Models Empirical/Molecular Modeling Semi Empirical Ab Initio/DFT Neglect Electrons Neglect Core Electrons Approximate/parameterize HF Integrals Full Accounting of Electrons Molecular Models
Molecular Models. Methodology: Modify Wavefunction.
Dec 14, 2015
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Molecular Models
Empirical/Molecular Modeling Semi Empirical Ab Initio/DFT
Neglect ElectronsNeglect Core Electrons
Approximate/parameterize HF IntegralsFull Accounting of Electrons
Molecular Models
Methodology: Modify Wavefunction
Theory: Wavefunction
Computation: Basis Set
AO Type
Functional Forms
s e-ar2
Px x e-ar2
Py y e-ar2
Pz z e-ar2
dx2 x2 e-ar2
dy2 y2 e-ar2
dz2 z2 e-ar2
dxy xy e-ar2
dxz xz e-ar2
dyz yz e-ar2
Computation: Basis Set
Basis set# functions
Basis set# functions
Basis set# functions
STO-3G 5 6-31G 9 6-311G 13
3-21G 9 6-31G* 15 6-311G* 18*
4-31G 9 6-31+G* 19 6-311+G* 22*
Computation: Electron Correlation
Configuration Interaction (CI)
N
i
HFii
HF aa1
00
unoccupied
occupied
Moller Plesset (MP)
Hartree-Fock close to Full Hamiltonian
VHH HFexact 0
Perturbation
Computation: Computation Time
Results: Geometry
BasisBond Length Error (Å)
Bond Angle Error (deg.)
STO-3G 0.054 2.3
3-21G 0.016 3.8
3-21G(*) 0.017 3.3
6-31G* 0.014 1.5
6-31G** 0.014 1.8
6-311G** 0.013 --
Mean Absolute Errors for A-H bond parameters
BasisBond Length Error (Å)(single bonds)
Bond Length Error (Å)(multipe bonds)
Bond Angle Error (deg.)
STO-3G 0.049 0.017 1.3
3-21G 0.029 0.012 1.0
3-21G(*) 0.029 0.012 0.9
6-31G* 0.044 0.023 --
6-31G** 0.046 0.021 --
6-311G** 0.039 0.025 --
Mean Errors for A-B bond parameters
Results: Geometry
Molecule Coordinate HF MP2 CCSD MP4 CCSD(T)
Error in Bond Length (Å)
H2O O-H -0.006 0.005 0.004 0.005 0.005
NH3 N-H -0.011 0.002 0.003 0.004 0.004
CH4 C-H -0.001 0.003 0.005 0.006 0.006
C2H2C-HC-C
-0.002-0.012
0.0060.024
0.0070.016
0.0080.025
0.0080.023
CH2OC-HC=O
-0.005-0.015
0.0030.022
0.0040.015
0.0080.023
0.0060.021
HCNC-HC-N
-0.003-0.017
0.0040.032
0.0050.019
0.0060.030
0.0060.024
HCNN-HC-N
-0.008-0.010
0.0070.025
0.0060.017
0.0070.031
0.0080.024
CO2 C-O -0.015 0.022 0.012 0.028 0.018
Average Abs. Error () -0.009 0.013 0.009 0.015 0.013
Error in Bond Angle (deg.)
H2O H-O-H 2.1 -0.1 0.1 0.0 0.0
NH3 H-N-H 1.5 0.0 -0.2 -0.3 -0.4
CH20 H-C-O -0.3 -0.2 -0.2 -0.6 -0.2
Average Error (deg.) 1.3 -0.1 -0.1 -0.3 -0.2
Results: Geometry
Results: Energy
Results: Energy
Method sto-3g 3-21G d95 4-31G 4-31g* 4-31g** 6-31G 6-31G*6-31G**
6-311 G**
6-311 ++G**
6-311++ (3df,2pd)
cc-pvdz cc-pvtz cc-pvqc
# Basis fumctions: 7 13 14 13 19 25 13 19 25 30 36 69 24 58 115
UHF 36.1 33.1 32.6 34.5 28.2 28.1 33.9 27.6 27.6 26.0 25.5 24.7 25.3 25.1 25.0RHF 39.5 36.0 35.4 37.4 31.5 31.5 36.8 30.9 30.9 29.3 28.8 28.1 28.6 28.6 28.4MP2 31.6 28.1 27.0 29.3 21.5 20.7 28.7 20.8 20.1 18.0 17.4 15.0 17.5 15.43 14.3MP3 28.7 25.8 24.7 27.0 18.9 18.1 26.4 18.3 17.5 15.3 14.8 12.6 14.7 12.9 12.1MP4D 27.3 24.7 23.6 25.9 17.7 16.8 25.3 17.1 16.3 14.1 13.5 11.3 13.4 11.6 10.9
MP4DQ 27.3 24.9 23.8 26.1 18.0 17.1 25.4 17.3 16.6 14.4 13.9 11.8 13.8 12.2 11.5
MP4SDTQ 27.3 24.6 23.7 25.8 17.6 16.7 25.2 17.0 16.2 14.1 13.5 11.4 13.5 11.7 11.0
MP5 26.5 24.1 23.1 25.2 17.0 16.1 24.6 16.4 15.6 13.5 13.0 10.9 12.9 11.3 NA
GVB/ROHF 23.8 23.2 23.0 24.5 14.7 14.7 24.0 14.3 14.4 12.6 12.3 10.5 11.9 10.8 10.5
CCSD 24.9 23.5 22.6 24.6 16.5 15.7 24.1 16.0 15.2 13.2 12.8 10.9 12.5 11.2 10.6
CCSD(T) 24.8 22.9 22.2 24.1 15.7 14.8 23.5 15.2 14.4 12.4 12.0 10.0 11.8 10.3 9.6
CID 26.2 24.7 23.7 25.9 18.1 17.5 25.3 17.5 17.0 15.0 14.6 12.7 14.3 13.0 12.4CISD 26.1 24.7 23.8 25.9 18.0 17.4 25.3 17.5 16.9 15.0 14.6 12.9 14.3 13.2 12.6
QCISD 24.9 23.4 22.6 24.6 16.5 15.6 24.0 15.9 15.2 13.2 12.8 10.9 12.5 11.2 10.6
QCISD(T) 24.8 22.9 22.2 24.1 15.7 14.8 23.5 15.2 14.4 12.4 12.0 10.0 11.8 10.3 9.6
BLYP 17.0 15.8 17.2 17.5 12.7 12.5 17.0 12.3 12.2 11.3 10.7 9.9 10.9 10.4 10.1
ROBLYP 16.1 15.1 16.4 16.7 11.6 11.5 16.2 11.2 11.2 10.2 9.7 8.8 9.9 9.3 9.0
Singlet-Triplet Splittings (kcal/mole):
Eexp = 9.2 kcal/mole
Results: Energy
ReactionHF/6-31FG** //HF6-31G*
MP2/6-31G** //MP2/6-31G*
MP3/6-31G** //MP3/6-31G*
MP4/6-31G** //MP4/6-31G*
Expt.
H2->H*+H* 85 101 105 106 109
Li->Li*+H* 32 45 48 49 58
BeH->Be*+H* 52 52 49 47 50,56
BH->B*+H* 62 77 79 80 82
CH*->C+H*(2) 55 73 75 76 84
CH*->C+H*(4-) 62 68 66 66 67
NH->N*+H* 50 71 72 73 79,<85
OH*->O+H* 67 96 96 96 107 FH->F*+H* 93 131 127 128 141
BH2*->BH+H* 84 88 87 85 99-130
CH2->CH*+H*(3B1) 101 109 108 107 105,106
CH2->CH*+H*(1A1) 70 89 90 91 98
NH2*->NH+H* 65 90 90 90 102
OH2->OH*+H* 86 119 115 116 126
BH3->BH2*+H* 90 106 108 109 57-107
CH3*->CH2+H* 88 110 112 112 117
NH3->NH2*+H* 83 110 108 109 116
CH4->CH3*+H* 87 109 110 110 113
Results: Energy
Results: Charge
Example: Chlorine atomic charge in CH3Cl, HF Mulliken and NPA charges ; calculated with many basis sets (at the HF/6-31G* optimized geometry).
Problems: BSSE
Basis Set Superposition Error
Molecules MethodBSSEkcal/mol
HF+HFHF+HF
HF/6-31+G*MP2/6-31+G*
0.962.16
H2+NH3 HF/DZP 0.65
(CH3COOH)2
(CH3COOH)2
HF/6-31G*MP2/6-31G*
2.55.6
Problems: Size Consistency
Problems: UHF Instability
MethodErelative
(Anthracene- Phenanthrene)
UHF/6-31G* 1.42
RHF/6-31G* 6.88
MP2/6-31G** 7.09
MP3/6-31G 6.17
MP4(SDQ)/6-31G 6.48
CISD/DZ 7.49
CCSD 6.32
CCSD(T) 5.98
Problems:Variational Principle
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