A.2.d Vibrational scale factors
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Methods with predefined basis sets
semi-empirical AM1 0.9532
PM3 0.9761
MNDOd 0.0000
Methods with standard basis sets
3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* cc-pVDZ cc-pVTZ aug-cc-pVDZ 6-311+G(3df,2p)
hartree
fock HF 0.9085 0.9085 0.8953 0.8991 0.9029 0.9045 0.9047 0.9083 0.9104 0.8930 0.8992
ROHF 0.9085 0.9085 0.8953 0.8953 0.8992 0.8992 0.8953 0.8992 0.8992 1.0000 0.9085
density
functional BLYP 0.9945 0.9945 0.9945 0.9945 0.9945 0.9945 0.9945 0.9945 0.9945 1.0000 0.9945
B3LYP 0.9614 0.9614 0.9614 0.9614 0.9620 0.9614 0.9614 0.9614 0.9614 0.9614 0.9614
B3PW91 0.9573 0.9573 0.9573 0.9573 0.9573 0.9573 0.9573 0.9573 0.9573 1.0000 0.9573
MPW1PW91 0.9575 0.9565 0.9565 0.9499 0.9565 0.9527 0.9565 0.9565 0.9565 1.0000 1.0000
Moller
Plesset
perturbation MP2FC 0.9434 0.9434 0.9434 0.9434 0.9370 0.9370 0.9434 0.9370 0.9370 0.9370 0.9434
MP2FU 0.9427 0.9427 0.9427 0.9427 0.9427 0.9427 0.9427 0.9427 0.9427 1.0000 0.9427
PMP2 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
MP4 0.9438 0.9438 0.9438 0.9438 0.9438 0.9438 0.9438 0.9438 0.9438 1.0000 0.9438
Configuration
interaction CID 0.9240 0.9240 0.9240 0.9240 0.9240 0.9240 0.9240 0.9240 0.9240 1.0000 0.9240
CISD 0.9218 0.9218 0.9218 0.9218 0.9218 0.9218 0.9218 0.9218 0.9218 1.0000 0.9218
QuadratQCISD 0.90.950.90.950.950.9530.950.9530.9531.0000 0.9537 ic
configuration
interaction
537 37 537 37 37 7 37 7 7
QCISD(T) 0.9537 0.9537 0.9537 0.9537 0.9537 0.9537 0.9537 0.9537 0.9537 1.0000 0.9537
Coupled
Cluster CCD 0.9431 0.9431 0.9431 0.9431 0.9431 0.9431 0.9431 0.9431 0.9431 1.0000 0.9431
CCSD 0.9431 0.9431 0.9431 0.9431 0.9431 0.9431 0.9431 0.9431 0.9431 1.0000 0.9431
CCSD(T) 0.9431 0.9431 0.9431 0.9431 0.9431 0.9431 0.9431 0.9431 0.9431 1.0000 0.9431
Methods with effective core potentials
CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD
hartree fock HF 0.8925 0.8930 0.8930 0.8930 0.8930 0.8930
ROHF 0.9085 0.9085 0.9085 0.9085 0.9085 0.9085
density
functional BLYP 0.9945 0.9945 0.9945 0.9945 0.9945 0.9945
B3LYP 0.9614 0.9614 0.9614 0.9614 0.9614 0.9614
B3PW91 0.9573 0.9573 0.9573 0.9573 0.9573 0.9573
MPW1PW91 0.9499 0.9499 0.9499 0.9499 0.9499 0.9499
Moller
Plesset
perturbation MP2FC 0.9434 0.9434 0.9434 0.9434 0.9434 0.9434
MP2FU 0.9427 0.9427 0.9427 0.9427 0.9427 0.9427
PMP2 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
MP4 0.9438 0.9438 0.9438 0.9438 0.9438 0.9438
Configuration interaction CID 0.9240 0.9240 0.9240 0.9240 0.9240 0.9240
CISD 0.9218 0.9218 0.9218 0.9218 0.9218 0.9218 Quadratic
configuration
interaction
QCISD 0.9537 0.9537 0.9537 0.9537 0.9537
0.9537
QCISD(T) 0.9537 0.9537 0.9537 0.9537 0.9537 0.9537
Coupled
Cluster CCD 0.9431 0.9431 0.9431 0.9431 0.9431 0.9431
CCSD 0.9431 0.9431 0.9431 0.9431 0.9431 0.9431
CCSD(T) 0.9431 0.9431 0.9431 0.9431 0.9431 0.9431
For descriptions of the methods (AM1, HF, MP2, ...) and basis sets (3-21G, 3-21G*, 6-31G, ...) see
the glossary in section I.C. Predefined means the basis set used is determined by the method.
Some of the above values were taken from
A.P. Scott, L. Radom, Harmonic Vibrational Frequencies: An Evaluation of
Hartree-Fock, Moller-Plesset, Quadratic Configuration Interaction,
Density Functional Theory and Semiempirical Scale Factors, J. Phys. Chem.
100, 16502, 1996
In this table many scale factors were assumed to be the same for different
basis sets and similar methods.
References dealing with the scaling of vibrational frequencies
Title Journal Volume Issue Pages Year Authors
Ab initio Vibrational Spectra and
Their Use in the Identification of
Unusual Molecules Chem.
Rev. 86 4 709-730 1986 BA Hess, LJ
Schaad, P Carsky,
R Zahradnik
Harmonic Vibrational
Frequencies: An Evaluation of
Hartree-Fock, Moller-Plesset,
Quadratic Configuration
Interaction, Density Funcitonal
Theory and Semiempirical Scale
Factors J. Phys.
Chem. 100 16502 1996 AP Scott, L
Radom
The Theoretical Prediction of
Molecular Radical Species: a
Systematic Study of Equilibrium
Geometries and Harmonic
Vibrational Frequencies J. Phys.
Chem. A 105 42 9736-9747 2001 CD Sherrill, EFC
Byrd, M
Head-Gordon
Harmonic Frequency scaling
factors for Hartree-Fock, S-VWN, Theor.
Chem. 105 413-421 2001 MD Halls, J
Velkovski, HB