Anharmonic Frequency
EDF2 functional
Description
Density functional theory is often used to
predict the vibrational (i.e. infra-red or Raman) spectra
of molecules but the distinction between harmonic and anharmonic
modes is not always made: when a calculated harmonic frequency agrees
with an experimental anharmonic one, one is obviously getting the
right answer for the wrong reason. The EDF2 functional has been
explicitly designed to give accurate harmonic frequencies.
Applications
Users who wish to predict the harmonic vibrational
frequencies of a molecule should perform a harmonic frequency calculation
in Q-Chem using the EDF2 functional.
Users who wish to predict the experimental vibrational frequencies of a molecule should perform an anharmonic frequency calculation in Q-Chem using the EDF2 functional.
Uniqueness/Innovation
EDF2 is the first density functional
that has been optimised for the prediction of molecular vibrational
frequencies. Although it is designed primarily to model the curvatures
of potential surfaces, it is also found to perform well (comparable
to B3LYP) in structural and thermochemical predictions.
Competition
EDF2 is not available in any other commercial
package
Application limit; technical limits
As for any DFT frequency
calculation
Application scope
Useful for studying small-to-moderate
organic and inorganic molecules
Publication
C.Y. Lin, M.W. George and P.M.W. Gill, Aust.
J. Chem. 57
(2004) 365–370
Graphs
Experimental and EDF2 harmonic frequencies of the benzene molecule
Errors Dw = w calc – w exp (cm –1) in EDF2 harmonic frequencies of 315 molecules
Anharmonic vibrational frequencies
Description
Most quantum chemical calculations
of molecular vibrational frequencies employ the harmonic
approximation, viz. that
the molecule executes simple harmonic motion within each
of its normal modes. Anharmonic frequency calculations
are more computationally demanding but yield a better picture
of reality. They also provide a more accurate picture of
overtone and combination bands.
Applications
Anharmonic frequency calculations
are preferable to harmonic calculations when users wish
to compare against well resolved experimental spectra.
Computed (B3LYP/cc-pVTZ) harmonic and anharmonic frequencies for H2O
|
Harmonic |
Anharmonic |
Experimental |
Bend |
1647 |
1574 |
1595 |
Symm Stretch |
3801 |
3693 |
3657 |
Asym Stretch |
3900 |
3705 |
3756 |
Uniqueness/Innovation
The anharmonic methods
in Q-Chem 3.0 use new algorithms based on TOSH (transition-optimized
shifted Hermite) functions that are significantly more
efficient than earlier schemes.
Competition
Some other packages can perform anharmonic
frequency calculations but Q-Chem uses a faster algorithm
than most of its competitors (including Gaussian 03).
Application limit; technical limits
The fastest
of Q-Chem’s anharmonic methods is only
a little more expensive than the corresponding harmonic
calculation. The slower, more accurate, methods are roughly
an order of magnitude more expensive.
Application scope
The fast anharmonic methods
are preferable to harmonic calculations for most purposes.
Publication
None yet.
SG-0 grid
Description
A small quadrature grid suitable
for routine use in DFT calculations.
Applications
The SG-0 grid is roughly half the
size of the SG-1 grid and its use therefore significantly
reduces the cost of DFT calculations. It is a useful grid
for preliminary and broad-brush examinations of potential
surfaces.
Graph
None.
Uniqueness/Innovation
The SG-0 quadrature roots
and weights for the most important elements (H, C, N and
O) have been carefully optimised to minimize the number
of grid points and maximize the accuracy of the resulting
quadrature.
Competition
All of our competitors’packages
offer a choice of DFT quadrature grids but SG-0 is one
of the most cost-effective grids currently available.
Application limit; technical limits
The SG-0
grid can be used in any DFT calculation.
Application scope
SG-0 will be widely used and
is the default grid for most of Q-Chem’s DFT calculations.
Publication
P.M.W. Gill and S.H. Chien, J.
Comput. Chem. 24
(2003) 732–740