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