Vibrational Frequencies & Thermochemistry

• Harmonic vibrational frequencies can be calculated in ORCA either numerically or analytically.

• For reliable frequencies the SCF should be well converged  (i.e. TightSCF) and make sure the DFT grid is good enough (default defgrid2 is usually sufficient, sometimes defgrid3 is required). Rarely you might need tighter geometry optimization convergence criteria (TightOpt) as well to get rid of imaginary modes.

• Always perform frequency calculations on optimized structures. Theory level must be identical for the structure and frequencies or you will get imaginary frequencies or meaningless results. A combined Opt+Freq job is the easiest way of making sure of this (even though you have already optimized the geometry). Note that in ORCA 4.0, if a geometry optimization does not converge within the Max. number of cycles, ORCA will not go on to do a frequency calculation.

• See Restarting calculations for information on restarting numerical frequency jobs.

• In ORCA 4.0 Grimme's quasi-RRHO approach for low energy frequencies has been implemented where frequencies below 35 cm-1 are treated as free rotors instead of harmonic vibrations. This is an improvement over the harmonic oscillator approximation which breaks dwon for these low-energy frequencies and is especially problematic for the vibrational entropy term. The quasi-RRHO approach is automatically used in ORCA.

Numerical frequency calculations

Numerical frequencies are available for any method in ORCA that has analytical gradients available. Use this option when analytical (below) are not available.

! Opt NumFreq

To improve the accuracy of the numerical frequencies, the numerical increment can be modified:

! Opt NumFreq

%freq
Increment 0.001 # value in Bohrs. Default value is 0.005
end

Analytical frequency calculations

• Analytical frequencies are available in ORCA for HF and DFT(GGA and hybrid GGA functionals) and MP2. They are more accurate and faster than the numerical ones, albeit memory-consuming.

• Current limitations are: not available for meta-GGA functionals, not available with COSMO/CPCM solvation (will be in ORCA 4.1) and Raman intensities are also not yet available (see below). 

• It is recommended to give as much memory as possible to the analytical frequency job as this reduces batches and results in a faster calculation. Memory has to be set manually and is given per core via the %maxcore keyword.

! Opt Freq Pal6
%maxcore 1000 # Giving 1000 MB of memory per core. This job would request 1000MB*6 = 6000MB of memory in total. Make sure not to exceed the physical memory on the node.

Using RIJCOSX to speed up the Hessian calculation is possible:

! Opt Freq RIJCOSX
%freq
Hess2ElFlags 1,2,2,1 # See Chapter 5.3 in the manual for the meaning of the flags.
end

If the CPSCF equations inside the Frequencies module, run into convergence problems, one can try switching solvers. The recommended solver is Pople, but occasionally DIIS might be required (usually slower). Note that the DIIS solver will automatically be used during the CP-SCF equations if it has been explicitly requested for the SCF (for example if using the Slowconv keyword). If that is the case, use of the Pople solver for CP-SCF can be explicitly requested using the %method block. For problematic systems, the maximum number of CP-SCF iterations can also be changed: 

! Opt Freq
%method
Z_solver Pople # Pople usually recommended. DIIS sometimes.
Z_MaxIter 300
end

Visualizing frequencies

See Visualization and printing.

IR and Raman spectra from vibrational frequency calculations

IR intensities are automatically calculated in Freq or NumFreq calculations and are in the Frequencies output. 

A broadened IR spectrum can easily be plotted. See more details in Visualization and printing:

orca_mapspc job.out ir -w50   

Currently, Raman intensities can only be obtained from numerical vibrational frequency calculations.

Raman intensities require polarizabilities and can be calculated by requesting a polarizability calculation at the same time as a NumFreq calculation. Analytical polarizabilities are available for HF and DFT. They are considerably more expensive than IR intensities.

! Opt NumFreq
%elprop Polar 1 end

The Raman spectrum can then be plotted. See more details in Visualization and printing: 

orca_mapspc job.out raman -w50   

If the CPSCF calculation fails (because of the Raman polarizability calculation) then one can try switching solvers (CG or DIIS):

%elprop
Polar 1
Solver CG # default is Pople, alternatives are CG and DIIS
end

Get Thermochemistry output for different temperatures

One way is to choose the temperatures when running the frequency calculation.

! Opt Freq
%freq  Temp  290, 295, 300
end

If you already have performed a frequency calculation and would like to get thermochemistry for a different temperature but want to avoid recalculating the Hessian you can try a frequency restart. Since ORCA will read the Hessian file and notice that it is complete it should then immediately skip the Hessian calculation and print the thermochemistry at the selected temperature:

!
%numfreq 
restart true
Temp  290, 295, 300
end

See this forum post for information about how to do this for an already converged analytical frequency job.