Frequencies · Thermochemistry

Why compute frequencies

A frequency job after an optimisation serves three purposes:

1. Characterise the stationary point: all real frequencies → stable minimum; exactly one imaginary frequency → transition state.
2. Provide thermochemical corrections: zero-point energy (ZPE), thermal corrections, entropy → Gibbs free energy G.
3. Predict IR / Raman spectra: vibrational spectra directly comparable to experiment.

Basic usage: AnFreq and NumFreq

Two flavours are available:

# Analytical frequencies (preferred when available)
! B3LYP D4 def2-TZVP Freq

# Numerical frequencies (when analytical derivatives are unavailable, e.g. CCSD(T))
! CCSD(T) cc-pVDZ NumFreq

Combined with optimisation

The most common pattern is to chain Opt and Freq on the same keyword line:

! B3LYP D4 def2-TZVP RIJCOSX def2/J TightOpt Freq

* xyzfile 0 1 mol.xyz

Once the optimisation converges, ORCA automatically launches the frequency calculation at the same level. If you find an imaginary frequency, distorting the geometry along that mode and re-optimising usually resolves it.

Reading the output

After a frequency calculation the output contains a table like this:

-----------------------
VIBRATIONAL FREQUENCIES
-----------------------

Scaling factor for frequencies =  1.000000000  (already applied!)

   0:         0.00 cm**-1
   1:         0.00 cm**-1
   2:         0.00 cm**-1
   3:         0.00 cm**-1
   4:         0.00 cm**-1
   5:         0.00 cm**-1
   6:      1659.34 cm**-1
   7:      3805.21 cm**-1
   8:      3914.47 cm**-1

The first six entries (five for linear molecules) are the translational and rotational modes, which should always appear near zero. The remaining entries are the true vibrational modes. In the example above water has three modes: the bend (1659), symmetric stretch (3805) and antisymmetric stretch (3914).

Visualising normal coordinates

Displacement vectors for each mode appear in the NORMAL MODES section:

------------
NORMAL MODES
------------
                  0          1          2          3          4
      0    0.000000   0.000000  -0.000000   0.000000  -0.000000
      1    0.000000   0.000000   0.000000  -0.000000   0.000000
      ...

To inspect normal coordinates intuitively, use the orca_pltvib utility to generate a trajectory of the vibration:

# Extract a trajectory for mode 6 (writes an XYZ file)
orca_pltvib mol.hess 6

Handling imaginary frequencies

Imaginary frequencies appear as negative numbers in the output:

   6:      -456.78 cm**-1   ***imaginary mode***
   7:      1234.56 cm**-1
   8:      ...

If you did not intend to find a transition state, this is how to resolve it:

1. Displace every atom slightly along the imaginary mode's normal coordinate (say ± 0.1 Å). Extracting the first amplitude frame from orca_pltvib is the easiest way.
2. Re-optimise from this new geometry. Consider tightening to VeryTightOpt.
3. Re-run the frequencies and confirm all modes are real.

Thermochemistry and Gibbs free energy

Once the frequencies are in, ORCA automatically prints the thermochemistry. The default reference conditions are 298.15 K and 1 atm:

-------------------------
THERMOCHEMISTRY AT 298.15K
-------------------------

Temperature         ... 298.15 K
Pressure            ... 1.00 atm
Total Mass          ... 18.01 AMU

Zero point energy                ...     0.02143521 Eh      13.45 kcal/mol
Thermal vibrational correction   ...     0.00010256 Eh       0.06 kcal/mol
Thermal rotational correction    ...     0.00141572 Eh       0.89 kcal/mol
Thermal translational correction ...     0.00141572 Eh       0.89 kcal/mol
-------------------------------------------------
Total thermal energy                  -76.39541321 Eh
Total enthalpy                        -76.39447892 Eh
Final Gibbs free energy               -76.42157345 Eh
-------------------------------------------------
G-E(el)                            ...   0.00219978 Eh       1.38 kcal/mol

The key entries are:

Changing T and p

%freq
   Temp     373.15   # 100 °C
   Pressure 1.0      # atm
end

IR · Raman spectra

IR intensities are always printed alongside the frequencies. Raman intensities require either ! NumFreq or a polarisability calculation in the same job.

To turn the printed table into a spectrum, use the orca_mapspc utility:

# IR spectrum (.dat file)
orca_mapspc mol.out ir -w25

# Raman spectrum
orca_mapspc mol.out raman -w50

# Open mol.out.ir.dat or mol.out.raman.dat in gnuplot, matplotlib, …

The -w flag sets the Lorentzian / Gaussian line width in cm⁻¹. Running orca_mapspc with no arguments prints the full option list.

Useful options

%freq
   CentralDiff   true     # central differences in NumFreq (default: forward). More accurate, 2× slower.
   Increment     0.005    # displacement size (bohr). Default 0.005.
   Restart       true     # resume an interrupted NumFreq
   ProjectTR     true     # project out translational / rotational modes (default on)
   Mass2016      true     # IUPAC 2016 atomic masses
   QuasiRRHO     true     # quasi-RRHO entropy correction
   CutOffFreq    35.0     # quasi-RRHO cutoff (cm^-1), default 35
end