*Anharmonic*, i.e. *cubic* and *quartic force fields* can be computed using the keyword
**ANHARM**. With **ANHARM=VIBROT** those parts of the *cubic force field* are computed which are
required for the calculation of *vibration-rotation interaction constants* (i.e., vibrational corrections to rotational constants). **ANHARM=VPT2** initiates the calculation of the *full cubic force field* together with the *semidiagonal part of the quartic force field* and is sufficient to obtain *fundamental frequencies* using second-order perturbation theory starting from the harmonic-oscillator rigid-rotator approximation. **ANHARM=FULLQUARTIC** finally requests the calculation of a *full quartic force field*.

With at most *analytic second derivatives* available, the required *cubic* force field (*third geometrical derivatives* of the energy) and *quartic* force fields (*fourth geometrical derivatives* of the energy) have to be obtained by means of *finite difference* techniques. In CFour, this is done by differentiating the analytically evaluated harmonic force constants *numerically* with respect to the *normal coordinates* of the molecule. The default displacement is here 0.05 in terms of
reduced normal coordinates. The displacement can be controlled using the keyword **ANH_STEPSIZ**.

For advanced analysis of vibrational energies and properties using explicitly summed Rayleigh-Schrödinger type perturbation theory see Manual for GUINEA (not part of the public release). Vibrational energies, deperturbation of resonances, transition intensities, dipole moment corrections and harmonic derivatives may all be calculated at the VPT2 (second-order) level of perturbation theory within this module.

**Examples**

calculation of vibration-rotation interaction constants

calculation of fundamental vibrational frequencies

**Recommendations**