Calculation Of Anharmonic Force Fields
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.