Vibrational Frequencies - Isotope Effects

The vibrational frequencies computed in the harmonic vibrational analysis by Gaussian do not only depend on the computed force constants, but also on the atomic masses. Substitution of, for example, one hydrogen by a deuterium atom therefore leads to dramatic changes in the calculated vibrational frequencies. As the Hessian is not affected by the changes in the masses, the same Hessian can be used for all isotopomers. In order to read the Hessian out of the checkpoint file and compute the vibrational frequency spectrum for different masses, the keywords


must be combined with additional information of the atomic masses of the system. Using hydrogen chloride H-Cl as an example, the calculated frequency for the H-Cl stretching vibration amounts to 3186.1 cm-1 at the HF/6-31G(d) level of theory and an equilibrium bond length of 126.62 pm. The vibrational frequency calculation for D-Cl can be executed efficiently provided that the checkpoint file already contains the Hessian matrix for H-Cl:

The additional input section after charge and multiplicity information contains a first line specifying the temperature (in K), the pressure (in atm), and a uniform scaling factor for all frequencies (normally 1.0). On subsequent lines the atomic masses are given in the input order, one mass per line. The atomic masses can either be entered accurately (as a real number) or as an integer closest to the true mass. Specifying the mass of deuterium using an integer (2) Gaussian will take the exact mass of the deuterium isotope (2.01410au) from an internally stored list of values. The vibrational frequency calculated for D-Cl at the HF/6-31G(d) level of theory using the same geometrical structure and Hessian as for H-Cl amounts to 2285.04 cm-1.