Analytic evaluation and basis set dependence of intensities of infrared spectra

Equations are presented for the analytic determination of dipole moment derivatives with respect to nuclear coordinates for closed-shell, open-shell unrestricted, and open-shell restricted Hartree–Fock wave functions. The efficient evaluation of these derivatives and the resulting infrared intensities simultaneously with determination of the vibrational frequencies is discussed. Intensities are presented for a selection of test molecules with a wide variety of basis sets. It is concluded that basis sets of double-zeta polarized or higher quality usually give correct qualitative information about the ordering of the intensities, while smaller basis sets may not even predict the most intense mode correctly. Quantitative accuracy using the larger basis sets seems to be limited primarily by the use of the double harmonic approximation.