Efficient implementation of the analytical second derivatives of hartree–fock and hybrid DFT energies within the framework of the conductor‐like polarizable continuum model

Calculation of vibrational frequencies for solvated systems is essential to study reactions in complex environments. In this paper, we report the implementation of the analytical self-consistent field Hessian at the Hartree-Fock and density functional theory levels in the framework of the conductor-like polarizable continuum model (C-PCM) into the ORCA quantum chemistry suite. The calculated vibrational frequencies agree very well with those computed through numerical differentiation of the analytical gradients. The deviation between both sets of data is smaller than 3 cm-1 for frequencies larger than 200 cm-1 and smaller than 5 cm-1 for the low-frequency regime (100 cm-1 < ω < 200 cm-1 ). The accuracy of the frequencies is not significantly affected by the size of the density functional theory (DFT) integration grid, with a deviation lower than 0.5 cm-1 between data computed with the smallest and that with the largest DFT grid size. The calculation of the analytical Hessian is between 3 and 12 times faster than its numerical counterpart. The C-PCM terms only add an overhead of 10-30% relative to the gas phase calculations. Finally, for acetone, the (B3LYP) values for the frequency shifts obtained in going from the gas phase to liquid acetone are in agreement with experiment. © 2019 Wiley Periodicals, Inc.