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Vibrational spectroscopy is a viable tool to reveal the mechanism of various molecular systems at the atomic and molecular resolution; yet the interpretation of the observed spectrum is often non-trivial and requires a theoretical assistance. Although it is rather common to calculate the vibrational spectrum based on the harmonic approximation, anharmonicity plays a crucial role, in particular, for the OH and NH stretching vibrations that lie in a high frequency region. In this article, recent advances in the vibrational structure theory are reviewed regarding: (1) The generation of anharmonic potential energy surface by the electronic structure calculation, (2) An efficient solver of vibrational Schrödinger equation by the vibrational quasi-degenerate perturbation theory based on variationally optimized coordinates, (3) A weight average approach to simulate the vibrational spectrum of condensed phase systems.

Development of Molecular Vibrational Structure Theory with an Explicit Account of Anharmonicity