Anharmonicity in Molecular Crystals: Generalized Perturbation Theory Meets Periodic Computations

Accurate simulation of vibrational spectra in the solid state remains a major challenge due to the combined effects of anharmonicity, intermolecular interactions, and resonance phenomena. In this work, we introduce a generalized second-order vibrational perturbation theory (GVPT2) framework for the quantitative computational spectroscopy of molecular solids. The method balances efficiency and accuracy through a perturb-then-diagonalize approach in which resonant terms are excluded in the initial perturbative treatment and subsequently handled more accurately through a variational approach. This strategy ensures numerical stability while capturing essential vibrational couplings. As a representative application, we investigated the infrared spectrum of solid carbon dioxide (dry ice), a prototypical system exhibiting strong anharmonic effects and Fermi resonances. The generalized VPT2 approach accurately reproduces both absolute band positions and splitting patterns, yielding results in excellent agreement with the experimental data. These findings demonstrate the potential of the method for reliable and transferable anharmonic vibrational analysis across a broad class of solid-state systems.