Nuclear-electronic orbital quasiclassical trajectory method for vibrational spectroscopy

Simulations of vibrational spectra are important for interpreting experimental data as well as understanding molecular structure and dynamics. Herein, we present an approach for the efficient and accurate incorporation of anharmonicity into such simulations. Real-time nuclear-electronic orbital time-dependent density functional theory treats specified protons quantum mechanically on the same level as the electrons, propagating the electronic and protonic densities according to the time-dependent Schrödinger equation. This approach inherently includes the anharmonicity of the quantum protons and can be combined with Ehrenfest dynamics for the classical nuclei. Herein, this real-time nuclear-electronic orbital (NEO)-Ehrenfest approach is combined with the quasiclassical trajectory (QCT) approach for generating initial conditions that include the zero-point energy of the classical nuclei, thereby enabling sampling of the anharmonic regions of the potential energy surface. The resulting NEO-QCT approach is shown to capture the anharmonic heavy nuclear motion, as well as the anharmonicity of the quantum protons, for a series of molecular systems, including HCN, HNC, FHF⁻, CH₂O, and HCOOH. The NEO-QCT method also captures the distinct spectral features of the formate-water complex ( CHO 2 − ⋅ H₂O), including the redshifted and broadened OH stretch band due to strong anharmonicity arising from hydrogen bonding and coupling between the motions of the hydrogen nuclei and the heavy nuclei. The NEO-QCT method enables computationally practical simulations of vibrational spectra of molecules that exhibit significant anharmonicity and coupling between vibrational modes.