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J Phys Chem Lett. 2019 Mar 21;10(6):1167-1172. doi: 10.1021/acs.jpclett.9b00299. Epub 2019 Feb 28.

Molecular Vibrational Frequencies within the Nuclear-Electronic Orbital Framework.

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Department of Chemistry , Yale University , 225 Prospect Street , New Haven , Connecticut 06520 , United States.


A significant challenge for multicomponent quantum chemistry methods is the calculation of vibrational frequencies for comparison to experiment. The nuclear-electronic orbital (NEO) approach treats specified nuclei, typically key protons, quantum mechanically. The Born-Oppenheimer separation between the quantum and classical nuclei prevents the direct calculation of vibrational frequencies corresponding to modes composed of both types of nuclei. Herein an effective strategy for calculating the vibrational frequencies of the entire molecule within the NEO framework is devised and implemented. This strategy requires diagonalization of an extended NEO Hessian that depends on the expectation values of the quantum nuclei as well as the coordinates of the classical nuclei and is constructed with input from multicomponent time-dependent density functional theory (NEO-TDDFT). Application of this NEO-DFT(V) approach to molecular systems illustrates that it accurately incorporates the most significant anharmonic effects. This general theoretical formulation opens up a broad spectrum of new directions for multicomponent quantum chemistry.

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