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Perturbative treatment of anharmonic vibrational effects on bond distances: An extended langevin dynamics method
Author(s) -
Shen Tonghao,
Su Neil Qiang,
Wu Anan,
Xu Xin
Publication year - 2013
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.23516
Subject(s) - anharmonicity , physics , perturbation theory (quantum mechanics) , harmonic oscillator , potential energy , amplitude , quantum , quantum mechanics , statistical physics , molecular dynamics , perturbation (astronomy) , classical mechanics
In this work, we first review the perturbative treatment of an oscillator with cubic anharmonicity. It is shown that there is a quantum‐classical correspondence in terms of mean displacement, mean‐squared displacement, and the corresponding variance in the first‐order perturbation theory, provided that the amplitude of the classical oscillator is fixed at the zeroth‐order energy of quantum mechanicsE QM ( 0 ). This correspondence condition is realized by proposing the extended Langevin dynamics (XLD), where the key is to construct a proper driving force. It is assumed that the driving force adopts a simple harmonic form with its amplitude chosen according toE QM ( 0 ), while the driving frequency chosen as the harmonic frequency. The latter can be improved by using the natural frequency of the system in response to the potential if its anharmonicity is strong. By comparing to the accurate numeric results from discrete variable representation calculations for a set of diatomic species, it is shown that the present method is able to capture the large part of anharmonicity, being competitive with the wave function‐based vibrational second‐order perturbation theory, for the whole frequency range from ∼4400 cm −1 (H 2 ) to ∼160 cm −1 (Na 2 ). XLD shows a substantial improvement over the classical molecular dynamics which ceases to work for hard mode when zero‐point energy effects are significant. © 2013 Wiley Periodicals, Inc.