Abstract
This paper proposes a new mixed quantum mechanics (QM)—molecular mechanics (MM) approach, where MM is replaced by quantum Hamilton mechanics (QHM), which inherits the modeling capability of MM, while preserving the state-dependent nature of QM. QHM, a single mechanics playing the roles of QM and MM simultaneously, will be employed here to derive the three-dimensional quantum dynamics of diatomic molecules. The resulting state-dependent molecular dynamics including vibration, rotation and spin are shown to completely agree with the QM description and well match the experimental vibration-rotation spectrum. QHM can be incorporated into the framework of a mixed quantum-classical Bohmian method to enable a trajectory interpretation of orbital-spin interaction and spin entanglement in molecular dynamics.
Highlights
One of the greatest challenges in molecular dynamics (MD) is to model processes involving many degrees of freedom, some of which have to be treated quantum mechanically
The angular momentum given by Equation (5.12), which is derived from the state-dependent molecular dynamics, provides us with a trajectory-based method to determine the rotational energy of a diatomic molecule and its rotational spectrum
A new quantum mechanics (QM)/molecular mechanics (MM) approach called quantum Hamilton mechanics (QHM), is proposed in this paper to establish state-dependent molecular dynamics (SDMD) in such a way that the governing equations of SDMD can be derived by MM with solutions compatible with QM
Summary
One of the greatest challenges in molecular dynamics (MD) is to model processes involving many degrees of freedom, some of which have to be treated quantum mechanically. The mean-field method calculates the force for the classical motion by averaging over the quantum wave function This method is invariant to the choice of quantum representations and applicable to both bound and continuum states, but it suffers from the neglect of correlations between classical and quantum degree of freedom. The surface-hopping method was developed to manifest quantum-classical correlation, but it is not invariant to the choice of quantum representations and is intrinsically limited to discrete quantum states. With the proposed modifications by QHM, the computational procedures of MQCB developed in the literature can be used to simulate molecular dynamics, including vibration, rotation and spin motions. The correctness of the derived state-dependent molecular dynamics will be verified by comparing with the quantum mechanical description of a diatomic molecule for which the Schrödinger equation has an analytical solution. The resulting state-dependent molecular dynamics is found to agree with the prediction of QM and well match the experimental vibration-rotation spectrum
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