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Multidimensional Quantum Tunneling: Direct Instanton Calculation with Application to Polyatomic Molecules

Multidimensional Quantum Tunneling: Direct Instanton Calculation with Application to Polyatomic Molecules

Year:    2006

Communications in Computational Physics, Vol. 1 (2006), Iss. 6 : pp. 1096–1116

Abstract

Multidimensional tunneling appears in many problems at nano scale. The high dimensionality of the potential energy surface (e.g. many degrees of freedom) poses a great challenge in both theoretical and numerical description of tunneling. Numerical simulation based on Schrödinger equation is often prohibitively expensive. We propose an accurate, efficient, robust and easy-to-implement numerical method to calculate the ground state tunneling splitting based on imaginary-time path integral ('instanton' formulation). The method is genuinely multi-dimensional and free from any additional ad hoc assumptions on potential energy surface. It enables us to calculate the effects of all coupling modes on the tunneling degree of freedom without loss. We also review in this paper some theoretical background and survey some recent work from other groups in calculating multidimensional quantum tunneling effects in chemical reactions.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2006-CiCP-7996

Communications in Computational Physics, Vol. 1 (2006), Iss. 6 : pp. 1096–1116

Published online:    2006-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords: