Commun. Comput. Phys., 1 (2006), pp. 1096-1116.


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

Jing Shi 1*

1 Program in Applied and Computational Mathematics, Princeton University, NJ 08544, USA.

Received 20 March 2006; Accepted (in revised version) 8 May 2006

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 Schrodinger 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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Key words: Quantum tunneling; path integral; chemical reaction.


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Correspondence to: Jing Shi , Program in Applied and Computational Mathematics, Princeton University, NJ 08544, USA. Email: jshi@math.princeton.edu
 

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