Quantum tunneling plays crucial roles in some physical and chemical
processes, ranging from quantum cosmology to enzymatic reactions.
The quantum nature of the motion often comes along with
multidimensionality, namely the coupled motion of many degrees of freedom.
The high dimensionality of the potential energy surface
poses a great challenge in both theoretical and numerical descriptions of
tunneling. Numerical simulation based on the Schrodinger equation is often
prohibitively expensive.
We develop an efficient and accurate numerical method to calculate the
tunneling transition, based on the path integral formulation
('instanton') of quantum transition state theory.
It is free from any further ad hoc assumptions ('adiabatic' or 'sudden')
and does not require pre-defined reaction coordinates.
The application to hydrogen tunneling transfer in polyatomic molecules will
also be demonstrated.
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