Tunneling splitting and decay of metastable states in polyatomic molecules: invariant instanton theory

This paper gives an overview of recently developed instanton theory of multidimensional tunneling and demonstrates its applicability to real polyatomic systems. One of the key features of the present formulation is rigorous solution of the multidimensional Hamilton-Jacoby and transport equations which constitutes the basis of the semiclassical theory accurate up to the first order in the Planck constant variant Planck's over 2pi. Apart from this fundamental assumption of the semiclassical dynamics the present instanton theory is exact, i.e. it neither involves any further approximation, nor relies on any models. For practical application, the theory is supplemented by numerical methods to construct a multi-dimensional tunneling path (instanton) and to combine the semiclassical theory with high-quality quantum chemical calculations. Emphasis is put on the instanton theory of tunneling splitting in polyatomic molecules. Importance of accurate potential energy surface (PES) information and multidimensional effects is demonstrated by applications to real molecules. The theory of life time of metastable states is also briefly explained.