Review of Feynman's Path Integral in Quantum Statistics: from the Molecular Schrödinger Equation to Kleinert's Variational Perturbation Theory

摘要: Feynman’s path integral reformulates the quantum Schrodinger differential equation to be an equation. It has been being widely used compute internuclear quantum-statistical effects on many-body molecular systems. In this Review, will first introduced, together with Born-Oppenheimer approximation that decouples electronic and motions. Some effective semiclassical potentials, e.g., centroid potential, which are all formulated in terms of integral, discussed compared. These potentials can directly calculate canonical partition function without individual Schrodinger’s energy eigenvalues. As a result, integrations conventionally performed Monte Carlo dynamics sampling techniques. To complement these techniques, we examine how Kleinert’s variational perturbation (KP) theory provide complete theoretical foundation for developing non-sampling/non-stochastic methods systematically potential. enable powerful KP practical systems, have proposed new path-integral method: automated integration-free (AIF-PI) method. Due computationally inexpensive characteristics our AIF-PI method, it perform ab initio calculations kinetic isotope proton-transfer RNA-related phosphoryl-transfer chemical reactions. The computational procedure using along features at minimum absolute-zero (AMAZE), also highlighted review.