Feynman path integral techniques

Another class of methods have been developed to handle the problem of the solvated electron. These usually involve the treatment of the electron as a quantum particle embedded in a classical fluid using Feynman path-integral techniques. 

The techniques of discretized Feynman path integrals make the use of Eq. 41 practical for the more general case of quantized nuclear motion which is not restricted to harmonic behavior [36, 94, 99b[. Applications of this approach are discussed in Section 1.5 of this chapter. 

Because the path integral techniques can account for quantum effect directly in the simulations, the methodology has been used mostly in studies of the behavior of quantum solutes, including tunneling, charge transfer between solutes, and hydrated electrons. Simulations of pure water ° investigated quantum corrections to effective potentials. The Feynman-Hibbs effective potential is a computationally simple method for estimating quantum effects and has been used to examine the differences in the properties of H2O and 02 . ... 

The PIQMC method is the result of coupling of Feynman s path integral formulation of quantum mechanics with Monte Carlo sampling techniques to produce a method for finite temperature quantum systems. The calculations are not much more complicated than DQMC and produce a sum over all possible states occupied as for a Boltzmann distribution. In the limit of zero temperature... 

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