Study of the hydrogen bonding using quantum Monte Carlo method

The continuum Quantum Monte Carlo (QMC) method has been developed to calculate the properties of assemblies of interacting particles. It is generally capable of doing so with great accuracy. Two particular variants of QMC are in relatively common use, namely variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). VMC is simple in concept and is designed just to sample a given trail wave function and calculate the expectation value of the Hamiltonian using Monte Carlo numerical integration. DMC is one of a class of so-called projector methods which attempt the much more difficult job of simultaneously creating and sampling the unknown exact ground state wave function. The computational cost of a QMC calculation increases as the cube of number of electron, which makes applications to large systems feasible, and there is no fundamental reason why the accuracy should fall off for large system [1]. When using the Monte Carlo method it is necessary to sample complicated probability distribution in high-dimensional spaces. The Metropolis rejection algorithm has the great advantage that it allows an arbitrarily complex distribution to be sampled in a straight forward way without knowledge of its normalization.