Quantum Monte Carlo method trial functions

The variational quantum Monte Carlo method (VMC) is both simpler and more efficient than the DMC method, but also usually less accurate. In this method the Rayleigh-Ritz quotient for a trial function 0 is evaluated with Monte Carlo integration. The Metropolis-Hastings algorithm " is used to sample the distribution... 

In the variational quantum Monte Carlo (VQMC) method, the expectation value of the energy ( ) and/or another average property of a system is determined by Monte Carlo integrations. The expectation value of the energy is typically determined for a trial function j/q using Metropolis sampling based on tj/g. It is given by... 

The difference 5 between a true wavefunction > and a trial wavefunc-tion fQ may be determined directly in quantum Monte Carlo calculations. For an analytic trial function from any source, the difference 8 may be calculated and used to correct the trial function to obtain a wavefunction of higher accuracy and a more accurate eigenvalue. Successive correaions offer the possibility of unlimited accuracies. Thus fai the number of applications has been very few, and the method has not been utilized in treating the prob-... 

The Cu (001) surface is exposed. This truncation of the bulk lattice, as well as adsorption, leads to drastic changes in electronic correlation. They are not adequately taken into account by density-functional theory (DFT). A method is required that gives almost all the electronic correlation. The ideal choice is the quantum Monte Carlo (QMC) approach. In variational quantum Monte Carlo (VMC) correlation is taken into account by using a trial many-electron wave function that is an explicit function of inter-particle distances. Free parameters in the trial wave function are optimised by minimising the energy expectation value in accordanee with the variational principle. The trial wave functions that used in this work are of Slater-Jastrow form, consisting of Slater determinants of orbitals taken from Hartree-Fock or DFT codes, multiplied by a so-called Jastrow factor that includes electron pair and three-body (two-electron and nucleus) terms. 

In this brief review we have chosen to concentrate upon the character of some new methods for the Monte Carlo modelling of quantum systems. In so doing we have emphasized certain deficiencies of the older method which rests upon the product trial function in a variational expression. It is necessary to remark that this latter technique remains useful it is a reasonable guide to the phenomena in quantum systems and for soft-core systems gives results for the equation of state of liquids and crystals which are adequate for most purposes. The extension of the Monte Carlo variational method to include three-body correlations is straightforward but computationally slow it should be done to provide reliable checks on the theoretical work on such effects in He-4. The study of inhomogeneous systems and mixtures remains largely unexplored. 

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