Fixed-node diffusion Monte Carlo

The quality of a variational quantum Monte Carlo calculation is determined by the choice of the many-body wavefunction. The many-body wavefunction we use is of the parameterized Slater-Jastrow type which has been shown to yield accurate results both for the homogeneous electron gas and for solid silicon (14) (In the case of silicon, for example, 85% of the fixed-node diffusion Monte Carlo correlation energy is recovered). At a given coupling A, 4>A is written as... 

All of l3ie effective potential studies that we are aware of have employed relatively simple fixed-node diffusion Monte Carlo algorithms. This is not to suggest that these are preferable, but rather easy to program. One should not underestimate the advantages of Green s Function [see references (50.51) for instance] or other more recently developed approaches (80). 

Keywords Electronic structure theory ab initio quantum chemistry Many-body methods Quantum Monte Carlo Fixed-node diffusion Monte Carlo Variational Monte Carlo Electron correlation Massively parallel Linear... 

Non-relativistic QMC Variational Monte Carlo and fixed-node Diffusion Monte Carlo. 

This method is known as fixed-node diffusion quantum Monte Carlo (FN-DMC). 

Reptation quantum Monte Carlo (RQMC) [15,16] allows pure sampling to be done directly, albeit in common with DMC, with a bias introduced by the time-step (large, but controllable in DMC e.g. [17]) and the fixed-node approach (small, but not controllable e.g. [18]). Property estimation in this manner is free from population-control bias that plagues calculation of properties in diffusion Monte Carlo (e.g. [19]). Inverse Laplace transforms of the imaginary time correlation functions allow simulation of dynamic structure factors and other properties of physical interest. 

Today, the most important QMC method for molecules is the diffusion quantum Monte Carlo method (DMC). It has been presented in the review articles mentioned above and in detail in the monograph by Hammond et al Here only an overview is given without mathematical rigor. A mathematical analysis of the DMC method, and in particular of its fixed-node approximation, has recently been published by Cances et al. ... 

Figure 1 A family tree of quantum chemistry DFT, density functional theory QMC, quantum Monte Carlo RRV, Rayleigh-Ritz variational theory X-a, X-alpha method KS, Kohn-Sham approach LDA, BP, B3LYP, density functional approximations VQMC, variational QMC DQMC, diffusion QMC FNQMC, fixed-node QMC PIQMC, path integral QMC EQMC, exact QMC HF, Hartree-Fock EC, explicitly correlated functions P, perturbational MP2, MP4, Maller-Plesset perturbational Cl, configuration interaction MRCI, multireference Cl FCI, full Cl CC, CCSD(T), coupled-cluster approaches. Other acronyms are defined in the text.

We reserve a description of the quantum Monte Carlo (QMC) branch until the next section. We note, however, the names variational (VQMC), diffusion (DQMC), fixed-node (FNQMC), path integral (PIQMC), and EQMC (exact quantum Monte Carlo) in the third branch of the family tree of Figure 1. 

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