Diffusion Quantum Monte Carlo

Ra]agopal G, Needs R J, James A, Kenney S D and Foulkes W M C 1995 Variational and diffusion quantum Monte Carlo calculations at nonzero wave vectors theory and application to diamond-structure germanium Phys. Rev. B 51 10 591-600... 

Starting from the normal mode approximation, one can introduce anharmonicity in different ways. Anharmonic perturbation theory [206] and local mode models [204] may be useful in some cases, where anharmonic effects are small or mostly diagonal. Vibrational self-consistent-field and configuration-interaction treatments [207, 208] can also be powerful and offer a hierarchy of approximation levels. Even more rigorous multidimensional treatments include variational calculations [209], diffusion quantum Monte Carlo, and time-dependent Hartree approaches [210]. 

S. Manten, A. Liichow, Improved Scaling in Diffusion Quantum Monte Carlo with Localized Molecular Orbitals, in Quantum Monte Carlo Methods, Part II, ed. by S.M. Rothstein, W.A. Lester Jr., S. Tanaka (World Scientific, Singapore, 2002), pp. 30 10... 

A diffusion quantum Monte Carlo method based on floating spherical Gaussian orbitals and Gaussian geminals Dipole moment of lithium hydride molecule. 

Ornstein-Uhlenbeck diffusion quantum Monte Carlo calculations on BH and HF with the floating spherical Gaussian orbitals and spherical Gaussian geminals. 

The accuracy of diffusion quantum Monte Carlo simulations in the determination of molecular equilibrium structures. 

Electron affinities with diffusion quantum Monte Carlo for C2 and BO molecules. 

Hinde, R. J. 1998. Structural control of Ar-HF i omplexes using dc electric fields a diffusion quantum Monte Carlo study . Chem. Phys. Lett. 283, 125-130. Jungwirth P. and R. B. Gerber 1995, Quantum dynamics of large polyatomic systems using a classically based separable potential method . J. Chem. Phys. 102. 6046 6056. 

D. M. Benoit, A. X. Chavagnac, and D. C. Clary, Speed improvement of diffusion quantum Monte Carlo calculations on weakly bound clusters, Chem. Phys. Lett. 283, 269-276 (1998). 

Figure 3.1 Size dependence of cohesive energies per atom (CE/n) of mercury clusters Hgn from calculations using a large-core EC-PP and CPP for Hg. Valence correlation is accounted for either within die hybrid model approach (HM) by a pair-potential adjusted for Hg2 or by pure-diffusion quantum Monte Carlo (PDMC) calculations (Wang etal 2000).

Joslin and Goldman [105] in 1992 studied this problem by using the Diffusive Quantum Monte Carlo Methods. By resorting to the hard spherical box model, they performed calculations, not only on the ground state of helium atom, but also for H- and Li+. In this method the Schrodinger equation is... 

The Diffusion Quantum Monte Carlo (DQMC) algorithm and related methods such as the Vibrational Quantum Monte Carlo approach have the important property of scahng well with system size (number of degrees of freedom). At the same time the method can be pursued in principle to yield a numerically exact energy. DQMC was introduced... 

The FN-DQMC calculation in the table uses the diffusion quantum Monte Carlo method. quantum Monte Carlo (QMC) method uses a random process to solve the Schrftdinger equation. Many QMC methods exist, but the diffusion QMC (DQMC) method is most commonly used for molecular calculations. Defining the imaginary time variable t s itjh. 

OOSok Sokolova, S., Ltlchow, A. An ab initio study ofTiC with the diffusion quantum Monte Carlo method, Chem. Phys. Lett. 320 (2000) 421 24. 

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. ... 

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

Table 5.2. Experimental vibrational redshifts for DF and HF with sequential addition of argon solvent atoms. Also shown are redshifts calculated using diffusion quantum Monte Carlo techniques from Ref. 66 and bound state variational calculations by Ernesti and Hutson from Refs. 9,11. The two columns reflect the values calculated within the approximation of pairwise additivity, and including the corrective three-body terms as described more fully in the text. 

Carlo method (VQMC), the diffusion quantum Monte Carlo method (DQMC), the Green s function quantum Monte Carlo method (GFQMC), and the path integral quantum Monte Carlo method (PIQMC). These methods are by their nature strongly related and each has its own peculiar advantages and disadvantages relative to the others. 

The diffusion quantum Monte Carlo method (DQMC) approaches the solution of the Schrodinger equation in a way completely different from that of variational methods. The basic ideas were given above in the succinct description quoted from the original report by Metropolis and Ulam. Here we give a more complete description. 

The standard quantum mechanical problem of the harmonic oscillator may be used to demonstrate the diffusion quantum Monte Carlo method. The system is illustrated in Figure 2. The potential energy is given by the function V = Vikx. The potential energy may be shifted by an arbitrary constant energy to make V negative in the central region near x = 0 and positive away from the center. 

Figure 2 Illustration of a diffusion quantum Monte Carlo calculation for the harmonic oscillator.

To obtain the importance sampling version of diffusion quantum Monte Carlo, we first multiply the basic equation, Eq. [9] by a trial wavefunction /q and define a new function f - x A /o, which is the product of the true wavefunction and the trial wavefunction. After several pages of rearrangement, one may obtain the basic equation for DQMC with importance sampling, ... 

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