Diffusion Monte Carlo

Other quantum simulations involve simulations with effective Hamiltonians [261-263] or the simulation of ground state wave properties by Green s function Monte Carlo or diffusion Monte Carlo for reviews and further references on these methods see Refs. 162, 264-268. 

The correlation energy is known analytically in the high-and low-density limits. For typical valence electron densities (1 < r, < 10) and lower densities (r, > 10), it is known numerically from release-node Diffusion Monte Carlo studies [33]. Various parametrizations have been developed to interpolate between the known limits while fitting the Monte Carlo data. The first, simplest and most transparent is that of Perdew and Zunger (PZ) [34] ... 

Analytic or semi-analytic many-body methods provide an independent estimate of ec( .>0- Before the Diffusion Monte Carlo work, the best calculation was probably that of Singwi, Sjblander, Tosi and Land (SSTL) [38] which was parametrized by Hedin and Lundqvist (HL) [39] and chosen as the = 0 limit of Moruzzi, Janak and Williams (MJW) [40]. Table I shows that HL agrees within 4 millihartrees with PW92. A more recent calculation along the same lines, but with a more sophisticated exchange-correlation kernel [42], agrees with PW92 to better than 1 millihartree. 

In this chapter, I have provided a brief overview of the QMC method for electronic structure with emphasis on the more accurate diffusion Monte Carlo (DMC) variant of the method. The high accuracy of the approach for the computation of energies is emphasized, as well as the adaptability to large multiprocessor computers. Recent developments are presented that shed light on the capability of the method for the computation of systems larger than those accessible by other first principles quantum chemical methods. 

A.B. McCoy, in Vibrational Excited States by Diffusion Monte Carlo. Proceedings of the Pacifichem Symposium on Advances in Quantum Monte Carlo. ACS Symposium Series, ed. by J.B. Anderson, S.M. Rothstein, vol. 953 (American Chemical Society, Washington, DC, 2007), pp. 147-164... 

C.J. Umrigar, M.P. Nightingale, K. Runge, A diffusion Monte Carlo algorithm with very small time-step errors. J. Chem. Phys. 99, 2865-2890 (1993)... 

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... 

Jakowski J, Chalasinski G, Gallegos J, Severson MW, Szczesniak MM (2003) Characterization of AmO clusters from ab initio and diffusion Monte Carlo calculations. J Chem Phys 118 2748-2759... 

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). 

INITIAL VIBRATIONAL WAVEFUNCTION OF LARGE CLUSTERS SEPARABLE APPROACH AND DIFFUSION MONTE CARLO METHOD... 

Principally exact solution of the vibrational Schrodinger equation can be found by applying the Diffusion Monte Carlo (DMC) method [40], where the a<-,cnracy for ground state calculations is limited only by the statistical noise, which can be reduced to a desired level bj a sufficient investment of computer time. 

Auer, B. M. and A. B. McCoy 2003, Using diffusion Monte Carlo to evaluate the initial conditions for classical studies of the photodissociation dtriamics of HCl dimer . J. Phys. Chem. A 107. 4 12. 

Finally, we stress that the quantum chemical method presented here has the advantage over DFT-based techniques that it also furnishes wavefunctions that can be used to perform computations of spectra, and therefore have a better contact with the experiment. Another advantage of this approach is that, unlike the diffusion Monte-Carlo method, it can coherently be applied to studies of fermion and mixed boson/fermion doped clusters. An example can be found in our recent work on the Raman spectra of (He)w-Br2(X) clusters [27,28]. 

Figure 9.13 Energy per He atom as a fiinction of ID density from the diffusion Monte Carlo (DMC) calculation (circles and foil curve) of Boninsegni and Moroni [58]. Crosses are hypemetted chain results of Krotscheck and Miller [57]. Analogous DMC results were obtained by Gordillo, Boronat, Casulleras [59].

Relevant calculations using both versions of MM have been reported for (0H )H20 [21, 26] and H5O2+ [27, 28] and some very recent results will be presented below. Diffusion Monte Carlo calculations, done by and in collaboration with Anne McCoy have also been done on these systems, however, these are not reviewed in detail here. 

The more recent ASP potentials of MUlot et al. [183] and their counterparts fitted to the experimental dimer spectra, VRT(ASP-W) [52] and VRT(ASP-W)III [53], have been utihzed in diffusion Monte Carlo (DMC) simulation of water clusters of different sizes [192,193]. The three- and higher body effects were described by a polarization model only, similarly as in empirical polarizable potentials. While polarization models are quite efficient in describing the nonadditive induction in the asymptotic regime, they fail to properly model the short-range nonadditivities, which are definitely non-negligible in smaller trimers. 

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