Quantum Monte Carlo calculations

Anderson J B, Traynor C A and Boghosian B M 1993 An exact quantum Monte-Carlo calculation of the helium-helium intermolecular potential J. Chem. Phys. 99 345... 

Hollenstein H, Marquardt R, Quack M and Suhm M A 1994 Dipole moment function and equilibrium structure of methane In an analytical, anharmonic nine-dimenslonal potential surface related to experimental rotational constants and transition moments by quantum Monte Carlo calculations J. Chem. Phys. 101 3588-602... 

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... 

Umrigar C J, Wilson K G and Wilkins J W 1988 Optimized trial wavefunctions for quantum Monte Carlo calculations Phys. Rev. Lett. 60 1719-22... 

Accurate values of the correlation functional are available thanks to the quantum Monte Carlo calculations of Ceperley and Alder (1980). These values have been interpolated in order to give an analytic form to the correlation potential (Vosko, Wilk and Nusair, 1980). 

Static charge-density susceptibilities have been computed ab initio by Li et al (38). The frequency-dependent susceptibility x(r, r cd) can be calculated within density functional theory, using methods developed by Ando (39 Zang-will and Soven (40 Gross and Kohn (4I and van Gisbergen, Snijders, and Baerends (42). In ab initio work, x(r, r co) can be determined by use of time-dependent perturbation techniques, pseudo-state methods (43-49), quantum Monte Carlo calculations (50-52), or by explicit construction of the linear response function in coupled cluster theory (53). Then the imaginary-frequency susceptibility can be obtained by analytic continuation from the susceptibility at real frequencies, or by a direct replacement co ico, where possible (for example, in pseudo-state expressions). 

The exchange-correlation functional for the uniform electron gas is known to high precision for all values of the electron density, n. For some regimes, these results were determined from careful quantum Monte Carlo calculations, a computationally intensive technique that can converge to the exact solution of the Schrodinger equation. Practical LDA functionals use a continuous function that accurately fits the known values of gas(/i). Several different... 

A.J. Williamson et al., Linear-scaling quantum Monte Carlo calculations. Phys. Rev. Lett. 87, 246406 (2001)... 

M. Burkatzki, C. Filippi, M. Dolg, Energy-consistent pseudopotentials for quantum Monte Carlo calculations. J. Chem. Phys. 126, 234105 (2007) (and references contained therein)... 

In this way Filippi, Umrigar and Gonze [27] have recently calculated the exchange potentials corresponding to the exact (not the x-only) densities of some atoms where the exact densities were determined in a quantum Monte-Carlo calculation. Likewise, for any given approximate functional Ec[ g>i ], the corresponding correlation potential... 

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... 

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

D. Alfe, M. Gillan, M. D. Towler, and R. J. Needs (2004) Efficient localized basis set for quantum Monte Carlo calculations on condensed matter. Phys. Rev. B 70, p. 161101... 

Y. Kwon, D. M. Ceperley, and R. M. Martin (1994) Quantum Monte Carlo calculation of the Fermi-liquid parameters in the two-dimensional electron gas. Phys. Rev. B 50, pp. 1684-1694... 

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). 

For the quantum generalization of the APR model (QAPR) the system corresponding to the all-J case also shows reentrance. This was first predicted by mean-field theory, and then verified via quantum Monte Carlo calculations as well as quantum Monte Carlo calculations analyzed via finite size scaling.Reentrance was also found in the corresponding model of granular superconductors. ... 

The United States is currently a leader in most areas of theoretical/ computational chemistry. In basic theory, Europe has many talented young investigators. Within the next 10 years, given these demographics, the U.S. leadership will be challenged by Europe in electronic structure and basic theory development. This trend does not characterize the entire field of theoretical chemistry. For example, Monte Carlo and molecular dynamics simulation methods were invented in the United States, and to this day, the United States maintains a strong position, especially in quantum Monte Carlo calculations. 

Figure 17 is a plot of ladder-diagram expression[66] for high densities does the RPA2X result agree well with the exact value. 

In spite of these apparent difficulties, the quantum Monte Carlo calculations of cooling rates in ID agree very well with the observations. This indicates that the basic physical interactions aire all understood. What is lacking is a good physical picture of the cooling process, such as the Sisyphus picture that has guided the development of laser cooling so well until now. 

Another important issue in density functional theory is the form of the exchange and correlation potential. In most investigations of metal surfaces, the simple local density approximation is used, again, with surprisingly successful results. In the case of a homogeneous electron gas, the effective exchange-correlation potential is given exactly by and is accurately known from quantum Monte Carlo calculations. Outside the metal, decays... 

The correlation energy for a uniform electron gas can be obtained from quantum Monte Carlo calculations. A widely used functional, derived from such calculations, is that one from Vosko, Wilk, and Nusair [6]. Combined with the exchange funtional of Slater, it is the so-called LDA SVWN functional. 

Williamson AJ, Hood RQ, Grossman JC (2001) linear-scaling quantum Monte Carlo calculations. Phys Rev Lett 8724(24) 246406-(4)... 

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