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  • 1
    Electronic Resource
    Electronic Resource
    Quantum chemistry by random walk: Exact treatment of many-electron systems (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 7418-7425 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We report an improved Monte Carlo method for quantum chemistry which permits the exact treatment of many-electron systems. The method combines many of the best features of earlier fixed-node, released-node, and positive/negative cancellation methods with new ideas for relocation after node crossing, self-cancellations, multiple cancellations, maximum use of symmetry in promoting cancellations, and rigorous evaluation of energies using importance sampling with trial wave functions. The method is illustrated with applications to the problems of the first excited state of a particle in a two-dimensional box, the two-electron system of excited H2 3Σ+u, and the three-electron system of linear symmetric HHH, the intermediate for the reaction H+H2→H2+H.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.461368
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  • 2
    Electronic Resource
    Electronic Resource
    Quantum chemistry by random walk: Higher accuracy for H+3 (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 3702-3706 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: An improved quantum Monte Carlo calculation for the ground state of the molecular ion H+3 gives higher accuracies than previously attained. The nonrelativistic electronic energy for the equilateral triangle configuration of side length 1.6500 bohrs is found to be −1.343 835±0.000 001 hartrees.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.461924
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  • 3
    Electronic Resource
    Electronic Resource
    Direct Monte Carlo simulation of chemical reaction systems: Simple bimolecular reactions (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 971-978 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In applications to several simple reaction systems we have explored a "direct simulation'' method for predicting and understanding the behavior of gas phase chemical reaction systems. This Monte Carlo method, originated by Bird, has been found remarkably successful in treating a number of difficult problems in rarefied dynamics. Extension to chemical reactions offers a powerful tool for treating reaction systems with nonthermal distributions, with coupled gas-dynamic and reaction effects, with emission and adsorption of radiation, and with many other effects difficult to treat in any other way. The usual differential equations of chemical kinetics are eliminated. For a bimolecular reaction of the type A+B→C+D with a rate sufficiently low to allow a continued thermal equilibrium of reactants we find that direct simulation reproduces the expected second order kinetics. Simulations for a range of temperatures yield the activation energies expected for the reaction models specified. For faster reactions under conditions leading to a depletion of energetic reactant species, the expected slowing of reaction rates and departures from equilibrium distributions are observed. The minimum sample sizes required for adequate simulations are as low as 1000 molecules for these cases. The calculations are found to be simple and straightforward for the homogeneous systems considered. Although computation requirements may be excessively high for very slow reactions, they are reasonably low for fast reactions, for which nonequilibrium effects are most important.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.461052
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  • 4
    Electronic Resource
    Electronic Resource
    A quantum Monte Carlo calculation of the ground state energy of the hydrogen molecule (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 3657-3664 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We have calculated the ground state energy of the hydrogen molecule using the quantum Monte Carlo (QMC) method of solving the Schrödinger equation, without the use of the Born–Oppenheimer or any other adiabatic approximations. The wave function sampling was carried out in the full 12-dimensional configuration space of the four particles (two electrons and two protons). Two different methods were employed: the diffusion quantum Monte Carlo (DQMC) method and the Green's function quantum Monte Carlo (GFQMC) method. This computation is very demanding because the configurations must be evolved on the time scale of the electronic motion, whereas the finite nuclear mass effects are resolved accurately only after equilibration on the much slower time scale of the nuclear motion. Thus, a very large number of iterations is required. The calculations were performed on the CM-2 Connection Machine computer, a massively parallel supercomputer. The enormous speedup afforded by the massive parallelism allowed us to complete the computation in a reasonable amount of time. The total energy from the DQMC calculations is −1.163 97±0.000 05 a.u. A more accurate result was obtained from the GFQMC calculations of −1.164 024±0.000 009 a.u. Expressed as a dissociation energy, the GFQMC result is 36 117.9±2.0 cm−1, including the corrections for relativistic and radiative effects. This result is in close agreement with accurate nonadiabatic-relativistic dissociation energies from variational calculations (corrected for radiative effects) in the range of 36 117.9–36 118.1 cm−1 and with the best experimentally determined dissociation energy of McCormack and Eyler 36 118.1±0.2 cm−1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459737
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  • 5
    Electronic Resource
    Electronic Resource
    Direct Monte Carlo simulation of chemical reaction systems: Internal energy transfer and an energy-dependent unimolecular reaction (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 6607-6612 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We report a direct Monte Carlo simulation of an energy-dependent unimolecular reaction system of the type A→B in which the rates of the reactions of specific states Ai of A increase with their internal energies. Intermolecular exchange of translational and internal energies among colliding species Ai+Aj→Ak+Al is incorporated with use of a simple flexible statistical model satisfying all requirements of momentum and energy conservation, microscopic reversibility, and equilibrium. The required calculations are straight forward and rapid. The observed variation of overall reaction rate with pressure deviates from that of a simple Lindemann–Christiansen mechanism. For unrestricted energy exchange allowing transitions between all levels of A the deviations are small. For restricted (ladder) energy exchange limited to transitions up or down one level per collision the deviations are larger and the behavior is similar to that observed in a number of experimental studies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.466185
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  • 6
    Electronic Resource
    Electronic Resource
    An exact quantum Monte Carlo calculation of the helium–helium intermolecular potential (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 345-351 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We report "exact'' ab initio calculations of potential energies for the interaction of two helium atoms. The quantum Monte Carlo method used is exact in that it requires no mathematical or physical approximations beyond those of the Schrödinger equation. As in most Monte Carlo methods there is a statistical or sampling error which is readily estimated. For the equilibrium internuclear distance of 5.6 bohr, the calculated electronic energy is −5.807 483 6±0.000 000 3 hartrees and the corresponding well depth (ε/k) is 11.01±0.10 K. The calculated total energies are approximately 0.004 hartrees or 1200 K below the most recent variational calculations of Liu and McLean [J. Chem. Phys. 92, 2348 (1989)]. The calculated interaction energies are in excellent agreement with the interaction energies of Liu and McLean and with a recent experimental/theoretical compromise potential energy curve of Aziz and Slaman [J. Chem. Phys. 94, 8047 (1991)] which successfully predicts a variety of experimental measurements. The error bars of the "exact'' quantum Monte Carlo interaction energies straddle the Liu–McLean and Aziz–Slaman results. The Monte Carlo results support the existence of a bound dimer state.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.465812
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  • 7
    Electronic Resource
    Electronic Resource
    Exact quantum Monte Carlo calculations of the potential energy surface for the reaction H+H2→H2+H (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 100 (1994), S. 8089-8095 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We report "exact'' quantum Monte Carlo calculations of the potential energy surface for the reaction H+H2→H2+H. The method used is free of systematic error. The statistical or sampling error was reduced to ±0.10 kcal/mol for several hundred points distributed across the surface, to ±0.02 kcal/mol for the minimum energy approach of H to H2, to ±0.02 kcal/mol near the saddle point, and to ±0.01 kcal/mol at the saddle point. The upper and lower surfaces in the region of the Jahn–Teller cusp were determined with a statistical error of ±0.2 kcal/mol.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.466802
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  • 8
    Electronic Resource
    Electronic Resource
    A simplified released-node quantum Monte Carlo calculation of the ground state of LiH (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 4491-4494 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We report an exact ab initio calculation of the ground state of the LiH molecule using a simplified released-node Green's function quantum Monte Carlo method. The energy determined for an internuclear separation of 3.015 bohr is −8.070 21±0.000 05 hartree, a value lower than that of the lowest-energy variational calculation, more accurate than that of prior quantum Monte Carlo calculations, and in excellent agreement with the nonrelativistic energy of −8.070 21 hartree determined from experimental measurements. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.469497
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  • 9
    Electronic Resource
    Electronic Resource
    Potential energy surface for the hydrogen–iodine reaction (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 100 (1994), S. 4253-4255 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The potential energy surface for the H2–I2 system was determined in analytic variational electronic structure calculations with single- and double-substitution configuration interactions for the 16 valence electrons and with effective potentials for the iodine core electrons. The favored pathway for the overall reaction H2+I2→HI+HI was found to pass through the region of the collinear configuration I–H–H–I. The pathway is accessible to bound and unbound iodine atom pairs and it allows the bimolecular and termolecular reactions, H2+I2→HI+HI and H2+I+I→HI+HI, both proposed by Bodenstein 100 years ago.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.466307
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  • 10
    Electronic Resource
    Electronic Resource
    Improved quantum Monte Carlo calculation of the ground-state energy of the hydrogen molecule (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 2802-2805 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We report an improved Green's function quantum Monte Carlo calculation of the nonrelativistic ground-state energy of the hydrogen molecule, without the use of the Born–Oppenheimer or any other adiabatic approximations. A more accurate trial function for importance sampling and the use of the exact cancellation method combine to yield an energy which is a factor of 10 more accurate than that of previous quantum Monte Carlo calculations. The energy is less accurate than that of recently improved analytic variational calculations. The calculated energy is −1.164 0239 ±0.000 0009 hartree. Expressed as the dissociation energy and corrected for relativistic and radiative effects, the result is 36 117.84±0.20 cm−1, a value in agreement with the most recent experimental value 36 118.11±0.08 cm−1 obtained by Balakrishnan et al. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.468656
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