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  • 1
    Electronic Resource
    Electronic Resource
    Stochastic calculation of interaction energies (1982)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 86 (1982), S. 1200-1204 
    Details
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/j100396a028
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  • 2
    Electronic Resource
    Electronic Resource
    A Bayesian analysis of Green's function Monte Carlo correlation functions (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 8415-8423 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Imaginary-time correlation functions calculated by quantum Monte Carlo (QMC) are analyzed using the maximum entropy method (MaxEnt) to determine the ground-state energy and spectral overlap function. In contrast to earlier applications of MaxEnt, the data is obtained from importanced-sampled zero-temperature quantum Monte Carlo simulations. The analysis includes two steps. First, that spectral overlap function and ground state energy which maximizes the entropy and agrees with the QMC correlation functions is obtained. Then the errors in the energy are evaluated by averaging over all the possible images (average MaxEnt method), the multidimensional integrals being computed using the Metropolis algorithm. The central feature of this approach is that all the information present in the correlation functions is used in the only way consistent with fundamental probabilistic hypotheses. This allows us to fully exploit the information contained in the correlation functions at small imaginary times, thus avoiding large statistical fluctuations associated with large imaginary times. In addition, the computed errors include both the statistical errors and systematic extrapolation errors. The method is illustrated with a harmonic oscillator and the four-electron LiH molecule.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.463411
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  • 3
    Electronic Resource
    Electronic Resource
    The calculation of excited states with quantum Monte Carlo. II. Vibrational excited states (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 552-561 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Using a new Monte Carlo method for computing properties of excited quantum states, correlation function quantum Monte Carlo, we calculate the lowest ten vibrational excited state energies of H2O and H2CO in the Born–Oppenheimer approximation. The statistical errors for H2O are 0.1 cm−1 for the ground state and 15 cm−1 for the tenth excited state while for H2CO they are 2 cm−1 for the ground state and 30 cm−1 for the eighth excited state. The algorithm presented here is easily extensible to larger systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459555
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  • 4
    Electronic Resource
    Electronic Resource
    Erratum: The calculation of excited states with quantum Monte Carlo. II. Vibrational excited states [J. Chem. Phys. 93, 552 (1990)] (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 7782-7782 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.461359
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  • 5
    Electronic Resource
    Electronic Resource
    The calculation of excited state properties with quantum Monte Carlo (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 6316-6328 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new Monte Carlo method for computing excited state properties of quantum systems is introduced. It is a generalization of the transient estimate method used for fermion Green's function Monte Carlo and of subspace projection methods used for computing eigenstates of matrices. The time dependent autocorrelation function of a vector of trial functions is calculated for a random walk generated by the imaginary-time Schrödinger equation and estimates of energy levels are determined by the eigenvalues of the matrix of correlation functions. This method is especially useful for treating states with the same symmetry as it automatically keeps higher states orthogonal to lower states. The estimated energy converges to the exact eigenvalue with a rate which decreases with increasing excitation energy, thus limiting the method to relatively low-lying states. The method is zero variance in the sense that as better trial functions are introduced, the statistical error decreases to zero. The method has a nontrivial bias which is analyzed. As an illustration, the eigenvalues of a double well are computed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.455398
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  • 6
    Electronic Resource
    Electronic Resource
    The penalty method for random walks with uncertain energies (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 9812-9820 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We generalize the Metropolis et al. random walk algorithm to the situation where the energy is noisy and can only be estimated. Two possible applications are for long range potentials and for mixed quantum-classical simulations. If the noise is normally distributed, we are able to modify the acceptance probability by applying a penalty to the energy difference and thereby achieve exact sampling even with very strong noise. When one has to estimate the variance we have an approximate formula, good in the limit of a large number of independent estimates. We argue that the penalty method is nearly optimal. We also adapt an existing method by Kennedy and Kuti and compare to the penalty method on a one-dimensional double well. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478034
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  • 7
    Electronic Resource
    Electronic Resource
    The He2 potential at small distances (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 84 (1986), S. 820-821 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Quantum Monte Carlo methods have been used to determine the exact Born–Oppenheimer interaction energy of two helium atoms with internuclear separations between 0.5 and 1.8 A(ring). There is reasonable agreement with potentials derived from scattering data, however the semiempirical Aziz potential is too repulsive for separation less than 1.8 A(ring). We propose a new potential for this region.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.450581
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  • 8
    Electronic Resource
    Electronic Resource
    Fermion nodes (1991)
    Springer
    Journal of statistical physics 63 (1991), S. 1237-1267 
    Details
    ISSN: 1572-9613
    Keywords: Nodes ; fermions ; density matrix ; simulations of quantum systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The knowledge of the nodes of the many-fermion wave function would enable exact calculation of the properties of fermion systems by Monte Carlo methods. It is proved that fermion nodal regions have a tiling property, there is only one distinct kind of nodal region. All others are related to it by permutational symmetry. For some free particle systems, it is shown that there are only two nodal regions. An explicit form for the nodes of the many-fermion density matrix would enable exact simulations to be carried out at finite temperature. In the high-temperature limit, its nodes are related to Voronoi polyhedra. Twodimensional cross sections of nodes are depicted. General computable families of fermion wave functions and density matrices are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01030009
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  • 9
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    Effect of Disorder on the Critical Temperature of a Dilute Hard-Sphere Gas (2000)
    American Physical Society
    Details
    Publication Date: 2000-11-27
    Print ISSN: 0031-9007
    Electronic ISSN: 1079-7114
    Topics: Physics
    Published by American Physical Society
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  • 10
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    Off-Diagonal Long-Range Order in SolidHe4 (2006)
    American Physical Society
    Details
    Publication Date: 2006-03-16
    Print ISSN: 0031-9007
    Electronic ISSN: 1079-7114
    Topics: Physics
    Published by American Physical Society
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