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  • 1
    Electronic Resource
    Electronic Resource
    Reply to "Comment on: ‘Sampling the exact electron distribution by diffusion quantum Monte Carlo' '' (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 2120-2120 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457999
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  • 2
    Electronic Resource
    Electronic Resource
    Infinitesimal differential diffusion quantum Monte Carlo: Diatomic molecular properties (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 1221-1227 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We show how to estimate, for a given molecule, the first and higher derivatives of the expected value of an operator with respect to one or more physical parameters. This is done with high accuracy achieved by sampling to within a certain approximation from the exact electron distribution, compatible with the Hellmann–Feynman theorem. Finite difference approximations are avoided. The required derivatives of the unknown exact wave function are determined by averaging expressions involving only the total serial correlation of known quantities. The operator is not restricted to the case of the molecular Hamiltonian. This allows for computation of virtually all ground-state properties of a molecule by a single, relatively trivial computer program. Our formulas are presented and applied in the context of a diatomic molecule (LiH), but they can be readily extended to polyatomics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458130
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  • 3
    Electronic Resource
    Electronic Resource
    A Green's function used in diffusion Monte Carlo (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 1902-1903 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.453211
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  • 4
    Electronic Resource
    Electronic Resource
    Sampling the exact electron distribution by diffusion quantum Monte Carlo (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 4880-4884 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: By the accummulation of branching factors in diffusion quantum Monte Carlo (DQMC) and their use as statistical weights, instead of the standard deletion and replication of configurations, we can estimate the averages of (nondifferential) operators taken over the exact electron distribution. This requires only a trivial modification of existing DQMC codes. We illustrate our algorithm by computing ground-state properties for H2 and LiH which are related to the interelectron distance. We also estimate the dipole moment of LiH.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.455657
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  • 5
    Electronic Resource
    Electronic Resource
    Estimating the relativistic energy by diffusion quantum Monte Carlo (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 88 (1988), S. 3784-3787 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We report formulas to estimate the relativistic corrections for atoms or molecules (treated as the first order perturbation) by diffusion quantum Monte Carlo (DQMC) simulations. Our formulas involve primarily quantities which are routinely computed in nonrelativistic simulations. Hence our approach entails only minor additional modifications of existing (all electron) DQMC codes. We illustrate our algorithm by estimating various relativistic corrections to the ground state energy of LiH.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.453877
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  • 6
    Electronic Resource
    Electronic Resource
    Reliable diffusion quantum Monte Carlo (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 3629-3637 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: By introducing perturbations of O(τ) type (where τ is the time step used in the simulation) to our diffusion quantum Monte Carlo algorithm we obtain a simulated energy which is reasonably constant over a wide range of τ values. Reliable estimation of the fixed-node energy (τ=0 intercept) results, as extrapolation becomes more robust and a radical change in small τ behavior becomes less likely. We apply our techniques to the problem of estimating the ground-state energy of LiH and H2O.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.454883
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  • 7
    Electronic Resource
    Electronic Resource
    Dirac equation and Clifford algebra (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2309-2314 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Dirac equation is rewritten in the framework of a Clifford algebra, revealing some new features, of which the most interesting is the U(1)×SU(2) symmetry of the corresponding Lagrangian.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530554
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  • 8
    Electronic Resource
    Electronic Resource
    Diffusion quantum Monte Carlo calculation of nondifferential properties for atomic ground states (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 8525-8535 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: An algorithm to sample the exact (within the nodal error) ground state distribution to find nondifferential properties of multielectron systems is developed and applied to first-row atoms. Calculated properties are the distribution moments and the electronic density at the nucleus (expected value of the δ operator). For this purpose compact trial functions are developed and optimized, and a new estimator for the δ is formulated. A comparison is made with results of highly accurate post-Hartree-Fock calculations, thereby illuminating the nodal error in our estimates. In general, we obtain more accurate estimates for the distribution moments than those obtained previously using Monte Carlo methods, despite the relative crudeness of our trial functions. We confirm the literature values for the electron density at the nucleus for the lighter atoms (Li-C), but disagree with previous (Monte Carlo) estimates for the heavier ones (N-Ne). © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.475004
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  • 9
    Electronic Resource
    Electronic Resource
    Infinitesimal differential diffusion quantum Monte Carlo study of diatomic vibrational frequencies (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 2071-2076 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We show how to extend the formalism of infinitesimal differential diffusion quantum Monte Carlo to the case of higher derivatives of the ground-state energy of a molecule with respect to the molecular geometry. We use LiH as an example, but the technique can be extended to more complicated, nonliner molecules as well. We obtain good agreement with experimental values for the energy derivatives and for the harmonic and anharmonic frequencies of LiH and LiD, despite using a compact single-determinant wave function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.462059
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  • 10
    Electronic Resource
    Electronic Resource
    Infinitesimal differential diffusion quantum Monte Carlo study of CuH spectroscopic constants (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 98 (1993), S. 6401-6405 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We show how to extend the formalism of infinitesimal differential diffusion quantum Monte Carlo to the case of higher derivatives of the ground-state energy of a molecule with respect to the molecular geometry for a large-Z molecule. We propose a new all-electron approach based on the idea of using different simulation time-scales for different shells of the constituent atoms, viz., a substantially smaller time-step for innermost shells, and relatively large time-steps for the valence electrons. We avoid the approximations inherent in pseudopotential methods while at the same time, when used in conjunction with variational Monte Carlo, the sampling is done on a firm theoretical basis. We use CuH as an example, obtaining properties with an accuracy on par with those from SDCI, despite our using a crude single-determinant wave function with only two adjustable parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.464838
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