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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 117 (2002), S. 3020-3026 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: New path integral Monte Carlo constant volume specific heat (CV) estimators are presented that improve upon the thermodynamic, virial, and centroid virial CV estimators via a free particle projection. These projected estimators significantly reduce the numerical noise of the traditional estimators. The new projected thermodynamic estimator has particular advantages when derivatives of the potential are expensive to evaluate. A double virial estimator is derived for real space path integrals and comparisons are made to it. The centroid virial estimators are found to be significantly better than the noncentroid virial estimators. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 5951-5955 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new path integral energy estimator is presented that improves upon the thermodynamic energy estimator via a free particle projection. This centroid thermodynamic estimator significantly reduces the numerical noise of the thermodynamic estimator. The debate as to which estimator is better (virial, centroid virial, or thermodynamic) is partially resolved. The centroid estimators are found to be significantly better than their noncentroid analogues. The new centroid thermodynamic estimator has accuracy close to the centroid virial estimator, and may have particular advantages when derivatives of the potential are expensive to evaluate.© 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 10738-10745 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Density functional theory (DFT) has gained popularity because it can frequently give accurate energies and geometries. The evaluation of DFT integrals in a fully analytical manner is generally impossible; thus, most implementations use numerical quadrature over grid points. The grid-free approaches were developed as a viable alternative based upon the resolution of the identity (RI). Of particular concern is the convergence of the RI with respect to basis set in the grid-free approach. Conventional atomic basis sets are inadequate for fitting the RI, particularly for gradient corrected functionals [J. Chem. Phys. 108, 9959 (1998)]. The focus of this work is on implementation of and selection of auxiliary basis sets. Auxiliary basis sets of varying sizes are studied and those with sufficient flexibility are found to adequately represent the RI. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The natural orbitals and their corresponding occupation numbers are constructed for several interesting problems to demonstrate that the existence of negative natural orbital occupation numbers for single reference correlation methods provides a simple diagnostic for the need for a multiconfigurational description of the wave function. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 6580-6582 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The Almlöf–Zheng approach to grid-free density functional theory (DFT) uses the resolution of the identity (RI) instead of a finite grid to evaluate the integrals. Application of the RI can lead to stability problems, particularly when gradients are involved. The focus of the current work is on choosing a stable method of evaluating the gradient correction using the RI. A stable method is compared to several unstable methods. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 9959-9969 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Density functional theory (DFT) has gained popularity, because it can frequently give accurate energies and geometries. Because evaluating DFT integrals fully analytically is usually impossible, most implementations use numerical quadrature over grid points, which can lead to numerical instabilities. To avoid these instabilities, the Almlöf-Zheng (AZ) grid-free approach was developed. This approach involves application of the resolution of the identity (RI) to evaluate the integrals. The focus of the current work is on the implementation of the AZ approach into the electronic structure code GAMESS, and on the convergence of the resolution of the identity with respect to basis set in the grid-free approach. Both single point energies and gradients are calculated for a variety of functionals and molecules. Conventional atomic basis sets are found to be inadequate for fitting the RI, particularly for gradient corrected functionals. Further work on developing auxiliary basis set approaches is warranted. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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