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  • 1
    Electronic Resource
    Electronic Resource
    Quantum time correlation functions from complex time Monte Carlo simulations: A maximum entropy approach (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 114 (2001), S. 1075-1088 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a way of combining real-time path integral Monte Carlo simulations with a maximum entropy numerical analytic continuation scheme in a new approach for calculating time correlation functions for finite temperature many body quantum systems. The real-time dynamics is expressed in the form of the symmetrized time correlation function, which is suitable for Monte Carlo methods, and several simulation techniques are presented for evaluating this function accurately up to moderate values of time. The symmetrized time correlation function is then analytically continued in combination with imaginary time data to obtain the real-time correlation function. We test this approach on several exactly solvable problems, including two one-dimensional systems, as well two cases of vibrational relaxation of a system coupled to a dissipative environment. The computed time correlation functions are in good agreement with exact results over several multiples of the thermal time β(h-dash-bar), and exhibit a significant improvement over analytic continuation of imaginary time correlation functions. Moreover, we show how the method can be systematically improved. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1331613
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  • 2
    Electronic Resource
    Electronic Resource
    Real time quantum correlation functions. I. Centroid molecular dynamics of anharmonic systems (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 9140-9146 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We investigate the accuracy of the recently proposed centroid molecular dynamics (CMD) method [J. Cao and G. A. Voth, J. Chem. Phys. 100, 5106 (1994)] in the presence of highly anharmonic steep short range repulsive potentials. Such potentials are often present in condensed phases and govern collisions between solvent particles. We compare the results of CMD simulations with exact quantum results for several model one- and two-dimensional nondissipative systems and a one-dimensional system under isobaric conditions. We show that, for nondissipative systems, CMD is accurate only for very short times, and is unable to reproduce the effects of quantum coherences, which play an important role in these few-dimensional systems. CMD gives much better results under isobaric conditions. The correlation functions and the general lineshape of the absorption cross-section in the dipole limit are well reproduced. This is primarily due to dephasing of quantum coherences through inhomogeneous broadening. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.479829
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  • 3
    Electronic Resource
    Electronic Resource
    Real time quantum correlation functions. II. Maximum entropy numerical analytic continuation of path integral Monte Carlo and centroid molecular dynamics data (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 9147-9156 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We propose a method which uses centroid molecular dynamics (CMD) [J. Cao and G. A. Voth, J. Chem. Phys. 100, 5106 (1994)] real-time data in conjunction with the imaginary-time data generated using path integral Monte Carlo simulations in a numerical analytic continuation scheme based on the maximum entropy approach. We show that significant improvement is achieved by including short-time CMD data with the imaginary-time data. In particular, for a particle bilinearly coupled to a harmonic bath, these methods lead to significant improvements over previous calculations and even allow accurate determination of transport coefficients such as the diffusion coefficient and mobility for this system. In addition we show how maximum entropy method can be used to extract accurate dynamic information from short-time CMD data, and that this approach is superior to the direct Fourier transform of long-time data for systems characterized by broad, featureless spectral distributions. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.480028
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  • 4
    Electronic Resource
    Electronic Resource
    Bond profiles for cuboctahedron and twist cuboctahedron (1996)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 1851-1863 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Using the information on the interatomic separations in a molecule, one can construct structural invariants that are the components of a molecular profile. The entries in the profile are derived by averaging different powers of the interatomic separations, suitably normalized so that the increasing powers do not dominate the sequence. Although only a few hundreds of structures have been so analyzed, no two different chemical structures were found to be characterized by the same sequences. A critical test for the conjecture that molecular profiles are unique is to consider structurally closely related systems that are very similar and have several similar properties. In this contribution we investigated the cuboctahedron and the accompanying polyhedron obtained by rotating half of the cuboctahedron against the other half, resulting in the so-called twist cutoctahedron. We show that even this pair of closely related structures has different profiles. We have also examined the generalized molecular profiles obtained by inserting n additional points along each edge of the polyhedra. The convergence of the profiles as n increases is discussed. It appears thus that these generalized molecular profiles, called line profiles or bond profiles, are likely to lead to a unique characterization of structures in which not only the geometry of atoms is recorded but also the geometry of the connectivity of the structure. © 1996 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    On characterization of molecular surfaces (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 65 (1997), S. 1065-1076 
    Details
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We consider the problem of quantitative characterization of the molecular surface. We start with a set of matrices, the elements of which give interatomic separation and higher powers of the separations. Averaged row sums of individual matrices suitably normalized give molecular profiles. The problem that we consider is how to generalize this approach to 2-dimensional and 3-dimensional objects. By using a large number of random points distributed over the molecular surface or molecular volume, respectively, we arrive at matrices from which one can extract invariants that offer a good characterization of the molecular surface and the molecular volume. It is suggested that the ratio V/S, where V and S are components of the volume and surface profile for a molecule, respectively, represents a novel shape index.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 1065-1076, 1997
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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