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  • 1
    Electronic Resource
    Electronic Resource
    Nonadiabatic molecular theory and its application. II. Water molecule Presented at the 1997 Sanibel Conference. (1998)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 69 (1998), S. 629-637 
    Details
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We introduce a new molecular theory beyond the Born-Oppenheimer approximation, where both electrons and nuclei are treated quantum mechanically and equivalently. First, we develop the coupled mean-field theory (CMFT) for both the electronic and nuclear fields. Then, to take into account the dynamic correlation between these particles, we develop a new molecular theory using the generator coordinate method (GCM) based upon the CMFT, which enables us to calculate the molecular eigenstate and eigenvalue directly. Finally, we apply this method to a water molecule and analyze the isotope effect on the vibrational frequency and the particle density.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 629-637, 1998
    Additional Material: 2 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Path integral Monte Carlo method for ab initio calculation (1996)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 1223-1230 
    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: The Feynman path integral method is applied to the many-electron problem. We first give new closure relations in terms of ordinary complex and real numbers, which could be derived from an arbitrary complete set of state vectors. Then, in the path integral form, the partition function of the system and the ensemble average of energy are explicitly expressed in terms of these closure relations. It is impossible to evaluate the path integral by direct numerical integrations because of its huge amount of integration variables. Therefore, we develop an algorithm by the Monte Carlo method with constraints corresponding to the normalization condition of states to calculate the required integral. Finally, the ensemble average of energy for the hydrogen molecule is explicitly evaluated by the quantum Monte Carlo method and results are compared with the result obtained by the ordinary full configuration interaction (CI) method. © 1996 John Wiley & Sons, Inc.
    Additional Material: 1 Tab.
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  • 3
    Electronic Resource
    Electronic Resource
    Path integral formulation for many-electron system (1996)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 59 (1996), S. 457-469 
    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: The Feynman path integral method is applied to the many-electron problem of quantum chemistry. We begin with constructing new closure relations in terms of the linear combination of atomic orbital (LCAO) coefficients and investigate the transition amplitude and the partition function of the system in question; then a “classical path of electrons,” which is described by the time-dependent Hartree-Fock-Roothaan equation, is obtained by minimizing the action integral of the system with respect to the “electron coordinate.” The next order approximation is obtained by evaluating the deviation from this classical path, which is approximately written by a Gaussian integral. The result is expected to be the random-phase approximation. © 1996 John Wiley & Sons, Inc.
    Additional Material: 6 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    Path integral approach to correlation energy (1994)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 51 (1994), S. 265-283 
    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: The Feynman path integral method is applied to the many-electron problem of quantum chemistry. We begin with investigating the partition function of the system in question; then, “a classical path of electron” that corresponds to the Hartree-Fock approximation is obtained by minimizing the thermodynamic potential of the system with respect to the electron coordinate. The next-order approximation is obtained by evaluating the deviation from this classical path, which is approximately written by an easily integrable Gaussian integral. The result is expected to be the random-phase approximation. As numerical examples, the hydrogen molecule and butadiene are treated. © 1994 John Wiley & Sons, Inc.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560510503
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  • 5
    Electronic Resource
    Electronic Resource
    Nonadiabatic treatment of molecular systems by the wavepackets method (1996)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 1261-1270 
    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: We have already developed the many-electron wavepackets (MEWP) method in order to study the dynamics and electronic structure of molecular systems. We extended the MEWP method to study the nonadiabatic effects and formulated a nonadiabatic molecular theory, where both electron and nucleus are treated equivalently. Then we applied our method to the isotope series of hydrogen molecule i.e., H2, HD, and D2, and calculated the total energy and the average distance between nucleus-nucleus, electron-electron, and nucleus-electron in order to analyze numerically the nonadiabatic effect in the molecule. Finally we calculated the real-time evolution of the polarization by means of Chebyshev scheme; and by Fourier transforming this, we found out the excitation spectrum of the system, which corresponds to the electronic excitation and the nuclear vibrational frequency. © 1996 John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Finite temperature ab initio calculation by path integral Monte Carlo method (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 65 (1997), S. 471-476 
    Details
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We develop the path integral method for quantum chemistry, apply the Monte Carlo method to an evaluation of the path integral, and calculate the ensemble average of the energy. For finite temperature, a simple Monte Carlo evaluation of the path integral brings out the negative-sign problem. In this work, to avoid this problem in the numerical evaluation, we apply the new reweighting method to the Monte Carlo integration, and calculate effectively the ensemble average of the energy for finite temperature.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 471-476, 1997
    Additional Material: 3 Ill.
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