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Books on the topic 'Hartree-Fock approximation'

Author: Grafiati

Published: 4 June 2021

Last updated: 29 July 2024

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1

Dyall, Kenneth G. All-electron molecular Dirac-Hartree-Fock calculations: Properties of the Group IV monoxides GeO, SnO and Pbo. [Washington, D.C: National Aeronautics and Space Administration, 1991.

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2

Dyall, Kenneth G. All-electron molecular Dirac-Hartree-Fock calculations: Properties of the Group IV monoxides GeO, SnO and Pbo. [Washington, D.C: National Aeronautics and Space Administration, 1991.

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3

Dyall, Kenneth G. Polyatomic molecular Dirac-Hartree-Fock calculations with Gaussian basis sets. [Moffett Field, CA: NASA Ames Research Center, 1990.

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4

Mestechkin, M. M. Nestabilʹnostʹ uravneniĭ Khartri-Foka i ustoĭchivostʹ molekul. Kiev: Nauk. dumka, 1986.

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5

Ramón, Carbó, and Klobukowski M, eds. Self-consistent field: Theory and applications. Amsterdam: Elsevier New York, NY, U.S.A., 1990.

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6

Tomas, Brage, and Jönsson Per, eds. Computational atomic structure: An MCHF approach. Bristol, UK: Institute of Physics Publ., 1997.

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7

H, Adachi, Mukoyama T, and Kawai J, eds. Hartree-Fock-Slater method for materials science: The DV-Xa method for design and characterization of materials. Berlin: Springer, 2006.

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8

Gross, E. K. U. Many-particle theory. Bristol: A. Hilger, 1991.

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9

(Editor), H. Adachi, T. Mukoyama (Editor), and J. Kawai (Editor), eds. Hartree-Fock-Slater Method for Materials Science: The DV-X Alpha Method for Design and Characterization of Materials (Springer Series in Materials Science). Springer, 2005.

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10

All-electron molecular Dirac-Hartree-Fock calculations: Properties of the Group IV monoxides GeO, SnO and Pbo. [Washington, D.C: National Aeronautics and Space Administration, 1991.

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11

Froese-Fischer, Charlotte. Computational Atomic Structure: An MCHF Approach. CRC Press LLC, 2019.

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12

Froese-Fischer, Charlotte. Computational Atomic Structure: An MCHF Approach. CRC Press LLC, 2019.

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13

Computational Atomic Structure: An MCHF Approach. CRC Press LLC, 2019.

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14

Brage, Tomas, Per Jonsson, and Charlotte Froese-Fischer. Computational Atomic Structure: An MCHF Approach. CRC Press LLC, 2021.

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15

Brage, Tomas, Per Jonsson, and Charlotte Froese-Fischer. Computational Atomic Structure: An MCHF Approach. CRC Press LLC, 2021.

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16

Brage, Tomas, Per Jonsson, and Charlotte Froese-Fischer. Computational Atomic Structure: An MCHF Approach. CRC Press LLC, 2021.

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17

Brage, Tomas, Per Jonsson, and Charlotte Froese-Fischer. Computational Atomic Structure: An MCHF Approach. CRC Press LLC, 2021.

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18

Computational Atomic Structure: An MCHF Approach. CRC Press LLC, 2019.

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19

Computational Atomic Structure. Taylor & Francis Group, 2019.

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20

Kawai, Jun, Takeshi Mukoyama, and Hirohiko Adachi. Hartree-Fock-Slater Method for Materials Science: The DV-X Alpha Method for Design and Characterization of Materials. Springer, 2010.

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21

Lauderdale, Walter John. Many body perturbation theory using a restricted open-shell Hartree-Fock (ROHF) reference function. 1991.

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22

Clerc, Daryl G. Periodic Hartree-Fock studies of LixTiS₂, 0 [less than or equal to] x [less than or equal to] 1 and LixCd₂P₂S₆, x = 0, 1, 2 and 3. 1995.

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23

Trucks, Gary W. The analytic evaluation of molecular properties and gradients for correlated wavefunctions. 1988.

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24

Kohanoff, Jorge. Electronic Structure Calculations for Solids and Molecules: Theory and Computational Methods. Cambridge University Press, 2010.

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25

Electronic Structure Calculations for Solids and Molecules. Cambridge University Press, 2006.

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26

Morawetz, Klaus. Approximations for the Selfenergy. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0010.

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The systematic expansion of the selfenergy is presented with the help of the closure relation of chapter 7. Besides Hartree–Fock leading to meanfield kinetic equations, the random phase approximation (RPA) is shown to result into the Lennard–Balescu kinetic equation, and the ladder approximation into the Beth–Uehling–Uhlenbeck kinetic equation. The deficiencies of the ladder approximation are explored compared to the exact T-matrix by missing maximally crossed diagrams. The T-matrix provides the Bethe–Salpeter equation for the two-particle correlation functions. Vertex corrections to the RPA are presented. For a two-dimensional example, the selfenergy and effective mass are calculated. The structure factor and the pair-correlation function are introduced and calculated for various approximations.

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27

Dahl, Jens Peder, and John Avery. Local Density Approximations in Quantum Chemistry and Solid State Physics. Springer London, Limited, 2013.

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28

Dahl, Jens Peder, and John Avery. Local Density Approximations in Quantum Chemistry and Solid State Physics. Springer, 2013.

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29

Giuliani, Gabriele, and Giovanni Vignale. Quantum Theory of the Electron Liquid. Cambridge University Press, 2005.

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30

Giuliani, Gabriele, and Giovanni Vignale. Quantum Theory of the Electron Liquid. Cambridge University Press, 2005.

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31

Giuliani, Gabriele, and Giovanni Vignale. Quantum Theory of the Electron Liquid. Cambridge University Press, 2012.

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32

Giuliani, Gabriele, and Giovanni Vignale. Quantum Theory of the Electron Liquid. Cambridge University Press, 2005.

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33

Giuliani, Gabriele, and Giovanni Vignale. Quantum Theory of the Electron Liquid. Cambridge University Press, 2008.

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34

Boudreau, Joseph F., and Eric S. Swanson. Quantum mechanics II–many body systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0023.

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Chapter 23 develops formalism relevant to atomic and molecular electronic structure. A review of the product Ansatz, the Slater determinant, and atomic configurations is followed by applications to small atoms. Then the self-consistent Hartree-Fock method is introduced and applied to larger atoms. Molecular structure is addressed by introducing an adiabatic separation of scales and the construction of molecular orbitals. The use of specialized bases for molecular computations is also discussed. Density functional theory and its application to complicated molecules is introduced and the local density approximation and the Kohn-Sham procedure for solving the functional equations are explained. Techniques for moving beyond the local density approximation are briefly reviewed.

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35

Fox, Raymond. The Use of Self. Oxford University Press, 2011. http://dx.doi.org/10.1093/oso/9780190616144.001.0001.

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This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic potential functions using NNs; (v) self-starting methods for obtaining analytic PES from ab inito electronic structure calculations using direct dynamics; (vi) development of a novel method, namely, combined function derivative approximation (CFDA) for simultaneous fitting of a PES and its corresponding force fields using feedforward neural networks; (vii) development of generalized PES using many-body expansions, NNs, and moiety energy approximations; (viii) NN methods for data analysis, reaction probabilities, and statistical error reduction in chemical reaction dynamics; (ix) accurate prediction of higher-level electronic structure energies (e.g. MP4 or higher) for large databases using NNs, lower-level (Hartree-Fock) energies, and small subsets of the higher-energy database; and finally (x) illustrative examples of NN applications to chemical reaction dynamics of increasing complexity starting from simple near equilibrium structures (vibrational state studies) to more complex non-adiabatic reactions. The monograph is prepared by an interdisciplinary group of researchers working as a team for nearly two decades at Oklahoma State University, Stillwater, OK with expertise in gas phase reaction dynamics; neural networks; various aspects of MD and Monte Carlo (MC) simulations of nanometric cutting, tribology, and material properties at nanoscale; scaling laws from atomistic to continuum; and neural networks applications to chemical reaction dynamics. It is anticipated that this emerging field of NN in chemical reaction dynamics will play an increasingly important role in MD, MC, and quantum mechanical studies in the years to come.

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36

Raff, Lionel, Ranga Komanduri, Martin Hagan, and Satish Bukkapatnam. Neural Networks in Chemical Reaction Dynamics. Oxford University Press, 2012. http://dx.doi.org/10.1093/oso/9780199765652.001.0001.

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This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic potential functions using NNs; (v) self-starting methods for obtaining analytic PES from ab inito electronic structure calculations using direct dynamics; (vi) development of a novel method, namely, combined function derivative approximation (CFDA) for simultaneous fitting of a PES and its corresponding force fields using feedforward neural networks; (vii) development of generalized PES using many-body expansions, NNs, and moiety energy approximations; (viii) NN methods for data analysis, reaction probabilities, and statistical error reduction in chemical reaction dynamics; (ix) accurate prediction of higher-level electronic structure energies (e.g. MP4 or higher) for large databases using NNs, lower-level (Hartree-Fock) energies, and small subsets of the higher-energy database; and finally (x) illustrative examples of NN applications to chemical reaction dynamics of increasing complexity starting from simple near equilibrium structures (vibrational state studies) to more complex non-adiabatic reactions. The monograph is prepared by an interdisciplinary group of researchers working as a team for nearly two decades at Oklahoma State University, Stillwater, OK with expertise in gas phase reaction dynamics; neural networks; various aspects of MD and Monte Carlo (MC) simulations of nanometric cutting, tribology, and material properties at nanoscale; scaling laws from atomistic to continuum; and neural networks applications to chemical reaction dynamics. It is anticipated that this emerging field of NN in chemical reaction dynamics will play an increasingly important role in MD, MC, and quantum mechanical studies in the years to come.

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37

Horing, Norman J. Morgenstern. Equations of Motion with Particle–Particle Interactions and Approximations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0008.

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Starting with the equation of motion for the field operator ψ(x,t) of an interacting many-particle system, the n-particle Green’s function (Gn) equation of motion is developed, with interparticle interactions generating an infinite chain of equations coupling it to (n+1)- and (n−1)-particle Green’s functions (Gn+1 and Gn−1, respectively). Particularly important are the one-particle Green’s function equation with its coupling to the two-particle Green’s function and the two-particle Green’s function equation with its coupling to the three-particle Green’s function. To develop solutions, it is necessary to introduce non-correlation decoupling procedures involving the Hartree and Hartree-Fock approximations for G2 in the G1 equation; and a similar factorization “ansatz” for G3 in the G2 equation, resulting in the Sum of Ladder Diagrams integral equation for G2, with multiple Born iterates and finite collisional lifetimes. Similar treatment of the G11-equation for the joint propagation of one-electron and one-hole subject to mutual Coulomb attraction leads to bound electron-hole exciton states having a discrete hydrogen like spectrum of energy eigenstates. Its role in single-particle propagation is also discussed in terms of one-electron self-energy Σ‎ and the T-matrix

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