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561 results on '"correlation energy"'

101. Semiconductors and Insulators

Author

Fulde, P., Cardona, Manuel, editor, Fulde, Peter, editor, von Klitzing, Klaus, editor, Queisser, Hans-Joachim, editor, Merlin, Roberto, editor, Störmer, Horst, editor, and Fulde, P.

Published
1995
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102. Correlations in Atoms and Molecules

Author

Fulde, P., Cardona, Manuel, editor, Fulde, Peter, editor, von Klitzing, Klaus, editor, Queisser, Hans-Joachim, editor, Merlin, Roberto, editor, Störmer, Horst, editor, and Fulde, P.

Published
1995
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104. Density Functional Theory

Author

Fulde, P., Cardona, Manuel, editor, Fulde, Peter, editor, von Klitzing, Klaus, editor, Queisser, Hans-Joachim, editor, Merlin, Roberto, editor, Störmer, Horst, editor, and Fulde, P.

Published
1995
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107. Analysis of quantum correlations within the ground state of a three level Lipkin model

Author

Javier Faba, Vicente Martín, Luis Robledo, and UAM. Departamento de Física Teórica

Subjects
Quantum Discords, Mean Field Methods, Quantum Physics, Lipkin Model, Field Values, Nuclear Theory, Performance, Física, FOS: Physical sciences, Three-Level, Correlation Energy, Nuclear Theory (nucl-th), Quantum Many-Body Problems, Quantum Correlations, Quantum Physics (quant-ph)
Abstract

The performance of beyond mean field methods in solving the quantum many body problem for fermions is usually characterized by the correlation energy measured with respect to the underlying mean field value. In this paper we address the issue of characterizing the amount of correlations associated to different approximations from a quantum information perspective. With this goal in mind, we analyze the traditional Hartree-Fock (HF) method with spontaneous symmetry breaking, the HF with symmetry restoration and the generator coordinate method (GCM) in a exactly solvable fermion model known as the three-level Lipkin model. To characterize correlations including entanglement and beyond we use the quantum discord between different partition orbitals. We find that for physically motivated partitions, the quantum discord of the exact ground state is reasonably well reproduced by the different approximations. However, other partitions create "fake quantum correlations" in order to capture quantum correlations corresponding to partitions for which the Hartree-Fock solution fails. Those are removed and redistributed through a symmetry restoration process., Comment: 13 pages, 9 figures

Published
2022
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109. Exercises with solutions

Author

Lindh, Roland, Malmqvist, Per-Åke, Berthier, Gaston, editor, Dewar, Michael J. S., editor, Fischer, Hanns, editor, Fukui, Kenichi, editor, Hall, George G., editor, Hinze, Jürgen, editor, Jortner, Joshua, editor, Kutzelnigg, Werner, editor, Ruedenberg, Klaus, editor, Tomasi, Jacopo, editor, and Roos, Björn O., editor

Published
1994
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110. Coupled-cluster Methods in Quantum Chemistry

Author

Taylor, Peter R., Berthier, Gaston, editor, Dewar, Michael J. S., editor, Fischer, Hanns, editor, Fukui, Kenichi, editor, Hall, George G., editor, Hinze, Jürgen, editor, Jortner, Joshua, editor, Kutzelnigg, Werner, editor, Ruedenberg, Klaus, editor, Tomasi, Jacopo, editor, and Roos, Björn O., editor

Published
1994
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113. Semiconductors and Insulators

Author

Fulde, Peter, Cardona, Manuel, editor, Fulde, Peter, editor, von Klitzing, Klaus, editor, Queisser, Hans-Joachim, editor, and Lotsch, Helmut K. V., editor

Published
1993
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117. Density Functional Theory

Author

Fulde, Peter, Cardona, Manuel, editor, Fulde, Peter, editor, von Klitzing, Klaus, editor, Queisser, Hans-Joachim, editor, and Lotsch, Helmut K. V., editor

Published
1993
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118. Low Temperature Plasmas

Author

Isihara, Akira, Cardona, Manuel, editor, Fulde, Peter, editor, von Klitzing, Klaus, editor, Queisser, Hans-Joachim, editor, Lotsch, Helmut K. V., editor, and Isihara, Akira

Published
1993
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120. Introduction

Author

Fraga, Serafin, Klobukowski, M., Muszynska, J., Fabian, E. San, Saxena, K. M. S., Sordo, J. A., Sordo, T. L., Berthier, Gaston, editor, Dewar, Michael J. S., editor, Fischer, Hanns, editor, Fukui, Kenichi, editor, Hall, George G., editor, Hinze, Jürgen, editor, Jaffé, Hans, editor, Jortner, Joshua, editor, Kutzelnigg, Werner, editor, Ruedenberg, Klaus, editor, Tomasi, Jacopo, editor, Fraga, Serafin, Klobukowski, M., Muszynska, J., Fabian, E. San, Saxena, K. M. S., Sordo, J. A., and Sordo, T. L.

Published
1993
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123. Introduction

Author

Herschbach, Dudley R., Herschbach, Dudley R., editor, Avery, John, editor, and Goscinski, Osvaldo, editor

Published
1993
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124. Correlation energy, correlated electron density, and exchange-correlation potential in some spherically confined atoms.

Author

Vyboishchikov, Sergei F.

Subjects
*LINEAR free energy relationship, *DENSITY functional theory, *ELECTRON density, *MOLECULAR dynamics, *COMPUTATIONAL chemistry
Abstract

We report correlation energies, electron densities, and exchange-correlation potentials obtained from configuration interaction and density functional calculations on spherically confined He, Be, Be2+, and Ne atoms. The variation of the correlation energy with the confinement radius Rc is relatively small for the He, Be2+, and Ne systems. Curiously, the Lee-Yang-Parr (LYP) functional works well for weak confinements but fails completely for small Rc. However, in the neutral beryllium atom the CI correlation energy increases markedly with decreasing Rc. This effect is less pronounced at the density-functional theory level. The LYP functional performs very well for the unconfined Be atom, but fails badly for small Rc. The standard exchange-correlation potentials exhibit significant deviation from the 'exact' potential obtained by inversion of Kohn-Sham equation. The LYP correlation potential behaves erratically at strong confinements. © 2016 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Published
2016
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125. Informational energy as a measure of electron correlation.

Author

Flores-Gallegos, N.

Subjects
*ELECTRON configuration, *ATOMS, *LINEAR free energy relationship, *MOLECULES, *INFORMATION theory
Abstract

In this letter we introduce a redefinition of the Onicescu’s discrete informational energy, and show that our definition may be used as a correlation measure in atomic and molecular systems, we analyzed the correlation effects atoms and in a set of 1864 molecules. [ABSTRACT FROM AUTHOR]

Published
2016
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126. Informatics-Based Energy Fitting Scheme for Correlation Energy at Complete Basis Set Limit.

Author

Seino, Junji and Nakai, Hiromi

Subjects
*INFORMATION science, *ENERGY auditing, *NUMERICAL analysis, *EXTRAPOLATION, *GAUSSIAN processes
Abstract

Energy fitting schemes based on informatics techniques using hierarchical basis sets with small cardinal numbers were numerically investigated to estimate correlation energies at the complete basis set limits. Numerical validations confirmed that the conventional two-point extrapolation models can be unified into a simple formula with optimal parameters obtained by the same test sets. The extrapolation model was extended to twopoint fitting models by a relaxation of the relationship between the extrapolation coefficients or a change of the fitting formula. Furthermore, n-scheme fitting models were developed by the combinations of results calculated at several theory levels and basis sets to compensate for the deficiencies in the fitting model at one level of theory. Systematic assessments on the Gaussian-3X and Gaussian-2 sets revealed that the fitting models drastically reduced errors with equal or smaller computational effort. [ABSTRACT FROM AUTHOR]

Published
2016
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127. Calculation of Zn, Cd, Hg adsorption on graphene with incremental CCSD(T) and range-separated hybrid DFT*.

Author

Weber, Fabian, Müller, Carsten, Paulus, Beate, and Reinhardt, Peter

Subjects
*GRAPHENE, *DENSITY functional theory, *ADSORPTION (Chemistry), *ATOMS, *EXTRAPOLATION, *MOLECULAR orbitals
Abstract

At the hand of the adsorption of the metal atoms Zn, Cd and Hg on a graphene sheet, we propose a combination of range-separated hybrid density-functional theory in combination with the incremental scheme in localised orbitals and extrapolation procedures for the description of this type of extended systems. Using only dispersion terms for the long-range part, we were able to obtain results comparable to incremental coupled-cluster calculations with singles, doubles and perturbative triples (CCSD(T)). Repulsive three-centre increments reduce the overall correlation contribution to the binding energy by 20 %. [ABSTRACT FROM PUBLISHER]

Published
2016
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128. Atomic decomposition of Kohn–Sham molecular energies: the kinetic energy component.

Author

Patrikeev, Leonid, Joubert, Laurent, and Tognetti, Vincent

Subjects
*KINETIC energy, *MOLECULAR energy levels (Quantum mechanics), *CHEMICAL decomposition, *ATOMS in molecules theory, *REACTIVITY (Chemistry)
Abstract

The decomposition of molecular energies into atomic contributions within Bader's atoms-in-molecules theory is instrumental in rationalising and accounting for not only the stability but also the reactivity of chemical species. Regardless of how it is achieved, it requires the partitioning of the electronic kinetic energy. While this is ‘natural’ (but computationally expensive) in the context of wavefunction approaches, it is not more practically straightforward in the framework of Kohn–Sham density functional theory, since the corresponding atomic fictitious (related to the non-interacting system) and correlation components must be calculated. In this paper, we discuss the ability of various approaches, based on either exact formal relationships or previously proposed functional approximations, to estimate them in an efficient way for a wide variety of molecular systems. Such results might pave the way toward the realistic modelling of larger systems of chemical interest and may provide new atomic descriptors to characterise atom types. [ABSTRACT FROM PUBLISHER]

Published
2016
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129. Correlation energy for elementary bosons: Physics of the singularity.

Author

Shiau, Shiue-Yuan, Combescot, Monique, and Chang, Yia-Chung

Subjects
*BOSONS, *FERMIONS, *FEYNMAN diagrams, *MOMENTUM transfer, *GROUND state (Quantum mechanics)
Abstract

We propose a compact perturbative approach that reveals the physical origin of the singularity occurring in the density dependence of correlation energy: like fermions, elementary bosons have a singular correlation energy which comes from the accumulation, through Feynman “bubble” diagrams, of the same non-zero momentum transfer excitations from the free particle ground state, that is, the Fermi sea for fermions and the Bose–Einstein condensate for bosons. This understanding paves the way toward deriving the correlation energy of composite bosons like atomic dimers and semiconductor excitons, by suggesting Shiva diagrams that have similarity with Feynman “bubble” diagrams, the previous elementary boson approaches, which hide this physics, being inappropriate to do so. [ABSTRACT FROM AUTHOR]

Published
2016
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131. The Configuration Interaction Method

Author

Siegbahn, Per E. M., Berthier, Gaston, editor, Dewar, Michael J. S., editor, Fischer, Hanns, editor, Fukui, Kenichi, editor, Hall, George G., editor, Hinze, Jürgen, editor, Jaffé, Hans, editor, Jortner, Joshua, editor, Kutzelnigg, Werner, editor, Ruedenberg, Klaus, editor, Tomasi, Jacopo, editor, and Roos, Björn O., editor

Published
1992
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133. Electron-plasmon model in the electron liquid theory

Author

M.V.Vavrukh and S.B.Slobodyan

Subjects
electron liquid, plasmon oscillation, correlation energy, transition operator, structural factor, Physics, QC1-999
Abstract

Here we propose an accurate approach to the description of the electron liquid model in the electron and plasmon terms. Our ideas in the present paper are close to the conception of the collective variables which was developed in the papers of Bohm and Pines. However we use another body of mathematics in the transition to the expanded space of variable particles and plasmons realized by the transition operator. It is evident that in the Random Phase Approximation (RPA), the model which consists of two interactive subsystems of electrons and plasmons is equivalent to the electron liquid model with Coulomb interaction.

Published
2005
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134. Density Functional Theory

Author

Fulde, P., Cardona, Manuel, editor, Fulde, Peter, editor, von Klitzing, Klaus, editor, Queisser, Hans-Joachim, editor, Lotsch, Helmut K. V., editor, and Fulde, P.

Published
1991
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136. Semiconductors and Insulators

Author

Fulde, P., Cardona, Manuel, editor, Fulde, Peter, editor, von Klitzing, Klaus, editor, Queisser, Hans-Joachim, editor, Lotsch, Helmut K. V., editor, and Fulde, P.

Published
1991
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143. Ab Initio Simulation of the IR Spectrum of Hydrated Kaolinite

Author

A.G. Kochur, Tatiana Nazdracheva, Andrey Morozov, Yakov Ermolov, and Victor Yavna

Subjects
basal surfaces, Crystallography, Materials science, kaolinite, General Chemical Engineering, Hartree–Fock method, Ab initio, Infrared spectroscopy, Condensed Matter Physics, Molecular physics, Inorganic Chemistry, electronic and spatial structures, Adsorption, QD901-999, cluster method, correlation energy, Cluster (physics), Kaolinite, Molecule, General Materials Science, Perturbation theory, hydration
Abstract

The hydration of the basal surfaces of kaolinite is studied by theoretical methods. The cluster method was used to simulate the positions of atoms. The positions of the atoms of the basal surfaces of dry and hydrated minerals are optimized by minimizing the total energy in the Hartree–Fock approximation. The adsorption energies of water molecules were calculated taking into account the fourth-order correlation corrections of Møller–Plesset perturbation theory. The formation of the IR spectrum of kaolinite in the range of wave numbers 2500–4500 cm−1 is studied. The experimentally observed effect of the change in relative intensity and position of the band with a change in the moisture content of the sample is interpreted.

Published
2021
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144. POTENTIAL REGULARIZATION AS THE METHOD ACCOUNTING FOR SHORT-RANGE CORRELATIONS IN THE ELECTRON LIQUID THEORY

Author

M.V.Vavrukh and N.L.Tyshko

Subjects
short-range correlation, local-field correction function, correlation energy, binary distribution function, compressibility, Physics, QC1-999
Abstract

In our previous paper [Vavrukh M., Koval' S., Tyshko N., Journal of Physical Studies (Lviv), 2000, vol. 4, p. 403 (in Ukrainian)] we proposed a Coulomb potential regularization as one of the methods for short-range correlation accounting in the electron liquid model. The present paper formulates the criterions of optimal choice of regularization as well as calculates the energetic, structural and dielectric characteristics of the model.

Published
2004
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145. RCCPAC: A parallel relativistic coupled-cluster program for closed-shell and one-valence atoms and ions in FORTRAN.

Author

Mani, B.K., Chattopadhyay, S., and Angom, D.

Subjects
*COUPLED-cluster theory, *CALCULATIONS & mathematical techniques in atomic physics, *MESSAGE passing (Computer science), *WAVE functions, *HYPERFINE interactions
Abstract

We report the development of a parallel FORTRAN code, RCCPAC, to solve the relativistic coupled-cluster equations for closed-shell and one-valence atoms and ions. The parallelization is implemented through the use of message passing interface, which is suitable for distributed memory computers. The coupled-cluster equations are defined in terms of the reduced matrix elements, and solved iteratively using Jacobi method. The ground and excited states of coupled-cluster wave functions obtained from the code could be used to compute different properties of closed-shell and one-valence atom or ion. As an example we compute the ground state correlation energy, attachment energies, E1 reduced matrix elements and hyperfine structure constants. Program summary Program Title: RCCPAC Program Files doi: http://dx.doi.org/10.17632/34rwtn27nb.1 Licensing provisions: MIT licence Programming language: FORTRAN 90 Nature of problem: Compute the ground and excited state wave functions, correlation energy, attachment energies, and E1 transition amplitude and hyperfine structure constant of closed-shell and one-valence atoms or ions using relativistic coupled-cluster theory. Solution method: The basic input data required is an orbital basis set generated using the Dirac–Coulomb Hamiltonian. For the present case, closed-shell and one-valence systems, the orbitals are grouped into occupied, valence and virtual. The relativistic coupled-cluster equations of the single and double excitation cluster amplitudes, which form a set of coupled nonlinear equations, are defined in terms of reduced matrix elements of the residual Coulomb interaction. The equations are solved iteratively in parallel using Message Passing Interface (MPI) with the Jacobi method. However, to overcome the slow convergence of the method, we use Direct Inversion in the Iterated Sub-space (DIIS) to accelerate the convergence. For enhanced performance, the two-electron integrals and 6 j - symbols are precalculated and stored. Furthermore, to optimize memory requirements, selected groups of integrals are computed and stored only by the thread which needs the integrals during computation. Restrictions: For efficient computations, the two-electron reduced Coulomb matrix elements consisting of three and four virtual states are stored in RAM. This limits the size of the basis set, as there should be sufficient space in RAM to store all the integrals. Unusual features: To avoid replication of data across the cores, and optimize the RAM use, the three particle and four particle two-electron Coulomb integrals are distributed. That is, following the loop structure in the driver, each core stores only the integrals it requires. With this feature there is enormous reduction in the RAM required to store the integrals. Additional comments: The code can be modified, with minimal changes, to compute properties other than electromagnetic transitions and hyperfine constants with appropriate modifications. The required modifications are addition of subroutine to compute the single-electron matrix element, and inclusion of calling sequence in the main driver subroutine. [ABSTRACT FROM AUTHOR]

Published
2017
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