Using Gaussian Process Regression to Integrate the Transition Structure Factor Curve for the Many-Body Correlation Energy

2020 ◽  
Author(s):  
Laura Weiler
Keyword(s):  
Gaussian Process ◽  
Structure Factor ◽  
Correlation Energy ◽  
Gaussian Process Regression ◽  
Many Body ◽  
Transition Structure ◽  
The Many ◽  
Structure Factor Curve ◽  
Body Correlation

scholarly journals THE METHOD OF INCREMENTS — A WAVEFUNCTION-BASED AB-INITIO CORRELATION METHOD FOR SOLIDS

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2204-2214 ◽  
Author(s):  
BEATE PAULUS
Keyword(s):  
Experimental Data ◽  
Ab Initio ◽  
Ground State ◽  
Infinite System ◽  
Correlation Energy ◽  
Correlation Method ◽  
Many Body ◽  
Hartree Fock ◽  
The Many ◽  
Good Agreement

The method of increments is a wavefunction-based ab initio correlation method for solids, which explicitly calculates the many-body wavefunction of the system. After a Hartree-Fock treatment of the infinite system the correlation energy of the solid is expanded in terms of localised orbitals or of a group of localised orbitals. The method of increments has been applied to a great variety of materials with a band gap, but in this paper the extension to metals is described. The application to solid mercury is presented, where we achieve very good agreement of the calculated ground-state properties with the experimental data.

Correlation energy in triplet electronic states. Application of the many-body Rayleigh-Schrödinger perturbation theory in the restricted Roothaan-Hartree-Fock formalism

1981 ◽  
Vol 46 (6) ◽  
pp. 1324-1331 ◽  
Author(s):  
Petr Čársky ◽  
Ivan Hubač
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Correlation Energy ◽  
Electronic States ◽  
Many Body ◽  
Third Order ◽  
Explicit Formulas ◽  
Hartree Fock ◽  
The Many ◽  
Schrödinger Perturbation

Explicit formulas over orbitals are given for the correlation energy in triplet electronic states of atoms and molecules. The formulas were obtained by means of the diagrammatic many-body Rayleigh-Schrodinger perturbation theory through third order assuming a single determinant restricted Roothaan-Hartree-Fock wave function. A numerical example is presented for the NH molecule.

Exciton Gas versus Electron Hole Liquid in the Double Quantum Wells

2013 ◽  
Vol 1617 ◽  
pp. 37-42
Author(s):  
Vladimir S. Babichenko ◽  
Ilya Ya. Polishchuk
Keyword(s):  
Quantum Wells ◽  
Gas Phase ◽  
Double Quantum ◽  
Many Body ◽  
Electron Hole ◽  
Coupled Quantum Wells ◽  
The Many ◽  
Special Case ◽  
Selection Of ◽  
Body Correlation

ABSTRACTThe many-body correlation effects in the spatially separated electron and hole layers in the coupled quantum wells (CQW) are investigated. A special case of the many-component electron-hole system is considered, ν>>1 being the number of the components. Keeping the main diagrams in the parameter 1/ν allows us to justify the selection of the RPA diagrams. The ground state of the system is found to be the electron-hole liquid with the energy smaller than the dense exciton gas phase. The possible connection is discussed between the results obtained and the experiments in which the inhomogeneous state in the CQW is found.

scholarly journals Learning (from) the Electron Density: Transferability, Conformational and Chemical Diversity

2020 ◽  
Vol 74 (4) ◽  
pp. 232-236 ◽  
Author(s):  
Alberto Fabrizio ◽  
Ksenia Briling ◽  
Andrea Grisafi ◽  
Clémence Corminboeuf
Keyword(s):  
Machine Learning ◽  
Electron Density ◽  
Density Functional ◽  
Gaussian Process Regression ◽  
Chemical Diversity ◽  
Local Regression ◽  
Many Body ◽  
Decomposition Scheme ◽  
Local Environments ◽  
The Many

Machine-learning in quantum chemistry is currently booming, with reported applications spanning all molecular properties from simple atomization energies to complex mathematical objects such as the many-body wavefunction. Due to its central role in density functional theory, the electron density is a particularly compelling target for non-linear regression. Nevertheless, the scalability and the transferability of the existing machine-learning models of ρ(r) are limited by its complex rotational symmetries. Recently, in collaboration with Ceriotti and coworkers, we combined an efficient electron density decomposition scheme with a local regression framework based on symmetry-adapted Gaussian process regression able to accurately describe the covariance of the electron density spherical tensor components. The learning exercise is performed on local environments, allowing high transferability and linear-scaling of the prediction with respect to the number of atoms. Here, we review the main characteristics of the model and show its predictive power in a series of applications. The scalability and transferability of the trained model are demonstrated through the prediction of the electron density of Ubiquitin.

Optimized Quasiparticle Energies in Many-Body Perturbation Theory

2003 ◽  
Vol 68 (2) ◽  
pp. 331-339 ◽  
Author(s):  
Peter R. Surján ◽  
Dóra Kőhalmi ◽  
Ágnes Szabados
Keyword(s):  
Perturbation Theory ◽  
Correlation Energy ◽  
Rayleigh Quotient ◽  
Energy Functional ◽  
Many Body ◽  
Size Extensivity ◽  
Level Shifts ◽  
Many Body Perturbation Theory ◽  
Moller Plesset ◽  
The Many

For the calculation of the electron correlation energy, usual Koopmans one-electron energies (used in Møller-Plesset partitioning) are replaced by energy-optimized ones to form the denominators of the many-body perturbation theory. Changing these quasiparticle energies can be interpreted as applying special level shifts to the zero-order Hamiltonian, thus it is related to the problem of partitioning in the perturbation theory. The energy functional chosen to be optimized with respect to the quasiparticle energies is the Rayleigh quotient evaluated with the first-order wavefunction Ansatz, expanded up to the third order. The resulting level shifts preserve size extensivity of the many-body perturbation theory.

On the many-body theory of nuclear reactions

1968 ◽  
Vol 111 (1) ◽  
pp. 392-416 ◽  
Author(s):  
K DIETRICH ◽  
K HARA
Keyword(s):  
Nuclear Reactions ◽  
Many Body ◽  
Many Body Theory ◽  
The Many ◽  
Body Theory
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