University of Jyväskylä | JYX Digital Repository

  • English  | Give feedback |
    • suomi
    • English
 
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
View Item 
  • JYX
  • Artikkelit
  • Matemaattis-luonnontieteellinen tiedekunta
  • View Item
JYX > Artikkelit > Matemaattis-luonnontieteellinen tiedekunta > View Item

Density gradient expansion of correlation functions

ThumbnailPublisher's PDF
View/Open
225.3 Kb

Downloads:  
Show download detailsHide download details  
van Leeuwen, R. (2013). Density gradient expansion of correlation functions. Physical Review B, 87, Article 155142. https://doi.org/10.1103/PhysRevB.87.155142
Published in
Physical Review B
Authors
van Leeuwen, Robert
Date
2013
Discipline
FysiikkaNanoscience CenterPhysicsNanoscience Center
Copyright
© 2013 American Physical Society. Published in this repository with the kind permission of the publisher.

 
We present a general scheme based on nonlinear response theory to calculate the expansion of correlation functions such as the pair-correlation function or the exchange-correlation hole of an inhomogeneous manyparticle system in terms of density derivatives of arbitrary order. We further derive a consistency condition that is necessary for the existence of the gradient expansion. This condition is used to carry out an infinite summation of terms involving response functions up to infinite order from which it follows that the coefficient functions of the gradient expansion can be expressed in terms of the local density profile rather than the background density around which the expansion is carried out. We apply the method to the calculation of the gradient expansion of the one-particle density matrix to second order in the density gradients and recover in an alternative manner the result of Gross and Dreizler [Gross and Dreizler, Z. Phys. A 302, 103 (1981)], which was derived using the Kirzhnits method. The nonlinear response method is more general and avoids the turning point problem of the Kirzhnits expansion. We further give a description of the exchange hole in momentum space and confirm the wave vector analysis of Langreth and Perdew [Langreth and Perdew, Phys. Rev. B 21, 5469 (1980)] for this case. This is used to derive that the second-order gradient expansion of the system averaged exchange hole satisfies the hole sum rule and to calculate the gradient coefficient of the exchange energy without the need to regularize divergent integrals. ...
Publisher
American Physical Society
ISSN Search the Publication Forum
1098-0121
Keywords
theoretical nanoscience
DOI
https://doi.org/10.1103/PhysRevB.87.155142
URI

http://urn.fi/URN:NBN:fi:jyu-201601191152

Publication in research information system

https://converis.jyu.fi/converis/portal/detail/Publication/23217644

Metadata
Show full item record
Collections
  • Matemaattis-luonnontieteellinen tiedekunta [5281]

Related items

Showing items with similar title or keywords.

  • Towards nonlocal density functionals by explicit modelling of the exchange-correlation hole in inhomogeneous systems 

    Giesbertz, Klaas; van Leeuwen, Robert; von Barth, U. (American Physical Society, 2013)
    We put forward an approach for the development of a nonlocal density functional by a direct modeling of the shape of exchange-correlation (xc) hole in inhomogeneous systems. The functional is aimed at giving an accurate ...
  • Analytic density-functionals with initial-state dependence and memory 

    Ruggenthaler, Michael; Nielsen, S.E.B.; van Leeuwen, Robert (American Physical Society, 2013)
    We analytically construct the wave function that, for a given initial state, produces a prescribed density for a quantum ring with two noninteracting particles in a singlet state. In this case the initial state is ...
  • Merging Features from Green's Functions and Time Dependent Density Functional Theory : A Route to the Description of Correlated Materials out of Equilibrium? 

    Hopjan, M.; Karlsson, Daniel; Ydman, S.; Verdozzi, C.; Almbladh, C.-O. (American Physical Society, 2016)
    We propose a description of nonequilibrium systems via a simple protocol that combines exchangecorrelation potentials from density functional theory with self-energies of many-body perturbation theory. The approach, aimed ...
  • Time-dependent density-functional theory for strongly correlated electrons 

    Cort Barrada, Luis (2019)
    One of the most used methods in condensed matter theory and quantum chemistry for the description of matter properties is Time-dependent density-functional theory (TDDFT), an alternative formalism to wave function methods ...
  • Computation of generalized time-periodic waves using differential forms, exact controllability, least-squares formulation, conjugate gradient method and discrete exterior calculus Part 1, Theoretical considerations 

    Pauly, Dirk; Rossi, Tuomo (University of Jyväskylä, 2008)
  • Browse materials
  • Browse materials
  • Articles
  • Conferences and seminars
  • Electronic books
  • Historical maps
  • Journals
  • Tunes and musical notes
  • Photographs
  • Presentations and posters
  • Publication series
  • Research reports
  • Research data
  • Study materials
  • Theses

Browse

All of JYXCollection listBy Issue DateAuthorsSubjectsPublished inDepartmentDiscipline

My Account

Login

Statistics

View Usage Statistics
  • How to publish in JYX?
  • Self-archiving
  • Publish Your Thesis Online
  • Publishing Your Dissertation
  • Publication services

Open Science at the JYU
 
Data Protection Description

Accessibility Statement

Unless otherwise specified, publicly available JYX metadata (excluding abstracts) may be freely reused under the CC0 waiver.
Open Science Centre