The variation of the energy functional with respect to the density matrix of first order

Baumann, G.; Duscher, R.

doi:10.1007/bf01307281

Z. Physik B - Condensed Matter

1987

DOI: 10.1007/bf01307281

|View full text |Cite

The variation of the energy functional with respect to the density matrix of first order

G. Baumann

R. Duscher

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1990

2009

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

The Functional Equations for the Kinetic and Exchange Energy Functionals

Baumann

Duscher

1990

Physica Status Solidi (b)

View full text Add to dashboard Cite

The Hohenberg-Kohn theorem proves the existence of a universal energy functional. But still its explicit structure is unknown. Unknown parts of the energy functional, namely the kinetic and the exchange interaction energy are discussed. Based on a functional formulation of the virial theorem "functional equations" for these unknown quantities are deduced establishing a relation between the functional and its derivative. Though there is no general formalism for solving such equations they may be used to determine the structure of the unknown functionals. Starting with simple formal assumptions for the exchange energy, some well-known approximations are derived for this functional thus proving the value of this new technique.Das Hohenberg-Kohn-Theorem weist die Existenz eines universellen Energiefunktionals nach. Allerdings ist seine explizite Struktur nach wie vor unbekannt. Die unbekannten Teile des Energiefunktionals werden diskutiert. Dies sind, das Funktional der kinetischen und der Austausch-Energie. Aufbauend auf einer funktionalen Formulierung des Virial-Theorems werden "Funktionalgleichungen" fur diese unbekannten Energieanteile abgeleitet, welche die Funktionale und ihre Funktionalableitungen in Beziehung zueinander setzen. Obwohl kein allgemeiner Losungsformalismus fur derartige Gleichungen bekannt ist, lassen sie sich zur Bestimmung der unbekannten Funktionale verwenden. Ausgehend von einfachen, formalen Annahmen hinsichtlich der Austausch-Energie werden wohlbekannte Naherungen fur dieses Funktional abgeleitet. Dies zeigt den Nutzen dieser neuen Technik auf.

show abstract

The Functional Equations for the Kinetic and Exchange Energy Functionals

Baumann

Duscher

1990

Physica Status Solidi (b)

View full text Add to dashboard Cite

show abstract

The calculation of adiabatic-connection curves from full configuration-interaction densities: Two-electron systems

Teale

Coriani

Helgaker

2009

The Journal of Chemical Physics

121

View full text Add to dashboard Cite

The Lieb formulation of density-functional theory is briefly reviewed and its straightforward generalization to arbitrary electron-electron interaction strengths discussed, leading to the introduction of density-fixed and potential-fixed adiabatic connections. An iterative scheme for the calculation of the Lieb functionals under the appropriate constraints is outlined following the direct optimization approach of Wu and Yang [J. Chem. Phys. 118, 2498 (2003)]. First- and second-order optimization schemes for the calculation of accurate adiabatic-connection integrands are investigated and compared; the latter is preferred both in terms of computational efficiency and accuracy. The scheme is applicable to systems of any number of electrons. However, to determine the accuracy that may be achieved, the present work focuses on two-electron systems for which a number of simplifications may be exploited. The procedure is applied to the helium isoelectronic series and the H(2) molecule. The resulting adiabatic-connection curves yield the full configuration-interaction exchange-correlation energies extrapolated to the basis-set limit. The relationship between the Kohn-Sham and natural orbitals as functions of the electron-electron interaction strength is explored in detail for H(2). The accuracy with which the exchange-correlation contributions to the modified local potential can be determined is discussed. The new accurate adiabatic-connection curves are then compared with some recently investigated approximate forms calculated using accurate full configuration-interaction input data. This study demonstrates that the adiabatic-connection integrand may be determined accurately and efficiently, providing important insights into the link between the Kohn-Sham and traditional quantum-chemical treatments of the exchange-correlation problem in electronic-structure theory.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

The variation of the energy functional with respect to the density matrix of first order

Cited by 2 publications

References 7 publications

The Functional Equations for the Kinetic and Exchange Energy Functionals

The Functional Equations for the Kinetic and Exchange Energy Functionals

The calculation of adiabatic-connection curves from full configuration-interaction densities: Two-electron systems

Contact Info

Product

Resources

About