On-top pair-density interpretation of spin density functional theory, with applications to magnetism (bibtex)

by John P. Perdew, Matthias Ernzerhof, Kieron Burke, Andreas Savin

Abstract:

The on-top pair density P(r, r) gives the probability that one electron will be found on top of another at position r. We find that the local spin density (LSD) and generalized gradient (GGA) approximations for exchange and correlation predict this quantity with remarkable accuracy. We show how this fact and the usual sum-rule arguments explain the success of these approximations for real atoms, molecules, and solids, where the electron spin densities do not vary slowly over space. Self-consistent LSD or GGA calculations make realistic predictions for the total energy E, the total density n(r), and the on-top pair density P(r,r), even in those strongly \textquoteleft\textquoteleftabnormal\textquoteright\textquoteright systems (such as stretched H2) where these approximations break symmetries and yield unrealistic spin magnetization densities m(r). We then suggest that ground-state ferromagnetic iron is a \textquoteleft\textquoteleftnormal\textquoteright\textquoteright system, for which for LSD or GGA m(r) and the related local spin moment are trustworthy, but that iron above the Curie temperature and antiferromagnetic clusters at all temperatures are abnormal system for which the on-top pair density interpretation is more viable than the standard physical interpretation. As an example of a weakly abnormal system, we consider the four-electron ion with nuclear charge Z \textrightarrow $infty$ \copyright 1997 John Wiley & Sons, Inc.

Reference:

On-top pair-density interpretation of spin density functional theory, with applications to magnetism John P. Perdew, Matthias Ernzerhof, Kieron Burke, Andreas Savin, International Journal of Quantum Chemistry 61, 197-205 (1997).

Bibtex Entry:

@article{PEBS97, Pub-num = {32}, Abstract = {The on-top pair density P(r, r) gives the probability that one electron will be found on top of another at position r. We find that the local spin density (LSD) and generalized gradient (GGA) approximations for exchange and correlation predict this quantity with remarkable accuracy. We show how this fact and the usual sum-rule arguments explain the success of these approximations for real atoms, molecules, and solids, where the electron spin densities do not vary slowly over space. Self-consistent LSD or GGA calculations make realistic predictions for the total energy E, the total density n(r), and the on-top pair density P(r,r), even in those strongly {\textquoteleft}{\textquoteleft}abnormal{\textquoteright}{\textquoteright} systems (such as stretched H2) where these approximations break symmetries and yield unrealistic spin magnetization densities m(r). We then suggest that ground-state ferromagnetic iron is a {\textquoteleft}{\textquoteleft}normal{\textquoteright}{\textquoteright} system, for which for LSD or GGA m(r) and the related local spin moment are trustworthy, but that iron above the Curie temperature and antiferromagnetic clusters at all temperatures are abnormal system for which the on-top pair density interpretation is more viable than the standard physical interpretation. As an example of a weakly abnormal system, we consider the four-electron ion with nuclear charge Z {\textrightarrow} $\infty$ {\copyright} 1997 John Wiley \& Sons, Inc.}, Author = {John P. Perdew and Ernzerhof, Matthias and Kieron Burke and Savin, Andreas}, Date-Modified = {2013-02-12 00:16:04 +0000}, Doi = {10.1002/(SICI)1097-461X(1997)61:2<197::AID-QUA2>3.0.CO;2-R}, Issn = {1097-461X}, Journal = {International Journal of Quantum Chemistry}, Number = {2}, Pages = {197-205}, Publisher = {John Wiley \& Sons, Inc.}, Title = {On-top pair-density interpretation of spin density functional theory, with applications to magnetism}, Url = {http://dx.doi.org/10.1002/(SICI)1097-461X(1997)61:2<197::AID-QUA2>3.0.CO;2-R}, Volume = {61}, Year = {1997}, Bdsk-Url-1 = {http://dx.doi.org/10.1002/(SICI)1097-461X(1997)61:2%3C197::AID-QUA2%3E3.0.CO;2-R}}

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