Title 



Exchange, idempotent density matrices and beyond
 
Author 


  
Abstract 



After a brief historical introduction, emphasis is placed on the treatment of exchange using density matrices that are explicitly idempotent. This embraces both HarteeFock and density functional 'exchangeonly' methods. For an atom, the exchange energy density can be evaluated asymptotically, and unlike the local density approximation it involves not just one length, rho(r)(1/3), but two, the second being the distance from the nucleus. It is also emphasized, following March and Santamaria [N.H. March, R. Santamaria, Phys. Chem. Liquids 19 (1984) 187] that nonlocal generalizations of kinetic and exchange energy densities can be related via idemopotency of the Dirac, firstorder, density matrix. Examples are then given, starting with the twolevel Be atom and its isoelectronic ions, where both HartreeFock and density functional exchangeonly idempotent density matrices can be expressed in terms of the diagonal density and its gradient, grad rho. This example is followed by the example of a metal surface, but now within a jelliumlikemodel framework. Some explicit results are again given for such models. Attention is then shifted to a formally exact expression for the exchangecorrelation potential, using the differential virial theorem following Holas and March [A. Holas, N.H. March, Phys. Rev. A 51 (1995) 2040]. After a brief physical discussion of the result, in terms now of interacting las well as noninteracting reference) density matrices; both the now nonidempotent firstorder density matrix and the interacting electron pair correlation function, the separation of the HolasMarch exchange potential into a sum of exchange and correlation pieces is effected, following the approach of Levy and March [M. Levy, N.H. March, Phys. Rev. A 55 (1997) 1885], in which the strength of the electronelectron interactions is scaled appropriately. Finally, the exact equation of motion for the firstorder density matrix is treated, and it is stressed here that this is satisfied exactly by the HartreeFock idempotent density matrix. Of course, the correct interacting matrix gamma satisfies gamma(2) < gamma, where gamma now includes the full electronelectron interactions. An example of gamma as a function of the electron density is given for Helike atomic ions in the limit of large atomic number. (C) 2000 Published by Elsevier Science B.V. All rights reserved.   
Language 



English
 
Source (journal) 



Theochem: applications of theoretical chemistry to organic, inorganic and biological problems.  Amsterdam, 1981  2010  
Publication 



Amsterdam : 2000
 
ISSN 



01661280
 
Volume/pages 



501(2000), p. 1727
 
ISI 



000087541100003
 
Full text (Publisher's DOI) 


  
Full text (publisher's version  intranet only) 


  
