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To Multireference or not to Multireference: That is the Question?
Int. J. Mol. Sci. 2002, 3(6), 604-638; doi:10.3390/i3060604
Article

Implicit and Explicit Coverage of Multi-reference Effects by Density Functional Theory

1,* , 1, 1, 1 and 2
1 Department of Theoretical Chemistry, G¨oteborg University, Reutersgatan 2, S-413 20 G¨oteborg, Sweden 2 Department of Organic Chemistry and The Lise Meitner-Minerva Center for Computational Quantum Chemistry, Hebrew University, Jerusalem, 91904 Jerusalem, Israel
* Author to whom correspondence should be addressed.
Received: 4 December 2001 / Accepted: 6 April 2002 / Published: 30 June 2002
(This article belongs to the Special Issue Multireference Quantum Chemical Methods)
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Abstract

Multi-reference effects can be covered by density functional theory (DFT) either implicitly via the exchange-correlation functional or explicitly via the form of the Kohn-Sham wave function. With the help of the exchange hole it is shown that the self-interaction error of the exchange functional will mimic long-range electron correlation effects if restricted Kohn-Sham theory is used. Functionals based on Slater or Becke exchange have a relatively large self-interaction error and, therefore, lead to a relatively large implicit coverage of long-range correlation, which, because of the possibility of doublecounting of electron correlation, has to be considered when using these functionals in connection with two- or multi-configurational descriptions based on ensemble DFT methods such as REKS (spin-Restricted Ensemble-referenced KS-DFT). Arguments are given that a REKS description of a multireference problem avoids a double-counting of long-range correlation effects, in particular as in this situation the self-interaction error of the exchange functional simulates more short- rather than longrange correlation effects. There is, however, no guarantee that the short-range effects are not doublecounted, namely once via the exchange and once via the correlation functional. Therefore, one should use hybrid functionals such as B3LYP in connection with multi-reference DFT methods because for hybrid functionals the self-interaction error and by this the implicit coverage of long(short)-range correlation effects is reduced due to the admixture of exact exchange. This rule applies also to broken-symmetry UDFT, which performs better with hybrid rather than GGA functionals. A way of avoiding the implicit coverage of multi-reference effects is given by the combination of wave function theory and DFT methods. The advantages and disadvantages of CAS-DFT are discussed and it is shown that an effective reduction of a double-counting of correlation effects is possible within this method.
Keywords: Exchange functional; self-interaction error; non-dynamic electron correlation; multireference effects; two-configurational DFT; REKS; ensemble theory; CAS-DFT Exchange functional; self-interaction error; non-dynamic electron correlation; multireference effects; two-configurational DFT; REKS; ensemble theory; CAS-DFT
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Cremer, D.; Filatov, M.; Polo, V.; Kraka, E.; Shaik, S. Implicit and Explicit Coverage of Multi-reference Effects by Density Functional Theory. Int. J. Mol. Sci. 2002, 3, 604-638.

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