Int. J. Mol. Sci. 2002, 3(6), 604-638; doi:10.3390/i3060604

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

1,* email, 1, 1, 1 and 2
Received: 4 December 2001; Accepted: 6 April 2002 / Published: 30 June 2002
(This article belongs to the Special Issue Multireference Quantum Chemical Methods)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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
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MDPI and ACS Style

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.

AMA Style

Cremer D, Filatov M, Polo V, Kraka E, Shaik S. Implicit and Explicit Coverage of Multi-reference Effects by Density Functional Theory. International Journal of Molecular Sciences. 2002; 3(6):604-638.

Chicago/Turabian Style

Cremer, Dieter; Filatov, Michael; Polo, Victor; Kraka, Elfi; Shaik, Sason. 2002. "Implicit and Explicit Coverage of Multi-reference Effects by Density Functional Theory." Int. J. Mol. Sci. 3, no. 6: 604-638.

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