Exchange-correlation functional, in density

Kohn W, Sham LJ (1964) Phys Rev A 140 1133 Hohenberg P, Kohn W (1964) Phys Rev B 136 864 Gross EG, Kohn W (2005) Exchange-correlation functionals in density functional theory. Plenum, New York... 

BSSE exists for basis sets of all types and even for approximate or alternative Hamiltonians such as semiempirical forms or density functional methods. It is also not negligible if Slater-type functions are used but the magnitude is often less in these circumstances because the outer regions of the wavefunction are usually better represented than with Gaussians. Likewise for various approximate Hamiltonians, the errors can be large or small. So, for example, since using exchange correlation functions in density functional calculations does not require an expansion in terms of virtual orbitals to obtain some electron correlation, there is a relatively small BSSE for the correlation effect in those calculations. 

Becke A D 1995 Exchange-correlation approximations in density-functional theory Modern Eiectronic Structure Theory vol 2, ed D R Yarkony (Singapore World Scientific) pp 1022-46... 

Becke, A. D., 1995, Exchange-Correlation Approximations in Density-Functional Theory in Modem Electronic Structure Theory, Part II, Yarkony, D. R., World Scientific, Singapore. 

As a consequence of the size limitations of the ab initio schemes, a large number of more-approximate methods can be found in the literature. Here, we mention only the density functional-based tight binding (DFTB) method, which is a two-center approach to DFT. The method has been successfully applied to the study of proton transport in perov-skites and imidazole (see Section 3.1.1.3). The fundamental constraints of DFT are (i) treatment of excited states and (ii) the ambiguous choice of the exchange correlation function. In many cases, the latter contains several parameters fitted to observable properties, which makes such calculations, in fact, semiempirical. 

The choice of the exchange correlation functional in the density functional theory (DFT) calculations is not very important, so long as a reasonable double-zeta basis set is used. In general, the parameterized model will not fit the quantum mechanical calculations well enough for improved DFT calculations to actually produce better-fitted parameters. In other words, the differences between the different DFT functionals will usually be small relative to the errors inherent in the potential model. A robust way to fit parameters is to use the downhill simplex method in the parameter space. Having available an initial set of parameters, taken from an analogous ion, facilities the fitting processes. 

In recent years, density functional theory (DFT) has become the most widely used electronic structure method for large molecular systems. The Kohn-Sham DFT method accounts for exchange and correlation effects via a particular exchange correlation functional. In its present form, Kohn-Sham DFT is not, strictly speaking, an ab initio method, since the functionals contain empirical parameters. 

Perdew, J. P. Schmidt, K. Jacob s ladder of density functional approximations for the exchange-correlation energy, In Density Functional Theory and its Application to Materials Doren, V. V, Alsenoy, C. V, Geerlings, P, Eds. AlP-Press Melville,... 

Appendix B. The exchange-correlation functional in Local Density Approximation... 

In addition to the ab initio approach to relativistic electronic structure of molecules, four-component Kohn-Sham programs, which approximate the electron-electron interaction by approximate exchange-correlation functionals from density functional theory, have also been developed (Liu et al. 1997 Sepp et al. 1986). However, we concentrate on the ab initio methods and refer the reader to Chapter 4, which treats relativistic density functional theory (RDFT). 

Recent advances in electronic structure theory achieved in our group have been reviewed. Emphasis is put on development of ab initio multireference-based perturbation theory, exchange and correlation functionals in density functional theory, and molecular theory including relativistic effects. 

Liu, S., Ayers, P. W., Parr, R. G. (1999). Alternative definition of exchange-correlation charge in density functional theory. J. Chem. Phys. Ill, 6197-6203. 

Nowadays, many electronic structure codes include efficient implementations [37—41] of the Ramsey equations [42] for the calciflations of nonrelativistic spin—spin coupling constants. A vast number of publications devoted to the calculation of/-couplings can be found in the Hterature, covering different aspects such as the basis set effects [43-55], the comparison of wave function versus density functional theory (DFT) methods [56-60], or the choice of exchange-correlation functional in DFT approaches [61-68]. Excellent recent reviews of Contreras [69] andHelgaker [70] cover these particular aspects. 

The problem, of course, is that we still don t know the exchange-correlation functional Exc. However, we can come up with approximate forms of Exc, the development of density functional theory and its application to chemical problems reflects improved approximations of the exchange-correlation functional. In the early formalisms, the exchange-correlation functional was approximated by that in the limiting behavior of a... 

The PW86 exchange and the P86 correlation functionals are used to approximate the exchange-correlation functional in both the KS and in the KSCED calculations. Previous supermolecule Kohn-Sham studies of the same systems by Eriksson showed that this approximation of the exchange-correlation functional is sufficiently accurate to describe the spin-density of CO in the MCO2 complex. 

The local density approximation (LDA) constitutes the simplest way of representing the exchange-correlation functional. In particular, this approximation assumes that the density can be locally treated as a uniform electron gas. The general expression for the functional Exc in the LDA is ... 

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