Exchange and correlation effects

Kohn W and Sham L J 1965 Self-consistent equations including exchange and correlation effects Phys. Rev A 140 1133-8... 

Kohn W and L J Sham 1965. Self-consistent Equations Including Exchange and Correlation Effects. Physical Review A140 1133-1138. 

Self-Consistent Equations Including Exchange and Correlation Effects W. Kohn and L. J. Sham Physical Review 140 (1965) All33... 

In this chapter we make first contact with the electron density. We will discuss some of its properties and then extend our discussion to the closely related concept of the pair density. We will recognize that the latter contains all information needed to describe the exchange and correlation effects in atoms and molecules. An appealing avenue to visualize and understand these effects is provided by the concept of the exchange-correlation hole which emerges naturally from the pair density. This important concept, which will be of great use in later parts of this book, will finally be used to discuss from a different point of view why the restricted Hartree-Fock approach so badly fails to correctly describe the dissociation of the hydrogen molecule. 

The rest of the exchange and correlation effects will be taken into account to the first two orders of PT by the total interelectron interaction [13-19], The electron density is determined by an iteration algorithm [11, 14], In the first iteration we... 

The description of bonding at transition metal surfaces presented here has been based on a combination of detailed experiments and quantitative theoretical treatments. Adsorption of simple molecules on transition metal surfaces has been extremely well characterized experimentally both in terms of geometrical structure, vibrational properties, electronic structure, kinetics, and thermo-chemistry [1-3]. The wealth of high-quality experimental data forms a unique basis for the testing of theoretical methods, and it has become clear that density functional theory calculations, using a semi-local description of exchange and correlation effects, can provide a semi-quantitative description of surface adsorption phenomena [4-6]. Given that the DFT calculations describe reality semi-quantitatively, we can use them as a basis for the analysis of catalytic processes at surfaces. 

We need to develop methods to understand trends for complex reactions with many reaction steps. This should preferentially be done by developing models to understand trends, since it will be extremely difficult to perform experiments or DFT calculations for all systems of interest. Many catalysts are not metallic, and we need to develop the concepts that have allowed us to understand and develop models for trends in reactions on transition metal surfaces to other classes of surfaces oxides, carbides, nitrides, and sulfides. It would also be extremely interesting to develop the concepts that would allow us to understand the relationships between heterogeneous catalysis and homogeneous catalysis or enzyme catalysis. Finally, the theoretical methods need further development. The level of accuracy is now so that we can describe some trends in reactivity for transition metals, but a higher accuracy is needed to describe the finer details including possibly catalyst selectivity. The reliable description of some oxides and other insulators may also not be possible unless the theoretical methods to treat exchange and correlation effects are further improved. 

The first term in brackets is the usual kinetic energy operator. The noninteracting reference system has the property that its one-determinantal wavefunction of the lowest N orbitals yields the exact density of the interacting system with external potential v(r) as a sum over densities of the occupied orbitals, that is, p(r) = Xl<)>,l2, and the corresponding exact energy E[p(r)]. The Kohn-Sham potential should account for all effects stemming from the electron-nuclear and electron-electron interactions. Not only does the Kohn-Sham potential contain the attractive potential v(r) of the nuclei and the classical Coulomb repulsion VCoul(r) within the electron density p(r), but it also accounts for all exchange and correlation effects, which have so to say been folded into a local potential vxc r) ... 

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. 

Baerends, E.J., Perspective on self-consistent equations including exchange and correlation effects , Theor. Chem. Acc., 103, 265-269, 2000. 

Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation Effects, Phys Rev, 140A 1133-1138... 

Gunnarsson O, Jonson M, Lundqvist BI (1979) Descriptions of exchange and correlation effects in inhomogeneous electron systems, Phys Rev B, 20 3136-3164... 

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