Kohn-Sham exchange

The basic concepts of the one-electron Kohn-Sham theory have been presented and the structure, properties and approximations of the Kohn-Sham exchange-correlation potential have been overviewed. The discussion has been focused on the most recent developments in the theory, such as the construction of from the correlated densities, the methods to obtain total energy and energy differences from the potential, and the orbital dependent approximations to v. The recent achievements in analysis of the atomic shell and molecular bond midpoint structure of have been... 

Nesbet, R.K. and Colle, R. (2000). Tests of the locality of exact Kohn-Sham exchange potentials, Phys. Rev. A 61, 012503. 

USING THE EXACT KOHN-SHAM EXCHANGE ENERGY DENSITY FUNCTIONAL AND POTENTIAL TO STUDY ERRORS INTRODUCED BY APPROXIMATE CORRELATION FUNCTIONALS... 

IV. Structure of the Pauli and correlation-kinetic components of Kohn-Sham exchange potential... 

V. Construction of approximate Kohn-Sham exchange energy... 

IV. STRUCTURE OF THE PAULI AND CORRELATION-KINETIC COMPONENTS OF KOHN-SHAM EXCHANGE POTENTIAL... 

V. CONSTRUCTION OF APPROXIMATE KOHN-SHAM EXCHANGE ENERGY FUNCTIONAL AND DERIVATIVE WITH EXACT ASYMPTOTIC STRUCTURE... 

Kohn-Sham exchange only (Xa with a=2/3) KS pV3 exchange only for electron gas... 

Density functional techniques are available for the calculation of the molecular and electronic structures of ground state systems. With the functionals available today, these compete with the best ab initio methods. This article focuses on the theoretical aspects associated with the Kohn Sham density functional procedure. While there is much room for improvement, the Kohn-Sham exchange-correlation functional offers a great opportunity for theoretical development without returning to the uniform electron gas approximation. Theoretical work in those areas will contribute significantly to the development of new, highly precise density functional methods. 

The direct route, obviously, involves the solution of the canonical Kohn-Sham equations of Eq. (85). This is, however, not feasible because we do not know the expression for the exact Kohn-Sham exchange-correlation potential Of... 

The above difficulty has been bypassed in actual applications of the Kohn-Sham equations by resorting to approximate exchange-correlation functionals. These functionals, however, as discussed in Sections 2.2 - 2.4, do not comply with the requirement of functional iV-representability. The calculation of the exact Kohn-Sham exchange-correlation potential is nonetheless feasible by means of the inverse method" provided that one has the exact ground-state one-particle density p(r). Although such densities can be obtained from experiment, the most accurate ones are obtained from highly accurate quantum mechanical calculations. 

An iterative procedure can be set up in order to calculate the effective Kohn-Sham potential. The details of this procedure are given elsewhere [85, 86, 88]. Once this potential is obtained, we can analize it in terms of its components and extricate from it the Kohn-Sham exchange-correlation potential which, in turn, can be written as a sum of the exchange and the correlation potentials ... 

Finally, we consider density functional theory (DFT) computations of p-space properties. A naive way of calculating p-space properties is to use the Kohn-Sham orbitals obtained from a DFT computation to form a one-electron, r-space density matrix Fourier transform / according to Eq. (14), and proceed further. This approach is incorrect because the Kohn-Sham density matrix F is not the true one and, in fact, corresponds to a fictitious non-interacting system with the same p(r) as the true system. On the other hand, Hamel and coworkers [112] have shown that if the exact Kohn-Sham exchange potential is used, then the spherically averaged momentum densities of the Kohn-Sham orbitals should be very close to those of the Hartree-Fock orbitals. Of course, in practical computations the exact Kohn-Sham exchange potential is not used since it is generally not known. 

Comparing this to the form chosen by Slater, we note that this form, known as Kohn-Sham exchange, differs by a factor of i.e. = j. For a number of years, some controversy existed as to whether the... 

Kinetic energy of electrons, 3 free-electron gas, 348f local approximation, 351, 377f, 541 Kleinman s internal displacement parameter, 198f tables, 196, 208, 220 Kohn anomalies, 395f Kohn-Sham exchange, 540 Koster-Slaler tables, 481 Kramers-Kronig relations, 99 Krypton, properties of. See Inert gas solids... 

There is then the question of understanding the physical origin of the discontinuity [2] of the Kohn-Sham exchange-correlation potential Vxc (r) as the number N of electrons passes through an integer. It would thus be of interest to learn whether and how each component WP(r), WP(r) and W, (r) of the potential contributes to the discontinuity. The addition of an infinitesimal amount of charge changes the density infinitesimally. However, the functional... 

The corresponding Kohn-Sham exchange energy EP[p] is the energy of interaction between the density p(r) and the Fermi hole Px (r, F) ... 

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