Slater s exchange potential

The DV-Xx cluster method [11], which is one of the first principle molecular orbital calculation methods, was used for the calculation of the electronic state of the Li3N crystal. In this method, Slater s exchange potential was used [12],... 

The molecular potential in the present method is composed of a coulomb potential and Slater s exchange potential of the density functional theory and is given by... 

Since the relativistic DV-Xa method takes into account fully relativistic effects under Slater s exchange potential approximation, this is very useful for studying the electronic structures and chemical bonding in molecules containing heavy... 

This is remarkably similar to Slater s exchange potential, Eq. (2.48), which was based on an ad hoc assumption. In fact it differs from the Slater exchange potential by only a factor of 2/3. 

The number of random sampling points in the DV-Xa calculations was 8000 for S03 molecule and 24,000 for S03Pt12. Slater s exchange parameter (a) was fixed at 0.7 for all the atoms in the cluster. All atoms were contained inside a potential well of radius 5.0bohr (1 bohr=0.529A) and depth —l.Ohartree (1 hartree=27.2 eV). 

The DV-Xa molecular orbital (MO) calculations were performed to analyze the Li-K XANES spectra of lithium halides powder. The computational details of the DV-Xa method have been previously described [10]. In this method, the exchange-correlation interaction, Vxcr between electrons is given by the Slater s Xa potential,... 

The DV-Xa cluster method is a molecular orbital calculating method, assuming a Hartree-Fock-Slater (HFS) approximation. In this calculation, the exchange-correlation between electrons, is given by the following Slater s Xa potential. 

One-electron cluster calculations are carried out based on the local density functional approach using the DV-Xtt computation code developed by Adachi et al. (5). The exchange-correlation energy is taken into account using the Slater s XCl potential (6). In the present work, a is set at 0.7, which is found to be the most appropriate value in many cases (7). The MOs are obtained as linear combinations of atomic orbitals (LCAO). The most remarkable feature of our program is that the atomic orbitals (AOs) are numerically calculated in each iteration and optimized for the chemical environment. The details of this program have been discribed in ref. (5)... 

Electronic structure methods that use the electron density as the basic variable trace their origin to the Thomas-Permi [2], Thomas-Permi-Dirac [3], and related models [4-7] developed in the early years of quanmm mechanics. Many similarities with the present day DPT can be also found in Caspar s exchange potential [8] and Slater s Xa-methods [9-11]. By the 1960s, these precursors of DPT were fuUy developed and used extensively for the calculations of atoms and solids, but their impact on molecular quanmm chemistry remained insignificant. The Thomas-Permi and Thomas-Permi-Dirac models proved to be of little use in chemistry because they can never yield a lower... 

We initiate a preliminary formulation of this algorithm with a self-consistent field (SCF) HF calculation for the He atom. We first obtain the best HF calculation and then replace the exchange term by Slater s Xot potential [34] Vxa, the simpler expression for DFT, but sufficient for this experiment. We interpret a as the generator coordinate and we weight the exchange-correlation term for different values of the parameter a, i.e. 

The impurity-state orbitals for the Cl crdculation were obtained by the spin-restricted LDA cluster calculation using the ordinary SCAT computation code. Although the Slater s Xa potential with a = 0.7 was used as the exchange-correlation potential, it has been confirmed that the results of the spin-restricted calculation is almost identical with those by the VWN potential. ... 

Just to remind you, the electron density and therefore the exchange potential are both scalar fields they vary depending on the position in space r. We often refer to models that make use of such exchange potentials as local density models. The disagreement between Slater s and Dirac s numerical coefficients was quickly resolved, and authors began to write the exchange potential as... 

Here ip is an orbital of an electron with Mg = 1/2(t), e is its one-electron energy, is the classical Coulomb potential (including electron self-interaction terms), and represents the effects of electron exchange. In Slater s model, this is related to p h, the local density of electrons of the same spin... 

A density-functional molecular method with Slater s local exchange approximation, muffin-tin averaging of the potential, and a composite basis... 

The calculation of x-ray emission spectra of molecules or solids are one of the most successful applications of the discrete variational (DV) Hartree-Fock-Slater (Xa) MO method using cluster approximation [8-10], which was originally coded by Ellis and his CO workers [11-14] based on Slater s Xa exchange potential [15]. The DV-Xa method has several advantages for the calculation of x-ray transition process as follows. 

Here we use the self-consistent-charge (SCC) approximationto construct the coulomb potential Vc. The effective atomic charges are estimated by Mulliken population analysis and are spherically averaged around each nucleus. Then, they are superimposed to construct the molecular coulomb potential. For the exchange potential. Slater s approximation ... 

There is, in principle, nothing which limits the self-consistent field method to any particular form of the exchange-correlation potential, and the procedure outlined above has been used in connection with several approximations for exchange and correlation. Most notable in this respect is SLATER S Xa method [1.4] which has been applied to all atoms in the periodic table, to some molecules, and in the majority of the existing electronic-structure calculations for crystalline solids. 

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