Xa method

Becke A D 1983 Numerical Hartree-Fock-Slater calculations on diatomic molecules J. Chem. Phys. 76 6037 5 Case D A 1982 Electronic structure calculation using the Xa method Ann. 

Seifert G, Eschrig FI and Bieger W 1986 An approximate variation of the LCAO-Xa method Z. Phys. Chem. 267 529... 

Rdsch N, Sandl P, Gorling A and Knappe P 1988 Toward a chemisorption cluster model using the LCGTO-Xa method application to Ni(100)/Na Int. J. Ouantum Chem. Symp. 22 275... 

Density functionals can be broken down into several classes. The simplest is called the Xa method. This type of calculation includes electron exchange but not correlation. It was introduced by J. C. Slater, who in attempting to make an approximation to Hartree-Fock unwittingly discovered the simplest form of DFT. The Xa method is similar in accuracy to HF and sometimes better. 

In order to give you some background to Slater s Xa method, I would like to describe some very simple models that were used many years ago in order to understand the behaviour of electrons in metallic conductors. 

The molecular HF-Xa method has been reviewed by Connolly, and you might like to see how it works for the H2O example. 

Slater s Xa method is now regarded as so much history, but it gave an important stepping stone towards modem density functional theory. In Chapter 12, I discussed the free-electron model of the conduction electrons in a solid. The electrons were assumed to occupy a volume of space that we identified with the dimensions of the metal under smdy, and the electrons were taken to be non-interacting. 

The availability of high-intensity, tunable X-rays produced by synchrotron radiation has resulted in the development of new techniques to study both bulk and surface materials properties. XAS methods have been applied both in situ and ex situ to determine electronic and structural characteristics of electrodes and electrode materials [58, 59], XAS combined with electron-yield techniques can be used to distinguish between surface and bulk properties, In the latter procedure X-rays are used to produce high energy Auger electrons [60] which, because of their limited escape depth ( 150-200 A), can provide information regarding near surface composition. 

The conformational properties of various 1,1 -diheteroferrocenes (7-10) have been the subject of three computational studies using extended Huckel methods.19,46 471,1 -Diphosphaferrocene has also been studied using the Fenske-Hall approach.48 and an MS Xa method.46 Where they overlap, the four treatments are in reasonable qualitative agreement. 

If no correlation is introduced (ec = 0), the KS equations reduce to the well known Xa method proposed by Slater22 as a simplification of the Hartree-Fock scheme with a local exchange operator ... 

Case, D. A. 1982. Electronic Structure Calculations Using the Xa Method. Annu. Rev. Phys. Chem. 33,151. 

I do not recall when I first heard of the Hohenberg-Kohn-Sham papers, but I do know that the quantum chemistry community at first paid little attention to them. In June of 1966 Lu Sham spoke about DFT at a Gordon Conference. But in those days, there was more discussion about another prescription that had been on the scene since 1951, the Slater Xa method. The Xa method was a well-defined, substantial improvement over the Thomas-Fermi method, a sensible approximation to exact Kohn-Sham. Debate over Xa went on for a number of years. Slater may never have recognized DFT as the major contribution to physics that it was. [When I asked John Connolly five or six years ago how he thought Slater had viewed DFT, he replied that he felt that Slater regarded it as obvious. ]... 

Bond distances and angles determined by X-ray absorption spectroscopy (XAS) methods. See reference 138 and Figures 7.44 and 7.47. References 138 and 159. 

Many of the characterization techniques described in this chapter require ambient or vacuum conditions, which may or may not be translatable to operational conditions. In situ or in opemndo characterization avoids such issues and can provide insight and information under more realistic conditions. Such approaches are becoming more common in X-ray adsorption spectroscopy (XAS) methods ofXANES and EXAFS, in NMR and in transmission electron microscopy where environmental instruments and cells are becoming common. In situ MAS NMR has been used to characterize reaction intermediates, organic deposits, surface complexes and the nature of transition state and reaction pathways. The formation of alkoxy species on zeolites upon adsorption of olefins or alcohols have been observed by C in situ and ex situ NMR [253]. Sensitivity enhancement techniques play an important role in the progress of this area. In operando infrared and RAMAN is becoming more widely used. In situ RAMAN spectroscopy has been used to online monitor synthesis of zeolites in pressurized reactors [254]. Such techniques will become commonplace. 

The use of XAS for structural characterization of the metal sites in metalloproteins has increased dramatically in the last ten years. Throughout most of this period, advances in biological XAS have bren driven largely by the increasing availability of synchrotron ra ation and by the increasing quality of synchrotron sources. With each new increase in the available synchrotron intensity, new classes of experiments have become feasible. Some of the inherent limitations of the XAS method have already been discussed. It is appropriate now to consider more practical concerns regarding the future of biological XAS, and the way in which this will be affected by the development of new synchrotron sources. 

Methods of density functional theory (DFT) originate from the Xa method originally proposed by Slater [78] on the base of statistical description of atomic electron structure within the Thomas-Fermi theory [79]. From the point of view of Eq. (3), fundamental idea of the DFT based methods consist first of all in approximate treatment of the electron-electron interaction energy which is represented as ... 

It is of interest that atomic hydrogen centres, which are unstable even at 4 K in quartz, were observed in both coesite and stishovite at 77K.66 The electron centre associated with Ti impurity was observed in stishovite, but not clearly in coesite. Electronic structures of these paramagnetic centres were calculated with the discrete variational (DV)-Xa method to establish a model for centres having substitutional impurities of Al, Ge and Ti.67... 

Imoto has reported calculations of the electronic structures of the model compounds [Mo6E8(PH3)6] (E = S, Se) by the DV Xa method (53-55, 66). Oh symmetry is assumed for the Mo6 cluster. Stepwise calculations beginning from the Mo6 cluster, followed by the inclusion... 

The electronic levels of a model compound [Mo4S6Cl2(PH3)6] have been calculated by the DV-Xa method (100). In a cluster of C2A symmetry, five metal—metal bonding orbitals (two ag, one au, one bg, and one bu) are expected. These orbitals are strongly mixed with the ligand orbitals and show large HOMO-LUMO gaps (Fig. 24), which may be the characteristics of the electron-precise clusters with 10 electrons. 

The LDA, Slater, and Xa methods can all be extended to the spin-polarized regime using... 

A related but somewhat different approach has been suggested by the recently introduced MS Xa method. Calculation of the continuum functions within this method is relatively straightforward,51 52 and the method has been applied to the AT-shell X-ray absorption spectrum53 of N2 and very recently to photoionization of N2 and CO near threshold.54 This last... 

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