Electronic states density functional method

The scheme analyzed so far is, in a way, a simplification of the Hartree-Fock scheme. As such, it is only a model approximation. The most serious drawback is the replacement of a fundamentally quantum mechanical term, whose very nature is to be non local, by a local approximation. Of course, when the system is in an electronic degenerate state, or when the BO approximation is no longer valid, the density functional method cannot be applied. For a discussion of this and other limitations the reader is referred to the paper by Bersuker [117],... 

The density functional methods were, in the views of many, legitimized by the introduction of the first Hohenberg-Kohn theorem [10]. The consequence of this celebrated theorem is that for a non-degenerate ground state and a given external potential, v(r), the electronic ground state energy can be expressed as... 

Modern density functional theory (DFT) provides an enormous simplification of the many-body problem [1-7], It enables one to replace the complicated conventional wavefiinction approach with the simpler density functional formalism. The ground-state properties of the system under investigation are obtained through a minimization over densities rather than a minimization over wavefunctions. The electron density is especially attractive for calculations involving large systems, because it contains only three dimensions regardless of the size of the system. In addition, even for relatively small systems, it has been found that density-functional methods, for certain situations, often yield results competitive with, or superior to those obtained from various traditional wavefiinction approaches. 

In the implementation of density functional methods for atoms and molecules, accurate wave functions can be utilized to test or construct the energy density functional[l]. Except for one-electron systems, however, these wave functions are necessarily approximate. Beyond hydrogen, the most precise wave functions available are obtained by the use of variational methods. For the simplest, few-electron systems, such calculations are capable of producing energies and wave functions of very high accuracy, more than sufficient for the present requirements of density functional theory. In this article we review the development and present state of accurate, variational calculations on simple atomic and molecular systems. In order to facilitate comparison of various alternative... 

Between the wall of the cell and any ions (H+, H30+, H502+) forces of supermolecular hydrogen P-bonds and electrostatic y-bonds operate (see Fig. 2). Surfaces of intermolecular potential energy have been calculated by density functional method stated in our paper [6], Necessary data about spatial distributions of electron charge density inside framework of aqua multiparticle had been taken from calculations of aquatic ions and the ring of water (H20)n by using of standard molecular orbital method in the minimal basis set (STO-3G). Results of calculations are shown in Table 1. 

The electron affinities of the main group homonuclear diatomic anions have been measured by PES. A few experimental values for the transition metal dimers are also available. The electron affinities of all the 3d homonuclear diatomic molecules have been calculated using density functional methods [1-4], Only the AEa of I2, 2.524 eV C2, 3.27 Si2, 2.2o S2, 1.67 F2, 3.0g Cl2, 2.4s Br2, 2.5, and 02, 1.07 have been measured by more than one method [1-3]. CURES-EC calculations confirm these to within 0.1 eV. Positive excited states Ea have been measured for 02, C2, and I2 and are inferred for other X2 [5-8]. Just as in the case of the atomic Ea, the trends in the Periodic Table can support the assignments of AEa for the other elements. 

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