Molecular charge density, exchange correlation

In the present paper, first we investigate the photoionization cross sections for atomic orbitals calculated with different scaling parameters of exchange-correlation potential, and for those of different oxidation states, namely different charge densities. We discuss the effect of the variation of the spatial extension of the atomic orbital on the photoionization cross section. Next we make LCAO (linear combination of atomic orbitals) molecular orbital (MO) calculations for some compounds by the SCF DV-Xa method with flexible basis functions including the excited atomic orbitals. We calculate theoretical photoelectron spectrum using the atomic orbital components of MO levels and the photoionization cross sections evaluated for the flexible atomic orbitals used in the SCF MO calculation. The difference between the present result and that calculated with the photoionizaion cross section previously reported is discussed. 

All summations are over atoms in subsystem a. In the expressions rA = j r - RA and xA = 0.5/rA. pA is the DFT atomic density from the same exchange-correlation functional. pA is the hydrogenic atomic density. ZA is die nuclear charge. Figure 2 illustrates, along the molecular backbone direction, g ( r) and P ( r) corresponding... 

As mentioned above, the nuclei are assumed to be fixed and are thus nothing more than sources of an external electrostatic potential in which the electrons move. If there is no magnetic field external to the molecule under consideration, and if external electric fields are time-independent, we arrive at the so-called electrostatic limit of relativistic density functional theory. Note that most molecular systems fall within this regime. In this case, one can prove the relativistic Hohen-berg-Kohn theorem using the charge density, p(r) = J f), only. This leads to a definition of an exchange-correlation functional -Exc[p( )]... 

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 summarized. The consistent formulation of the discontinuous dependence of on the particle number and its effect on the spatial form of and charge transfer within the system have been presented. The recently developed direct approximations of the long- and short-range components of have been overviewed. 

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