Electronic density functions

Weinert M, Wimmer E and Freeman A J 1982 Total-energy all-electron density functional method for bulk solids and surfaces Phys. Rev. B 26 4571-8... 

Another approach to calculating molecular geometry and energy is based on density functional theory (DFT). DFT focuses on the electron cloud corresponding to a molecule. The energy of a molecule is uniquely specified by the electron density functional. The calculation involves the construction of an expression for the electron density. The energy of the system is then expressed as... 

The one-electron density function is the first of a series of density functions which relate to clusters of any numbers of electrons. The second member of the series is... 

For every electronic wavefunction that is an eigenfunction of the electron spin operator S, the one-electron density function always comprises an spin part... 

In our discussion of the electron density in Chapter 5, I mentioned the density functions pi(xi) and p2(xi,X2). I have used the composite space-spin variable X to include both the spatial variables r and the spin variable s. These density functions have a probabilistic interpretation pi(xi)dridii gives the chance of finding an electron in the element dri d i of space and spin, whilst P2(X], X2) dt] d i dt2 di2 gives the chance of finding simultaneously electron 1 in dri dii and electron 2 in dr2di2- The two-electron density function gives information as to how the motion of any pair of electrons is correlated. For independent particles, these probabilities are independent and so we would expect... 

Estimation of the stability of clusters with the aid of the theory of the electron density functional. Y. A. Borisov, Russ. Chem. Rev. (Engl. Transl.), 1985,54, 361 (104). 

Burke, K., Perdew, J. P., Emzerhof, M., 1998, Mixing Exact Exchange With GGA When to Say When in Electronic Density Functional Theory. Recent Progress and New Directions, Dobson, J. F., Vignale, G., Das, M. P. (eds.), Plenum Press, New York. 

Maerker, C., Schleyer, P. v. R., Liedl, K. R., Ha, T. K., Quack, M., Suhm, M. A., 1997, A Critical Analysis of Electronic Density Functionals for Structural, Energetic, Dynamic, and Magnetic Properties of Hydrogen Fluoride Clusters , J. Comput. Chem., 18, 1695. 

According to the aspherical-atom formalism proposed by Stewart [12], the one-electron density function is represented by an expansion in terms of rigid pseudoatoms, each formed by a core-invariant part and a deformable valence part. Spherical surface harmonics (multipoles) are employed to describe the directional properties of the deformable part. Our model consisted of two monopole (three for the sulfur atom), three dipole, five quadrupole, and seven octopole functions for each non-H atom. The generalised scattering factors (GSF) for the monopoles of these species were computed from the Hartree-Fockatomic functions tabulated by Clementi [14]. 

In this chapter our focus is on one of these indices, the electrostatic potential V(r) that is created in the space around a molecule by its nuclei and electrons. V(r) can be computed rigorously, given the electronic density function p(r), by Eq. (3.1). 

The electronic wave function of an n-electron molecule is defined in 3n-dimensional configuration space, consistent with any conceivable molecular geometry. If the only aim is to characterize a molecule of fixed Born-Oppenheimer geometry the amount of information contained in the molecular wave function is therefore quite excessive. It turns out that the three-dimensional electron density function contains adequate information to uniquely determine the ground-state electronic properties of the molecule, as first demonstrated by Hohenberg and Kohn [104]. The approach is equivalent to the Thomas-Fermi model of an atom applied to molecules. 

Averaging over the two-electron density function p leads to the global value t7 = 2 q. The constant part of the kinetic energy does not change with changes in p. Also, it has a negative value. 

This chapter has dealt with introducing the main concepts within a theory called MQS. It has discussed the different steps to be taken to evaluate and quantify a degree of similarity between molecules in some molecular set but also fragments in molecules. QSM provides a scheme that relieves the arbitrariness of molecular similarity by using the electron density function as the sole descriptor, in agreement with the Hohenberg-Kohn theorems. It also addressed the different pitfalls that are present, for example the dependence on proper molecular alignment. 

Amat, L. and Carbo-Dorca, R. (1999) Fitted electronic density functions from H to Rn for use in quantum similarity measures cis-diamminedichloroplatinum(II) complex as an application example. 

C. Maerker, P. von Rague Schleyer, R. Liedl, T. K. Ha, M. Quack, and M. A. Suhm, A critical analysis of electronic density functionals for structural, energetic, dynamic and magnetic properties of hydrogen fluoride clusters. J. Comput. Chem. 18, 1695 1719 (1997). 

More recently, electrostatic theory has been revived due to the concept of molecular electrostatic potentials. The potential of the solute molecule or ion was used successfully to discuss preferred orientations of solvent molecules or solvation sites 50—54). Electrostatic potentials can be calculated without further difficulty provided the nuclear geometry (Rk) and the electron density function q(R) or the molecular wave function W rxc, [Pg.14]

Self-Consistent Hartree-Fock-Wigner Calculations A Two-Electron-Density Functional Theory... 

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