Electron density partitioning

If the electron density partitioning results in subsystems without boundaries and with convergence properties which closely resemble the convergence properties of the complete system, then it is possible to avoid one of the conditions of the Holographic Electron Density Fragment Theorem , by generating fuzzy electron density fragments which do not have boundaries themselves, but then the actual subsystems considered cannot be confined to any finite domain D of the ordinary three-dimensional space E3. 

The fact that the exact ground-state electron density can be obtained as a sum of two components a trial electron density belonging to the class of functions, such that Px = Po — p1 0,1 is noninteracting pure-state v-representable, and the electron density derived from Eq. 31 provides a formal basis for the electron-density-partitioning based strategy in multi-level modelling. If subsystem A represents a small part of the... 

Tran, F. Weber. J. Wesolowski. T.A. Theoretical study of the benzene dimer by the density-functional-theory formalism based on electron-density partitioning. Helv. Chim. Acta 2001, 84 (6), 1489-1503. 

Volkov, A., and Coppens, P. (2004). Calculation of electrostatic interaction energies in molecular dimers from atomic multipole moments obtained by different methods of electron density partitioning, /. Comput. Chem. 25, pp. 921-934. 

Boyd RJ (1977) Electron density partitioning in atoms. J Chem Phys 66 356-358... 

Here, the composite coordinates of the total molecule in the laboratory frame is described by R = (Ra,Rb, r). a and b denote atoms in the molecule. In this formulation, the electron density partitioning for atoms... 

It is worthwhile to recall at this point that the applied implementation of KSCED which uses localized spin-densities of subsystems and non-relaxed P2 involves a substantial reduction of the computational effort compared to that of the supermolecule KS calculations. It is, however, applicable only to such complexes for which the electron density partitioning can be made in such a way that there are no covalent bonds between the subsystems and the distribution of the total charge between the subsystems is known. In such a case, the computer cost is determined not by the total size of the system but by the size of the subsystem of interest. 

Koritsanszky, T. S. Coppens, P. Chemical applications of X-ray charge-density analysis, Chem. Revs. 2001, 101, 1583-1627 Volkov, A. Coppens, P. Calculation of electrostatic interaction energies in molecular dimers from atomic multipole moments obtained by different methods of electron density partitioning, J. Comp. Chem. 2004, 25, 921-934 Suponitsky, K. Y Tsirelson, V. G. Fell, D. Electron-density-based calculations of intermolecular energy the case of urea, Acta Cryst. 1999, A55, 821-827. 

Schematic of DDEC/c3 electron density partitioning. Atoms 2, 3, and 4 are buried" while atoms 1 and 5 are not. Each atom has an exponentially decaying tail accurately describing the atom-atom overlaps.

Partitioning Electron Density The Theory of Atoms in Molecules... 

R F W Bader s theory of atoms in molecules [Bader 1985] provides an alternative way to partition the electrons between the atoms in a molecule. Bader s theory has been applied to many different problems, but for the purposes of our present discussion we will concentrate on its use in partitioning electron density. The Bader approach is based upon the concept of a gradient vector path, which is a cuiwe around the molecule such that it is always perpendicular to the electron density contours. A set of gradient paths is drawn in Figure 2.14 for formamide. As can be seen, some of the gradient paths terminate at the atomic nuclei. Other gradient paths are attracted to points (called critical points) that are... 

Chemists are able to do research much more efficiently if they have a model for understanding chemistry. Population analysis is a mathematical way of partitioning a wave function or electron density into charges on the nuclei, bond orders, and other related information. These are probably the most widely used results that are not experimentally observable. 

Vector quantities, such as a magnetic field or the gradient of electron density, can be plotted as a series of arrows. Another technique is to create an animation showing how the path is followed by a hypothetical test particle. A third technique is to show flow lines, which are the path of steepest descent starting from one point. The flow lines from the bond critical points are used to partition regions of the molecule in the AIM population analysis scheme. 

DFT methods compute electron correlation via general functionals of the electron density (see Appendix A for details). DFT functionals partition the electronic energy into several components which are computed separately the kinetic energy, the electron-nuclear interaction, the Coulomb repulsion, and an exchange-correlation term accounting for the remainder of the electron-electron interaction (which is itself... 

This exercise will examine other ways of computing charges other than Mulliken population analysis. Since atomic charge is not a quantum mechanical observable, all methods for computing it are necessarily arbitrary. We ll explore the relative merits of various schemes for partitioning the electron density among the atoms in a molecular system. 

There is actually no unique way to calculate (or measure) atomic charges, simply because there is no way to uniquely partition a molecule s electrons among the atoms. For example, it is impossible to say what fraction of the electrons contained in the electron density surface for hydrogen fluoride belongs to fluorine. None of the partitions shown below is more reasonable than any of the others. 

Bader et al. have developed a theory of molecular structure [8], based on the topological properties of the electron density p(r). In this theory, a molecule may be partitioned into atoms or fragments by using zero-flux surfaces that satisfy the condition... 

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