Many-electron densities

Molecular rearrangement resulting from molecular collisions or excitation by light can be described with time-dependent many-electron density operators. The initial density operator can be constructed from the collection of initially (or asymptotically) accessible electronic states, with populations wj. In many cases these states can be chosen as single Slater determinants formed from a set of orthonormal molecular spin orbitals (MSOs) im as / =... 

In most cases, the orbital relaxation contribution is negligible and the Fukui function and the FMO reactivity indicators give the same results. For example, the Fukui functions and the FMO densities both predict that electrophilic attack on propylene occurs on the double bond (Figure 18.1) and that nucleophilic attack on BF3 occurs at the Boron center (Figure 18.2). The rare cases where orbital relaxation effects are nonnegligible are precisely the cases where the Fukui functions should be preferred over the FMO reactivity indicators [19-22], In short, while FMO theory is based on orbitals from an independent electron approximation like Hartree-Fock or Kohn-Sham, the Fukui function is based on the true many-electron density. 

Reduced Density Matrix Workshop, Kingston, August 29-31, 1999. Sponsored by Queen s University. Organizer A. J. Coleman. Monograph (Instead of Proceedings) Jerzy Cioslowski, editor, Many-Electron Densities and Reduced Density Matrices, Kluwer Academic/Plenum (2000), 301 pp. 

M. Rosina, Some theorems on uniqueness and reconstruction of higher-order density matrices, in Many-Electron Densities and Reduced Density Matrices (J. Cioslowski, ed.), Kluwer Academic/ Plenum Pubhshers, New York, 2000, pp. 19—32. 

Many-Electron Densities and Reduced Density Matrices (J. Cioslowski, ed.) Kluwer, Norwell, MA, 2000. 

The existence of clathrate-like water structure adjacent to the hydrophobic surfaces of macromolecules is an attractive hypothesis. Models have been proposed which have received some support from thermodynamical arguments [808]. However, this concept has proved ineffective as a basis for the interpretation of the structure associated with the many electron density solvent peaks, separated by 2.8 A to 3.0 A, which are frequently observed on the Fourier X-ray maps close to the surface of a protein [809, 810], Recently, however, some local clathrate-like water has been observed in special cases in the high-resolution studies of the small plant protein, crambin [811], in a hydrated deoxydinucleoside-phosphate drug complex [812], in (Phe4Val6) antamanide hydrate [8131 and in an oligodeoxy-nucleotide duplex [814],... 

Minimum entropy deficiency partitioning of many-electron densities 155... 

MINIMUM ENTROPY DEFICIENCY PARTITIONING OF MANY-ELECTRON DENSITIES... 

The basic postulate of the many-electron density functional theory [1-8]... 

Nevertheless, the density matrix—path integral description allows the general formulation for the many-electronic density through the so-called canonical density algorithm it prescribes that the system is firstly solved for the single electron evolution under the concerned potential for which the time-space density matrix is analytically formulated, in an evolution manner, as the propagator (x, x, tj then, the partition function is com-... 

The quantum circle is closed by linking the many-electronic density with the total number of electrons with the aid of the integral conservation law... 

The many-electron density of the electronic ground state wavefunction if/ may be written by picking any electron, say electron 1, and integrating over the positions of all the other electrons (2 through N) to average out their effects on the position of electron 1. Then we multiply the result by the number of electrons N. We can write the density in this way, picking any one electron that we wish, because in the correct wavefunction all the electrons are indistinguishable. The expression for po looks like this ... 

Rosina M (2(X)1) In Cioslowsky J (ed) Many-electron densities and reduced density matrices. Kluwer, Dordrecht... 

Clearly it is possible to obtain many-electron density matrices in the same way. Thus, by applying two transposition operators, we obtain instead of (7.4.11)... 

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