Additive fuzzy density fragmentation AFDF scheme

For each nuclear family fk an additive fuzzy electron density fragment pk (r) can be defined by a general Additive Fuzzy Density Fragmentation (AFDF) scheme proposed earlier [19]. According to this scheme a fragment density matrix P of dimension nxn is defined in terms of its matrix elements P-k as... 

The computation of fuzzy electron density fragments and the construction of ab initio quality macromolecular electron densities is a novel approach to the quantum-chemical study and detailed modeling of large molecules. The additive ffizzy density fragmentation (AFDF) scheme of Mezey, described in a general form elsewhere, -is employed in the molecular electron density lego assembler (MEDLA) technique of Walker... 

A general, additive, fuzzy density fragmentation scheme (AFDF scheme) has been described in [19], as outlined below. 

The AFDF fanuly of electron density computation methods involves a formal assignment of fuzzy, additive electron density contributions to subsets of nuclei. One divides the set of nuclei of the molecule into m mutually exclusive families, fi, f2,..., f, ... f , corresponding to fuzzy electron density fragments Fj, F2,..., F, . . . F , described by fragment density functions p (r). P (r). . P (r). p (X), respectively. The general AFDF scheme proposed in refs. 26,27 can be given in terms of an AO membership function mj i) defined as. 

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