Fuzzy density fragmentation

In more recent years, additional progress and new computational methodologies in macromolecular quantum chemistry have placed further emphasis on studies in transferability. Motivated by studies on molecular similarity [69-115] and electron density representations of molecular shapes [116-130], the transferability, adjustability, and additivity of local density fragments have been analyzed within the framework of an Additive Fuzzy Density Fragmentation (AFDF) approach [114, 131, 132], This AFDF approach, motivated by the early charge assignment approach of Mulliken [1, 2], is the basis of the first technique for the computation of ab initio quality electron densities of macromolecules such as proteins [133-141],... 

Approximate transferability of fuzzy density fragments is a key feature of the method, where the fuzzy fragments are custom-made in order to reproduce interfragment interactions. By increasing the size of the interaction shell about each fuzzy density fragment, the error of transferred fragment densities can be reduced below any positive threshold. One tool for this purpose is the Adjustable Density... 

Mezey, P.G. (1998) A crystallographic structure refinement approach using ab initio quality additive fuzzy density fragments. In Advances in Molecular Structure Research, Hargittai, M. and Hargittai, I. (Eds.), JAI Press, New York. 

Based on the fragment density matrix Pk for the k-th fragment, the electron density of Mezey s fuzzy density fragment pk(r) is defined as... 

Using the additive, fuzzy density fragmentation (AFDF) approach of the macromolecular density pM(r)> the fuzzy fragment electron density... 

Electron density decreases exponentially with distance that suggests that an Additive Fuzzy Density Fragmentation (AFDF) approach can be used for both a fuzzy decomposition and construction of molecular electron densities. The simplest AFDF technique is the Mulliken-Mezey density matrix fragmentation [12,13], that is the basis of both the Molecular Electron Density Loge Assembler (MEDLA) [14-17] and the Adjustable Density Matrix Assembler (ADMA) [18-21] macromolecular quantum chemistry methods. 

Additive fuzzy density fragment force (AFDFF) method. ... 

Note that both the density matrix P of the complete molecule M and the additive fragment density matrix AFDM P of the kth fragment involve the same, full set of AOs. Based on the fragment density matrix P, the electron density p (r) of Mezey s kth additive fuzzy density fragment is defined as... 

Keywords Quantum chemical localization, Subsystems of molecules, Fuzzy density fragmentation, Holographic density theorem, Symmetry deficiency... 

Within the quantum chemical description of molecular electron density clouds, a natural criterion, the Density Domain criterion, provides a quantum chemical definition for functional groups [14-18]. Furthermore, techniques that generate fuzzy electron density contributions for local molecular moieties that are analogous to the fuzzy electron density clouds of complete molecules, determined by the analytic Additive Fuzzy Density Fragmentation (AFDF) method [19-21], or the earlier numerical-grid MEDLA method [22,23], are also... 

Local Electron Densities, the Additive Fuzzy Density Fragmentation (AFDF) Principle, and the Adjustable Density Matrix Assembler (ADMA) Method... 

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

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... 

Specific aspects of the quantum chemical concept of local electron densities and functional groups of chemistry have been discussed, with emphasis on the Additive Fuzzy Density Fragmentation (AFDF) Principle, on the Adjustable Density Matrix Assembler (ADMA) Method of using a local density matrix formalism of fuzzy electron density fragments in macromolecular quantum chemistry, and on the fundamental roles of the holographic electron density theorem, local symmetry, and symmetry deficiency. 

A CRYSTALLOGRAPHIC STRUCTURE REFINEMENT APPROACH USING AB /N/T/O QUALITY ADDITIVE, FUZZY DENSITY FRAGMENTS... 

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