Linear scaling methods using additive fuzzy density fragmentation

Abstract

The Additive Fuzzy Density Fragmentation (AFDF) principle provides the basis for the linear scaling Adjustable Density Matrix Assembler (ADMA) method, developed for detailed, ab initio quality macromolecular electron density computations, directed primarily towards protein studies. The same principle is the basis for novel approaches to the local analysis of electron density fragments, such as functional groups and regions surrounding reactive centers in various biomolecules. The basic theoretical developments as well as the implementation of the ADMA and related methods are subject to the conditions represented by the Holographic Electron Density Theorem: in any non-degenerate ground state, any positive volume local part of the electron density contains the complete information about the entire, boundaryless molecule. This represents a limitation on the transferability of molecular fragments, however, by a fuzzy fragmentation, some of the difficulties can be circumvented. Approximate transferability is a viable option if the relations between local and global properties are properly taken into account. Specifically, the interplay between local and global molecular properties, as manifested, for example, by symmetry properties and the topological shape constraints on molecular features has a strong influence on molecular energies. A better understanding of the interactions between local and global features also leads to fragment-based combinatorial quantum chemistry approaches. A general framework for such studies can be formulated based on the insight obtained by macromolecular quantum chemistry computations using the linear scaling ADMA method.