Fuzzy Electron Density Fragments in Macromolecular Quantum Chemistry, Combinatorial Quantum Chemistry, Functional Group Analysis, and Shape–Activity Relations

Abstract

Conspectus Just as complete molecules have no boundaries and have "fuzzy" electron density clouds approaching zero density exponentially at large distances from the nearest nucleus, a physically justified choice for electron density fragments exhibits similar behavior. Whereas fuzzy electron densities, just as any fuzzy object, such as a thicker cloud on a foggy day, do not lend themselves to easy visualization, one may partially overcome this by using isocontours. Whereas a faithful representation of the complete fuzzy density would need infinitely many such isocontours, nevertheless, by choosing a selected few, one can still obtain a limited pictorial representation. Clearly, such images are of limited value, and one better relies on more complete mathematical representations, using, for example, density matrices of fuzzy fragment densities. A fuzzy density fragmentation can be obtained in an exactly additive way, using the output from any of the common quantum chemical computational techniques, such as Hartree-Fock, MP2, and various density functional approaches. Such "fuzzy" electron density fragments properly represented have proven to be useful in a rather wide range of applications, for example, (a) using them as additive building blocks leading to efficient linear scaling macromolecular quantum chemistry computational techniques, (b) the study of quantum chemical functional groups, (c) using approximate fuzzy fragment information as allowed by the holographic electron density theorem, (d) the study of correlations between local shape and activity, including through-bond and through-space components of interactions between parts of molecules and relations between local molecular shape and substituent effects, (e) using them as tools of density matrix extrapolation in conformational changes, (f) physically valid averaging and statistical distribution of several local electron densities of common stoichiometry, useful in electron density databank mining, for example, in medicinal drug design, and (g) tools for combinatorial quantum chemistry approaches using fuzzy fragment databanks and rapid construction of a large number of approximate electron densities for large sets of related molecules, relevant in theoretical molecular and nanostructure design.

A quantum mechanical computational method for modeling electrostatic and solvation effects of protein

“…Based on this chemical intuition, the system is divided into many individual subsystems (fragments) and subsequently the properties of the whole system can be obtained by taking a linear combination of the properties of these fragments. Over the past decade, many fragmentation QM methods have been proposed 46 , 47 , including the fragment molecular orbital (FMO) method 48 , the systematic fragmentation method (SFM) 49 , the molecular tailoring approach (MTA) 50 , the molecular fractionation with conjugate caps (MFCC) method 21 , 51 , the adjustable density matrix assembler (ADMA) method 52 , the electrostatically embedded many-body (EE-MB) expansion approach 53 , the explicit polarizatioin (X-Pol) potential 54 .…”

An alternative to the “Star Path” enhancement of the ADMA linear scaling method for protein modeling

“…In the initial stages of geometry or reaction path optimization involving crude searches, the less accurate but more rapid method is sufficient, such as the L€ owdin-Inverse-L€ owdin (LIL) density matrix extrapolation, [11,34,40] relying only overlap matrix calculations at any new nuclear geometry, and after a reasonably reduced neighborhood of the desired conformation is found in the configuration space by the crude method, the fullfledged ADMA approach is used for a more accurate determination. [47,48,50,51,53,54] These two methods, ADMA and LIL, are, indeed, fully compatible, as they both use, as input as well as output, density matrices of the same dimension and involving a common AO basis set.…”

“…Whereas the inherent fuzziness of electron densities appear to limit the value of models based on localization, even such localization approaches reflect fuzziness . Fuzzy electron density modeling approaches have provided a variety of methods for molecular shape analysis, as well as molecular fragment studies and perhaps most importantly, efficient linear‐scaling macromolecular quantum chemistry computational methods …”

“…One such simplification is based on a simple principle: a combination of two, fully compatible methods, one is rapid although rather crude and not very accurate method based on density matrix extrapolation, and another, the full‐fledged ADMA linear‐scaling method, involving an accurate but also more expensive calculation. In the initial stages of geometry or reaction path optimization involving crude searches, the less accurate but more rapid method is sufficient, such as the Löwdin‐Inverse‐Löwdin (LIL) density matrix extrapolation, relying only overlap matrix calculations at any new nuclear geometry, and after a reasonably reduced neighborhood of the desired conformation is found in the configuration space by the crude method, the full‐fledged ADMA approach is used for a more accurate determination …”

Communications on quantum similarity (4): collective distances computed by means of similarity matrices, as generators of intrinsic ordering among quantum multimolecular polyhedra

“…In modern times, the quantum structure of DF plays a leading role within similar and related purposes as the present work ones. For instance, the interested reader can peruse the contemporary references of Mezey et al where the DF shape similarity analysis is described and employed to understand chemical behavior.…”