Modeling large macromolecular structures using promolecular densities

An information-theoretic approach to basis-set fitting of electron densities and other non-negative functions

The numerical ill-conditioning associated with approximating an electron density with a convex sum of Gaussian or Slater-type functions is overcome by using the (extended) Kullback-Leibler divergence to measure the deviation between the target and approximate density. The optimized densities are non-negative and normalized, and they are accurate enough to be used in applications related to molecular similarity, the topology of the electron density, and numerical molecular integration. This robust, efficient, and general approach can be used to fit any non-negative normalized functions (e.g., the kinetic energy density and molecular electron density) to a convex sum of non-negative basis functions. We present a fixed-point iteration method for optimizing the Kullback-Leibler divergence and compare it to conventional gradient-based optimization methods. These algorithms are released through the free and open-source BFit package, which also includes a L2-norm squared optimization routine applicable to any square-integrable scalar function.

Description of non-covalent interactions in benzyl chalcocyanate crystals from smoothed Cromer-Mann electron density distribution functions

A well-known method to characterize non-covalent interactions consists in the topological analysis of electron density distribution (EDD) functions, complemented by the search for minima in the reduced density gradient (RDG) distributions. Here, we characterize intermolecular interactions occurring in crystals of benzyl chalcocyanate compounds through bond critical points (BCP) of the promolecular electron density (ED) built from the crystallographic Cromer-Mann parameters, at several smoothing levelst. The trajectories formed by thet-dependent BCP locations are interpreted in terms of the intermolecular interactions occurring within the crystal arrangements. Chalcogen…nitro BCPs are clearly present in the unsmoothed EDDs but are annihilated astincreases, while chalcogen…chalcogen BCPs appear and are among the only BCPs left at the highest smoothing level. The chalcogen bonds are differentiated from the other chalcogen interactions through the linear chalcogen…BCP…nitro geometry at low smoothing level and their more negative Laplacian values. The annihilation of CPs can be followed by the apparition of a RDG minimum, associated with a very weak interaction. Along the BCP trajectories, the Laplacian shows a progressive concentration of the ED in the intermolecular space within the crystals and adopts the most negative values at the shortest atom…atom separations. At the termination point of a BCP trajectory, the drastic increase of the ellipticity value illustrates the flattening of the EDD.

Electron density shape analysis of a family of through-space and through-bond interactions

A family of styrene derivatives has been used to study the effects of through-space and through-bond interactions on the local and global shapes of electron densities of complete molecules and a set of substituents on their central rings. Shape analysis methods which have been used extensively in the past for the study of molecular property-molecular shape correlations have shown that in these molecules a complementary role is played by the through-space and through-bond interactions. For each specific example, the dominance of either one of the two interactions can be identified and interpreted in terms of local shapes and the typical reactivities of the various substituents. Three levels of quantum chemical computational methods have been applied for these structures, including the B3LYP/cc-pVTZ level of density functional methodology, and the essential conclusions are the same for all three levels. The general approach is suggested as a tool for the identification of specific interaction types which are able to modify molecular electron densities. By separately influencing the through-space and through-bond components using polar groups and groups capable of conjugation, some fine-tuning of the overall effects becomes possible. The method described may contribute to an improved understanding and control of molecular properties involving complex interactions with a possible role in the emerging field of molecular design.

Communications on quantum similarity (2): A geometric discussion on holographic electron density theorem and confined quantum similarity measures

The so-called holographic electron density theorem (HEDT) is analyzed from an algebraic perspective, and a brief analytical point of view is also given. The connection of the HEDT with quantum similarity measures (QSM) over electronic density functions (DF) is studied using GTO functions, atomic ASA DF, and promolecular ASA DF. Restricted integration of QSM over a box of finite side length is discussed for all this DF. This work emphasizes the geometric aspects of HEDT, but for the sake of completeness, some analytical insight based on a general Taylor series expansion is also given at the end.

CheckDen, a program to compute quantum molecular properties on spatial grids

CheckDen, a program to compute quantum molecular properties on a variety of spatial grids is presented. The program reads as unique input wavefunction files written by standard quantum packages and calculates the electron density rho(r), promolecule and density difference function, gradient of rho(r), Laplacian of rho(r), information entropy, electrostatic potential, kinetic energy densities G(r) and K(r), electron localization function (ELF), and localized orbital locator (LOL) function. These properties can be calculated on a wide range of one-, two-, and three-dimensional grids that can be processed by widely used graphics programs to render high-resolution images. CheckDen offers also other options as extracting separate atom contributions to the property computed, converting grid output data into CUBE and OpenDX volumetric data formats, and perform arithmetic combinations with grid files in all the recognized formats.

Similarity measures based on Gaussian-type promolecular electron density models: Alignment of small rigid molecules

Various molecular similarity measures (overlap, Coulomb, kinetic, electrostatic energy) and similarity indices (Carbó, Hodgkin-Richards, Kulczynski, Shape Tanimoto) are applied to the superposition of 3D promolecular electron density (PED) distributions. The original aspect of the paper lies in the consideration of smoothed PEDs, which allow to decrease the number of local solutions to a superposition problem, together with the use of the less common kinetic and electrostatic energy similarity measures. Results are obtained for a family of five rigid endothiapepsin ligands that were already considered in previous applications, based on graph representations of their PED. In the present work, it is observed that the use of smoothed PED and the kinetic similarity measure, together with the Kulczynski or Shape Tanimoto index, performed the best to align molecules of different sizes.

Quality of approximate electron densities and internal consistency of molecular alignment algorithms in molecular quantum similarity

The calculation of molecular quantum similarity measures using the molecular electron density requires the electron density and molecular alignment between two molecules. To obtain meaningful quantum similarity matrices, the electron density should be calculated efficiently and accurately and the alignment should be internally consistent. The internal consistency of the alignment for a series of molecules is investigated through distance geometry concepts. The calculation of the quantum similarity matrix requires the calculation of a quadratic number of similarity integrals, and a scheme to obtain these efficiently is developed. Both the alignment procedure and the ASA method for approximate molecular electron densities are tested for a set of steroid molecules.

Quantum similarity superposition algorithm (QSSA): a consistent scheme for molecular alignment and molecular similarity based on quantum chemistry

The use of the molecular quantum similarity overlap measure for molecular alignment is investigated. A new algorithm is presented, the quantum similarity superposition algorithm (QSSA), expressing the relative positions of two molecules in terms of mutual translation in three Cartesian directions and three Euler angles. The quantum similarity overlap is then used to optimize the mutual positions of the molecules. A comparison is made with TGSA, a topogeometrical approach, and the influence of differences on molecular clustering is discussed.