An alternative to the "Star Path" enhancement of the ADMA linear scaling method for protein modeling.

With the aim of improving the performance of macromolecular quantum chemistry conformation analysis and reaction path following methods, the Adjustable Density Matrix Assembler (ADMA) method has already been combined with some faster although less accurate density matrix extrapolation methods, such as the Löwdin-Inverse-Löwdin (LIL) extrapolation along a potential energy surface, and a strategically arranged back-and-forth switching between these methods has been proven to be advantageous. Here, an alternative approach is proposed and investigated, based on several actual test calculations, where the "inexpensive" LIL density matrix extrapolation steps are replaced by only somewhat more expensive, but still ADMA-based calculations, where in the "rough-search stage," only interactions of shorter distances within the macromolecule are considered. It is shown that this approach is viable, as an alternative to the "Star Path" method including both ADMA and LIL steps. © 2017 Wiley Periodicals, Inc.

Compensation effects in molecular interactions and the quantum chemical le Chatelier principle.

Components of molecular interactions and various changes in the components of total energy changes during molecular processes typically exhibit some degrees of compensation. This may be as prominent as the over 90% compensation of the electronic energy and nuclear repulsion energy components of the total energy in some conformational changes. Some of these compensations are enhanced by solvent effects. For various arrangements of ions in a solvent, however, not only compensation but also a formal, mutual enhancement between the electronic energy and nuclear repulsion energy components of the total energy may also occur, when the tools of nuclear charge variation are applied to establish quantum chemically rigorous energy inequalities.

Fuzzy electron density fragments in macromolecular quantum chemistry, combinatorial quantum chemistry, functional group analysis, and shape-activity relations.

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.

Substituent effects and local molecular shape correlations.

Using a detailed electron density shape analysis methodology, a new method is proposed for studying the main components of substituent effects in a series of disubstituted benzenes, in correlation with their activating and deactivating characteristics as observed by the induced shape changes of a local electron density cloud. The numerical measures obtained for the extent of shape changes can be correlated with known and with some unexpected effects of various substituents. The insight obtained from the shape analysis provides a theoretical, electron density based justification for some well-known trends, but it also provides new explanations for some of the unexpected features of these substituent effects.

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.

Natural molecular fragments, functional groups, and holographic constraints on electron densities.

One of the tools of the shape analysis of molecular electron densities, the Density Threshold Progression Approach used in Shape Group studies can also serve as a criterion for the selection of "natural" molecular fragments, relevant to functional group comparisons, reactivity studies, as well as to the study of levels of relative "autonomy" of various molecular regions. The relevance of these approaches to the fragment-based studies of large molecules, such as biopolymers and nanostructures is emphasized, and the constraints represented by the holographic electron density theorem to this and alternative recent fragment approaches are discussed. The analogies with potential energy hypersurface analysis using the Energy Threshold Progression Approach and connections to level set methods are discussed, and the common features of these seemingly distant problems are described.

Laterally extended spiral graphite analogue boron-nitrogen helices.

Ab initio self-consistent field molecular orbital and density functional theory calculations have been performed on a series of extended helical boron-nitrogen analogues of a "spiral graphite", the [N]polymethylenylnaphthalenes (N = 6, 8, and 12), with the molecular formula N(x)B(y)H(z) (where x = 28, 37, and 55, y = 27, 36, and 54, z = 23, 29, and 41). Interchanging the positions of the boron and nitrogen atoms in the helix leads to very similar structures N(x-1)B(y+1)H(z) in all three studied cases. The electronic structure and the optimum geometries of these helices were investigated at the HF/6-31G(d,p) and B3LYP/6-31G(d,p) levels of theory. Electron density contours were calculated for the largest helices at the B3LYP/6-31G(d,p) level of theory.

Helices of boron-nitrogen hexagons and decagons. A theoretical study.

Ab initio self-consistent field molecular orbital and density functional theory calculations have been performed on a series of helical boron-nitrogen structures comprised of fused hexagons and larger polygons. The presence of an even number N of rings in the boron-nitrogen [N]helicenes leads to the possibility of angular isomers. The electronic structure and stability of three isomeric nonhydrogenated boron-nitrogen helices were investigated at the HF/6-31G(d) and the B3LYP/6-31G(d) levels of theory. According to this study some of the initially assumed regular helical structures are unstable; two types of the isomeric structures convert to characteristically different equilibrium geometries. Electron density contours were calculated in order to interpret the existing bonding patterns.

Theoretical study on the structure and stability of some unusual boron-nitrogen helices.

Ab initio self-consistent field molecular orbital and density functional theory calculations have been performed on a series of helical structures comprised of boron-nitrogen analogues of extended helicenes, with helically arranged N fused benzene rings, and alternating N benzene units fused to N - 1 cyclobutadiene rings as reference structures. The electronic structure and stability of boron-nitrogen analogues of angular [N]helicenes, [N]phenylenes (N = 5, 6, 7, 12), and [N]methylenylnaphthalenes (N = 6) were investigated at the HF/6-31G(d) and the B3LYP/6-31G(d) levels of theory. The presence of an even number N of rings in the boron-nitrogen [N]helicenes leads to the possibility of angular isomers. Electron density contours were calculated in order to interpret the existing bonding patterns. These structures may provide supramolecular building blocks and macromolecular "springs" with unusual electronic properties.

On the Balance of Simplification and Reality in Molecular Modeling of the Electron Density.

Fused-sphere (van der Waals) surfaces and their variants such as solvent accessible surfaces and molecular surfaces are simple molecular models that are commonly used for many diverse purposes across a broad range of scientific disciplines due to their low computational resource demands. Fused-sphere models require atomic radii to be defined. Many different atomic radii have been proposed, with each set of radii being applicable to a relatively limited scope of molecular types or situations. The large number of differing radii sets actually serves to emphasize the simplicity of the model and its inability to accurately represent the reality of the molecule: its electron density. By measuring the similarity of fused-sphere, fuzzy fused-sphere, and calculated electron density representations of a set of small molecules via symmetric volume differences and the shape group method, it can be seen that fused-sphere models are very poor at representing the real electronic charge distribution of small molecules, especially where π bond systems, lone pair electrons, and aromatic rings are involved. Larger molecules, conceivably, will be even more poorly represented. With advances in computational power and modeling techniques to arrive at high-quality calculated electron density representations for large molecules already in existence, abandoning the use of fused-sphere models should be considered for many applications.

Stability and electronic properties of nitrogen nanoneedles and nanotubes.

The electronic structures and stability of nitrogen nanostructures, nanotubes, and fiberlike nanoneedles of various diameters, formed by units N2m (m = 2-6), were studied by quantum chemistry computational modeling methods. The geometrical structures with various cross-sections and terminal units, their energetic stability, and their rather peculiar electron density distributions were investigated. The tightest nitrogen nanoneedle (NNN) studied theoretically in this work is the structure (N4n with D2h symmetry, whereas the nitrogen nanotube (NNT) with the largest diameter discussed here is the structure (N12)n with D2 symmetry. These families of NNNs and NNTs can be considered as nanostructures not only for potential applications as devices in nanotechnology or as possible scaffold structures but also as ligands in synthetic chemistry and high-energy density materials (HEDMs). As a consequence of the lone-pair electrons present around the walls of these NNNs and NNTs, these nitrogen nanostructures and the nitrogen nano-bundles (NNB) formed by aligning and combining them using intermediate carbon atoms, can have highly variable electronic properties controlled by the changing charge environment. In particular, for extended systems based on the units studied here, the band gaps of each of these systems can be affected greatly by the local charge of the environment.

The electronic structures and properties of open-ended and capped carbon nanoneedles.

The existence of a family of very thin carbon needlelike nanostructures is predicted: the geometry and stability of several carbon nanoneedles (CNNs) formed by C4 and C6 units have been studied by quantum chemistry computational modeling methods. The structures of carbon nanoneedles are tighter than even the smallest single wall nanotubes (SWNTs) based on (4, 0) naphthacene. The electronic properties, energetic stability of geometrical structures with various terminal units are investigated. The relatively large band gaps, the strong bonding, and additional orbital interactions within the C4 rings and between the C4 layers make the H4(C4)(n)H4 type molecules nonmetallic. We have found indications that if the CNN (3, 0) structures are very long (in the limit of infinite-length), then they are likely to have semiconducting properties and could possibly be used as actual semiconductors. The studied families of CNNs can be considered as carbon nanostructures with unique structural and chemical properties and with possible potential for unusual electronic properties, with likely practical applications as nanomaterials and nanostructure devices.

Stability and properties of polyhelicenes and annelated fused-ring carbon helices: models toward helical graphites.

The geometrical structures and properties of conjugated polyhelicenes and annelated fused-ring carbon helices with analogous frameworks were theoretically studied at the HF/6-31G and B3LYP/6-31G levels. These studies focused on the stability of the fused-ring structures with special emphasis on the helical geometrical arrangements. To elucidate bonding patterns, the orbitals, electron density contours, and the electrostatic potential of these helical compounds were analyzed. The structure of fused polynaphthalenes arranged in a helical spiral can be regarded as part of a locally helical graphite lattice that is expected to give rise to special electronic properties along the helically layered conjugated single sheet that can be regarded as a single extended pi system but also involving local layer-to-layer pi-pi interactions that are typical in ordinary graphite. This dual feature might lead to novel materials.

Theoretical derivation of heuristic molecular lipophilicity potential: a quantum chemical description for molecular solvation.

We present the theoretical derivation of a heuristic molecular lipophilicity potential (HMLP), which gives a structure-based and quantum chemical description of an important aspect of molecular solvation. The quantum mechanical electrostatic potential (ESP) V(r) on a formal molecular surface is calculated, and then the molecular lipophilicity potential L(r) is constructed by comparing the local electron density with the ESP on the surrounding atoms using a screening function. The screening function is derived from statistical mechanical theory treating the polar solvent molecules as dipoles. HMLP is able to describe the main interactions of solute molecules with polar and nonpolar solvent molecules. HMLP is a unified lipophilicity and hydrophilicity potential: its positive values represent lipophilicity, and its negative values represent hydrophilicity. In this paper, several examples show that HMLP gives more reliable descriptions for the molecular solvation than some other methods, such as atomic partial charges and the empirical lipophilicity potential.

A theoretical study of nitrogen-rich phosphorus nitrides P(Nn)m.

Ab initio calculations predict that structures P(Nn)m (n = 3, 4; m = 1-4; with linear N3, tetrahedral N4, and square N4) correspond to local energy minima characterized by having real frequencies for all eigenvectors of the Hessian matrix. The central P atom often prefers having an odd number of bonds, although we also found some stable structures where P is evenly bonded. The special role of the phosphorus atom in the geometrical arrangements of the P(Nn)m systems was investigated. The low barriers of P(N4)m in the gas-phase decomposition reactions mean that these nitrogen-rich systems require external stabilization if they are to be used as high-energy density materials or starting materials for further syntheses.

Predicted high-energy molecules: helical all-nitrogen and helical nitrogen-rich ring clusters.

Helical all-nitrogen and nitrogen-rich ring clusters, new types of potential high-energy molecules, were investigated in the computational study reported here. Stable helical all-nitrogen clusters N26 and N46 and nitrogen-rich helical structure N26H16 formed by fused six-membered rings were found and characterized as proper energy minima by having real frequencies for all eigenvectors of the Hessian matrix. Furthermore, the stability of [6] N-ring helix was studied by calculating the barrier of dissociation reaction. The potential of these type molecules as high-energy density materials was studied. For a better intuitive understanding of the unusual bonding patterns, the molecular isodensity contour (MIDCO) surfaces for [6] N-ring helix and [6] N-helicene were compared at some characteristic density threshold values of 0.20, 0.32, and 0.35 au. As indicated at these threshold values of the isodensity surfaces, the bonds of all-nitrogen clusters appear stronger than those of nitrogen-rich clusters. Apparently, the nitrogen-rich clusters are of higher energy than the all-nitrogen structures, especially if one takes into account the energy balance of bonds involving hydrogen.

The degree of rotation independence of conjugation of S-N bonds.

The electron delocalization in pi-electron systems is frequently described qualitatively by the concept of conjugation between formal double bonds separated by a formal single bond. In carbon compounds the optimum conjugation usually requires a rather strict, geometrical condition: the exact or near coplanarity of the participating carbon atoms. However, the geometrical conditions are much less strict for third-row atoms if the bonding involves valence-shell d orbitals. In some sulfur compounds, such as N-sulfonylsulfilimines, the conjugation is almost unaffected within large ranges of bond-rotation angles, which amounts to rotation-independent conjugation. On the basis of the indications of earlier, limited studies using only minimal basis set and no geometry optimization, in the more extensive present study Density Functional Theory B3LYP calculations using 6-31G basis set provide more reliable evidence for such flexible conjugation in some sulfur compounds and give an explanation for the experimentally observed interconversion of chiral conformers of N-sulfonylsulfilimines.

Evaluation of the field-adapted ADMA approach: absolute and relative energies of crambin and derivatives.

A large number of conformations and chemically modified variants of the protein crambin were used to extensively test the field-adapted adjustable density matrix assembler (FA-ADMA) method developed for ab initio quality quantum chemistry computations of proteins and other macromolecules, introduced in an earlier publication. In this method, the fuzzy density matrix fragmentation scheme of the original adjustable density matrix assembler (ADMA) method has been made more efficient by combining it with an approach of using point charges to approximate the effects of additional, distant parts of a given macromolecule in the quantum chemical calculation of each fragment. In this way, smaller parent molecules can be used for fragment generation, while achieving accuracy that can be obtained only with large parent molecules in the original ADMA method. Whereas in both methods the error relative to the Hartree-Fock result can be reduced below any threshold by choosing large enough parent molecules, this can be done more efficiently with the new method. In order to obtain reliable test results for the accuracy obtainable by the new method when compared to conventional Hartree-Fock calculations, we performed a large number of energy calculations for the protein crambin using various conformations available in the Protein Data Bank, various protonation states, and side chain mutations. Additionally, in order to test the performance of the method for protein-solvent interaction studies, the energy changes due to the formation of complexes with ethanol and single and multiple water molecules were investigated.

Ab initio quality properties for macromolecules using the ADMA approach.

We describe new developments of an earlier linear scaling algorithm for ab initio quality macromolecular property calculations based on the adjustable density matrix assembler (ADMA) approach. In this approach, a large molecule is divided into fuzzy fragments, for which quantum chemical calculations can easily be done using moderate-size "parent molecules" that contain all the local interactions within a selected distance. If greater accuracy is required, a larger distance is chosen. With the present extension of this approximation, properties of the large molecules, like the electron density, the electrostatic potential, dipole moments, partial charges, and the Hartree-Fock energy are calculated. The accuracy of the method is demonstrated with test cases of medium size by comparing the ADMA results with direct quantum chemical calculations.