Application of error-ranked singular value decomposition for the determination of potential-derived atomic-centered point charges

The present work provides a detailed investigation on the use of singular value decomposition (SVD) to solve the linear least-squares problem (LLS) for the purposes of obtaining potential-derived atom-centered point charges (PD charges) from the ab initio molecular electrostatic potential (V(QM)). Given the SVD of any PD charge calculation LLS problem, it was concluded that (1) all singular vectors are not necessary to obtain the optimal set of PD charges and (2) the most effective set of singular vectors do not necessarily correspond to those with the largest singular values. It is shown that the efficient use of singular vectors can provide statistically well-defined PD charges when compared with conventional PD charge calculation methods without sacrificing the agreement with V(QM). As can be expected, the methodology outlined here is independent of the algorithm for sampling V(QM) as well as the basis set used to calculate V(QM). An algorithm is provided to select the best set of singular vectors used for optimal PD charge calculations. To minimize the subjective comparisons of different PD charge sets, we also provide an objective criterion for determining if two sets of PD charges are significantly different from one another.     

Reactivity of molecular oxygen on the surface of ionic crystals

A possibility of multiplicity change for ground‐state molecular oxygen adsorbed on the surface of regular and doped broad‐gap ionic crystals was considered in the framework of cluster approximation by using SCF MO LCAO quantum chemical methods [semiempirical INDO approximation and ab initio calculation with the 6‐311G** basis set taking into account the correlation effects on the level of second‐order Meller–Plesset perturbation theory (MP2)]. The formation energetics of cyclic products of addition reactions of dioxygen in different multiplet states to furan and cis‐butadiene in the gas phase and on the surface of ionic crystals was considered. (These reactions are typical for the O₂ singlet state in the gas phase.) It is shown that the presence of sites with high effective charge on the crystal surface can result in a situation not requiring, as in the gas phase, multiplicity change in the transition of a system from an initial to the final state, which can significantly affect the kinetic parameters of the reactions. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Dielectric relaxation in proteins: a continuum electrostatics model incorporating dielectric heterogeneity of the protein and time‐dependent charges

A boundary element formulation of continuum electrostatics is used to examine time‐independent dielectric relaxation and screening in two proteins, and time‐dependent relaxation in two simpler solutes. Cytochrome c oxidation is modeled by inserting partial charges on the heme, using one to three dielectric regions in the protein. It was suggested recently that for charge insertion on a protein‐bound ligand, all or part of the ligand should be treated as a cavity within the protein medium. Here, the effect of an internal cavity surrounding the central heme atoms is examined, considering separately the static and relaxation (or reorganization) free energies. The former is the free energy to remove the redox electron while maintaining the rest of the structure and charge distribution fixed; the latter is the free energy associated with the relaxation into the product state after the corresponding constraints are released. The effect of the cavity is found to be small for the static free energy, while for the relaxation free energy it is large, as polarization of groups immediately around the heme dominates the relaxation. If the protein surface groups are treated as a distinct medium with a dielectric of 25 (as suggested by recent molecular dynamics simulations), the relaxation free energy decreases significantly (from −37.0 to −43.9 kcal/mol), compared to a model where the whole protein has a dielectric constant of two. Therefore, with this model, although polarization of groups immediately around the heme still dominates the relaxation, polar groups near the protein surface also contribute significantly, and solvent negligibly. The screening of an applied field within myoglobin is calculated, with the protein surrounded by either a low‐dielectric or a high‐dielectric glass. In the vicinity of the CO ligand, the screening is approximately isotropic with a low‐dielectric glass. It is anisotropic with a high‐dielectric glass, but the applied and local fields are still approximately parallel. This has implications for experiments that probe dielectric screening in proteins with the newly developed technique of vibrational Stark spectroscopy: with a high‐dielectric glass, a single, rotationally averaged screening factor can be used, the local field being about 1.65 times the applied field. Finally, we calculate the time‐dependent relaxation in response to instantaneous charge insertion within a spherical cavity in a Debye solvent, and to photoexcitation of a tryptophan solute, illustrating the extension of the boundary element formulation to time‐dependent problems. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 290–305, 2001     

To the question on radiationless transitions in electronically excited zones of molecular crystals

A model is proposed describing the dynamics of radiationless transitions in the energy zones corresponding to excited electronic states in molecular crystals. In this model, the migration effect is explicitly reflected, which initially appears under pulse excitation of the systems with a periodical structure of a density distribution of states in separate parts of molecular crystals.     

Off‐atomic site charges in some anions,metal cations,and complexes: Significance for electrostatic properties and binding

Electronic structures and properties of several anions, metal cations, and their complexes with neutral molecules were investigated at the HF/6‐31G** and B3LYP/6‐31G** levels of theory. Charges shifted from atomic sites due to atomic orbital hybridization called hybridization displacement charges (HDC) were investigated in detail. It has been found that many components of HDC are associated with each atom of ion that are shifted from the atomic sites, those associated with metal cations being shifted by large distances as found previously in electrically neutral systems. It is shown that atomic orbitals are appreciably rehybridized in going from neutral molecules to anions and cations. Molecular dipole moments and surface molecular electrostatic potentials (MEP) are obtained satisfactorily using HDC for the various types of species mentioned above. In the OH^?? H₂O complex, reversal of direction of shift of an HDC component associated with the hydrogen atom of H₂O involved in hydrogen bonding, indicates that the hydrogen bond between OH^? and H₂O would have some covalent character. Other atomic site‐based point charge models cannot provide such information about the nature of bonding. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem 2007     

A surface site interaction point methodology for macromolecules and huge molecular databases

Determining the position and magnitude of Surface Site Interaction Points (SSIP) is a useful technique for understanding intermolecular interactions. SSIPs have been used for the prediction of solvation properties and for virtual co‐crystal screening. To determine the SSIPs for a molecule, the Molecular Electrostatic Potential Surface (MEPS) is first calculated using ab initio methods such as Density Functional Theory. This leads to a high cost in terms of computation time and is not compatible with the analysis of huge molecular databases. Herein, we present a method for the fast estimation of SSIPs, which is based on the MEPS calculated from MMFF94 atomic partial charges. The results show that this method can be used to calculate SSIPs for large molecular databases with a much higher speed than the original ab initio methodology. © 2017 Wiley Periodicals, Inc.     

Conformational sensitivity of polyether macrocycles to electrostatic potential: Partial atomic charges,molecular mechanics,and conformational prediction

Molecular recognition (whether by enzymes, the immune system, or chelating ligands) depends critically on molecular conformation. Molecular mechanics predicts energetically favorable molecular conformations by locating low energy conformations using an empirical fit of molecular potential energy as a function of internal coordinates. Molecular mechanics analysis of 18-crown-6 demonstrates that the nonbonded term (primarily the electrostatic part) is the largest contributor to the conformational energy. Nevertheless, common methods of treating the electrostatic interaction for 18-crown-6 yield inconsistent values for conformational energies partly because partial charges assigned to each atom can change with conformation due to through-space inductive effects which are not considered in most molecular mechanics programs. Similar findings from several other groups are reviewed to support our conclusions. We argue for care and caution in predicting conformational preferences of molecules with two or more highly polar atoms. We also discuss the desirability of using an empirical method of partial charge determination such as the charge equilibration algorithm of Rappé and Goddard (or a suitable generalization which includes polarization) as a method of including these effects in molecular mechanics and molecular dynamics calculations.     

Molecular orbital theory of the electronic structures of one-dimensional molecular crystals

A non-empirical tight-binding LCAO SCF MO treatment of one-dimensional molecular crystals based on the SCF perturbation theory is presented. The simpler version of this method at the level of the CNDO/2 approximation is also given.     

Atomic charges in the multiple scattering molecular orbital method

The concept of atomic charges in molecular orbital theory is discussed. A definition which pays special attention to the behaviour of the orbitals close to the atomic nuclei, is suggested. This new definition is particularly simple to apply in the multiple scattering method. Some transition metal complexes are considered as examples. The existence of the back donation effect is demonstrated for a series of octahedral cyanides.Supported by NFR, the Swedish Natural Science Research Council.     

Study of the molecular configuration and the dipole moment in fluorinated liquid crystals

We have investigated the relationship between the molecular configuration and dipole moment of some fluorinated liquid crystals (LCs). The geometries of the molecules were preliminarily optimized at empirical AM1 and then were further optimized at B3LYP/6‐31G(d) level. The dipole moment has been calculated. It is strongly influenced by the position and number of fluorine substituents in the benzene ring of the molecule. The polarizability, mean polarizabilities, and anisotropic polarizability of the phenylbicyclohexane (PBC) fluorine substituents are also given and discussed. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

High‐spin behavior of molecular crystals and extended π systems

The qualitative rules for the existence of high‐spin ground states in extended systems and molecular crystals are examined here on a firmer theoretical footing. Extended systems have been categorized into three groups, namely, type I, type II, and type III, depending on the type of bonding interactions. The general form of the spin Hamiltonian operators have been written down. The active spaces have been restricted to the minimum size for each of these three types of spin systems. The zeroth‐order state vectors and the Hartree–Fock ground‐state energies have been identified for unit species of each type. The extended system Hamiltonian operators are further truncated in such a way that only the nearest‐neighbor interactions are retained. Expressions have been derived for the energy gap from a molecular orbital approach. The relatively small effects of electron correlation on the energy gaps have been estimated for the type I systems, which belong to the systems of solid‐state physics. In particular, it has been shown that for the type I systems the singlet–triplet gap, and hence the ferromagnetic coupling constant, primarily depends upon the difference of one‐electron kinetic energies and not on the two‐electron exchange integrals. This result agrees with the concept of kinetic exchange that was introduced in the context of a resonating valence‐bond formalism. Type II systems are exemplified by extended systems that can be prepared from conjugated molecules while organic molecular crystals form examples of type III species. For these systems, however, the Coulomb exchange interaction has been shown to dominate the energy gap. A quick review of the Heisenberg spin Hamiltonian for the H₂ molecule is sufficient to point out that the sign of the calculated ferromagnetic coupling constant depends on the method of calculation, the nature of the basis set, and the bond length. This is amply supported by ab initio calculations on this species. Numerical data have also been obtained from computations on m‐phenylene‐coupled nitroxy radicals and stacks of α‐nitronyl nitroxide, but these calculations have been based on a semiempirical quantum chemical methodology (INDO) since some of the species involved are exceedingly large. Computed energy gaps are in good agreement with experimental and other theoretical (AM1, PM3) results. Nevertheless, for the dimer, trimer, tetramer, and pentamer of the type II specimen, the important π orbitals are far from being degenerate. The quantitative results clearly deviate from the criterion of degeneracy that was suggested from qualitative theories for the existence of a high‐spin ground state. Therefore, the criteria for the existence of high spins have been reformulated in terms of the monomer orbitals. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 308–324, 2000     

Solvated ensemble averaging in the calculation of partial atomic charges

In the calculation of partial atomic charges, for use in molecular mechanics or dynamics simulations, it is common practice to select only a single conformation for the molecule of interest. For molecules that contain rotatable bonds, it is preferable to compute the charges from several relevant conformations. We present here results from a charge derivation protocol that determines the partial charges by averaging charges computed for conformations selected from explicitly solvated MD simulations, performed under periodic boundary conditions. This approach leads to partial charges that are weighted by a realistic population of conformations and that are suitable for condensed phase simulations. This protocol can, in principle, be applied to any class of molecule and to nonaqueous solvation. Carbohydrates contain numerous hydroxyl groups that exist in an ensemble of orientations in solution, and in this report we apply ensemble averaging to a series of methyl glycosides. We report the extent to which ensemble averaging leads to charge convergence among the various monosaccharides and among the constituent atoms within a given monosaccharide. Due to the large number of conformations (200) in our ensembles, we are able to compute statistically relevant standard deviations for the partial charges. An analysis of the standard deviations allows us to assess the extent to which equivalent atom types may, nevertheless, require unique partial charges. The configurations of the hydroxyl groups exert considerable influence on internal energies, and the limits of ensemble averaged charges are discussed in terms of these properties.     

Partition coefficients of methylated DNA bases obtained from free energy calculations with molecular electron density derived atomic charges

Partition coefficients serve in various areas as pharmacology and environmental sciences to predict the hydrophobicity of different substances. Recently, they have also been used to address the accuracy of force fields for various organic compounds and specifically the methylated DNA bases. In this study, atomic charges were derived by different partitioning methods (Hirshfeld and Minimal Basis Iterative Stockholder) directly from the electron density obtained by electronic structure calculations in a vacuum, with an implicit solvation model or with explicit solvation taking the dynamics of the solute and the solvent into account. To test the ability of these charges to describe electrostatic interactions in force fields for condensed phases, the original atomic charges of the AMBER99 force field were replaced with the new atomic charges and combined with different solvent models to obtain the hydration and chloroform solvation free energies by molecular dynamics simulations. Chloroform–water partition coefficients derived from the obtained free energies were compared to experimental and previously reported values obtained with the GAFF or the AMBER‐99 force field. The results show that good agreement with experimental data is obtained when the polarization of the electron density by the solvent has been taken into account, and when the energy needed to polarize the electron density of the solute has been considered in the transfer free energy. These results were further confirmed by hydration free energies of polar and aromatic amino acid side chain analogs. Comparison of the two partitioning methods, Hirshfeld‐I and Minimal Basis Iterative Stockholder (MBIS), revealed some deficiencies in the Hirshfeld‐I method related to the unstable isolated anionic nitrogen pro‐atom used in the method. Hydration free energies and partitioning coefficients obtained with atomic charges from the MBIS partitioning method accounting for polarization by the implicit solvation model are in good agreement with the experimental values. © 2018 Wiley Periodicals, Inc.     

Concerning virial-based estimations of strength of bonding intermolecular interactions in molecular crystals and supramolecular complexes

It is shown that the electronic virial-based correlation should be used to estimate bonding contributions to the rigidity of molecular vibrations in crystals.     

Auxiliary functions for molecular integrals with Slater‐type orbitals. I. Translation methods

Many types of molecular integrals involving Slater functions can be expressed, with the ζ‐function method in terms of sets of one‐dimensional auxiliary integrals whose integrands contain two‐range functions. After reviewing the properties of these functions (including recurrence relations, derivatives, integral representations, and series expansions), we carry out a detailed study of the auxiliary integrals aimed to facilitate both the formal and computational applications of the ζ‐function method. The usefulness of this study in formal applications is illustrated with an example. The high performance in numerical applications is proved by the development of a very efficient program for the calculation of two‐center integrals with Slater functions corresponding to electrostatic potential, electric field, and electric field gradient. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Charge-transfer exciton trapping at vacancies in molecular crystals: photoconductivity quenching,optical damage and detonation

Calculations are presented that show that vacancies can trap charge-transfer (CT) states in anthracene, acetanilide and hexahydro-1,3,5-trinintro-1,3,5-triazine (RDX). Such trapping provides a mechanism for photoconductivity quenching by geminate recombination, and for optical damage and detonation by concentrating optical or mechanical energy stored in CT states.     

A computationally inexpensive modification of the point dipole electrostatic polarization model for molecular simulations

We present an approximation, which allows reduction of computational resources needed to explicitly incorporate electrostatic polarization into molecular simulations utilizing empirical force fields. The proposed method is employed to compute three-body energies of molecular complexes with dipolar electrostatic probes, gas-phase dimerization energies, and pure liquid properties for five systems that are important in biophysical and organic simulations-water, methanol, methylamine, methanethiol, and acetamide. In all the cases, the three-body energies agreed with high level ab initio data within 0.07 kcal/mol, dimerization energies-within 0.43 kcal/mol (except for the special case of the CH(3)SH), and computed heats of vaporization and densities differed from the experimental results by less than 2%. Moreover, because the presented method allows a significant reduction in computational cost, we were able to carry out the liquid-state calculations with Monte Carlo technique. Comparison with the full-scale point dipole method showed that the computational time was reduced by 3.5 to more than 20 times, depending on the system in hand and on the desired level of the full-scale model accuracy, while the difference in energetic results between the full-scale and the presented approximate model was not great in the most cases. Comparison with the nonpolarizable OPLS-AA force field for all the substances involved and with the polarizable POL3 and q90 models for water and methanol, respectively, demonstrates that the presented technique allows reduction of computational cost with no sacrifice of accuracy. We hope that the proposed method will be of benefit to research employing molecular modeling technique in the biophysical and physical organic chemistry areas.     

Modeling emission features of salicylidene aniline molecular crystals: A QM/QM’ approach

A new computational protocol relying on the use of electrostatic embedding, derived from QM/QM’ ONIOM calculations, to simulate the effect of the crystalline environment on the emission spectra of molecular crystals is here applied to the β‐form of salicylidene aniline (SA). The first singlet excited states (S₁) of the SA cis‐keto and trans‐keto conformers, surrounded by a cluster of other molecules representing the crystalline structure, were optimized by using a QM/QM’ ONIOM approach with and without electronic embedding. The model system consisting of the central salicylidene aniline molecule was treated at the DFT level by using either the B3LYP, PBE0, or the CAM‐B3LYP functional, whereas the real system was treated at the HF level. The CAM‐B3LYP/HF level of theory provides emission energies in good agreement with experiment with differences of ?20/?32 nm ( cis‐keto form) and ?8/?14 nm ( trans‐keto form), respectively, whereas notably larger differences are obtained using global hybrids. Though such differences on the optical properties arise from the density functional choice, the contribution of the electronic embedding is rather independent of the functional used. This plays in favor of a more general applicability of the present protocol to other crystalline molecular systems. © 2016 Wiley Periodicals, Inc.     

Orientation and Dynamics of ZnO Nanorod Liquid Crystals in Electric Fields

ZnO nanorod polymer hybrids (i.e., ZnO nanorods coated with a block copolymer with a short anchor block (dopamine) and a longer solubilizing block of polystyrene (PS)) form liquid crystalline (LC) phases if they are dispersed at high concentration e.g., in a PS oligomer matrix. Due to the high mobility of the low T_g‐matrix the nanorod polymer hybrids show a switching behavior under an applied AC electric field. Hence, the orientation of the nanorod mesogens can be changed from planar (parallel to the substrate) to homeotropic (perpendicular) in full analogy to the switching of low molecular liquid crystals in an electric field. Dielectric measurements show that such a switching is mainly due to the cooperative LC behavior, because the rods themselves exhibit only a very small effective dipole moment. The process can be investigated by polarizing microscopy. SEM images show the orientations of the individual nanorods, which correspond to the Fredericks transition well known for liquid crystals aligned in an electric field. This was the first time such a transition could be visualized by electron microscopy due to the large nanorod mesogens. The observation is interesting to orient nanorods perpendicular to an electrode and can help to improve optoelectronic devices.