Conformational dependence of electrostatic potential derived charges of a lipid headgroup: Glycerylphosphorylcholine

Atomic monopoles are routinely determined through a least squares fit to molecular electrostatic potentials. We report studies of the variation in atomic monopoles with variation in conformation for the zwitterionic polar head group of lecithins, a common class of lipid. The monopole of one atom, a relatively buried carbon, varied by 1.3 electron units between different conformers. “Exterior” atoms, as seen previously, showed smaller changes in charge and smaller estimated standard deviations. The total charge of local groups of atoms varied less than the charge of individual atoms, indicating that shifts in charge occurred mostly between neighboring atoms. This effect might be reflected in the high correlations seen between charges of many neighboring atoms. These correlations, while present for many logical groupings of atoms (such as within methylene and methyl groups), are curiously absent between some bonded atoms. Monopoles were fit to multiple conformations simultaneously to provide a charge set that could optimally reproduce the electrostatic potential of all the conformers as a means of generating monopoles for molecular dynamics simulations or other studies where conformation varies. In some cases, the charges on chemically equivalent atoms (e.g., the hydrogen atoms in a methyl group) were different by more than their estimated error of fit. These studies lead to the suggestion that a minimum error in reported charges is on the order of 10%. All conformations show that the positive charge of the trimethylalkyl ammonium group is carried by the methyl hydrogens; the total charge on the nine hydrogens is over 2 electron units, counterbalanced by negative monopoles on the carbons. The presence of this diffuse cloud of substantial charge would appear to be a disindicator of the use of a “united” atoms approach for these methyl groups. The effects of the charge variation on intermolecular interactions is also examined.     

Fast assignment of accurate partial atomic charges: an electronegativity equalization method that accounts for alternate resonance forms

A fast, accurate method of assigning partial atomic charges is described. The method is based upon the concept of electronegativity equalization and is parametrized to fit electrostatic potentials obtained from ab initio quantum calculations. A novel algorithm for identifying alternate resonance forms is used to ensure that chemically equivalent atoms are assigned equal charges. The resulting charges are independent of conformation, yield good agreement with ab initio electrostatic potentials, and are similar to standard force field charges for common biochemical components. The method is broadly parametrized and generates charges for a drug-like compound in about 0.45 s on a 2.26 GHz Pentium 4 PC. It should thus be useful in a range of applications, such as molecular design and QSAR. The resonance algorithm is expected to have additional applications, such as in atom-typing and detection of molecular symmetry.     

Principal coordinate maps of molecular potential energy surfaces

Obtaining useful representations of molecular conformation spaces and visualizing the associated potential energy surfaces is a complex task, mainly due to the high dimensionality of these spaces. Principal component analysis (PCA), which projects multidimensional data on low-dimensional subspaces, is thus becoming a common technique for studying such spaces. Three issues, relating to the use of principal component techniques for mapping molecular potential energy surfaces, are discussed in this study: the effectiveness of the projection; its accuracy; and the mapping procedure. The effectiveness of PCA is demonstrated through detailed analyses of principal component projections of several peptides. In these cases PCA projected conformation space into a subspace smaller even than that defined by the peptide's backbone dihedral angles. The average accuracy as well as the distribution of errors in the projection (i.e., the errors in reproducing individual distances) are studied as a function of the dimensionality of the projection. The wide variation in accuracy between different systems suggests that it is imperative to indicate the accuracy of the projection whenever PCA projections are used. Furthermore, when projecting potential energy surfaces on the principal two-dimensional (2D) plane, the projection errors result in artificial roughening of the surface. A new mapping procedure, the “minimal energy envelope” procedure, is introduced to overcome this problem. This procedure yields relatively smooth “energy landscapes,” which highlight the basin structure of the real multidimensional energy surface. It is demonstrated that the projected potential energy maps can be used for charting conformational transitions or dynamic trajectories in the system. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1255–1267, 1998     

Evaluating data for atmospheric models,an example: CH3O2 + NO2 = CH3O2NO2

Data in both directions for the title reaction have been statistically fit (weighted nonlinear least squares) to the different formalisms used by the NASA and IUPAC data evaluation panels. The data are well represented by either formalism. Master equation/RRKM methods were then employed in an attempt to reconcile the statistical formulae with theory. This was possible within reasonable bounds using the NASA formulation but more difficult using the IUPAC results. There are sufficient assumptions and unknowns in this attempt, such that the real “bottom line” is that while assuring reasonable agreement with theory is satisfying, spending much time and energy on details needed to represent pressure‐dependent rate coefficients for use in atmospheric or other models of “engineering” problems is not terribly worthwhile. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 625–632, 2005     

Consensus bond-charge increments fitted to electrostatic potential or field of many compounds: Application to MMFF94 training set

Bond-charge increments (BCIs) are additive parameters used to assign atomic charges for the MMFF force field. BCI parameters are classified parsimoniously according to two atom types and the bond order. We show how BCIs may be fitted rapidly by linear least squares to the calculated ab initio electrostatic potential (ESP) or to the electrostatic field. When applied simultaneously to a set of compounds or conformations, the method yields consensus values of the BCIs. The method can also derive conventional “ESP-fit” atomic charges with improved numerical stability. The method may be generalized to determine atom multipoles, multicenter charge templates, or electronegativities, but not polarizability or hardness. We determine 65 potential-derived (PD) BCI parameters, which are classified as in MMFF, by fitting the 6-31G* ESP or the electrostatic field of the 45 compounds in the original MMFF94 training set. We compare the consensus BCIs with classified BCIs that were fit to each molecule individually and with “unique-bond” BCIs (ESP-derived atom charges). Consensus BCIs give a satisfactory representation for about half of the structures and are robust to the adjustment of the alkyl CH bond increment to the zero value employed in MMFF94. We highlight problems at three levels: Point approximation: the potential near lone pairs on sulfur and to some extent nitrogen cannot be represented just by atom charges. Bond classification: BCIs classified according to MMFF atom types cannot represent all delocalized electronic effects. The problem is especially severe for bonds between atoms of equivalent MMFF type, whose BCI must be taken as zero. Consensus: discrepancies that occur in forming the consensus across the training set indicate the need for a more detailed classification of BCIs. Contradictions are seen (e.g., between acetic acid and acetone and between guanidine and formaldehydeimine). We then test the three sets of PD-BCIs in energy minimizations of hydrogen-bonded dimers. Unique-bond BCIs used with the MMFF buffered 14–7 potential reproduce unscaled quantum chemical dimer interaction energies within 0.9 kcal/mol root mean square (or 0.5, omitting two N-oxides). These energies are on average 0.7 (or 0.5) kcal/mol too weak to reproduce the scaled quantum mechanical (SQM) results that are a benchmark for MMFF parameterization. Consensus BCIs tend to weaken the dimer energy by a further 0.4–0.6 kcal/mol. Thus, consensus PD-BCIs can serve as a starting point for MMFF parameterization, but they require both systematic and individual adjustments. Used with a “harder” AMBER-like Lennard–Jones potential, unique-bond PD-BCIs without systematic adjustment give dimer energies in fairly good agreement with SQM. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1495–1516, 1999     

Linear calibrations in chromatography: The incorrect use of ordinary least squares for determinations at low levels,and the need to redefine the limit of quantification with this regression model

Ordinary least squares is widely applied as the standard regression method for analytical calibrations, and it is usually accepted that this regression method can be used for quantification starting at the limit of quantification. However, it requires calibration being homoscedastic and this is not common. Different calibrations have been evaluated to assess whether ordinary least squares is adequate to quantify estimates at low levels. All calibrations evaluated were linear and heteroscedastic. Despite acceptable values for precision at limit of quantification levels were obtained, ordinary least squares fitting resulted in significant and unacceptable bias at low levels. When weighted least squares regression was applied, bias at low levels was solved and accurate estimates were obtained. With heteroscedastic calibrations, limit values determined by conventional methods are only appropriate if weighted least squares are used. A “practical limit of quantification” can be determined with ordinary least squares in heteroscedastic calibrations, which should be fixed at a minimum of 20 times the value calculated with conventional methods. Biases obtained above this “practical limit” were acceptable applying ordinary least squares and no significant differences were obtained between the estimates measured using weighted and ordinary least squares when analyzing real‐world samples.     

Neutron diffraction and simulation studies of the exocyclic hydroxymethyl conformation of glucose

The techniques of neutron diffraction with isotopic substitution (NDIS) and molecular dynamics (MD) simulations have been used to examine the rotational conformation of the exocyclic hydroxymethyl group of D-glucopyranose. First order H/D NDIS experiments were performed on the H6 position in 3m aqueous glucose solutions where the average coherent scattering length of the exchangeable hydrogen atoms was zero (i.e., all correlations between exchangeable hydrogen atoms and other atoms cancel and thus are not present in the scattering data). This H6 experimental result suggests that no single conformation for the C4-C5-C6-O6 dihedral reproduces the observed scattering data well, but that a mixture of the gg and gt conformations, which has been suggested by NMR experiments, gives a reasonable agreement between the MD and experimental data.     

Bond stretching force constants and compressibilities of nitride,oxide, and sulfide coordination polyhedra in molecules and crystals

Molecular quadratic stretching force constants are calculated for a variety of MX bonds (X = N, O, S) in coordinated polyhedra containing row 1 and 2 metal atoms, M, using SCF molecular orbital methods and 6-31G^* basis sets. The resulting data scatter along three distinct trends, depending on whether the bonds involve row 1 atoms, row 1 and row 2 atoms, or row 2 atoms. When compared with spectroscopically determined force constants, the calculated force constants are found to be 20% larger. A single trend seems to obtain when the calculated force constants are plotted as a function of the effective nuclear charges of the bonded atoms and their interatomic separations. Scaled force constants calculated for the SiO bond are in rough agreement with values provided by spectroscopic measurements for silicic acid molecules and silicate crystals. Polyhedral compressibilities for nitride-, oxide-, and sulfide-coordinated polyhedra are inversely related with force constants calculated for their MX bonds. The close similarity of these compressibilities and those recorded for chemically similar crystals suggests that force constant-compressibility relationships in chemically similar molecular and crystalline systems are not significantly different.     

On the charge distribution in ethanes and disilanes and correlations with equilibrium bond lengths; an ab initio study

The equilibrium electronic wave-functions for a series of fluoro- and chloro-ethanes and disilanes of general formula M₂H_6−nX_n, (M=C, Si; X=F, Cl), were analysed by the most commonly used methods for electron distribution, using the Mulliken and Löwdin populations, natural atomic orbital (NAO) populations and atoms in molecules (AIM) electron densities. Although the numerical values for local atomic charges vary greatly, all the methods correlate, but in markedly differing ways. The Mulliken charges seem the most selective in relation to systematic change of substituents in the current type of molecular structure. A number of examples occur where the AIM charges at C, Si centres are effectively identical in different molecules, where some differences might have been anticipated. These are often distinguished by Mulliken populations. The fluoroethanes exemplify this, since a plot of the AIM charges (for example on either the F or H centres) against the Mulliken charges for all members of the series, shows three nearly parallel lines, corresponding to those centres with 0, 1 or 2 fluorine atoms on the centre under study. The bond critical points at which the AIM charges are determined seem to be counter to intuition in some cases. This is a density rather than atomic orbital size issue however. The Mulliken and NAO charges seem more reasonable than those from the AIM method. There is an unexpected correlation of the local bond dipoles from the Mulliken analyses, with the calculated equilibrium bond lengths. These correlations lead to bond length values for the non-polarised bonds MX, which agree with data based on covalent radii for some bonds.     

Gradient‐driven molecule construction: An inverse approach applied to the design of small‐molecule fixating catalysts

Rational design of molecules and materials usually requires extensive screening of molecular structures for the desired property. The inverse approach to deduce a structure for a predefined property would be highly desirable, but is, unfortunately, not well defined. However, feasible strategies for such an inverse design process may be successfully developed for specific purposes. We discuss options for calculating “jacket” potentials that fulfill a predefined target requirement—a concept that we recently introduced (Weymuth and Reiher, MRS Proceedings 2013, 1524, DOI:10.1557/opl.2012.1764). We consider the case of small‐molecule activating transition metal catalysts. As a target requirement we choose the vanishing geometry gradients on all atoms of a subsystem consisting of a metal center binding the small molecule to be activated. The jacket potential can be represented within a full quantum model or by a sequence of approximations of which a field of electrostatic point charges is the simplest. In a second step, the jacket potential needs to be replaced by a chemically viable chelate‐ligand structure for which the geometry gradients on all of its atoms are also required to vanish. To analyze the feasibility of this approach, we dissect a known dinitrogen‐fixating catalyst to study possible design strategies that must eventually produce the known catalyst. © 2014 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.     

Reassessment of large dipole moment enhancements in crystals: a detailed experimental and theoretical charge density analysis of 2-methyl-4-nitroaniline

The molecular dipole moment of MNA in the crystal has been critically reexamined, to test the conclusion from an earlier experimental charge density analysis that it was substantially enhanced due to a combination of strong intermolecular interactions and crystal field effects. X-ray and neutron diffraction data have been carefully measured at 100 K and supplemented with ab initio crystal Hartree-Fock calculations. Considerable care taken in the measurement and reduction of the experimental data excluded most systematic errors, and sources of error and their effects on the experimental electron density have been carefully investigated. The electron density derived from a fit to theoretical structure factors assisted in the determination of the scale and thermal motion model. The dipole moment enhancement for MNA in the crystal is much less than that reported previously and only on the order of 30-40% (approximately 2.5 D). In addition to the dipole moment, experimental deformation electron density maps, bond critical point data, electric field gradients at hydrogen nuclei, and atomic and group charges all agree well with theoretical results and trends. Anisotropic modeling of the motion of hydrogen atoms, integral use of periodic ab initio calculations, and improved data quality are all aspects of this study that represent a considerable advance over previous work.     

The meaning and definition of “charge” in molecules

Atomic charges have been calculated by a simple model involving partition of total molecular bonding energy into “ionic” and “covalent” components. These charges agree well with those obtained by Politzer's electron-count method of assigning charge but not with charges obtained by populational analysis. It is argued that Politzer's definition of charge is closer to the intuitive use of the word “charge” by chemists than is that based on populational analysis. Further examples of the importance of consideration of valence state electronegativities and charge capacities are discussed.     

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.     

Étude conformationnelle théorique des dithiéno (c,e) dihydro azépine,oxépinne et thiépinne

The PCILO method is used to study the conformations of the dithieno-(c,e)-dihydroazepin, and of the oxepin and thiepin analogues. The optimization of all the parameters of the seven membered ring is achieved by using the steepest gradient method. The energetically favoured conformation is the “twisted” form, whatever the position of the orthocondensation of the thiophen cycles. This form is predominant in particular when the thiophen cycles are linked in (c) to the seven membered ring. The energy difference between the “twisted” form and the “half boat” form vary in the order S > NH ~ O and the same sequence is observed for the torsion of the cycles in the “twisted” form. An initial estimation of the solvation process is carried out by using the Jano's formalism.     

VESPA: A new,fast approach to electrostatic potential-derived atomic charges from semiempirical methods

An improved semiempirical method for computing electrostatic potential-derived atomic charges is described. It includes a very fast algorithm for the generation of the grid points around the molecule and the calculation of the electrostatic potential at these points. The dependency of the atomic point charges obtained on the number of grid points used in the fitting procedure is examined. For “buried” atoms a high density grid is necessary. It is possible to obtain 6–31G*-quality atom-centered point charges, even for phosphorus compounds, using AM1 or PM3. This approach can therefore be recommended for general use in QSAR or molecular mechanics for any organic and bioorganic system up to about 200 atoms. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 744–756, 1997     

A chemically useful definition of electron difference densities

Molecular difference densities (DD ) are conventionally constructed using spherically averaged atomic densities at the appropriate positions. For atoms in degenerate ground states, this is an unphysical choice, and artifacts dominate the DD . We suggest the extraction of both the position and the orientation of an atom with an open valence shell from x-ray scattering or molecular density data. Subtracting the oriented atoms yields a uniquely defined, as well as chemically meaningful, DD. Covalent bonds to electronegative atoms such as O are no longer exceptional but show bond charges of normal magnitude. Lone pairs are characterized by a dipolar density shift from the bond to the back side of the atomic core.     

A chemically useful definition of electron difference densities

Molecular difference densities (DD ) are conventionally constructed using spherically averaged atomic densities at the appropriate positions. For atoms in degenerate ground states, this is an unphysical choice, and artifacts dominate the DD . We suggest the extraction of both the position and the orientation of an atom with an open valence shell from x-ray scattering or molecular density data. Subtracting the oriented atoms yields a uniquely defined, as well as chemically meaningful, DD . Covalent bonds to electronegative atoms such as O are no longer exceptional but show bond charges of normal magnitude. Lone pairs are characterized by a dipolar density shift from the bond to the back side of the atomic core.     

Reversible Topotactic Redox Reactions of Solids by Electron/Ion Transfer

Solids having suitable structural and electronic properties are able to form intercalation compounds by reversible redox reactions at room temperature via topotactic electron/ion transfer processes. The host lattices range from inorganic solids with different structural dimensionality to organic molecular solids. Similarly, depending on the host lattice type, the guest species may vary from protons and metal ions to large inorganic and organic molecular ions. The possibilities of a systematic “tailoring” of new stable or metastable compounds, the controlled modification of physical properties of solids, and the technical application of electronic/ionic conductors, provide a wide and attractive field for academic and applied research in an interdisciplinary area that involves solid state chemistry and physics, molecular chemistry, electrochemistry, and interface science.