MEPSIM: A computational package for analysis and comparison of molecular electrostatic potentials

Summary MEPSIM is a computational system which allows an integrated computation, analysis, and comparison of molecular electrostatic potential (MEP) distributions. It includes several modules. Module MEPPLA supplies MEP values for the points of a grid defined on a plane which is specified by a set of three points. The results of this program can easily be converted into MEP maps using third-parties graphical software. Module MEPMIN allows to find automatically the MEP minima of a molecular system. It supplies the cartesian coordinates of these minima, their values, and all the geometrical relationships between them (distances, angles, and dihedral angles). Module MEPCOMP computes a similarity coefficient between the MEP distributions of two molecules and finds their relative position that maximizes the similarity. Module MEPCONF performs the same process as MEPCOMP, considering not only the relative position of both molecules but also a conformational degree of freedom of one of them. The most recently developed module, MEPPAR, is another modification of MEPCOMP in order to compute the MEP similarity between two molecules, but only taking into account a particular plane. The latter module is particularly useful to compare MEP distributions generated by systems of aromatic rings. MEPSIM can use several wavefunction computation approaches to obtain MEP distributions. MEPSIM has a menu type interface to simplify the following tasks: creation of input files from output files of external programs (GAUSSIAN and AMPAC/MOPAC), setting the parameters for the current computation, and submitting jobs to the batch queues of the computer. MEPSIM has been coded in FORTRAN and its current version runs on VMS/VAX computers.     

Quantitative comparison of molecular electrostatic potentials for structure-activity studies

An approach for representing, efficiently calculating and comparing discrete three-dimensional molecular electrostatic potentials using a quantitative similarity index (MEP-SI) based on a Carbo-type formalism is presented. A radial-type (MACRA) grid representation is described that provides more efficient storage of MEP information than a cubic grid of similar range, appropriate emphasis, and a convenient means for restricting the comparison of MEP functions to a local molecule region. The MACRA based MEP-SI formalism was used to evaluate the suitability of a variety of approximate methods for efficiently calculating the MEP for use in MEP-SI comparison of dissimilar molecules. The Mulliken charge method was found inadequate, while the method of potential-derived charges (PDCs), with additional charges for lone electron pairs included on sulfur, provided an efficient and sufficiently accurate representation of the MEP for this purpose. Convergence of the MEP-SI with respect to MACRA grid extent and mesh size was demonstrated; the effect of MEP error and different grid point emphasis in the MACRA versus the cubic grid results was investigated, and MEP-SI results were compared for different forms of the SI equation. The methodology proposed in this study provides an efficient and practical means for comparing MEP functions for two molecules and gives discriminating results for a sample series of molecular analogues consistent with expectations.     

Properties of hydrogen molecular ion with static screened coulomb and exponential cosine screened coulomb potentials

We have investigated the properties of hydrogen molecular ion (H) interacting with screened Coulomb potentials. Two types of potentials have been considered, namely, static screened Coulomb potential and exponential cosine‐screened Coulomb potential. Simulating the localized motion of the nuclei by using high powers of the internuclear coordinate in the generalized Hylleraas‐type wave function we have been able to obtain reasonably accurate binding energies for 1¹S(J = 0, ν = 0) and 2¹S(J = 0, ν = 1) states for various values of the screening parameter within the frame work of Ritz variational method. Borromean bindings are found to exist in the ion for a wide range of the screening parameter. Furthermore, expectation values for various operators and cusp condition have been calculated. Results for the unscreened case are in nice agreement with some of the accurate results available in the literature. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Topography of approximate molecular electrostatic potentials

A new method is described for the approximation of the molecular electrostatic potential (MESP). This method is used for the study of the topography of small molecules. The critical points of the approximate and the exact MESP are compared. It is found that most of the critical points of the exact MESP are retained, but in regions where the exact MESP changes slowly near critical points the number of critical points of the approximate MESP can be reduced.     

Nonlinear dependence in comparative molecular field analysis

Summary The applicability of the comparative molecular field analysis (CoMFA) approach to describe the nonlinear dependence of biological activity on lipophilicity in 3D quantitative structure-activity relationships (QSAR) has been demonstrated. The results indicate that the CoMFA approach is appropriate for describing nonlinear effects in 3D QSAR studies.     

Multilinear regression and comparative molecular field analysis (CoMFA) of azo dye-fiber affinities. 2. Inclusion of solution-phase molecular orbital descriptors

For a data set with 30 direct azo dyes taken from literature, quantitative structure-activity relationship (QSAR) analyses have been performed to model the affinity of the dye molecules for the cellulose fiber. The electronic structure of the compounds was characterized using quantum chemical gas-phase (AM1) and continuum-solvation molecular orbital parameters. As regards the solution phase, COSMO appears to be better suited than SM2 in quantifying relative trends of the aqueous solvation energy. For the dye-fiber affinity, the leave-one-out prediction capability of multilinear regression equations is superior to CoMFA, with predictive squared correlation coefficients ranging from 0.63 (pure CoMFA) to 0.89. At the same time, solution-phase CoMFA is superior to previously derived AM1-based CoMFA models. As a general trend, the dye-fiber affinity increases with increasing electron donor capacity that corresponds to an increasing hydrogen bond acceptor strength of the azo dyes. The discussion includes the consideration of structural features that are likely to be involved in dye-fiber and dye-dye hydrogen bonding interactions, and possible links between CoMFA electrostatic results and the atomic charge distribution of the compounds.     

Influence of polarization functions on molecular electrostatic potentials

We study the effects of d-polarization functions, centered on the heavy atoms, on the SCF molecular electrostatic potentials calculated for some molecules. The positions and energies of the minima found are very sensitive to the inclusion of polarization functions in the basis set used. The variations depend on the heavy atom involved and on the possible anisotropy of its charge distribution. These variations are particularly important for second-row atoms.     

Semiempirical AM1 electrostatic potentials and AM1 electrostatic potential derived charges: A comparison with ab initio values

Electrostatic potentials calculated from AM1 wave functions have been compared with ab initio STO-3G values and qualitative agreement has been found. Atomic charges derived from AM1 electrostatic potentials for both experimental and AM1 optimized geometries are of comparable quality with STO-3G potential derived charges. These results suggest that the AM1 electrostatic potential may be useful both in its own right and also for deriving atomic charges for use in molecular dynamics studies.     

An analysis of molecular electrostatic potentials obtained by a local density functional approach

Local density functional theory (DFT –LDA ) has been explored as a tool for obtaining the molecular electrostatic potential V(r), using the code DMol. We have presented and discussed DFT –LDA electrostatic potentials for a representative series of molecules: ethylene, benzene, formamide, cytosine, and 2,3,7,8–tetrachlorodibenzo–p–dioxin. V(r) results obtained with a double numerical plus polarization (DNP ) basis set show the key features that are characteristic of the ab initio potentials of these compounds and suggest that this is a useful approach, especially for large molecules that are difficult to study by ab initio methods.     

A finite expansion method for the calculation and interpretation of molecular electrostatic potentials

Because it is useful to have the molecular electrostatic potential as an element in a complex scheme to assess the toxicity of large molecules, efficient and reliable methods are needed for the calculation and characterization of these potentials. A multicenter multipole expansion of the molecular electron charge density calculated with a limited Gaussian basis set is shown here to have only a finite number of nonzero terms from which the molecular electrostatic potential can be calculated. The discrete contributions to the electrostatic potentials from the terms of this expansion provide a physically meaningful decomposition of the potential and a means for its characterization. With pyrrole as an example, the electrostatic potential calculated from this finite expansion of the electron density is compared to that obtained from exact calculations from the same wave function. Good agreement is obtained at distances greater than 1.5 A from any atom in the molecule. In contrast, rearrangement of the terms into an expansion corresponding only to Mulliken atomic charges and dipoles yields a decomposition that produces electrostatic potentials which agree less well with the exact potential. This discrepancy is attributable to the neglect of terms due to higher moments.     

Suitability of the PM3-derived molecular electrostatic potentials

A systematic study of the suitability of PM3-derived molecular electrostatic potentials (MEPs) is presented. Forty-six MEP minima, 81 electrostatic charges, and 17 electrostatic dipoles were determined at the PM3 level and compared with those obtained from the ab initio 6-31G* wave function, as well as from the semiempirical MNDO and AM1 wave functions. The statistical results of the comparison analysis between semiempirical and ab initio 6-31G* MEPs show that PM3 is in general reliable for the study of the MEP minima but a mediocre method as a source of electrostatic charges. © 1993 John Wiley & Sons, Inc.     

Molecular modeling of the intestinal bile acid carrier: A comparative molecular field analysis study

A structure–binding activity relationship for the intestinal bile acidtransporter has been developed using data from a series of bile acid analogsin a comparative molecular field analysis (CoMFA). The studied compoundsconsisted of a series of bile acid–peptide conjugates, withmodifications at the 24 position of the cholic acid sterol nucleus, andcompounds with slight modifications at the 3, 7, and 12 positions. For theCoMFA study, these compounds were divided into a training set and a test set,comprising 25 and 5 molecules, respectively. The best three-dimensionalquantitative structure–activity relationship model found rationalizesthe steric and electrostatic factors which modulate affinity to the bile acidcarrier with a cross-validated, conventional and predictive r²of 0.63, 0.96, and 0.69, respectively, indicating a good predictive model forcarrier affinity. Binding is facilitated by positioning an electronegativemoiety at the 24–27 position, and also by steric bulk at the end of theside chain. The model suggests substitutions at positions 3, 7, 12, and 24that could lead to new substrates with reasonable affinity for the carrier.     

A divide and conquer real-space approach for all-electron molecular electrostatic potentials and interaction energies

A computational scheme to perform accurate numerical calculations of electrostatic potentials and interaction energies for molecular systems has been developed and implemented. Molecular electron and energy densities are divided into overlapping atom-centered atomic contributions and a three-dimensional molecular remainder. The steep nuclear cusps are included in the atom-centered functions making the three-dimensional remainder smooth enough to be accurately represented with a tractable amount of grid points. The one-dimensional radial functions of the atom-centered contributions as well as the three-dimensional remainder are expanded using finite element functions. The electrostatic potential is calculated by integrating the Coulomb potential for each separate density contribution, using our tensorial finite element method for the three-dimensional remainder. We also provide algorithms to compute accurate electron-electron and electron-nuclear interactions numerically using the proposed partitioning. The methods have been tested on all-electron densities of 18 reasonable large molecules containing elements up to Zn. The accuracy of the calculated Coulomb interaction energies is in the range of 10(-3) to 10(-6) E(h) when using an equidistant grid with a step length of 0.05 a(0).     

On the similarity between molecular electron densities, electrostatic potentials and bare nuclear potentials

The similarities among the molecular contours of three scalar fields, viz. electron density (ED), electrostatic potential (ESP) and bare nuclear potential (BNP) have been investigated. The topological resemblance between ESP and ED contour diagrams (as prompted by the Thomas-Fermi model) is more pronounced than that for BNP and ED contour diagrams (as predicted by the local density functional model of Parr, Gadre and Bartolotti) with three-membered ring systems as test cases. An analysis of critical points of these distributions has also been included. Thus it may be conjectured that ED maps may prove useful in predicting reactive sites in molecules.     

Site charge models for molecular electrostatic potentials of cycloalkanes and tetrahedrane

The molecular structures of cycloalkanes (from cyclopropane to cyclodecane) and tetrahedrane were optimized at the Hartree–Fock/6–31G** level and their molecular electric potentials (MEPs) were calculated using a geodesic grid. The MEPs were fitted using net atomic charges and several site charge models. The net atomic charge model gave very poor fits to the MEPs in every case. A model with additional methylene bisector charge sites, similar to one successfully used previously for linear alkanes, greatly improved the fits to the MEPs of these cycloalkanes. The MEPs of the highly strained molecules cyclopropane and tetrahedrane were further studied using ring center and displaced bond charge sites. The fitting of the MEP of cyclopropane was consistent with a banana bond model with asymmetrically displaced electron density in the C C bonds. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 579–585, 1999     

Theoretical studies on the molecular electron densities and electrostatic potentials in azacubanes

Energetics and the charge distributions in azacubanes (C₈NH_8–) have been obtained using the ab initio Hartree–Fock, second-order Mø øller–Plesset perturbation theory and hybrid density functional methods. For diazacubane to hexaazacubane the lowest-energy conformers have nitrogen atoms occupying the face opposite corners of a cube. The topography of the molecular electrostatic potential and the electron density of azacubane conformers have been investigated. The electrostatic potential studies have shown that successive substitution of nitrogen instead of CH groups of cubane engenders smaller and more localized electron-rich regions around the nitrogens of a cube. Further the bond ellipticity and the electron density at the bond critical point of the X–N bonds (X=C or N) in a cubanoid increase from azacubane to octaazacubane. The heats of formation of azacubanes calculated by the isodesmic reaction approach using different levels of theory correlate well with the electron density at the bond critical point of X–N (X=C or N) bonds in a cubanoid.