Improved electrostatic properties using combined Mulliken and hybridization-displaced charges for radicals

Effects of explicit consideration of charges displaced from atomic sites due to atomic orbital hybridization called hybridization-displaced charges (HDC) on dipole moments and surface molecular electrostatic potentials of certain radicals and their complexes with closed-shell molecules have been studied. HDC were computed for several radicals and their complexes at the B3LYP/6–31G** level of theory. At this level, HDC consist of three point charges associated with hydrogen atoms and seven point charges associated with heavy atoms belonging to the second row of the periodic table. HDC are so calculated that the contribution of each atom to the component of molecular dipole moment arising due to atomic orbital hybridization is preserved. It is found that dipole moments and electrostatic potentials of the systems studied here can be obtained with a significantly improved accuracy using a combination of Mulliken charges and HDC over that obtained by Mulliken charges only. Figure Surface MEP map of H₂O-HO· radical complex obtained using Mulliken charges combined with HDC     

Ab initio and DFT conformational study on N-nitrosodiethylamine, (C2H5)2N-N=O

Ab initio (MP2) and DFT (B3LYP) calculations, using the cc-pVTZ and aug-cc-pVTZ basis sets, have been performed to characterize some stationary points on the ground state potential energy surface of the title molecules. Several properties as, for instance, relative energies, the barriers for NO rotation around the NN bond, NBO charges on O and amino N atoms, as well as the dipole moments, have been calculated and analyzed in the light of the structures found. Both computational levels here employed yield three minima, in which the C₂NNO frame is ‘planar’ or ‘quasi-planar’. Important correlations between NBO charges and geometric parameters, as well as between some structural features and dipole moments are also discussed. A total of 17 structures have been found for the (C₂H₅)₂N-N=O molecule. Two ranges of values have been obtained for the dipole moment, with the largest values occurring for the structures in which the nitrogen lone pair is parallel to the NO group π system. For instance, these two ranges are from ~4.1 to 4.5 D, and from ~1.6 to 2.1 D, at the MP2/cc-pVTZ level. These ranges are consistent with a larger and a smaller contribution of a dipolar resonance structure, respectively. As the method or basis set changes the values of the dipole moments change by at most ~0.23 D.     

Chiroptical structure‐property relations in cyclo[18]carbon and its in silico hydrogenation products

The anisotropy of the optical activity of cyclo[18]carbon (C₁₈), fully hydrogenated C₁₈ (C₁₈H₃₆), and 26 hydrogenated compounds of intermediate composition, C₁₈H_2n, n = 1,2…17, were computed. These compounds were selected because they resemble loops of wire. The maximum gyration for acetylenic and cumulenic subgroups of compounds was linearly proportional to the product of the geometric area over which the charge can circulate, multiplied by the largest separation between carbon atoms on opposing sides of the loops. These geometric quantities can be likened to transition magnetic dipole moments and transition electric dipole moments, respectively, that can be generated in electronic excitations and which contribute in the main to nonresonant optical activity. The correlation between a computed geometric product of distance and area, and a quantum chemical property, establishes that chiroptical structure‐activity relationships can be well established for judiciously chosen series of comparatively large compounds.     

On contribution of known atomic partial charges of protein backbone in electrostatic potential density maps

Partial charges of atoms in a molecule and electrostatic potential (ESP) density for that molecule are known to bear a strong correlation. In order to generate a set of point‐field force field parameters for molecular dynamics, Kollman and coworkers have extracted atomic partial charges for each of all 20 amino acids using restrained partial charge‐fitting procedures from theoretical ESP density obtained from condensed‐state quantum mechanics. The magnitude of atomic partial charges for neutral peptide backbone they have obtained is similar to that of partial atomic charges for ionized carboxylate side chain atoms. In this study, the effect of these known atomic partial charges on ESP is examined using computer simulations and compared with the experimental ESP density recently obtained for proteins using electron microscopy. It is found that the observed ESP density maps are most consistent with the simulations that include atomic partial charges of protein backbone. Therefore, atomic partial charges are integral part of atomic properties in protein molecules and should be included in model refinement.     

PSI-DOCK: towards highly efficient and accurate flexible ligand docking

We have developed a new docking method, Pose-Sensitive Inclined (PSI)-DOCK, for flexible ligand docking. An improved SCORE function has been developed and used in PSI-DOCK for binding free energy evaluation. The improved SCORE function was able to reproduce the absolute binding free energies of a training set of 200 protein-ligand complexes with a correlation coefficient of 0.788 and a standard error of 8.13 kJ/mol. For ligand binding pose exploration, a unique searching strategy was designed in PSI-DOCK. In the first step, a tabu-enhanced genetic algorithm with a rapid shape-complementary scoring function is used to roughly explore and store potential binding poses of the ligand. Then, these predicted binding poses are optimized and compete against each other by using a genetic algorithm with the accurate SCORE function to determine the binding pose with the lowest docking energy. The PSI-DOCK 1.0 program is highly efficient in identifying the experimental binding pose. For a test dataset of 194 complexes, PSI-DOCK 1.0 achieved a 67% success rate (RMSD < 2.0 A) for only one run and a 74% success rate for 10 runs. PSI-DOCK can also predict the docking binding free energy with high accuracy. For a test set of 64 complexes, the correlation between the experimentally observed binding free energies and the docking binding free energies for 64 complexes is r = 0.777 with a standard deviation of 7.96 kJ/mol. Moreover, compared with other docking methods, PSI-DOCK 1.0 is extremely easy to use and requires minimum docking preparations. There is no requirement for the users to add hydrogen atoms to proteins because all protein hydrogen atoms and the flexibility of the terminal protein atoms are intrinsically taken into account in PSI-DOCK. There is also no requirement for the users to calculate partial atomic charges because PSI-DOCK does not calculate an electrostatic energy term. These features are not only convenient for the users but also help to avoid the influence of different preparation methods.     

A molecular dynamics study of liquid aliphatic alcohols: simulation of density and self-diffusion coefficient using a modified OPLS force field

A set of 13 aliphatic alcohols was modelled by molecular dynamics simulations at temperatures from 288 to 338 K using the optimised potential for liquid simulations (OPLS) united-atom force field, the OPLS all-atom force field and the OPLS all-atom force field with modified partial charges of the hydroxyl group. The set includes primary and secondary alcohols, and mono-, di- and trialcohols, and covers a broad range of polarities from log P = ? 0.74 (methanol) to log P = 2.9 (octanol). The density, the radial distribution function, the self-diffusion coefficient and the dielectric constant were evaluated. A long equilibration time of at least 50 ns and a large size of the molecular system of more than 75,000 atoms were used. Except for glycerol, the OPLS all-atom force field reliably reproduced the experimentally determined density with deviations of less than 4% over the whole temperature range. In contrast, the modelled self-diffusion coefficient deviated from its experimental value by up to 55%. To modify the force field, the partial charges of the hydroxyl group were varied by up to 3%. Using the modified OPLS force field, the deviation of the self-diffusion coefficients from their experimental values decreased to less than 19%, while the densities changed by less than 1%.     

Monte Carlo Study of Structural and Thermodynamic Properties of Liquid Chloroform Using a Five Site Model

A five site potential model combining Lennard–Jones plus Coulomb potential functions has been developed for chloroform molecule. The partial charges needed for Coulombic interactions were derived using the chelpg procedure implemented in the gaussian 92 program. These calculations were performed at the MP2 level with MC-311G* basis set for Cl and 6-311G** for C and H atoms. The parameters for the Lennard–Jones potentials were optimized to reproduce experimental values for the density and enthalpy of vaporization of the pure liquid at 298 K and 1 atm. The statistical mechanics calculations were performed with the Monte Carlo method in the isothermic and isobaric (NpT) ensemble. Besides the values obtained for density, ρ, and molar enthalpy of vaporization at constant pressure, Δ H_V, for liquid chloroform, results for molar volume, V_m, molar heat capacity, C_p, isobaric thermal expansivity, α_p, and isothermal compressibility, κ_T, for this pure liquid are also in very good agreement with experimental observations. Size effects on the values of thermodynamic properties were investigated. The potential model was also tested by computing the free energy for solvating one chloroform molecule into its own liquid at 298 K using a statistical perturbation approach. The result obtained compares well with the experimental value. Site–site pair correlation functions were calculated and are in good accordance with theoretical results available in the literature. Dipole–dipole correlation functions for the present five site model were also calculated at different carbon–carbon distances. These correlations were compared to those obtained using the four site model reported in the literature. An investigation of the solvent dependence of the relative free energy for cis/trans conversion of a hypothetical solute in TIP4P water and chloroform was accomplished. The results show strong interaction of water and chloroform molecules with the gauche conformer. The value obtained for the free energy barrier for cis/trans rotation in TIP4P water is higher than that for chloroform. This result is in agreement with the continuous theory for solvation as the conformer with higher dipole moment is more favoured by the solvent with higher dieletric constant. The results also show an increase in entropy as the solute goes from the cis to the trans geometry and this result is more appreciable in the aqueous solution. This revised version was published online in June 2006 with corrections to the Cover Date.     

Dye–tissue interactions: mechanisms,quantification and bonding parameters for dyes used in biological staining

Staining of tissues by dyes is accomplished through various types of bonds, some of which have been poorly defined in traditional biological literature. Here, basic principles of bonding are reviewed to establish uniform terminology and definitions consistent with the field of chemistry. The concept of charge – its presence or absence, magnitude, extent of delocalization and potential for being displaced by outside forces – underlies all bonding phenomena. These same attributes influence solubility and resistance to extraction during dehydration of tissue sections. Covalent bonds involve shared electrons; they are very strong and essentially irreversible under conditions encountered during staining. Polar covalent bonds within dye molecules generate partial atomic charges that create the potential for hydrogen bonding. This is measured by the hydrogen bonding parameter (h), the number of groups bearing charges within the ranges ?0.15 to ?0.50 eV or +0.15 to +0.30 eV. The potential for ionic bonding is indicated by net charge (Z), while the strength of such bonds is a function of charge site geometry on both bonding partners. Charge delocalization owing to conjugation, electron influencing groups, and resonance creates soft charge sites in which the ionic charge is spread over a large volume. Poorly delocalized charges or point charges are hard (small in volume). Firm bonds result from hard-hard or soft-soft pairs. Hard-soft combinations are weak, readily displaced in competitive interactions, and disrupted by solvents. Coordinate bonds with certain metals are involved with mordant staining and metal chelation dyes. Three different van der Waals attractions comprise the remainder of bonding types, all involving dipoles: Keesom (dipole-dipole) forces, Debye (dipole-induced dipole) forces and London (induced dipole-induced dipole) forces. Potentials for engaging in any of these is quantified by measures of polarity (dipole moment, d), polarizability (crudely with π atoms describing the size of the conjugated system, or more directly with α), hydrophobicity (with the octanol-water partition coefficient, log P or the more convenient Hydrophobic Index, HI), and the number of halogen atoms (X). By using molecular modeling software, quantitative measures of bonding potential (bonding parameters) have been determined for over 400 dyes.     

The Mobility of The Coordinates of a Subjective Semantic Space As a Manifestation of Categorical Set

The perception and objective semantic interpretation of an object depend on categorical set. Categorical set is the readiness of the subject to interact with objects of a specified category. A multitude of experimental evidence confirms the existence of categorical set. This evidence can be divided into three groups: (a) data indicating that perception depends on experimental instructions; (b) data indicating that perception depends on the category to which the preceding stimulation belongs; and, finally, (c) data indicating that perception depends on individual differences in motivation, which are a priori with regard to the experiment. The reasons for the appearance of sets vary; but in the end they all lead to one and the same result: the evocation of diverse expectations (hypotheses) in different subjects in the same situation, or in the same subject at different moments in time (Bruner, 1977).     

Benchmark of different charges for prediction of the partitioning coefficient through the hydrophilic/lipophilic index

A few different theoretical methods for assigning the partial atomic charges were benchmarked for calculation of the hydrophilic/lipophilic index (HLI). The coefficients were selected to produce the best correlation of the HLI values with the experimental octanol-water partition. Different parameters were checked in calculations of partial charges to get the best performance of the HLI values obtained. Thus, four partitioning schemes (Coulson, Mulliken, Merz-Kollman, Ford-Wang) were benchmarked for calculations of atomic charges with six semiempirical methods (AM1, PM3, RM1, PM6, PM6-D3H4, PM7). Moreover, five distinct types of partial atomic charges (Mulliken, Hirshfeld, Löwdin, CHELPG, NPA), obtained at the Hartree–Fock and DFT levels of theory with three basis sets, were tested for their ability to produce the HLI values with the best correlation to experimental logP coefficients of 50 mono-charged organic anions. In the case of the semiempirical methods, the best correlation between the HLI and logP values (the correlation coefficient r?=?0.9216) was obtained with the AM1 Ford–Wang parametric electrostatic potential charges. The Mulliken and Coulson charges calculated with the PM7 method can be used as an alternative to AM1, with the r values of 0.9107 and 0.8984, respectively. In the case of the DFT, the PBE/def2-TZVP natural population analysis charges produce the best correlation (r?=?0.9220). Nevertheless, in spite of a marginally lower performance (r?=?0.9159), the NPA charges computed at the PBE/def2-SVP level are more robust and can be regarded as the optimum choice for calculating the HLI values.

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Graphical abstract The hydrophilic/lipophilic index (HLI)

     

Computation of the dipole moments of proteins.

A simple and computationally feasible procedure for the calculation of net charges and dipole moments of proteins at arbitrary pH and salt conditions is described. The method is intended to provide data that may be compared to the results of transient electric dichroism experiments on protein solutions. The procedure consists of three major steps: (i) calculation of self energies and interaction energies for ionizable groups in the protein by using the finite-difference Poisson-Boltzmann method, (ii) determination of the position of the center of diffusion (to which the calculated dipole moment refers) and the extinction coefficient tensor for the protein, and (iii) generation of the equilibrium distribution of protonation states of the protein by a Monte Carlo procedure, from which mean and root-mean-square dipole moments and optical anisotropies are calculated. The procedure is applied to 12 proteins. It is shown that it gives hydrodynamic and electrical parameters for proteins in good agreement with experimental data.     

Molecular Dynamics Simulations with Interaction Potentials Including Polarization Development of a Noniterative Method and Application to Water

A general method is suggested for the implementation of polarization in molecular dynamics simulations of small molecules. Induced dipole moments are evaluated on selected polarizability centers and represented by separation of charges. The positive polarization charges reside on the selected atoms. The negative polarization charges are treated as additional particles. The positions of these polarization charges are determined from the electrical fields due to the permanent charges of the system. Thus the induction is treated explicitly, while the higher order contributions, the polarization due to induced dipoles, are taken into account in an average way by modification of potential parameters. The forces can be evaluated for the new charge distribution in the conventional way. As an illustration of this approach initial results are reported for the development of a polarizable water model. The higher order polarization is treated in an average way by slight increase of the permanent charges as compared to the values that would give the gas phase dipole moment. The increase in CPU time is comparable to the addition of one atom per polarizable center.     

Molecular and statistical modeling of reduction peak potential and lipophilicity of platinum(IV) complexes

We report the results of the quantitative structure–property relationship analysis of 31 Pt(IV) complexes, for three of which the synthesis is reported for the first time. The X-ray structural analysis of one complex of the series was performed to demonstrate that the PM6 semiempirical method satisfactorily reproduces key features of the geometry of the complexes investigated. Molecular properties extracted from such calculations were then used to construct models of experimental data such as electrochemical peak potentials (evaluated by cyclic voltammetry) and the octanol–water partition coefficient (evaluated by a reversed-phase high performance liquid chromatography method), which are key aspects in the design of such Pt(IV) complexes as potential anticancer prodrugs. Statistically accurate models for both properties were found using combinations of surface areas, orbital energies, dipole moments, and atomic partial charges. These models could form the basis of virtual screening of potential drug molecules, allowing the prediction of properties, closely related to the antiproliferative activity of Pt(IV) complexes, directly from calculated data.     

Calculation and measurement of the dipole moment of small proteins: Use of protein data base

The dipole moments of small protein molecules were determined experimentally in order to validate the calculated dipole moments by previous investigators. We found that the agreements are satisfactory for some proteins. There are, however, many proteins for which the agreement is less than satisfactory. In order to find the cause of the disagreement, the dipole moments of these proteins were recalculated using the Brookhaven Protein Data Bank. We calculated the dipole moment due to fixed surface charges and the bond moments of all the carbonyl groups in main chain and side chains. The calculation consists of the mean moments and their mean square fluctuations. In addition, we investigated the effect of electrostatic interactions between charged sites for several proteins. These results show that incorporation of the interactions does not affect substantially the calculated dipole moments. The rms fluctuation of the dipole moment is found to be small but not negligible. In conclusion, recalculated dipole moments are in good agreement with the observed values. © 1993 John Wiley & Sons, Inc.     

Molecular Mechanics: The Conjugate Nitro Group Parameters in the MM2 Force Field

The conjugated nitro group has been included in the π system calculation within the MM2 force field. New parameters have been estimated by a statistical process from X-ray molecular structures recorded in the C.S.D.S. Comparison of the corresponding results with those given by the MM2(91) force field parameters show a clear improvement for dihedral and bond angles. For N-O and C-N bond lengths a slight global improvement is also observed. A closer examination of the results for the latter bond shows that sometimes MM2(91) gives better results for six membered ring nitro compounds. By contrast the parameters proposed here are more adapted to five membered ring derivatives. The derived linear relations permit the study of molecules over a wider range of π indices. The introduction of a correction factor to the calculated molecular π dipole moment in conjunction with a necessary reestimation of some σ-bond dipole moments also leads to improved total molecular dipole moments.     

Molecular Mechanics: The Cross-conjugated Carbonyl Group in Heterocyclic Compounds. 2. Parameterisation (MM2) of the Adjacent C-O and C-N Bonds

The definition, in a previous paper, of a new type of carbon atom (type 44) in the MM2 force field, i.e. when it is cross-conjugated, implies the reparameterisation of the bonds adjacent to the carbonyl bond. By means of a statistical study based on data issued from the Cambridge Structural Data System, we propose here new σ dipole moments and new stretching parameters for the C(44)-O(41) and C(44)-N(40) bonds included in heterocyclic compounds. These stretching parameters, which are π-bond-order dependent, are quite satisfactory (mean of unsigned deviations: 0.023Å) within limited π-bond-order ranges: 0.25 to 0.32 for the C-O bond, 0.37 to 0.53, for the C-N bond. As for the C(44)=O(7) bond the parameters are generally inappropriate for compounds in which both atoms connected to the type 44 carbon are heteroatoms. The maximum deviation from the experimental bond length, for both bond types can reach ±0.03Å. Here also, part of the dispersion of the results could be attributed to the variation of the effective dielectric constant D from one crystal to another.     

Ab initio Molecular Electrostatic Potential Grid Maps for Quantitative Similarity Calculations of Organic Compounds

The program MolSim designed to calculate the similarity of different molecules quantitatively in a fast and easy way is described. The molecular similarity is estimated for the molecular shape as well as for the electrostatic potentials of the molecules derived from ab initio calculations. A grid-based method is used to determine the steric and electrostatic similarities between a lead compound and the corresponding test set by calculating the Spearman correlation coefficient. The superpositioning of the molecules was accomplished with the SEAL algorithm incorporating a Monte Carlo simulated annealing approach while preserving the conformational flexibility of the calculated structures.The ability of the program was tested on a set of Sandalwood odour compounds, a class of substances that is difficult to analyse with respect to its structure-activity relationship because of the structural diversity of Sandalwood odour compounds, in contrast to their high selectivity and pronounced structural specificity. The application of the program on a small test set of these compounds showed that the program is able to explain the Sandalwood odour activity correctly.Electronic Supplementary Material available.     

A reinterpretation of the infrared linear dichroism of oriented nucleic acid films and a calculation of some effective partial changes on the ribose phosphate backbone.

In this paper we show, based on symmetry considerations, that structural information cannot be obtained from the linear infrared dichroism of the dioxy vibrations of the phosphate group of nucleic acids. Consequently, the discrepancies between the results of x-ray structure measurements and linear dichroism measurements are not meaningful. The linear dichroism measurements are instead important for a calculation of transition dipole moments that involve both the vibrations of all the atoms of the nucleotide and their charges. Independent information on either the atomic displacements contributing to a given vibration or the atomic charges permits a refinement of the unknown quantities. Based on the molecular dynamics calculations of Prohofsky et al., atomic charges of DNA are calculated to reproduce the observed linear dichroism results. Some of the resulting charges are unexpected and may reflect the inadequacy of the molecular dynamic calculation.