Effect of charge distribution on electrostatic chromophore—protein interactions in Bacteriorhodopsin

Charge distributions of a protonated and unprotonated Schiff base model compound are determined using different quantum chemical methods. After fitting the model molecule onto the protonated retinal Schiff base in Bacteriorhodopsin, electrostatic interaction energies between the model molecule and protein are calculated. Interaction energies as well as the calculated pK_1/2 values of the model molecule are shown to depend considerably on the chosen charge distribution. Electrostatic potential derived partial charges determined at different ab initio levels reveal interaction energies between the model molecule and nearby residues such as ARG-82, ASP-85, and ASP-212, which are relatively method independent. Consequently, such charge distributions also result in pK_1/2 values for the model molecule that are very similar. Larger deviations in the electrostatic interaction energies, however, are found in the case of charge distributions derived according to the Mulliken population analysis. Nevertheless, some sets of Mulliken derived partial charges predicted pK_1/2 values for the model molecule that are close to those determined with electrostatic potential derived partial charges. This agreement, however, is only achieved because the individual errors of the contributing terms are approximately compensated. The use of the extended atom model is shown to be problematic. Although potential derived charges can correctly describe electrostatic interaction energies, they fail to predict pK_1/2 values. On the basis of the present investigation a new set of partial charges for the protonated and unprotonated retinal Schiff base is proposed to be used in molecular dynamics simulations and electrostatics calculations. © 1997 by John Wiley & Sons, Inc.     

On the use of AM1 and MNDO wave functions to compute accurate electrostatic charges

A new strategy to evaluate accurate electrostatic charges from semiempirical wave functions is reported. The rigorous quantum mechanical molecular electrostatic potentials computed from both MNDO and AM1 wave functions are fitted to the point-charge molecular electrostatic potential to obtain the electrostatic charges. The reliability of this strategy is tested by comparing the semiempirical electrostatic charges for 21 molecules with the semiempirical Mulliken charges and with the ab initio STO-3G and 6-31G* electrostatic charges. The ability of the dipoles derived from the semiempirical electrostatic and Mulliken charges as well as from the SCF charge distributions to reproduce the ab initio 6-31G* electrostatic dipoles and the gas phase experimental values is determined. The statistical analysis clearly point out the goodness of the semiempirical electrostatic charges, specially when the MNDO method is used. The excellent relationships found between the MNDO and 6-31G* electrostatic charges permit to define a scaling factor which allows to accurately reproduce the 6-31G* electrostatic charge distribution as well as the experimental dipoles from the semiempirical electrostatic charges.     

Long-range electrostatic interactions in hybrid quantum and molecular mechanical dynamics using a lattice summation approach

A method based on a lattice summation technique for treating long-range electrostatic interactions in hybrid quantum mechanics/molecular mechanics simulations is presented in this article. The quantum subsystem is studied at the semiempirical level, whereas the solvent is described by a two-body potential of molecular mechanics. Molecular dynamics simulations of a (quantum) chloride ion in (classical) water have been performed to test this technique. It is observed that the application of the lattice summations to solvent-solvent interactions as well as on solute-solvent ones has a significant effect on solvation energy and diffusion coefficient. Moreover, two schemes for the computation of the long-range contribution to the electrostatic interaction energy are investigated. The first one replaces the exact charge distribution of the quantum solute by a Mulliken charge distribution. The long-range electrostatic interactions are then calculated for this charge distribution that interacts with the solvent molecule charges. The second one is more accurate and involves a modified Fock operator containing long-range electron-charge interactions. It is shown here that both schemes lead to similar results, the method using Mulliken charges for the evaluation of long-range interactions being, however, much more computationally efficient.     

High Resolution Synchrotron Diffraction Study on Charge Density Distribution of Ampicillin Trihydrate

Charge density distribution in ampicillin trihydrate was investigated experimentally. Results were compared with the quantum calculations using density functional theory. The charge derived properties including Mulliken atomic charges, dipole moment, and molecular electrostatic potential were calculated. The multipole analysis was done for the refinement of experimental population parameters. The structure factors obtained from multipole treatment were used for the construction of Fourier maps. Topological properties of the charge distribution were discussed and the characteristics of (3,-1) critical points were analyzed.     

On combining Thole's induced point dipole model with fixed charge distributions in molecular mechanics force fields

The Thole induced point dipole model is combined with three different point charge fitting methods, Merz–Kollman (MK), charges from electrostatic potentials using a grid (CHELPG), and restrained electrostatic potential (RESP), and two multipole algorithms, distributed multipole analysis (DMA) and Gaussian multipole model (GMM), which can be used to describe the electrostatic potential (ESP) around molecules in molecular mechanics force fields. This is done to study how the different methods perform when intramolecular polarizability contributions are self‐consistently removed from the fitting done in the force field parametrization. It is demonstrated that the polarizable versions of the partial charge models provide a good compromise between accuracy and computational efficiency in describing the ESP of small organic molecules undergoing conformational changes. For the point charge models, the inclusion of polarizability reduced the the average root mean square error of ESP over the test set by 4–10%. © 2015 Wiley Periodicals, Inc.     

A generalization of the charge equilibration method for nonmetallic materials

Assigning effective atomic charges that properly reproduce the electrostatic fields of molecules is a crucial step in the construction of accurate interatomic potentials. We propose a new approach to calculate these charges, which as previous approaches are, is based on the idea of charge equilibration. However, we only allow charge to flow between covalently bonded neighbors by using the concept of so-called split charges. The semiempirical fit parameters in our approach do not only reflect atomic properties (electronegativity and atomic hardness) but also bond-dependent properties. The new method contains two popular but hitherto disjunct approaches as limiting cases. We apply our methodology to a set of molecules containing the elements silicon, carbon, oxygen, and hydrogen. Effective charges derived from electrostatic potential surfaces can be predicted more than twice as accurately as with previous works, at the expense of one additional fit parameter per bond type controlling the polarizability between two bonded atoms. Additional bond-type parameters can be introduced, but barely improve the results. An increase in accuracy of only 30% over existing techniques is achieved when predicting Mulliken charges. However, this could be improved with additional bond-type parameters.     

An ab initio study of crystal field effects,part 3: Solid- and gas-phase geometry of formamide,modeling the changes in a peptide group due to hydrogen bonds

A model of the solid state of formamide is constructed by optimizing a central molecule in an electrostatic field of the proper symmetry. Attention is paid to the way the electrostatic charges are obtained. Point charges obtained from a Mulliken population analysis yield a final set of atomic charges in the central molecule that agree reasonably well with those obtained experimentally after ak-refinement of formamide. Point charges from a so-called stockholder partitioning agree slightly less. Furthermore, the simple crystal field adaptation of standard ab initio methods reproduces within experimental limits the differences in C=O and C-N lengths, observed between the gas-phase and the solid state geometry. Again, a Mulliken field agrees slightly better than a stockholder field, but the difference in performance is statistically insignificant. In a survey of 221 high-quality single-crystal x-ray determinations of compounds containing the peptide group N-C=O, we found evidence supporting quantitatively the conclusion that the increase of C=O and the decrease of C-N bond length in the gas-to-solid transition is dominated by the effects of hydrogen bonding. It was shown that the C=O bond lengthens by about 0.011 å per H-bond it accepts, while the N-C bond diminishes by about 0.015 å per H-bond it donates.Part 2, see Ref. [5].     

Charge distribution in the water molecule--a comparison of methods

The charge distribution in the water molecule has been analyzed using a broad variety of basis sets, four different quantum mechanical methods (Hartree-Fock, Becke3LYP, MP2, and QCISD), and six population analysis methods (Mulliken, NPA, AIM, CHELPG, Merz-Kollman, and Resp). The influence of the molecular structure on the calculated atomic charges has been studied using small perturbations of the experimentally determined structure.     

The effect of isodensity surface sampling on ESP derived charges and the effect of adding bondcenters on DMA derived charges

The effect of sampling the electrostatic potential around a molecule on the quality of electrostatic potential derived charges is investigated. In addition, the effect of the number of expansion sites in a Distributed Multipole Analysis (DMA) on the quality of charges fitted to the DMA derived electrostatic potential is investigated. Sampling on constant electron density surfaces gives a better fit between the quantum mechanical potential and the potential derived from the fitted charges, compared to sampling on a van der Waals surface composed of intersecting spheres. The fit between the electrostatic potential derived from point charges and the quantum mechanical potential becomes poorer with increasing quality of the employed basis set. The inclusion of bondcenters into the calculations improves the fit between the Quantum Mechanical (QM) electrostatic potential and the DMA derived potential. The number of expansion sites needed for an accurate approximation of the QM electrostatic potential increases with increasing quality of the used basis set.     

Insights into the binding mechanism of 2,5-substituted 4-pyrone derivatives as therapeutic agents for fused dimeric interactions: A computational study using QTAIM,dynamics and docking simulations of protein–ligand complexes

The study is focused on examining 2,5-Substituted 4-Pyrone based compounds through quantum chemical and topological analysis techniques, evaluating the properties of these compounds, including their geometrical structure, intermolecular interactions and assess their possible applications. Additionally, the molecular stability, charge delocalization and UV-Visible data was investigated and compared with the calculated energy and oscillator strength using the TD-DFT approach. The researchers observed that charge transfer occurred within the molecule, indicated by the HOMO and LUMO energies. It was also found that the compound exhibited planarity and higher chemical reactivity. The calculated Mulliken charges and molecular electrostatic potential were used to interpret the Fukui index data that help predict reactive sites and understand the reactivity patterns of specific atoms in a compound. The study is aimed to understand the role of NCI in the molecule under investigation using electron localization functions and localized orbit locator methods. Molecular docking and ADMET studies were conducting involving a detailed MD simulation of a protein-ligand complex using the OPLS3e force field and the SPC water model. These findings could prove to be beneficial in developing new therapeutic agents with various pharmacological effects and potential toxicities.     

Calculation of the electrostatic charges and energies for intercalation of aromatic drug molecules with DNA

In this work, we analyzed the influence of the charge model on the magnitudes of atomic charges and electrostatic energies for the binding of aromatic drug molecules with DNA. The dependence of the charge and energy on the level of theory (HF, DFT (B3LYP), MP2, semi‐empirical methods), basis set (STO‐3G, 3‐21G, 6‐31G, 6‐31G*, 6‐31G**), method of charge computation (Mulliken, Natural Population Analysis, CHelpG, Merz–Kollman), and force field charge (CHARMM27, AMBER99) has been tracked for typical aromatic drugs of different structure and charge state. Recommendations and restrictions have been formulated for the use of particular approaches in charge/electrostatic energy calculations. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Building molecular charge distributions from fragments: Application to HIV-1 protease inhibitors

Interaction energies are a function of the molecular charge distribution. In previous work, we found that the set of atomic partial charges giving the best agreement with experimental vacuum dipole moments were from density functional theory calculations using an extended basis set. Extension of such computations to larger molecules requires an atomic partial charge calculation beyond present computational resources. A solution to this problem is the calculation of atomic partial charges for segments of the molecule and reassociation of such fragments to yield partial charges for the entire molecule. Various partitions and reassociation methods for five molecules relevant to HIV-1 protease inhibitors are examined. A useful method of reassociation is introduced in which atomic partial charges for a large molecule are computed by fitting to the combined electrostatic potential calculated from the fragment partial charges. As expected, the best sites for partitions are shown to be carbon—carbon rather than carbon—nitrogen bonds. © 1997 by John Wiley & Sons, Inc.     

Energy decomposition in molecular complexes: implications for the treatment of polarization in molecular simulations

This study examines the contribution of electrostatic and polarization to the interaction energy in a variety of molecular complexes. The results obtained from the Kitaura-Morokuma (KM) energy decomposition analysis at the HF/6-31G(d) level indicate that, for intermolecular distances around the equilibrium geometries, the polarization energy can be determined as the addition of the polarization energies of interacting blocks, as the mixed polarization term is typically negligible. Comparison of KM and QM/MM results shows that the electrostatic energy determined in the KM method is underestimated (in absolute value) by QM/MM methods. The reason of such underestimation can be attributed to the simplified representation of treating the interaction between overlapping charge distribution by the interaction of a QM molecule with a set of point charges. Nevertheless, the polarization energies calculated by KM and QM/MM methods are in close agreement. Finally, a consistent, automated strategy to derive charge distributions that include implicitly polarization effects in pairwise, additive force fields is presented. The strategy relies in the simultaneous fitting of electrostatic and polarization energies computed by placing a suitable perturbing particle at selected points around the molecule. The suitability of these charges to describe molecular interactions is discussed.     

Comparison of atomic charges derived via different procedures

Atomic charges were obtained from ab initio molecular orbital calculations using a variety of procedures to compare them and assess their utility. Two procedures based on the molecular orbitals were examined, the Mulliken population analysis and the Weinhold–Reed Natural Population Analysis. Two procedures using the charge density distribution were included; the Hirshfeld procedure and Bader's Atoms in Molecules method. Charges also were derived by fitting the electrostatic potential (CHELPG) and making use of the atomic polar tensors (GAPT). The procedures were first examined for basis set independence, and then applied to a group of hydrocarbons. The dipole moments for these molecules were computed from the various atomic charges and compared to the total SCF dipole moments. This was followed by an examination of a series of substituted methanes, simple hydrides, and a group of typical organic compounds such as carbonyl derivatives, nitriles, and nitro compounds. In some cases, the ability of the charges to reproduce electrostatic potentials was examined. © John Wiley & Sons, Inc.     

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.     

Electrostatic potential and electric field mapping of some sweeteners of the suosan series: A search for the structure–activity relationship

Electrostatic potential and electric field maps of some suosan series of sweeteners have been studied. Geometries optimized using the MNDO molecular orbital method and charge distributions obtained by the Mulliken population analysis were employed in the calculations. Sweetness potencies of the molecules were compared with electrostatic potentials and electric field strengths near the terminal COOH group. The observed sweetness potencies of the compounds and calculated electric fields near the carbonyl oxygen of the COOH group are found to be strongly correlated. © 1994 John Wiley & Sons, Inc.     

Another look at bonds and bonding

Structural Chemistry - Because electrostatic flux does not depend on the location of the charges it links, it is independent of the quantum mechanical charge distribution in a molecule. By...