Charges derived from distributed multipole series

A novel method to calculate electrostatic charges is proposed. Partial charges are fitted to reproduce the electrostatic potential of a distributed multipole series without explicitly evaluating electrostatic potentials. The calculation is economical and results in charges reflecting the symmetry properties of charge centers and being independent of molecular orientation.     

A multipole approximation of the electrostatic potential of molecules

The problem of approximating three-dimensional spatial distributions of quantum-mechanical electrostatic potentials of molecules by analytic potentials on the basis of atomic charges, real dipoles, and atomic multipoles up to quadrupoles inclusive was considered. Real dipole potentials are created by pairs of point charges of opposite signs, and the search for their arrangement in the volume of a molecule is part of the approximation problem. A FitMEP program was developed for the optimization of the parameters of models of the types specified taking into account molecular symmetry. It was shown for the example of several molecules (HF, CO, H₂O, NH₃, CH₄, formaldehyde, methanol, formamide, ethane, cyclopropane, cyclobutane, cyclohexane, tetrahedrane, cubane, adamantane, ethylene, and benzene) that the real dipole and atomic multipole models gave errors in approximated quantum-mechanical electrostatic potential values smaller by one or two orders of magnitude compared with the atomic charge model. The atomic charge model was shown to be virtually inoperative as applied to saturated hydrocarbons. Real dipole models were slightly inferior to atomic multipole models in quality but had all the advantages of the potential of point charges as concerned simplicity and compactness, and their use in potential energy calculations did not require changes in the existing program codes.     

Multipole correction of atomic monopole models of molecular charge distribution. I. Peptides

The defects in atomic monopole models of molecular charge distribution have been analyzed for several model-blocked peptides and compared with accurate quantum chemical values. The results indicate that the angular characteristics of the molecular electrostatic potential around functional groups capable of forming hydrogen bonds can be considerably distorted within various models relying upon isotropic atomic charges only. It is shown that these defects can be corrected by augmenting the atomic point charge models by cumulative atomic multipole moments (CAMMs). Alternatively, sets of off-center atomic point charges could be automatically derived from respective multipoles, providing approximately equivalent corrections. For the first time, correlated atomic multipoles have been calculated for N-acetyl, N'-methylamide-blocked derivatives of glycine, alanine, cysteine, threonine, leucine, lysine, and serine using the MP2 method. The role of the correlation effects in the peptide molecular charge distribution are discussed.     

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.     

Point charge representation of multicenter multipole moments in calculation of electrostatic properties

Summary Distributed Point Charge Models (PCM) for CO, (H₂O)₂, and HS-SH molecules have been computed from analytical expressions using multicenter multipole moments. The point charges (set of charges including both atomic and non-atomic positions) exactly reproduce both molecular and segmental multipole moments, thus constituting an accurate representation of the local anisotropy of electrostatic properties. In contrast to other known point charge models, PCM can be used to calculate not only intermolecular, but also intramolecular interactions. Comparison of these results with more accurate calculations demonstrated that PCM can correctly represent both weak and strong (intramolecular) interactions, thus indicating the merit of extending PCM to obtain improved potentials for molecular mechanics and molecular dynamics computational methods.Dedicated to Prof. Alberte PullmanPacific Northwest Laboratory is operated for the US Department of Energy by Battelle Memorial Institute under contract DE-ACO6-76RLO 1830     

On the molecular origin of the sensitivity to impact of cyclic nitramines

Nitramine explosives can combine relative insensitivity to initiation and great energy content. In this work, based on a previous approach developed for nitroaromatic explosives, we propose four mathematical models to correlate impact sensitivity, given by the h₅₀ value, to molecular charge properties. Fourteen cyclic nitramines were studied using Density Functional Theory (DFT). Six molecules of the set have measured h₅₀ values, which were used to evaluate the sensitivity models. Converged DFT charge densities of the molecules were partitioned and analyzed according to the distributed multipole analysis (DMA) atom-centered method. The sensitivity models were based on the DMA electric multipole values. The electron withdrawing role of the nitro group and the strong polarization of the charges of the nitrogen atom in the amine group were clearly identified. The influence of the electronic properties on the sensitivity of the explosives was characterized by including in the sensitivity models the charge values of the nitro or the nitramine groups and electron delocalization, the latter quantified by the DMA quadrupole values of the ring atoms. Inclusion of electron delocalization effects can improve the prediction of h₅₀ values for two out of the five strained-ring nitramines in the set. The charge values of the nitramine groups are the most important molecular property affecting the impact sensitivity. The h₅₀ values of eight nitramine explosives of the set not available experimentally were computed.     

Charge distributions and multipole moments in molecules

The consideration of multipole moments is suggested as a new criterion for the validity of assignments of atomic charges in molecules. The total quadrupole and octupole moments generated by our definition of atomic charges are compared with the exact moments of the underlying wavefunction for various basis sets in selected diatomics. The analysis includes also total overlap and total dipole moment partitioning as well as 1σ MO overlap partitioning. All considerations together allow us to assess the validity of our charge definition as compared to Mulliken's and Löwdin's and the quality of the basis set.     

Kirchhoff atomic charges fitted to multipole moments: implementation for a virtual screening system

The Kirchhoff charge model is a viable method of generating inexpensive and electrostatically reasonable atomic charges for molecular mechanical force fields. The charging method uses a computationally fast algorithm based on the principle of electronegativity relaxation. Parameters of the method, orbital electronegativities and hardnesses, are fitted to reproduce reference, ab initio calculated dipole and quadrupole moments of a representative training set of neutral and charged organic molecules covering most medicinal chemistry relevant bonding situations. Transferability and accuracy of the derived parameters are confirmed on an external test set. Comparisons to other charge models are made. Implementation of the new Kirchhoff charges into a virtual screening engine is elucidated.     

Polarisable multipolar electrostatics from the machine learning method Kriging: an application to alanine

We present a polarisable multipolar interatomic electrostatic potential energy function for force fields and describe its application to the pilot molecule MeNH-Ala-COMe (AlaD). The total electrostatic energy associated with 1, 4 and higher interactions is partitioned into atomic contributions by application of quantum chemical topology (QCT). The exact atom–atom interaction is expressed in terms of atomic multipole moments. The machine learning method Kriging is used to model the dependence of these multipole moments on the conformation of the entire molecule. The resulting models are able to predict the QCT-partitioned multipole moments for arbitrary chemically relevant molecular geometries. The interaction energies between atoms are predicted for these geometries and compared to their true values. The computational expense of the procedure is compared to that of the point charge formalism.     

Cumulative coordinates for approximations of high‐order atomic multipole moments in aluminosilicate and aluminophosphate sieves*

A scheme to obtain approximate analytical functions for the atomic distributed multipole moments of the crystallographically different atoms within aluminosilicate and aluminophosphate sieves is discussed. Respective atomic multipole moments are derived within the CRYSTAL95 ab initio periodic Hartree–Fock code with different basis sets, from minimal STO‐3G to 6‐21G*. In order to illustrate the possible applications, distributed analyses are carried out for various structural models from all‐siliceous zeolites and aluminophosphates with ratio Al/P=1 to hydrogen forms of aluminosilicates. Simple approximate forms based on charge and geometry coordinates are proposed for the high‐order moments of each atom, which are further required for the calculation of the electrostatic field within the structures. The possibility to use this analytical approach to evaluate the electrostatic field within embedded cluster models is also shortly discussed. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 70–85, 2001     

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.     

Topological analysis of the molecular charge density and impact sensitivy models of energetic molecules

Important explosives of practical use are composed of nitroaromatic molecules. In this work, we optimized geometries and calculated the electron density of 17 nitroaromatic molecules using the Density Functional Theory (DFT) method. From the DFT one-electron density matrix, we computed the molecular charge densities, thus the electron densities, which were then decomposed into electric multipoles located at the atomic sites of the molecules using the distributed multipole analysis (DMA). The multipoles, which have a direct chemical interpretation, were then used to analyze in details the ground state charge structure of the molecules and to seek for correlations between charge properties and sensitivity of the corresponding energetic material. The DMA multipole moments do not present large variations when the size of the Gaussian basis set is changed; the largest variations occurred in the range 10-15% for the dipole and quadrupole moments of oxygen atoms. The charges on the carbon atoms of the aromatic ring of each molecule become more positive when the number of nitro groups increases and saturate when there are five and six nitro groups. The magnitude and the direction of the dipole moments of the carbon atoms, indicators of site polarization, also depend on the nature of adjacent groups, with the largest dipole value being for C-H bonds. The total magnitude of the quadrupole moment of the aromatic ring carbon atoms indicates a decrease in the delocalized electron density due to an electron-withdrawing effect. Three models for sensitivity of the materials based on the DMA multipoles were proposed. Explosives with large delocalized electron densities in the aromatic ring of the component molecule, expressed by large quadrupole values on the ring carbon atoms, correspond to more insensitive materials. Furthermore, the charges on the nitro groups also influence the impact sensitivity.     

Atomic forces for geometry‐dependent point multipole and Gaussian multipole models

In standard treatments of atomic multipole models, interaction energies, total molecular forces, and total molecular torques are given for multipolar interactions between rigid molecules. However, if the molecules are assumed to be flexible, two additional multipolar atomic forces arise because of (1) the transfer of torque between neighboring atoms and (2) the dependence of multipole moment on internal geometry (bond lengths, bond angles, etc.) for geometry‐dependent multipole models. In this study, atomic force expressions for geometry‐dependent multipoles are presented for use in simulations of flexible molecules. The atomic forces are derived by first proposing a new general expression for Wigner function derivatives . The force equations can be applied to electrostatic models based on atomic point multipoles or Gaussian multipole charge density. Hydrogen‐bonded dimers are used to test the intermolecular electrostatic energies and atomic forces calculated by geometry‐dependent multipoles fit to the ab initio electrostatic potential. The electrostatic energies and forces are compared with their reference ab initio values. It is shown that both static and geometry‐dependent multipole models are able to reproduce total molecular forces and torques with respect to ab initio, whereas geometry‐dependent multipoles are needed to reproduce ab initio atomic forces. The expressions for atomic force can be used in simulations of flexible molecules with atomic multipoles. In addition, the results presented in this work should lead to further development of next generation force fields composed of geometry‐dependent multipole models. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Fast tools for calculation of atomic charges well suited for drug design1

Two novel approaches to construct empirical schemes for partial atomic charge calculation were proposed. The charge schemes possess important benefits. First, they produce both topologically symmetrical and environment dependent charges. Second, they can be parameterised to reasonably reproduce ab initio molecular electrostatic potential (MEP), which guarantees their successful use in molecular modelling. To validate the approaches, the parameters of the proposed charge schemes were fitted to best reproduce MEP simultaneously on grids around a set of 227 diverse organic compounds. The residual errors in MEP reproduction due to calculated atomic charges were compared to those due to charges from known charge schemes.     

Using multipole point charge distributions to provide the electrostatic potential in the variational explicit polarization (X-Pol) potential

The equations defining the variational explicit polarization (X-Pol) potential introduced in earlier work are modified in the present work so that multipole point charge distributions are used instead of Mulliken charges to polarize the monomers that comprise the system. In addition, when computing the electrostatic interaction between a monomer whose molecular orbitals are being optimized and a monomer whose electron density is being used to polarize the first monomer, the electron densities of both monomers are represented by atom-centered multipole point charge distributions. In the original formulation of the variational X-Pol potential, the continuous electron density of the monomer being optimized interacts with external Mulliken charges, but this corresponds to the monopole truncation in a multipole expansion scheme in the computation of the Fock matrix elements of the given monomer. The formulation of the variational X-Pol potential introduced in this work (which we are calling the “multipole variational X-Pol potential”) represents the electron density of the monomer whose wave function is being variationally optimized in the same way that it represents the electron densities of external monomers when computing the Coulomb interactions between them.