A combined electronegativity equalization and electrostatic potential fit method for the determination of atomic point charges

We report an approach for the determination of atomic monopoles of macromolecular systems using connectivity and geometry parameters alone. The method is appropriate also for the calculation of charge distributions based on the quantum mechanically determined wave function and does not suffer from the mathematical instability of other electrostatic potential fit methods.     

Accurate conformation‐dependent molecular electrostatic potentials for high‐throughput in silico drug discovery

The atom‐centered partial charges‐approximation is commonly used in current molecular modeling tools as a computationally inexpensive alternative to quantum mechanics for modeling electrostatics. Even today, the use of partial charges remains useful despite significant advances in improving the efficiency of ab initio methods. Here, we report on new parameters for the EEM and SFKEEM electronegativity equalization‐based methods for rapidly determining partial charges that will accurately model the electrostatic potential of flexible molecules. The developed parameters cover most pharmaceutically relevant chemistries, and charges obtained using these parameters reproduce the B3LYP/cc‐pVTZ reference electrostatic potential of a set of FDA‐approved drug molecules at best to an average accuracy of 13 ± 4 kJ mol^?1; thus, equipped with these parameters electronegativity equalization‐based methods rival the current best non‐quantum mechanical methods, such as AM1‐BCC, in accuracy, yet incur a lower computational cost. Software implementations of EEM and SFKEEM, including the developed parameters, are included in the conformer‐generation tool BALLOON , available free of charge at http://web.abo.fi/fak/mnf/bkf/research/johnson/software.php . © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Molecular electronegativity in density functional theory (II) --Direct calculation of group electronegativity and the atomic charges in a group

On the basis of a more precise expression of the atomic effective electronegativity deduced from the density functional theory and electronegativity equalization principle, a new scheme for calculating the group electronegativity and the atomic charges in a group is proposed and programed, and various parameters of electronegativity and hardness are given for some common atoms. Through calculation, analysis and comparison of more than one hundred groups, it is shown that the results from this scheme are reasonable and may be extended.     

Fast,efficient generation of high‐quality atomic charges. AM1‐BCC model: I. Method

The AM1‐BCC method quickly and efficiently generates high‐quality atomic charges for use in condensed‐phase simulations. The underlying features of the electron distribution including formal charge and delocalization are first captured by AM1 atomic charges for the individual molecule. Bond charge corrections (BCCs), which have been parameterized against the HF/6‐31G* electrostatic potential (ESP) of a training set of compounds containing relevant functional groups, are then added using a formalism identical to the consensus BCI (bond charge increment) approach. As a proof of the concept, we fit BCCs simultaneously to 45 compounds including O‐, N‐, and S‐containing functionalities, aromatics, and heteroaromatics, using only 41 BCC parameters. AM1‐BCC yields charge sets of comparable quality to HF/6‐31G* ESP‐derived charges in a fraction of the time while reducing instabilities in the atomic charges compared to direct ESP‐fit methods. We then apply the BCC parameters to a small “test set” consisting of aspirin, d ‐glucose, and eryodictyol; the AM1‐BCC model again provides atomic charges of quality comparable with HF/6‐31G* RESP charges, as judged by an increase of only 0.01 to 0.02 atomic units in the root‐mean‐square (RMS) error in ESP. Based on these encouraging results, we intend to parameterize the AM1‐BCC model to provide a consistent charge model for any organic or biological molecule. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 132–146, 2000     

Off‐atomic site charges in some anions,metal cations,and complexes: Significance for electrostatic properties and binding

Electronic structures and properties of several anions, metal cations, and their complexes with neutral molecules were investigated at the HF/6‐31G** and B3LYP/6‐31G** levels of theory. Charges shifted from atomic sites due to atomic orbital hybridization called hybridization displacement charges (HDC) were investigated in detail. It has been found that many components of HDC are associated with each atom of ion that are shifted from the atomic sites, those associated with metal cations being shifted by large distances as found previously in electrically neutral systems. It is shown that atomic orbitals are appreciably rehybridized in going from neutral molecules to anions and cations. Molecular dipole moments and surface molecular electrostatic potentials (MEP) are obtained satisfactorily using HDC for the various types of species mentioned above. In the OH^?? H₂O complex, reversal of direction of shift of an HDC component associated with the hydrogen atom of H₂O involved in hydrogen bonding, indicates that the hydrogen bond between OH^? and H₂O would have some covalent character. Other atomic site‐based point charge models cannot provide such information about the nature of bonding. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem 2007     

Solvated ensemble averaging in the calculation of partial atomic charges

In the calculation of partial atomic charges, for use in molecular mechanics or dynamics simulations, it is common practice to select only a single conformation for the molecule of interest. For molecules that contain rotatable bonds, it is preferable to compute the charges from several relevant conformations. We present here results from a charge derivation protocol that determines the partial charges by averaging charges computed for conformations selected from explicitly solvated MD simulations, performed under periodic boundary conditions. This approach leads to partial charges that are weighted by a realistic population of conformations and that are suitable for condensed phase simulations. This protocol can, in principle, be applied to any class of molecule and to nonaqueous solvation. Carbohydrates contain numerous hydroxyl groups that exist in an ensemble of orientations in solution, and in this report we apply ensemble averaging to a series of methyl glycosides. We report the extent to which ensemble averaging leads to charge convergence among the various monosaccharides and among the constituent atoms within a given monosaccharide. Due to the large number of conformations (200) in our ensembles, we are able to compute statistically relevant standard deviations for the partial charges. An analysis of the standard deviations allows us to assess the extent to which equivalent atom types may, nevertheless, require unique partial charges. The configurations of the hydroxyl groups exert considerable influence on internal energies, and the limits of ensemble averaged charges are discussed in terms of these properties.     

Effective atomic charges in alanine dipeptide

A new set of effective atomic charges of different conformers of alanine dipeptide is presented. These charges are obtained by fitting the electrostatic potential resulting from the ab initio SCF wave function of the system obtained in a 6-31G basis set. A specific fit procedure is used providing charges weakly dependent on the fit points as well as on the geometry of the molecule. It is shown that these charges retain a reasonable chemical meaning. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 473–482, 1999     

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     

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.     

Accuracy of free energies of hydration using CM1 and CM3 atomic charges

Absolute free energies of hydration (DeltaGhyd) have been computed for 25 diverse organic molecules using partial atomic charges derived from AM1 and PM3 wave functions via the CM1 and CM3 procedures of Cramer, Truhlar, and coworkers. Comparisons are made with results using charges fit to the electrostatic potential surface (EPS) from ab initio 6-31G* wave functions and from the OPLS-AA force field. OPLS Lennard-Jones parameters for the organic molecules were used together with the TIP4P water model in Monte Carlo simulations with free energy perturbation theory. Absolute free energies of hydration were computed for OPLS united-atom and all-atom methane by annihilating the solutes in water and in the gas phase, and absolute DeltaGhyd values for all other molecules were computed via transformation to one of these references. Optimal charge scaling factors were determined by minimizing the unsigned average error between experimental and calculated hydration free energies. The PM3-based charge models do not lead to lower average errors than obtained with the EPS charges for the subset of 13 molecules in the original study. However, improvement is obtained by scaling the CM1A partial charges by 1.14 and the CM3A charges by 1.15, which leads to average errors of 1.0 and 1.1 kcal/mol for the full set of 25 molecules. The scaled CM1A charges also yield the best results for the hydration of amides including the E/Z free-energy difference for N-methylacetamide in water.     

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.     

Suitability of density functional methods for calculation of electrostatic properties

A systematic analysis was performed on the suitability of the molecular electrostatic potential (MEP) and MEP-derived properties determined by means of density functional (DFT) methods. Attention was paid to the electrostatic potential (ESP) derived charges, the ESP and exact quantum mechanical dipole moments, the depth of MEP minima, and the MEP distribution in layers around the molecule for a large series of molecules. The electrostatic properties were determined at either local or nonlocal DFT levels using different functionals. The results were compared with the values estimated from quantum mechanical calculations performed at Hartree–Fock, Møller–Plesset up to fourth order, and CIPSI levels. The suitability of the MEP-derived properties estimated from DFT methods is discussed for application in different areas of chemical interest. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 980–991, 1997     

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.     

Comparison of methods for point‐charge representation of electrostatic fields

The calculation of the electrostatic potential resulting from an infinite or extended array of charges in the interior of a region of interest is a frequent task in computational chemistry. In case of a periodic potential this can, for example, be done by Ewald summation or by multipole methods. An important alternative are those methods where arrays of auxiliary point charges are optimized with respect to charge and/or position to reproduce the original electrostatic potential. In the literature different variations are reported. We compare the performance of some of these with respect to their ability to reproduce the original potential and the computational effort required. Between (1) surface charges determined by the conductor‐boundary condition, (2) optimized surface charges, and (3) surface charges floating on the surface we find that (2) offers good quality with small computational costs involved. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Conformational dependence of charges in protein simulations

We have studied the conformational dependence of molecular mechanics atomic charges for proteins by calculating the charges fitted to the quantum mechanical (QM) electrostatic potential (ESP) for all atoms in complexes between avidin and seven biotin analogues for 20 snapshots from molecular dynamics simulations. We have studied how various other charge sets reproduce those charges. The QM charges, even if averaged over all snapshots or all residues, in general have a larger magnitude than standard Amber charges, indicating that the restraint toward zero in the restrained ESP method is too strong. This has a significant influence on the electrostatic conformational energies and the interaction energy between the biotin ligand and the protein, giving a difference between the QM and Amber charges of 43 and 8 kJ/mol for the negatively charged and neutral biotin analogues, respectively (3-4%). However, this energy difference is strongly reduced if the solvation energy (calculated by the Poisson-Boltzmann or Generalized Born methods) is added, viz., to 7 kJ/mol for charged and 3 kJ/mol for uncharged ligand. In fact, charges need to be recalculated with a QM method only for residues within 7 or 4 A of the ligand, if the error should be less than 4 kJ/mol. Unfortunately, the QM charges do not give significantly better MM/PBSA estimates of ligand-binding affinities than standard Amber charges.     

A surface site interaction point methodology for macromolecules and huge molecular databases

Determining the position and magnitude of Surface Site Interaction Points (SSIP) is a useful technique for understanding intermolecular interactions. SSIPs have been used for the prediction of solvation properties and for virtual co‐crystal screening. To determine the SSIPs for a molecule, the Molecular Electrostatic Potential Surface (MEPS) is first calculated using ab initio methods such as Density Functional Theory. This leads to a high cost in terms of computation time and is not compatible with the analysis of huge molecular databases. Herein, we present a method for the fast estimation of SSIPs, which is based on the MEPS calculated from MMFF94 atomic partial charges. The results show that this method can be used to calculate SSIPs for large molecular databases with a much higher speed than the original ab initio methodology. © 2017 Wiley Periodicals, Inc.