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.     

A practical procedure for the determination of electrostatic charges of large molecules

Summary A practical procedure for the precise determination of electrostatic charges, which are evaluated by fitting the rigorous quantum mechanical molecular electrostatic potential to a monopole-monopole expression, is presented. The proposal of this procedure arises from the study of the minimum requirements necessary to obtain reliable electrostatic charges. Such a study is focused on: (i) the dependence of the electrostatic charges on the set of points where the quantum mechanical and the monopole-monopole molecular electrostatic potentials are fitted; thus, both the influence of the number of points and their distribution in layers located out of the van der Waals radii of the atoms are examined, and (ii) the reliability of the use of fractional models for the evaluation of electrostatic charges of large molecules. Results point out that the optimum number of points is defined by a density of points ranging from 0.45 to 0.60 points/Ų when four layers (separated by 0.2 Å) are considered. Nevertheless, the use of only two layers (separated by 0.4 Å) for large molecules is recommended, thus enabling one to obtain reliable charges at a reduced computational cost. Moreover, results justify the use of fractional models for the determination of electrostatic charges of extremely large molecules, even when aromatic structures exist.     

The influence of discrete surface charges on the force between charged surfaces

The force between two parallel charged flat surfaces, with discrete surface charges, has been calculated with Monte Carlo simulations for different values of the electrostatic coupling. For low electrostatic coupling (small counterion valence, small surface charge, high dielectric constant, and high temperature) the total force is dominated by the entropic contribution and can be described by mean field theory, independent of the character of the surface charges. For moderate electrostatic coupling, counterion correlation effects lead to a smaller repulsion than predicted by mean field theory. This correlation effect is strengthened by discrete surface charges and the repulsive force is further reduced. For large electrostatic coupling the total force for smeared out surface charges is known to be attractive due to counterion correlations. If discrete surface charges are considered the attractive force is weakened and can even be turned into a repulsive force. This is due to the counterions being strongly correlated to the discrete surface charges forming effective, oppositely directed, dipoles on the two walls.     

Ligand atom partial charges assignment for complementary electrostatic potentials

Summary The design of molecules to fit into the active site of receptors is a rapidly developing area of pharmacology and medicinal chemistry. A good ligand needs a suitable geometry and also appropriate electrostatic properties. The electrostatic properties of the ligand should complement those of the receptor. We present a method for the assignment of atom-centred point charges for a ligand, based on the electrostatic potential of the receptor. These point charges are chosen to give the best possible complementarity to the receptor electrostatic potential over the van der Waals surface of the ligand. We demonstrate that point charges can be chosen to give good electrostatic complementarity, and suggest that a molecule with similar electrostatic properties should bind well to the receptor.     

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.     

Generation of OPLS-like charges from molecular electrostatic potential using restraints

A new method for generating atom-centered charges for use in condensed phase computer simulations is presented, which is based on a restrained electrostatic potential (RESP) procedure. Charges are calculated from a least-squares fit to the quantum mechanical electrostatic potential with a restraint applied to reduce their magnitude. The restraint developed here offers advantages over that used in RESP. The magnitude of the restraint is optimized to yield charges as close to the equivalent OPLS values as possible while still reproducing the molecule's electrostatic potential. A cross-validation analysis is used to show that the restraint is insensitive to the selection of OPLS molecules from which it is derived. Thus, with this method, OPLS-like charges may be produced from the electrostatic potential for atom types not in the OPLS force field. In addition, the restraint is shown to reduce the conformational dependence of the charges. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 483–498, 1999     

Fast assignment of accurate partial atomic charges: an electronegativity equalization method that accounts for alternate resonance forms

A fast, accurate method of assigning partial atomic charges is described. The method is based upon the concept of electronegativity equalization and is parametrized to fit electrostatic potentials obtained from ab initio quantum calculations. A novel algorithm for identifying alternate resonance forms is used to ensure that chemically equivalent atoms are assigned equal charges. The resulting charges are independent of conformation, yield good agreement with ab initio electrostatic potentials, and are similar to standard force field charges for common biochemical components. The method is broadly parametrized and generates charges for a drug-like compound in about 0.45 s on a 2.26 GHz Pentium 4 PC. It should thus be useful in a range of applications, such as molecular design and QSAR. The resonance algorithm is expected to have additional applications, such as in atom-typing and detection of molecular symmetry.     

A nano-confined charged layer defies the principle of electrostatic interaction

The reactivity between two charged molecules and the activity of charged biomolecules are mainly governed by the principle of electrostatic interaction, i.e., like charges repel and opposite charges attract. In the present study it is shown that the principle of electrostatic interaction is violated in the nano-confined biomimetic environment. Thus a positively charged molecule shows more preference to a positively charged surface compared to a negatively charged surface.     

On the representation of electrostatic fields around ab initio charge distributions

Summary We compare two methods (Mulliken charges and a distributed multipole analysis, DMA) of representing an ab initio charge distribution for calculating the electrostatic field and potential outside the molecule, using pyrimidine and the RNA base uracil as examples. This is done using a 3-D graphical display of the electrostatic fields, which, when used with real-time rotation, zooming and clipping, has many advantages for qualitatively assessing the electrostatic interactions of a molecule. The errors involved in using Mulliken point charges may be of similar magnitude to the total electrostatic field in regions which are important in recognition processes. The DMA representation automatically includes the anisotropic electrostatic effects of non-spherical features in the charge distribution of each atom, and yet the displayed electrostatic fields around the atoms which have lone-pair density do not show marked anisotropy.     

Atomic multipoles and perpendicular electrostatic forces in diatomic and planar molecules

Current methods for assigning atomic multipoles focus on reproduction of the molecular electrostatic potential. Another aspect of electrostatic interaction, which is usually overlooked, is the forces that an external electric field exerts on the nuclei of a molecule. In a self-consistent theory, both the electrostatic potential and force should be accounted for. However, in general it is not easy to meet this requirement for the force. For planar molecules, though, a formal solution is available in terms of atomic multipoles that are extracted from the molecular multipolar tensors. These Force-Related (FR) atomic multipoles are discussed in detail for some typical diatomics and planar polyatomics, and are shown to provide a solid uniform framework for treating both aspects of the electrostatics. In contrast, the commonly used potential-derived charges (i.e., the atomic charges obtained by fitting the electrostatic potential) can yield large deviations with respect to electrostatic forces on the nuclei, even when the electrostatic potential is very well reproduced.     

Multi-layer coarse-graining polarization model for treating electrostatic interactions of solvated α-conotoxin peptides

A multi-layer coarse-graining (CG) model is presented for treating the electrostatic interactions of solvated α-conotoxin peptides. According to the sensitivity to the electrostatic environment, a hybrid set of electrostatic parameters, such as secondary-structure- and residue-based dipoles, and atom-centered partial charges, are adopted. For the polarization "inert" secondary-structures and residues, the fragment dipole moments are distributed within narrow ranges with the magnitude close to zero. The coarse-graining fragment dipoles are parameterized from a large training set (10,000 configurations) to reproduce the electrostatic features of molecular fragments. In contrast, the electrostatically "sensitive" atoms exhibit large fluctuations of charges with the varied environments. The environment-dependent variable charges are updated in each energetic calculation. The electrostatic interaction of the whole chemical system is hence partitioned into several sub-terms coming from the fragment dipole-dipole, (fragment) dipole-(atom) charge, and atom charge-charge interactions. A large number of test calculations on the relative energies of cyclo-peptide conformers have demonstrated that the multi-layer CG electrostatic model presents better performance than the non-polarized force fields, in comparison with the density-functional theory and the fully polarized force field model. The selection of CG fragment centers, mass or geometric center, has little influence on the fragment-based dipole-dipole interactions. The multi-layer partition of electrostatic polarization is expected to be applied to many biologically interesting and complicated phenomena.     

A Quantum Chemical and Electrostatic Study of Alkyl and Substituted Benzenonium Cations and Related Molecules: The Effect of Atomic Charge Distribution on Carbocation Energy and Geometry

Geometries, NMR chemical shifts, atomic charges, and bond orders were calculated at the MP2/6-31G* level of theory for the isopropyl, sec-butyl, tert-butyl, benzenonium, and six methyl- and trifluoromethyl-substituted benzenonium ions. The NPA charges correlate better than the CHELPG, MK, and AIM charges with the experimental and calculated carbon chemical shifts. The electrostatic energies of isomeric ions, calculated by treatment of the NPA charges as point charges, are comparable to their MP2 energy differences. The electrostatic calculations, although classical approximations, provide a qualitative understanding of the coulombic basis of the methyl and trifluoromethyl substituent effects. It is apparent that these species are stabilized by having adjacent, oppositely charged atoms (for example, having the negatively charged carbon of a methyl group bonded to a positive carbon). It is proposed that a methyl group be termed a nucleophilic (rather than electron-donating) substituent and that a trifluoromethyl group be termed an electrophilic substituent. In the benzenonium ions and in toluene, fluoromethylbenzene, difluoromethylbenzene, and benzotrifluoride, the endocyclic angle at the substituent increases with increasing electrophilicity of the substituent. An electrostatic calculation again provides some insight into the coulombic basis of these changes.     

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     

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.     

Various atomic charge calculation schemes of CoMFA on HIF‐1 inhibitors of moracin analogs

Selection of appropriate partial charges in a molecule is crucial to derive good quantitative structure–activity relationship models. In this work, several partial atomic charges were assigned and tested in a comparative molecular field analysis (CoMFA) models. Many CoMFA models were generated for a series of hypoxia inducible factor 1 (HIF‐1) inhibitors using various partial atomic charges including charge equalization, Mülliken population analysis (MPA), natural population analysis, and electrostatic potential (ESP)‐derived charges. These atomic charges were investigated at various theoretical levels such as empirical, semiempirical, Hartree–Fock (HF), and density functional theory (DFT). Among them, Merz‐Singh‐Kollman (MK) ESP‐derived charges at the level of HF/6‐31G* gave the highest predictive q² with experimental pIC₅₀ values. With this charge scheme, a detailed analysis of CoMFA model was performed to understand the electrostatic interactions between ligand and receptor. More elaborate charge calculation schemes such as HF and DFT correlated more strongly with activity than empirical or semiempirical schemes. The choice of optimization methods was important. As geometries were fully optimized at the given levels of theory, the aligned structures were different. They differed considerably, especially for the flexible parts. This was likely the source of the substantial variation of q² values, even when the same steric factor was considered without electrostatic parameters. ESP‐derived charges were most appropriate to describe CoMFA electrostatic interactions among MPA, NBA, and ESP charges. Overall q² values vary considerably (0.8–0.5) depending on the charge schemes applied. The results demonstrate the need to consider more appropriate atomic charges rather than default CoMFA charges. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

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.     

Potential-derived point-charge model study of electrostatic interactions in DNA base components

Ab initio electrostatic potentials obtained using STO-3G wavefunctions for guanine, cytosine, adenine, and thymine are used to calculate potential-derived (PD) point charges for these base components. Calculated PD point charges are used to estimate the electrostatic contributions to hydrogen-bonding and stacking interaction energies of ten sequence isomers of B-DNA. These estimates are in excellent agreement with the results of the more elaborate segmental multipole moment expansion technique.     

Geometry-dependent atomic charges: Methodology and application to alkanes,aldehydes, ketones,and amides

A general methodology for deriving geometry-dependent atomic charges is presented. The main ingredient of the method is a model that describes the molecular dipole moment in terms of geometry-dependent point charges. The parameters of the model are determined from ab initio calculations of molecular dipole moments and their Cartesian derivatives at various molecular geometries. Transferability of the parameters is built into the model by fitting ab initio calculations for various molecules simultaneously. The results show that charge flux along the bonds is a major contributing factor to the geometry dependence of the atomic charges, with additional contributions from fluxes along valence angles and adjacent bonds. Torsion flux is found to be smaller in magnitude than the bond and valence angle fluxes but is not always unimportant. A set of electrostatic parameters is presented for alkanes, aldehydes, ketones, and amides. Transferability of these parameters for a host of molecules is established to within 3 ?5% error in the predicted dipole moments. A possible extension of the method to include atomic dipoles is outlined. With the inclusion of such atomic dipoles and with the set of transferable point charges and charge flux parameters, it is demonstrated that molecular electrostatic potentials as well as electrostatic forces on nuclei can be reproduced much better than is possible with other models (such as potential derived charges). © 1995 by John Wiley & Sons, Inc.     

Communication: Quantum polarized fluctuating charge model: a practical method to include ligand polarizability in biomolecular simulations

We present a simple and practical method to include ligand electronic polarization in molecular dynamics (MD) simulation of biomolecular systems. The method involves periodically spawning quantum mechanical (QM) electrostatic potential (ESP) calculations on an extra set of computer processors using molecular coordinate snapshots from a running parallel MD simulation. The QM ESPs are evaluated for the small-molecule ligand in the presence of the electric field induced by the protein, solvent, and ion charges within the MD snapshot. Partial charges on ligand atom centers are fit through the multi-conformer restrained electrostatic potential (RESP) fit method on several successive ESPs. The RESP method was selected since it produces charges consistent with the AMBER/GAFF force-field used in the simulations. The updated charges are introduced back into the running simulation when the next snapshot is saved. The result is a simulation whose ligand partial charges continuously respond in real-time to the short-term mean electrostatic field of the evolving environment without incurring additional wall-clock time. We show that (1) by incorporating the cost of polarization back into the potential energy of the MD simulation, the algorithm conserves energy when run in the microcanonical ensemble and (2) the mean solvation free energies for 15 neutral amino acid side chains calculated with the quantum polarized fluctuating charge method and thermodynamic integration agree better with experiment relative to the Amber fixed charge force-field.