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     

Accurate modeling of the intramolecular electrostatic energy of proteins

The (?, ψ) energy surface of blocked alanine (N-acetyl–N′-methyl alanineamide) was calculated at the Hartree-Fock (HF)/6-31G* level using ab initio molecular orbital theory. A collection of six electrostatic models was constructed, and the term electrostatic model was used to refer to (1) a set of atomic charge densities, each unable to deform with conformation; and (2) a rule for estimating the electrostatic interaction energy between a pair of atomic charge densities. In addition to two partial charge and three multipole electrostatic models, this collection includes one extremely detailed model, which we refer to as nonspherical CPK. For each of these six electrostatic models, parameters—in the form of partial charges, atomic multipoles, or generalized atomic densities—were calculated from the HF/6-31G* wave functions whose energies define the ab initio energy surface. This calculation of parameters was complicated by a problem that was found to originate from the locking in of a set of atomic charge densities, each of which contains a small polarization-induced deformation from its idealized unpolarized state. It was observed that the collective contribution of these small polarization-induced deformations to electrostatic energy differences between conformations can become large relative to ab initio energy differences between conformations. For each of the six electrostatic models, this contribution was reduced by an averaging of atomic charge densities (or electrostatic energy surfaces) over a large collection of conformations. The ab initio energy surface was used as a target with respect to which relative accuracies were determined for the six electrostatic models. A collection of 42 more complete molecular mechanics models was created by combining each of our six electrostatic models with a collection of seven models of repulsion + dispersion + intrinsic torsional energy, chosen to provide a representative sample of functional forms and parameter sets. A measure of distance was defined between model and ab initio energy surfaces; and distances were calculated for each of our 42 molecular mechanics models. For most of our 12 standard molecular mechanics models, the average error between model and ab initio energy surfaces is greater than 1.5 kcal/mol. This error is decreased by (1) careful treatment of the nonspherical nature of atomic charge densities, and (2) accurate representation of electrostatic interaction energies of types 1—2 and 1—3. This result suggests an electrostatic origin for at least part of the error between standard model and ab initio energy surfaces. Given the range of functional forms that is used by the current generation of protein potential functions, these errors cannot be corrected by compensating for errors in other energy components. © 1995 by John Wiley & Sons, Inc.     

Base stacking in cytosine dimer. A comparison of correlated ab initio calculations with three empirical potential models and density functional theory calculations

Ab initio MP2/6-31G* interaction energies were calculated for more than 80 geometries of stacked cytosine dimer. Diffuse polarization functions were used to properly cover the dispersion energy. The results of ab initio calculations were compared with those obtained from three electrostatic empirical potential models, constructed as the sum of a Lennard-Jones potential (covering dispersion and repulsion contributions) and the electrostatic term. Point charges and point multipoles of the electrostatic term were also obtained at the MP2/6-31G* level of theory. The point charge MEP model (atomic charges derived from molecular electrostatic potential) satisfactorily reproduced the ab initio data. Addition of π-charges localized below and above the cytosine plane did not affect the calculated energies. The model employing the distributed multipole analysis gave worse agreement with the ab initio data than the MEP approach. The MP2 MEP charges were also derived using larger sets of atomic orbitals: cc-pVDZ, 6-311 + G(2d, p), and aug-cc-pVDZ. Differences between interaction energies calculated using these three sets of point charges and the MP2/6-31G* charges were smaller than 0.8 kcal/mol. The correlated ab initio calculations were also compared with the density functional theory (DFT) method. DFT calculations well reproduced the electrostatic part of interaction energy. They also covered some nonelectrostatic short-range effects which were not reproduced by the empirical potentials. The DFT method does not include the dispersion energy. This energy, approximated by an empirical term, was therefore added to the DFT interaction energy. The resulting interaction energy exhibited an artifact secondary minimum for a 3.9-4.0 vertical separation of bases. This defect is inherent in the DFT functionals, because it is not observed for the Hartree-Fock + dispersion interaction energy.© 1996 John Wiley & Sons, Inc.     

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.     

Application of Static Charge Transfer within an Ionic‐Liquid Force Field and Its Effect on Structure and Dynamics

The effects of linear scaling of the atomic charges of a reference potential on the structure, dynamics, and energetics of the ionic liquid 1,3‐dimethylimidazolium chloride are investigated. Diffusion coefficients that span over four orders of magnitude are observed between the original model and a scaled model in which the ionic charges are ±0.5 e. While the three‐dimensional structure of the liquid is less affected, the partial radial distribution functions change markedly—with the positive result that for ionic charges of ±0.7 e, an excellent agreement is observed with ab initio molecular dynamics data. Cohesive energy densities calculated from these partial‐charge models are also in better agreement with those calculated from the ab initio data. We postulate that ionic‐liquid models in which the ionic charges are assumed to be ±1 e overestimate the intermolecular attractions between ions, which results in overstructuring, slow dynamics, and increased cohesive energy densities. The use of scaled‐charge sets may be of benefit in the simulation of these systems—especially when looking at properties beyond liquid structure—thus providing an alternative to computationally expensive polarisable force fields.     

Conformational preferences for hydroxyl groups in substituted tetrahydropyrans

Quantum mechanical (ab initio and semiempirical) and force field calculations are reported for representative torsion potentials in several tetrahydropyran derivatives. The overall agreement between the various methods is quite good except that the AMBER torsion profiles are sensitive to the choice of atomic point charges. Using electrostatic potential (ESP) derived atomic point charges determined with the STO-3G basis set we find that AMBER is able to match the best quantum mechanical results quite well. However, when the point charges are derived using the 6-31G* basis set we find that scaling the intramolecular electrostatic nonbond interactions is necessary. AM1 does not work very well for these compounds when compared to the ab initio methods and, therefore, should only be used in cases when ab initio calculations would be prohibitive. Based upon our results we feel that any force field that makes use of 6-31G* ESP derived atomic point charges will need to scale intramolecular interactions. Implications of scaling intramolecular interactions to the development of force fields based on 6-31G* ESP derived atomic point charges are discussed. © 1992 by John Wiley & Sons, Inc.     

Comparison of Hydrogen and Gold Bonding in [XHX]−, [XAuX]−, and Isoelectronic [NgHNg]+, [NgAuNg]+ (X=Halogen,Ng=Noble Gas)

Quantum chemical calculations at the MP2/aug‐cc‐pVTZ and CCSD(T)/aug‐cc‐pVTZ levels have been carried out for the title compounds. The electronic structures were analyzed with a variety of charge and energy partitioning methods. All molecules possess linear equilibrium structures with D_∞h symmetry. The total bond dissociation energies (BDEs) of the strongly bonded halogen anions [XHX]^? and [XAuX]^? decrease from [FHF]^? to [IHI]^? and from [FAuF]^? to [IAuI]^?. The BDEs of the noble gas compounds [NgHNg]⁺ and [NgAuNg]⁺ become larger for the heavier atoms. The central hydrogen and gold atoms carry partial positive charges in the cations and even in the anions, except for [IAuI]^?, in which case the gold atom has a small negative charge of ?0.03 e. The molecular electrostatic potentials reveal that the regions of the most positive or negative charges may not agree with the partial charges of the atoms, because the spatial distribution of the electronic charge needs to be considered. The bonding analysis with the QTAIM method suggests a significant covalent character for the hydrogen bonds to the noble gas atoms in [NgHNg]⁺ and to the halogen atoms in [XHX]^?. The covalent character of the bonding in the gold systems [NgAuNg]⁺ and [XAuX]^? is smaller than in the hydrogen compound. The energy decomposition analysis suggests that the lighter hydrogen systems possess dative bonds X^?→H⁺←X^? or Ng→H⁺←Ng while the heavier homologues exhibit electron sharing through two‐electron, three‐center bonds. Dative bonds X^?→Au⁺←X^? and Ng→Au⁺←Ng are also diagnosed for the lighter gold systems, but the heavier compounds possess electron‐shared bonds.     

A quantitative analysis of light‐driven charge transfer processes using voronoi partitioning of time dependent DFT‐derived electron densities

An analytical method is presented that provides quantitative insight into light‐driven electron density rearrangement using the output of standard time‐dependent density functional theory (TD‐DFT) computations on molecular compounds. Using final and initial electron densities for photochemical processes, the subtraction of summed electron density in each atom‐centered Voronoi polyhedron yields the electronic charge difference, Q ^VECD. This subtractive method can also be used with Bader, Mulliken and Hirshfeld charges. A validation study shows Q ^VECD to have the most consistent performance across basis sets and good conservation of charge between electronic states. Besides vertical transitions, relaxation processes can be investigated as well. Significant electron transfer is computed for isomerization on the excited state energy surface of azobenzene. A number of linear anilinepyridinium donor‐bridge‐acceptor chromophores was examined using Q ^VECD to unravel the influence of its pi‐conjugated bridge on charge separation. Finally, the usefulness of the presented method as a tool in optimizing charge transfer is shown for a homologous series of organometallic pigments. The presented work allows facile calculation of a novel, relevant quantity describing charge transfer processes at the atomic level. © 2017 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Atomic charges derived from semiempirical methods

It is demonstrated that semiempirical methods give electrostatic potential (ESP) derived atomic point charges that are in reasonable agreement with ab initio ESP charges. Furthermore, we find that MNDO ESP charges are superior to AM1 ESP charges in correlating with ESP charges derived from the 6-31G* basis set. Thus, it is possible to obtain 6-31G* quality point charges by simply scaling MNDO ESP charges. The charges are scaled in a linear (y = Mx) manner to conserve charge. In this way researchers desiring to carry out force field simulations or minimizations can obtain charges by using MNDO, which requires much less computer time than the corresponding 6-31G* calculation.     

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     

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.     

Intrinsic Surface Reaction Constant in 1-pK Model of Mg-Fe Hydrotalcite-like Compounds

The relationship among intrinsic surface reaction constant (K) in 1-pK model, point of zero net charge (PZNC) and structural charge density (σst) for amphoteric solid with structural charges was established in order to investigate the effect of σst on pK. The theoretical analysis based on 1-pK model indicates that the independent PZNC of electrolyte concentration (c) exists for amphoteric solid with structural charges. A common intersection point (CIP) should appear on the acid-base titration curves at different c, and the pH at the CIP is pHPZNC. The pK can be expressed as pK=-pHPZNC log[(1 2αPZNC)/(1-2αPZNC)], where αPZNC≡σst/eNANs, in which e is the elementary charge, NA the Avogadro‘s constant and Ns the total density of surface sites. For solids without structural charges, pK=-pHPZNC. The pK values of hydrotalcite-like compounds (HTlc) with general formula of [Mg1-xFex(OH)2](Cl,OH)x were evaluated. With increasing x, the pK increases, which can be explained based on the affinity of metal cations for H^- or OH^- and the electrostatic interaction between charging surface and H^- or OH^-.     

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     

Multiscale fast summation of long‐range charge and dipolar interactions

Here we present a linear order multiscale method for the fast summation of long range forces in a system consisting of a large number of charge and dipolar particles. For a N‐body system, our algorithm requires an order of work that is proportional to O(N), in comparison to order O(N²) of the direct pairwise computation. Our method is demonstrated on two‐dimensional homogeneous point‐charge and dipolar systems, and a combined heterogeneous particle system, for the calculation of the induced electrostatic potential and energy. The electrostatic interaction is decomposed into a local part and a smooth part. The method thus, has several potential advantages over other O(N log N) or O(N) techniques, especially for calculation with moving particles or implicit charges locations. This approach is beneficial to large‐scale problems such as molecular statics, molecular dynamics, equilibrium statistics (Monte‐Carlo simulations), molecular docking, and in areas such as magnetism and astrophysics. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 717–731, 2001     

Electrostatic Energies in the 1,4‐Dichlorobenzene Polymorph Crystals: the Role of Charge Density Overlap Effects in Crystal Packing Analysis

Electrostatic and polarization energies for the three known polymorphic crystal structures of 1,4‐dichlorobenzene, as well as for one particularly stable virtual crystal structure generated by computer search, were calculated by a new accurate numerical integration method over static molecular charge densities obtained from high level ab initio molecular‐orbital calculations. Results are compared with those from standard empirical atom‐atom force fields. The new electrostatic energies, which include charge density overlap (penetration) effects, are seen to be much larger than and sometimes of opposite sign to those derived from point‐charge models. None of the four polymorphs is substantially more stable than the others on electrostatic‐energy grounds. Molecule‐molecule electrostatic energies have been calculated for the more important molecular pairs in each of the four structures; trends are found to be very different from those indicated by point‐charge energies or by total energies estimated with a parametric atom‐atom force field. Conclusions based exclusively on analysis of intermolecular atom contacts and point‐charge electrostatics may need to be modified in the light of the new kind of calculation.     

Accurate partial atomic charges for high-energy molecules using class IV charge models with the MIDI! basis set

We have recently developed a new class IV charge model for calculating partial atomic charges in molecules. The new model, called charge model 3 (CM3), was parameterized for calculations on molecules containing H, Li, C, N, O, F, Si, S, P, Cl, and Br by Hartree–Fock theory and by hybrid density functional theory (HDFT) based on the modified Perdew–Wang density functional with several basis sets. In the present article, we extend CM3 for calculating partial atomic charges by Hartree–Fock theory with the economical but well balanced MIDI! basis set. Then, using a test set of accurate dipole moments for molecules containing nitramine functional groups (which include many high-energy materials), we demonstrate the utility of several parameters designed to improve the charges in molecules containing both N and O atoms. We also show that one of our most recently developed CM3 models that is designed for use with wave functions calculated at the mPWXPW91/MIDI! level of theory (where X denotes a variable percentage of Hartree–Fock exchange) gives accurate charge distributions in nitramines without additional parameters for N and O. To demonstrate the reliability of partial atomic charges calculated with CM3, we use these atomic charges to calculate polarization free energies for several nitramines, including the commonly used explosives 1,3,5-trinitro-s-triazine (RDX) and 2,4,6,8,10,12-hexanitrohexaazaisowurtzitane (HNIW), in nitromethane. These polarization energies are large and negative, indicating that electrostatic interactions between the charge distribution of the molecule and the solvent make a large contribution to the free energy of solvation of nitramines. By extension, the same conclusion should apply to solid-state condensation. Also, in contrast to some other charge models, CM3 yields atomic charges that are relatively insensitive to the presence of buried atoms and small conformational changes in the molecule, as well as to the level of treatment of electron correlation. This type of charge model should be useful in the future development of solvation models and force fields designed to estimate intramolecular interactions of nitramines in the condensed phase.     

An N log N approximation based on the natural organization of biomolecules for speeding up the computation of long range interactions

Presented here is a method, the hierarchical charge partitioning (HCP) approximation, for speeding up computation of pairwise electrostatic interactions in biomolecular systems. The approximation is based on multiple levels of natural partitioning of biomolecular structures into a hierarchical set of its constituent structural components. The charge distribution in each component is systematically approximated by a small number of point charges, which, for the highest level component, are much fewer than the number of atoms in the component. For short distances from the point of interest, the HCP uses the full set of atomic charges available. For long‐distance interactions, the approximate charge distributions with smaller sets of charges are used instead. For a structure consisting of N charges, the computational cost of computing the pairwise interactions via the HCP scales as O(N log N), under assumptions about the structural organization of biomolecular structures generally consistent with reality. A proof‐of‐concept implementation of the HCP shows that for large structures it can lead to speed‐up factors of up to several orders of magnitude relative to the exact pairwise O(N²) all‐atom computation used as a reference. For structures with more than 2000–3000 atoms the relative accuracy of the HCP (relative root‐mean‐square force error per atom), approaches the accuracy of the particle mesh Ewald (PME) method with parameter settings typical for biomolecular simulations. When averaged over a set of 600 representative biomolecular structures, the relative accuracies of the two methods are roughly equal. The HCP is also significantly more accurate than the spherical cutoff method. The HCP has been implemented in the freely available nucleic acids builder (NAB) molecular dynamics (MD) package in Amber tools. A 10 ns simulation of a small protein indicates that the HCP based MD simulation is stable, and that it can be faster than the spherical cutoff method. A critical benefit of the HCP approximation is that it is algorithmically very simple, and unlike the PME, the HCP is straightforward to use with implicit solvent models. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010