VESPA: A new,fast approach to electrostatic potential-derived atomic charges from semiempirical methods

An improved semiempirical method for computing electrostatic potential-derived atomic charges is described. It includes a very fast algorithm for the generation of the grid points around the molecule and the calculation of the electrostatic potential at these points. The dependency of the atomic point charges obtained on the number of grid points used in the fitting procedure is examined. For “buried” atoms a high density grid is necessary. It is possible to obtain 6–31G*-quality atom-centered point charges, even for phosphorus compounds, using AM1 or PM3. This approach can therefore be recommended for general use in QSAR or molecular mechanics for any organic and bioorganic system up to about 200 atoms. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 744–756, 1997     

Charges fit to electrostatic potentials. II. Can atomic charges be unambiguously fit to electrostatic potentials?

The present work examines the conditioning of the least-squares matrix for obtaining potential derived charges and presents a modification of the CHELP method for fitting atomic charges to electrostatic potentials. Results from singular value decompositions (SVDs) of the least-squares matrices show that, in general, the least-squares matrix for this fitting problem will be rank deficient. Thus, statistically valid charges cannot be assigned to all the atoms in a given molecule. We find also that, contrary to popular notions, increasing the point density of the fit has little or no influence on the rank of the problem. Improvement in the rank can best be achieved by selecting points closer to the molecular surface. Basis set has, as expected, no effect on the number of charges that can be assigned. Finally, a well-defined, computationally efficient algorithm (CHELP-SVD) is presented for determining the rank of the least-squares matrix in potential-derived charge fitting schemes, selecting the appropriate subset of atoms to which charges can be assigned based on that rank estimate, and then refitting the selected set of charges. © 1996 by John Wiley & Sons, Inc.     

Molecular electrostatic charge models: A topographical approach

Electrostatic charge models for molecules have been developed by employing the critical topographical features of the molecular electrostatic potential (MESP ) as the “fitting” criterion. These models include one or more spherical Gaussians for incorporating the continuous electron-charge distribution in addition to the positive valued point charges representing the nuclei. The model parameters (point charges, the orbital exponents, and Gaussian centers) are optimized so as to mimic the extremal characteristics of the corresponding quantum chemical MESP . The test cases reported here include methane, ethylene, and methanol molecules. The charge models developed using the present method are seen to satisfactorily reproduce the ab initio MESP and its extremal features. © 1994 John Wiley & Sons, Inc.     

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 molecular mechanics force field for biologically important sterols

A parameterization has been performed of the biologically important sterols cholesterol, ergosterol, and lanosterol for the CHARMM27 all-atom molecular mechanics force field. An automated parameterization method was used that involves fitting the potential to vibrational frequencies and eigenvectors derived from quantum-chemical calculations. The partial charges were derived by fitting point charges to quantum-chemically calculated electrostatic potentials. To model the dynamics of the hydroxyl groups of the sterols correctly, the parameter set was refined to reproduce the energy barrier for the rotation of the hydroxyl group around the carbon connected to the hydroxyl of each sterol. The frequency-matching plots show good agreement between the CHARMM and quantum chemical normal modes. The parameters are tested in a molecular dynamics simulation of the cholesterol crystal structure. The experimental geometry and cell dimensions are well reproduced. The force field derived here is also useful for simulating other sterols such as the phytosterols sigmasterol, and campesterol, and a variety of steroids.     

Atomic multipoles: Electrostatic potential fit,local reference axis systems,and conformational dependence

Currently, all standard force fields for biomolecular simulations use point charges to model intermolecular electrostatic interactions. This is a fast and simple approach but has deficiencies when the electrostatic potential (ESP) is compared to that from ab initio methods. Here, we show how atomic multipoles can be rigorously implemented into common biomolecular force fields. For this, a comprehensive set of local reference axis systems is introduced, which represents a universal solution for treating atom‐centered multipoles for all small organic molecules and proteins. Furthermore, we introduce a new method for fitting atomic multipole moments to the quantum mechanically derived ESP. This methods yields a 50–90% error reduction compared to both point charges fit to the ESP and multipoles directly calculated from the ab initio electron density. It is shown that it is necessary to directly fit the multipole moments of conformational ensembles to the ESP. Ignoring the conformational dependence or averaging over parameters from different conformations dramatically deteriorates the results obtained with atomic multipole moments, rendering multipoles worse than partial charges. © 2012 Wiley Periodicals, Inc.     

原子簇量子化学从头算的自洽晶体场模型

本文提出一种收敛的点电荷和Hartree-Fock表面势构成的自洽晶体场Madelung势用于原子簇量子化学从头计算。前者的计算类似于核吸引积分的单电子积分, 后者可以通过点群对称性操作从原子簇内的积分矩阵元得到。点电荷的大小和原子簇内对应的原子电荷相等, 其数目以晶体场势收敛为标准确定。介绍加速计算的程序技巧。该模型用于高温超导体YBa2Cu3O7的全电子从头计算并得到一些新结果。     

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.     

Gaussian induced dipole polarization model

A new induced dipole polarization model based on interacting Gaussian charge densities is presented. In contrast to the original induced point dipole model, the Gaussian polarization model is capable of finite interactions at short distances. Aspects of convergence related to the Gaussian model will be explored. The Gaussian polarization model is compared with the damped Thole-induced dipole model and the point dipole model. It will be shown that the Gaussian polarization model performs slightly better than the Thole model in terms of fitting to molecular polarizability tensors. An advantage of the model based on Gaussian charge distribution is that it can be easily generalized to other multipole moments and provide effective damping for both permanent electrostatic and polarization models. Finally, a method of parameterizing polarizabilities is presented. This method is based on probing a molecule with point charges and fitting polarizabilities to electrostatic potential. In contrast to the generic atom type polarizabilities fit to molecular polarizability tensors, probed polarizabilities are significantly more accurate in terms of reproducing molecular polarizability tensors and electrostatic potential, while retaining conformational transferability.     

Prediction of hydration free energies for the SAMPL4 diverse set of compounds using molecular dynamics simulations with the OPLS-AA force field

All-atom molecular dynamics computer simulations were used to blindly predict the hydration free energies of a range of small molecules as part of the SAMPL4 challenge. Compounds were parametrized on the basis of the OPLS-AA force field using three different protocols for deriving partial charges: (1) using existing OPLS-AA atom types and charges with minor adjustments of partial charges on equivalent connecting atoms and derivation of new parameters for a number of distinct chemical groups (N-alkyl imidazole, nitrate) that were not present in the published force field; (2) calculation of quantum mechanical charges via geometry optimization, followed by electrostatic potential (ESP) fitting, using Jaguar at the LMP2/cc-pVTZ(-F) level; and (3) via geometry optimization and CHelpG charges (Gaussian09 at the HF/6-31G* level), followed by two-stage RESP fitting. The absolute hydration free energy was computed by an established protocol including alchemical free energy perturbation with thermodynamic integration. The use of standard OPLS-AA charges (protocol 1) with a number of newly parametrized charges and the use of histidine derived parameters for imidazole yielded an overall root mean square deviation of the prediction from the experimental data of 1.75 kcal/mol. The precision of our results appears to be mainly limited by relatively poor reproducibility of the Lennard-Jones contribution towards the solvation free energy, for which we observed large variability that could be traced to a strong dependence on the initial system conditions.     

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.     

用第一性原理方法获取周期体系中原子的部分电荷

利用量子化学软件包Crystal计算了立方周期性边界条件下液态水体系的静电势(ESP)和静电场(EF).在此基础上,提出了一种由第一性原理方法获取周期体系中原子的部分电荷的快捷方法.该方法把由周期性边界条件引入的平均静电势准mean作为一个拟合参数,通过对第一性原理静电势与Ewald加和法静电势的最小二乘法拟合而实现.值得说明的是,比较静电势与静电场拟合方法,前者的相对拟合误差仅为2%-3%,比后者小一个数量级.考察了四种电荷限制条件下,静电势、静电场拟合的水分子原子部分电荷及偶极矩的分布情况.     

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.     

Conformational dependence of electrostatic potential-derived charges: Studies of the fitting procedure

Atomic monopole “point charges” are routinely determined through a least squares fit to molecular electrostatic potentials [potential-derived (PD) charges]. Previously, it has been shown that these charges vary with variation in molecular conformation. Also, it has been observed that these swings in charges are highly correlated between neighboring atoms. Here, we examine the least squares variance–covariance data matrices for a set of data in the literature and find further indications of high colinearity within the data. These colinearities effectively reduce the dimensionality of the data to a value well below the number of atoms in the molecules. This suggests that the data is not of sufficient dimensionality to support calculation of the charges for all of the atoms in a statistically significant way. We experiment with fixing the charges of atoms whose PD charges reflect large errors in the fit. The resulting estimates of fit of the remaining charges are little degraded from the estimates of fit when the charges of all of the atoms are fit. In addition, the charges that are fit take what would be considered more reasonable and “chemically intuitive” values, often of smaller magnitude. Although most of the free charges continue to vary with molecular conformation, their range is no larger than when all charges were fit and, in some cases, the ranges of the charges for the fit atoms is actually reduced over those that are found when all of the atoms take part in the fitting procedure. The errors of fit are lower and the unconstrained charges appear more reasonable when more chemically “reasonable” charges are used for the fixed values. This suggests that in many cases charges are transferable between molecules. Further, it shows a way to justifiably reduce the large fluctuations in PD charges that occur with variations in conformation. © 1993 John Wiley & Sons, Inc.     

Remarks on the molecular mechanical calculations of functionalized hydrocarbons

Molecular mechanical calculations for hetero-substituted hydrocarbons present certain difficulties that are not encountered in dealing with hydrocarbons. Ways are proposed to overcome such difficulties, sometimes by two-step or iterative computation. The following topics are considered: fitting the force field by using data from studies in solution; ways to estimate atomic charges or, alternatively, bond moments; ways to account for field effects upon atomic charges and bond moments.     

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.     

Multicenter point charge model for high-quality molecular electrostatic potentials from AM1 calculations

The natural atomic orbital/point charge (NAO-PC) model based upon the AM1 wave function has been developed to calculate molecular electrostatic potentials (MEPs). Up to nine point charges (including the core charge) are used to represent heavy atoms. The positions and magnitudes of the eight charges that represent the atomic electron cloud are calculated from the natural atomic orbitals (NAOs) and their occupations. Each hybrid NAO is represented by two point charges situated at the centroid of each lobe. The positions of the centroids and the magnitudes of the charges were obtained by numerical integration of the Slater-type hybrids and the results used to set up polynomials and look-up tables that replace the integration step in the actual MEP calculation. The MEPs calculated using this method are found to be in better agreement with those obtained using RHF/6-31G* than those obtained from the AM1 wave function using Coulson charges or with MOPAC-ESP. The MEP calculations are extremely fast and have, for instance, been incorporated into an interactive graphics package. © 1993 John Wiley & Sons, Inc.     

Numerical fitting of molecular properties to Hermite Gaussians

A procedure is presented to fit gridded molecular properties to auxiliary basis sets (ABSs) of Hermite Gaussians, analogous to the density fitting (DF) method (Dunlap; et al. J. Chem. Phys. 1979, 71, 4993). In this procedure, the ab initio calculated properties (density, electrostatic potential, and/or electric field) are fitted via a linear- or nonlinear-least-squares procedure to auxiliary basis sets (ABS). The calculated fitting coefficients from the numerical grids are shown to be more robust than analytic density fitting due to the neglect of the core contributions. The fitting coefficients are tested by calculating intermolecular Coulomb and exchange interactions for a set of dimers. It is shown that the numerical instabilities observed in DF are caused by the attempt of the ABS to fit the core contributions. In addition, this new approach allows us to reduce the number of functions required to obtain an accurate fit. This results in decreased computational cost, which is shown by calculating the Coulomb energy of a 4096 water box in periodic boundary conditions. Using atom centered Hermite Gaussians, this calculation is only 1 order of magnitude slower than conventional atom-centered point charges.     

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     

水在石墨(0001)面簇模型桥位上吸附的量子化学研究

用从头计算方法对水在石墨(0001)面桥位上的吸附进行了研究.用C₆H₈原子簇模拟石墨表面,在6-31G^*水平上计算了水在不同方向和位置上的吸附能量.研究表明:水在石墨面上的吸附很弱,属于物理吸附;在中性或带负电荷的石墨表面,当水分子中的氢原子靠近石墨面时,体系存在能量最小值,而在带正电荷的表面,当氧原子靠近石墨面时存在稳定的吸附点;不论表面带正电荷还是带负电荷,均对水分子的吸附起增强作用.