Estimation of pKa for organic oxyacids using calculated atomic charges

A method for the estimation of pK_a from empirically calculated atomic charges has been developed and tested on a diverse set of organic oxyacids. The approach involves a comparison of the atomic charges calculated for both the acid and the negative ion that is formed after loss of the acidic proton. These charges have been used in conjunction with the familiar concepts of induction and resonance to develop an accurate formula to predict pK_a. Results for a set of 135 compounds, including alcohols, phenols, and carboxylic acids, yielded a fit of pK_a with r = 0.993 and an rms error of 0.455. © John Wiley & Sons, Inc.     

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     

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.     

Rapid Estimation of Basis Set Error and Correlation Energy Based on Mulliken Charges and Mulliken Matrix with the Small 6-31g* Basis Set

Good, density functional quality (B3LYP/6-31G*) ground state total electronic energies have been approximated using single point Hartree–Fock-self consistent field (HF-SCF/6-31G*) total energies and Mulliken partial charges versus. Mulliken matrix (electrons assigned to atoms and atoms pairs from Mulliken population analysis). This is a development of our rapid estimation of basis set error and correlation energy from partial charges (REBECEP) method, published earlier (see references [21,22,30]. The development is as follows: (1) A larger set of atoms (H, C, N, O, F, Si, P and S) are considered as building blocks for closed shell, neutral, ground state molecules at their equlibrium geometry; (2) geometries near equilibrium geometry are also considered; (3) A larger set, containing 115 molecules, was used to fit REBECEP parameters; (4) most importantly, electrons belonging to chemical bonds (between atom pairs) are also considered (Mulliken matrix) in addition to the atoms (Mulliken charges), using more REBECEP parameters to fit and yielding a more flexible algorithm. With these parameters a rather accurate closed shell ground state electronic total energy can be obtained from a small basis set HF-SCF calculation in the vicinity of optimal geometry. The 3.3 kcal/mol root mean square deviation of REBECEP improves to 1.5 kcal/mol when using Mulliken matrix instead of Mulliken charges.     

Ab initio compact group model potentials for describing environment effects in cluster calculations

A method for the determination of ab initio group model potentials within the Hartree–Fock framework is reported. Following the theory of separability of many electron systems, a new way to incorporate the effect of complete chemical entities by means of polycenter compact model potentials is presented. The interaction between active and frozen electrons is partitioned as a sum of long- and short-range terms. The long-range term is described as the effect of −2e charges placed in the center of the charge of the frozen group molecular orbitals; the short-range one, the exchange and Pauli repulsion, is developed as a spectral representation in a nonorthogonal basis set. An algorithm to solve the problem associated with the rotation of the polycenter model potential is presented and implemented in an all-purpose quantum chemical program. In order to check the method, a group model potential for H₂O was obtained and tested. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1145–1152, 1999     

Consensus bond-charge increments fitted to electrostatic potential or field of many compounds: Application to MMFF94 training set

Bond-charge increments (BCIs) are additive parameters used to assign atomic charges for the MMFF force field. BCI parameters are classified parsimoniously according to two atom types and the bond order. We show how BCIs may be fitted rapidly by linear least squares to the calculated ab initio electrostatic potential (ESP) or to the electrostatic field. When applied simultaneously to a set of compounds or conformations, the method yields consensus values of the BCIs. The method can also derive conventional “ESP-fit” atomic charges with improved numerical stability. The method may be generalized to determine atom multipoles, multicenter charge templates, or electronegativities, but not polarizability or hardness. We determine 65 potential-derived (PD) BCI parameters, which are classified as in MMFF, by fitting the 6-31G* ESP or the electrostatic field of the 45 compounds in the original MMFF94 training set. We compare the consensus BCIs with classified BCIs that were fit to each molecule individually and with “unique-bond” BCIs (ESP-derived atom charges). Consensus BCIs give a satisfactory representation for about half of the structures and are robust to the adjustment of the alkyl CH bond increment to the zero value employed in MMFF94. We highlight problems at three levels: Point approximation: the potential near lone pairs on sulfur and to some extent nitrogen cannot be represented just by atom charges. Bond classification: BCIs classified according to MMFF atom types cannot represent all delocalized electronic effects. The problem is especially severe for bonds between atoms of equivalent MMFF type, whose BCI must be taken as zero. Consensus: discrepancies that occur in forming the consensus across the training set indicate the need for a more detailed classification of BCIs. Contradictions are seen (e.g., between acetic acid and acetone and between guanidine and formaldehydeimine). We then test the three sets of PD-BCIs in energy minimizations of hydrogen-bonded dimers. Unique-bond BCIs used with the MMFF buffered 14–7 potential reproduce unscaled quantum chemical dimer interaction energies within 0.9 kcal/mol root mean square (or 0.5, omitting two N-oxides). These energies are on average 0.7 (or 0.5) kcal/mol too weak to reproduce the scaled quantum mechanical (SQM) results that are a benchmark for MMFF parameterization. Consensus BCIs tend to weaken the dimer energy by a further 0.4–0.6 kcal/mol. Thus, consensus PD-BCIs can serve as a starting point for MMFF parameterization, but they require both systematic and individual adjustments. Used with a “harder” AMBER-like Lennard–Jones potential, unique-bond PD-BCIs without systematic adjustment give dimer energies in fairly good agreement with SQM. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1495–1516, 1999     

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.     

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.     

Accurate thermochemistry from corrected Hartree–Fock results: rapid estimation of nearly experimental quality total energy using the small 6-31G(d) basis set

Gaussian-3 ground-state total electronic energies have been approximated using single point 6-31G(d) basis set Harteee–Fock self-consistent-field (HF-SCF) total energies and partial charges based on our earlier rapid estimation of correlation energy from partial charges method. Sixty-five closed-shell neutral molecules (composed of H, C, N, O, and F atoms) of the G2/97 thermochemistry database were selected for the present study. The main feature in this work is that the␣basis set error has been treated by the least squares fit of rapid estimation of basis set error and correlation energy from partial charges (REBECEP) atomic parameters. With these parameters a rather accurate closed-shell ground-state electronic total energy can be obtained from a small basis set HF-SCF calculation in the vicinity of stationary points. The average absolute deviation of the best REBECEP enthalpies of formation from the experimental enthalpies of formation is 1.39 kcal/mol for the test set of 65 enthalpies of neutral molecules. Received: 11 December 2000 / Accepted: 6 February 2001/Published online: 11 October 2001     

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.     

Ab initio and molecular mechanics study of n-phenyl phthalimide and its crystal structure

Ab initio molecular orbital calculations are reported on the energetics for torsional motion of N-phenyl phthalimide using 3-21G, 6-31G, and 6-31G^** basis sets and incorporating electron correlation effects for selected geometries. With the largest basis set, a minimum energy is found for a torsion angle of 59.2°. Atomic charges are assigned to the molecules on the basis of a least-squares fit to the molecular electrostatic potential. This information is then used in molecular mechanics calculations of the crystal structure, where the calculated unit cell parameters are in good agreement with those observed experimentally.     

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.     

Theoretical study of 3d‐metal mononitrides using DFT method

3d‐Metal mononitrides are studied using the density functional theory method. The lowest spin state for these dimers is obtained using the B3LYP hybrid functional with the 6‐311+G* basis set. The equilibrium geometries, vibrational frequencies, binding energies, Mulliken, and natural orbital population analysis charges, natural orbital electronic configuration, electron affinity, and ionization potential are obtained. Mulliken as well as natural orbital population analysis charges indicate that for all dimers, in cations most of the positive charge localized on the transition metal atom where in anions most of the negative charge localized on nitrogen atom. The binding energies for 3d‐metal mononitrides are higher than those for monocarbides and monoxides. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Electrosurface characteristics of titanium dioxide in solutions of simple electrolytes: II. Calculation of electrical double layer parameters of TiO<Subscript>2</Subscript> from adsorption and electrokinetic measurements

A set of experimental data is used to calculate parameters of a 2-pK model for charging titanium dioxide surface in NaCl solutions, as well as the capacities, charges, and potentials of electrical double layers in terms of different models. It is shown that, according to the Graham model, good agreement between the experimental and calculated surface charges can only be achieved at variable capacity of the second capacitor.     

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.     

Ab initioSCF study of guanidine and substituted guanidines

Proton affinities, geometries with optimized parameters, and net atomic charges are reported for guanidine-, methyl-, amino-, and fluoro-substituted guanidines. The results are obtained using the ab initio SCF method as implemented by the GAUSSIAN-70 computer program with a 6–31G basis set. Basicity is discussed in terms of electron distribution and intramolecular attraction forces.     

An ab initio study of crystal field effects,part 3: Solid- and gas-phase geometry of formamide,modeling the changes in a peptide group due to hydrogen bonds

A model of the solid state of formamide is constructed by optimizing a central molecule in an electrostatic field of the proper symmetry. Attention is paid to the way the electrostatic charges are obtained. Point charges obtained from a Mulliken population analysis yield a final set of atomic charges in the central molecule that agree reasonably well with those obtained experimentally after ak-refinement of formamide. Point charges from a so-called stockholder partitioning agree slightly less. Furthermore, the simple crystal field adaptation of standard ab initio methods reproduces within experimental limits the differences in C=O and C-N lengths, observed between the gas-phase and the solid state geometry. Again, a Mulliken field agrees slightly better than a stockholder field, but the difference in performance is statistically insignificant. In a survey of 221 high-quality single-crystal x-ray determinations of compounds containing the peptide group N-C=O, we found evidence supporting quantitatively the conclusion that the increase of C=O and the decrease of C-N bond length in the gas-to-solid transition is dominated by the effects of hydrogen bonding. It was shown that the C=O bond lengthens by about 0.011 å per H-bond it accepts, while the N-C bond diminishes by about 0.015 å per H-bond it donates.Part 2, see Ref. [5].     

A generalization of the charge equilibration method for nonmetallic materials

Assigning effective atomic charges that properly reproduce the electrostatic fields of molecules is a crucial step in the construction of accurate interatomic potentials. We propose a new approach to calculate these charges, which as previous approaches are, is based on the idea of charge equilibration. However, we only allow charge to flow between covalently bonded neighbors by using the concept of so-called split charges. The semiempirical fit parameters in our approach do not only reflect atomic properties (electronegativity and atomic hardness) but also bond-dependent properties. The new method contains two popular but hitherto disjunct approaches as limiting cases. We apply our methodology to a set of molecules containing the elements silicon, carbon, oxygen, and hydrogen. Effective charges derived from electrostatic potential surfaces can be predicted more than twice as accurately as with previous works, at the expense of one additional fit parameter per bond type controlling the polarizability between two bonded atoms. Additional bond-type parameters can be introduced, but barely improve the results. An increase in accuracy of only 30% over existing techniques is achieved when predicting Mulliken charges. However, this could be improved with additional bond-type parameters.