Atomic charges derived from electrostatic potentials: A detailed study

A new algorithm for fitting atomic charges to molecular electrostatic potentials is presented. This method is non-iterative and rapid compared to previous work. Results from a variety of gaussian basis sets, including STO-3G, 3-21G and 6-31G*, are presented. Charges for a representative collection of molecules, comprising both first and second row atoms and anions are tabulated. The effects of using experimental and optimized geometries are explored. Charges derived from these fits are found to adequately reproduce SCF dipole moments. A small split valence representation, 3-21G, appears to yield consistently good results in a reasonable amount of time.     

Atomic charges derived from a fast and accurate method for electrostatic potentials based on modified AM1 calculations

Atomic charges derived from a recently described approach to the very rapid computation of AM1 electrostatic potentials (ESP) accurately parallel, but are ca. 20% smaller than, the corresponding HF/6-31G* values. The dipole moments computed from the AM1 charges are virtually identical to those derived directly from the wave function and in rather better agreement with the experimental values than those computed using the HF/6-31G* charges. Unlike other approaches to the semiempirical calculation of ESP-derived charges, the present method also yields near HF/6-31G* quality potentials close to the molecular periphery. For medium-sized organic molecules (40-100 basis functions), the method is approximately two orders of magnitude faster than those involving prior deorthogonalization of AM1 wave function and explicit computation of the full ESP integral matrix. © 1994 by John Wiley & Sons, Inc.     

Molecular electrostatic potentials: Comparison of ab initio and CNDO results

The possibilities of utilization of CNDO wave functions for computing molecular electrostatic potentials are studied by comparison with ab initio results for H₂O and H₂CO.

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Zusammenfassung Die Möglichkeiten der Verwendung von CNDO-Wellenfunktionen zur Berechnung molekularer elektrostatischer Potentiale werden durch Vergleich mit ab initio Rechnungen für H₂O und H₂CO untersucht.

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Résumé Les possibilités d'utilisation de fonctions d'onde CNDO pour le calcul des potentiels électrostatiques moléculaires sont étudiées par comparaison avec des résultats ab initio pour H₂O et H₂CO.

     

Quantitative comparison of molecular electrostatic potential distributions from several semiempirical and ab initio wave functions

A quantitative comparative analysis of molecular electrostatic potential (MEP) distributions generated from different wave functions was carried out. Wave functions were computed by using MNDO, AMl, STO-3G, 3-21G, 4-31G, 6-31G, 4-31G*, 6-31G*, and 6-31G** methods. Ten different compounds, which include usual atoms and groups of biomolecules, such as hydroxyl, carbonyl, amine, amide, imine, double and triple bonds, and heteroaromatic rings, were studied. For each compound, MEP values in the points of a common 3-D grid were computed; thereafter, the similarity between each pair of MEP distributions generated by different methods was assessed. Similarities were measured using the Spearman rank correlation coefficient. A similarity matrix was obtained for each compound. Similarity matrices were averaged and a hierarchical cluster analysis was carried out to classify the different quantum chemical methods. In the compounds studied, the main conclusion is the negligible difference between the pattern of MEP distributions generated from all split valence basis sets (with and without polarization functions). © 1993 John Wiley & Sons, Inc.     

Comparative study between ab initio and semiempirical electrostatic potentials on molecular surfaces

The electrostatic potentials of 21 molecules containing different functional groups has been computed at the ab initio RHF/6-31G* level on a series of solvent accessible surfaces and compared with MNDO, AM1, and PM3-derived pontentials. We analyzed in detail the distribution of electrostatic potentials on the surfaces around their maximum and minimum values and found out that consistently MNDO gives results similar to ab initio potentials. The actual values of the MNDO electrostatic potentials show a systematic deviation from the “correct” results, but the pattern of the MEP distribution on the surface is similar to that of the ab initio results. In contrast, PM3 fails in some cases to give even the correct number or distribution of “hot spots” of potential (low MEP) on the surface. AM1 behaves somewhere between these two semiempirical methods. As a conclusion, MNDO would be suggested as the best approach to analyses requiring a fast and efficient mapping of electrostatic potentials on simplified models of molecular surfaces. © 1993 John Wiley & Sons, Inc.     

Experimental atomic charges from infrared intensities. Comparison with “ab initio” values

Atomic charges can be derived from observed infrared intensities and molecular dipole moments. The atomic charges so drived for a series of simple organic molecules are compared with atomic electron population data computed by quantum-mechanical calculations at various levels. It is shown that experimental charges agree very well with those computed by 6-31G^**.     

Water liquid-vapor equilibria predicted by refined ab initio derived potentials

Coexistence properties for water near the critical point using several ab initio models were calculated using grand canonical Monte Carlo simulations with multiple histogram reweighting techniques. These models, that have proved to yield a good reproduction of the water properties at ambient conditions, perform rather well, improving the performance of a previous ab initio model. It is also shown that bulk geometry and dipole values, predicted by the simulation, can be used and a good approximation obtained with a polarizable rigid water model but not when polarization is excluded.     

Semiempirical treatment of electrostatic potentials and partial charges in combined quantum mechanical and molecular mechanical approaches

A semiempirical treatment of electrostatic potentials and partial charges is presented. These are the basic components needed for the evaluation of electrostatic interaction energies in combined quantum mechanical and molecular mechanical approaches. The procedure to compute electrostatic potentials uses AM1 and MNDO wave functions and is based on one previously suggested by Ford and Wang. It retains the NDDO approximation and is thus both easy to implement and computationally efficient. Partial atomic charges are derived from a semiempirical charge equilibration model, which is based on the principle of electronegativity equalization. Large sets of ab initio restricted Hartee-Fock (RHF/6-31G*) reference data have been used to calibrate the semiempirical models. Applying the final parameters (C, H, N, O), the ab initio electrostatic potentials are reproduced with an average accuracy of 20% (AM1) and 25% (MNDO), respectively, and the ab initio potential derived charges normally to within 0.1 e. In most cases our parameterized models are more accurate than the much more expensive quasi ab initio techniques, which employ deorthogonalized semiempirical wave functions and have generally been preferred in previous applications. © 1996 John Wiley & Sons, Inc.     

Structure and dynamics of mesogens using intermolecular potentials derived from ab initio calculations

A method for the calculation of the two-body intermolecular potential which can be applied to large molecules is presented. Each monomer is fragmented in a number of moieties whose interaction energies are used to recover the interaction energy of the whole dimer. For these reasons this strategy has been called fragmentation reconstruction method (FRM). By a judicious choice of the fragmentation scheme it is shown that very accurate interaction energies can be obtained. The sampling of the potential energy surface of a dimer is then used to obtain intermolecular force fields at several levels of complexity, suitable to be employed in bulk phase computer simulations. Applications are presented for benzene and for some mesogenic molecules which constitute the principal interest of the authors. A number of properties ranging from phase stability, thermodynamic quantities, orientational order parameter and collective dynamics properties are computed and discussed.     

Conformational dependence of electrostatic potential derived charges of a lipid headgroup: Glycerylphosphorylcholine

Atomic monopoles are routinely determined through a least squares fit to molecular electrostatic potentials. We report studies of the variation in atomic monopoles with variation in conformation for the zwitterionic polar head group of lecithins, a common class of lipid. The monopole of one atom, a relatively buried carbon, varied by 1.3 electron units between different conformers. “Exterior” atoms, as seen previously, showed smaller changes in charge and smaller estimated standard deviations. The total charge of local groups of atoms varied less than the charge of individual atoms, indicating that shifts in charge occurred mostly between neighboring atoms. This effect might be reflected in the high correlations seen between charges of many neighboring atoms. These correlations, while present for many logical groupings of atoms (such as within methylene and methyl groups), are curiously absent between some bonded atoms. Monopoles were fit to multiple conformations simultaneously to provide a charge set that could optimally reproduce the electrostatic potential of all the conformers as a means of generating monopoles for molecular dynamics simulations or other studies where conformation varies. In some cases, the charges on chemically equivalent atoms (e.g., the hydrogen atoms in a methyl group) were different by more than their estimated error of fit. These studies lead to the suggestion that a minimum error in reported charges is on the order of 10%. All conformations show that the positive charge of the trimethylalkyl ammonium group is carried by the methyl hydrogens; the total charge on the nine hydrogens is over 2 electron units, counterbalanced by negative monopoles on the carbons. The presence of this diffuse cloud of substantial charge would appear to be a disindicator of the use of a “united” atoms approach for these methyl groups. The effects of the charge variation on intermolecular interactions is also examined.     

Copolymers of carbon dioxide and nitrogen: an AM1 and ab initio computational study

Extending work by various groups on possible dimers, trimers, etc. of dinitrogen and of carbon dioxide, the authors have studied analogous copolymers of N₂ and CO₂ computationally. Twelve cyclic structures were examined with the AM1, HF/3-21G, HF/6-31G* and MP2(FC)/6-31G* methods, and the acyclic “monomer” to “tetramer” HO(C(O)O–N= N–)_nH, n=1–4, were studied at the AM1 and HF/3-21G levels; the cyclic species included 2-oxa-3,4-diazacyclobut-3-ene-1-one, 2-oxa-3,4,5,6-tetraazacyclohexa-3,5-diene-1-one, and various aza/oxa bicyclo[2.2.0] and bicyclo[2.2.2] systems. For the cyclic species, it was concluded that only the MP2(FC)/6-31G* results, which differ considerably from those at the other three levels, are likely to be reliable. These MP2 calculations indicate that only seven of the 12 cyclic structures studied are stationary points (one is a transition structure), and none of them is kinetically stable at room temperature. Although some have high energy densities (ca. 7–10 kJ g⁻¹), their expected low kinetic stabilities seems to make this of little practical value. The acyclic “copolymers” were all relative minima at the AM1 and HF/3-21G levels; unlike the cyclic species, their kinetic stabilities were not investigated directly by comparing the energies of reactants and decomposition transition states. The energy density of the infinite acyclic polymer was found by extrapolation to be 5.1 (AM1) or 5.6 (3-21G) kJ g⁻¹. The calculated vibrational spectra of the MP2 stationary points and of the acyclic molecules gave some indication of instability by the presence of low-frequency modes leading in the limit to decomposition.     

Analysis of a large data base of electrostatic potential derived atomic charges

A large data base of 6-31G*, MNDO, AM1, and PM3 electrostatic potential (ESP) derived point charges of amino acids and monosaccharides is analyzed. We find that MNDO correlates well with 6-31G* ESP derived point charges, while AM1 and PM3 do so quite poorly. Furthermore, scaling MNDO ESP derived point charges enhances the ability of MNDO to reproduce 6-31G* results. We used our data base to attempt to derive a 6-31G* transferable charge model at an atom-by-atom level. We find that it is simple to derive a transferable model for monosaccharides, but for the amino acids statistical difficulties make this a less attractive approach. The transferable charge model for the monosaccharides is slightly better than MNDO, but scaled MNDO charges perform significantly better than the transferable model. We also carried out a QMD simulation on the alanine dipeptide to assess the fluctuations that would be expected in atomic point charges during the course of an MD simulation. Relatively large charge fluctuations are observed and their impact on molecular simulation is addressed. © 1992 by John Wiley & Sons, Inc.     

Semiempirical hyperfine structure and ab initio isotope shift predictions in Zr II

The fine structure of the even‐parity low configurations has been reanalyzed by simultaneous parameterization of the one‐ and two‐body interactions for the model space (4d + 5s)³. Using the calculated eigenfunctions, the magnetic‐dipole A hyperfine constants for the whole 37 existing levels of the model space were predicted and compared partially to those obtained using relativistic configuration‐interaction approach. Moreover, volume shifts (VS) and specific mass shifts (SMS) of numerous configurations of singly ionised zirconium are deduced by means of ab initio estimates combined with a few experimental isotope shift data available in literature: VS(4d¹5s²) = 840 MHz, VS(4d³) = ?649 MHz, VS(4d¹5p²) = ?387 MHz, VS(5s²5p¹) = 1250 MHz, and SMS(4d¹5s²) = ?634 MHz, SMS(4d³) = 484 MHz, SMS(5s²5p¹) = ?1459 MHz, referred to 4d²5s for the pair Zr⁹⁰–Zr⁹². © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Near ab initio quality molecular electrostatic potential maps using hybridization displacement charges at PM3 level and effects of geometrical changes in amino groups

Charge distributions, dipole moments, and molecular electrostatic potentials (MEP) around several molecules consisting of carbon, nitrogen, oxygen, fluorine, sulfur, and chlorine atoms were studied using the PM3 semiempirical method and the results compared with those obtained using ab initio calculations at the RHF/6‐31G** level. Thus it is shown that relative MEP values near different atoms can be obtained using hybridization displacement charges (HDC) obtained by employing PM3 density matrices that usually agree quite satisfactorily with the ab initio ones. Further, positions of ab initio MEP minima are correctly located and the corresponding relative MEP values usually correctly predicted using the PM3(HDC) charges distributed continuously in three dimensions according to the forms of squares of valence s atomic orbitals. The necessary parameters for HDC calculations using the PM3 method were optimized. It is shown how within the frameworks of both PM3 and AM1 methods the π electrons or lone pairs associated with amino group nitrogen atoms and ring atoms can be satisfactorily treated in different situations. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 299–312, 2001     

Accurate molecular electrostatic potentials based on modified PRDDO/M wave functions. I. Electrostatic potential derived atomic charges

A new approach for the calculation of electrostatic potential derived atomic charges is presented. Based on molecular orbital calculations in the PRDDO/M approximation, the new parametrized electrostatic potential (PESP) method is parametrized against ab initio MP2/6-31G** calculations. For a data set of 820 atoms in 145 molecules containing H, C, N. O, F, P, S, Cl, and Br (including hypervalent species), the PESP method achieves a mean absolute error of 0.037 e⁻ with a correlation coefficient of 0.990. Unlike other approximate approaches, no scaling factor is required to improve the agreement between PESP charges and the underlying ab initio results. PESP calculations are an order of magnitude faster than the simplest ab initio calculation (STO-3G) on large molecules while achieving a level of accuracy that rivals much more elaborate ab initio methods. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 955–969, 1997     

Complexes of ammonia with propane and cyclopropane: electrostatic guidelines for ab initio treatment

A model based on the molecular electrostatic potential (MESP) is employed for the investigation of structures and energies of complexes of ammonia with propane and cyclopropane. The electrostatic model geometries are employed as starting points for an ab initio investigation at the self-consistent field and second-order M?ller-Plesset (MP2) levels. The most stable structures of C₃H₆..NH₃ and C₃H₈..NH₃ complexes have the interaction energies of 10.07 kJ/mol and 8.15 kJ/mol, respectively, at the MP2/6-31G(d,p) level. The energy rank order of the structures is not altered with the use of the 6-31++G(d,p) basis set, and the basis␣set superposition error has little effect. The interaction energy decomposition analysis shows that the electrostatic component is dominant over the other ones. MESP topography thus seems to offer valuable hints for predicting the structures of weakly bonded complexes. Received: 8 July 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998     

密度泛函理论和从头算方法对富勒烯分子静电势的比较研究

分别在Hartree-Fock和密度泛函B3LYP理论下,用6-31G*基组研究了C60和C70分子的静电势,比较了这方法计算得到上述分子静电势值的大小,静电势图形和静电势差值曲线,分析了富勒烯的电子相关效应.     

A comparative AM1 and ab initio study of the intramolecular proton transfer in tautomeric organic compounds

The proton-transfer barriers along the intramolecular hydrogen bond in a series of substituted salicylaldehyde anils were calculated using the AM1 SCF semiempirical method. The reliability of this method for the calculation of proton-transfer barriers was analyzed by the comparison of AM1 barriers for a series of different tautomeric organic compounds with those calculated using ab initio SCF and second-order perturbation theory with extended basis sets. In general, the AM1 method systematically overestimates the barrier height. However, this error is approximately constant for given pairs of groups involved in the intramolecular proton transfer. © 1996 John Wiley & Sons, Inc.