Modeling the electric field third-order nonlinear responses of an infinite aggregate of hexatriene chains using the electrostatic interaction model

A classical electrostatic polarization scheme using the additive distribution procedure has been applied to determine the static longitudinal polarizability and second hyperpolarizability of a all-trans hexatriene molecule in an infinite stretched fiber. The parameters have been derived from ab initio coupled-perturbed Hartree-Fock calculations and the electrostatic scheme has been validated via comparison with ab initio results on small clusters. Upon packing, the polarizability of all-trans hexatriene increases by 7% whereas the second hyperpolarizability increases by as much as 61%. These increases result from the balance between the enhancement of the (hyper)polarizability due to collinear packing and the reduction associated with lateral packing.     

Ab initioLCAO-MO-SCF calculation of the electrostatic molecular potential of chlorpromazine and promazine

The electrostatic potential V( r ) arising from the ab initio LCAO-MO-SCF wave functions of chlorpromazine (CPZ ) and promazine (PZ ) has been calculated and discussed. In this approximation, the most probable sites of attack and reaction paths of electrophilic reagents are pointed out and compared. The analysis of V( r ) shows that the phenothiazine group has strong nucleophilic properties which are influenced by the phenothiazine substituent and that the electrostatic reactivity of CPZ and PZ is decidedly different near the phenothiazine substituent and similar near the side chain N atom. The dependence of V( r ) on the accuracy of the wave function has also been discussed by comparing some ab initio results on pyrrole, pyrazole, and imidazole obtained with a large basis set with an ab initio minimum basis set and with CNDO calculations.     

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.     

Hyperpolarizabilities of hydrogen-bonded complexes of phenol derivatives with ammonia: PM3 and ab initio studies

Polarizability and first hyperpolarizability values of the hydrogen-bonded complexes formed by nitrosubstituted phenols with ammonia have been calculated using PM3 and ab initio (STO-3G) methods. It has been shown that enhancement of the polarizability (Δα) as well as the first hyperpolarizability (Δβ) of the complex arises from the hydrogen bond interaction between the phenol derivative and ammonia.     

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.     

A finite field method for calculating molecular polarizability tensors for arbitrary multipole rank

A finite field method for calculating spherical tensor molecular polarizability tensors α_lm;l′m′ = ?Δ_lm/??_l′m′* by numerical derivatives of induced molecular multipole Δ_lm with respect to gradients of electrostatic potential ?_l′m′* is described for arbitrary multipole ranks l and l′. Interconversion formulae for transforming multipole moments and polarizability tensors between spherical and traceless Cartesian tensor conventions are derived. As an example, molecular polarizability tensors up to the hexadecapole–hexadecapole level are calculated for water using the following ab initio methods: Hartree–Fock (HF), Becke three‐parameter Lee‐Yang‐Parr exchange‐correlation functional (B3LYP), Møller–Plesset perturbation theory up to second order (MP2), and Coupled Cluster theory with single and double excitations (CCSD). In addition, intermolecular electrostatic and polarization energies calculated by molecular multipoles and polarizability tensors are compared with ab initio reference values calculated by the Reduced Variation Space method for several randomly oriented small molecule dimers separated by a large distance. It is discussed how higher order molecular polarizability tensors can be used as a tool for testing and developing new polarization models for future force fields. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

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.     

All-trans- and t,T,t,C,t,T,t-deca-1,3,5,7,9-Pentaenes: Ab Initio Structures,Vibrational Analyses,and Some Regularities in the Series of Related Molecules

Total geometry optimization and calculation of the force constants for all-transand t,T,t,C,t,T,tdeca-1,3,5,7,9-pentaene were carried out at the ab initio, HF/6-31G level. The HF/6-31G//HF/ 6-31G force fields were modified using empirical scale factors transferred from trans-buta-1,3-diene augmented by an additional scale factor for the central formal carbon-carbon double bond coordinates (determined previously for all-trans-hexa-1,3,5-triene). The total number of scale factors was seven. The vibrational problems for both decapentaenes were solved using the respective scaled HF/6-31G//HF/6-31G force field. Infrared intensities and Raman activities were calculated from the unscaled HF/6-31G//HF/6-31G force fields. Complete assignment of all the fundamental vibrational frequencies is given. Geometrical parameters, vibrational frequencies and force constants are compared with the corresponding values of buta-1,3-diene, hexa-1,3,5-triene and octa-1,3,5,7-tetraene. Regularities in the properties of this molecular series are discussed. Special attention is given to the possibility of using the vibrational spectra for detection of distortions from the regular trans structure of these oligoenes.     

A polarizable electrostatic model of the N‐methylacetamide dimer

Our previously developed polarizable electrostatic model is applied to isolated N‐methylacetamide (NMA) and to three hydrogen‐bonded configurations of the NMA dimer. Two versions of the model are studied. In the first one (POL1), polarizability along the valence bonds is described by induced bond charge increments, and polarizability perpendicular to the bonds is described by cylindrically isotropic induced atomic dipoles. In the other version (POL2), the induced bond charge increments are replaced by induced atomic dipoles along the bonds. The parameterization is done by fitting to ab initio MP2/6‐31++G(d,p) electric potentials. The polarizability parameters are determined by subjecting the NMA molecule to various external electric fields. POL1 turns out to be easier to optimize than POL2. Both models reproduce well the ab initio electric potentials, molecular dipole moments, and molecular polarizability tensors of the monomer and the dimers. Nonpolarizable models are also investigated. The results show that polarization is very important for reproducing the electric potentials of the studied dimers, indicating that this is also the case in hydrogen bonding between peptide groups in proteins. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1933–1943, 2001     

Force field for computation of conformational energies,structures, and vibrational frequencies of aromatic polyesters

A CFF93¹ all-atom force field for aromatic polyesters based on ab initio calculations is reported. The force field parameters are derived by fitting to quantum mechanical data which include total energies, first and second derivatives of the total energies, and electrostatic potentials. The valence parameters and the ab initio electrostatic potential (ESP) derived charges are then scaled to correct the systematic errors originating from the truncation of the basis functions and the neglect of electron correlation in the HF/6-31G* calculations. Based on the force field, molecular mechanics calculations are performed for homologues of poly(p-hydroxybenzoic acid) (PHBA) and poly(ethylene terephthalate) (PET). The force field results are compared with available experimental data and the ab initio results. © 1994 by John Wiley & Sons, Inc.     

Implementation of ab initio multiple spawning in the Molpro quantum chemistry package

The ab initio multiple spawning (AIMS) method has been developed to solve the electronic and nuclear Schrodinger equations simultaneously for application to photochemical reaction dynamics. We discuss some details of the implementation of AIMS in the Molpro program package. A few aspects of the implementation are highlighted, including a new multiple timescale integrator and a scheme for solving the coupled-perturbed multiconfiguration self-consistent field (CP-MCSCF) equations in the context of ab initio molecular dynamics. The implementation is very efficient and we demonstrate calculations on the photoisomerization of ethylene using more than 5000 trajectory basis functions. We have included the capability for hybrid quantum mechanics/molecular mechanics (QM/MM) simulations within AIMS, and we investigate the role of an argon solvent in the photoisomerization of ethylene. Somewhat surprisingly, the surrounding argon has little effect on the timescale of non-adiabatic quenching in ethylene.     

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.     

Ab initio calculations of electrostatic potentials and deformation densities for a series of choline ester model systems

Ab initio LCAO-MO-SCF calculations using a double zeta basis set have been performed for the methyl esters of acetic acid, carbamic acid, methylcarbonic acid, and trifluoracetic acid, in order to model the corresponding choline esters. The systems have been compared by means of population analyses, electron density differences, electrostatic potentials and potential differences. The significance of the electrostatic potential in connection with crystal structure and packing has been studied. The differences in the proton affinity of the compounds have been correlated to differences in the potentials.     

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     

Cation-binding to biomolecules

Ab initio SCF computations indicate that Mg²⁺ should bind essentially to the oxygen atoms of uracil, the remaining part of the base being rather repulsive towards such an interaction. The Coulombic component predominates in the interaction, the essential feature of which may thus be deduced from the study of the molecular electrostatic potential of uracil. These ab initio results contradict an earlier CNDO prediction that the binding of uracil and Mg²⁺ should occur preferentially at the C₅=C₆ double bond of the base. It is shown that the CNDO result is an artifact due to an exaggeration by this method of the charge transfer between the ligand and the cation. The small amount of available experimental data seem in favor of the ab initio results.     

Molecular Structure of ortho-Fluoronitrobenzene Studied by Gas Electron Diffraction and Ab Initio MO Calculations

The molecular structure of ortho-fluoronitrobenzene (o-FNB) has been investigated by gas-phase electron diffraction and ab initio MO calculations. The geometrical parameters and force fields of o-FNB were calculated by ab initio and DFT methods. The obtained force fields were used to calculate vibrational amplitudes required as input parameters in an electron diffraction analysis. Within the experimental error limits, the geometrical parameters obtained from the gas-phase electron diffraction analysis are mostly in agreement with the results obtained from the ab initio calculations. The main results are: the molecular geometry of o-FNB is nonplanar with a dihedral angle about C–N of 38(3)°. The r _g (C–F) bond is shortened to 1.307(13) Å in comparison with r _g (C–F) = 1.356(4) Å in C₆H₅F.     

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.     

Multiobjective evolutionary algorithm with many tables for purely ab initio protein structure prediction

This article focuses on the development of an approach for ab initio protein structure prediction (PSP) without using any earlier knowledge from similar protein structures, as fragment‐based statistics or inference of secondary structures. Such an approach is called purely ab initio prediction. The article shows that well‐designed multiobjective evolutionary algorithms can predict relevant protein structures in a purely ab initio way. One challenge for purely ab initio PSP is the prediction of structures with β‐sheets. To work with such proteins, this research has also developed procedures to efficiently estimate hydrogen bond and solvation contribution energies. Considering van der Waals, electrostatic, hydrogen bond, and solvation contribution energies, the PSP is a problem with four energetic terms to be minimized. Each interaction energy term can be considered an objective of an optimization method. Combinatorial problems with four objectives have been considered too complex for the available multiobjective optimization (MOO) methods. The proposed approach, called “Multiobjective evolutionary algorithms with many tables” (MEAMT), can efficiently deal with four objectives through the combination thereof, performing a more adequate sampling of the objective space. Therefore, this method can better map the promising regions in this space, predicting structures in a purely ab initio way. In other words, MEAMT is an efficient optimization method for MOO, which explores simultaneously the search space as well as the objective space. MEAMT can predict structures with one or two domains with RMSDs comparable to values obtained by recently developed ab initio methods (GAPF_CG, I‐PAES, and Quark) that use different levels of earlier knowledge. © 2013 Wiley Periodicals, Inc.