Accurate molecular electrostatic potentials based on modified PRDDO/M wave functions: III. Extension of the PESP method for calculation of electrostatic potential-derived atomic charges to compounds containing Li+, Na+, Mg2+, K+, Ca2+, Zn2+, and I

The PESP (Parameterized ElectroStatic Potential) method for calculating molecular electrostatic potentials, previously parameterized for H, C, N, O, F, P, S, Cl, and Br, is extended to molecules containing Li⁺, Na⁺, Mg²⁺, K⁺, Ca²⁺, Zn²⁺, and I. For a collection of 166 molecules containing 1668 atoms with at least one metal or iodine atom, PESP achieves an average absolute deviation in electrostatic potential-derived atomic charges of 0.042e⁻ compared with ab initio MP2/6-31G** calculations, with a correlation coefficient of 0.996. For a larger data set, consisting of 311 molecules encompassing all of the 16 elements just listed (2488 total atoms), PESP achieves an average absolute deviation of 0.040e⁻ and a correlation coefficient of 0.995. PESP calculations are an order of magnitude faster than the simplest ab initio method (STO-3G) on large molecules, while achieving a level of accuracy that rivals much more elaborate ab initio methods. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1456–1469, 1998     

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     

A theoretical study of the rotational isomers of nitrosomethanol by semiempirical (AM1) and ab initio methods

The conformational potential energy surface as a function of the two internal torsion angles in C-nitrosomethanol has been obtained using the semiempirical AM1 method. Optimized geometries are reported for the local minima on this surface and also for the corresponding points on the HF/6-31G, 6-31G*, and 6-31G** surfaces. All methods predict cis and trans minima which occur in degenerate pairs, each pair being connected by a transition state of C_s symmetry. The AM1 structures are found to compare well with the corresponding ab initio structures. Ab initio HF/6-31G and HF/6-31G* harmonic vibrational frequencies are reported for the cis and trans forms of nitrosomethanol. When scaled appropriately the calculated frequencies are found to compare well with experimental frequencies. The ab initio calculations predict the energy barrier for cis → trans isomerization to be between 5.8 and 6.5 kcal/mol with the trans → cis isomerization barrier lying between 2.3 and 6.5 kcal/mol. The corresponding AM1 energy barriers are around 1 kcal/mol lower in energy. The ab initio calculations predict the barrier to conversion between the two cis rotamers to be very small with the AM1 value being around 1 kcal/mol. Both AM1 and ab initio calculations predict interconversion between trans rotamers to require between 1.2 and 1.4 kcal/mol.     

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.     

New approach to the rapid semiempirical calculation of molecular electrostatic potentials based on the am1 wave function: Comparison with ab initio hf/6-31g* results

A new approach to the computation of molecular electrostatic potentials based on the AM1 wave function is described. In contrast to the prevailing philosophy, but consistent with the underlying NDDO approximation, no deorthogonalization of the wave function is carried out. The integrals required for the computation of the electronic contributions to the molecular electrostatic potential are evaluated in a manner similar to that of the AM1 core-electron attraction integrals, while the nuclear contributions are computed using a new semiempirical function—Z_A(S^AS^A, S^pS^p)[1 + exp[ – ω_A(R_Ai – δ_A)]]—where the atomic parameters ω_A and δ_A are obtained by calibration against the results of ab initio HF/6-31G* calculations. Isopotential contour maps for guanine and cytosine obtained with the new method are qualitatively almost indistinguishable from their HF/6-31G* counterparts, while quantitative comparisons for the minima for a wide range of molecules are reproduced with an rms error of 5.2 kcal mol^?1. The locations of the “lone-pair” minima for a wide range of heterosubstituted organic molecules generally fall within 0.02 Å of the corresponding HF/6-31G* minima while those in the π-regions of unsaturated molecules are generally within 0.2 Å. Because of the rapid integral evaluation, the fully semiempirical method described here is extremely economical. For example, for the guanine–cytosine base pair it is >500 times faster than calculations in which the complete integral matrix is computed analytically from the deorthogonalized AM1 wave function. © John Wiley & Sons, Inc.     

Comparative study of the molecular electrostatic potential obtained from different wavefunctions. Reliability of the semiempirical MNDO wavefunction

A systematic analysis of the molecular electrostatic potential (MEP) is presented. This study has been performed with a twofold purpose: first, to study the MEP dependence with regard to the quality of the basis set used to compute the ab initio SCF wavefunction and second, to develop and to assess a new strategy for computing isoelectrostatic potential maps using the semiempirical MNDO wavefunction. The only differences between this procedure and the ab initio SCF MEP computation lie in the freezing of the inner electrons and in the origin of the first-order density matrix. The statistical analysis of MEPs computed for a large number of molecules from MNDO wavefunction and ab initio SCF wavefunctions obtained using STO-3G, 4-31G, 6-31G, 4-31G*, 6-31G*, and 6-31G** basis sets points out the ability of any wavefunction to reproduce the general topological characteristics of the MEP surfaces. Nevertheless, split-valence basis sets including polarization functions are necessary to obtain accurate MEP minimum energy values. MNDO wavefunction tends to overestimate the MEP minima depth by a constant factor and shows an excellent ability to reflect the relative variation of MEP minima energies derived from a rather sophisticated (6-31G*) basis set, lacking of the shortcomings detected in the semiempirical CNDO approximation.     

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.     

Ab initio study of the ground and excited states of HCP and its isomer HPC

The potential energy surface of HCP converting to HPC in its ground electronic state has been investigated with ab initio methods at levels up to MP2/6-311G**//MP4/6-311G** as well as TZV + + ** CASSCF. All geometries are fully optimized and compare favorably to previous theoretical and experimental values. The HCP molecule is predicted to be 85.4 kcal/mol lower in energy than its linear isomer at the-MP2/6-31G*//MP2/6-31G* level. The energy barrier for hydrogen rearrangement is found to be merely 2.3 kcal from the HPC end. CASSCF studies were initiated to clarify the low barrier and lent support to a flat surface as HPC converts to stable, linear HCP at the TZV + + ** level. CASSCF also predicts that HPC is unstable with respect to bending. Harmonic vibrational frequencies for HCP results in 5% accuracy or better. A bent triplet is found to be the lowest excited state using the CASSCF method. © 1993 John Wiley & Sons, Inc.     

Comparison of NDDO and quasi-ab initio approaches to compute semiempirical molecular electrostatic potentials

The suitability of the two most widely used strategies to compute semiempirical MEPs is examined. For this purpose, MEP minima, electrostatic charges, and dipoles for a large number of molecules were computed at the AM1, MNDO, and PM3 levels using both the NDDO strategy developed by Ferenczy, Reynolds, and Richards and our own quasi-ab initio method. Results demonstrate that the quasi-ab initio is preferred over the NDDO method for the computation of MEP minima. It is also found that the best set of semiempirical charges and dipoles are obtained using either the AM1 NDDO or the MNDO quasi-ab initio methods. In these two cases, the quality of the results is fully comparable with 6-31G* values. © 1994 by John Wiley & Sons, Inc.     

Quantum Chemical Model of a Lysozyme+Substrate Complex and a Cooperative Process in It

This paper presents an ab initio (RHF/6-31G** and MP2(full)6-31G**) and density functional (DFT) study of the structure and energetics of formation of an intermolecular complex which is the simplest model of an active center lysozyme with a substrate. The calculated energy of complex formation is 41.4 (RHF), 53.4 (MP2), and 52.7 kcal/mole (DFT). The proton transfer reaction is a concerted reaction having an energy barrier of 41.1 (RHF), 31.6 (MP2), and 25.3 (DFT) kcal/mole.     

An ab initio study of heterodienophiles addition to 2,3-diaza-1,3-butadiene: An example of endo-lone-pair effect on the reaction energy barrier

Transition states for the Diels-Alder reactions of 2,3-diaza-1,3-butadiene with ethylene, formaldehyde, formaldimine, cis- and trans- diazene, and nitrosyl hydride were located by ab initio molecular orbital calculations. The bond orders of the new forming bonds have been used to determine the asynchronicity of the reactions. Ab initio calculations show that the energy barrier for the hetero-Diels-Alder reactions is relatively high. The highest energy barrier of 34.76 kcal/mol calculated at the MP4/6-31G*//MP2/6-31G* level was found for the exo-cis-diazene addition to 2,3-diaza-1,3-butadiene. In all cases, when two diastereomeric transition structures are possible, the one with the endo hydrogen, exo lone pair was predicted to have a lower activation barrier. This behavior can be explained by the n-π and n-n loan pair repulsion interaction between the dienophile and diene heteroatoms in the corresponding transition state. The barrier is higher for those reactions which in the transition state have more lone electron pairs. Also, the barrier is higher when the lone pairs are endo oriented than when they are exo oriented in the transition state. © 1996 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.     

Molecular mechanics studies (MM4) of sulfides and mercaptans

The MM4 force field has been extended to the title class of compounds. The vibrational spectra, structures, conformational equilibria, and heats of formation have been studied for 47 conformers of 29 compounds. In general, the properties may be calculated with accuracy that is competitive with that for hydrocarbons. The structures are better fit than previously because of the inclusion of a torsion–bend interaction term, which has its origin in the lone pair (Bohlmann) effect. Available experimental data do not suffice to yield detailed torsional potentials, or geometries as a function of torsion angle, and these quantities were determined by ab initio calculations at the MP2/6-31G* level. The rms error in the calculated frequencies of seven representative structures (with a total of 64 experimental and 96 ab initio frequencies) is 25 cm⁻¹. The heats of formation for 23 compounds have a weighted rms error of 0.36 kcal/mol. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1827–1847, 1997     

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.     

OPLS all-atom force field for carbohydrates

The OPLS all-atom (AA) force field for organic and biomolecular systems has been expanded to include carbohydrates. Starting with reported nonbonded parameters of alcohols, ethers, and diols, torsional parameters were fit to reproduce results from ab initio calculations on the hexopyranoses, α,β-d -glucopyranose, α,β-d -mannopyranose, α,β-d -galactopyranose, methyl α,β-d -glucopyranoside, and methyl α,β-d -mannopyranoside. In all, geometry optimizations were carried out for 144 conformers at the restricted Hartree–Fock (RHF)/6–31G* level. For the conformers with a relative energy within 3 kcal/mol of the global minima, the effects of electron correlation and basis-set extension were considered by performing single-point calculations with density functional theory at the B3LYP/6–311+G** level. The torsional parameters for the OPLS-AA force field were parameterized to reproduce the energies and structures of these 44 conformers. The resultant force field reproduces the ab initio calculated energies with an average unsigned error of 0.41 kcal/mol. The α/β ratios as well as the relative energies between the isomeric hexopyranoses are in good accord with the ab initio results. The predictive abilities of the force field were also tested against RHF/6–31G* results for d -allopyranose with excellent success; a surprising discovery is that the lowest energy conformer of d -allopyranose is a β anomer. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1955–1970, 1997     

Ab initio and molecular mechanics (MM2 and MM3) calculations of nonconjugated positively charged nitrogen-containing compounds

High-level ab initio calculations have been performed on N-methyl-N-methyleneammonium and related compounds to obtain accurate rotational barriers, structures, and vibrational frequencies. The 6-31G** basis set has been utilized at the Hartree-Fock level of theory for these calculations because little experimental data are available. The MM2(91) and MM3(94) force fields have been parameterized to include these nonconjugated charged nitrogen-containing compounds. Molecular mechanics geometries and vibrational frequencies compare well with the ab initio results. © 1995 John Wiley & Sons, Inc.     

Ab initio investigation of tautomeric stability,molecular structure,and internal rotation of methylphosphonic dicyanide,methoxydicyanophosphine, and their isocyano analogs

The equilibrium geometric parameters and structures of the transition states of internal rotation for MeP(O)(CN)₂, McOP(CN)₂, and their isocyano analogs, MeP(O)(NC)₂ and MeOP(NC)₂, have been calculated by theab initio SCF method and with inclusion of electron correlation effects according to the second-order Muuller-Plesset perturbation theory (MP2). At both levels the 6-31G* basis set has been used. The estimation of relative stability of these tautomeric forms depends largely on the calculation level. The total energies of the cyanides calculated by the MP2 method are 25–30 kcal mol^–1 lower than those of the corresponding isocyanides. The oxo-tautomeric forms containing four-coordinate phosphorus are 15–25 kcal mol^–1 more stable than the three-coordinate phosphorus aci-derivatives. The internal rotation potential curves of the aci-forms are characterized by a deep minimum for thetrans-arrangement of the methoxy group and phosphorus lone electron pair. Two additional less clearly pronounced minima are located symmetrically on both sides of the weak maximum, which corresponds to thecis-arrangement. The equilibrium oxo-form structures have a staggered configuration of the methyl group with respect to the phosphorus atom bonds.Translated from izvestiyaAkademii Nauk. Seriya Khimicheskaya, No. 5, pp. 1104–1115, May, 1996.     

Molecular electrostatic potentials and partial atomic charges from correlated wave functions: Applications to the electronic ground and excited states of 3-methylindole

Procedures have been developed to generate molecular electrostatic potentials based on correlated wave function from ab initio or semiempirical electronic structure programs. A new algorithm for point-wise sampling of the potential is described and used to obtain partial atomic charges via a linear, least squares fit between classical and quantum mechanical electrostatic potentials. The proposed sampling algorithm is efficient and promises to introduce less rotational variance in the potential derived partial charges than algorithms applied previously. Electrostatic potentials and fitted atomic charges from ab initio (HF/6–31G* and MP2/6-31G*) and semiempirical (INDO/S; HF, SECI, and SDCI) wave functions are presented for the electronic ground (S₀) and excited (¹L_b, ¹L_a) states of 3-methylindole. © 1992 by John Wiley & Sons, Inc.     

The effect of electron correlation on the conformational space of melatonin

The pineal gland hormone melatonin regulates several physiological processes including circadian rhythm and also alleviates oxidative stress‐induced degenerative diseases. In spite of its important biological roles, no high level ab initio conformational study has been conducted to reveal its structural features. In this work, the conformational flexibility of melatonin was investigated using correlated ab initio calculations. Conformers, obtained previously at the Hartree‐Fock level (HF/6‐31G*), were fully optimized using second order Møller‐Plesset perturbation theory applying the frozen core approximation (MP2(FC)/6‐31G*). Furthermore, single‐point MP4(SDQ,FC)/6‐31G*//MP2(FC)/6‐31G* computations were performed to investigate the effect of higher order perturbation terms. The HF and MP2 conformational spaces are considerably different: the initial 128 structures converged into 102 different local minima as confirmed by frequency calculations; 28 new minima appeared and 26 previous HF local minima disappeared; no “all‐trans” C3 side chain conformations are seen at the MP2(FC) level. The MP2 global minimum conformation is stabilized by an aromatic‐side chain interaction. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008