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.     

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.     

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.     

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.     

Development of optimized MST/SCRF methods for semiempirical calculations: The MNDO and PM3 Hamiltonians

The self-consistent reaction field (SCRF) method proposed by Miertus, Scrocco, and Tomasi (MST) has been optimized for MNDO and PM3 semiempirical Hamiltonians. Different algorithms used to compute the molecular electrostatic potential (MEP) and different solute cavities have been investigated. The ability of the optimized models to reproduce experimental free energies of solvation and to mimic the solvent effect in several chemical processes has been compared with the ab initio and AM1 versions of the MST method as well as with experimental data. © 1995 by John Wiley & Sons, Inc.     

Analysis of the core-repulsion functions used in AM1 and PM3 semiempirical calculations: Conformational analysis of ring systems

The AM1 and PM3 potential energy surfaces of cyclopentane have been compared and the energy difference between two (boat and chair) cyclohexane conformers analyzed. The effects of reparameterization and different core-repulsion functions (CRFs) have been studied. The H? H, C? H, and C? C CRF energy contributions have been calculated separately. The results show that the CRF energy corrections stabilize the correct (MM2 and ab initio) geometries. The PM3 equilibrium geometry of cyclopentane is closer to the MM2 and ab initio results than the AM1 geometry. It is known that above 190 pm the AM1 H? H CRF curve is smooth and negative but the PM3 H? H CRF curve has a trough and a shoulder. It has been shown that this latter oscillation is not damped by other parameters. As a result, the H? H PM3 energy gradient curve is different from the quasilinear AM1 and ab initio gradient curves. © 1993 John Wiley & Sons, Inc.     

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     

Semiempirical AM1 electrostatic potentials and AM1 electrostatic potential derived charges: A comparison with ab initio values

Electrostatic potentials calculated from AM1 wave functions have been compared with ab initio STO-3G values and qualitative agreement has been found. Atomic charges derived from AM1 electrostatic potentials for both experimental and AM1 optimized geometries are of comparable quality with STO-3G potential derived charges. These results suggest that the AM1 electrostatic potential may be useful both in its own right and also for deriving atomic charges for use in molecular dynamics studies.     

Pyrrolizidine alkaloids necine bases: Ab initio,semiempirical, and molecular mechanics approaches to molecular properties

The structural stabilities of endo and exo conformations of retronecine and heliotridine molecules were analyzed using different ab initio, semiempirical, and molecular mechanics methods. All electron and pseudopotential ab initio calculations at the Hartree-Fock level of theory with 6-31G* and CEP-31G* basis sets provided structures in excellent agreement with available experimental results obtained from X-ray crystal structure and ¹H-NMR (nuclear magnetic resonance) studies in D₂O solutions. The exo conformations showed a greater stability for both molecules. The most significant difference between the calculations was found in the ring planarity of heliotridine, whose distortion was associated with the interaction between the O(11)H group and the C(1)-C(2) double bond as well as with a hydrogen bond between O(11)H and N(4). The discrepancy between pseudopotential and all-electron optimized geometries was reduced after inclusion of the innermost electrons of C(1), C(2), and N(4) in the core potential calculation. The MNDO, AM1, and PM3 semiempirical results showed poor agreement with experimental data. The five-membered rings were observed to be planar for AM1 and MNDO calculations. The PM3 calculations for exo-retronecine showed a greater stability than the endo conformer, in agreement with ab initio results. A good agreement was observed between MM3 and ab initio geometries, with small differences probably due to hydrogen bonds. While exo-retronecine was calculated to be more stable than the endo conformer, the MM3 calculations suggested that endo-heliotridine was slightly more stable than the exo form. © 1996 by John Wiley & Sons, Inc.     

Semiempirical study of compounds with intramolecular O?H…︁O hydrogen bonds. II. Further verification of a modified MNDO method

In the forerunner of this article, we described a MNDO modification designed for studies of compounds with intramolecular O? H…?O hydrogen bonds. Here, we report the further verification of the modification by means of its application to 14 compounds not considered in its development. Comparison of the calculated structural parameters and proton transfer characteristics with available experimental or ab initio results, and with those obtained using MNDO, AM1, MNDO/H, MNDO/M, and PM3, supports the validity of the new modification for prediction of hydrogen bond characteristics. © 1994 by John Wiley & Sons, Inc.     

An examination of intermolecular and intramolecular hydrogen bonding in biomolecules by AM1 and MNDO/M semiempirical molecular orbital studies

The recent NMDO/M modification and parameterization of the MNDO molecular orbital method has been used to analyze intermolecular hydrogen bonding between amino acids and water, and intramolecular hydrogen bonding in monosaccharides. The results have been compared to AM1 calculations on the same systems. The MNDO/M calculations gave values which were similar to ab initio calculations with respect to the intermolecular interactions, but yielded significantly poorer results for the intramolecular interactions. The AM1 procedure performed better on the intramolecular interactions than the MNDO/M procedure, but frequently provided unfavorable three-centered hydrogen bonding geometries for the intermolecular interactions.     

Tautomeric equilibria of heterocyclic molecules. A test of the semiempirical AM1 and MNDO-PM3 methods

Tautomeric equilibria (mainly of the lactam-lactim type) for a rather large number of six-membered heterocyclic molecules are calculated by the semiempirical AM1, MNDO-PM3, and MNDO methods. Except for compounds with adjacent pyridine-like lone pairs both AM1 as well as MNDO-PM3 give rather reliable predictions for relative stabilities of the various tautomeric species–comparable to quite high level ab initio calculations. The known errors associated with MNDO in the treatment of heterocyclic tautomerism are thus largely corrected in AM1 as well as MNDO-PM3. For 2-hydroxypyridine-pyrid-2(1H)-one the effect of self-association is less satisfactorily described by MNDO-PM3 than by AM1. MNDO-PM3 calculated relative stabilities of methylated derivatives are, however, in considerably closer agreement with experimental values than those obtained by AM1. Ionization potentials, especially those for lone-pair orbitals, are overestimated by all three semiempirical methods. MNDO-PM3 results for nitrogen lone-pair orbital energies are slightly better than those obtained by the AM1 or MNDO method.     

Correlation of the acidity of substituted phenols,anilines, and benzoic acids calculated by MNDO,AM1, and PM3 with Hammett-type substituent constants

Heats of formation and net atomic charges of some 120 structures involving substituted phenols, anilines, and benzoic acids and the corresponding anions were calculated by MNDO, AM1, and PM3 semiempirical methods. The gas phase acidities of substituted phenols and anilines and the net atomic charges on the anionic heteroatoms of the corresponding anions have been successfully correlated with σ^? constants. Moreover, good correlations with σ were found for the charges on the acidic hydrogens of substituted phenols and anilines. In contrast, the gas phase acidities of substituted benzoic acids and the charges on the anionic oxygens of the corresponding anions are better correlated with Taft σ° constants. Comparisons of these results with experimental data and ab initio theoretical calculations indicate that AM1 and PM3 methods are much better than MNDO in predicting the acidity of aromatic compounds.     

Comparative Study of the Structure of Rhodanine, Isorhodanine, Thiazolidine-2,4-dione, and Thiorhodanine

Ab initio (HF and MP2 level) and semiempirical (AM1, PM3, MNDO) calculations on the relative stabilities and structures of the potential tautomeric forms of rhodanine, isorhodanine, thiazolidine-2,4-dione, and thiorhodanine are reported. Ab initio calculations predict that the thiooxo, oxothio, dioxo, and dithio tautomers are the most stable. These results correspond to the known experimental data. Infrared spectra of the investigated compounds were recorded for the region 4000-150 cm^-1, and the characteristic bands were compared with ab initio calculated frequencies at the HF/3-21G^(*)* level.     

Molecular interaction potential: A new tool for the theoretical study of molecular reactivity

A new methodology to compute molecular interaction potentials (MIPs) is developed and tested. The calculation of the MIP is based upon the generalization of the rigorous quantum mechanical molecular electrostatic potential (MEP) and further addition of a classical repulsion-dispersion term. As a result, the MIP is able to represent not only with high accuracy electrostatic interactions but also represent in a suitable way steric effects. The analysis of the results obtained for different molecules demonstrates the superiority of the MIP with regard to the standard MEP to describe nonbonded interactions, in particular hydrogen bonds. The comparison of results calculated at the ab initio I 6-31G* and semiempirical AM1 levels points out the suitability of semiempirical calculations to qualitatively reproduce the most relevant reactive features of the molecules. Finally, possible applications of the MIP in different fields are discussed. © 1993 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.     

A new scaling procedure to correct semiempirical MEP and MEP-derived properties

Summary The MNDO, AM1, PM3, and ab initio 6–31G^* and 6–31+G^* MEPs for 21 neutral and 12 charged molecules were computed in layers ranging from 1.2 to 2.0 times the van der Waals radii of atoms. Semiempirical and ab initio MEPs for each layer and two groups of layers were compared to gain insight into the relationships between semiempirical and ab initio MEPs. A detailed statistical study allowed us to obtain a new set of scaling coefficients able to correct the semiempirical MEPs to provide better representations of the ab initio values. The corrected semiempirical MEPs were used to obtain electrostatic charges, whose quality was tested by the comparison between semiempirical Coulombic MEPs and ab initio quantum mechanical MEPs.     

Comparative semiempirical and ab initio study of the harmonic vibrational frequencies of aniline—I. The ground state

The harmonic vibrational frequencies of the ground state S₀ of aniline obtained from various ab initio methods [6-31G, 6-31G(*) and 6-31G* basis sets] and semiempirical methods (MINDO/3, MNDO, AM1 and PM3) have been compared to the experimental vibrational spectra. Detailed theoretical analyses of the atomic Cartesian displacements of all normal modes are presented. The semiempirical PM3 method reproduces the experimental frequencies of aniline with comparable accuracy to the ab initio methods. Ale PM3 method will be useful in predicting the vibrational spectra of larger aromatic amines.