Multicenter point charge model for high-quality molecular electrostatic potentials from AM1 calculations

The natural atomic orbital/point charge (NAO-PC) model based upon the AM1 wave function has been developed to calculate molecular electrostatic potentials (MEPs). Up to nine point charges (including the core charge) are used to represent heavy atoms. The positions and magnitudes of the eight charges that represent the atomic electron cloud are calculated from the natural atomic orbitals (NAOs) and their occupations. Each hybrid NAO is represented by two point charges situated at the centroid of each lobe. The positions of the centroids and the magnitudes of the charges were obtained by numerical integration of the Slater-type hybrids and the results used to set up polynomials and look-up tables that replace the integration step in the actual MEP calculation. The MEPs calculated using this method are found to be in better agreement with those obtained using RHF/6-31G* than those obtained from the AM1 wave function using Coulson charges or with MOPAC-ESP. The MEP calculations are extremely fast and have, for instance, been incorporated into an interactive graphics package. © 1993 John Wiley & Sons, Inc.     

Multipole moments for embedding potentials: Exploring different atomic allocation algorithms

Polarizable quantum mechanical (QM)/molecular mechanics (MM)‐embedding methods are currently among the most promising methods for computationally feasible, yet reliable, production calculations of localized excitations and molecular response properties of large molecular complexes, such as proteins and RNA/DNA, and of molecules in solution. Our aim is to develop a computational methodology for distributed multipole moments and their associated multipole polarizabilities which is accurate, computationally efficient, and with smooth convergence with respect to multipole order. As the first step toward this goal, we herein investigate different ways of obtaining distributed atom‐centered multipole moments that are used in the construction of the electrostatic part of the embedding potential. Our objective is methods that not only are accurate and computationally efficient, but which can be consistently extended with site polarizabilities including internal charge transfer terms. We present a new way of dealing with well‐known problems in relation to the use of basis sets with diffuse functions in conventional atomic allocation algorithms, avoiding numerical integration schemes. Using this approach, we show that the classical embedding potential can be systematically improved, also when using basis sets with diffuse functions, and that very accurate embedding potentials suitable for QM/MM embedding calculations can be acquired. © 2016 Wiley Periodicals, Inc.     

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.     

A molecular electrostatic potential bond critical point model for atomic and group electronegativities

A consistent set of atomic electronegativities of main block and d-block transition elements has been obtained from the position and value of the molecular electrostatic potential bond critical point of the C-E bond of a methyl-element-hydride system, H(3)C-EH(n) (E is an element and n = 0, 1, 2, 3, 4, and 5 depending on the position of E in the periodic table). The new scale shows very good agreement with the popular electronegativity scales such as Pauling, Allen, Allred-Rochow, Mulliken, and Sanderson scales of electronegativity, especially for the main block elements. The present scale of electronegativity for transition elements is expected to be more accurate than the previously derived values because of a more consistent approach. Further, the same approach has led to the evaluation of group electronegativities when the hydrogens of E are replaced by other substituent groups. These group electronegativity values are found to correlate well with Inamoto and Mullay scales.     

Site charge models for molecular electrostatic potentials of cycloalkanes and tetrahedrane

The molecular structures of cycloalkanes (from cyclopropane to cyclodecane) and tetrahedrane were optimized at the Hartree–Fock/6–31G** level and their molecular electric potentials (MEPs) were calculated using a geodesic grid. The MEPs were fitted using net atomic charges and several site charge models. The net atomic charge model gave very poor fits to the MEPs in every case. A model with additional methylene bisector charge sites, similar to one successfully used previously for linear alkanes, greatly improved the fits to the MEPs of these cycloalkanes. The MEPs of the highly strained molecules cyclopropane and tetrahedrane were further studied using ring center and displaced bond charge sites. The fitting of the MEP of cyclopropane was consistent with a banana bond model with asymmetrically displaced electron density in the C C bonds. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 579–585, 1999     

PM3-SM3: A general parameterization for including aqueous solvation effects in the PM3 molecular orbital model

Our recently proposed scheme for including aqueous solvation free energies in parameterized NDDO SCF models is extended to the Parameterized Model 3 semiempirical Hamiltonian. The solvation model takes accurate account of the hydrophobic effect for hydrocarbons, as well as electric polarization of the solvent, the free energy of cavitation, and dispersion interactions. Eight heteroatoms are included (along with H and C), and the new model is parameterized accurately for the water molecule itself, which allows meaningful treatments of specifically hydrogen bonded water molecules. The unphysical partial charges on nitrogen atoms predicted by the Parameterized Model 3 Hamiltonian limit the accuracy of the predicted solvation energies for some compounds containing nitrogen, but the model may be very useful for other systems, especially those for which PM3 is preferred over AM1 for the solute properties of the particular system under study. © 1992 by John Wiley & Sons, Inc.     

Development of spherical gaussian-based point charge models for the evaluation of electrostatic potentials

A set of charge- and dipole moment-conserving point charge models of the electron density of a spherical Gaussian-based wavefunction is described. A particular model may be chosen to satisfy the computational and/or accuracy requirements of a given application. Criteria for selection of models for the evaluation of electrostatic potentials are detailed and tested in an application to the porphyrin molecule.     

Analytical calculation of atomic and molecular electrostatic potentials from the Poisson equation

An analytic formulation is given for the total potential in atomic and molecular systems, based on the electrostatic approach from the Hellmann-Feynman theorem. The potential function is obtained from the analytic solution of the Poisson equation using charge densities expressed as a superposition of gaussian functions. The method is independent of the specific LCAO approximation used for the calculation of the charge distribution function. The calculation of the potential and its derivatives to a rapid algorithm form, which can be used for the evaluation of various electronic properties and the treatment of experimental situation, even for large molecular systems.     

Comment on analytical calculation of atomic and molecular electrostatic potentials from the poisson equation

High resolution measurements of the differential cross sections of Na atoms scattered from symmetrical top molecules exhibit a double rainbow structure which is attributed to the anisotropy of the potential. Calculations based on a semi-classical model in the sudden limit are in agreement with the measurements.     

Point atomic multipole moments for simulation of electrostatic potential and field in all-siliceous zeolites

Calibration method of atomic multipole moments (AMMs) is presented with respect to geometries of all-siliceous zeolite models obtained with X-ray diffraction (XRD) methods. Mulliken atomic charges and AMMs are calculated for all-siliceous types possessing small size elementary unit cells at the hybrid density functional theory (DFT) (B3LYP) and general gradient approximation (GGA) Perdew-Burke-Ernzerhof (PBE) levels and then used to fit the dependences versus geometry variables for the Mulliken charges and versus special coordinate for the AMMs. Fitted and exact charges and AMMs are used to compute electrostatic potential (EP) and electric field (EF) for all-siliceous zeolites with CRYSTAL. A possibility of application of the point AMMs to quantum mechanical/molecular mechanics computations or classic simulation of physical adsorption is evaluated. The considered models expand over wide range of structural parameters and could be applied even to amorphous all-siliceous systems.     

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Summary Generally contracted Basis sets for the atoms H-Kr have been constructed using the atomic natural orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANO's are constructed by averaging over the most significant electronic states, the ground state of the cation, the ground state of the anion for some atoms and the homonuclear diatomic molecule at equilibrium distance for some atoms. The contracted basis sets yield excellent results for properties of molecules such as bond-strengths and-lengths, vibrational frequencies, and good results for valence spectra, ionization potentials and electron affinities of the atoms, considering the small size of these sets. The basis sets presented in this article constitute a balanced sequence of basis sets suitable for larger systems, where economy in basis set size is of importance.     

A computationally inexpensive modification of the point dipole electrostatic polarization model for molecular simulations

We present an approximation, which allows reduction of computational resources needed to explicitly incorporate electrostatic polarization into molecular simulations utilizing empirical force fields. The proposed method is employed to compute three-body energies of molecular complexes with dipolar electrostatic probes, gas-phase dimerization energies, and pure liquid properties for five systems that are important in biophysical and organic simulations-water, methanol, methylamine, methanethiol, and acetamide. In all the cases, the three-body energies agreed with high level ab initio data within 0.07 kcal/mol, dimerization energies-within 0.43 kcal/mol (except for the special case of the CH(3)SH), and computed heats of vaporization and densities differed from the experimental results by less than 2%. Moreover, because the presented method allows a significant reduction in computational cost, we were able to carry out the liquid-state calculations with Monte Carlo technique. Comparison with the full-scale point dipole method showed that the computational time was reduced by 3.5 to more than 20 times, depending on the system in hand and on the desired level of the full-scale model accuracy, while the difference in energetic results between the full-scale and the presented approximate model was not great in the most cases. Comparison with the nonpolarizable OPLS-AA force field for all the substances involved and with the polarizable POL3 and q90 models for water and methanol, respectively, demonstrates that the presented technique allows reduction of computational cost with no sacrifice of accuracy. We hope that the proposed method will be of benefit to research employing molecular modeling technique in the biophysical and physical organic chemistry areas.     

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Summary Generally contracted basis sets for second row atoms have been constructed using the Atomic Natural Orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over several atomic states, positive and negative ions, and atoms in an external electric field. The contracted basis sets give virtually identical results as the corresponding uncontracted sets for the atomic properties, which they have been designed to reproduce. The design objective has been to describe the ionization potential, the electron affinity, and the polarizability as accurately as possible. The result is a set of well balanced basis sets for molecular calculations. The starting primitive sets are 17s12p5d4f for the second row atoms Na-Ar. Corresponding ANO basis sets for first row atoms have recently been published.     

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Generally contracted basis sets for the first row transition metal atoms Sc-Zn have been constructed using the atomic natural orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over the three electronic configurationsd ⁿ ,d ^n–1 s, andd ^n–2 s ² for the neutral atom as well as the ground state for the cation and the ground state atom in an external electric field. The primitive sets are 21s15p10d6f4g. Contraction to 6s5p4d3f2g yields results that are virtually identical to those obtained with the corresponding uncontracted basis sets for the atomic properties, which they have been designed to reproduce. Slightly larger deviations are obtained with the 5s4p3d2f1g for the polarizability, while energetic properties still have only small errors. The design objective has been to describe the ionization potential, the polarizability and the valence spectrum as accurately as possible. The result is a set of well-balanced basis sets for molecular calculations, which can be used together with basis sets of the same quality for the first and second row atoms.