Properties of atoms in molecules. a proposed method for calculating the extent of distortion of an atom

A procedure for calculating the extent of distortion of an atom in a molecule is proposed and applied to the first-and second-row diatomic hydrides. The atomic charges in these molecules were also computed.     

A robust force field based method for calculating conformational energies of charged drug-like molecules

The binding affinity of a drug-like molecule depends among other things on the availability of the bioactive conformation. If the bioactive conformation has a significantly higher energy than the global minimum energy conformation, then the molecule is unlikely to bind to its target. Determination of the global minimum energy conformation and calculation of conformational penalties of binding is a prerequisite for prediction of reliable binding affinities. Here, we present a simple and computationally efficient procedure to estimate the global energy minimum for a wide variety of structurally diverse molecules, including polar and charged compounds. Identifying global energy minimum conformations of such compounds with force field methods is problematic due to the exaggeration of intramolecular electrostatic interactions. We demonstrate that the global energy minimum conformations of zwitterionic compounds generated by conformational analysis with modified electrostatics are good approximations of the conformational distributions predicted by experimental data and with molecular dynamics performed in explicit solvent. Finally the method is used to calculate conformational penalties for zwitterionic GluA2 agonists and to filter false positives from a docking study.     

Ensemble representable densities for atoms and molecules. I. General theory

A method to obtain ensemble representable densities from experimental diffraction data is proposed. The method uses ab initio molecular densities instead of the commonly employed one-electron orbital densities, and as a result, few parameters need to be optimized in the fitting procedure to the experimental structure factors. The optimized coefficients can provide information about intra- and intermolecular electronic correlations, spin-orbit coupling, etc. This work also provides new explicit formulas to determine the rank of a fermionic wave function, i.e., the rank of the one-fermion density matrix. © 1995 John Wiley & Sons, Inc.     

Electrostatic interaction energies of independent aspherical atoms in molecules

Matter may be looked upon as consisting of superimposed independent atoms, which are spatially confined around specific positions by the chemical forces and which are weakly deformed thereby. Independent atoms with degenerate ground states are not fixed to be spherically symmetric as often supposed; it is more convenient for the interpretation of molecular and crystal charge distribution to refer to nonspherical atomic ground-state densities, the orientation of which is also determined by the chemical forces. In accordance with the virial theorem, one half of the quasiclassical electrostatic interaction energy, EE, of superimposed independent atoms is an approximation to the total bond energy, BE. The BE≈EE/2 correlation also improves if oriented nonspherical instead of spherically averaged atoms are superimposed. This correlation does not mean that the bond energy has been explained electrostatically, because one must know the atomic positions (and orientations) in advance. Furthermore, density deformations due to the quantum-mechanical interactions contribute 2–3 eV to BE.     

Parametric method for calculating the vibronic spectra of complex molecules. Diphenylpolyenes

The absorption and fluorescence spectra of diphenylpolyenes (diphenylbutadiene, diphenylhexatriene, diphenyloctatetraene, and 1,6-di(4′-methylphenyl)-1,3,5-hexatriene) are calculated by a recently proposed parametric method using the fragmentation approach for designing molecular models. The parameters of the^H>C=molecular fragment (derivatives of the Coulomb and resonance integrals with respect to internal coordinates in the HAO basis set) obtained in calculation for polyenes were transferred to the molecular models of diphenylpolyenes without changes (∂H_e/∂q⁽⁰⁾=0.055 and ∂²H_e/∂q _k ⁽⁰⁾ ∂q _l ⁽⁰⁾ =0.1 au). The theoretical spectra are sufficiently adequate to quantitatively and qualitatively reproduce the main features of the vibrational structure of the experimental absorption and fluorescence spectra, and the parameters of the models of the potential surfaces of the excited states of diphenylpolyenes are consistent with the previous estimations. It is shown that this method allows predictive calculations of the vibronic spectra of complex molecules and the developed parametrization posesses all needed properties: locality, transferability, invariance to minor changes in electron density, ranking according to magnitude, small number of parameters for molecular fragments, etc. K. A. Timiryazev Moscow Agricultural Academy. Translated fromZhurnal Struktumoi Khimii, Vol. 37, No. 6, pp. 1040–1049, November–December, 1996. Translated by I. Izvekova     

Diatomic interaction energies in the topological theory of atoms in molecules

Summary A partitioning of theab initio total energy into one-center and two-center terms is proposed. The partitioning scheme is developed using the auxiliary function (2, 1; 1, 2) = γ(2, 1)γ(1, 2) and the topological theory of atoms in molecules. It is shown that this scheme can be used at theoretical levels beyond Hartree-Fock. The numerical results indicate that the two-center terms follow the experimental trend of the dissociation energies for a series of related compounds.     

A procedure for obtaining lower bounds for ground state energies of atoms and molecules

Using Löwdin's partition method we have re-derived the D. Weinstein lower bound, E > H ₁₁ - . By the same method, plus the assumption that the calculated first excited state energy is lower than a certain weighted average of approximate energies of all the excited states, we have derived a moderately better lower bound.     

Diatomic interaction energies in the topological theory of atoms in molecules

Summary.  A partitioning of the ab initio total energy into one-center and two-center terms is proposed. The partitioning scheme is developed using the auxiliary function L˜(2, 1; 1, 2)=γ(2, 1)γ(1, 2) and the topological theory of atoms in molecules. It is shown that this scheme can be used at theoretical levels beyond Hartree–Fock. The numerical results indicate that the two-center terms follow the experimental trend of the dissociation energies for a series of related compounds. Received March 5, 1996/Final revision received August 19, 1996/Accepted August 29, 1996     

Perturbation calculation of correlation energies for polyatomic molecules I. Initial results

The calculation of correlation energies for polyatomic molecules is discussed. Four second-order perturbation expressions are considered; only the simplest, a Rayleigh-Schroedinger expansion with the Moller-Plesset partitioning of the Hamiltonian is invariant to an arbitrary mixing of degenerate orbitals and has the correct dependence on the number of particles. In the absence of degeneracies an iterative Brillouin-Wigner method is proposed. Calculations predict that correlation effects favor the non-classical form of carbonium ions.     

A generalized formula for the energies of alternant molecular orbitals. I. Homonuclear molecules

Using the method of alternant molecular orbitals (AMO ) it is shown that the energies of AMO 's (E_k), for any alternant homonuclear molecule having a singlet ground state, are connected with the energies of the MO 's (e_k) obtained by the conventional Hartree–Fock (HF ) method by the formula \documentclass{article}\pagestyle{empty}\begin{document}$ E_{k\alpha (\beta )} = \pm \sqrt {\Delta ^2 + e_k ^2 } $\end{document}, where Δ is the correlation correction. The formula is applicable in the semiempirical LCAO form used in the Pariser–Parr–Pople theory, by Hubbard's approximation of γ integrals.