A description of nitrogen-nitrogen bond in terms of charge distributions

A theoretical analysis of properties of the shared interactions between two neighbouring nitrogen atoms in a variety of compounds is presented, based on properties of charge distributions derived from 6-31 ⁺⁺G^** wave functions. Bond is characterized in terms of its bond order, bond ellipticity and the quantity of Laplacian of ρ at the bond critical point. The difference between the bond path angle and the corresponding geometrical angle provides a measure of the degree of relaxation for the charge density away from the geometrical constraints imposed by the nuclear framework. Comparisons have been made between the nitrogen-containing compounds and isoelectronic hydrocarbons. Values of the NN bond energies, based on the properties of NN bond interatomic surface, are determined in three schemes.     

The calculations of charge distributions,bond orders and conformations for a number of oxygen- and fluorine-containing molecules by CNDO-BW and EHT me

The electronic structure for a number of highly fluorinated ethanes, ketones and aldehydes has been calculated using the CNDO-BW method. Bond orders for these molecules were obtained by the Wiberg method, by the transformation to the basis of hybrid Orbitals and from the Mulliken's population analysis. The method cannot describe internal rotation barriers. A sufficiently reliable bond order-bond length correlation for both C-C and C-O bonds appears impossible to find. The most stable conformations for the given molecules seem to be defined by the minimum of coulomb interaction energy of atomic charges. Valence angles can be calculated with precision. The charge distributions obtained correspond to the available data on the chemistry and IR spectroscopy of these molecules. The EHT method is shown to be incorrect when both the most stable conformations and charge distributions are considered.     

QTAIM characteristics of halogen bond and related interactions

Different types of noncovalent interactions such as, for example, halogen bond, hydrogen bond, and dihalogen bond are analyzed. The analysis is based on ab initio calculations which were performed on complexes of the F(3)CCl molecule. This choice is connected with the features of the Cl atom which may act as the Lewis acid and also as the Lewis base center. Such a dual role is a consequence of the existence of negative and positive regions of the electrostatic potential of the Cl center. Hence, the F(3)CCl molecule forms complexes linked by various interactions. The formation of the complexes leads to the electron charge redistribution which is reflected in the quantum theory of atoms in molecules (QTAIM) characteristics. Numerous correlations and tendencies were found here between QTAIM, geometrical and energetic parameters. It was found that the mechanism of the formation of complexes linked through various interactions is generally the same as that known for the hydrogen bond formation. The dependencies and QTAIM characteristics considered here are in agreement with Bent's rule.     

Static charge distributions which generate exact potential curves for diatomic molecules

For a diatomic molecule, there exists a charge density which can be used to generate the exact potential energy curve for the molecule, by integration of the classical Poisson equation. This density is displayed for H⁺₂, H₂ and LiH, and it is shown to be similar in shape to the united-atom electron density.     

Charge density distributions and sigma bond inductive effects in hydrocarbons and hydrocarbon ions

Atomic orbital charge densities have been calculated for the electron systems of a number of hydrocarbon molecules, by an electronegativity equalization method. These electron distributions have been used to analyze the relative inductive effects of alkyl groups, the transmission of electronic effects through localized bonds, the inductive stabilization of simple hydrocarbon ions, and the dependence of the ¹H and ¹³C chemical shifts on the corresponding partial charges of the atoms. The charge densities calculated by electronegativity equalization were compared to those predicted by various molecular orbital methods.

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Zusammenfassung Mit Hilfe einer Methode, die auf der Angleichung von Elektronegativitäten beruht (electronegativity equalization), sind atomare Orbitalladungsdichten für -Elektronensysteme einer Reihe von Kohlenwasserstoffmolekülen berechnet worden. Die Ladungsdichten werden mit den Voraussagen verschiedener MO-Methoden verglichen.Diese Elektronenverteilungen werden zur Analyse der relativen induktiven Effekte von Alkylgruppen, der Weiterleitung elektronischer Effekte durch lokalisierte Bindungen, der induktiven Stabilisierung einfacher Kohlenwasserstoffionen und der Abhängigkeit der chemischen Verschiebung von ¹H und ¹³C von den partiellen Ladungen der Atome benutzt.

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Résumé Les densités de charge dans les orbitales atomiques ont été calculées pour les systèmes d'électrons d'un certain nombre de molécules d'hydrocarbure à l'aide d'une méthode d'égalisation des électronégativités. Ces distributions électroniques ont été utilisées pour analyser les effects inductifs relatifs des groupements alkyles, la transmission des effets électroniques à travers les liaisons localisées, la stabilisation par effet inductif des ions hydrocarbures simples, et la relation entre les déplacements chimiques de ¹H et ¹³C et les charges atomiques partielles correspondantes. Les densités de charges calculées ici ont été comparées à celles obtenues par différentes méthodes d'orbitales moléculaires.

     

A theoretical study of the Si-O bond in disiloxane and related molecules

Summary A comparison of semi-empirical (MNDO) and ab initio (GAUSSIAN) calculations for disiloxane and related molecules is given. The STO-3G^* basis set well reproduced the observed geometries of disiloxane (*), DZP, TZVP) gave much poorer agreement with the observed geometries.Comparison of the STO-3G^* and the STO-3G basis sets demonstrates the necessity of including d-orbitals on the silicon. However, the semi-empirical MNDO program gave, despite the absence of d-orbitals, a better approximation to the molecular geometry than the complex ab initio basis sets.Force field parameters have been calculated for k_SiOSi, k_OSiO, 0.089 and 0.73 mdyneÅ/rad², and the SiOSiO torsion which has a V₁ potential of –0.68 kcal/mol. In addition, the HSiOH torsion is shown to have a three-fold potential of 0.78 kcal/mol. These are profoundly different from the analogous carbon-oxygen force constants, demonstrating that C-O parameters cannot be transferred to the corresponding Si-O systems.     

Classical and quantum mechanical calculations of conformational probability density distributions. Two-rotor molecules

In order to study the dynamical structure of a two-rotor molecule, such as acetone, as a function of temperature, conformational probability density distributions are computed by using three different approaches: the so-called current approach, the classical approach, and the quantum mechanical oscillator approach. It is found that the three procedures yield comparable results, at least at normal temperature (25°C), although the current and, especially, the classical approaches give rise to too sharp distributions when compared with the quantum mechanical results. Owing to its simplicity, the current approach may be used advantageously, and it is easily extendible to many-rotor systems. Finally, it is verified that deuteration does not affect appreciably the conformation.     

Testing theory beyond molecular structure: Electron density distributions of complex molecules

The electron density distribution (EDD) of a molecular system can be determined experimentally from elaborate X‐ray diffraction measurements or calculated with quantum mechanical methods: This provides a unique opportunity for mutual validation of the experimental and theoretical methods—a validation that goes far beyond comparison of molecular structures. Two examples of complex molecular systems of biologic relevance are presented. The first is the cocrystallized complex of betaine, imidazole, and picric acid, 1, which is a 75‐atom molecular complex serving as a model for the active site in the serine proteases class of enzymes, the so‐called catalytic triad. For 1 the experimental charge density was determined by combined modeling of single crystal synchrotron X‐ray and neutron diffraction data measured at 28(1) K, and it is compared with ab initio theoretical calculations at the B3LYP/6‐311G(d,p) level of theory. Overall, the agreement is good, but in one strong N? H? O hydrogen bond clear differences are observed. The second example concerns the EDD of the mixed valence trinuclear oxo‐centered iron carboxylate, [Fe₃O(OOCC(CH₃)₃)₆(NC₅H₅)₃], 2. This molecule contains 133 atoms (542 electrons) including three open‐shell iron atoms, and the experimental investigation is based on synchrotron X‐ray diffraction data. Calculations in the experimental geometry at the commonly used UB3LYP/LanL2DZ level of theory are not able to reproduce a number of experimentally observed electron density features. In particular, the sp³‐like distribution on the central oxygen atom and the electron deformations on the iron centers are at variance with experiment. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Benchmark of density functional theory methods on the prediction of bond energies and bond distances of noble-gas containing molecules

We have tested three pure density functional theory (DFT) functionals, BLYP, MPWPW91, MPWB95, and ten hybrid DFT functionals, B3LYP, B3P86, B98, MPW1B95, MPW1PW91, BMK, M05-2X, M06-2X, B2GP-PLYP, and DSD-BLYP with a series of commonly used basis sets on the performance of predicting the bond energies and bond distances of 31 small neutral noble-gas containing molecules. The reference structures were obtained using the CCSD(T)∕aug-cc-pVTZ theory and the reference energies were based on the calculation at the CCSD(T)∕CBS level. While in general the hybrid functionals performed significantly better than the pure functionals, our tests showed a range of performance by these hybrid functionals. For the bond energies, the MPW1B95∕6-311+G(2df,2pd), BMK∕aug-cc-pVTZ, B2GP-PLYP∕aug-cc-pVTZ, and DSD-BLYP∕aug-cc-pVTZ methods stood out with mean unsigned errors of 2.0-2.3 kcal∕mol per molecule. For the bond distances, the MPW1B95∕6-311+G(2df,2pd), MPW1PW91∕6-311+G(2df,2pd), and B3P86∕6-311+G(2df,2pd), DSD-BLYP∕6-311+G(2df,2pd), and DSD-BLYP∕aug-cc-pVTZ methods stood out with mean unsigned errors of 0.008-0.013 A? per bond. The current study showed that a careful selection of DFT functionals is very important in the study of noble-gas chemistry, and the most recommended methods are MPW1B95∕6-311+G(2df,2pd) and DSD-BLYP∕aug-cc-pVTZ.     

Topological analysis of the molecular charge density and impact sensitivy models of energetic molecules

Important explosives of practical use are composed of nitroaromatic molecules. In this work, we optimized geometries and calculated the electron density of 17 nitroaromatic molecules using the Density Functional Theory (DFT) method. From the DFT one-electron density matrix, we computed the molecular charge densities, thus the electron densities, which were then decomposed into electric multipoles located at the atomic sites of the molecules using the distributed multipole analysis (DMA). The multipoles, which have a direct chemical interpretation, were then used to analyze in details the ground state charge structure of the molecules and to seek for correlations between charge properties and sensitivity of the corresponding energetic material. The DMA multipole moments do not present large variations when the size of the Gaussian basis set is changed; the largest variations occurred in the range 10-15% for the dipole and quadrupole moments of oxygen atoms. The charges on the carbon atoms of the aromatic ring of each molecule become more positive when the number of nitro groups increases and saturate when there are five and six nitro groups. The magnitude and the direction of the dipole moments of the carbon atoms, indicators of site polarization, also depend on the nature of adjacent groups, with the largest dipole value being for C-H bonds. The total magnitude of the quadrupole moment of the aromatic ring carbon atoms indicates a decrease in the delocalized electron density due to an electron-withdrawing effect. Three models for sensitivity of the materials based on the DMA multipoles were proposed. Explosives with large delocalized electron densities in the aromatic ring of the component molecule, expressed by large quadrupole values on the ring carbon atoms, correspond to more insensitive materials. Furthermore, the charges on the nitro groups also influence the impact sensitivity.     

Translation of STO charge distributions

Barnett and Coulson's zeta-function method (M. P. Barnett and C. A. Coulson, Philos. Trans. R. Soc., Lond. A 1951, 243, 221) is one of the main sources of algorithms for the solution of multicenter integrals with Slater-type orbitals. This method is extended here from single functions to two-center charge distributions, which are expanded at a third center in terms of spherical harmonics times analytical radial factors. For s-s distributions, the radial factors are given by a series of factors corresponding to the translation of s-type orbitals. For distributions with higher quantum numbers, they are obtained from those of the s-s distributions by recurrence. After analyzing the convergence of the series, a computational algorithm is proposed and its practical efficiency is tested in three-center (AB/CC) repulsion integrals. In cases of large basis sets, the procedure yields about 12 correct significant figures with a computational cost of a few microseconds per integral.     

Partitioning of FSGO charge distributions

A procedure for analyzing charge distributions of FSGO wavefunctions, by partitioning bonding electrons according to the location of the orbital centers, is proposed. Electron populations are given for singlet states of eighteen diatomic species, and are shown to be in excellent agreement with results obtained from virial partitioning of Hartree-Fock wavefunctions.     

Spin density distributions in some radical anions exhibiting restricted rotation about a carbon-carbon bond

In the radical anions of styrene, 4-vinyl pyridine and p-fluoro-styrene it has been found earlier by ESR experiments that the two ortho protons, as well as the two meta protons of the six-membered ring are not equivalent. We have made a systematic theoretical study of these systems by using the unrestricted Hartree-Fock method. Satisfactory agreement with the experimental results has been obtained without invoking the so called effect or effect.     

The relation of harmonic force constant and charge density in bonding region for diatomic molecules

The perfectly following density (PFD) model of Anderson and Parr is used to formulate semiempirical model relatings electron density at the saddle point to the harmonic force constant of the diatomic molecule. The most importants of the model are shortly discussed.     

Modelling of repulsive potentials from atom charge density distributions: interactions of inert gas atoms

Using electron charge density overlap integrals, a correlation procedure for estimating short-range repulsive intermolecular potentials has been investigated. It is found that the repulsive potentials correlate well with the density overlap integral divided by the square of the distance. A simple combining rule for inert gas atoms is obtained and compared with an accurate determination of repulsive potentials for all the mixed rare gases and with other combining rules.     

Magnetic susceptibility of alkali-tetracyanoquinodimethane salts and extended Hubbard models with bond order and charge density wave phases

The molar spin susceptibilities χ(T) of Na-tetracyanoquinodimethane (TCNQ), K-TCNQ, and Rb-TCNQ(II) are fit quantitatively to 450 K in terms of half-filled bands of three one-dimensional Hubbard models with extended interactions using exact results for finite systems. All three models have bond order wave (BOW) and charge density wave (CDW) phases with boundary V = V(c)(U) for nearest-neighbor interaction V and on-site repulsion U. At high T, all three salts have regular stacks of TCNQ(-) anion radicals. The χ(T) fits place Na and K in the CDW phase and Rb(II) in the BOW phase with V ≈ V(c). The Na and K salts have dimerized stacks at T < T(d) while Rb(II) has regular stacks at 100 K. The χ(T) analysis extends to dimerized stacks and to dimerization fluctuations in Rb(II). The three models yield consistent values of U, V, and transfer integrals t for closely related TCNQ(-) stacks. Model parameters based on χ(T) are smaller than those from optical data that in turn are considerably reduced by electronic polarization from quantum chemical calculation of U, V, and t of adjacent TCNQ(-) ions. The χ(T) analysis shows that fully relaxed states have reduced model parameters compared to optical or vibration spectra of dimerized or regular TCNQ(-) stacks.     

The use of ab initio quantum molecular self-similarity measures to analyze electronic charge density distributions

Exact quantum molecular overlaplike and Coulomb-like self-similarity measures are studied in a selected series of molecules with the same number of electrons. It is found that quantum molecular overlap self-similarity measures can be used to estimate the concentration of electronic charge in molecules. A good linear relationship between the overlap self-similarity measure and the volume is found for molecules with the same number of electrons when the atoms of the systems being compared belong to the same row of the periodic table. Finally, an upper bound for the quantum molecular overlap self-similarity measure of molecules with a number of electrons up to 54 is given from the atomic quantum self-similarity measures obtained using Slater-type functions. © 1996 John Wiley & Sons, Inc.