Dependence of energies on the bond lengths in molecules and crystals

The dependence of the binding energies in molecules and crystals on the interatomic distances near the equilibrium position was established in the framework of the Mie equation using the force constants of molecules and the elasticity moduli of solids. To evaluate the repulsion forces, we used the Morse function for molecules and the Born-Landé approach for ionic crystals.     

Variation of mean SiO bond lengths in silicon-oxygen octahedra

The mean bond length SiO in silicon-oxygen octahedra is a function of the mean coordination number of the oxygen atoms (CN) in the octahedron: (SiO)_mean = 1.729 + 0.013CN. The radius of Si in six coordination against oxygen is 0.407 Å.     

Effects of wave function modifications on calculated carbon–hydrogen bond lengths

The two-level factorial design (FD) and principal component analysis (PCA) chemometric techniques were used to investigate the carbon–hydrogen bond lengths dependence on the basis set size and quantum chemistry method, for H–C≡CH, H–C≡CF, H–C≡CCH₃, H–C≡CCN, H–C≡CCl and H–C≡CCCH molecular systems. The calculations were performed by using Hartree-Fock (HF), Møller-Plesset 2 (MP2) and Density Functional Theory (DFT) with B3LYP exchange-correlation functional methods. The effects concerning basis set size include the number of valence and polarization functions as well as the cooperative effect between them, at all computational levels. The increase in the number of valence functions decreases the calculated C–H bond lengths by approximately 0.0022 Å, while the inclusion of polarization functions at HF and B3LYP levels increases the C–H bond length, in contrast to the behavior obtained at MP2 level. The effect of the inclusion of diffuse functions is non-significant, at all three computational levels. Moreover, the valence–polarization interaction effects are not significant, except at the MP2 calculational level, in which such effects lead to an increase in the calculated C–H bond lengths. When the computational level changes from HF→B3LYP and B3LYP→MP2 the calculated C–H bond length values increase (on average) by +0.0100 and +0.0027 Å, respectively. Algebraic models (one for each level of calculation) successfully employed to reproduce the calculated values for H–C≡N bond length, a system not included in the training set. The HF/6-31G(d,p) and HF/6-31++G(d,p) results yield the lowest standard errors (0.0015 and 0.0014 Å, respectively) and correspond to the calculated points in closest proximity to the experimental one.     

Correlation between intramolecular bond lengths and K-shell σ-shape resonances in gas-phase molecules

Analysis of K-shell excitation spectra of gas-phase molecules containing at least two atoms of either B, C. N. O or F reveals the existence of a striking correlation between the bond length of the atomic pair. the sum of their atomic numbers and the associated α-shape resonance energy. Empirical rules are established which allow the derivation of intramolecular distances with accuracies reliably better than ± 0.05 A from the K-.shell absorption spectrum of one of the atoms in the Molecule.     

A simple method for quantitative estimation of C-H bond lengths in hydrocarbon radical cations

A quantitative correlation between deviations of the C-H bond lengths of hydrocarbon molecules during their adiabatic single ionization and isotropic hyperfine coupling constants with protons of their primary radical cations (RC) was established. A simple method for estimation of the C-H bond lengths of hydrocarbon RC was proposed on the basis of the correlation found. Specific features of the structure of the RC of methane and severaln-alkanes of the general formula [H^*(CH_{2 n} H^*]⁺,n = 0 to 12, were analyzed. A widely used empirical rule, according to which deprotonation of hydrocarbon RC during the ion-molecular process is determined by the proton possessing the highest spin density, was refined and geometrically substantiated.     

Manifestation of stereoelectronic effects on the calculated carbon-nucleophile bond lengths in nucleophilic addition to sterically unbiased ketones

Calculations at the B3LYP/6-311G(d,p) level of the structures of diastereoisomeric pairs of alcohols 1E-12E and 1Z-12Z, resulting from either reduction or methylation of sterically unbiased ketones show that the newly formed C-Nu bond lengths of the major isomers are larger than those of the minor isomers.     

Valence bond and molecular orbital studies of the A-F bond lengths in some AFn type molecules and their fluorinated cations

The results of ab initio MP2(full)/cc-pVTZ and DFT MPW1PW91/cc-pVTZ molecular orbital calculations of the bond lengths are reported for non-hypercoordinate and hypercoordinate systems of the general type AF_n^q+, with q≥0 and A = N, P, O, S and Cl. They show that except for OF₄²⁺ the bond lengths decrease as the cationic character increases. Increased-valence structures are used to provide valence bond (VB) rationalizations for the bond length shortenings. In these valence bond structures, the degree of multiple bonding increases as the cationic character increases.     

Pauling's criterion of bond strength and the relative bond lengths in molecule MLk

In this paper, the bond strengths, defined by Pauling, for a series of molecules in the type of ML_k have been calculated by using the generalized method obtained from the maximum overlap method in a preceding paper and by using Pauling's pair–defect–sum approximation. A number of geometrical bonding situations are investigated. It is demonstrated why a previous study purporting to use of Pauling's criterion of bond strength to find that the axial bonds in trigonal bipyramidal ML₅ are stronger than the equatorial bonds is incorrect. The results obtained from the two methods approach each other and are in good agreement with the experimental bond lengths, which show that Pauling's criterion is viable and that the pair–defect–sum approximation is indeed an excellent one that agrees with the maximum overlap method.     

Isoelectronic sequences of hydride molecules

The theory of the electronic structure of diatomic hydrides in which the nuclear charge of the second nucleus is varied freely is investigated. By the use of a scale factor which varies with both the nuclear charge and the internuclear distance, the electronic equation can be put into a form suitable for a perturbation expansion. The zero and first order energies are computed for á number of isoelectronic sequences but comparisons with experiment show that higher order terms are needed in order to explain the basic properties of the molecules.

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Zusammenfassung Die Theorie der Elektronenstruktur zweiatomiger Hydride wird untersucht, wobei die zweite Kernladungszahl frei veränderbar bleibt. Durch Einführung eines Maßstabfaktors, der sowohl von Kernladungszahl als auch zwischenatomarem Abstand abhängt, läßt sich die Schrödingergleichung in eine die Durchführung einer Störungsrechnung möglich machende Form bringen. Die Energien nullter und erster Näherung werden für eine Anzahl isoelektrischer Reihen berechnet, allein der Vergleich mit dem Experiment zeigt, daß Terme höherer Ordnung in die Rechnung mit einbezogen werden müssen, um Grundeigenschaften der Moleküle deuten zu können.

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Résumé La théorie de la structure électronique des hydrures diatomiques est étudiée, où la charge nucléaire du second noyau est variable. A l'aide d'un facteur d'échelle dépendant de la charge nucléaire et de la distance internucléaire l'équation de Schrödinger peut être mise dans une forme convenable à un calcul perturbateur. Les énergies de nullième et de premier ordre sont calculées pour quelques séquences isoélectroniques; mais la comparaison de l'expérience montre qu'il faut des termes de plus grand ordre pour expliquer les propriétés fondamentales des molécules.

     

A comparison of calculated and experimental metal-ligand bond lengths in early transition-metal complexes using the method of partial retention of diatomic differential overlap

Basis sets are developed for PRDDO calculations on complexes of the metals Ti, V, Cr, and Mn in high oxidation states Twenty-three unique metal-ligand bond distances were optimized, with an average absolute error of 0.034 Å.     

Ornstein-Uhlenbeck diffusion quantum Monte Carlo study on the bond lengths and harmonic frequencies of some first-row diatomic molecules

This article accesses the performance of the Ornstein-Uhlenbeck diffusion quantum Monte Carlo with regard to the calculation of molecular geometries and harmonic frequencies of H2, LiH, HF, Li2, LiF, CO, N2, and F2 molecules. A comparison of the results for the eight first-row diatomic molecules from experiments, CCSD(T)/6-311G(3df,3pd) and CCSD(T)/cc-pV5Z levels of theory as well as our work is given. The results presented show that quantum Monte Carlo is becoming powerful tools for ab initio electronic structure calculations.     

Effects of exchange on equilibrium bond lengths of heavy,almost spherical,tetrahedral molecules XH4

The simplest nonrelativistic density functional theory, namely, that of Thomas, Fermi, and Dirac, is used to study the effect of exchange on the equilibrium bond lengths of heavy tetrahedral molecules XH₄. In particular, the limiting bond length as the central atom X becomes infinitely heavy is shown to be reduced by exchange by some 0.34 Å. Comparison with experiment shows that the main features of the bond-length variation through the series CH₄? PbH₄ are reflected by the Thomas–Fermi–Dirac predictions, though the bond lengths remain too large for finite atomic number Z of the central atom. Therefore, a semiempirical correction is proposed, which, however, tends to zero as Z tends to infinity.     

The variation of carbon-carbon bond lengths with environment as determined by spectroscopic studies of simple polyatomic molecules

A brief and critical review of the spectroscopic method of determining molecular structures is given. The difficulties and present experimental accuracies of the method are discussed and comparisons with available diffraction values are made. Spectroscopic data on carbon-carbon bond lengths (accurate to 0·005 Å) which have been accumulated in recent years are summarized. These show a simple dependence on bond environment, namely, that bond lengths increase linearly with an increase in the number of adjacent bonds.     

Molecular orbital calculations of bond lengths in benzenoid hydrocarbons

The correlation between bond lengths and bond orders in benzenoid hydrocarbons has been considered. Bond orders for six molecules were obtained by means of a simple MO-LCAO-SC treatment, and a procedure is suggested for calculating accurate bond lengths from such self-consistent bond orders.     

Pi-systems as simultaneous hydride and hydrogen bond acceptors

A theoretical study of the hydride bond complexes with tetrafluoro- and tetracyanoethylene, C2F4 and C2(CN)4, has been carried out by means of density functional theory (DFT) and ab initio methods, up to the MP2/aug-cc-pVTZ computational level. In addition, the ternary complexes formed by an additional standard hydrogen bond donor, such as hydrogen fluoride, have been explored. The results show that the hydride bond complexes are stable and an electron transfer took place from the hydride to the C2F4 and C2(CN)4 molecules. While these molecules are not able to form stable complexes between the pi-electrons and hydrogen bond donors, the presence of the hydrides in the opposite face of the pi-system of C2F4 stabilizes the ternary complexes showing cooperativity effects.