1,2,4-Triazincs XIII. The bond lengths and bond angles of a 1,2,4-triazine

The bond distances and bond angles of 5-(p-chlorophenyl)-1,2,4-triazine determined by three dimensional X-ray crystallographic analysis are reported. The pertinent bond lengths are N₁? N₂, 1.335Å, N₂-C₃, 1.314Å, C₃? N₄, 1.339; N₄-C₅, 1.317; C₅-C₆, 1.401; C₆? N₁, 1.317Å. A comparison of these bond distances with those of similar polyazabenzenes shows that the canonical structure of 1,2,4-triazine with a N₁? N₂ single bond more closely represents the ground state of this ring system, than the one with a N₁? N₂ double bond.     

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.     

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.     

Polymer complexes: supramolecular modeling for determination and identification of the bond lengths in novel polymer complexes from their infrared spectra

Synthesis and characterization of allyl propenyl‐2‐(4‐derivatives phenylazo)butan‐3‐one (HL_n) are described. The monomers obtained contain N?N and carbonyl functional groups in different positions with respect to the allyl group. This structural difference affects the stereochemical structure of the uranyl polymer complexes prepared by the direct reaction of uranyl acetate with the monomers. The polymer complexes are characterized by elemental analyses, ¹H and ¹³C NMR, electronic and vibrational spectroscopy and other theoretical methods. The bonding sites of the hydrazone are deduced from IR and NMR spectra and each of the ligands were found to bond to the UO₂²⁺ ion in a bidentate fashion. The monomers obtained contain N?N and carbonyl functional groups in different positions with respect to the allyl group. IR spectra show that the allyl azo homopolymer (HL_n) acts as a neutral bidentate ligand by coordinating via the two oxygen atom of the carbonyl group, thereby forming a six‐membered chelating ring. The υ₃ frequency of UO₂²⁺ has been shown to be a good molecular probe for studying the coordinating power of the ligands. The υ₃‐values of UO₂²⁺ from IR spectra have been used to calculate the force constant, F_UO (in 10^?8 N/Å) and the bond length R_UO (in Å) of the U? O bond. We adopted a strategy based upon both theoretical and experimental investigations. The theoretical aspects are described in terms of the well‐known theory of 5d–4f transitions. The necessary structural data (coordination geometries and electronic structures) are determined from a framework for the modeling of novel polymer complexes. The Wilson, G. F. matrix method, Badger's formula and the Jones and El‐Sonbati equations were used to determine the stretching and interaction force constants from which the U? O bond distances were calculated. The bond distances of these complexes were also investigated. The effect of Hamett's constant is also discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

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.     

Correlations between bond lengths and stretching frequencies in the O—D...O hydrogen bridge and their consequences

Based on modern neutron diffraction data and the known empirical correlations between the geometric and spectroscopic parameters of hydrogen bonds, the analytical expression describing the relation between the O—D covalent and D...O hydrogen bond lengths in the O—D...O hydrogen bridge was obtained. The distribution functions of the interatomic and nearest intermolecular distances in heavy water were calculated from the Raman band shapes in the 10 to 90 °C temperature interval in the framework of the fluctuation theory of hydrogen bonding.     

Databases for transition element bonding: metal-metal bond energies and bond lengths and their use to test hybrid, hybrid meta, and meta density functionals and generalized gradient approximations

We propose a data set of bond lengths for 8 selected transition metal dimers (Ag(2), Cr(2), Cu(2), CuAg, Mo(2), Ni(2), V(2), and Zr(2)) and another data set containing their atomization energies and the atomization energy of ZrV, and we use these for testing density functional theory. The molecules chosen for the test sets were selected on the basis of the expected reliability of the data and their ability to constitute a diverse and representative set of transition element bond types while the data sets are kept small enough to allow for efficient testing of a large number of computational methods against a very reliable subset of experimental data. In this paper we test 42 different functionals: 2 local spin density approximation (LSDA) functionals, 12 generalized gradient approximation (GGA) methods, 13 hybrid GGAs, 7 meta GGA methods, and 8 hybrid meta GGAs. We find that GGA density functionals are more accurate for the atomization energies of pure transition metal systems than are their meta, hybrid, or hybrid meta analogues. We find that the errors for atomization energies and bond lengths are not as large if we limit ourselves to dimers with small amounts of multireference character. We also demonstrate the effects of increasing the fraction of Hartree-Fock exchange in multireference systems by computing the potential energy curve for Cr(2) and Mo(2) with several functionals. We also find that BLYP is the most accurate functional for bond energies and is reasonably accurate for bond lengths. The methods that work well for transition metal bonds are found to be quite different from those that work well for organic and other main group chemistry.     

Archimedean structure of the carbon cluster C12: Alternation of bond lengths and aromaticity

We consider the possibility that the stability of the Archimedean structure C₆₀ (a truncated icosahedron) is a consequence of the aromaticity of this nonalternant molecule. As the model, we used the structure of C₁₂ in the form of a truncated tetrahedron — the first of the Archimedean solids, having triangular faces in addition to hexagonal faces (rather than the pentagonal faces in the analogous C₆₀ molecule of symmetry I_h). On the basis of calculation of the topological resonance energy of the C₁₂ molecule of T_d symmetry, we conclude that the structure with different bond lengths is antiaromatic, while the C₁₂ molecule (whose hexagonal faces are benzene rings of the Kekulé type) has a slight degree of aromatic character. MNDO and AMl calculations have shown that these structures for C₁₂ correspond to minima on the potential energy surface, but the structure with different bond lengths has lower energy. We also observe an isomer of C₁₂ having benzene rings of the quinoid type, which corresponds to a minimum on the potential energy surface but is less stable than the structure with equal bonds. Aromatic stabilization is expected, as shown by the calculation for the tetracation C⁴⁺ ₁₂ of Td symmetry with virtually equal lengths of all the carbon-carbon bonds.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 2, pp. 229–233, March–April, 1990.     

Optimized bond lengths and electron densities on atoms in heterosubstituted polyenes

Bond lengths and electron density distribution in the polymethine chain of various heterosubstituted polyenes having carbonyl, cyano, and amino end groups are calculated in geometry-optimized CNDO/2 aproximation. It is shown that the significant alternation of the carbon-carbon bond lengths is largely independent of the nature of the end group, the arrangement of long and short bonds being determined by the form of the polyene. Heterosubstitution causes the electron density to alternate and the alternation amplitude, which decreases towards the middle of the chain, is dependent on the electron-donor properties of the polyene.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, No. 4, pp. 313–319, July–August, 1992.     

The fifth overtones of the C-H stretching vibrations and the bond lengths in some heterocyclic compounds

The fifth overtones of the C-H stretching vibrations of pyridine, pyrazine, thiophene, 3-methylthiophene, furan and pyrrole in the liquid state have been observed by a thermal lens technique. It was found that their frequency shifts from that of benzene are proportional to the decrease in the relevant C-H bond length.     

Monte Carlo simulation of freely jointed chains with variable bond lengths

Monte Carlo simulation of freely jointed off-lattice chains with variable bond length is usually done with local random displacements of beads and with reptation moves (displacements of a bead along a chain). In dense systems, the acceptance ratio of reptations decreases strongly with density. We discuss versions of reptation moves, which are effective in dense systems. The idea, which comes from lattice systems, is to use a pseudovacancy (walker), which has the same size as a bead of a chain. The walker is attached to a neighbor chain and then another bead of that chain is cleaved. This is equivalent to a reptation move and a nonlocal displacement of the walker and since no free volume is needed, the move can be used with advantage in dense systems. A related technique are cooperative motions, which were introduced by T. Pakula for lattice models, where several chains change their conformation concomitantly. Such cooperative loops are implemented in the Monte Carlo algorithm by creating a temporary walker by cleaving a bead from a chain, moving it with reptations and finally annihilating the walker by attaching it to the same chain it was cleaved from. These moves and the condition of detailed balance are discussed in detail. As an example, we study the integrated autocorrelation time τ_int for the radius of gyration for a two-dimensional system. For reduced densities larger than 0,4, we find that with standard reptations and local bead displacements τ_int increases strongly with density. If reptations with either a permanent or a temporary walker are used in addition to local moves, the integrated autocorrelation time changes only very little with density and very dense systems can still be simulated efficiently.     

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.     

Conjugation, hybridization, and steric hindrance in relation to bond lengths

Three theories which have been proposed to explain the observed shortening of a single bond when it is adjacent to a double bond are discussed. Possible predictions from these theories are examined, especially for comparison with various quantities measurable by microwave spectroscopy. It is concluded that the steric theory is probably untenable, that some conjugation appears necessary to explain observed barries to internal rotation, and that it is difficult to find testable predictions from the hybridization theory.     

Correlation between hydrogen bond lengths and reduction potentials in Clostridium pasteurianum rubredoxin

15N NMR hyperfine-shift data were collected for wild-type and site-specific mutant (V44I, V44A, and V44G) Clostridium pasteurianum rubredoxins in the oxidized state. Whereas most of the (15)N NMR signals did not exhibit large systematic changes upon mutation of residue 44, the signal from the backbone nitrogen of residue 44 itself (arrows) shifted by approximately 400 ppm. These shifts were used to determine the lengths of the hydrogen bond between the backbone amide of residue 44 and the side-chain sulfur of cysteine-44, which is covalently ligated to the iron of the metal center. The results, which demonstrated that this hydrogen bond is shorter in mutants with higher reduction potential, point to the importance of hydrogen bonds in modulating the reduction potential of iron-sulfur proteins.     

The effects of fluorine and chlorine substitution on bond lengths in ethanes and disilanes: comparisons of ab initio and experimental information

Ab initio and some density functional theory calculations of bond lengths in fluoro- and chloro-ethanes and disilanes are reported with a precision of ±0.0001 Å under strictly comparable conditions. The resulting changes in MH and MX (M=C, Si; X=F, Cl) bond length are analysed for the effects of halogens substituted in geminal (), or vicinal (gauche or trans) positions. The shortening effect of halogen on an MH bond is markedly reduced or even reversed by the introduction of electron correlation at the MP2 or B3LYP level. MX bonds are little affected. gauche halogen consistently shortens both MH and MX bonds, while trans halogen has no effect on an MH bond but a small and variable effect on the MX bond.

The reality of these calculated changes in bond length is tested in two ways. MH bond lengths are plotted against experimental values of the isolated stretching frequencies ν^isMH, which themselves correlate well with experimental r₀ bond lengths. Agreement on the resulting substituent effects is generally good for the gauche and trans effects of halogen but variable for effects. Unobserved ν^isMH values are predicted from computed bond lengths in fluoroethanes, chloroethanes and chlorodisilanes.

Calculated MX and MM bond lengths are compared with experimental values, notably those from electron diffraction studies amongst the ethanes. Most calculations underestimate the changes found experimentally in CF and CCl bond lengths. CC bond length changes are underestimated in fluoroethanes and overestimated in the chloro-compounds.

The ‘offset’ value (r_e(calc)−r_e(true)) for a CH or SiH bond calculated with a given basis set and level of theory in most cases varies markedly throughout the series of compounds. The same is true for CF, CCl, CC and SiSi bonds if the corresponding offset values for the r_a lengths are constant.

The need is stressed for extended experimental work on many of the compounds, especially the disilanes. It is recommended that structures should be refined with ab initio derived constraints on the bond lengths involved and differences between spectroscopic and diffraction-based geometries reconciled through the calculation of r_z structures.     

Variation of calculated single bond lengths in saturated hydrocarbon and silicon hydride molecules

A series of saturated X_nH_m (X being either C or Si) molecules is studied using the MINDO /3 and MNDO quantum-chemistry procedures. We find that the proximity of H atoms tends to shorten X? X bonds, and that this effect is (especially for MINDO /3) much larger than a similar trend in experimental values. The connection between this and hybridization values calculated from localized orbitals is investigated. It is found that the hybridization model works well for X? H bonds, whereas for X? X bonds non-σ-bond effects also play a significant role. It is shown that the changes in electronic structure may be directly connected to differences in X and H atomic levels, so that similar bond length differences may be expected in other molecular orbital calculations.