Bond bonding interaction

The effect shown in Fig. 9 is a result of the bond-bond interaction which is a characteristic feature for chains and rings of two-valent chalcogen atoms. It can also be recognized from the relatively large bond interaction force constants fir of such compounds. The stretching force constants /r(SS) of polysulfur compounds depend on the SS bond distances as shown in Fig. 10. The data used in this figure include several excited electronic states of the S2 molecule as well as the disulfide anion and a number of sulfur homocycles [77]. 

Fig. 2. Relationship between the bond lengths of neighboring bonds in sulfur rings indicating strong bond-bond interaction. The distance, d, of a bond between two-coordinated atoms is. a function of the arithmetic mean of the lengths of the two neighboring bonds, V2(di dj). The values were taken from the compounds indicated in the Figure. The curve ends on the right side at d2 = 189 pm, the bond length of the diatomic molecule Sj...

By adjusting the calculated to the observed wave numbers, the following five Urey-Bradley force constants have been obtained for Se6 (in N/cm) K = 1.188 (bond stretching), H = 0.102 (bond-angle bending), F = 0.082 (next nearest atom repulsion), Y = 0.242 (torsion), and P = 0.207 (bond-bond interaction) (18,19). 

The vibrational problem of a symmetric molecule XY2 is most frequently described in terms of a quadratic valence force field. This is given in terms of a bond stretching force constant K1U the bond-bond interaction constant K12 and the bending force constant Koo ... 

More recently Carnall, et al. (6) have pointed out that the symmetric stretching frequency cannot be determined in many uranyl compounds, thus preventing the calculation of Fro- Since the error introduced by neglecting bond-bond interactions should be only several percent, they suggest use of the asymmetric stretching frequency only, thus permitting modification of the equation to... 

Table 11 records force constants and calculated bond orders in several azides. (/(N Nb/NtN ) is the bond-bond interaction force constant.)... 

Over the years various approximate formulas for interactions between large molecules have been derived from perturbation theory (91) The better of such perturbation theory expansions customarily include a short-range first order "exchange" term and long range terms (electrostatic, polarization and dispersion). Various approximations (such as the multi-centered multipole expansion, representation of transition densities by bond dipole and the decomposition of molecular polarizability into bond polarizabilities, the use of atomic polarizabilities, bond-bond interaction terms, etc.) have been introduced for the calculation of certain of the terms. 

Fig. 21 Relationship between the bond lengths in sulfur rings S5 to S13 indicating strong bond-bond interactions. The bond length 2 is plotted as a function of the two neighboring bonds, /2 di+d ), see the inset. Experimental values are shown by open triangles, MD calculated values by full circles [67]...

The calculated values are given in Table 12. For the localized orbitals connected to different centers the calculated multipole interactions agree well (within 2%) with the corresponding Coulomb integrals (bond-bond interactions in Table 12). For the localized orbitals connected to the same nucleus (lone-lone interactions) the deviations are rather large (>50% in some cases). 

Bond-bond interactions are important in doubly bonded or 7t systems, such as polyenes and aromatic molecules, and even in partially conjugated... 

The amount of information contained in a measured vibrational spectrum is exploited to some, but not full extent. For example, vibrational spectra are never used to characterize all bonds of the molecule and to describe its electronic structure and charge distribution in detail. Of course, aspects of such investigations can be found off and on in the literature, however, both quantum chemists and spectroscopists fail to use vibrational spectra on a routine basis as a source of information on bond properties, bond-bond interactions, bond delocalization or other electronic features. Therefore, it is correct to say that the information contained in the vibrational spectra of a molecule is not fully utilized. This has to do with the fact that the analysis of vibrational spectra is always carried out in a way that is far from chemical thinking. The basic instrument in this respect is the normal mode analysis (NMA), which describes the displacements of the atomic nuclei during a molecular vibration in terms of delocalized normal modes [1-6]. 

The TT interactions reinforce the metal-carbon bond (bonding interactions M—C) but weaken the CO bond (antibonding interactions C—O) (3-17b). This electronic reorganization can be represented by tbe Lewis structures shown in 3-18. 

Supposing no bond-bond interaction (no short-range interactions), all the bonds are of the same length I, and... 

Bond-Bond Interactions. Bond angles variability is much more important to structural analysis of polyatomic molecules than the variability of bond lengths, but no theoretical basis for an analytical presentation of bond angle energy potentials has been offered as yet. However, quantum mechanics has given us a comprehensive conceptual insight into the nature of the forces which determine bond... 

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