Stretching and bending forces

Ground-state effects, i.e., the effects on the bond lengths and angles, stretching and bending force constants, and other spectroscopic properties of the other ligands. 

Table 6 shows that the variation in the reported symmetric stretch and bending force constants is relatively small. For the asymmetric stretching force constant only the Shavitt et al. and Liu values of —0.061 a.u. and —0.058 a.u., respectively, are in substantial agreement, the PK surface yielding a value of —0.124 a.u. which is more than a factor of two greater. 

The observed stretching and bending force constants from Eqn. (10) and (13) are then expressed as... 

The major source of the disorder energy is the bond strain within the random network. Phillips (1979) proposed a model to explain the relation between network coordination and disorder. A four-fold continuous random network is overcoordinated, in the sense that there are too many bonding constraints compared to the number of degrees of freedom. The constraints are attributed to the bond stretching and bending forces, so that for a network of coordination Z , their number, NciZJ is. 

Zeolites have also been recently studied using molecular mechanics simulation (Mabilia et al., 1987) with stretching and bending force constants and partial atomic charges taken from ab initio calculations. These calculations indicate that the sodalite cage structure is stabilized by replacement of Si by A1 and by local concentration of Al for a given Si Al ratio, but these results seem to be inconsistent with experiment. 

The factors in determining the barriers to ring-inversion in the spin paired and odd-electron molecules are proposed to be different bond lengths and angles associated with the oxygen atoms, related stretching and bending force constants, tor-... 

The bond distances HC and CO were estimated to be the same as those in HCN and HCO molecules, respectively. The vibrational frequencies were calculated by the valence force method from the estimated stretching and bending force constants which were obtained from HCN(g). 

The description of the forces between these atoms (bond-stretching and bending-force constants, barriers to internal rotation, and other large amplitude motions) and... 

Qualitative explanations advanced prior to 1952 were reviewed by Stuart in his book of that date. Le F vre et al. (1956) attempted an a priori quantitative treatment of anomalous anisotropy in centro-symmetric non-polar structures along lines used previously for atomic polarizations (Le Fevre and Rao, 1954, 1955). The expression reached for the mK of a CX4 molecule involved link moments pcx, c—x and i x, stretching and bending force constants, effective charges on atoms, and the rates of change of b% x and with elongation or contraction... 

An isotope effect reflects the sum of changes in all the bond stretching and bending forces experienced by an atom, so it is not possible to determine an isotope effect from the shift of a single peak in a vibrational spectrum. 

This type of potential field is called a generalized valence force (GVF) field. It consists of stretching and bending force constants, as well as the interaction force constants between them. When using such a potential field, four force constants are needed to describe the potential energy of a bent XY2 molecule. Since only three vibrations are observed in practice, it is impossible to determine all four force constants simultaneously. One method used to circumvent this difficulty is to calculate the vibrational frequencies of isotopic molecules (e.g., D2O and HDO for H2O), assuming the same set of force constants.+ This method is satisfactory, however, only for simple molecules. As molecules become more complex, the number of interaction force constants in the GVF field becomes too large to allow any reliable evaluation. 

In another approach, Shimanouchi [82] introduced the Urey-Bradley force (UBF) field, which consists of stretching and bending force constants, as well as repulsive force constants between nonbonded atoms. The general form of the potential field is given by... 

A potential field consisting of stretching and bending force constants only is called a simple valence force field. 

The stretching and bending force constants ki and k2 have been estimated using data of the related PH3 molecule or theoretically calculated. ki =3.10 mdyn/A for ground-state PH2 was taken from PH3 [7]. k =7.260 mdyn/A and k2 = 0.01021 mdyn/A were calculated by an ab initio MO-SCF method [37]. Apparently more reliable data for k2 are given below for the ground state X 2Bi and the excited state A Ai (for units, see also the remarks) ... 

Stretching and bending force constants were calculated by an ab initio MO-SCF method... 

The Urey-Bradley force field (UBFF) is also commonly used. This consists of diagonal stretch and bend force constants together with repulsive force constants representing nonbonded atom-atom interaction. 

The general valence force field of pyramidal XY3-type molecules contains six independent constants. In internal coordinates, these are the stretching and bending force constants f and f , and four interaction constants f r for two adjacent bends, fr and fr . for a stretch and an adjacent and a nonadjacent bend, and fo two bends. Besides the four fundamental frequencies, additional spectroscopic data such as isotopic frequency shifts, centrifugal distortion constants, and Coriolis coupling constants are required to fix a unique set of force constants. Various authors have performed such calculations, and the sets so obtained [13, 14, 25, 26, 35 to 38, 45] agree reasonably well. As a representative example, the symmetry and valence force constants, all in mdyn/A, of Sawodny et al. [25] are presented below. 

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