Bending force constants

I lic 3-alorn and 4-atoni rcstrairiis behave just like those for two atoms, except tliat the dialog hox requests an angle rather than a distance and the accompanying request for a force constant requires either a bending force constant (3-atorn case) or a torsional force con Stan t (4-atorn case). 

A larger value for the bending force constant K0 leads to a greater tendency for the angle to remain at its equilibrium value 0g. There may be cubic, quartic, etc. terms as with the corresponding bond stretch term in addition to the quadratic term shown here. 

The MM+ force field uses special values for the bending force constants when the atoms are in a three- or four-membered ring. 

If atom i or atom j is a hydrogen, the deformation (r-r ) is considered to be zero. Thus, no stretch-bend interaction is defined for XH2 groups. The stretch-bend force constants are incorporated... 

The constant 2.51118 converts between MM-t stretch-bend force constants expressed in millidynes per radian and HyperChem s default, kcal per degree. 

The functional form for angle bending in BIO+ is quadratic only and is identical with that shown in equation (12) on page 175. The angle bending force constants are in units of kcal/mol per radian2 and are in the file pointed to by the QuadraticBend entry for the parameter set in the Registry or the chem.ini file, usually called ben.txt(dbf). 

All default bending force constants are assigned the value 100 kcal/mol/rad ... 

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. 

Experimental harmonic frequencies, Duncan, J. L. Allan, A. McKean, D. C. Mol. Phys. 1970, IS, 289. dFor PES1 (Br) the H-C-Cl and H-C-Br bending force constants are the ab initio values, while these ab initio force constants are scaled for PES2(Br) to obtain better agreement with experiment. 

For PES3, the ab initio < >-bending force constants are scaled as described above for PES2. 

The preceding suggests that the structure of the density of vibrational states in the hindered translation region is primarily sensitive to local topology, and not to other details of either structure or interaction. This is indeed the case. Weare and Alben 35) have shown that the density of vibrational states of an exactly tetrahedral solid with zero bond-bending force constant is particularly simple. The theorem states that the density of vibrational states expressed as a function of M (o2 (in our case M is the mass of a water molecule) consists of three parts, each of which contains one state per molecule. These arb a delta function at zero, a delta function at 8 a, where a is the bond stretching force constant, and a continuous band which has the same density of states as the "one band Hamiltonian... 

In Eq. (6.1) 1 is the unit operator, there is one state /> associated with each lattice site, and l and l A A = 1, 2, 3, 4) label a molecule and its nearest neighbors in the tetrahedral lattice. Weare and Alben show also that the theorem remains valid when small distortions away from tetrahedrality exist, hence it can be used to describe a random amorphous solid derived from a tetrahedral parent lattice. Basically, the density of states of the amorphous solid is a somewhat washed out version of that of the parent lattice. The general shape of the frequency spectrum is not much altered by the inclusion of a non zero bond-bending force constant provided the ratio of it to the bond stretching force constant is small relative to unity. 

Fractionation factors are calculated using measured vibrational spectra supplemented by simplified empirical force-field modeling (bond-stretching and bond-angle bending force constants only). 

The X-ray structure of 1-dimethylphosphono-l-hydroxycycloheptane (65) was compared only with MM calculations of cycloheptane (216), but it should now be possible to include the substituents with one of the force fields in Table 9. Inorganic perhalophosphazenes, (N=PX2) have been subjected to MM analysis. Compared to hydrocarbons, the P—N—P bending force constant and the two-fold torsional barrier are small (217). 

Diborane. As shown in Table I, the B-H terminal stretching modes of diborane occur at an average frequency of 2563 cm-1, whereas the average of the bridging B-H stretches v% y6, 3, and vyi) occurs 28% lower, at 1847 cm-1. The existing normal coordinate vibrational analyses display some abnormalities, such as a near zero Hb-B-Hb bending force constant, but the general features of the force field for diborane are reasonably well understood. The vibrational analyses indicate that the B-Hb force constant is about half of that for B-Ht (i, 2,3). This... 

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