Force Constants for Bond Stretching

The forces between bonded atoms are very strong and considerable energy is required to cause a bond to deviate significantly from its equilibrium value. This is reflected in the magnitude of the force constants for bond stretching some typical values from the MM2 force field are shown in Table 4.1, where it can be seen that those bonds one would... 

Table 1. Block diagonalized G and F matrices for tetrahedral XY4 and octahedral XYn molecules, using the modified Urey-Bradley force field. Adapted from Nakmoto (1997). nix and nij are the masses of atoms ofX and Y, and r is the length of the X-Y bond. K, H, and are force constants for bond stretching, bond-angle bending, and non-bonded repulsion, respectively.

For a number of linear polymers, values of E for single crystals have been determined. This has been performed by direct measurements or by calculation from molecular dimensions and force constants for bond stretching and valence angle deformation (Treloar, 1960 Frensdorff, 1964 Sakurada and co-workers, 1962, 1970 Frank, 1970). 

Suppose we first consider benzene, and decide how we might deal with it in a force-field calculation. Can we find a natural bond length and a force constant for bond stretching, which would presumably be somewhere in between those for a carbon- carbon single bond and a carbon- carbon double bond, and which will adequately reproduce the structure of benzene The answer is that we can, and simple benzene derivatives can then be dealt with using these parameters by the methods previously discussed. We only need to call the benzene bond a special kind of carbon-carbon bond with its own parameters. 

Equilibrium geometries of molecules can be derived from gas-phase experiments, such as electron diffraction and microwave spectroscopy [60]. Raman and infrared vibrational frequencies can also be used to determine force constants for bond stretching and angle bending. If available, experimental data on relative configuration stabilities and barrier heights can be used to parameterize torsional and improper potential terms [19]. 

Force Constants for Bond Stretching Fundamental Vibrational Frequencies of Small Molecules Spectroscopic Constants of Diatomic Molecules Infrared Correlation Charts... 

It is possible to obtain expressions for SI and SO in terms of the applied force /. Consideration of the bond stretching allows SI to be determined. The component of the force acting along the bond direction is/cos a. This can be related to the extension through the force constant for bond stretching ki which can be determined from infra-red or Raman spectroscopy. ki is the constant of proportionality relating the force along the bond to its extension. It follows therefore that... 

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