Bond length stretching constant

The relationships between bond length, stretching force constant, and bond dissociation energy are made clear by the potential energy curve for a diatomic molecule, the plot of the change in the internal energy AU of the molecule A2 as the internuclear separation is increased until the molecule dissociates into two A atoms ... 

For each pair of interacting atoms (/r is their reduced mass), three parameters are needed D, (depth of the potential energy minimum, k (force constant of the par-tictilar bond), and l(, (reference bond length). The Morse ftinction will correctly allow the bond to dissociate, but has the disadvantage that it is computationally very expensive. Moreover, force fields arc normally not parameterized to handle bond dissociation. To circumvent these disadvantages, the Morse function is replaced by a simple harmonic potential, which describes bond stretching by Hooke s law (Eq. (20)). 

The default parameters for bond stretching are an ec iiilibriiim bond length an d a stretch in g force eon starit. fb e fun etion al form isjiist that of the. M.M+ force field including a correction for cubic stretches. The default force constant depends only on the bond... 

The correlation of stretching wavenumbers to the bond lengths is a spec-troscopical expression of the dependence of the valence force constant fr from the bond length r [197-199] which is presented in Fig. 33 ... 

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. 

A quantum-mechanical description of spin-state equilibria has been proposed on the basis of a radiationless nonadiabatic multiphonon process [117]. Calculated rate constants of, e.g., k 10 s for iron(II) and iron(III) are in reasonable agreement with the observed values between 10 and 10 s . Here again the quantity of largest influence is the metal-ligand bond length change AR and the consequent variation of stretching vibrations. 

They found that the order for the M—0 stretching modes (M—0 force constants) was (02)Pd(02) > Pd(Oj) and (02)Ni(02) > Ni(02), and since the 0-0 force constant increased as the M-0 force constant decreased, reversibility could not be equated with shorter 0—0 bond length. To test the proposed isosceles model they predicted the various absorptions that would be expected on the basis of the symmetrical structure (a) and unsymmetrical structure (c), Fig. 8. If the isotopic ratio of 0 0 is 1 1, then three bands would be expected for structure (a), with relative intensities 1 2 1, and four bands would be expected for structure (c), with relative intensities 1 1 1 1, the two oxygen atoms now being in different environments. These workers 189) then obtained the IR spectrum for the cocondensation product from the reaction between nickel and O2 (4.2—10°K), in isotopic ratio 0 =1 1, and found three bands with relative inten-... 

---