Bonds, chemical stretching force constants

Both intramolecular force constants are lowered somewhat through complex formation (Table 6). As expected this effect is larger in the proton-donor than in the proton-acceptor molecule. In Table 7 we present calculated and experimental data on the vibrational spectrum of (HF)2. General agreement is obtained. The most remarkable feature is the strict separation of intra- and intermolecular modes on the frequency axis. Hydrogen bond formation is a weak interaction compared to the formation of a chemical bond hence, the normal frequencies are well separated. However, Hartree-Fock calculations of bond stretching force constants... 

Compute the stretching force constants (k, kg, k, and k P) and discuss their magnitudes in terms of the strengths of the chemical bonds and the likely interactions among these. Two independent determinations of the quantity k - k are obtained using the isotopic data and Eq. (7c), but the calculation of k + k , kg, and k g requires the combined... 

The constant of proportionality (k) in both cases is the stretching force constant and, in the same way that a force constant can measure the strength of a mechanical spring, k gives a measure of the strength of a chemical bond. Indeed, the force constant measures bond strength when the atoms are near their equilibrium positions, a far more subtle measure than the dissociation energy. 

The importance of bond stretching force constants is that they measure the strength of chemical bonds and therefore can be related to bond length r and bond order P. A useful relation between these properties is given by Gordy s equation... 

Wagner claims that this structure con-esponds to HNg, but no consideration was given to the effect of the H atom. He carried out similar calculations on various pseudohalide anions and was able to show that the pA of the corresponding acids varies linearly with the difference in the 7r-energy between the ions and their acids. Linear correlations were also found betw een (a) calculated bond orders and stretching force constants, (b) calculated charge densities and n.m.r. chemical shifts. 

Chemical Studies. Stretching force constants have been used in an investigation of the valence bond wave function from which an estimate has been made... 

This expression is the same as that used by Johnston and Parr [63] in their bond-energy - bond-order (BEBO) method for describing potential energy surfaces of simple chemical reactions. It shows an exponential dependence of dissociation energy on change in ground-state distance. Stretching force constants k n) and equilibrium distance are related as follows... 

FIG. 3.4. Plots of the dependencies between experimental atomic equilibrium charges of halogens in CH3a and (a) difference of electronegativity between halogen and carbon, (b) stretching force constant of the bond aC, and (c) interatomic distance aC (Reproduced from Ref. [81] widi permission. Copyright [1984] American Chemical Society). 

Most of the molecules we shall be interested in are polyatomic. In polyatomic molecules, each atom is held in place by one or more chemical bonds. Each chemical bond may be modeled as a harmonic oscillator in a space defined by its potential energy as a function of the degree of stretching or compression of the bond along its axis (Fig. 4-3). The potential energy function V = kx j2 from Eq. (4-8), or W = ki/2) ri — riof in temis of internal coordinates, is a parabola open upward in the V vs. r plane, where r replaces x as the extension of the rth chemical bond. The force constant ki and the equilibrium bond distance riQ, unique to each chemical bond, are typical force field parameters. Because there are many bonds, the potential energy-bond axis space is a many-dimensional space. 

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