Bond force constants

As a simple example of a normal mode calculation consider the linear triatomic system ir Figure 5.16. We shall just consider motion along the long axis of the molecule. The displace ments of the atoms from their equilibrium positions along this axis are denoted by It i assumed that the displacements are small compared with the equilibrium values Iq and th( system obeys Hooke s law with bond force constants k. The potential energy is given by ... 

Cl bond force constants in MCI2 species and MCI4... 

Sodium Acetate Complexes of U(VI), Np(VI), Pu(VI) and Am(VI). A Comparison of Metal Oxygen Bond Distance and Bond Force Constant in this Series. Report AECU-3088 (1954). J- chem. Phys. 23, 2105 (1955). 

Compound Bond Force constant (mdyne/A) Calcd. Obsd. ... 

For this case, the primary change that is observable in the IR spectrum is due to changes in the vibrahonal frequencies of the probe molecule due to modificahons in bond energies. This can lead to changes in bond force constants and the normal mode frequencies of the probe molecule. In some cases, where the symmetry of the molecule is perturbed, un-allowed vibrational modes in the unperturbed molecule can be come allowed and therefore observed. A good example of this effect is with the adsorption of homonuclear diatomic molecules, such as N2 and H2 (see Section 4.5.6.8). 

For (-)-cyclohexanone-2,6-chair conformations are equivalent, with the axial and equatorial CD bonds chirally oriented. The CD stretching VCD, positive at —2200 cm and negative between 2130-2170 cm , is consistent with that predicted for coupled motion of the two CD bonds. In this case, the splitting between the modes is due to different CD bond force constants for the axial and equatorial positions. 

Fig. 8a and b. First neighbour bonds of a central atom which is a bulk atom of a fee crystal. It has 12 first-neighbour bonds, b A cobalt atom in a monolayer of cobalt on copper (111). In this case the three upper bond force constants are reduced to zero (surface effect) while the effect of the copper substrate is to reduce the values of the three lower bonf force constants by about 15%... 

There are, fortunately, several properties that do correlate well with the bond valence as discussed below. They include the bond length and its thermal expansion as well as a bond force constant that can be used for a semi-quantitative analysis of the Raman and infrared spectra of crystals. 

Length and energy of the bond force constants vfera- ... 

The Lowering of the vXH Frequency on H-hond Formation If an investigation of the effect of mechanical interaction between harmonic XH and H Y vibrations is made with the help of the usual equations for the vibrations of a triatomic molecule [16], it is found that, for a fixed value of the XH force constant, the rXH frequency increases as the force constant of H Y is raised from zero.. As the experimentally observed effect is a large one in the opposite direction, i.e, the rXH frequency decreases markedly with an increase in the strength of the H-bond, the only reasonable explanation of the spectroscopic facts seems to be that the lowered frequency is a reflection of a lowered XH bond force constant [17, IS]. 

The frequency of the vibration can be described by Hooke s law, which describes the relationship between the wavenumber (v), the strength of the bond (force constant, k) and the reduced mass /z ... 

In this expression, s and Re have the same physical meaning as discussed above, and the width parameter a is related to the bonding force constant k by... 

The effectiveness of the second type of overlap presumably determines the extent of oMnic character of tho epoxide. That ethylene oxides are less unaaturated in character than the corresponding cyclopropane derivatives is then attributable to a less favorable oxygen atomic-orbital orientation. The Walsh model is a satisfactory one in that it predicts accurately the C—H bond force constants... 

Clearly, as already summarized in Figure 4, benzene and allyl radical are quite special in having a combination of strong o-resistance which overcomes a moderately distortive Tr-component. On the contrary, in cyclobutadiene the fine balance is tipped in favor of the r-distortivity. However, this balance is fragile and can be tampered with. Even substituted cyclobutadienes have been considered at times to be effectively square.144-146 As we shall see later, manipulation of the o-resistance by proper substitution of benzene enables its r-distortivity to become manifest. Heilbronner s expression13 of the fragility of the jt o-balance for benzene and allyl radical is perhaps a most appropriate one If by an act of God all the spf—spf o-bond force constants were reduced to half... 

Bonding in a diatomic molecule may be described by the curve given in Fig. 2.5, which represents the potential energy (K(r)) as a function of the structure (r). The bonding force constant, k, is given by the second derivative of the potential with respect to the structural parameter r, which corresponds to the curvature of the potential energy function. The anharmonicity can be described by higher-order derivatives. 

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