Bond vibration force constants

The parameters D and a can be obtained by fitting 1E to the actual ground state of the given molecule (D is determined by the observed bond dissociation energy and a is determined by the vibrational force constant). This allows one to express J and K in terms of available experimental information. That is, from eqs. (1.47), (1.49), and (1.52) we obtain... 

Force constants of have been calculated from the data in Table 2 using the general valence force field (GVFF) [148, 149] as well as the Urey-Bradley force field [80] (UBFF) although there is insufficient data to evaluate all the interaction constants since no isotopomers of Se have been measured by vibrational spectroscopy. The stretching and bond interaction force constants were reported as/r = 2.24 andf = 0.53 N cm, respectively [149]. However, because of the uncertainty regarding the Am mode of Se the published force constants [80, 148, 149] maybe unreliable. 

The usefulness of quantum-chemical methods varies considerably depending on what sort of force field parameter is to be calculated (for a detailed discussion, see [46]). There are relatively few molecular properties which quantum chemistry can provide in such a way that they can be used directly and profitably in the construction of a force field. Quantum chemistry does very well for molecular bond lengths and bond angles. Even semiempirical methods can do a good job for standard organic molecules. However, in many cases, these are known with sufficient accuracy a C-C single bond is 1.53 A except under exotic circumstances. Similarly, vibrational force constants can often be transferred from similar molecules and need not be recalculated. 

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 Equation 12.8 Be is the rotational constant, Be = h/(8jt2I), (I is the moment of inertia), coe is the vibrational frequency, 27T(oe = (k/ix)1, (k the vibrational force constant and x the reduced mass), re the equilibrium bond length (isotope independent to reasonable approximation), and ae is the vibration-rotation interaction constant... 

Q The C-H stretching vibrations in dimethyl sulfoxide (Figure 3.18) occur at 2997 and 2909 cm" . Using Hooke s law, and assuming that the C-H bond is the same strength as the C-D bond (same force constant, k, calculate the stretching frequencies of the C-D bonds in dimethyl sulfoxide-t/. ... 

The trans influence can be measured by many techniques, including bond lengths from X-ray structures, bond stretching force constants from vibrational spectroscopy, or from 197Au Mossbauer or NQR parameters. 

Detailed measurements have been made of the low-frequency Raman spectra of [Zn(py)2X2] (X = C1 or Br) and of the far-IR spectra of the complex where X = Q at liquid nitrogen temperature. It is found that skeletal molecular vibrations couple with lattice vibrations in the crystal, except for the Zn—X stretching vibrations. Force constant calculations indicate the Zn—N bond to be stronger in the bromide, while the Zn—Cl bond is stronger than the Zn—Br bond.477... 

The molecule HI has a bond stretching force constant of 314 N m I. Calculate for both H127I and 2D127I, (a) the classical vibrational frequency v in hertz, and (b) the wavenumber of photons corresponding to the n - 0 to n = 1 transition in the vibrational spectrum. 

The repulsive frequency shift, Av0, is expressed explicitly in terms of the first and second derivatives of the excess chemical potential (equation 2) along with the vapor phase vibrational transition frequency, vvib, equilibrium bond length, re, and harmonic and anharmonic vibrational force constants, f and g (232528). 

The vibrational force constants are obtained from measured vibrational frequencies and bond lengths along with extended Barger s rule correlations (36). 

The set of functions, together with the collection of terms that parameterize them (kb, r0, etc.), is referred to as the force field. In some cases force field parameters can be related to experimentally determinable values. For example, the bond stretching force constant kb is approximately equivalent to the vibrational force constant derived from an infrared spectrum. However, in general die force field terms are derived empirically with the target of reproducing experimental structures and energy distributions. 

From the separations of the progression members the vibrational constants coe, cOgXe, (oeye,... (Equation 6.16) for II) can be obtained. Comparison of coe = 2322 cm-1 for the X2Zg state of II) with coe = 3115 cm 1 for the XlZg state of H2 shows that the vibrational force constant (see Equation 6.2) is much smaller in the ground state of H)" than in H2. This, in turn, implies a weaker bond in H)" consistent with the removal of a bonding electron. 

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... 

The same subdivision is used in the qualitative discussion of ionic solvation energies, and it is found that the outer-sphere part is satisfactorily predicted by electrostatic continuum theories (as reviewed in Section III), whereas the inner-sphere part is best obtained by considering the distortion of individual bonds, using force constants from vibrational spectroscopy. 

In this section available vibrational data for the main group binary fluorides will be reviewed in an attempt to establish trends in both structures and bond-stretching force constants. The review is restricted primarily to molecular entities that were observed either in the gas phase or in inert matrices. The emphasis on the matrix data in this review is in contrast with the more general approach taken by Reynolds in an earlier review of the vibrational spectra of inorganic fluorides (2). 

The vibrational problem of a symmetric molecule XY2 is most frequently described in terms of a quadratic valence force field. This is given in terms of a bond stretching force constant K1U the bond-bond interaction constant K12 and the bending force constant Koo ... 

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