Frequency-bond length relationships

One can use stretching frequency/bond length relationships to predict geometrical features of molecules from measured infrared spectra. This should be first checked for a case where verification of the prediction is possible due to an available geometry obtained from an ab initio calculation. 

Bond length vs. bond stretching frequency A good linear relationship ha been establi ed between the S=0 bond length (r) and S=0 bond stretching frequency (v) in the XSO2Y sulphone series ... 

Even small differences in the P-Cl bond lengths of chlorocyclophosphazenes give rise to a multiple line Cl NQR spectrum [309-314]. An increase in the P-Cl bond length is accompanied by a decrease in the C1 NQR frequency, and this most probably reflects an increased ionic character of the P-Cl bonds. Closely related chlorocyclophosphazenes show a linear relationship between CI NQR frequencies and P-Cl bond lengths [314]. 

Attempts at correlating endocyclic phosphorus bond angles with the phosphorus chemical shifts and P-N bond distances with C1 NQR frequencies have been made [314]. It appears that for closely related compounds there exists a narrow relationship between chemical shifts and endocyclic phosphorus angles [96, 358]. No generalized trend has yet emerged. The differences in the P-Cl bond lengths in PCl2 and PRCl units have been correlated with the C1 NQR frequencies [314],... 

Qualitative ways of analyzing a problem in molecular vibrations, that is, methods for determining the number of normal modes of each symmetry type which will arise in the molecule as a whole and in each set of equivalent internal coordinates, have been developed. There is also the quantitative problem of how the frequencies of these vibrations, which can be obtained by experiment, are related to the masses of the atoms, the bond angles and bond lengths, and most particularly the force constants of the individual bonds and interbond angles. In this section we shall show how to set up the equations which express these relationships, making maximum use of symmetry to simplify the task at every stage. 

A linear relationship was established between 4-carboxyl bond length (as determined by X-ray diffraction) and IR vibration frequency in a series of 4//-pyrido[l,2-a]pyrimidin-4-ones (78ACH1819). 

Related to this topic is the exhaustive discussion of the relationship between C-Cl bond length and 35C1NQR frequencies of organochlorine compounds29. A number of the investigations of the effect on halogen NQR frequencies in particular systems are discussed below. 

There is an approximately linear relationship between 35C1 NQR frequencies and P—Cl bond lengths in closely related chlorocyclo-phosphazene derivatives [e.g., N3P3Cl6 Ph (n = 0, 2, 4) N3P3C13-(NMe2)3 isomers). An increase in bond length is accompanied by a decrease in the NQR frequency, and this change presumably reflects an increase in the ionic character of the bond (248). 

This relationship between K and -interaction is supported by the electronic and ESCA spectra of these complexes (41). A rough correlation has also been shown to exist between the A8 values for a series of ethylene complexes and both the C=C stretching frequency and the C=C bond length (41, 42). In addition, several groups have shown that the upheld shift of the olefinic carbon atoms in phosphine complexes correlates with the basicity of the phosphine (vide infra). 

The inverse relationship between uranyl bond length and asymmetric stretching frequency has been shown to agree reasonably well over a rather substantial range with the predictions of Badger s rule. The form of the rule proposed by Jones (16) is... 

Figure 9.40 shows another example of residual strain effects on the Raman spectrum. The Si stretching vibration changes its frequency when Si is in the form of a thin film on sapphire. We can compare the Raman band positions between the strain-free sample and strained sample to evaluate the bond length change, which can be converted to residual strain. The residual strain is commonly elastic in nature. Thus, the residual stress in materials can be determined with the linear elastic relationship between strain and stress. 

Meyers, F., Bredas, J.L., Pierce. B.M.. Marder, S.R. Nonlinear optical properties of donor-acceptor polyenes Frequency-dependent calculations of the relationship among molecular polarizabilities, a, 13, and y, and bond-length alternation. Nonlinear Optic.s 14, 61-71 (1995)... 

The correlation has been corroborated by low level ab initio calculations (HF/4-21G) [71]. Although the theoretical (r ) bond lengths are systematically off, the variations of unequal C-H distances in similar environments agree with those determined by the bond length - frequency relationship (Eq. 62). Demaison and Wlodarczak have evaluated the correlation between experimental Vg distances and... 

Fig. 21. Relationship between the U-O bond length, derived from Eq. (5) using the U02 symmetric stretching frequency, and the energy of the first electronic excited state. Data points and their sources are as follows ...

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