Badger’s rules

By equating to zero the differential of this with respect to r, we find the equilibrium distance as a function of x and the ratio of force constants C2/C1. For Q/Ci = 3, r2 = 1.34, and f = 1.54, this function is that given by Equation 1. The value 3 for the ratio of force constants is somewhat larger than that indicated by Badger s rule, which is about 2.3 it is probable that this increase is needed to compensate for the neglect of resonance energy in the assumed potential function. 

It would be most desirable to have a direct link between the geometrical relaxations and the force constant changes. From molecular vibrational spectroscopy it is well known that the intramolecular force constants show a scaling behavior, Badger s rule ... 

Let us now come back to Badger s rule. The parameter a is expected to lie somewhere between S and 10. By fitting the experimental MS7 frequency of h(o= 19.4 meV with the lattice dynamical model described above, we find... 

Badger s rule phys chem An empirical relationship between the stretching force constant for a molecular bond and the bond length. baj-orz, rul baeckeol org chem C13H18O4 A phenolic ketone that is crystalline and pale yellow ... 

Most diatomic molecules have a force constant in the range 10 to 10 N m h A common tool for the calculation of Kp in diatomic molecules (often extended to couples of atoms in polyatomic molecules) is Badger s rule ... 

R. C. Herman and R. Hofstadter, Phy. Rev. 33,940 (1938) J. Chem. Pkyt. 6, 534 (1938). This value is obtained by applying Badger s rule to frequencies observed in the infrared absorption spectra of light and heavy aottic add... 

For the finer differences in bond energy of various bonds between similar atoms, information can be obtained from vibration frequencies in the infrared and Raman spectrum and from small variations in the bond length, which are connected with each other and with the bond energy through semi-empirical relations (Badger s rule etc.). 

Infrared spectroscopy has the advantage that it can be applied to the same compound in all three states of matter. However, there still appears to be insufficient data from gas-phase studies of hydrogen-bonded complexes to permit a correlation between X-H stretching frequencies and bond lengths, so as to improve on the long-standing empirical Badger s Rule [158]. 

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... 

The internuclear distance (r ) is the value estimated by Barrow and Beale (5) from spectroscopic work on SrF. The value of (D is calculated from Badger s rule (6) which can be written in the form = 3.159 x 10 /ji(r... 

There are several empirical relationships which relate the force constant to the bond distance. Badger s rule [68] is given by... 

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