Birge-Sponer

These so-ealled Birge-Sponer plots ean also be used to determine dissoeiation energies of moleeules. By linearly extrapolating the plot of experimental AEyj values to... 

Alternatively, the sum ean be eomputed from the Birge-Sponer graph by measuring the area... 

Figure 6.5 A Birge-Sponer extrapolation (dashed line) for determining the dissociation energy, Dq, relative to the zero-point level. The actual points lie on the solid line in a typical case...

If a sufficient number of vibrational term values are known in any electronic state the dissociation energy Dq can be obtained from a Birge-Sponer extrapolation, as discussed in... 

Figure 2.3 A plot of the spacing, AE( ). between two adjacent eigenvalues versus v for H2 (Iachello, 1981 Iachello and Levine, 1982). For Eq. (2.74) such a plot should be linear (with an intercept at the quantum number of the highest bound state). This is a Birge-Sponer plot. The original application to H2 is due to Beutler (1934). Using Eq. (2.76), see also Eq. (2.123), one can account for deviations from linearity.

Birge-Sponer extrapolation spect A method of calculating the dissociation limit of a diatomic molecule when the convergence limit cannot be observed directly, based on the assumption that vibrational energy levels converge to a limit for a finite value of the vibrational quantum number. bir-go spon-or ik Strap-3 la-sh3n ( bis- chem a prefix indicating doubled or twice. bis ... 

Alternatively, the sum can be computed from the Birge-Sponer graph by measuring the area under the straight-line fit to the graph of AEVj or vj from vj = 0 to vj = Vj inax ... 

Beveridge, D. L., 380 Binomial coefficients, 351,374 Biochemical applications of ESR, 380-381 of IR spectroscopy, 268 of NMR, 357, 363-364 of Raman spectroscopy, 270-271 Birge-Sponer extrapolation, 304-305 Blackbody radiation, 121-122 Bloch, F 328 Block-diagonal form, 15 Bohr (unit), 23 Bohr magneton, 51, 368 Bohr radius, 42 Bolometer, 260... 

Thrush and Zwolenik163 passed a dc pulse discharge through fluorocarbon vapors and, from the observation of predissociation in the absorption spectra, deduced upper limits of 132 and 120 kcal/mole, respectively, for D C—F and D CF—F. This upper limit for D C—F is 18 kcal/mole greater than deduced by Andrew and Barrow54 from a Birge-Sponer extrapolation. 

Application of the anharmonic diatomic approximation as discussed for the Re2Xg" ions was also employed to estimate a bond dissociation energy for Mo2C18 (243). Employing the w, and Xi i values obtained by Clark and Franks (47) as data for the Birge-Sponer extrapolation led to a calculated energy of 172 20, 190 25, and 127 15 kcal mole"1 for the molybdenum-... 

If all anharmonic constants except coexe are neglected, AG +1/2 is a linear function of v (Equation 6.18) and D() is the area under a plot of AG +1/2 versus v shown by a dashed line in Figure 6.5. In many cases only the first few AG values can be observed and a linear extrapolation to AG,-,, /2 = 0 has to be made. This is called a Birge Sponer extrapolation and the area under the extrapolated plot gives an approximate value for D0. However, most plots deviate considerably from linearity at high v in the way shown in Figure 6.5, so that the value of D0 is usually an overestimate. 

The dissociation energy D0 has been derived by Johns and Barrow 61) from a linear Birge-Sponer extrapolation as 125 10 kcal/mol, whereas Hastie and Margrave report the value >298 = 5.9 0.1 eV (136 2 kcal/Mol). 

In this way, the enthalpy contribution of the rhenium-rhenium quadruple bond in the octabromodirhenate (III) ion is estimated as (408+50) kJ mol l. This can be compared with an earlier estimate (23) of D(Re-Re) 500 kJ mol- which is based on a questionable (22) Birge-Sponer extrapolation applied to the frequencies of the vibrational progression in v(Re-Re) observed in the resonance Raman spectrum of the Re2Brg ion in the solid state. 

Calculate and Dq for both states using Eqs. (5) and (6) and compare the lower state IZ value with the more accurate value obtained from Eq. (7). If emission data have been recorded, analyze these to get improved values for the A-state parameters. If a Birge-Sponer plot of these data shows curvature, you might see whether inclusion of a Ve/e term improves your fit. 

The local mode parameters, and a>iXi, can be determined from a Birge-Sponer fit of the observed pure local mode transitions to... 

Figure 5,3.2.1. Franck-Condon diagrams for (a) absorption showing a convergence limit, (b) absorption suitable for Birge-Sponer extrapolation, (c) continuous absorption.

Gaydon has discussed the OH spectrum. He derives Z>(OH) =4 46 0 2 eV (103 kcal) from the data of Tanaka and Koana o . Edse 134 derives 103 9 from the same data. Gaydon has also mentioned the vibrational levels of the ground state given by Meinel 342. He states that a good Birge-Sponer extrapolation leads to a value of 4 8 eV, and that it would be difficult to bring this down to 4 34 eV. 

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