Birge-Sponer plot

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... 

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.

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. 

Errors when given are based on the statistics of Birge-Sponer plots. Rotationally analyzed as pure Hund s ease (a) transitions. 

Errors when given are based on the statistics of Birge-Sponer plots. 

Figure 3.11 Birge-Sponer plot of AG(v) versus v for the electronic ground state of Nag. The area under the AG(v) curve yields the ground state dissociation energy D. Linear extrapolation of the points for low v (straight line) would clearly yield a gross overestimate of Nonlinear extrapolation of the points exhibited for 0 < v < 45 (P. Kusch and M. M. Hessel, J. Chem. Phys. 68 2591 (1978)) leads to an improved estimate of D. A still better approximation to can be made by analyzing vibrational levels for v up to 55 from the more recent Na2 fluorescence spectrum shown in Fig. 4.1.

The first anharmonicity constant, at the first overtone (V02), was computed by using X = voi — (vo2/2), whereas the anharmonicity constant at the second overtone (fos) was obtained from X = (vo2/2) — (vqj/S). Fundamentals, overtones and anharmonic constants are expressed in cm units. In the case of cycloalkanes (30) and hydrocarbons (31), a Birge-Sponer plot was used to determine anharmonicity constants. Axial and equal stand for axial and equatorial CH groups of cycloalkanes, respectively. 

De Araujo and Y. Kawano used curve fitting calculations and local mode theory to assign overtone and combination frequencies in the NIR spectra of polyamide 6 (PA 6), poly(vinyl chloride) (PVC), and polychlorotrifluoroethylene (PCTFE). Anharmonicity correction and mechanical frequency were determined from a Birge-Sponer plot. Anharmonicity corrections of 55, 61, and 20 cm were obtained for CH2 NH, and CO stretch modes of PA 6, respectively, and of 60 and 66 cm for CH2 and CH stretch modes of PVC, respectively. The local mode model seemed to be adequate to interpret the origin of the bands of PA 6 and PVC. Anharmonicity corrections of 33, 19, and 16 cm were... 

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. 

COMMENT. This value of the dissociation energy is close to the experimental value of 5.08 eV quoted by Herzberg [Further reading, Chapters 13 and 14], but differs somew/hat from the value obtained in Problem 14.2, The difficulty arises from the Birge-Sponer extrapolation, which works best when the experimental data fit a linear extrapolation curve as in Example 13.5. A glance at Figure 14.3 shows that the plot... 

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