Potential function Morse

An independent estimate of the amount of p character of these bonds can be made with use of the assumption that a linear extrapolation of the low-lying vibrational energy levels (as indicated by the Morse potential function) will lead to the energy level of the atomic state involved in the bond. The equation... 

This is simply the Morse potential function with... 

If one transforms this expression to Morse potential functions, one then finds... 

In the case of a harmonic oscillator, the separation between the two successive vibrational levels is always the same (hv). This is not the case of an actual molecule whose potential is approximated by the Morse potential function shown by the solid curve in Fig. 1-6. 

As mentioned above, HOSi(OA)3 may be taken as the simplest cluster model of the terminal hydroxyl group in silicas. Indeed, even with this cluster CNDO/BW provided a quite satisfactory description of the lower part of the curve representing potential energy as a function of the OH stretching vibration coordinate ROH (Fig. 2) (48,49). The respective experimental curve was plotted by Kazansky et al. (49) based on the analysis of the fundamental frequency vOH and the first overtone of the characteristic OH stretching vibration in terms of the Morse potential function. The frequencies of the second and third overtones were also determined in that work, and it was shown that the Morse potential reproduced well the potential curve within a rather wide range of ROH. 

One of the most useful features of spreadsheets is the ease with which repetitive calculations can be done by copying the formula in one cell to others. A formula in a cell is a mathematical operation that can utilize values contained in other cells, as shown by the formula content of the active cell B14. This formula is displayed in the information bar at the top of the spreadsheet of Fig. 1 and is the equation for the Morse potential function, with the cell addresses of the constants Dg, /3, and the variable r entered instead of numerical values. By using the Edit menu (or the right mouse button), the formula operation of B14 can be Copied and then Pasted into cells B15, B16.B73, thus giv-... 

The value of r Is obtained from that for gaseous BaBrgC ) with r (BaBr)/r (BaBrg) = 0.96. This value for the ratio Is calculated from bond lengths (4) for several other alkaline earth halide systems. Two other estimates (5, 6) of r agree with the adopted value to within 0.05 A. The rotational constant Is calculated from the estimated value for r. The value of Is obtained from a Morse potential function. 

Electronic levels and vibrational constants are taken from the review of Rosen (9). The level at 10351.1 cm" is T rather than T. Vibrational constants are adjusted for natural isotopic abundances. B is calculated from r which is estimated by comparison of the bond lengths of MX2estimated from the Morse potential function. 

The ground state vibrational constants are from the compilation of Rosen (J ). The adopted value of r estimated by Margrave (3) and is also the bond distance in Bal Cg) (7). B is calculated from the adopted assuming a Morse potential function. 

We estimate r to be 0.08 A less than that for BeBrg (3). This estimation is made based on the observation that the ratio r (MX)/r (MX,) is near 0.96 for several alkaline-earth halides (3). The value of is calculated from r. The value of is obtained from the other constants by assuming a Morse potential function. 

The vibrational constants used to calculate the functions were derived by Novikov ( ) from a two constant equation [-(2 v" + l)u) x = AG "(w")]. The electronic levels were obtained from Herzberg (5). B was obtained from the estimated bond length, which was taken to be slightly less than that in BeCl (g) and a was estimated from the Morse potential function. 

The value of Is calculated from the Morse potential function. 

The rotational constant is adjusted for the natural Isotopic abundances of lead and chlorine. The value for r is obtained from the adopted value. The results of an earlier rotational analysis of the same bands by Rao and Rao (13) are in reasonable agreement with our adopted values. The value for is estimated from the other constants assuming a Morse potential function. 

Bg compares with r = 2.061 A given in Rosen ( ). The value for is calculated assuming a Morse potential function. References... 

The spectroscopic data with the exception of the value for o are those given by Rosen (,8). o is calculated from the other constants assuming a Morse potential function. The electronic states and levels are also taken from the compilation of Rosen (8). 

Jordan ( ) predicted five electronic levels (X E, A a, B e, D n, B e) based on the reported value (2) of 29560 cm" for the C n level (this level is designated A II by Herzberg (2)). Several qualitative spectroscopic investigations of PH(g) have been reported and are in general accord with the predictions of Jordan (1 ). Ishaq and Pearse (3 ) reported the values of the rotational constant B and the fundamental vibrational frequency The value of is calculated from the Morse potential function. The... 

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