Vibrational constants

For diatomic molecules, lj0 is the vibrational constant to use with equation (10.125) for calculating anharmonicity and nonrigid rotator corrections, while J)e and tDe-Ve... 

Tables 10.1, 10.2, and 10.3e summarize moments of inertia (rotational constants), fundamental vibrational frequencies (vibrational constants), and differences in energy between electronic energy levels for a number of common molecules or atoms/The values given in these tables can be used to calculate the rotational, vibrational, and electronic energy levels. They will be useful as we calculate the thermodynamic properties of the ideal gas.

Fermi resonance in, 278-279 IR bands, table of, 264 normal modes, 242, 248, 262, 265 nuclear statistical weights for, 287-288 vibrational constants of, 275 vibrational levels of, 253 vibrations of, and group theory, 449-451,456... 

Table 4.1 lists rotational and vibrational constants for some diatomic-molecule states. The most extensive compilation of such data is Bourcier. 

Use the vibrational constants (6.58) of water to calculate o0 for vibrational transitions from the (000) level to each of the following levels compare the calculated values with the observed values in Table 6.1 (a) (001) (b) (111) (c) (211). Why is there a large discrepancy between calculated and observed values for (c) ... 

Note that the vibrational constants are different for the different electronic states. There is no restriction on the change in the vibrational quantum number, and we generally get many vibrational bands for a given electronic transition. 

Fluorescence has been observed by laser excitation in the region 4579 to 4880 A [Sakurai ct al. (851)], corresponding to the transition A2A2X2Bl. Vibrational constants of the ground state have been calculated from the fluorescence bands. 

For diatomic molecules, <2>o is the vibrational constant to use with the equations in Table A6.1 to calculate the thermodynamic values for a diatomic molecule, assuming the rigid rotator and harmonic oscillator approximations are valid. The vibrational constants Qe and u>exe are the values to use with the equations in Table A6.5 to calculate the anharmonicity and non-rigid rotator corrections. They are related to u>o by... 

For polyatomic molecules, G> is the vibrational constant to use when making calculations for polyatomic molecules with the equations in Table A6.1. 

In addition, also the equilibrium NCoN angle is changed due to the contribution of these symmetry coordinates in the Q(at) coordinate given above. The deuterated complex treated in similar way has almost equal molecular constants although, as we have seen in the corresponding complex with NH3 ligands, their vibrational constants are quite different [97]. 

R = K exp (Q/T), where the constant K incorporates spectroscopic and optical system constants. The value of K was experimentally determined by calibration against a premixed laminar flame with a known temperature produced on a porous plug burner. The characteristic vibrational temperature Q = hcco/k = 3374°K for nitrogen. Here, h is Planck s constant, c is the speed of light, 0) is the vibrational constant, k is Boltzmann s constant, and T is the temperature in Kelvin. 

From the separations of the progression members the vibrational constants coe, cOgXe, (oeye,... (Equation 6.16) for II) can be obtained. Comparison of coe = 2322 cm-1 for the X2Zg state of II) with coe = 3115 cm 1 for the XlZg state of H2 shows that the vibrational force constant (see Equation 6.2) is much smaller in the ground state of H)" than in H2. This, in turn, implies a weaker bond in H)" consistent with the removal of a bonding electron. 

Just how much of the data are fitted is largely arbitrary and variations can cause dramatic changes in the so-called constants. A striking example in a seemingly simple situation is the case of the ground-state vibrational constants of H2. Here fourteen vibrational energy levels can be observed. They may then be fitted to a formula of the type... 

Table 1 The vibrational constants 0/H2 I1 EJ for various energy expressions...

The A 3 + state has a radiative lifetime of 2 s, and is therefore long-lived on the time scale of the molecular beam experiments, where it was produced by electron impact on a beam of N2 diluted with Ar, cooled to liquid nitrogen temperature. Calculations of the Franck-Condon factors show that direct excitation of the A state is expected to populate many vibrational levels, and a major feature of the magnetic resonance studies was that spectra involving the first thirteen vibrational levels (v = 0 to 12) were obtained. The accurate and extensive determination of the vibrational constants, given above, was therefore of considerable importance. 

A remarkably large proportion of the constants in the effective Hamiltonian were determined from the analysis of the FIR laser magnetic resonance spectrum, supplemented by data from other spectroscopic regions which allowed equilibrium values of some of the constants to be determined. The following rotational and vibrational constants are listed by Nelis, Beaton, Evenson and Brown [76] (in cm-1) ... 

As the size of the systems increases, when going from tricycle 45 to pentacycle 112, the Huang-Rhys factors (the electron- and hole-vibration constants) for high-frequency vibrations decrease as expected. In contrast, the vibronic interaction with low-energy vibrational modes shows an opposite trend for both electrons and holes. The electron-vibrational interaction with low-energy vibrations is much larger than the hole-vibrational interaction a similar pattern is also characteristic for oligoacenes. 

Ultraviolet bands of the HgCl, HgBr and Hgl molecules have been investigated [41-43]. The authors coupled their measurements with computer analysis to determine precise vibrational constants for the molecules. For Hgl a vibrational... 

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