Vibration level, definition

NO is decomposed by the 2265 A and 2144 A lines from a Cd arc187 which selectively excite the ground and first vibrational levels, respectively, of the A2h+ state. There is some evidence188 that the ground vibrational state of NO (A2 +) may be unreactive, but this fact has not been definitely established. The following scheme accounts for the experimental observations to date... 

The rotational levels are sketched for two lowest vibrational levels, v = 0 and v = 1. Since vibrational and rotational levels are quantized just like electrons, therefore, for a given molecular species these energy changes will have certain definite values. 

When an excited molecule also consists of a definite vibrational level as shown in Fig. 5.1(a), there shall be no direct dissociation of molecule and a fine structure in the electronic band spectra of the molecule will be observed. The excess energy, in usual course may be dissipated as heat or may give rise to fluorescence. But the molecule may retain its energy until it has not reacted with another molecule or transfer its energy to another molecule, e.g. decomposition of NOC1 as follows ... 

Fig. 4. Excitation of a definite level (u, J ) in an upper electronic state of a diatomic molecule by absorption of a laser line, and subsequent fluorescence to different vibrational levels of the electronic ground state (example Na2>...

The wavefunction which fits the equation and leads to discrete values of V is the eigenfunction. The search for such eigenfunctions and eigenvalues can be a most demanding mathematical excercise, and need not be considered here. Let us note however that the solutions of the Schrodinger equation lead to the definitions of the orbital quantum numbers n, l and m. The quantum numbers of rotational and vibrational levels are also derived from the Schrodinger equation. 

Figure 5.8. Stokes shift a) definition and b) dependence on the difference in equilibrium geometries of ground and excited states. Shown is the probability distribution in various vibrational levels, which is proportional to the square of the vibrational wave function (adapted from Philips and Salisbury, 1976).

To proceed further, we now assume that, because of Franck-Condon factors, only a> can combine in absorption from the initial state g. That is, a> is an absorption doorway state.29 (The assumption that only a few out of many S, vibrational levels have any appreciable dipole-induced transition probability to or from any given S0 vibrational level is a good approximation for a large number of molecules.) This, with the definition of the fiHm and Eqs. (3.1), gives nlg = (xnag and fi2g = PHag- We also assume, for similar reasons, that either a> or i>> combines in emission with the final state /> (i.e., a> or f > is a doorway state in emission to / . If a> is the emission doorway state,... 

The R- or w-dependence of second-order constants (o,p,q, 7, etc.) is more important than that of the off-diagonal perturbation parameters themselves (as determined from a direct fit to perturbed levels) because, in their definitions as sums over the interactions with energetically remote levels [Eqs. (5.5.1a) - (5.5.3a)], the off-diagonal matrix elements are taken between nondegenerate vibrational levels. Thus the ii-centroid, R vi, will vary with v and v and will not be equal to Rc- Since a+ and b are not independent of RuV and RvVi is not independent of v at fixed v, it is not permissible to remove the electronic factor from the summation over remote perturbers. Furthermore, the denominator of each term in the perturbation summation depends on an energy difference. This can cause a strong v, J-dependence of the second-order constants, especially when the vibrational levels of the state under consideration are near the energy... 

Measurements of r that are partially averaged over J,Cl,e/f will not agree with each other and will exhibit unexpected temperature and pressure dependences. However, since the 3n n and 3n 1E+ perturbation matrix elements are not J-dependent, the fractional 3n and 1E+ characters, summed over the six e// 3n components of a given J-value, are J-independent. This provides an unambiguous definition of an average, J-independent, vibrational-level... 

The LS state is characterised by the adiabatic potential surface i LS(r) having a minimum ifo.Ls at a certain geometry (metal-ligand distances rLS) with some definite curvature (the second derivative representing a force constant /LS). Within this nearly parabolic function a set of vibration levels e, LS occurs, the lowest one corresponding to the zero-point vibration, e0LS. The HS state differs in these characteristics in such a way that the relationships... 

To consider reaction out of specified mctant states it is necessary to modify slightly the definition of surinisal that was given in equation (28). Kaplan, Levine, and Manz consider the partially detailed rate constants for reaction from specified vibrational levels, the rotationaland translational d rees of freedom having thermal distributions defined by T. Now the (vibrational) surprisal is... 

The main contribution to the anti-Stokes generation comes from a small volume around the focus of the two incident beams. Therefore very small sample quantities (microliters for liquid samples or millibar pressures for gaseous samples) are required. Furthermore, a high spatial resolution is possible, which allows one to probe the spatial distribution of molecules in definite rotational-vibrational levels. The measurements of local temperature variations in flames from the intensity of anti-Stokes lines in CARS is an example where this advantage is utilized. 

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