Vibronic states

This means diat half the rotational levels of every vibronic state are missing in this molecule. Missing levels arise in other molecules and can also involve nuclei with nonzero spin they arise for the aimnonia molecule NH3. 

For molecules we can use Bom-Oppenlieimer wavefimctions and talk about emission from one vibronic level to another. Equation (B1.1.5T equation tb 1.1.6) and equation tb 1.1.7) can be used just as they were for absorption. If we have an emission from vibronic state iih to the lower state a, the rate constant for emission would be given by... 

The selection rule for vibronic states is then straightforward. It is obtained by exactly the same procedure as described above for the electronic selection rules. In particular, the lowest vibrational level of the ground electronic state of most stable polyatomic molecules will be totally synnnetric. Transitions originating in that vibronic level must go to an excited state vibronic level whose synnnetry is the same as one of the coordinates, v, y, or z. 

There is a single nondegenerate zeroth-order vibronic state uj- Dr 00 +). The zeroth-, first-, and second-order formulas read... 

Zeroth-order level, corresponding to the vibronic state l)r (r Uc (c +) = Ur Ur uc Uc +) is nondegenerate. The zeroth, first- and second-order energies are... 

We now take vibronic interactions into account. In this case, we must determine vibronic states rather than the electronic and vibrational ones. For example, if X3 in a degenerate E vibration is singly excited in an E electronic state, we obtain the vibronic states A 0 0 since "E 0 =... 

A l 0 Mj 0 2 . Table Xni shows the symmetries of the lowest 25 vibrational and vibronic states. In turn, the lowest 26 levels calculated for Li3... 

Assignment (v l, rf) in D3 Symmetry of Vibrational States Symmetry of Vibronic States Assignment (v, V2,vs) in C2v... 

Eor simplicity, the left superscripts v and ev are omitted in denoting the vibrational and vibronic states,... 

In this assignment, we keep the symmetry species of the vibronic state in D3/, but indicate the vibrational quantum numbers for the Civ normal modes. The energy increases from left to right, and up to down,... 

As discussed in preceding sections, FI and have nuclear spin 5, which may have drastic consequences on the vibrational spectra of the corresponding trimeric species. In fact, the nuclear spin functions can only have A, (quartet state) and E (doublet) symmetries. Since the total wave function must be antisymmetric, Ai rovibronic states are therefore not allowed. Thus, for 7 = 0, only resonance states of A2 and E symmetries exist, with calculated states of Ai symmetry being purely mathematical states. Similarly, only -symmetric pseudobound states are allowed for 7 = 0. Indeed, even when vibronic coupling is taken into account, only A and E vibronic states have physical significance. Table XVII-XIX summarize the symmetry properties of the wave functions for H3 and its isotopomers. 

For electronic or vibronic transitions there is a set of accompanying rotational transitions between the stacks of rotational levels associated with the upper and lower electronic or vibronic states, in a rather similar way to infrared vibrational transitions (Section 6.1.4.1). The main differences are caused by there being a wider range of electronic or vibronic transitions they are not confined to 2" — 2" types and the upper and lower states may not be singlet states nor need their multiplicities to be the same. These possibilities result in a variety of types of rotational fine structure, but we shall confine ourselves to 2" — 2" and — types of transitions only. 

The intensity distribution among the rotational transitions is governed by the population distribution among the rotational levels of the initial electronic or vibronic state of the transition. For absorption, the relative populations at a temperature T are given by the Boltzmann distribution law (Equation 5.15) and intensities show a characteristic rise and fall, along each branch, as J increases. 

The transition moment // between the vibronic states and where 0... 

The lowest adiabatic state is completely dissociative. The second and third are bound, but an efficient predissociation of the associated vibronic states can be predicted, on the basis of the strong couplings and small energy gaps in the region of the minima. 

NES is an elastic and coherent scattering process, i.e., it takes place without energy transfer to electronic or vibronic states and is delocalized over many nuclei. Owing to the temporal and spatial coherence of the radiation field in the sample. 

In Chapters 4 and 5 we made use of the theory of radiationless transitions developed by Robinson and Frosch.(7) In this theory the transition is considered to be due to a time-dependent intramolecular perturbation on non-stationary Bom-Oppenheimer states. Henry and Kasha(8) and Jortner and co-workers(9-12) have pointed out that the Bom-Oppenheimer (BO) approximation is only valid if the energy difference between the BO states is large relative to the vibronic matrix element connecting these states. When there are near-degenerate or degenerate zeroth-order vibronic states belonging to different configurations the BO approximation fails. 

Figure 10. Low-energy vibronic levels in the X2II state of HCCS computed in various approximations [152]. Hq zeroth-order approximation (both vibronic and spin-orbit couplings neglected). Hi. vibronic coupling taken into account, spin-orbit interaction neglected. Hi + Hs0 both vibronic and spin-orbit couplings taken into account. Solid horizontal lines K = 0 vibronic levels dashed line K — 1 dash-dotted lines K = 2 dotted lines K — 3. Values of the quantum numbers V4, N of the basis functions dominating the vibronic wave function of the level in question are indicated. Approximate correlation of vibronic states computed in various approximations is indicated by thin lines. In all cases the stretching quantum numbers are assumed to be zero.

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