1E+ states

Figure 1. Adiabatic potential surfaces (a) for the linear E x e case and (b) for a 1E state with linear Jahn-Teller coupling and spin-orbit coupling to a 2 A state.

Mulliken158 has carried out near-HF calculations on the 3E+and 1E+ excited states of BH. Convergence problems for the 1E+ state at R > 2.8 bohr were found but the two curves had the expected hump between 2.6 and 2.8 bohr. Browne and Greena-walt,159 using Cl, however, did obtain a double minimum for the 1E+ state. Calculations on the A1 II state at R = 2.316 bohr have been reported by Green.16 The SCF X-A transition energy of 2.48 eV compares with the experimental value of 2.86 eV. 

K+ is smaller than K, but the parameter K+ exhibits a stronger temperature dependence than K. Both functions n3(t) and n2(t) are bi-exponential. n3(t) describes the decrease of the 2A2u emission, whereby the relative portion of the slow component increases with increasing temperature (see also Sect. E.II.l.). The emission from the 1E state is composed of a fast increase, corresponding to K, and a slow decrease with the same time constant as the slow component of the 2A2u emission. 

A second example is given by the interaction between the 3E and 1E+ states that belong to a 7r2 configuration. Note again that Eq. (3.4.6) is only... 

An alternative method to obtain the nonadiabatic wavefunctions [Eq. (4.1.1)], the coupled equation approach, will be discussed in Section 4.4.3. It has been used for an excited 1E+ state of H2 and the error is now smaller than 1 cm-1 for the lowest vibrational levels (Yu and Dressier, 1994). Multichannel Quantum Defect Theory (MQDT), discussed in Chapter 8, has also been used with success for the same problem by Ross and Jungen (1994). Finally, a variational numerical approach (Wolniewicz, 1996), gives very good results for H2. 

The 3E and p-complex structures resemble each other because both consist of one unit of spin or electronic angular momentum (S or L) coupled to the nuclear rotation (R). However, since fj, operates exclusively on electron spatial coordinates, any resemblance between the rotational-branch intensity patterns for 3S —1E+ and p-complex —1E+ transitions would seem to be coincidental. A 3E —1E+ transition will look exactly like a p-complex —1E+ transition if, in addition to satisfying Eqs. (6.3.47), the cr-orbital of the 1E+ state is predominantly of scr united atom character. Then the transition moment ratio will be... 

Although 3IIoe can mix with many excited 1E+ states, mixing with the X1E+ state introduces a novel feature, namely, the appearance of permanent electric dipole moments as well as transition moments in the intensity borrowing model. For 3II in the case (a) limit (A > 21/2BJ),... 

The BaO A "1" state is perturbed by the b3II and A1 states. The effect of perturbations on the Stark tuning coefficients of a 1E+ state is more complicated than the situation described by Eq. (6.5.21) (because parity remains an almost good quantum number in A = 0 states at f-fields that are sufficiently large to cause complete parity mixing in A > 0 states). There will be Stark tuning... 

The propensity rules for collision-induced transitions between electronic states and among the fine-structure components of non-1E+ states depend on the identity of the leading term in the multipole expansion of the molecule/collision-partner interaction potential. Alexander (1982a) has considered the dipole-dipole term, which included both permanent and transition dipole contributions. In the limit that first-order perturbation theory applies (not the usual circumstance for thermal molecular collisions), the following collisional propensity rules for the permanent dipole term can be enumerated from the selection rules for both perturbations and pure rotational transitions... 

Propensity rules for collision-induced transitions with non-1E+ states have been discussed by Gottscho (1981), Nedelec and Dufayard (1984), Alexander... 

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