2II state

Figure 1. Representation of degenerate states from nonrelativistic components, (a) Degenerate zeroth-order states at R = RX,IJ. (b) Spin-orbit interaction splits 2II state, (c) With full spin-orbit interaction turned on, degeneracy is restored by changing geometry to R l = Ru ...

The reason for the weakness of the PFI spectrum is of interest in itself, in that the one-photon ionization from the B 2II state to the ground state of the ion is formally forbidden as it involves a nominal two-electron change ... 

It is therefore surprising that this process can be observed at all, and the intensity can be ascribed to a configuration mixing of the B 2II state with the C 2II state [configuration (3ff)2(lir)4(3pir)1]- Indeed, the rotational intensity distribution is similar to that shown in the ZEKE spectrum via the C state... 

All three radicals, B02, N3, and NCO, are linear in both their ground states and their excited states. The ground states of all three molecules are 2II states, as predicted, since there are now three electrons in the lng orbital. The structural data are included in Table II. 

More recently, potential curves for the lowest 2S+ and 2II states of XeF have been computed.298 Only a weak van der Waals attraction between Xe and F is predicted ( 0.15 kcal mol-1). This result is not consistent with the way in which a variety of experiments have been interpreted.298... 

Goddard has also computed GVB wavefunctions for CF, but details are not available.13 However, the GVB wavefunctions were compared with those of CH, and it was shown that additional repulsive interactions with the lone pairs on F should make the 2II state of CF much more strongly bound than the 4S state. (The calculated AE 2.8—2.9 eV.)... 

Although the theory of these related phenomena is fairly well established, very few calculations of the constants involved have been reported. Presumably this is because they involve the calculation of off-diagonal matrix elements. A detailed account of the theory of /l-doubling in 2II states of diatomics has been given by Van Vleck,123 Mulliken and Christy,124 and Hinkley, Hall, Walker, and Richards.125 A brief synopsis is presented here. 

In certain cases, the formulae for p and q may be simplified further. If the spectroscopic constants for the interacting states are similar, many of the vibrational matrix elements will reduce to zero. Consider the y = 0 level of a given 2II state. The principal matrix element will be with the v = 0 level of 2 2 and the value <2II[B 12S> between vibrational functions will be approximately the B value of 2n. By the orthogonality rules, the remaining matrix elements should be zero. This has led Van Vleck to suggest... 

The relative intensities of the CN bands depend strongly on the nature of the species added to active nitrogen [145, 146], With halogenated hydrocarbons, red emission from the A 2II state predominates this was classified by Bayes [146] as the P2 emission. The v distribution is broad, peaking at v = 7, and the red system is accompanied by bands from B 2S+ v = 0) that is populated via A 2II (y = 10) because of perturbations and collision-induced transitions. The Pa emission from mixtures of active nitrogen with halogen-containing compounds is quite different, and the relative band intensities in the red system show that v = 0 is now the most populated level. 

When X impinges on the core of M at R R2 the angular velocity increases and this causes transitions between the components, thus leading finally to transitions between 2P1/2 and 2P3/2 atomic states (mechanism 2). This mechanism is operative at smaller distances compared to those involved in mechanism 1. The transition probability for mechanism 2 is proportional to ratio (< /w)2, which does not appear in mechanism 1, Both factors tend to decrease the importance of mechanism 2 compared to mechanism 1. Nevertheless, the difference in steepness of the repulsive interaction between X and M in B 22 and A 2II states can lead to preference of mechanism 2 for nearly adiabatic collisions when the mixing cross section is very small. 

Ab initio quantum-mechanical calculations have been made for the two lowest electronic states of the Li02 molecule. For isosceles triangular configurations, the 2A2 state is the ground state, with equilibrium geometry r(LiO) = 1.82 A and 0(0—Li—O) = 44.5°. The 2B2 state is predicted to lie 14 kcal mol-1 higher, with r(LiO)=1.76A and 0(0—Li—0) = 46.5°. For symmetry the 2II state bond distances were predicted, r(Li—Oj = 1.62 A and r(0—0)=1.35A. There appears to be little or no barrier between the C2v and CU forms.150 The decomposition of anhydrous lithium... 

Figure 3.1a Natural rotational quantum numbers for Hund s cases (a) and (b). Reduced term value plots for 2S (B = 1.0 cm-1) and 2nr (B = 1.0 cm-1, A = 20.0 cm-1), (a) Plot °f — BJ(J + 1) versus J(J + 1) displays case (a) limiting behavior for the 2II state at very low J. The dotted lines illustrate the B2/A corrections to the near case (a) effective B-values (See Section 3.5.4). The 2S state does not exhibit case (a) behavior even at low J (at J = 0 the limiting slopes of the 2S Fi and h l curves are —oo and +oo).

The values of the coefficients are very similar to those for the excited 2II states of NO (Field, et al, 1975) and of PO (Roche and Lefebvre-Brion, 1973), but the signs of the depend on the choice of phases for the electronic functions. 

As is always a positive quantity (the orbital 7r appears twice in the matrix element), A > 0 the 2II state is regular for the nr configuration, as is well known. 

Second-order effects arising from the product of matrix elements involving J+ L and L+ S operators have the same form as 7J+S. In the case of H2, the second-order effect seems to be smaller than the first-order effect, but in other molecules this second-order effect will be more important than the first-order contribution to the spin-rotation constant. These second-order contributions can be shown to increase in proportion with spin-orbit effects, namely roughly as Z2, but the direct spin-rotation interaction is proportional to the rotational constant. For 2n states, 7 is strongly correlated with Ap, the spin-orbit centrifugal distortion constant [see definition, Eq. (5.6.6)], and direct evaluation from experimental data is difficult. On the other hand, the main second-order contribution to 7 is often due to a neighboring 2E+ state. Table 3.7 compares calculated with deperturbed values of 7 7eff of a 2II state may be deperturbed with respect to 2E+ by... 

Treat the evolution from case (a) to case (b) for 2II states and thereby provide an alternative derivation of the expressions for case (b) functions in terms of case (a) functions previously derived in Section 3.2.1.4 using Clebsch-Gordan coefficients. 

This e/f degeneracy between the two same-TV components will be lifted by interaction with a 2II state. If the potential curves of the 2 + and 2II states are identical and the configurations of the 2 + and 2II states axe Perturbation selection rules for unsymmetrized basis functions require that the following interactions be considered. The 2n1//2 state experiences two types of Afl = 0 interactions with 2E]f/,2 spin-orbit,... 

The 2n 2E+ interaction is different for the e and / levels. This difference gives rise to A-doubling in 2II and a spin-rotation splitting of the AN = 0 degeneracy of the 2E+ state. If the 2E+ state is sufficiently far from the 2II state, it is possible to use second-order perturbation theory to evaluate the A-doubling. The 2II /2 level is repelled by the 2E+ state with an energy shift of... 

If the 2n and 2E+ states (with identical potential curves) in question interact appreciably only with each other and not with other 2E or 2II states, then p = 7. When the pair of interacting 2II and 2E states are found to have p = 7, it is said that they are in a unique perturber relationship, which has nothing to do with the pure precession hypothesis, discussed below and in Section 5.5. 

There is one other mechanism by which the 2II 2E+ interaction results in A-doubling in the 2II state. The (2n3/2 H 2n3/2) matrix element is affected in a parity-independent sense by the II E interaction,... 

As discussed in Sections 3.5.4 and 5.5, the A-doubling in a 2II state can result from interactions with remote 2E+ and 2E states via Hrot and Hso. The Van Vleck transformation defines [Eqs. (5.5.1a) - (5.5.3a)] three second-order parameters (o,p, and q) that appear in the 2II block of IT2-. These second-order 2II 2E interaction parameters cause both e// independent level shifts as well as A-doubling. The e//-dependent terms all arise from the e//-dependence of the... 

Fitted parameters are often strongly correlated. This can be a consequence of the structure of the data set or it can be an intrinsic property of the Heff model (for example, 7 and Ad in a 2II state, Brown, et al., 1979). The former effect can be minimized by supplementing the data set. A combined fit to optical and microwave data or to two electronic transitions sharing a common state (e.g., 2II — 2E+ and 2E+ — 2E+ systems) can be very effective. Another approach is to replace the two correlated parameters by two new parameters that are the sum and difference of the original parameters (e.g., B + B" and B — B"). The correlation matrix [Eq. (4.4.15)] and the magnitudes of the eigenvalues of the normal matrix [Eq. (4.4.11)] provide useful insights (Albritton, et al, 1976 Curl, 1970). Isotope relationships, computed D -values, and other semiempirical constraints are frequently used to minimize both data set and intrinsic correlation effects. 

Figure 5.1 Isotope effect on a vibrational level of the B,2II state of the PO molecule.

In the unique perturber approximation (Zare, et al., 1973), only one 2E electronic state is considered to be responsible for the A-doubling of the 2II state. If the interacting 2II and 2E states belong to the 7r1 and a1 configurations, then the matrix elements of the exact many-electron wavefunctions may be replaced by the one-electron matrix elements (see Section 3.5.4),... 

An important and frequently encountered result, often mistakenly taken as evidence for pure precession, is that, in the unique perturber, identical potential curve limit, the effective spin-rotation constant of the 2E+ state, jv, is equal to Py. This result is a direct consequence of the second-order perturbation theoretical definition of the contribution of a 2II state to the spin-rotation splitting in a 2E state (see Section 3.5.4) ... 

A 2 virtual state would reverse the sense of the interference effect. Two-photon transitions between 2II states in Hund s case (a), case (b) and in intermediate coupling cases are discussed in more detail in Hippier, (1999), where also a more detailed account of the theory can be found. 

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