Pure precession hypothesis

In this book, we adopt a form in which the function is expressed as a linear combination of spherical harmonics. This form is particularly appropriate for systems with near-spherical symmetry (such as Rydberg states or molecules which conform to Van Vleck s pure precession hypothesis [68, 69]) and is also consistent with the spirit of spherical tensors, which have the same transformation properties under rotations as spherical harmonics. The functional form of the ket rj, A) is written... 

In writing this equation, we have made use of Van Vleck s pure precession hypothesis [12], in which the molecular orbital /.) is approximated by an atomic orbital with well-defined values for the quantum numbers n, l and /.. Such an orbital implies a spherically symmetric potential and its use is most appropriate when the electronic distribution is nearly spherical. Examples of this situation occur quite often in the description of Rydberg states. It is also appropriate for hydrides like OH where the molecule is essentially an oxygen atom with a small pimple, the hydrogen atom, on its side. Accepting the pure precession hypothesis allows the matrix elements of the orbital operators to be evaluated since... 

If the value of l is 1, o+ = 2l/2A. This is known as part of the pure precession hypothesis, which is approximately true only for hydrides, Rydberg states of an l > 0 complex, and certain highly ionic molecules (see Section 5.5). Although the pure precession hypothesis is frequently applied to homonuclear molecules, there is no justification for this. 

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. 

In Van Vleck s pure precession hypothesis (Van Vleck, 1929 Mulliken and Christy, 1931 see Section 5.5),... 

The first result has been obtained earlier in obtaining the second result, we have to take account of the sign change which results from the permutation of the order of the orbitals (required to set up the one-electron result). We have also used the pure precession hypothesis to evaluate the orbital matrix element. Using a = 151 cm , B = 18.535 cm and ( 0) — ( X1+) = -32600 cm , we obtain a value of -0.172 cm for y for OH in die H state, somewhat larger in magnitude than the... 

The hypothesis of pure precession (Van Vleck, 1929) is often used in the estimation of A-doubling constants. These constants, in the o,p, q notation suggested by Mulliken and Christy (1931), are introduced into the effective Hamiltonian... 

The hypothesis that the a and ir orbitals are in a pure precession (Section 5.5) relationship to each other is supported by ab initio calculations (Czarny, et al., 1971), which find dominant 2po character for these orbitals in the A2E+ and 4n states at the internuclear distance, Rc, of the curve crossing. The pure precession value of the 4IIi/2 A2X+ interaction is 3-1/2a+/2 = 57 cm-1, in satisfactory agreement with the value of 47 cm-1 obtained from the observed linewidths. 

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