Rydberg procedure

The extensive calculations of Serrano-Andres et al [31] have shown a spurious valence-Rydberg mixing in the CASSCF wave functions when valence (7t,7r )and Rydberg orbitals are optimized all together in a state average calculation it was shown that these orbitals loose their diffuse character and instead tend to provide an extra correlation to valence orbitals. To avoid such interaction, the orbitals used for the Cl treatment of the electronic spectrum were obtained by a two step procedure ... 

XAS, on the other hand has a core-excited final state for which the effect of the core-hole must be taken into account. To obtain the full spectrum, i.e., valence, Rydberg and continuum excitations, we use the Slater transition-state approach [22,23] with a half-occupied core-hole. This provides a balanced description of both initial and final states allowing the same orbitals to be used to describe both initial and final states and all transitions are obtained in one calculation [23,24]. Details of the computational procedure can be found in the original papers as referenced in the following sections. In the present chapter, the focus is on the surface chemical bond and the spectra, measured or calculated, will mainly be used to obtain the required information on the electronic structure. 

The analysis of spectroscopic data for bound states of diatomic molecules gives accurate potential curves if one follows the semi-classical Rydberg-Klein-Rees method. For a review of this see Ref. 126). It is sufficient to note that this gives the two values of r as a function of potential energy by considering the dependence of the total spectroscopic energy on the vibrational and rotational quantum numbers n and J. A somewhat simpler procedure, and the only one plicable to polyatomic molecule, is to use the Dunham expansion of the potential 127). 

The potential curves derived from such calculations can often be empirically improved by comparison with so-called experimental curves derived from observed spectroscopic data, using Rydberg-Klein-Rees (RKR) or other inversion procedures. It is often found, particularly for the atmospheric systems, that the remaining correlation errors in a configuration interaction (Cl) calculation are similar for many excited electronic states of the same symmetry or principal molecular-orbital description. Thus it is often possible to calibrate an entire family of calculated excited-state potential curves to near-spectroscopic accuracy. Such a procedure has been applied to the systems described here. 

The approach of Germann et al. [21], in contrast to other procedures, is applicable to the entire range of magnetic field strengths. Energies and expectation values for circular Rydberg states are presented in this work as functions of the field strength. 

It could also be that it is more beneficial to populate the Rydberg level in two steps, because it is easier to reach a level that is near to the ionization energy when very short wavelengths are not used. For an ionization potential of 7 eV, radiation with X < 220 nm is required, as for 1 eV = 1.6 x 10 16 erg, X is 1240 nm (because of = h c/X). In addition, the oscillator strength decreases with 2 — 1 and in the case of two-step procedures the selectivity also increases. 

There are other aspects of the application of the MCSCF method that have not been discussed in this review. The most notable of these probably is the lack of a discussion of orbital basis sets. Although the orbital basis set choice is very important in determining the quality of the MCSCF wavefunction, the general principles determined from other electronic structure methods also hold for the MCSCF method with very little change. For example, the description of Rydberg states requires diffuse basis functions in the MCSCF method just as any other method. The description of charge-transfer states requires a flexible description of the valence orbital space, triple or quadruple zeta quality, in the MCSCF method just as in other methods. Similarly, the efficient transformation of the two-electron integrals is crucial to the overall efficiency of the MCSCF optimization procedure. However, this is a relatively well understood problem (if not always well implemented) and has been described adequately in previous discussions of the MCSCF method and other electronic structure methods . ... 

The CH ion is of considerable importance in interstellar chemisty, and has also been studied by MCSCF and Cl methods It is therefore well suited as a full-scale demonstration of the spin-coupled VB procedure described above. The basis set used was of modest size (18cr, 20n, 6S Slater orbitals), and is the same as that used by Green except for omission of 4f functions. However, no diffuse 3s(C) or 3p(C) functions, which would be needed to describe any Rydberg character in excited states, were included. 

It Is, In particular, not common practice to describe the continuum electronic states of molecules In terms of Rydberg and valence contributions, nor to clarify their spatial characteristics In terms of atomic compositions, largely as a consequence of the absence of theoretical procedures for constructing continuum states In such fashion. 

Fig. 2). A relatively small basis set was used, but one that was capable of describing the Rydberg character of the C state. The AMfl-X E transition moment is well described by an SA-CASSCF procedure that includes the A13s and 3p and H Is orbitals in the CASSCF active space. As the C E" state is derived from the S(3s 4s ) state of Al, the active space must be expanded beyond the valence orbitals. When the 4s is added to the active space, all MRCI properties except the dipole moment of the C state are in good agreement with the FCI. Since the C E state is very diffuse, small...

In the procedure usually applied by Kelly [242], bound state wavefunc-tions were calculated up to about the tenth Rydberg member, and then the remainder obtained by extrapolation. In the continuum, a sufficiently large number of k values is chosen to represent all the interactions. Typically, this means that about 30 continuum states are required for each l value. 

Spectral fluctuations are a distinctive property of atomic spectra, but have rarely been studied in their own right. One example involving fluctuations is the procedure of Gailitis averaging near a series limit (see chapter 3), This involves taking the mean of the maximum and minimum excursions as the series limit is approached, and emphasises the fairly obvious result that spectral fluctuations tend to zero as the limit of a Rydberg series is approached. 

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