Rydberg orbitals

Because of the considerably larger size [Eq. (5.2.1)] of Rydberg ((r)3p = 3.7 A) than valence ((r)2p = 2.6 A) orbitals, Rydberg states have much larger pressure broadening cross-sections than valence states, as shown in the following data at 5 bar neon (Miladi, et al, 1978) ... 

This pieture is that deseribed by the BO approximation. Of eourse, one should expeet large eorreetions to sueh a model for eleetronie states in whieh loosely held eleetrons exist. For example, in moleeular Rydberg states and in anions, where the outer valenee eleetrons are bound by a fraetion of an eleetron volt, the natural orbit frequeneies of these eleetrons are not mueh faster (if at all) than vibrational frequeneies. In sueh eases, signifieant breakdown of the BO pieture is to be expeeted. 

When aos are eombined to form mos, eore, bonding, nonbonding, antibonding, and Rydberg moleeular orbitals ean result. The mos (j) are usually expressed in terms of the eonstituent atomie orbitals Xa iii the linear-eombination-of-atomie-orbital-moleeular-orbital (LCAO-MO) manner ... 

It is essential to keep in mind that all atoms possess excited orbitals that may become involved in bond formation if one or more electrons occupies these orbitals. Whenever aos with principal quantum number one or more unit higher than that of the conventional aos becomes involved in bond formation, Rydberg mos are formed. 

An example of the interaetion of 3 s Rydberg orbitals of a moleeule whose 2s and 2p orbitals are the valenee orbitals and of the evolution of these orbitals into united-atom orbitals is given below. 

The In-Phase ( 3s + 3s) Combination of Rydberg Orbitals Correlates to an s-type Orbital of the United Atom... 

The Out-of-Phase Combination of Rydberg Orbitals ( 3s - 3s ) Correlates to a p-type United-Atom Orbital... 

In summary, an atom or molecule has many orbitals (core, bonding, non-bonding, Rydberg, and antibonding) available to it occupancy of these orbitals in a particular manner gives rise to a configuration. If some orbitals are partially occupied in this configuration. 

Diffuse functions are those functions with small Gaussian exponents, thus describing the wave function far from the nucleus. It is common to add additional diffuse functions to a basis. The most frequent reason for doing this is to describe orbitals with a large spatial extent, such as the HOMO of an anion or Rydberg orbitals. Adding diffuse functions can also result in a greater tendency to develop basis set superposition error (BSSE), as described later in this chapter. 

The space spanning the CSFs used in the calculation is presented in Table 1. Orbitals are distributed into several sets, and ordered by symmetry. They are denoted in terms of loealized orbitals (Fig. 1) in order to emphasize their "ehemieal" signifieanee Table 1 presents the various distributions of the correlated eleetrons into these sets, with R standing for Rydberg orbitals or Rydberg states. 

We emphasize that the Rydberg states are included in the variational MCSCF treatment in order not to be undercorrelated relative to the valence states [48,49], Furthermore, it is seen that all the previous distributions are coupled to diexcitations from the oco to the oco orbital that way, we account for the non-dynamical repolarization of the polar acobond in a GVB-like approach. 

The analysis of the variational wavefunctions clearly shows admixtures of valence and Rydberg characters in many states, either at the orbital level or at the Cl level. We will not discuss this point here, but will focuse on transition energies. 

The quality of the ) states has been tested through their energy and also their transition moment. Moreover from the natural orbitals and Mulliken populations analysis, we have determined the predominant electronic configuration of each ) state and its Rydberg character. Such an analysis is particularly interesting since it explains the contribution of each ) to the calculation of the static or dynamic polarizability it allows a better understanding in the case of the CO molecule the difficulty of the calculation and the wide range of published values for the parallel component while the computation of the perpendicular component is easier. In effect in the case of CO ... 

The orbitals employed to build the reference configurations were taken from atomic SCF calculations for the appropriate states of B. B, . H. and. Hj, only for the valence orbitals of the Rydberg states, BPS.3sl Hf Sl and Bf P.dol Hf Sl. we have... 

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 ... 

To account for Rydberg states, the MCSCF/SD set of orbitals was extended by atomic... 

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