Orbital Rydberg

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... 

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. 

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 ... 

The lowest A, excited states of C3H2are of Rydberg type, arising from the promotion of one electron from the carbene lone pair orbital to 3s and 3p Rydberg orbitals, are better represented by orbitals generated by a MCSCF/SD treatment (Table 9). 

The prompt dissociation of the fast H atom in the pathway, for which character change and collapse of the 3s Rydberg orbital on the ethyl radical to the Is orbital of the H product are required,121-123 could be assisted by the conical intersection. Also, relaxation and internal conversion from the 3s state to the ground state ethyl can be facilitated by this conical intersection, in addition to other possible vibronic couplings in the A symmetry.39... 

Such long lifetimes are puzzling in view of the well-known n3 scaling of Rydberg state lifetimes observed from linewidths of resolvable series and predicted by theory. The n3 scaling derives from a fundamental property of Rydberg states. The normalization factor in the radial part of the Rydberg orbital scales as n 3/2. Thus... 

NBOs 3-5 are the three fluorine lone pairs ( LP ). As shown by the occupancies and hybrid composition, these lone pairs are inequivalent. LP(1) is the s-rich sigma-type sp0 26 lone pair (nF(cr) 79% s character), directed along the bond axis. LP(2) andLP(3) are the p-rich pi-type lone pairs (nF(7t) and nF(rf) 99.97% p-character), perpendicular to the bond axis. The lone pairs have occupancies slightly less than 2.000 00 (due to weak delocalization into Rydberg orbitals of the adjacent H), but overall, the correspondence with the elementary Lewis-structure description is excellent. 

Table 3.29. The NBO descriptors of XYZ triatomic anions (see Table 3.28), showing natural atomic charges (Q), percentage polarization of oxy and ayz NBOs toward terminal atoms, second-order nz— oxy and nx->OYZ stabilizations (A/s(2)), and occupancies of valence antibonds (oxy and ayz ) and extra-valent Rydberg orbitals (ry ) parenthesized values refer to Lewis structure of lower accuracy...

It is noteworthy that Rydberg orbital occupancies on the central atom (rY, final column of Table 3.29) are relatively negligible (0.01-0.03e), showing that d-orbital participation or other expansion of the valence shell is a relatively insignificant feature of hyperbonded species. However, the case of HLiH- is somewhat paradoxical in this respect. The cationic central Li is found to use conventional sp linear hybrids to form the hydride bonds, and thus seems to represent a genuine case of expansion of the valence shell (i.e., to the 2p subshell) to form two bonding hybrids. However, the two hydride bonds are both so strongly polarized toward H (93%) as to have practically no contribution from Li orbitals, so the actual occupancy of extra-valent 2pu orbitals ( 0.03< ) remains quite small in this case. 

Keywords electron-capture dissociation electron-transfer dissociation electron transfer Rydberg orbital Landau-Zener theory... 

Families of Rydberg states in which the excess electron has moved from the anion donor to reside in a Rydberg orbital (ground 3s, or excited 3p, 3d, 4s, etc.) on one of the polypeptide s protonated amine side chains. These curves (at least... 

If the electron enters a Rydberg orbital on one of the protonated amine sites, in addition to undergoing a cascade of radiative or non-radiative relaxation steps to lower-energy Rydberg states, it can subsequently undergo intra-peptide electron transfer to either an SS cr or an OCN n orbital after which disulfide or N-Cr, bond cleavage can occur [3r,3u-3w]. 

In the studies our group has undertaken [3h-3w] to date, we used LZ theory to estimate the probabilities P for an electron being transferred from such a Rydberg orbital to an SS cr or amide n orbital. In Figure 5 we show actual data from such a study on the H3C—S—S—(CH2)3—NH " model compound. 

In summary, ETD and ECD processes involve two kinds of electron-transfer events. The first occurs in the initial capture of an electron by the positively charged polypeptide. The second involves intra-peptide electron transfer from a Rydberg orbital residing on a positively charged site to an SS or OCN bond site. 

Hydrogenic and Rydberg orbitals have "sizes" that can be characterized by their expectation values of r and... 

In Figure 7, we show the SS a, excited-Rydberg, and ground-Rydberg orbitals for three model compounds + H3N-(CH2) -S-S-CH3 having n — 3,2, or 1 from left to right. 

It is important to recognize that the Rydberg orbitals have significant amplitudes in regions of space where the SS a orbital also does and that the degree of overlap between the Rydberg and SS a orbitals decreases as n increases, as expected. 

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