Broad shape resonance effects in CaF Rydberg states

Abstract

Results of ab initio R-matrix calculations [S. N. Altunata et al., J. Chem. Phys. 123, 084319 (2005)] indicate the presence of a broad shape resonance in electron-CaF(+) scattering for the (2)Sigma(+) electronic symmetry near the ionization threshold. The properties of this shape resonance are analyzed using the adiabatic partial-wave expansion of the scattered electron wave function introduced by Le Dourneuf et al. [J. Phys. B 15, L685 (1982)]. The qualitative aspects of the shape resonance are explained by an adiabatic approximation on the electronic motion. Mulliken's rule for the structure of the Rydberg state wave functions [R. S. Mulliken, J. Am. Chem. Soc. 86, 3183 (1964)] specifies that, except for an (n*)(-32) amplitude scale factor, every excited state wave function within one Rydberg series is built on an innermost lobe that remains invariant in shape and nodal position as a function of the excitation energy. Mulliken's rule implies a weak energy dependence of the quantum defects for an unperturbed molecular Rydberg series, which is given by the Rydberg-Ritz formula. This zero-order picture is violated by a single (2)Sigma(+) CaF Rydberg series at all Rydberg state energies (n*=5-->infinity, more so with increasing n*) below the ionization threshold, under the broad width of the shape resonance. Such a violation is diagnostic of a global "scarring" of the Rydberg spectrum, which is distinct from the more familiar local level perturbations.

Electric potential invariants and ions-in-molecules effective potentials for molecular Rydberg states

“…Multi-center potentials are useful for Rydberg states of polar molecules in the intermediate range where the core rotational structure cannot be averaged because of the presence of core-Kepler stroboscopic resonances, 33,90 and where the internal structure leads to shape resonances. 104 The difference between the truncated and the full two-center potentials is two-fold: molecular anisotropy predictions are larger in the full form, as in Table V for BaF + , and inferred atomic polarizabilities are smaller in the full model than in the truncated model. The full form is consistent with the Silberstein/Applequist/Thole approach often used in MM and QM/MM.…”

“…In this paper, we focus on optimizing effective potentials for use in Rydberg R-matrix calculations, 17,104,119 as a faithful representation of charge/molecular-ion interactions, and as a predictive tool for moments and polarizabilities. We have shown in Figure 1 how the origin chosen for a single-center multipole series affects the convergence properties of a multipole series, and the transition from penetrating to non-penetrating in the representation of Rydberg states.…”

“…In a ground-breaking 1997 paper, Arif, Jungen, and Roche 14 proposed a one-electron effective potential for polar diatomic Rydberg states and applied it to Rydberg states of CaF and BaF, both of which are effective one-electron systems. This AJR potential has been applied in MQDT calculations for rare-gas hydrides, 53,54 CaCl, 15 BaI, 16 and CaF, 17,104 allowing comparison to quantum-defect matrices derived from Rydberg experimental data. 19 The AJR potential, excluding core de-shielding terms, uses Coulomb, atomic polarization, and dipole energy terms in a way that is equivalent to the following expression:…”

Rydberg states of OH radical

“…This theory has been developed by many authors, primarily for non-polar molecules [18][19][20][21][22]. Later, MQDT was applied to some polar molecules, in particular, NO [23], CaF [24][25][26][27][28][29], BaF [15,[30][31][32][33], CaCl [34][35][36], SO [37] etc.…”

Ридберговские Состояния Радикала ОН

“…Эта теория развивалась многими авторами в первую очередь для неполярных молекул [18][19][20][21][22]. Позже MQDT применялась и к некоторым полярным молекулам, в частности, NO [23], CaF [24][25][26][27][28][29], BaF [15,[30][31][32][33], CaCl [34][35][36], SO [37] и др.…”