The electronic quasicontinuum

High n (=50-250) molecular Rydberg states are characterized by a high density (ρ ∝ n³/2Ry) of electronic states and by unique intramolecular couplings (V) which involve long-range Rydberg electron-core multipole interactions. We explore spectroscopic and dynamic implications of the dipole coupling V = C_D(nn′)^-3/2 of a doorway Rydberg state |n,l,N⁺,N〉 with a dense |{n′,l′,N⁺-1,N〉} manifold (n′ > n) of bound Rydberg states, which are described by Hund coupling case (d). We establish the conditions for the realization of the statistical limit (Vρ ≫ 1 and γρ > 1) and of the sparse mixed level structure (Vρ ≫ 1 and γρ < 1) within the mixed electronic manifold (where γ = Γ₀/n³ are the nonradiative decay widths). The statistical limit for an electronic quasicontinuum is realized for the coupling strength domain 1.109Ry(B/Ry)^3/8 < C_D < (Γ₀Ry/π)^1/2, establishing how the characteristics of the level structure and dynamics are determined by the rotational constant B, by the molecular dipole moment (C_D ∝ μ), by the decay width constant Γ₀, and by l (where C_D ∝ l^-7). The statistical limit within an electronic quasicontinuum is expected to be amenable for experimental observation in polar large molecules, while the np(N⁺=0)-n′d(N⁺=1) coupling in H₂O (Gilbert, R. D.; Child, M. S. Chem. Phys. Lett. 1991, 187, 153) corresponds to the sparse mixed level structure. Our analysis provides a generalization and unification of the theory of intramolecular coupling and dynamics for an electronic quasicontinuum.