First-Principles Calculation of Jahn–Teller Rotational Distortion Parameters

Abstract

A theoretical and computational framework is presented for the parameters h 1 and h 2 that appear in the rotational Hamiltonian for molecules subject to the Jahn− Teller effect. Expressions that relate h 1 and h 2 to first and second moments of the degenerate normal coordinates as well as derivatives of the inertia tensor are presented in detail for both cylindrical and Cartesian coordinate systems. The method is demonstrated for three situations in which experimental information about h 1 (and/or h 2 ) is available: the ground 2 E 1 ″ and 2 E states of the cyclopentadienyl (C 5 H 5 ) and methoxy (CH 3 O) radicals, respectively, and the excited 2 E″ state of the nitrate (NO 3 ) radical. Results for h 1 and h 2 parametrized by ab initio calculations exhibit good agreement with measured values, and they are demonstrably superior to those obtained with an approach based on first-order perturbation theory. The computational technology developed for h 1 and h 2 can be used to benchmark quantum chemistry calculations for molecules with Jahn−Teller effects and facilitate the analysis of their spectra.

Gas-Phase Formation of Fulvenallene (C7H6) via the Jahn–Teller Distorted Tropyl (C7H7) Radical Intermediate under Single-Collision Conditions

“…Here, the i2 → i4 isomerization can be rationalized as pseudorotation i2 (8) → 9 via 3 followed by an electrocyclic ring closure. Six consecutive isomerization steps from i3 involving [4,2] hydrogen shift (i5), cyclization (i6), ring opening forming an exocyclic CH 2 moiety (i8), cyclization (i11), ring opening leading to a five-membered ring intermediate (i12), hydrogen shift (i13), and atomic hydrogen elimination accompanied by aromatization lead to p1. Considering intermediate i4, the latter may ring open (i7), undergo two consecutive hydrogen migrations (i9, i10), and then emit atomic hydrogen forming p1.…”

“…1 Initially encountered in octahedral transition metal complexes such as of the d 9 ion copper(II), the Jahn−Teller theorem states that any nonlinear molecule with a degenerate electronic ground state undergoes a geometrical distortion along nontotally symmetric vibrational modes from its highest symmetry that eliminates that degeneracy since this distortion lowers the overall energy of the molecule. 2−4 The homologous series of the cyclic C 3 H 3 (1), C 5 H 5 (2), and C 7 H 7 (3) radicals (Scheme 1) has attracted particular interest from the physical organic, theoretical chemistry, and material science communities in exploiting the Jahn−Teller theorem to unravel the exotic electronic structure and chemical bonding of prototypes of JT distorted Huckel-aromatic transient radicals 5−7 along with implications to high-temperature superconductivity, 8 magnetoresistance, 9 and conical intersections. 10,11 The D 3h symmetric cyclopropenyl radical C 3 H 3 (1; X 2 E″) distorts through vibronic coupling involving the e″ (1030 cm −1 ), and a 2 ″ (778 cm −1 ) normal modes resulting in two nearly isoenergetic species holding C s point groups (4, 5).…”

Efficient Multi-Configurational Wavefunction Method with Dynamical Correlation Using Non-Orthogonal Configuration Interaction Singles and Doubles (NOCISD)

“…The Jahn-Teller distortion along a C 2 axis of the molecule has been the center of investigations into the equilibrium structure of the radical as well as the nature of the vibrational modes contributing to the Jahn-Teller distortion (see, for instance, Refs. [21][22][23] ).…”

Unified Hamiltonian Formalism of Jahn–Teller and Pseudo-Jahn–Teller Problems in Axial Symmetries

“…This is not just true for theoreticians, but for experimentalists as well. 32,[35][36][37][38] Without the knowledge of high order expansion formulas, spectroscopists will have to fit their accurate vibronic spectra using inaccurate models. This is likely to impair the interpretation of the spectra.…”