Molecular symmetry group analysis of the low-wavenumber torsions and vibration-torsions in the S1 state and ground state cation of p-xylene: an investigation using resonance-enhanced multiphoton ionization (REMPI) and zero-kinetic-energy (ZEKE) spectroscopy

For the first time, a molecular symmetry group (MSG) analysis has been undertaken in the investigation of the electronic spectroscopy of p-xylene (p-dimethylbenzene). Torsional and vibration-torsional (vibtor) levels in the S1 state and ground state of the cation of p-xylene (p-dimethylbenzene) are investigated using resonance-enhanced multiphoton ionization (REMPI) and zero-kinetic-energy (ZEKE) spectroscopy. In the present work, we concentrate on the 0–350 cm 1 region, where there are a number of torsional and vibtor bands and we discuss the assignment of this region. In an accompanying paper [Tuttle et al. J. Chem. Phys. XXX, xxxxxx (2016)], we examine the 350–600 cm 1 region where vibtor levels are observed as part of a Fermi resonance. The similarity of much of the observed spectral activity to that in the related substituted benzenes, toluene and para-fluorotoluene, is striking, despite the different symmetries. The discussion necessitates a consideration of the MSG of p-xylene, which has been designated G72, but we shall also designate [3,3]D2h and we include the symmetry operations, character table and direct product table for this. We also discuss the symmetries of the internal rotor (torsional) levels and the selection rules for the particular electronic transition of p-xylene investigated here

Sylow 2-subgroups of solvable Q-groups

A finite group whose irreducible characters are rational valued is called a rational or a Q-group. In this paper we obtain various results concerning the structure of a Sylow 2-subgroup of a solvable Q-group

Recognition of the group G 2 (5) by the prime graph

Abstract.Let G be a finite group. The prime graph of G is a graph Γ(G) with vertex set π(G), the set of all prime divisors of |G|, and two distinct vertices p and q are adjacent by an edge if G has an element of order pq. In this paper we prove that if Γ(G) = Γ(G 2 (5)), then G has a normal subgroup N such that π(N ) ⊆ {2, 3, 5} and G/N ∼ = G 2 (5)