Pseudo Jahn–Teller origin of instability of planar configurations of hexa-heterocycles C 4 N 2 H 4 X 2 (X = H, F, Cl, Br) Willian Hermoso a , Ali R. Ilkhani a,b , Isaac B. Bersuker a,⇑ a Institute for Theoretical Chemistry, University of Texas at Austin, Austin, TX 78712, USA b Department of Chemistry, Yazd Branch, Islamic Azad University, Yazd, Iran article info Article history: Received 8 August 2014 Received in revised form 3 October 2014 Accepted 5 October 2014 Available online 12 October 2014 Keywords: Symmetry breaking Origin of puckering Pseudo Jahn–Teller effect abstract Symmetry breaking in planar molecular-ring systems in nondegenerate states is due to the pseudo Jahn–Teller effect (PJTE), and the knowledge of the detailed mechanism of the latter allows one to manip- ulate the molecular properties, in particular, by restoring the planar configuration. We explore the origin of structural nonplanarity of hexa-heterocycles C 4 N 2 H 4 X 2 with X = H, F, Cl, Br, by means of ab initio elec- tronic structure calculations of ground and excited states, and revealing the PJT interactions that produce the instability of the ground state. The four structures are optimized in both equilibrium and unstable planar ground state geometries, and their electronic configurations and vibrational frequencies are eval- uated. In all these compounds the imaginary frequency in the planar configuration has b 3u symmetry, thus showing the direction (symmetrized coordinate) of bending (puckering) instability. Then the energy profiles (cross sections of the adiabatic potential energy surfaces) of the ground and two excited states in the planar configuration along the coordinate of instability are calculated, and the excited states produc- ing the instability of the ground state via the PJTE are revealed. Only one of these excited states contrib- utes to the b 3u instability via a two-level PJT vibronic coupling problem. The vibronic coupling constants are estimated by fitting the solutions of the secular equations to the corresponding ab initio calculated energy profiles. Ó 2014 Elsevier B.V. All rights reserved. 1. Introduction 1,4-dihydropyrazine ring, C 4 N 2 H 6 , is well studied due its pres- ence in many riboflavin coenzymes and marine luciferins [1–4]. The neuropeptide Y (NPY), a 36 amino acid peptide that is widely distributed in the central and peripheral nervous systems in human body, is implicated in a variety of biological functions including feeding behaviors; 1,4-dihydropyrazines act as antago- nists of NPY, promoting weight loss and treating eating disorders [5]. Therefore the structure of the 1,4-dihydropyrazine ring serves as an important step to elucidate the structure and properties of a variety of biochemically active compounds. 1,4-dihydropyrazine derivatives have been synthesized by different methods, such as Diels–Alder reaction and reaction of pyrazine with reducing agents [6]. This six-member ring system is in a nearly planar con- figuration, being a suitable model for the study of antiaromaticity in 8p electron molecules [7]. Several theoretical studies have been devoted to the 1,4-dihydropyrazine ring and its derivative structures in the planar configuration with D 2h symmetry and non-planar C 2h or C 2v symmetries [8–11]. In particular, it was shown [11] that the C 2v configuration is more stable than C 2h con- figuration by approximately 0.03 eV in the G1 and G2 levels of calculation [11], and by 0.05 eV in MP2/6-31 G(d) calculations [10]. In all these studies important information about the 1,4-dihy- dropyrazine ring structure and its derivatives was revealed and analyzed, but some no less important questions remain unan- swered. Of particular interest is the question about the origin of the nonplanarity of these ring compounds, their bending (pucker- ing). The interest in this question is not pure theoretical, as their properties are directly related to their structure, in particular, to the non-planar configuration, and the knowledge of the driving force of nonplanarity may serve as a tool for creating compounds with desired properties. On the other hand, it is known that the Jahn–Teller effect (JTE) for systems in degenerate states, and the pseudo JTE (PJTE) for nondegenerate states are the only source of structural instabilities and spontaneous symmetry breaking [12,13]. This means that the planar instability and consequent puckering in the 1,4-dihydropyrazine and its derivatives under consideration is caused by the PJTE (the ground state of these mol- ecules in the planar configuration is nondegenerate). http://dx.doi.org/10.1016/j.comptc.2014.10.007 2210-271X/Ó 2014 Elsevier B.V. All rights reserved. ⇑ Corresponding author. Tel.: +1 512 471 4671; fax: +1 512 471 8696. E-mail address: bersuker@cm.utexas.edu (I.B. Bersuker). Computational and Theoretical Chemistry 1049 (2014) 109–114 Contents lists available at ScienceDirect Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc