14 January 2000 Ž . Chemical Physics Letters 316 2000 248–256 www.elsevier.nlrlocatercplett On the behavior of single-surface nuclear wavefunctions in the vicinity of the conical intersection for an X system 3 A.J.C. Varandas ) , Z.R. Xu Departamento de Quımica, UniÕersidade de Coimbra, 3049 Coimbra Codex, Portugal ´ Received 2 February 1999; in final form 1 November 1999 Abstract The behavior of single-surface nuclear wavefunctions in the vicinity of the conical intersection at the equilateral triangle conformations of homonuclear triatomic systems is examined analytically by using spherical coordinates which are obtained from the usual D normal mode ones. They are described by a set of three quantum numbers and shown to approach zero 3h at the conical intersection, irrespective of whether the so-called geometric phase effects are taken into consideration. q 2000 Elsevier Science B.V. All rights reserved. 1. Introduction In recent years, there has been considerable inter- est in molecular vibronic dynamics which requires the consideration of two or more Born–Oppenheimer Ž . Ž . w x BO potential energy surfaces PES 1–4 . In par- ticular, recent interest has focused on the so-called conical intersections. The simplest systems exhibit- ing such an intersection are those formed by three 2 w x w x identical S atoms, i.e., H 5,6 , Li 7–9 , Na 3 3 3 w x 10 , etcetera. For these systems, symmetry consider- ations force the conical intersection to occur at D 3 h geometries; the behavior of the corresponding BO energies and the derivative coupling has been exam- w x ined by Mead and co-workers 2,4 . In particular, wx Mead 2 has proved that single-surface nuclear wavefunctions for such a system must approach zero wx at the conical intersection 2 , a finding which may ) Corresponding author. Fax: q351-39-27703; e-mail: varandas@qtvsl.uc.pt have implications on the behavior of the derivative wx coupling terms at the conical intersection 2 . How- ever, Mead’s demonstration is based on a two-di- Ž . mensional 2D model analysis, a limitation which has been removed in the present work while using a relatively straightforward formalism. Related to conical intersections are subtle compli- cations arising in the adiabatic treatment of the nu- clear motion, which are known as geometric phase Ž . w x Ž GP effects 11 also often called Bohm–Aharonov wx w x. effects 2 or Berry’s phase effects 12,2 . Such complications stem in molecular dynamics from two w x topological theorems due to Longuet-Higgins 13 Ž. which state 1 that on going once around any closed Ž . path on the adiabatic PES that contains the conical intersection the electronic wavefunction changes sign Ž. and 2 that if a real adiabatic electronic wavefunc- tion changes sign when a polyatomic traverses a one-dimensional closed loop on a 2D surface in the Ž . 3 N y 6 -dimensional nuclear configuration space, then the corresponding electronic state must become 0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. Ž . PII: S0009-2614 99 01275-0