Geometric phase effect potential energy surfaces

Finally, in brief, we demonstrate the influence of the upper adiabatic electronic state(s) on the ground state due to the presence of a Cl between two or more than two adiabatic potential energy surfaces. Considering the HLH phase, we present the extended BO equations for a quasi-JT model and for an A -1- B2 type reactive system, that is, the geometric phase (GP) effect has been inhoduced either by including a vector potential in the system Hamiltonian or... 

The full quantum mechanical study of nuclear dynamics in molecules has received considerable attention in recent years. An important example of such developments is the work carried out on the prototypical systems H3 [1-5] and its isotopic variant HD2 [5-8], Li3 [9-12], Na3 [13,14], and HO2 [15-18], In particular, for the alkali metal trimers, the possibility of a conical intersection between the two lowest doublet potential energy surfaces introduces a complication that makes their theoretical study fairly challenging. Thus, alkali metal trimers have recently emerged as ideal systems to study molecular vibronic dynamics, especially the so-called geometric phase (GP) effect [13,19,20] (often referred to as the molecular Aharonov-Bohm effect [19] or Berry s phase effect [21]) for further discussion on this topic see [22-25], and references cited therein. The same features also turn out to be present in the case of HO2, and their exact treatment assumes even further complexity [18],... 

The story begins with studies of the molecular Jahn-Teller effect in the late 1950s [1-3]. The Jahn-Teller theorems themselves [4,5] are 20 years older and static Jahn-Teller distortions of electronically degenerate species were well known and understood. Geometric phase is, however, a dynamic phenomenon, associated with nuclear motions in the vicinity of a so-called conical intersection between potential energy surfaces. 

Equation (31) is the standard nuclear Schrodinger equation in the absence of a conical intersection, while Eq. (30) evinces the changes attributable to the geometric phase effect that result from a conical intersection. This changes were termed the Molecular-Aharonov-Bohm (MAB) effect.The 6, term in Eq. (31), the adiabatic correction, modifies the Born-Oppenheimer potential energy surfaces and makes them mass dependent. 

J. Schon and H. Koppel, Geometric Phase Effects and Wave Packet Dynamics on Intersecting Potential Energy Surfaces , J. Chem. Phys. 103, 9292 (1995). 

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