Conical intersections molecular systems

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],... 

B. The Study of a Real Three-State Molecular System Strongly Coupled (2,3) and (3,4) Conical Intersections... 

By following Section II.B, we shall be more specific about what is meant by strong and weak interactions. It turns out that such a criterion can be assumed, based on whether two consecutive states do, or do not, form a conical intersection or a parabolical intersection (it is important to mention that only consecutive states can form these intersections). The two types of intersections are characterized by the fact that the nonadiabatic coupling terms, at the points of the intersection, become infinite (these points can be considered as the black holes in molecular systems and it is mainly through these black holes that electronic states interact with each other.). Based on what was said so far we suggest breaking up complete Hilbert space of size A into L sub-Hilbert spaces of varying sizes Np,P = 1,..., L where... 

At this stage, we wish to emphasize that a point (molecular geometry) on a conical intersection hyperline has a well-defined electronic structure (illustrated in Figure 9.6 or Eq. 9.2 with T = 0) and a well-defined geometry. Of course, the four electrons in four Is orbitals shown in Figure 9.6 is a very simple example, but we believe it is useful in order to be able to appreciate the generality of the conical intersection construct. In more complex systems, the conical intersection hyperline concept persists, but the rationalization may be less obvious. 

The ab initio molecular dynamics study by Hudock et al. discussed above for uracil included thymine as well [126], Similarly to uracil, it was found that the first ultrafast component of the photoelectron spectra corresponds to relaxation on the S2 minimum. Subsequently a barrier exists on the S2 surface leading to the conical intersection between S2 and Si. The barrier involves out-of-plane motion of the methyl group attached to C5 in thymine or out-of-plane motion of H5 in uracil. Because of the difference of masses between these two molecules, kinematic factors will lead to a slower rate (longer lifetime) in thymine compared to uracil. Experimentally there are three components for the lifetimes of these systems, a subpicosecond, a picosecond and a nanosecond component. The picosecond component, which is suggested to correspond to the nonadiabatic S2/S1 transition, is 2.4 ps in uracil and 6.4 ps in thymine. This difference in the lifetimes could be explained by the barrier described above. 

Matsika S (2007) Conical intersections in molecular systems. In Lipkowitz KB and Cundari TR (eds.) Reviews in computational chemistry, vol. 23, Wiley-VCH, New Jersey, pp 83-124... 

Density functional theory, direct molecular dynamics, complete active space self-consistent field (CASSCF) technique, non-adiabatic systems, 404-411 Density operator, direct molecular dynamics, adiabatic systems, 375-377 Derivative couplings conical intersections, 569-570 direct molecular dynamics, vibronic coupling, conical intersections, 386-389 Determinantal wave function, electron nuclear dynamics (END), molecular systems, final-state analysis, 342-349 Diabatic representation ... 

Intraanchor reactions, conical intersection, two-state systems, 437-438 Intramolecular electron transfer, electron nuclear dynamics (END), 349-351 Intrinsic reaction coordinate (IRC), direct molecular dynamics, theoretical background, 358-361... 

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