Derivative couplings conical intersections

Conical Intersections, Derivative Couplings and Geometric Phase 49... 

Maeda S, Ohno K, Morokuma K. Updated branching plane for finding conical intersections without coupling derivative vectors. J Chem Theory Comput. 2010 6 1538-1545. 

The ADT matrix for the lowest two electronic states of H3 has recently been obtained [55]. These states display a conical intersection at equilateral triangle geometi ies, but the GP effect can be easily built into the treatment of the reactive scattering equations. Since, for two electronic states, there is only one nonzero first-derivative coupling vector, w5 2 (Rl), we will refer to it in the rest of this... 

From Eqs. (30a)-(30c), the singularity in as the conical intersection is approached, is of order 1/p. Only /7, (n= 0, derivative coupling can be used to consfruct a local diabatic representation that removes the singularity [10]. 

We follow Thompson and Mead [13] to discuss the behavior of the electronic Hamiltonian, potential energy, and derivative coupling between adiabatic states in the vicinity of the D31, conical intersection. Let A be an operator that transforms only the nuclear coordinates, and A be one that acts on the electronic degrees of freedom alone. Clearly, the electronic Hamiltonian satisfies... 

Reference [73] presents the first line-integral study between two excited states, namely, between the second and the third states in this series of states. Here, like before, the calculations are done for a fixed value of ri (results are reported for ri = 1.251 A) but in contrast to the previous study the origin of the system of coordinates is located at the point of this particulai conical intersection, that is, the (2,3) conical intersection. Accordingly, the two polar coordinates (adiabatic coupling term i.e. X(p (— C,2 c>(,2/ )) again employing chain rules for the transformation... 

Han S, Yarkony DR (2003) Conical intersections of three states. Energies, derivative couplings, and the geometric phase effect in the neighborhood of degeneracy subspaces. Application to the allyl radical. J Chem Phys 119 11562... 

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 ... 

Equations (31) and (32) are unchanged, with W (Rx), W(2, (R>j, and now being 2x2 matrices. The adiabatic-to-diabatic transformation, as for the n-state case, eliminates any poles in both the first- and second-derivative coupling matrices at conical intersection geometries but in this case Eq. (52) yields... 

Elements of the matrix —(ft2/2p)W i are usually small in the vicinity of a conical intersection and can be added to zd to give a corrected diabatic energy matrix. As can be seen, whereas in Eq. (15) W ad contains both the singular matrix W ad and the nonsingular one W ad, Eq. (31) contains only the latter. Nevertheless, the residual first-derivative coupling term w ad Vr does not vanish. 

Fig. 8. Schematic representation of the potential surfaces leading to photoisomerisation of (BQA)PtMe2I from mer to fac isomer via a sloped conical intersection at / -like geometries. Shown to the right are the branching space vectors the gradient difference (gd=x1), and the derivative coupling (dc=x2). The primary orbitals involved in the electronic transition are shown to the left [Adapted from Ref. (110) with permission].

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