Conical intersections derivative coupling vector

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... 

Figure 3. Transverse (nonremovable) part of the ab initio first-derivative coupling vector, tra (p> 4>x) function of (()). for p = 4, 6, and 8 b and (a) 0 = 1° (near-conical intersection...

Figure 3.20 VB structures and branching space (X, GDV and X2 DCV) for fulvene conical intersection. GDV, gradient difference vector DCV, derivative coupling vector.

Figure 3.22 Branching space for the conical intersection of azulene. Xi (the gradient difference vector) is dominated by the change in the transannular bond X2, (the derivative coupling vector) is dominated by the re-aromatization of the rings (similar to benzene).

Levine BG, Coe JD, Martinez TJ. Optimizing conical intersections without derivative coupling vectors application to multistate multireference second-order permrbation theory (MS-CASPT2). J P/tys Chem B. 2008 112 405-413. 

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. 

In these last equations, g = <5 is the gradient difference vector and h = A is the linear derivative coupling vector. The space spanned by these two vectors is called the - ft space or branching space whereas the space orthogonal to the branching space is the intersection space, also called conical intersection seam. Thus, a conical intersection is a subspace of the nuclear configuration space of dimension 3N-8, where N denotes the number of atoms of the system (the space of the nuclear configurations is of dimension 3N-6). 

The X1 and X2 vectors presented in Fig. 2 are known as the gradient difference and derivative coupling vectors, which are special internal coordinates that lift the degeneracy to first order in nuclear motion. The remaining 3N-8 internal coordinates do not lift the degeneracy at first-order, and they span the intersection space, which is a hyperUne cmisisting of an infinite number of conical intersection points (known as the seam). 

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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