branching plane
At a conical intersection point, the plane spanned by the gradient difference vector (x1) and the gradient of the interstate coupling vector (x2): \[x_{1} = \frac{\delta(E_{2}-E_{1})}{\delta Q}\boldsymbol{q}\] \[x_{2} = <\boldsymbol{C_{1}}^{t}(\frac{\delta H}{\delta Q})\boldsymbol{C_{2}}>\boldsymbol{q}\] where C1 and C2 are the configuration interaction eigenvectors (i.e., the excited and ground-state adiabatic wavefunctions) in a conical intersection problem, H is the conical intersection Hamiltonian, Q represents the nuclear configuration vector of the system, and thus q is a unit vector in the direction of vector q. E1 and E2 are the energies of the lower and upper states, respectively.
The branching plane is also referred to as the g-h plane. Inspection of x1 and x2 provides information on the geometrical deformation imposed on an @[email protected] molecular entity immediately after decay at a @[email protected] Consequently, these vectors provide information on the @[email protected] species that will be formed after the decay.
PAC, 2007, 79, 293. 'Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)' on page 309 (