branching plane

At a conical intersection point, the plane spanned by the gradient difference vector ( $x 1$ ) and the gradient of the interstate coupling vector ( $x 2$ ):

$x 1 = ∂ ( E 2 − E 1 ) ∂ Q q$

$x 2 = C 1 t ∂ H ∂ Q C 2 q$

where $C 1$ and $C 2$ 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 $q$ . $E 1$ and $E 2$ are the energies of the lower and upper states, respectively.

Note:

The branching plane is also referred to as the g-h plane. Inspection of $x 1$ and $x 2$ provides information on the geometrical deformation imposed on an excited state molecular entity immediately after decay at a conical intersection. Consequently, these vectors provide information on the ground-state species that will be formed after the decay.

Source:

PAC, 2007, 79, 293 (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 309