## branching plane

https://doi.org/10.1351/goldbook.BT07335
At a @[email protected] point, the plane spanned by the @[email protected] difference vector ($$\boldsymbol{x_{1}}$$) and the @[email protected] of the interstate @[email protected] vector ($$\boldsymbol{x_{2}}$$): $x_{1} = \frac{\delta(E_{2}-E_{1})}{\delta Q}\boldsymbol{q}$ $x_{2} = <\boldsymbol{C_{1}}^{t}(\frac{\delta H}{\delta Q})\boldsymbol{C_{2}}>\boldsymbol{q}$ where $$\boldsymbol{C_{1}}$$ and $$\boldsymbol{C_{2}}$$ are the configuration interaction eigenvectors (i.e., the excited and ground-state @[email protected] wavefunctions) in a @[email protected] problem, $$H$$ is the @[email protected] Hamiltonian, $$\textbf{Q}$$ represents the nuclear configuration vector of the system, and thus $$\textbf{q}$$ is a unit vector in the direction of vector $$\textbf{q}$$. $$E_{1}$$ 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 $$\boldsymbol{x_{1}}$$ and $$\boldsymbol{x_{2}}$$ 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.
Source:
PAC, 2007, 79, 293. (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 309 [Terms] [Paper]