## branching plane

https://doi.org/10.1351/goldbook.BT07335
At a @CT07347@ point, the plane spanned by the @G02669@ difference vector ($$\boldsymbol{x_{1}}$$) and the @G02669@ of the interstate @C01025@ 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 @A00141@ wavefunctions) in a @CT07347@ problem, $$H$$ is the @CT07347@ 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 @E02257@ molecular entity immediately after decay at a @CT07347@. Consequently, these vectors provide information on the @G02704@ 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]