https://doi.org/10.1351/goldbook.BT07335

At a @CT07347@ point, the plane spanned by the @G02669@ difference vector (\(x_{1}\)) and the @G02669@ of the interstate @C01025@ vector (\(x_{2}\)): \[x_{1} = \frac{\delta(E_{2}-E_{1})}{\delta Q}\textbf{q}\] \[x_{2} = <\textbf{C}_{1}^{t}(\frac{\delta H}{\delta Q})\textbf{C}_{2}>\textbf{q}\] where \(C_{1}\) and \(C_{2}\) 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.

The branching plane is also referred to as the

**Note:**

The branching plane is also referred to as the

**-**

*g***plane. Inspection of \(x_{1}\) and \(x_{2}\) 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.**

*h*