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.

The branching plane is also referred to as the

**Note:**

The branching plane is also referred to as the

**-**

*g***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.**

*h*