Term: branching plane
https://doi.org/10.1351/goldbook.BT07335

Definition:
At a conical intersection point, the plane spanned by the gradient difference vector (x1) and the gradient of the interstate coupling vector (x2): \[x_{1} = \frac{\delta(E_{2}-E_{1})}{\delta Q}\boldsymbol{q}\] \[x_{2} = \boldsymbol{q}\] where C1 and C2 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. E1 and E2 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 x1 and x2 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.

Related Terms:
1) excited state (http://doi.org/10.1351/goldbook.E02257).
2) ground-state (http://doi.org/10.1351/goldbook.G02704).
3) conical intersection (http://doi.org/10.1351/goldbook.CT07347).
4) gradient (http://doi.org/10.1351/goldbook.G02669).
5) coupling (http://doi.org/10.1351/goldbook.C01025).
6) adiabatic (http://doi.org/10.1351/goldbook.A00141).

Source: PAC, 2007, 79, 293. 'Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)' on page 309 (https://doi.org/10.1351/pac200779030293)

Citation: 'branching plane' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. https://doi.org/10.1351/goldbook.BT07335

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