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branching plane

At a conical intersection point, the plane spanned by the gradient difference vector (x 1) and the gradient of the interstate coupling vector (x 2):
x 1 = ∂ ( E 2 − E 1 ) ∂ Q q
x 2 = C 1 t ∂ H ∂ Q C 2 q
where C 1 and C 2 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. 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 x 1 and x 2 provides information on the geometrical deformation imposed on an excited state molecular entity immediately after decay at a conical intersection. Consequently, these vectors provide information on the ground-state 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
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Cite as:
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook.
Last update: 2014-02-24; version: 2.3.3.
DOI of this term: doi:10.1351/goldbook.BT07335.
Original PDF version: http://www.iupac.org/goldbook/BT07335.pdf. The PDF version is out of date and is provided for reference purposes only. For some entries, the PDF version may be unavailable.
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