26 May 2000 Ž . Chemical Physics Letters 322 2000 358–362 www.elsevier.nlrlocatercplett Computational prediction of the ISC rate for triplet norbornene Jeremy N. Harvey a, ) , Stefan Grimme b,1 , Markus Woeller b , Sigrid D. Peyerimhoff b , David Danovich c , Sason Shaik c a School of Chemistry, UniÕersity of Bristol, Cantock’s Close, Bristol BS8 1TS, UK b Institut fur Physikalische und Theoretische Chemie der UniÕersitat Bonn, Wegelerstrasse 12, D-53115 Bonn, Germany ¨ ¨ c Department of Organic Chemistry and the Lise–Meitner–MinerÕa Centre for Computational Quantum Chemistry, The Hebrew UniÕersity, IL-91904 Jerusalem, Israel Received 10 February 2000; in final form 3 April 2000 Abstract The radiationless decay of T norbornene to the singlet ground state is studied using density-functional and ab initio 1 CASSCF calculations of the potential energy surface crossing and of the spin-orbit coupling. The rate of decay is predicted using two approximate multi-dimensional non-adiabatic methods, one of which is based on Fermi’s Golden Rule, and the other is a version of RRKM theory adapted for non-adiabatic processes. Unlike a previous Landau–Zener treatment of this w Ž . x process by some of us Chem. Phys. Lett. 287 1998 601–607 , both methods correctly predict a short lifetime for the triplet excited state, in reasonable agreement with experimental data. This underlines the importance of tunnelling in non-radiative relaxation processes. q 2000 Elsevier Science B.V. All rights reserved. 1. Introduction Ž . The triplet excited state of norbornene see Fig. 1 wx has been observed experimentally 1 to have a very short non-radiative lifetime of ca. 250 ns. This obser- vation is slightly puzzling, because the bicyclic ring structure might appear to lock the double bond, preventing it from undergoing the substantial twist which is involved in the most common T r S 1 0 crossing mechanism in olefins. Recently, some of us have used the Landau–Zener equation to examine ) Corresponding author. E-mail: Jeremy.Harvey@bris.ac.uk 1 Ž Present Address: Organisch-Chemisches Institut Abt. Theo- . retische Chemie , Westfalische Wilhelms-Universitat, Cor- ¨ ¨ rensstrasse 40, D-48149 Munster, Germany. ¨ wx this experimental observation 2 . The Landau–Zener Ž . w x LZ equation 3,4 is one of the simplest and most fundamental theoretical constructs for the treatment of surface crossing or very weakly avoided crossing, such as the one involved in this decay reaction. Our approach involved a density function theoretic calcu- lation of the S and T potential energy surfaces, in 0 1 order to locate a T r S crossing point which is 1 0 responsible for the T S decay according to the 1 0 LZ equation. This was followed by calculation of the Ž . spin-orbit coupling SOC matrix element around this crossing point. A significant barrier to surface crossing was found, with the T y S crossing point 1 0 well above the T minimum, which, in conjunction 1 with a small SOC matrix element, led to a very low predicted rate of decay, in poor agreement with experiment. As a possible explanation, we suggested 0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. Ž . PII: S0009-2614 00 00442-5