Maple™-assisted calculations of the J-integral: a key parameter for the understanding of excited state energy transfer in porphyrins and other chromophores

Abstract

The spectral overlap between the emission of a donor molecule and the absorption of an acceptor molecule, quantifiable using the J-integral calculation, is a parameter of extreme importance when studying the excited state energy transfer by either the Főrster or Dexter mechanism. Despite its extreme importance in both mechanisms, it is often misinterpreted, approximated or incorrectly calculated. The calculation of the J-integral is not trivial especially when one wishes to carry out the calculation on measured spectroscopic data. A detailed description for the correct calculation of the J-integral is herein reported and presents a Maple™ assisted template that is capable of performing this calculation in the two different energy scales (nm and cm-1) to yield the value of the J-integral in given units. Specific examples using porphyrin-containing compounds are provided. This Maple™ program is flexible and can be easily adapted to the needs of a researcher. A call for the standardization of the calculation of the J-integral for the facile comparison with other overlap integrals found in the literature is made.