Photophysics and Kinetics of Naphthopyran Derivatives, Part 6: A fundamental System of Equations to Describe ABC Dynamics. A contribution to the Elucidation of [2H] – Naphthopyran Kinetics

A new spectrokinetic method free of any assumption is developed in this paper to investigate photochemical systems obeying ABC(3k,6φ) kinetic mechanisms that can be characterized by up to 14 unknown parameters for a nonpreconceived mechanism. The mathematical framework of this method is derived as an application from an original formalism previously established to deal with the kinetic law descriptions relating to ABC reactive systems. The necessary number of linearly independent (but nonlinear) equations has been fully defined together with seven other supplementary equations useful as constraints during the iterative calculations. As a practical example, this spectrokinetic method has been used to investigate the dynamics of a new photochromic derivative belonging to the naphthopyran family (2,2-di(4-methoxyphenyl)-5-carbomethoxy-6-(4-methoxyphenyl)-9-methoxy-2H-naphtho[1,2-b]-pyran). The system of equations has been solved, and the problems of identifiability and distinguishability have been raised with relation to the degeneracy of the kinetic solution. To get more insight into the photochemical and thermal reaction steps involved, a progressive overall discussion leads to several quantitative conclusions whose background sets the dynamics for the present derivative to at least ABC(1k,4φ) kinetics.