A theoretical study of electron transfer in nanoparticle-catalysed redox reactions Alok Samanta, Swapan K. Ghosh * Theoretical Chemistry Section, RC & CD Division, Chemistry Group, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India Received 14 August 2001; in ®nal form 10 October 2001 Abstract Nanoparticle-catalysed electron transfer reactions have been investigated by using an extended version of the theory of electron transfer reactions for the bridge-mediated three-centre process and approximate expressions for various free energy quantities as well as the matrix elements. It is observed that the calculated rates for nanoparticle-catalysed reactions for the reduction of various dyes by standard reducing agents are considerably higher than the rates of direct electron transfer processes and are also found to agree quite well with recently reported experimental results. Ó 2001 Published by Elsevier Science B.V. 1. Introduction Electron transfer ET) reactions constitute an important class of processes [1±4] in various ®elds of chemistry, biology and physics. Along with a wide variety of experimental studies, there have also been major theoretical developments of ET reactions mainly based on the classical theory of Marcus [4] followed by many subsequent generalisations [1±7]. In recent years, there has been growing interest in the study of ET reac- tions mediated by nanoparticles whose physical and chemical properties are signi®cantly dierent from those of the bulk. It has been observed [8] that the reduction of several dyes by sodium borohydride is extremely slow, whereas in the presence of growing silver nanoparticles, the reaction rate becomes quite signi®cant. The redox potential of a small metal particle is much lower than that of the conventional metal electrode system but as the particle grows in size, the redox potential gradually increases and reaches the limiting value for the bulk metal. Therefore, these nanoparticles generated in solution can act as microelectrodes and the ET process can take place across these microelectrodes of suitable particle sizes. Our objective here is to investigate theoretically the ET reaction rates by considering the factors that control the nanoparticle bridge assisted ET which essentially reduces the eective barrier height as compared to the direct ET. In what follows, we present the theory of bridge- mediated three-centre ET reactions along with the expressions for the free energy of reaction, 7 December 2001 Chemical Physics Letters 349 2001) 483±488 www.elsevier.com/locate/cplett * Corresponding author. Fax: +91-22-5505151. E-mail address: skghosh@magnum.barc.ernet.in S.K. Ghosh). 0009-2614/01/$ - see front matter Ó 2001 Published by Elsevier Science B.V. PII:S0009-261401)01240-4