The quantum instanton (QI) model for chemical reaction rates: The "simplest" QI with one dividing surface

A new version of the quantum instanton (QI) approach to thermal rate constants of chemical reactions (Miller, W. H.; Zhao, Y.; Ceotto, M.; Yang, S. J. Chem. Phys. 2003, 119, 1329) is presented, namely, the simplest QI (SQI) approximation with one dividing surface (DS), referred to here as SQI1. (The SQI approximation presented originally was applicable only with two DSs.) As with all versions of the QI approach, the rate is expressed wholly in terms of the (quantum) Boltzmann operator (which, for complex systems, can be evaluated by Monte Carlo path integral methods). Test calculations on some simple model problems show the SQI1 model to be slightly less accurate than the original version of the QI approach, but it is the easiest version to implement; it requires only a constrained free-energy calculation, location of the (transition-state) DS so as to maximize this free energy, and the curvature (second derivative) of the free energy at this maximum.