One of the challenging issues in quantum chemistry is locating transition states on reaction pathways, that is, stationary points with a single negative eigenvalue of the molecular Hessian (a Hessian index of one).  Within a local quadratic approximation to the potential energy surface, it is possible to define an "image surface" by reversing the sign of one or more Hessian eigenvalues. The search for stationary points with a given number of imaginary modes then becomes a minimization on the image surface.  This has typically been used to try to locate transition states by changing the sign of one eigenvalue of the Hessian.  Unfortunately, for molecules with more than a few atoms this approach tends to locate low-lying transition states on pathways of conformational change rather than "interesting" chemical reactions.  We have implemented a scheme in which stationary points with multiple negative eigenvalues of the Hessian are sought, thus walking uphill to relatively high energies. In our scheme the walk then proceeds downhill, gradually reducing the target Hessian index until transition states of genuine chemical interest are located.  We call this scheme ALTRUISM --- ALpine TRUst-region Image Surface Method.  Some applications will be described, interspersed with some personal reflections on John Stanton and his work.

ALTRUISM: Walking up and down

ACS Spring 2022

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