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Transition path and path ensemble optimization with gradient-augmented
Harmonic Fourier Beads method

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Dr. Ilja Khavrutskii

HHMI, Chemistry-Biochemistry, and Ctr for Theoretical Biological Physics, UC San Diego

## Abstract

**
We present a simple method for solving a free boundary value problem of
locating either minimum free energy transition path ensemble or minimum
potential energy transition path between two configurations on a
corresponding energy surface. Our method, called gradient-augmented
Harmonic Fourier Beads, employs the global Fourier representation of the
path that is a curve interpolation of a discrete set of points on the
surface - beads. To optimize the path curve, the method computes energy
gradients for each bead from either convex optimization or molecular
dynamics or Monte Carlo simulations subject to harmonic restraints. The
path optimization is driven by primitive Steepest Descent procedure.
Line integration of the Fourier transformed forces along the path curve
provides complete and accurate structural and energetic information
regarding all the intermediates and saddle points present. The utility
of the HFB method is demonstrated by computing potentials of mean force
for various transformations of diverse molecular systems.
**