Abstract
A global optimisation scheme is presented using basin-hopping with the acceptance criterion based on approximate free energy for the corresponding local minima of the potential energy. The method is illustrated for atomic and colloidal clusters and peptides to examine how the predicted global free energy minimum changes with temperature. Using estimates for the local free energies based on harmonic vibrational densities of states provides a computationally effective framework for predicting trends in structure at finite temperature. The resulting scheme represents a powerful tool for exploration of energy landscapes throughout molecular science.
Highlights
Global optimisation is an important tool for structure prediction throughout molecular science, as well as for soft matter and condensed matter systems
We consider the regime where structure is still well defined in terms of competition between configurations associated with distinct potential energy minima
We have described a free energy basin-hopping (FEBH) global optimisation approach based on a harmonic approximation to the local vibrational partition function of individual potential energy minima
Summary
Global optimisation is an important tool for structure prediction throughout molecular science, as well as for soft matter and condensed matter systems. We will employ the harmonic normal mode approximation to obtain the vibrational density of states for each minimum This harmonic superposition approach has been used successfully for a variety of applications in previous work [21,23,24,25,26]. The approximate free energy of minimum i is given by Fi(T) = − kBT ln Zi(T) It is apparent from Eq (2) that the effect of temperature will come into play most rapidly for competing structures with different point group symmetries or mean vibrational frequencies. It is possible to calculate the local harmonic free energies for a sample of potential energy minima obtained after a conventional basin-hopping run, we find examples where FEBH locates the local free energy global minimum using fewer steps, on average
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