Abstract
We introduce grand and semigrand canonical global optimization approaches using basin-hopping with an acceptance criterion based on the local contribution of each potential energy minimum to the (semi)grand potential. The method is tested using local harmonic vibrational densities of states for atomic clusters as a function of temperature and chemical potential. The predicted global minima switch from dissociated states to clusters for larger values of the chemical potential and lower temperatures, in agreement with the predictions of a model fitted to heat capacity data for selected clusters. Semigrand canonical optimization allows us to identify particularly stable compositions in multicomponent nanoalloys as a function of increasing temperature, whereas the grand canonical potential can produce a useful survey of favorable structures as a byproduct of the global optimization search.
Highlights
Structure prediction is essential in many areas of computational science, ranging from molecular physics and biochemistry to soft and condensed matter
For a given system with definite size, the global optimization problem is usually nontrivial owing to highdimensional potential energy landscapes, and many methods have been proposed to locate low-energy configurations.[1−4] The global minimum is fundamentally important and often carries essential insight into the interactions responsible for the emergence of specific morphologies, and it plays an important role in explaining self-assembling motifs and symmetries.[5,6]
The same values were obtained in runs of 107 grand canonical basin-hopping (GCBH) steps with size moves attempted aThe μ values considered were in integer steps
Summary
Structure prediction is essential in many areas of computational science, ranging from molecular physics and biochemistry to soft and condensed matter. Examples of entropy-driven structural transitions have been reported in atomic clusters,[7,8] proteins,[9] colloids,[10] glasses,[11] and pressurized materials.[12] The determination of configurations that are low in free energy can proceed by the a posteriori analysis of molecular simulations, often employing biases in order to sample the energy landscape more efficiently and based on system-dependent order parameters.[13−17] Such free energies are global and can encompass many potential energy minima, as expected in the context of phase transitions.
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