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The HMA package implements the compute hma command for LAMMPS, which implements
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harmonically-mapped averaging for crystalline solids. The current
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implementation handles atomic crystals.
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Computing the heat capacity relies on being able to compute the second
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derivative of the energy with respect to atom positions. This capability is
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provided by the single2 method in Pair, but is currently only implemented for
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the shifted-force LJ potential (lj/smooth/linear). Pair::single2 takes a single
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pair and (like Pair::single) returns the energy and sets the force as an out
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parameter, but also sets the elements of 6-element double array out parameter,
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which are the unique components of the atomic Hessian tensor for the pair. A
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helper method exists (Pair::pairTensor), which will compute the tensor from
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linear derivatives and the vector between the positions. HMA Heat capacity can
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be computed for other models by implementing single2 in those Pair classes.
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More information about HMA is available in these publications:
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A. J. Schultz, D. A. Kofke, “Comprehensive high-precision high-accuracy
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equation of state and coexistence properties for classical Lennard-Jones
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crystals and low-temperature fluid phases”, J. Chem. Phys. 149, 204508 (2018)
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https://dx.doi.org/10.1063/1.5053714
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S. G. Moustafa, A. J. Schultz, D. A. Kofke, “Harmonically Assisted Methods for
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Computing the Free Energy of Classical Crystals by Molecular Simulation: A
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Comparative Study”, J. Chem. Theory Comput. 13, 825-834 (2017)
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https://dx.doi.org/10.1021/acs.jctc.6b01082
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S. G. Moustafa, A. J. Schultz, D. A. Kofke, “Very fast averaging of thermal
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properties of crystals by molecular simulation”, Phys. Rev. E 92, 043303 (2015)
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https://dx.doi.org/10.1103/PhysRevE.92.043303
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