(588a) Efficient Measurement of Anharmonic Mechanical Properties of Crystals Using Normal-Mode Mapping
AIChE Annual Meeting
2021
2021 Annual Meeting
Computational Molecular Science and Engineering Forum
Recent Advances in Molecular Simulation Methods
Thursday, November 11, 2021 - 8:00am to 8:15am
Statistical thermodynamics provides a connection between mechanical properties and free energy derivatives with respect to some external strain. For example, the stress tensors and elastic constants are expressed as first and second derivatives of the free energy, respectively. For crystalline systems, the harmonic model provides a (simple) first-order approximation to these properties, which has increasingly accurate results as the temperature decreases, but fails to describe the system at high temperatures due to anharmonic effects.
Measuring anharmonic effects, however, is not as straightforward as it requires running molecular simulation to generate several configurations. Standard expressions of crystalline properties (e.g., virial pressure) obtain the anharmonic contribution on an average-basis level, by a naïve subtraction of the harmonic contribution from the total. This introduces large noise in the (small) anharmonic effects, due to its contamination with large fluctuations from the harmonic behavior that exists for each configuration.
To alleviate this problem, we developed a configuration-based formulation that leverages the harmonic character to provide in essence a direct measurement of the anharmonic contributions to the properties. This was possible by applying our previously developed harmonically mapped averaging (HMA) theory [1,2] in the “natural†normal-mode coordinates of the crystalline systems; hence the name NM-HMA. The new formulation provides a significant CPU speedup (relative to conventional methods) in computing several mechanical properties (e.g., stress tensor) to a given precision. One of the advantages of the new formulation does not rely on external parameters like the original HMA method, rather it depends on the harmonic information of the system (e.g., Grüneisen parameters). As with other HMA methods, NM-HMA does not alter the molecular simulation sampling; hence, the properties can be computed by post-processing simulation data (e.g., configurations and forces), and several properties may be measured at once.
Measuring anharmonic effects, however, is not as straightforward as it requires running molecular simulation to generate several configurations. Standard expressions of crystalline properties (e.g., virial pressure) obtain the anharmonic contribution on an average-basis level, by a naïve subtraction of the harmonic contribution from the total. This introduces large noise in the (small) anharmonic effects, due to its contamination with large fluctuations from the harmonic behavior that exists for each configuration.
To alleviate this problem, we developed a configuration-based formulation that leverages the harmonic character to provide in essence a direct measurement of the anharmonic contributions to the properties. This was possible by applying our previously developed harmonically mapped averaging (HMA) theory [1,2] in the “natural†normal-mode coordinates of the crystalline systems; hence the name NM-HMA. The new formulation provides a significant CPU speedup (relative to conventional methods) in computing several mechanical properties (e.g., stress tensor) to a given precision. One of the advantages of the new formulation does not rely on external parameters like the original HMA method, rather it depends on the harmonic information of the system (e.g., Grüneisen parameters). As with other HMA methods, NM-HMA does not alter the molecular simulation sampling; hence, the properties can be computed by post-processing simulation data (e.g., configurations and forces), and several properties may be measured at once.
[1] S. Moustafa et al., Phys. Rev. E 92, 043303 (2015).
[2] A. Schultz et al., J. Chem. Theory Comput. 12, 1491 (2016).