Optimal Replica-Exchange Molecular Simulations in Combination with Evolution Strategies

Atomistic analysis of nematic phase transition in 4-cyano-4'-n-alkyl biphenyl liquid crystals: Sampling for the first-order phase transition and the free-energy decomposition

Molecular dynamics simulations were conducted using the generalized replica exchange method (gREM) on the 4-cyano-4'-n-alkyl biphenyl (nCB) system with n = 5, 6, 7, and 8, which exhibits a nematic-isotropic (NI) phase transition. Sampling near the phase transition temperature in systems undergoing first-order phase transitions, such as the NI phase transition, is demanding due to the substantial energy gap between the two phases. To address this, gREM, specifically designed for first-order phase transitions, was utilized to enhance sampling near the NI phase transition temperature. Free-energy calculations based on the energy representation (ER) theory were employed to characterize the NI phase transition. ER evaluates the insertion free energy of the nCB molecule for both nematic and isotropic phases, revealing a change in the temperature dependence across the NI phase transition. Further decomposition into energetic and entropic terms quantitatively shows the balance between these contributions at the NI phase transition temperature.

Hysteresis Elimination for an Anisotropic Liquid-Crystal Model via Molecule Design and Replica-Exchange Optimization

The phenomenon of hysteresis in simulations, in which a system's current state is correlated to previous states and inhibits the transition to a more stable phase, may often lead to misleading results in physical chemistry. In this study, in addition to the replica exchange method (REM), a novel approach was taken by combining an evolution strategy based on the evolutionary principles of nature to predict phase transitions for the Hess-Su liquid-crystal model. In this model, an anisotropy term is added to the simple 6-12 Lennard-Jones model to intuitively reproduce the behavior of liquid crystals. We first applied the pressure-temperature REM to the Hess-Su model and optimized the replica spacing for the energy distribution to gain the maximum advantage from the REM. We then used the same approach as for the Hamiltonian REM, seeking to optimize the replica spacing in the same way. Based on both results, we attempted to predict this coarse-grained liquid-crystal model's exact phase transition point. In the Hamiltonian REM, replicas were prepared with different molecular aspect ratios corresponding to the values of the anisotropy terms in the potential function. The Hess-Su liquid-crystal model, which undergoes a direct transition from the nematic to the solid phase without going through a smectic phase, is a challenging research target for understanding phase transitions. Despite the tremendous computational difficulty in overcoming the strong hysteresis present in this system, our method could predict the phase transition point clearly and significantly reduce the extent of hysteresis. Our approach is beneficial when simulating more complex systems and, above all, shows great potential for more accurate and efficient phase transition predictions in the field of molecular simulation in the future.