(469f) Crystal Structure Prediction of Rigid-Molecule Crystals: Application to Hydrate Clathrate

Authors: 
Moustafa, S., University at Buffalo, The State University of New York
Kofke, D. A., University at Buffalo, The State University of New York
Schultz, A. J., University at Buffalo, The State University of New York


In solid-state systems (both atomic and molecular), prediction of the most thermodynamically stable crystal structures is identified via the thermodynamic free energy of the candidate structures. Therefore, accurate and efficient methods to compute the solid-phase free energy are crucial for such applications. In this context, among the molecular crystals that have been studied extensively are the rigid-molecule systems, in which the intramolecular interactions (bending and stretching) are ignored. Although it is an approximation to real behavior, adopting rigid-molecule models can be justified for many applications. For example, it showed success in estimating the melting temperature [1], phase diagram [2], and equation of state [3] of different water crystalline phases. Adopting rigid-molecule models reduces the computational cost, as there are fewer degrees of freedom needed to describe the system. This is especially so when simulating large molecules or when measuring thermodynamic quantities that require performing extensive calculations (e.g. free-energy). 

For the purpose of computing the free energy of rigid-molecule crystals, special methods are needed to handle the additional libration degrees of freedom. The Frenkel-Ladd method has been used to treat such systems [2]; however the method is tedious to implement as the rotational field of the Einstein crystal reference depends on the point-symmetry of the molecule; also it requires Monte Carlo integration to evaluate its free energy. In addition, the spring-constants must be chosen carefully to guarantee accurate results [4]. Due to the difficulty of measuring the entropic contribution to the free energy, different approximate methods are employed instead. In many applications, the entropic contribution is ignored entirely and one is left with the lattice enthalpy as an approximation to the free-energy. This is valid only in the 0 K limit. The harmonic approximation to the free-energy is sometimes used to capture the thermodynamic behavior at non-zero temperatures. However, for a more accurate estimation, the harmonic crystal can be used as a reference for thermodynamic-integration methods [5] that work better than the Frenkel-Ladd method [6]. In this presentation, we describe a simple theoretical formulation of the harmonic free energy of nonlinear rigid molecular crystalline systems [7]. In this treatment, working with the well-known inertia-weighted dynamical matrices is avoided if the sole purpose is to compute the free energy. The method has been applied to different proton-disordered clathrate hydrate crystal structures (sI, sII and sH). The TIP4P potential was used, where the long-range Coulomb interactions are treated using the Ewald sum technique while a lattice sum is used for van der Waals 12-6 Lennard-Jones potential. The free-energy results agree well with previous work.

In previous work [7,8] we developed an efficient method (harmonically-targeted temperature perturbation (HTTP)) to efficiently estimate the anharmonic free energy. As an alternative to this method, we have developed a harmonically-targeted temperature integration (HTTI) method, and have applied it to rigid-molecule models of hydrate-clathrates. HTTI measures directly the anharmonic free energy, which we use along with the harmonic free energy to identify the boundaries between clathrate phases. The approach overall is very efficient. We compare our results with the previously studied phase diagrams for this model system.

[1] Y. Koyama, H. Tanaka, G. Gao, and X. C. Zeng, J. Chem. Phys. 121, 7926 (2004).

[2] C. Vega, E. Sanz, J. L. F. Abascal, and E. G. Noya, J. Phys.: Condens. Matter 20, 153101 (2008).

[3] T. Inerbaev, V. Belosludov, R. Belosludov, M. Sluiter, and Y. Kawazoe, Comput. Mater. Sci. 36, 229 (2006).

[4] Y. Koyama, H. Tanaka, G. Gao, and X. C. Zeng, J. Chem. Phys. 121, 7926 (2004).

[5] G. Gao, X. Zeng, and H. Tanaka, J. Chem. Phys. 112, 8534 (2000).

[6] T. B. Tan, A. J. Schultz, and D. A. Kofke, J. Chem. Phys. 133, 134104 (2010).

[7] T. B. Tan, A. J. Schultz, and D. A. Kofke, Journal of Chemical Physics 135, 044125 (2011).

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