A Monte Carlo study of crystal structure transformations

The recently proposed Einstein molecule approach is extended to compute the free energy of molecular solids. This method is a variant of the Einstein crystal method of Frenkel and Ladd[J.Chem. Phys. 81, 3188 (1984)]. In order to show its applicability, we have computed the free energy of a hard-dumbbells solid, of two recently discovered solid phases of water, namely, ice XIII and ice XIV, where the interactions between water molecules are described by the rigid non-polarizable TIP4P/2005 model potential, and of several solid phases that are thermodynamically stable for an anisotropic patchy model with octahedral symmetry which mimics proteins. Our calculations show that both the Einstein crystal method and the Einstein molecule approach yield the same results within statistical uncertainty. In addition, we have studied in detail some subtle issues concerning the calculation of the free energy of molecular solids. First, for solids with non-cubic symmetry, we have studied the effect of the shape of the simulation box on the free energy. Our results show that the equilibrium shape of the simulation box must be used to compute the free energy in order to avoid the appearance of artificial stress in the system that will result in an increase of the free energy. In complex solids, such as the solid phases of water, another difficulty is related to the choice of the reference structure. As in some cases there is not an obvious orientation of the molecules, it is not clear how to generate the reference structure. Our results will show that, as long as the structure is not too far from the equilibrium structure, the calculated free energy is invariant to the reference structure used in the free energy calculations. Finally, the strong size dependence of the free energy of solids is also studied.

Section: A the Einstein Molecule Approachmentioning

confidence: 99%

Computing the free energy of molecular solids by the Einstein molecule approach: Ices XIII and XIV, hard-dumbbells and a patchy model of proteins

Noya

Conde²,

Vega³

2008

“…28 Volume fluctuations were performed by sampling the elements of the h matrix, where h is the 3ϫ3 matrix that relates the real (r i ) and the scaled (s i ) coordinates of the molecular centers of mass, i.e., r i ϭhs i . 27,28 Note that hϭ͕a,b,c͖, where the vectors a, b, and c define the edges of the simulation box.…”

Section: B Simulation Of the Solid Phasementioning

confidence: 99%

“…In particular we used the Monte Carlo ͑MC͒ scheme developed by Yashonath and Rao 27 in which volume fluctuations are performed by allowing for arbitrary changes in the shape of the simulation box. This is important when simulating solids since it avoids any possible metastability resulting from the constraint of fixing the shape of the simulation cell.…”

Section: B Simulation Of the Solid Phasementioning

confidence: 99%

The global phase diagram of the Gay–Berne model

Miguel

Vega

2002

The phase diagram of the Gay-Berne model with anisotropy parameters ϭ3, Јϭ5 has been evaluated by means of computer simulations. For a number of temperatures, NPT simulations were performed for the solid phase leading to the determination of the free energy of the solid at a reference density. Using the equation of state and free energies of the isotropic and nematic phases available in the existing literature the fluid-solid equilibrium was calculated for the temperatures selected. Taking these fluid-solid equilibrium results as the starting points, the fluid-solid equilibrium curve was determined for a wide range of temperatures using Gibbs-Duhem integration. At high temperatures the sequence of phases encountered on compression is isotropic to nematic, and then nematic to solid. For reduced temperatures below Tϭ0.85 the sequence is from the isotropic phase directly to the solid state. In view of this we locate the isotropic-nematic-solid triple point at T INS ϭ0.85. The present results suggest that the high-density phase designated smectic B in previous simulations of the model is in fact a molecular solid and not a smectic liquid crystal. It seems that no thermodynamically stable smectic phase appears for the Gay-Berne model with the choice of parameters used in this work. We locate the vapor-isotropic liquid-solid triple point at a temperature T VIS ϭ0.445. Considering that the critical temperatures is T c ϭ0.473, the Gay-Berne model used in this work presents vapor-liquid separation over a rather narrow range of temperatures. It is suggested that the strong lateral attractive interactions present in the Gay-Berne model stabilizes the layers found in the solid phase. The large stability of the solid phase, particularly at low temperatures, would explain the unexpectedly small liquid range observed in the vapor-liquid region.

“…Since the solid CP1 structure does not have cubic symmetry the Rahman-Parrinello 23 modification of the constant-pressure NPT Monte Carlo technique is used in order to allow for nonisotropic changes in the simulation box shape. 24 On the other hand, in the case of the disordered structure, an fcc close-packed arrangement of atoms with the molecular bonds randomly distributed 51 is generated. The number of molecules in the disordered solid was Nϭ432.…”

Section: B the Solid Phasesmentioning

confidence: 99%

“…However, brute force computational power is not the only key to the success of simulation studies; much credit is due to the development of simulation techniques for the determination of phase equilibria. These techniques are the Gibbs ensemble Monte Carlo 19 and the NPTϩtest particle methods, 20 which are very useful in determining the vaporliquid equilibria, the Gibbs-Duhem integration method, 21,22 which becomes an invaluable tool when determining fluidsolid equilibria, the Rahman-Parrinello technique, essential in the study of solid phases, 23,24 and Einstein-crystal calculations, which provide the free energies of solid phases. 25 A general approach to the determination of global phase diagrams by computer simulation would entail:…”

Section: Introductionmentioning

confidence: 99%

The phase diagram of the two center Lennard-Jones model as obtained from computer simulation and Wertheim’s thermodynamic perturbation theory

Vega

McBride

Miguel

et al. 2003

The global phase diagram ͑i.e., vapor-liquid and fluid-solid equilibrium͒ of two-center Lennard-Jones ͑2CLJ͒ model molecules of bond length Lϭ has been determined by computer simulation. The vapor-liquid equilibrium conditions are obtained using the Gibbs ensemble Monte Carlo method and by performing isobaric-isothermal NPT calculations at zero pressure. In the case of the solid phase, two close-packed solid structures are considered: In the first structure, the molecules are located in layers and all molecular axes point in the same direction; and in the second structure, the atoms form a close-packed arrangement but the molecular axes of the diatomic molecules have random orientations. It is shown that at the vapor-liquid-solid triple-point temperature, the orientationally disordered solid is the stable structure for the solid phase of this model. The vapor-liquid-disordered solid triple-point temperature of the 2CLJ model, with bond length Lϭ , is located at T*ϭ0.650(4). This is very close to the triple-point temperature of the Lennard-Jones monomer system (T*ϭ0.687). At very low temperatures, the ordered solid is the stable phase. The vapor-ordered solid-disordered solid triple point is situated at T*ϭ0.282. The simulation data are compared to Wertheim's first-order thermodynamic perturbation theory ͑TPT1͒ for the fluid and solid phases. It is found that Wertheim's TPT1 not only provides an accurate description of the equation of state in both the fluid and solid phases, but also provides accurate values of the free energies. The prediction of Wertheim's TPT1 for the global phase diagram of the 2CLJ model shows excellent agreement with the simulation results, illustrating the possibility of using Wertheim's perturbation theory to determine not only the vapor-liquid equilibria but also the global phase diagram of simple chain model molecules.