Boundary conditions and the residual entropy of ice systems

Abstract

In this work we address the classical statistical mechanical problem of calculating the residual entropy of ice models. The numerical work found in the literature is usually based on extrapolating to infinite-size results obtained for finite-size systems with periodic boundary conditions. In this work we investigate how boundary conditions affect the calculation of the residual entropy for square, cubic, and hexagonal lattices using periodic, antiperiodic, and open boundary conditions. We show that periodic boundary conditions lead to noticeable oscillations in the entropy as a function of lattice size, and we calculate in open finite systems the contribution to the entropy from the open boundary. For our calculations we introduce a variation on multicanonical simulation methods that directly calculate the number of states in the ground state without the need of a Hamiltonian.

Understanding the impact of ammonium ion substitutions on heterogeneous ice nucleation

“…Most of these rely on either enhanced sampling techniques or thermodynamic integration, giving good agreement with both experimental and theoretical values of the entropy. [23][24][25][26][27] To the best of our knowledge, the current computational literature surrounding ice/ammonium/feldspar interaction is limited, and generally focused on the dynamics of the surface interactions. Kumar et al found evidence for the adsorption of ammonium onto feldspar surfaces, although with different strengths depending on the geometry of the exposed plane.…”

Calculation of the Residual Entropy of Ice Ih by Monte Carlo simulation with the Combination of the Replica-Exchange Wang-Landau algorithm and Multicanonical Replica-Exchange Method

“…As for computational simulations, two simulation models (2-state model and 6-state model), which satisfied the ice rules in the ground state, were proposed and the value was estimated [6][7][8][9] by the Multicanonical (MUCA) Monte Carlo (MC) Method [10,11] (for reviews, see, e.g., [12,13]). After these simulation models were suggested, many research groups estimated the residual entropy by various computational approaches for the last decade (see, e.g., [14][15][16][17][18]). The estimates by computer simulations seem to be equal to or more accurate than theoretical estimate by Nagle.…”

“…With the development of computer science, many research groups have tried to estimate the residual entropy by various computational approach (for example, Thermodynamic Integration method, Wang-Landau algorithm, and PEPS algorithm) [14][15][16][17][18]. However, there remain small differences between these results.…”

Calorimetric Signature of Deuterated Ice II: Turning an Endotherm to an Exotherm

“…Considering the actual structure of ice Ih and using a more rigorous approach, the Pauling expression has been corrected to R ln(1.507) = 3.40 J K/mol. 32 − 35 In spite of neglecting long-range effects such as ring closures, the Pauling approach is accurate to better than 1% for all ice structures. This accuracy is much better than the chemical accuracy aimed for here.…”

“…This expression is based on the number of microstates allowed according to the Bernal-Fowler ice rules, where only one central water molecule and four tetrahedrally connected water molecules are considered. Considering the actual structure of ice Ih and using a more rigorous approach, the Pauling expression has been corrected to R ln­(1.507) = 3.40 J K/mol. − In spite of neglecting long-range effects such as ring closures, the Pauling approach is accurate to better than 1% for all ice structures. This accuracy is much better than the chemical accuracy aimed for here. We note that Δ H ( T = 0 K) = Δ H ̃( T = 0 K) = Δ E lat ZPE ; that is, eqs , (), and () are identical at T = 0 K. Furthermore, we evaluated eqs , (), (), and () based on the quasi-harmonic approximation (QHA).…”