of approximating this number from first principles. Suppose there are a given number N of water molecules. The oxygen atoms form a bipartite lattice: they can be divided into two sets, with all the neighbors of an oxygen atom from one set lying in the other set. Focus attention on the oxygen atoms in one set: there are N/2 of them. Each has four hydrogen bonds, with two hydrogens close to it and two far away. This means there are allowed configurations of hydrogens for this oxygen atom. Thus, there are 6N/2 configurations that satisfy these N/2 atoms. But now, consider the remaining N/2 oxygen atoms: in general they won't be satisfied (i.e., they won't have precisely two hydrogen atoms near them). For each of those, there are possible placements of the hydrogen atoms along their hydrogen bonds, of which six are allowed. So, naively, we would expect the total number of configurations to be Using Boltzmann's principle, we conclude that where is the Boltzmann constant, which yields a value of 3.37 J mol−1 K−1, a value very close to the measured value. This estimate is 'naive', as it assumes the six out of 16 hydrogen configurations for oxygen atoms in the second set can be independently chosen, which is false. More complex methods can be employed to better approximate the exact number of possible configurations, and achieve results closer to measured values. By contrast, the structure of ice II is hydrogen-ordered, which helps to explain the entropy change of 3.22 J/mol when the crystal structure changes to that of ice I. Also, ice XI, an orthorhombic, hydrogen-ordered form of ice Ih, is considered the most stable form at low temperatures. See also Ice, for other crystalline forms of ice References Further reading Water ice