Quantum Rotation and Orientational Ordering of Molecules in Crystals

Abstract

According to the third law of thermodynamics, the entropy of crystals tends to zero as T → 0. In many molecular crystals, the configurational entropy S_c is zero and the remaining vibrational entropy S_v decreases with decreasing temperature, which vanishes as T → 0. However, in some crystals, molecules can move around even in the crystalline states, where S_c remains non-zero. In this study, we focused on two types of such compounds, one with partially deuterated methyl groups and endohedral fullerenes, and have investigated how the S_c in those crystals approach to zero as T → 0. In the first system, the locations of H and D atoms in a partially deuterated methyl group are exchangeable even in the crystalline phase, which remains S_c = R ln 3. The S_c is released at around 10 K where Schottky type anomalies are observed in heat capacity. This is caused by the splitting of the triply degenerated ground states due to the symmetry breaking by the partial deuteration. In the second system, a Li⁺ ion circulates quantum mechanically in a C₆₀ fullerene at 300 K, which localizes into two pockets below 100 K, and into one pocket below 24 K due to the Coulombic interactions with the neighboring ions. A H₂O encapsulated in a C₆₀, on the other hand, rotates quantum mechanically even at 1 K.