Periodic density functional theory and local-MP2 study of the librational modes of Ice XI

Two periodic codes, CRYSTAL and CRYSCOR, are here used to simulate and characterize the librational modes of the nuR band of Ice XI: this band has been found experimentally to be the region of the vibrational spectrum of ordinary ice most affected by the transition from the proton-disordered (Ice Ih) to the proton-ordered (Ice XI) phase. With CRYSTAL, the problem is solved using Hartree–Fock (HF), pure Kohn–Sham (PW91) or hybrid (B3LYP) one-electron Hamiltonians: the harmonic approximation is employed to obtain the vibrational spectrum after optimizing the geometry. The B3LYP results are those in best agreement with the experiment. For a given crystalline geometry, CRYSCOR computes the energy per cell in an ab initio HF+MP2 approximation using a local-correlation approach; this technique is employed for recalculating the frequencies of the different modes identified by the B3LYP approach, by fully accounting for long range dispersive interactions. The effect of anharmonicity is evaluated separately for each mode both in the B3LYP and HF+MP2 case. The two approaches accurately reproduce the four-peak structure of the librational band. The harmonic B3LYP nuR bandwidth of 70 meV is lowered to 60 meV by anharmonic corrections, and becomes 57 meV in the HF+MP2 anharmonic calculation, in excellent agreement with the experimental IINS data (56–59 meV). The assignment of the librational modes is discussed.