The katoite hydrogarnet Si-free Ca3Al2([OH]4)3: A periodic Hartree–Fock and B3-LYP study

Katoite under pressure: an ab initio investigation of its structural, elastic and vibrational properties sheds light on the phase transition

Structural, elastic and vibrational properties of the katoite hydrogarnet are investigated as a function of pressure, up to 65 GPa, with an ab initio simulation. A group-subgroup phase transition is found to occur in the 5–15 GPa range of pressure.

CRYSTAL: a computational tool for the ab initio study of the electronic properties of crystals

CRYSTAL [1] computes the electronic structure and properties of periodic systems (crystals, surfaces, polymers) within Hartree-Fock [2], Density Functional and various hybrid approximations.

CRYSTAL was developed during nearly 30 years (since 1976) [3] by researchers of the Theoretical Chemistry Group in Torino (Italy), and the Computational Materials Science group in CLRC (Daresbury, UK), with important contributions from visiting researchers, as documented by the main authors list and the bibliography.

The basic features of the program CRYSTAL are presented, with two examples of application in the field of crystallography [4, 5].

Vibrational Spectrum of Katoite Ca3Al2[(OH)4]3: A Periodic ab Initio Study

The vibrational spectrum of the Si-free katoite hydrogarnet (116 atoms in the unit cell) has been calculated at the periodic ab initio quantum mechanical level with the CRYSTAL program, by using a Gaussian type basis set and the hybrid B3LYP Hamiltonian. The harmonic frequencies at the Gamma point have been obtained by diagonalizing the mass-weighted Hessian matrix, that is evaluated by numerical differentiation of the analytical first derivatives of the energy with respect to the atomic Cartesian coordinates. The parameters controlling the numerical differentiation, as well as the numerical integration of the exchange-correlation functional for the self-consistent field (SCF) calculation, are shown to affect the obtained frequencies by less than 3 cm-1. Before diagonalization, the dynamical matrix is transformed to a block diagonal form according to the irreducible representations of the point group, so that the 345 vibrational modes are automatically classified by symmetry. Various tools are adopted (graphical representation, isotopic substitution, "freezing" part of the unit cell) that permit a complete classification of normal modes and, in particular, an analysis of the modes in terms of simple models (octahedra modes, Ca modes, H stretching, bending, rotations). The harmonic OH stretching band (48 modes) is quite narrow (20 cm-1), indicating that the interaction among OH groups is very weak. As the OH stretching modes are known to be totally separable from the other modes and strongly anharmonic, the one-dimensional Schroedinger equation for the anharmonic oscillator is solved numerically for the two extreme situations, corresponding to the vibration of one decoupled OH and of all 48 OH groups moving in phase. The anharmonic frequencies are 3682 and 3673 cm-1, respectively, in good agreement with IR experiments (a single band at 3661 cm-1 with a width at half band height of 33 cm-1) and confirming that the interaction between OH groups is extremely weak.