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The structure, lattice dynamics and mechanical properties of the magnesiumhydroxide have been investigated with static density functional theorycalculations as well as \it {ab initio} molecular dynamics. The hypothesis of asuperstructure existing in the lattice formed by the hydrogen atoms has beentested. The elastic constants of the material have been calculated with staticdeformations approach and are in fair agreement with the experimental data. Thehydrogen subsystem structure exhibits signs of disordered behaviour whilemaintaining correlations between angular positions of neighbouring atoms. Weestablish that the essential angular correlations between hydrogen positionsare maintained to the temperature of at least 150 K and show that they are welldescribed by a physically motivated probabilistic model. The rotational degreeof freedom appears to be decoupled from the lattice directions above 30K.

Structure and elastic properties of Mg(OH)$_2$ from density functional theory