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Ab initio investigations of structural, electronic, and dynamical propertiesof the high-temperature $\beta$ phase of copper pyrophosphate were performedusing density functional theory. The electronic band structure shows the Mottinsulating state due to electron correlations in copper ions. By calculatingphonon dispersion relations, the soft mode at the A point of the Brillouin zonewas revealed, showing the dynamical instability of the $\beta$ phase at lowtemperatures. The double-well potential connected with the soft mode is derivedand the mechanism of the structural phase transition to the $\alpha$ phase isdiscussed. The self-consistent phonon calculations based on thetemperature-dependent effective potential show the stabilization of the $\beta$phase at high temperatures, due to the anharmonic effects. The pronouncedtemperature dependence and the large line width of the soft mode indicate anessential role of anharmonicity in the structural phase transition.

Anharmonicity and structural phase transition in the Mott insulator Cu$_2$P$_2$O$_7$