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We present an inexpensive first-principles approach for describing quantumparaelectricity that combines density functional theory (DFT) treatment of theelectronic subsystem with quantum mechanical treatment of the ions throughsolution of the single-particle Schr\"odinger equation with the DFT-calculatedpotential. Using BaTiO$_3$, SrTiO$_3$ and KTaO$_3$ as model systems, we showthat the approach can straightforwardly distinguish between ferroelectric,paraelectric and quantum paraelectric materials, based on simple quantitiesextracted from standard density functional and density functional perturbationtheories. We calculate the influence of isotope substitution and strain on thequantum paraelectric behavior, and find that, while complete replacement ofoxygen-16 by oxygen-18 has a surprisingly small effect, experimentallyaccessible strains can induce large changes. Finally, we collect the variouschoices for the phonon mass that have been introduced in the literature. Weidentify those that are most physically meaningful by comparing with ourresults that avoid such a choice through the use of mass-weighted coordinates.

physical review research

Ferroelectric, quantum paraelectric or paraelectric? Calculating the  evolution from BaTiO$_3$ to SrTiO$_3$ to KTaO$_3$ using a single-particle  quantum-mechanical description of the ions