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### Ferroelectric, quantum paraelectric, or paraelectric? Calculating the 
    evolution from BaTiO3 to SrTiO3 to KTaO3 using a single-particle quantum 
    mechanical description of the ions
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T. Esswein and N. A. Spaldin
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#### Abstract:
We present an inexpensive first-principles approach for describing quantum 
paraelectricity that combines density functional theory (DFT) treatment of the 
electronic subsystem with quantum mechanical treatment of the ions through 
solution of the single-particle Schrödinger equation with the DFT-calculated 
potential. Using BaTiO3, SrTiO3, and KTaO3 as model systems, we show that the 
approach can straightforwardly distinguish between ferroelectric, paraelectric, 
and quantum paraelectric materials, based on simple quantities extracted from 
standard density functional and density functional perturbation theories. We 
calculate the influence of isotope substitution and strain on quantum 
paraelectric behavior and find that, while complete replacement of oxygen-16 
by oxygen-18 has a surprisingly small effect, experimentally accessible 
strains can induce large changes. Finally, we collect the various choices for 
the phonon mass that have been introduced in the literature. We identify those 
that are most physically meaningful by comparing them with our results that 
avoid such a choice through the use of mass-weighted coordinates.
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All calculations were performed using Quantum Esrepsso (version 6.4.1), with 
GBRV pseudopotentials using the PBE exchange-correlation functional.

The main folder contains input files for all calculations presented in the 
paper, with subfolders following the structure of the paper.