Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Monte Carlo study of the energetics of the rutile, anatase,
  brookite, and columbite TiO$_2$ polymorphs   The relative energies of the low-pressure rutile, anatase, and brookite
polymorphs and the high-pressure columbite polymorph of TiO$_2$ have been
calculated as a function of temperature using the diffusion quantum Monte Carlo
(DMC) method and density functional theory (DFT). The vibrational energies are
found to be important on the scale of interest and significant quartic
anharmonicity is found in the rutile phase. Static-lattice DFT calculations
predict that anatase is lower in energy than rutile, in disagreement with
experiment. The accurate description of electronic correlations afforded by DMC
calculations and the inclusion of anharmonic vibrational effects contribute to
stabilizing rutile with respect to anatase. Our calculations predict a phase
transition from anatase to rutile TiO$_2$ at $630 \pm 210$ K.

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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
3
The categories of this paper are: physics
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The categories of this paper are: math
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: stat