First Principles Computations of Second-Order Elastic Constants (SOEC) and Equations of State of Rutile 
                TiO<sub>2</sub>

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="8"><hr/></td></tr><tr class="thead"><td align="left"></td><td align="center"><span style="width: 22.174999px;"><svg height="14.3375" id="M87" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 22.174999 14.3375" width="22.174999" xmlns="http://www.w3.org/2000/svg">
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</svg></span></td></tr><tr><td class="thead-hr" colspan="8"><hr/></td></tr><tr><td align="left"> HF</td><td align="center">364. (36)</td><td align="center"> 216. (23)</td><td align="center">184. (25)</td><td align="center"> 626. (29)</td><td align="center">164. (32)</td><td align="center"> 277. (456)</td><td align="center">270. (27,17)</td></tr><tr><td align="left"> LDA</td><td align="center"> 311. (16)</td><td align="center"> 211. (21)</td><td align="center">175. <svg height="13.45" id="M94" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">)</tspan>
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</g>
</g>
</svg></td><td align="center"> 504. (28)</td><td align="center"> 159. (33)</td><td align="center">253. (15)</td><td align="center">243. (15,6)</td></tr><tr><td align="left">PWGGA</td><td align="center">266. (−1)</td><td align="center">177. <svg height="13.45" id="M95" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
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<tspan style="font-size: 12.50px; " x="4.1634989" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">)</tspan>
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</svg></td><td align="center">149. <svg height="13.45" id="M96" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">)</tspan>
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</svg></td><td align="center">462. (−5)</td><td align="center">138. (11)</td><td align="center"> 223. (17)</td><td align="center">208. (−2,−10)</td></tr><tr><td align="left"> PBE</td><td align="center">262. (−2)</td><td align="center">176. <svg height="13.45" id="M97" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="4.1634989" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">)</tspan>
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</svg></td><td align="center">146. (−1)</td><td align="center"> 458. (−6)</td><td align="center"> 135. (9)</td><td align="center">221. (16)</td><td align="center">205. (−3,−11)</td></tr><tr><td align="left">BLYP</td><td align="center">256. (−5)</td><td align="center">133. (−24)</td><td align="center">143. <svg height="13.45" id="M98" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="4.1634989" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">)</tspan>
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</svg></td><td align="center">478. (−1)</td><td align="center">154. (−19)</td><td align="center">206. (8)</td><td align="center">188. (−11,−18)</td></tr><tr><td align="left"> B3LYP</td><td align="center"> 281. (5)</td><td align="center"> 186. (6)</td><td align="center">157. (7)</td><td align="center">506. (5)</td><td align="center">140. (13)</td><td align="center">236. (24)</td><td align="center">220. (4,−4)</td></tr><tr><td align="left">B3PW</td><td align="center">294. (10)</td><td align="center">194. (11)</td><td align="center">164. (12)</td><td align="center">517. (7)</td><td align="center">147. (19)</td><td align="center">246. (29)</td><td align="center">229. (8,−1)</td></tr><tr><td align="left"> PBE0</td><td align="center">277. <svg height="13.45" id="M99" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">)</tspan>
</text>
</g>
</g>
</svg></td><td align="center">185. (6)</td><td align="center">155. (5)</td><td align="center">494. <svg height="13.45" id="M100" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 18.35 13.45" width="18.35" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">)</tspan>
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</g>
</svg></td><td align="center">139. (12)</td><td align="center">234. (23)</td><td align="center">217. (2,−6)</td></tr><tr><td align="left"> Exps. [<a href="/journals/physri/2011/536183/#B10">10</a>, <a href="/journals/physri/2011/536183/#B29">29</a>, <a href="/journals/physri/2011/536183/#B30">30</a>, <a href="/journals/physri/2011/536183/#B34">33</a>]</td><td align="center">268.00</td><td align="center">175.00</td><td align="center">147.00</td><td align="center">484.00</td><td align="center">124.00</td><td align="center">190.00</td><td align="center">212.00, 230.00</td></tr><tr class="table-tr"><td colspan="8"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

The elastic constants and bulk modulus computational results using the Hartree Fock and DFT LDA, PWGGA, BLYP, B3LYP, and B3PW potentials with basis set 1. All values are in GPa. The numbers within parentheses are percent differences from experiment. (See Sections <a href="https://static.hindawi.com/articles/physri/volume-2011/536183/figures/#sec2">2</a>, <a href="https://static.hindawi.com/articles/physri/volume-2011/536183/figures/#sec3">3</a>, <a href="https://static.hindawi.com/articles/physri/volume-2011/536183/figures/#sec5">5</a>, and <a href="https://static.hindawi.com/articles/physri/volume-2011/536183/figures/#sec7">7</a>).

Physics Research International

tab2

Table 2

Table 2: First Principles Computations of Second-Order Elastic Constants (SOEC) and Equations of State of Rutile 
                TiO<sub>2</sub> 

Physics Research International

First Principles Computations of Second-Order Elastic Constants (SOEC) and Equations of State of Rutile TiO2

Table 2

First Principles Computations of Second-Order Elastic Constants (SOEC) and Equations of State of Rutile TiO₂