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<li>pair_style smtbq command</li>
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<div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
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<div class="section" id="pair-style-smtbq-command">
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<span id="index-0"></span><h1>pair_style smtbq command</h1>
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<div class="section" id="syntax">
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<h2>Syntax</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">pair_style</span> <span class="n">smtbq</span>
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</pre></div>
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</div>
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</div>
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<div class="section" id="examples">
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<h2>Examples</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">pair_style</span> <span class="n">smtbq</span>
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<span class="n">pair_coeff</span> <span class="o">*</span> <span class="o">*</span> <span class="n">ffield</span><span class="o">.</span><span class="n">smtbq</span><span class="o">.</span><span class="n">Al2O3</span> <span class="n">O</span> <span class="n">Al</span>
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</pre></div>
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</div>
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</div>
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<div class="section" id="description">
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<h2>Description</h2>
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<p>This pair stylecomputes a variable charge SMTB-Q (Second-Moment
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tight-Binding QEq) potential as described in <a class="reference internal" href="#smtb-q-1"><span class="std std-ref">SMTB-Q_1</span></a> and
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<a class="reference internal" href="#smtb-q-2"><span class="std std-ref">SMTB-Q_2</span></a>. Briefly, the energy of metallic-oxygen systems
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is given by three contributions:</p>
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<img alt="_images/pair_smtbq1.jpg" class="align-center" src="_images/pair_smtbq1.jpg" />
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<p>where <em>E<sub>tot</sub></em> is the total potential energy of the system,
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<em>E<sub>ES</sub></em> is the electrostatic part of the total energy,
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<em>E<sub>OO</sub></em> is the interaction between oxygens and
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<em>E<sub>MO</sub></em> is a short-range interaction between metal and oxygen
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atoms. This interactions depend on interatomic distance
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<em>r<sub>ij</sub></em> and/or the charge <em>Q<sub>i</sub></em> of atoms
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<em>i</em>. Cut-off function enables smooth convergence to zero interaction.</p>
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<p>The parameters appearing in the upper expressions are set in the
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ffield.SMTBQ.Syst file where Syst corresponds to the selected system
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(e.g. field.SMTBQ.Al2O3). Exemples for TiO<sub>2</sub>,
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Al<sub>2</sub>O<sub>3</sub> are provided. A single pair_coeff command
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is used with the SMTBQ styles which provides the path to the potential
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file with parameters for needed elements. These are mapped to LAMMPS
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atom types by specifying additional arguments after the potential
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filename in the pair_coeff command. Note that atom type 1 must always
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correspond to oxygen atoms. As an example, to simulate a TiO2 system,
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atom type 1 has to be oxygen and atom type 2 Ti. The following
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pair_coeff command should then be used:</p>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">pair_coeff</span> <span class="o">*</span> <span class="o">*</span> <span class="n">PathToLammps</span><span class="o">/</span><span class="n">potentials</span><span class="o">/</span><span class="n">ffield</span><span class="o">.</span><span class="n">smtbq</span><span class="o">.</span><span class="n">TiO2</span> <span class="n">O</span> <span class="n">Ti</span>
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</pre></div>
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</div>
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<p>The electrostatic part of the energy consists of two components</p>
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<p>self-energy of atom <em>i</em> in the form of a second order charge dependent
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polynomial and a long-range Coulombic electrostatic interaction. The
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latter uses the wolf summation method described in <a class="reference internal" href="#wolf"><span class="std std-ref">Wolf</span></a>,
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spherically truncated at a longer cutoff, <em>R<sub>coul</sub></em>. The
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charge of each ion is modeled by an orbital Slater which depends on
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the principal quantum number (<em>n</em>) of the outer orbital shared by the
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ion.</p>
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<p>Interaction between oxygen, <em>E<sub>OO</sub></em>, consists of two parts,
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an attractive and a repulsive part. The attractive part is effective
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only at short range (< r<sub>2</sub><sup>OO</sup>). The attractive
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contribution was optimized to study surfaces reconstruction
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(e.g. <a class="reference internal" href="#smtb-q-2"><span class="std std-ref">SMTB-Q_2</span></a> in TiO<sub>2</sub>) and is not necessary
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for oxide bulk modeling. The repulsive part is the Pauli interaction
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between the electron clouds of oxygen. The Pauli repulsion and the
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coulombic electrostatic interaction have same cut off value. In the
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ffield.SMTBQ.Syst, the keyword <em>‘buck’</em> allows to consider only the
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repulsive O-O interactions. The keyword <em>‘buckPlusAttr’</em> allows to
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consider the repulsive and the attractive O-O interactions.</p>
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<p>The short-range interaction between metal-oxygen, <em>E<sub>MO</sub></em> is
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based on the second moment approximation of the density of states with
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a N-body potential for the band energy term,
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<em>E<sup>i</sup><sub>cov</sub></em>, and a Born-Mayer type repulsive terms
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as indicated by the keyword <em>‘second_moment’</em> in the
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ffield.SMTBQ.Syst. The energy band term is given by:</p>
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<img alt="_images/pair_smtbq2.jpg" class="align-center" src="_images/pair_smtbq2.jpg" />
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<p>where <em>&#951<sub>i</sub></em> is the stoichiometry of atom <em>i</em>,
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<em>&#948Q<sub>i</sub></em> is the charge delocalization of atom <em>i</em>,
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compared to its formal charge
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<em>Q<sup>F</sup><sub>i</sub></em>. n<sub>0</sub>, the number of hybridized
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orbitals, is calculated with to the atomic orbitals shared
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<em>d<sub>i</sub></em> and the stoichiometry
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<em>&#951<sub>i</sub></em>. <em>r<sub>c1</sub></em> and <em>r<sub>c2</sub></em> are the two
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cutoff radius around the fourth neighbors in the cutoff function.</p>
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<p>In the formalism used here, <em>&#958<sup>0</sup></em> is the energy
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parameter. <em>&#958<sup>0</sup></em> is in tight-binding approximation the
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hopping integral between the hybridized orbitals of the cation and the
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anion. In the literature we find many ways to write the hopping
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integral depending on whether one takes the point of view of the anion
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or cation. These are equivalent vision. The correspondence between the
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two visions is explained in appendix A of the article in the
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SrTiO<sub>3</sub> <a class="reference internal" href="#smtb-q-3"><span class="std std-ref">SMTB-Q_3</span></a> (parameter <em>&#946</em> shown in
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this article is in fact the <em>&#946<sub>O</sub></em>). To summarize the
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relationship between the hopping integral <em>&#958<sup>0</sup></em> and the
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others, we have in an oxide C<sub>n</sub>O<sub>m</sub> the following
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relationship:</p>
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<img alt="_images/pair_smtbq3.jpg" class="align-center" src="_images/pair_smtbq3.jpg" />
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<p>Thus parameter &#956, indicated above, is given by : &#956 = (&#8730n
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+ &#8730m) &#8260 2</p>
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<p>The potential offers the possibility to consider the polarizability of
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the electron clouds of oxygen by changing the slater radius of the
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charge density around the oxygens through the parameters <em>rBB, rB and
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rS</em> in the ffield.SMTBQ.Syst. This change in radius is performed
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according to the method developed by E. Maras
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<a class="reference internal" href="#smtb-q-2"><span class="std std-ref">SMTB-Q_2</span></a>. This method needs to determine the number of
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nearest neighbors around the oxygen. This calculation is based on
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first (<em>r<sub>1n</sub></em>) and second (<em>r<sub>2n</sub></em>) distances
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neighbors.</p>
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<p>The SMTB-Q potential is a variable charge potential. The equilibrium
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charge on each atom is calculated by the electronegativity
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equalization (QEq) method. See <a class="reference internal" href="#rick"><span class="std std-ref">Rick</span></a> for further detail. One
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can adjust the frequency, the maximum number of iterative loop and the
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convergence of the equilibrium charge calculation. To obtain the
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energy conservation in NVE thermodynamic ensemble, we recommend to use
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a convergence parameter in the interval 10<sup>-5</sup> -
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10<sup>-6</sup> eV.</p>
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<p>The ffield.SMTBQ.Syst files are provided for few systems. They consist
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of nine parts and the lines beginning with ‘#’ are comments (note that
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the number of comment lines matter). The first sections are on the
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potential parameters and others are on the simulation options and
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might be modified. Keywords are character type and must be enclosed in
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quotation marks (‘’).</p>
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<ol class="arabic simple">
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<li>Number of different element in the oxide:</li>
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</ol>
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<ul class="simple">
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<li>N<sub>elem</sub>= 2 or 3</li>
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<li>Divided line</li>
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</ul>
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<ol class="arabic simple" start="2">
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<li>Atomic parameters</li>
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</ol>
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<p>For the anion (oxygen)</p>
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<ul class="simple">
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<li>Name of element (char) and stoichiometry in oxide</li>
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<li>Formal charge and mass of element</li>
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<li>Principal quantic number of outer orbital (<em>n</em>), electronegativity (<em>&#967<sup>0</sup><sub>i</simulationub></em>) and hardness (<em>J<sup>0</sup><sub>i</sub></em>)</li>
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<li>Ionic radius parameters : max coordination number (<em>coordBB</em> = 6 by default), bulk coordination number <em>(coordB)</em>, surface coordination number <em>(coordS)</em> and <em>rBB, rB and rS</em> the slater radius for each coordination number. (<b>note : If you don’t want to change the slater radius, use three identical radius values</b>)</li>
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<li>Number of orbital shared by the element in the oxide (<em>d<sub>i</sub></em>)</li>
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<li>Divided line</li>
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</ul>
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<p>For each cations (metal):</p>
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<ul class="simple">
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<li>Name of element (char) and stoichiometry in oxide</li>
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<li>Formal charge and mass of element</li>
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<li>Number of electron in outer orbital <em>(ne)</em>, electronegativity (<em>&#967<sup>0</sup><sub>i</simulationub></em>), hardness (<em>J<sup>0</sup><sub>i</sub></em>) and <em>r<sub>Salter</sub></em> the slater radius for the cation.</li>
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<li>Number of orbitals shared by the elements in the oxide (<em>d<sub>i</sub></em>)</li>
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<li>Divided line</li>
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</ul>
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<ol class="arabic simple" start="3">
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<li>Potential parameters:</li>
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</ol>
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<ul class="simple">
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<li>Keyword for element1, element2 and interaction potential (‘second_moment’ or ‘buck’ or ‘buckPlusAttr’) between element 1 and 2. If the potential is ‘second_moment’, specify ‘oxide’ or ‘metal’ for metal-oxygen or metal-metal interactions respectively.</li>
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<li>Potential parameter: <pre><br/> If type of potential is ‘second_moment’ : <em>A (eV)</em>, <em>p</em>, <em>&#958<sup>0</sup></em> (eV) and <em>q</em> <br/> <em>r<sub>c1</sub></em> (&#197), <em>r<sub>c2</sub></em> (&#197) and <em>r<sub>0</sub></em> (&#197) <br/> If type of potential is ‘buck’ : <em>C</em> (eV) and <em>&#961</em> (&#197) <br/> If type of potential is ‘buckPlusAttr’ : <em>C</em> (eV) and <em>&#961</em> (&#197) <br/> <em>D</em> (eV), <em>B</em> (&#197<sup>-1</sup>), <em>r<sub>1</sub><sup>OO</sup></em> (&#197) and <em>r<sub>2</sub><sup>OO</sup></em> (&#197) </pre></li>
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<li>Divided line</li>
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</ul>
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<ol class="arabic simple" start="4">
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<li>Tables parameters:</li>
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</ol>
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<ul class="simple">
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<li>Cutoff radius for the Coulomb interaction (<em>R<sub>coul</sub></em>)</li>
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<li>Starting radius (<em>r<sub>min</sub></em> = 1,18845 &#197) and increments (<em>dr</em> = 0,001 &#197) for creating the potential table.</li>
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<li>Divided line</li>
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</ul>
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<ol class="arabic simple" start="5">
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<li>Rick model parameter:</li>
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</ol>
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<ul class="simple">
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<li><em>Nevery</em> : parameter to set the frequency (<em>1/Nevery</em>) of the charge resolution. The charges are evaluated each <em>Nevery</em> time steps.</li>
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<li>Max number of iterative loop (<em>loopmax</em>) and precision criterion (<em>prec</em>) in eV of the charge resolution</li>
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<li>Divided line</li>
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</ul>
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<ol class="arabic simple" start="6">
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<li>Coordination parameter:</li>
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</ol>
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<ul class="simple">
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<li>First (<em>r<sub>1n</sub></em>) and second (<em>r<sub>2n</sub></em>) neighbor distances in &#197</li>
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<li>Divided line</li>
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</ul>
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<ol class="arabic simple" start="7">
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<li>Charge initialization mode:</li>
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</ol>
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<ul class="simple">
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<li>Keyword (<em>QInitMode</em>) and initial oxygen charge (<em>Q<sub>init</sub></em>). If keyword = ‘true’, all oxygen charges are initially set equal to <em>Q<sub>init</sub></em>. The charges on the cations are initially set in order to respect the neutrality of the box. If keyword = ‘false’, all atom charges are initially set equal to 0 if you use “create_atom”#create_atom command or the charge specified in the file structure using <a class="reference internal" href="read_data.html"><span class="doc">read_data</span></a> command.</li>
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<li>Divided line</li>
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</ul>
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<ol class="arabic simple" start="8">
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<li>Mode for the electronegativity equalization (Qeq)</li>
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</ol>
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<ul class="simple">
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<li>Keyword mode: <pre> <br/> QEqAll (one QEq group) | no parameters <br/> QEqAllParallel (several QEq groups) | no parameters <br/> Surface | zlim (QEq only for z>zlim) </pre></li>
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<li>Parameter if necessary</li>
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<li>Divided line</li>
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</ul>
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<ol class="arabic simple" start="9">
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<li>Verbose</li>
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</ol>
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<ul class="simple">
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<li>If you want the code to work in verbose mode or not : ‘true’ or ‘false’</li>
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<li>If you want to print or not in file ‘Energy_component.txt’ the three main contributions to the energy of the system according to the description presented above : ‘true’ or ‘false’ and <em>N<sub>Energy</sub></em>. This option writes in file every <em>N<sub>Energy</sub></em> time step. If the value is ‘false’ then <em>N<sub>Energy</sub></em> = 0. The file take into account the possibility to have several QEq group <em>g</em> then it writes: time step, number of atoms in group <em>g</em>, electrostatic part of energy, <em>E<sub>ES</sub></em>, the interaction between oxygen, <em>E<sub>OO</sub></em>, and short range metal-oxygen interaction, <em>E<sub>MO</sub></em>.</li>
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<li>If you want to print in file ‘Electroneg_component.txt’ the electronegativity component (<em>&#8706E<sub>tot</sub> &#8260&#8706Q<sub>i</sub></em>) or not: ‘true’ or ‘false’ and <em>N<sub>Electroneg</sub></em>.This option writes in file every <em>N<sub>Electroneg</sub></em> time step. If the value is ‘false’ then <em>N<sub>Electroneg</sub></em> = 0. The file consist in atom number <em>i</em>, atom type (1 for oxygen and # higher than 1 for metal), atom position: <em>x</em>, <em>y</em> and <em>z</em>, atomic charge of atom <em>i</em>, electrostatic part of atom <em>i</em> electronegativity, covalent part of atom <em>i</em> electronegativity, the hopping integral of atom <em>i</em> <em>(Z&#946<sup>2</sup>)<sub>i<sub></em> and box electronegativity.</li>
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</ul>
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<div class="admonition note">
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<p class="first admonition-title">Note</p>
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<p class="last">This last option slows down the calculation dramatically. Use
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only with a single processor simulation.</p>
|
|
</div>
|
|
<hr class="docutils" />
|
|
<p><strong>Mixing, shift, table, tail correction, restart, rRESPA info:</strong></p>
|
|
<p>This pair style does not support the <a class="reference internal" href="pair_modify.html"><span class="doc">pair_modify</span></a>
|
|
mix, shift, table, and tail options.</p>
|
|
<p>This pair style does not write its information to <a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></a>, since it is stored in potential files. Thus, you
|
|
needs to re-specify the pair_style and pair_coeff commands in an input
|
|
script that reads a restart file.</p>
|
|
<p>This pair style can only be used via the <em>pair</em> keyword of the
|
|
<a class="reference internal" href="run_style.html"><span class="doc">run_style respa</span></a> command. It does not support the
|
|
<em>inner</em>, <em>middle</em>, <em>outer</em> keywords.</p>
|
|
<hr class="docutils" />
|
|
<p><strong>Restriction:</strong></p>
|
|
<p>This pair style is part of the USER-SMTBQ package and is only enabled
|
|
if LAMMPS is built with that package. See the <a class="reference internal" href="Section_start.html#start-3"><span class="std std-ref">Making LAMMPS</span></a> section for more info.</p>
|
|
<p>This potential requires using atom type 1 for oxygen and atom type
|
|
higher than 1 for metal atoms.</p>
|
|
<p>This pair style requires the <a class="reference internal" href="newton.html"><span class="doc">newton</span></a> setting to be “on”
|
|
for pair interactions.</p>
|
|
<p>The SMTB-Q potential files provided with LAMMPS (see the potentials
|
|
directory) are parameterized for metal <a class="reference internal" href="units.html"><span class="doc">units</span></a>.</p>
|
|
<hr class="docutils" />
|
|
<p><strong>Citing this work:</strong></p>
|
|
<p>Please cite related publication: N. Salles, O. Politano, E. Amzallag
|
|
and R. Tetot, Comput. Mater. Sci. 111 (2016) 181-189</p>
|
|
<hr class="docutils" />
|
|
<p id="smtb-q-1"><strong>(SMTB-Q_1)</strong> N. Salles, O. Politano, E. Amzallag, R. Tetot,
|
|
Comput. Mater. Sci. 111 (2016) 181-189</p>
|
|
<p id="smtb-q-2"><strong>(SMTB-Q_2)</strong> E. Maras, N. Salles, R. Tetot, T. Ala-Nissila,
|
|
H. Jonsson, J. Phys. Chem. C 2015, 119, 10391-10399</p>
|
|
<p id="smtb-q-3"><strong>(SMTB-Q_3)</strong> R. Tetot, N. Salles, S. Landron, E. Amzallag, Surface
|
|
Science 616, 19-8722 28 (2013)</p>
|
|
<p id="wolf"><strong>(Wolf)</strong> D. Wolf, P. Keblinski, S. R. Phillpot, J. Eggebrecht, J Chem
|
|
Phys, 110, 8254 (1999).</p>
|
|
<p id="rick"><strong>(Rick)</strong> S. W. Rick, S. J. Stuart, B. J. Berne, J Chem Phys 101, 6141
|
|
(1994).</p>
|
|
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