forked from lijiext/lammps
298 lines
13 KiB
Plaintext
298 lines
13 KiB
Plaintext
.. index:: pair_style smtbq
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pair_style smtbq command
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========================
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Syntax
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""""""
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.. parsed-literal::
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pair_style smtbq
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Examples
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""""""""
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.. parsed-literal::
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pair_style smtbq
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pair_coeff * * ffield.smtbq.Al2O3 O Al
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Description
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"""""""""""
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This pair stylecomputes a variable charge SMTB-Q (Second-Moment
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tight-Binding QEq) potential as described in :ref:`SMTB-Q_1 <SMTB-Q_1>` and
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:ref:`SMTB-Q_2 <SMTB-Q_2>`. Briefly, the energy of metallic-oxygen systems
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is given by three contributions:
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.. image:: Eqs/pair_smtbq1.jpg
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:align: center
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where *E<sub>tot</sub>* is the total potential energy of the system,
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*E<sub>ES</sub>* is the electrostatic part of the total energy,
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*E<sub>OO</sub>* is the interaction between oxygens and
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*E<sub>MO</sub>* is a short-range interaction between metal and oxygen
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atoms. This interactions depend on interatomic distance
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*r<sub>ij</sub>* and/or the charge *Q<sub>i</sub>* of atoms
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*i*\ . Cut-off function enables smooth convergence to zero interaction.
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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:
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.. parsed-literal::
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pair_coeff * * PathToLammps/potentials/ffield.smtbq.TiO2 O Ti
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The electrostatic part of the energy consists of two components
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self-energy of atom *i* 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 :ref:`Wolf <Wolf>`,
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spherically truncated at a longer cutoff, *R<sub>coul</sub>*\ . 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 (\ *n*\ ) of the outer orbital shared by the
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ion.
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Interaction between oxygen, *E<sub>OO</sub>*\ , 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. :ref:`SMTB-Q_2 <SMTB-Q_2>` 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 *'buck'* allows to consider only the
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repulsive O-O interactions. The keyword *'buckPlusAttr'* allows to
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consider the repulsive and the attractive O-O interactions.
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The short-range interaction between metal-oxygen, *E<sub>MO</sub>* 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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*E<sup>i</sup><sub>cov</sub>*\ , and a Born-Mayer type repulsive terms
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as indicated by the keyword *'second_moment'* in the
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ffield.SMTBQ.Syst. The energy band term is given by:
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.. image:: Eqs/pair_smtbq2.jpg
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:align: center
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where *η<sub>i</sub>* is the stoichiometry of atom *i*\ ,
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*δQ<sub>i</sub>* is the charge delocalization of atom *i*\ ,
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compared to its formal charge
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*Q<sup>F</sup><sub>i</sub>*\ . 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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*d<sub>i</sub>* and the stoichiometry
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*η<sub>i</sub>*\ . *r<sub>c1</sub>* and *r<sub>c2</sub>* are the two
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cutoff radius around the fourth neighbors in the cutoff function.
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In the formalism used here, *ξ<sup>0</sup>* is the energy
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parameter. *ξ<sup>0</sup>* 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> :ref:`SMTB-Q_3 <SMTB-Q_3>` (parameter *β* shown in
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this article is in fact the *β<sub>O</sub>*\ ). To summarize the
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relationship between the hopping integral *ξ<sup>0</sup>* 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:
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.. image:: Eqs/pair_smtbq3.jpg
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:align: center
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Thus parameter μ, indicated above, is given by : μ = (√n
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+ √m) ⁄ 2
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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 *rBB, rB and
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rS* 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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:ref:`SMTB-Q_2 <SMTB-Q_2>`. 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 (\ *r<sub>1n</sub>*\ ) and second (\ *r<sub>2n</sub>*\ ) distances
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neighbors.
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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 :ref:`Rick <Rick>` 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.
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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 ('').
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1) Number of different element in the oxide:
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* N<sub>elem</sub>= 2 or 3
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* Divided line
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2) Atomic parameters
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For the anion (oxygen)
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* Name of element (char) and stoichiometry in oxide
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* Formal charge and mass of element
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* Principal quantic number of outer orbital (\ *n*\ ), electronegativity (\ *χ<sup>0</sup><sub>i</simulationub>*\ ) and hardness (\ *J<sup>0</sup><sub>i</sub>*\ )
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* Ionic radius parameters : max coordination number (\ *coordBB* = 6 by default), bulk coordination number *(coordB)*\ , surface coordination number *(coordS)* and *rBB, rB and rS* 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>)
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* Number of orbital shared by the element in the oxide (\ *d<sub>i</sub>*\ )
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* Divided line
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For each cations (metal):
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* Name of element (char) and stoichiometry in oxide
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* Formal charge and mass of element
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* Number of electron in outer orbital *(ne)*\ , electronegativity (\ *χ<sup>0</sup><sub>i</simulationub>*\ ), hardness (\ *J<sup>0</sup><sub>i</sub>*\ ) and *r<sub>Salter</sub>* the slater radius for the cation.
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* Number of orbitals shared by the elements in the oxide (\ *d<sub>i</sub>*\ )
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* Divided line
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3) Potential parameters:
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* 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.
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* Potential parameter: <pre><br/> If type of potential is 'second_moment' : *A (eV)*\ , *p*\ , *ξ<sup>0</sup>* (eV) and *q* <br/> *r<sub>c1</sub>* (Å), *r<sub>c2</sub>* (Å) and *r<sub>0</sub>* (Å) <br/> If type of potential is 'buck' : *C* (eV) and *ρ* (Å) <br/> If type of potential is 'buckPlusAttr' : *C* (eV) and *ρ* (Å) <br/> *D* (eV), *B* (Å<sup>-1</sup>), *r<sub>1</sub><sup>OO</sup>* (Å) and *r<sub>2</sub><sup>OO</sup>* (Å) </pre>
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* Divided line
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4) Tables parameters:
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* Cutoff radius for the Coulomb interaction (\ *R<sub>coul</sub>*\ )
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* Starting radius (\ *r<sub>min</sub>* = 1,18845 Å) and increments (\ *dr* = 0,001 Å) for creating the potential table.
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* Divided line
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5) Rick model parameter:
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* *Nevery* : parameter to set the frequency (\ *1/Nevery*\ ) of the charge resolution. The charges are evaluated each *Nevery* time steps.
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* Max number of iterative loop (\ *loopmax*\ ) and precision criterion (\ *prec*\ ) in eV of the charge resolution
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* Divided line
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6) Coordination parameter:
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* First (\ *r<sub>1n</sub>*\ ) and second (\ *r<sub>2n</sub>*\ ) neighbor distances in Å
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* Divided line
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7) Charge initialization mode:
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* Keyword (\ *QInitMode*\ ) and initial oxygen charge (\ *Q<sub>init</sub>*\ ). If keyword = 'true', all oxygen charges are initially set equal to *Q<sub>init</sub>*\ . 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 :doc:`read_data <read_data>` command.
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* Divided line
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8) Mode for the electronegativity equalization (Qeq)
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* 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>
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* Parameter if necessary
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* Divided line
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9) Verbose
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* If you want the code to work in verbose mode or not : 'true' or 'false'
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* 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 *N<sub>Energy</sub>*\ . This option writes in file every *N<sub>Energy</sub>* time step. If the value is 'false' then *N<sub>Energy</sub>* = 0. The file take into account the possibility to have several QEq group *g* then it writes: time step, number of atoms in group *g*\ , electrostatic part of energy, *E<sub>ES</sub>*\ , the interaction between oxygen, *E<sub>OO</sub>*\ , and short range metal-oxygen interaction, *E<sub>MO</sub>*\ .
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* If you want to print in file 'Electroneg_component.txt' the electronegativity component (\ *∂E<sub>tot</sub> ⁄∂Q<sub>i</sub>*\ ) or not: 'true' or 'false' and *N<sub>Electroneg</sub>*\ .This option writes in file every *N<sub>Electroneg</sub>* time step. If the value is 'false' then *N<sub>Electroneg</sub>* = 0. The file consist in atom number *i*\ , atom type (1 for oxygen and # higher than 1 for metal), atom position: *x*\ , *y* and *z*\ , atomic charge of atom *i*\ , electrostatic part of atom *i* electronegativity, covalent part of atom *i* electronegativity, the hopping integral of atom *i* *(Zβ<sup>2</sup>)<sub>i<sub>* and box electronegativity.
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.. note::
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This last option slows down the calculation dramatically. Use
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only with a single processor simulation.
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----------
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**Mixing, shift, table, tail correction, restart, rRESPA info:**
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This pair style does not support the :doc:`pair_modify <pair_modify>`
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mix, shift, table, and tail options.
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This pair style does not write its information to :doc:`binary restart files <restart>`, since it is stored in potential files. Thus, you
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needs to re-specify the pair_style and pair_coeff commands in an input
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script that reads a restart file.
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This pair style can only be used via the *pair* keyword of the
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:doc:`run_style respa <run_style>` command. It does not support the
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*inner*\ , *middle*\ , *outer* keywords.
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----------
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**Restriction:**
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This pair style is part of the USER-SMTBQ package and is only enabled
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if LAMMPS is built with that package. See the :ref:`Making LAMMPS <start_3>` section for more info.
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This potential requires using atom type 1 for oxygen and atom type
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higher than 1 for metal atoms.
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This pair style requires the :doc:`newton <newton>` setting to be "on"
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for pair interactions.
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The SMTB-Q potential files provided with LAMMPS (see the potentials
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directory) are parameterized for metal :doc:`units <units>`.
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----------
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**Citing this work:**
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Please cite related publication: N. Salles, O. Politano, E. Amzallag
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and R. Tetot, Comput. Mater. Sci. 111 (2016) 181-189
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----------
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.. _SMTB-Q_1:
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**(SMTB-Q_1)** N. Salles, O. Politano, E. Amzallag, R. Tetot,
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Comput. Mater. Sci. 111 (2016) 181-189
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.. _SMTB-Q_2:
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**(SMTB-Q_2)** E. Maras, N. Salles, R. Tetot, T. Ala-Nissila,
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H. Jonsson, J. Phys. Chem. C 2015, 119, 10391-10399
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.. _SMTB-Q_3:
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**(SMTB-Q_3)** R. Tetot, N. Salles, S. Landron, E. Amzallag, Surface
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Science 616, 19-8722 28 (2013)
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.. _Wolf:
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**(Wolf)** D. Wolf, P. Keblinski, S. R. Phillpot, J. Eggebrecht, J Chem
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Phys, 110, 8254 (1999).
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.. _Rick:
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**(Rick)** S. W. Rick, S. J. Stuart, B. J. Berne, J Chem Phys 101, 6141
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(1994).
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.. _lws: http://lammps.sandia.gov
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.. _ld: Manual.html
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.. _lc: Section_commands.html#comm
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