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230 lines
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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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<H3>pair_style mgpt command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>pair_style mgpt
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</PRE>
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<P><B>Examples:</B>
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</P>
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<PRE>pair_style mgpt
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pair_coeff * * Ta6.8x.mgpt.parmin Ta6.8x.mgpt.potin Omega
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cp ~/lammps/potentials/Ta6.8x.mgpt.parmin parmin
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cp ~/lammps/potentials/Ta6.8x.mgpt.potin potin
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pair_coeff * * parmin potin Omega volpress yes nbody 1234 precision double
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pair_coeff * * parmin potin Omega volpress yes nbody 12
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>Within DFT quantum mechanics, generalized pseudopotential theory (GPT)
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(<A HREF = "#Moriarty1">Moriarty1</A>) provides a first-principles approach to
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multi-ion interatomic potentials in d-band transition metals, with a
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volume-dependent, real-space total-energy functional for the N-ion
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elemental bulk material in the form
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</P>
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<CENTER><IMG SRC = "Eqs/pair_mgpt.jpg">
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</CENTER>
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<P>where the prime on each summation sign indicates the exclusion of all
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self-interaction terms from the summation. The leading volume term
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E_vol as well as the two-ion central-force pair potential v_2 and the
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three- and four-ion angular-force potentials, v_3 and v_4, depend
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explicitly on the atomic volume Omega, but are structure independent
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and transferable to all bulk ion configurations, either ordered or
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disordered, and with of without the presence of point and line
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defects. The simplified model GPT or MGPT (<A HREF = "#Moriarty2">Moriarty2</A>,
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<A HREF = "#Moriarty3">Moriarty3</A>), which retains the form of E_tot and permits
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more efficient large-scale atomistic simulations, derives from the GPT
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through a series of systematic approximations applied to E_vol and the
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potentials v_n that are valid for mid-period transition metals with
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nearly half-filled d bands.
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</P>
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<P>Both analytic (<A HREF = "#Moriarty2">Moriarty2</A>) and matrix
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(<A HREF = "#Moriarty3">Moriarty3</A>) representations of MGPT have been developed.
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In the more general matrix representation, which can also be applied
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to f-band actinide metals and permits both canonical and non-canonical
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d/f bands, the multi-ion potentials are evaluated on the fly during a
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simulation through d- or f-state matrix multiplication, and the forces
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that move the ions are determined analytically. Fast matrix-MGPT
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algorithms have been developed independently by Glosli
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(<A HREF = "#Glosli">Glosli</A>, <A HREF = "#Moriarty3">Moriarty3</A>) and by Oppelstrup
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(<A HREF = "#Oppelstrup">Oppelstrup</A>)
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</P>
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<P>The <I>mgpt</I> pair style calculates forces, energies, and the total
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energy per atom, E_tot/N, using the Oppelstrup matrix-MGPT algorithm.
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Input potential and control data are entered through the
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<A HREF = "pair_coeff.html">pair_coeff</A> command. Each material treated requires
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input parmin and potin potential files, as shown in the above
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examples, as well as specification by the user of the initial atomic
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volume Omega through pair_coeff. At the beginning of a time step in
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any simulation, the total volume of the simulation cell V should
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always be equal to Omega*N, where N is the number of metal ions
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present, taking into account the presence of any vacancies and/or
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interstitials in the case of a solid. In a constant-volume
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simulation, which is the normal mode of operation for the <I>mgpt</I> pair
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style, Omega, V and N all remain constant throughout the simulation
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and thus are equal to their initial values. In a constant-stress
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simulation, the cell volume V will change (slowly) as the simulation
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proceeds. After each time step, the atomic volume should be updated
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by the code as Omega = V/N. In addition, the volume term E_vol and
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the potentials v_2, v_3 and v_4 have to be removed at the end of the
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time step, and then respecified at the new value of Omega. In all
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smulations, Omega must remain within the defined volume range for
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E_vol and the potentials for the given material.
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</P>
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<P>The default option volpress yes in the <A HREF = "pair_coeff.html">pair_coeff</A>
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command includes all volume derivatives of E_tot required to calculate
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the stress tensor and pressure correctly. The option volpress no
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disregards the pressure contribution resulting from the volume term
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E_vol, and can be used for testing and analysis purposes. The
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additional optional variable nbody controls the specific terms in
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E_tot that are calculated. The default option and the normal option
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for mid-period transition and actinide metals is nbody 1234 for which
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all four terms in E_tot are retained. The option nbody 12, for
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example, retains only the volume term and the two-ion pair potential
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term and can be used for GPT series-end transition metals that can be
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well described without v_3 and v_4. The nbody option can also be used
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to test or analyze the contribution of any of the four terms in E_tot
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to a given calculated property.
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</P>
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<P>The <I>mgpt</I> pair style makes extensive use of matrix algebra and
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includes optimized kernels for the BlueGene/Q architecture and the
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Intel/AMD (x86) architectures. When compiled with the appropriate
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compiler and compiler switches (-msse3 on x86, and using the IBM XL
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compiler on BG/Q), these optimized routines are used automatically.
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For BG/Q machines, building with the default Makefile for that
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architecture (e.g., "make bgq") should enable the optimized algebra
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routines. For x-86 machines, the here provided Makefile.mpi_fastmgpt
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(build with "make mpi_fastmgpt") enables the fast algebra routines.
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The user will be informed in the output files of the matrix kernels in
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use. To further improve speed, on x86 the option precision single can
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be added to the <A HREF = "pair_coeff.html">pair_coeff</A> command line, which
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improves speed (up to a factor of two) at the cost of doing matrix
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calculations with 7 digit precision instead of the default 16. For
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consistency the default option can be specified explicitly by the
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option precision double.
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</P>
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<P>All remaining potential and control data are contained with the parmin
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and potin files, including cutoffs, atomic mass, and other basic MGPT
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variables. Specific MGPT potential data for the transition metals
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tantalum (Ta4 and Ta6.8x potentials), molybdenum (Mo5.2 potentials),
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and vanadium (V6.1 potentials) are contained in the LAMMPS potentials
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directory. The stored files are, respectively, Ta4.mgpt.parmin,
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Ta4.mgpt.potin, Ta6.8x.mgpt.parmin, Ta6.8x.mgpt.potin,
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Mo5.2.mgpt.parmin, Mo5.2.mgpt.potin, V6.1.mgpt.parmin, and
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V6.1.mgpt.potin . Useful corresponding informational "README" files
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on the Ta4, Ta6.8x, Mo5.2 and V6.1 potentials are also included in the
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potentials directory. These latter files indicate the volume mesh and
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range for each potential and give appropriate references for the
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potentials. It is expected that MGPT potentials for additional
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materials will be added over time.
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</P>
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<P>Useful example MGPT scripts are given in the examples/USER/mgpt
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directory. These scripts show the necessary steps to perform
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constant-volume calculations and simulations. It is strongly
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recommended that the user work through and understand these examples
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before proceeding to more complex simulations.
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</P>
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<P>IMPORTANT NOTE: For good performance, LAMMPS should be built with the
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compiler flags "-O3 -msse3 -funroll-loops" when including this pair
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style. The src/MAKE/OPTIONS/Makefile.mpi_fastmgpt is an example
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machine Makefile with these options included as part of a standard MPI
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build. Note that as-is it will build with whatever low-level compiler
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(g++, icc, etc) is the default for your MPI installation.
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</P>
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<HR>
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<P><B>Mixing, shift, table tail correction, restart</B>:
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</P>
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<P>This pair style does not support the <A HREF = "pair_modify.html">pair_modify</A>
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mix, shift, table, and tail options.
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</P>
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<P>This pair style does not write its information to <A HREF = "restart.html">binary restart
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files</A>, 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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</P>
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<P>This pair style can only be used via the <I>pair</I> keyword of the
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<A HREF = "run_style.html">run_style respa</A> command. It does not support the
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<I>inner</I>, <I>middle</I>, <I>outer</I> keywords.
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</P>
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<HR>
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<P><B>Restrictions:</B>
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</P>
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<P>This pair style is part of the USER-MGPT package and is only enabled
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if LAMMPS is built with that package. See the <A HREF = "Section_start.html#start_3">Making
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LAMMPS</A> section for more info.
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</P>
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<P>The MGPT potentials require the <A HREF = "newton.html">newtion</A> setting to be
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"on" for pair style interactions.
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</P>
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<P>The stored parmin and potin potential files provided with LAMMPS in
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the "potentials" directory are written in Rydberg atomic units, with
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energies in Rydbergs and distances in Bohr radii. The <I>mgpt</I> pair
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style converts Rydbergs to Hartrees to make the potential files
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compatible with LAMMPS electron <A HREF = "units.html">units</A>.
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</P>
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<P>The form of E_tot used in the <I>mgpt</I> pair style is only appropriate
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for elemental bulk solids and liquids. This includes solids with
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point and extended defects such as vacancies, interstitials, grain
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boundaries and dislocations. Alloys and free surfaces, however,
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require significant modifications, which are not included in the
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<I>mgpt</I> pair style. Likewise, the <I>hybrid</I> pair style is not allowed,
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where MGPT would be used for some atoms but not for others.
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</P>
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<P>Electron-thermal effects are not included in the standard MGPT
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potentials provided in the "potentials" directory, where the
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potentials have been constructed at zero electron temperature.
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Physically, electron-thermal effects may be important in 3d (e.g., V)
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and 4d (e.g., Mo) transition metals at high temperatures near melt and
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above. It is expected that temperature-dependent MGPT potentials for
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such cases will be added over time.
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</P>
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "pair_coeff.html">pair_coeff</A>
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</P>
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<P><B>Default:</B>
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</P>
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<P>The options defaults for the <A HREF = "pair_coeff.html">pair_coeff</A> command are
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volpress yes, nbody 1234, and precision double.
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</P>
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<HR>
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<A NAME = "Moriarty1"></A>
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<P><B>(Moriarty1)</B> Moriarty, Physical Review B, 38, 3199 (1988).
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</P>
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<A NAME = "Moriarty2"></A>
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<P><B>(Moriarty2)</B> Moriarty, Physical Review B, 42, 1609 (1990).
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Moriarty, Physical Review B 49, 12431 (1994).
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</P>
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<A NAME = "Moriarty3"></A>
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<P><B>(Moriarty3)</B> Moriarty, Benedict, Glosli, Hood, Orlikowski, Patel, Soderlind, Streitz, Tang, and Yang,
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Journal of Materials Research, 21, 563 (2006).
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</P>
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<A NAME = "Glosli"></A>
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<P><B>(Glosli)</B> Glosli, unpublished, 2005.
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Streitz, Glosli, Patel, Chan, Yates, de Supinski, Sexton and Gunnels, Journal of Physics: Conference
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Series, 46, 254 (2006).
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</P>
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<A NAME = "Oppelstrup"></A>
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<P><B>(Oppelstrup)</B> Oppelstrup, unpublished, 2015.
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Oppelstrup and Moriarty, to be published.
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</P>
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</HTML>
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