forked from lijiext/lammps
570 lines
36 KiB
HTML
570 lines
36 KiB
HTML
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<title>compute sna/atom command — LAMMPS documentation</title>
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<link rel="top" title="LAMMPS documentation" href="index.html"/>
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<link rel="up" title="Computes" href="computes.html"/>
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<link rel="next" title="compute stress/atom command" href="compute_stress_atom.html"/>
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<a href="Manual.html" class="icon icon-home"> LAMMPS
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<p class="caption"><span class="caption-text">User Documentation</span></p>
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<ul>
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<li class="toctree-l1"><a class="reference internal" href="Section_intro.html">1. Introduction</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_start.html">2. Getting Started</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_commands.html">3. Commands</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_packages.html">4. Packages</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_accelerate.html">5. Accelerating LAMMPS performance</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_howto.html">6. How-to discussions</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_example.html">7. Example problems</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_perf.html">8. Performance & scalability</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_tools.html">9. Additional tools</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_modify.html">10. Modifying & extending LAMMPS</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_python.html">11. Python interface to LAMMPS</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_errors.html">12. Errors</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Section_history.html">13. Future and history</a></li>
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</ul>
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<p class="caption"><span class="caption-text">Index</span></p>
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<ul class="current">
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<li class="toctree-l1"><a class="reference internal" href="tutorials.html">Tutorials</a></li>
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<li class="toctree-l1"><a class="reference internal" href="commands.html">Commands</a></li>
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<li class="toctree-l1"><a class="reference internal" href="fixes.html">Fixes</a></li>
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<li class="toctree-l1 current"><a class="reference internal" href="computes.html">Computes</a><ul class="current">
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<li class="toctree-l2"><a class="reference internal" href="compute_ackland_atom.html">compute ackland/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_angle.html">compute angle command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_angle_local.html">compute angle/local command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_angmom_chunk.html">compute angmom/chunk command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_basal_atom.html">compute basal/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_body_local.html">compute body/local command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_bond.html">compute bond command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_bond_local.html">compute bond/local command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_centro_atom.html">compute centro/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_chunk_atom.html">compute chunk/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_cluster_atom.html">compute cluster/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_cna_atom.html">compute cna/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_com.html">compute com command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_com_chunk.html">compute com/chunk command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_contact_atom.html">compute contact/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_coord_atom.html">compute coord/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_damage_atom.html">compute damage/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_dihedral.html">compute dihedral command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_dihedral_local.html">compute dihedral/local command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_dilatation_atom.html">compute dilatation/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_dipole_chunk.html">compute dipole/chunk command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_displace_atom.html">compute displace/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_dpd.html">compute dpd command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_dpd_atom.html">compute dpd/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_erotate_asphere.html">compute erotate/asphere command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_erotate_rigid.html">compute erotate/rigid command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_erotate_sphere.html">compute erotate/sphere command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_erotate_sphere_atom.html">compute erotate/sphere/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_event_displace.html">compute event/displace command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_fep.html">compute fep command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_group_group.html">compute group/group command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_gyration.html">compute gyration command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_gyration_chunk.html">compute gyration/chunk command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_heat_flux.html">compute heat/flux command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_hexorder_atom.html">compute hexorder/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_improper.html">compute improper command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_improper_local.html">compute improper/local command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_inertia_chunk.html">compute inertia/chunk command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_ke.html">compute ke command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_ke_atom.html">compute ke/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_ke_atom_eff.html">compute ke/atom/eff command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_ke_eff.html">compute ke/eff command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_ke_rigid.html">compute ke/rigid command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_meso_e_atom.html">compute meso/e/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_meso_rho_atom.html">compute meso/rho/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_meso_t_atom.html">compute meso/t/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_msd.html">compute msd command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_msd_chunk.html">compute msd/chunk command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_msd_nongauss.html">compute msd/nongauss command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_omega_chunk.html">compute omega/chunk command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_orientorder_atom.html">compute orientorder/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_pair.html">compute pair command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_pair_local.html">compute pair/local command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_pe.html">compute pe command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_pe_atom.html">compute pe/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_plasticity_atom.html">compute plasticity/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_pressure.html">compute pressure command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_property_atom.html">compute property/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_property_chunk.html">compute property/chunk command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_property_local.html">compute property/local command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_rdf.html">compute rdf command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_reduce.html">compute reduce command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_reduce.html#compute-reduce-region-command">compute reduce/region command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_rigid_local.html">compute rigid/local command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_saed.html">compute saed command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_slice.html">compute slice command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_contact_radius.html">compute smd/contact/radius command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_damage.html">compute smd/damage command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_hourglass_error.html">compute smd/hourglass/error command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_internal_energy.html">compute smd/internal/energy command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_plastic_strain.html">compute smd/plastic/strain command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_plastic_strain_rate.html">compute smd/plastic/strain/rate command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_rho.html">compute smd/rho command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_tlsph_defgrad.html">compute smd/tlsph/defgrad command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_tlsph_dt.html">compute smd/tlsph/dt command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_tlsph_num_neighs.html">compute smd/tlsph/num/neighs command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_tlsph_shape.html">compute smd/tlsph/shape command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_tlsph_strain.html">compute smd/tlsph/strain command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_tlsph_strain_rate.html">compute smd/tlsph/strain/rate command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_tlsph_stress.html">compute smd/tlsph/stress command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_triangle_mesh_vertices.html">compute smd/triangle/mesh/vertices</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_ulsph_num_neighs.html">compute smd/ulsph/num/neighs command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_ulsph_strain.html">compute smd/ulsph/strain command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_ulsph_strain_rate.html">compute smd/ulsph/strain/rate command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_ulsph_stress.html">compute smd/ulsph/stress command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_smd_vol.html">compute smd/vol command</a></li>
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<li class="toctree-l2 current"><a class="current reference internal" href="#">compute sna/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="#compute-snad-atom-command">compute snad/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="#compute-snav-atom-command">compute snav/atom command</a><ul>
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<li class="toctree-l3"><a class="reference internal" href="#syntax">Syntax</a></li>
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<li class="toctree-l3"><a class="reference internal" href="#examples">Examples</a></li>
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<li class="toctree-l3"><a class="reference internal" href="#description">Description</a></li>
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<li class="toctree-l3"><a class="reference internal" href="#restrictions">Restrictions</a></li>
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<li class="toctree-l3"><a class="reference internal" href="#related-commands">Related commands</a></li>
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<li class="toctree-l3"><a class="reference internal" href="#default">Default</a></li>
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</ul>
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</li>
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<li class="toctree-l2"><a class="reference internal" href="compute_stress_atom.html">compute stress/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_tally.html">compute force/tally command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_tally.html#compute-heat-flux-tally-command">compute heat/flux/tally command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_tally.html#compute-pe-tally-command">compute pe/tally command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_tally.html#compute-pe-mol-tally-command">compute pe/mol/tally command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_tally.html#compute-stress-tally-command">compute stress/tally command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp.html">compute temp command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp.html#compute-temp-kk-command">compute temp/kk command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp_asphere.html">compute temp/asphere command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp_body.html">compute temp/body command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp_chunk.html">compute temp/chunk command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp_com.html">compute temp/com command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp_cs.html">compute temp/cs command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp_deform.html">compute temp/deform command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp_deform_eff.html">compute temp/deform/eff command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp_drude.html">compute temp/drude command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp_eff.html">compute temp/eff command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp_partial.html">compute temp/partial command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp_profile.html">compute temp/profile command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp_ramp.html">compute temp/ramp command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp_region.html">compute temp/region command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp_region_eff.html">compute temp/region/eff command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp_rotate.html">compute temp/rotate command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_temp_sphere.html">compute temp/sphere command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_ti.html">compute ti command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_torque_chunk.html">compute torque/chunk command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_vacf.html">compute vacf command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_vcm_chunk.html">compute vcm/chunk command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_voronoi_atom.html">compute voronoi/atom command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="compute_xrd.html">compute xrd command</a></li>
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</ul>
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</li>
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<li class="toctree-l1"><a class="reference internal" href="pairs.html">Pair Styles</a></li>
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<li class="toctree-l1"><a class="reference internal" href="bonds.html">Bonds</a></li>
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<li class="toctree-l1"><a class="reference internal" href="angles.html">Angle Styles</a></li>
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<li class="toctree-l1"><a class="reference internal" href="dihedrals.html">Dihedral Styles</a></li>
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<li class="toctree-l1"><a class="reference internal" href="impropers.html">Improper Styles</a></li>
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</ul>
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<div class="section" id="compute-sna-atom-command">
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<span id="index-0"></span><h1>compute sna/atom command</h1>
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</div>
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<div class="section" id="compute-snad-atom-command">
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<h1>compute snad/atom command</h1>
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</div>
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<div class="section" id="compute-snav-atom-command">
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<h1>compute snav/atom command</h1>
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<div class="section" id="syntax">
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<h2>Syntax</h2>
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<pre class="literal-block">
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compute ID group-ID sna/atom rcutfac rfac0 twojmax R_1 R_2 ... w_1 w_2 ... keyword values ...
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compute ID group-ID snad/atom rcutfac rfac0 twojmax R_1 R_2 ... w_1 w_2 ... keyword values ...
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compute ID group-ID snav/atom rcutfac rfac0 twojmax R_1 R_2 ... w_1 w_2 ... keyword values ...
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</pre>
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<ul>
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<li><p class="first">ID, group-ID are documented in <a class="reference internal" href="compute.html"><span class="doc">compute</span></a> command</p>
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</li>
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<li><p class="first">sna/atom = style name of this compute command</p>
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</li>
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<li><p class="first">rcutfac = scale factor applied to all cutoff radii (positive real)</p>
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</li>
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<li><p class="first">rfac0 = parameter in distance to angle conversion (0 < rcutfac < 1)</p>
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</li>
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<li><p class="first">twojmax = band limit for bispectrum components (non-negative integer)</p>
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</li>
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<li><p class="first">R_1, R_2,... = list of cutoff radii, one for each type (distance units)</p>
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</li>
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<li><p class="first">w_1, w_2,... = list of neighbor weights, one for each type</p>
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</li>
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<li><p class="first">zero or more keyword/value pairs may be appended</p>
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</li>
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<li><p class="first">keyword = <em>diagonal</em> or <em>rmin0</em> or <em>switchflag</em></p>
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<pre class="literal-block">
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<em>diagonal</em> value = <em>0</em> or <em>1</em> or <em>2</em> or <em>3</em>
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<em>0</em> = all j1, j2, j <= twojmax, j2 <= j1
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<em>1</em> = subset satisfying j1 == j2
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<em>2</em> = subset satisfying j1 == j2 == j3
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<em>3</em> = subset satisfying j2 <= j1 <= j
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<em>rmin0</em> value = parameter in distance to angle conversion (distance units)
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<em>switchflag</em> value = <em>0</em> or <em>1</em>
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<em>0</em> = do not use switching function
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<em>1</em> = use switching function
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</pre>
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</li>
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</ul>
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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">compute</span> <span class="n">b</span> <span class="nb">all</span> <span class="n">sna</span><span class="o">/</span><span class="n">atom</span> <span class="mf">1.4</span> <span class="mf">0.99363</span> <span class="mi">6</span> <span class="mf">2.0</span> <span class="mf">2.4</span> <span class="mf">0.75</span> <span class="mf">1.0</span> <span class="n">diagonal</span> <span class="mi">3</span> <span class="n">rmin0</span> <span class="mf">0.0</span>
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<span class="n">compute</span> <span class="n">db</span> <span class="nb">all</span> <span class="n">sna</span><span class="o">/</span><span class="n">atom</span> <span class="mf">1.4</span> <span class="mf">0.95</span> <span class="mi">6</span> <span class="mf">2.0</span> <span class="mf">1.0</span>
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<span class="n">compute</span> <span class="n">vb</span> <span class="nb">all</span> <span class="n">sna</span><span class="o">/</span><span class="n">atom</span> <span class="mf">1.4</span> <span class="mf">0.95</span> <span class="mi">6</span> <span class="mf">2.0</span> <span class="mf">1.0</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>Define a computation that calculates a set of bispectrum components
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for each atom in a group.</p>
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<p>Bispectrum components of an atom are order parameters characterizing
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the radial and angular distribution of neighbor atoms. The detailed
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mathematical definition is given in the paper by Thompson et
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al. <a class="reference internal" href="pair_snap.html#thompson2014"><span class="std std-ref">(Thompson)</span></a></p>
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<p>The position of a neighbor atom <em>i’</em> relative to a central atom <em>i</em> is
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a point within the 3D ball of radius <em>R_ii’ = rcutfac*(R_i + R_i’)</em></p>
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<p>Bartok et al. <a class="reference internal" href="pair_snap.html#bartok2010"><span class="std std-ref">(Bartok)</span></a>, proposed mapping this 3D ball
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onto the 3-sphere, the surface of the unit ball in a four-dimensional
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space. The radial distance <em>r</em> within <em>R_ii’</em> is mapped on to a third
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polar angle <em>theta0</em> defined by,</p>
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<img alt="_images/compute_sna_atom1.jpg" class="align-center" src="_images/compute_sna_atom1.jpg" />
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<p>In this way, all possible neighbor positions are mapped on to a subset
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of the 3-sphere. Points south of the latitude <em>theta0max=rfac0*Pi</em>
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are excluded.</p>
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<p>The natural basis for functions on the 3-sphere is formed by the 4D
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hyperspherical harmonics <em>U^j_m,m’(theta, phi, theta0).</em> These
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functions are better known as <em>D^j_m,m’,</em> the elements of the Wigner
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<em>D</em>-matrices <a class="reference internal" href="#meremianin2006"><span class="std std-ref">(Meremianin</span></a>,
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<a class="reference internal" href="#varshalovich1987"><span class="std std-ref">Varshalovich)</span></a>.</p>
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<p>The density of neighbors on the 3-sphere can be written as a sum of
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Dirac-delta functions, one for each neighbor, weighted by species and
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radial distance. Expanding this density function as a generalized
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Fourier series in the basis functions, we can write each Fourier
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coefficient as</p>
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<img alt="_images/compute_sna_atom2.jpg" class="align-center" src="_images/compute_sna_atom2.jpg" />
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<p>The <em>w_i’</em> neighbor weights are dimensionless numbers that are chosen
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to distinguish atoms of different types, while the central atom is
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arbitrarily assigned a unit weight. The function <em>fc(r)</em> ensures that
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the contribution of each neighbor atom goes smoothly to zero at
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<em>R_ii’</em>:</p>
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<img alt="_images/compute_sna_atom4.jpg" class="align-center" src="_images/compute_sna_atom4.jpg" />
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<p>The expansion coefficients <em>u^j_m,m’</em> are complex-valued and they are
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not directly useful as descriptors, because they are not invariant
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|
under rotation of the polar coordinate frame. However, the following
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|
scalar triple products of expansion coefficients can be shown to be
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|
real-valued and invariant under rotation <a class="reference internal" href="pair_snap.html#bartok2010"><span class="std std-ref">(Bartok)</span></a>.</p>
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|
<img alt="_images/compute_sna_atom3.jpg" class="align-center" src="_images/compute_sna_atom3.jpg" />
|
|
<p>The constants <em>H^jmm’_j1m1m1’_j2m2m2’</em> are coupling coefficients,
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analogous to Clebsch-Gordan coefficients for rotations on the
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|
2-sphere. These invariants are the components of the bispectrum and
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these are the quantities calculated by the compute <em>sna/atom</em>. They
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characterize the strength of density correlations at three points on
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the 3-sphere. The j2=0 subset form the power spectrum, which
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characterizes the correlations of two points. The lowest-order
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components describe the coarsest features of the density function,
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|
while higher-order components reflect finer detail. Note that the
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central atom is included in the expansion, so three point-correlations
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|
can be either due to three neighbors, or two neighbors and the central
|
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atom.</p>
|
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<p>Compute <em>snad/atom</em> calculates the derivative of the bispectrum components
|
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summed separately for each atom type:</p>
|
|
<img alt="_images/compute_sna_atom5.jpg" class="align-center" src="_images/compute_sna_atom5.jpg" />
|
|
<p>The sum is over all atoms <em>i’</em> of atom type <em>I</em>. For each atom <em>i</em>,
|
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this compute evaluates the above expression for each direction, each
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atom type, and each bispectrum component. See section below on output
|
|
for a detailed explanation.</p>
|
|
<p>Compute <em>snav/atom</em> calculates the virial contribution due to the
|
|
derivatives:</p>
|
|
<img alt="_images/compute_sna_atom6.jpg" class="align-center" src="_images/compute_sna_atom6.jpg" />
|
|
<p>Again, the sum is over all atoms <em>i’</em> of atom type <em>I</em>. For each atom
|
|
<em>i</em>, this compute evaluates the above expression for each of the six
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virial components, each atom type, and each bispectrum component. See
|
|
section below on output for a detailed explanation.</p>
|
|
<p>The value of all bispectrum components will be zero for atoms not in
|
|
the group. Neighbor atoms not in the group do not contribute to the
|
|
bispectrum of atoms in the group.</p>
|
|
<p>The neighbor list needed to compute this quantity is constructed each
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|
time the calculation is performed (i.e. each time a snapshot of atoms
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|
is dumped). Thus it can be inefficient to compute/dump this quantity
|
|
too frequently.</p>
|
|
<p>The argument <em>rcutfac</em> is a scale factor that controls the ratio of
|
|
atomic radius to radial cutoff distance.</p>
|
|
<p>The argument <em>rfac0</em> and the optional keyword <em>rmin0</em> define the
|
|
linear mapping from radial distance to polar angle <em>theta0</em> on the
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|
3-sphere.</p>
|
|
<p>The argument <em>twojmax</em> and the keyword <em>diagonal</em> define which
|
|
bispectrum components are generated. See section below on output for a
|
|
detailed explanation of the number of bispectrum components and the
|
|
ordered in which they are listed</p>
|
|
<p>The keyword <em>switchflag</em> can be used to turn off the switching
|
|
function.</p>
|
|
<div class="admonition note">
|
|
<p class="first admonition-title">Note</p>
|
|
<p class="last">If you have a bonded system, then the settings of
|
|
<a class="reference internal" href="special_bonds.html"><span class="doc">special_bonds</span></a> command can remove pairwise
|
|
interactions between atoms in the same bond, angle, or dihedral. This
|
|
is the default setting for the <a class="reference internal" href="special_bonds.html"><span class="doc">special_bonds</span></a>
|
|
command, and means those pairwise interactions do not appear in the
|
|
neighbor list. Because this fix uses the neighbor list, it also means
|
|
those pairs will not be included in the calculation. One way to get
|
|
around this, is to write a dump file, and use the <a class="reference internal" href="rerun.html"><span class="doc">rerun</span></a>
|
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command to compute the bispectrum components for snapshots in the dump
|
|
file. The rerun script can use a <a class="reference internal" href="special_bonds.html"><span class="doc">special_bonds</span></a>
|
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command that includes all pairs in the neighbor list.</p>
|
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</div>
|
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<p>;line</p>
|
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<p><strong>Output info:</strong></p>
|
|
<p>Compute <em>sna/atom</em> calculates a per-atom array, each column
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|
corresponding to a particular bispectrum component. The total number
|
|
of columns and the identities of the bispectrum component contained in
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each column depend on the values of <em>twojmax</em> and <em>diagonal</em>, as
|
|
described by the following piece of python code:</p>
|
|
<pre class="literal-block">
|
|
for j1 in range(0,twojmax+1):
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if(diagonal==2):
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print j1/2.,j1/2.,j1/2.
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elif(diagonal==1):
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for j in range(0,min(twojmax,2*j1)+1,2):
|
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print j1/2.,j1/2.,j/2.
|
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elif(diagonal==0):
|
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for j2 in range(0,j1+1):
|
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for j in range(j1-j2,min(twojmax,j1+j2)+1,2):
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print j1/2.,j2/2.,j/2.
|
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elif(diagonal==3):
|
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for j2 in range(0,j1+1):
|
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for j in range(j1-j2,min(twojmax,j1+j2)+1,2):
|
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if (j>=j1): print j1/2.,j2/2.,j/2.
|
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</pre>
|
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<p>Compute <em>snad/atom</em> evaluates a per-atom array. The columns are
|
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arranged into <em>ntypes</em> blocks, listed in order of atom type <em>I</em>. Each
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block contains three sub-blocks corresponding to the <em>x</em>, <em>y</em>, and <em>z</em>
|
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components of the atom position. Each of these sub-blocks contains
|
|
one column for each bispectrum component, the same as for compute
|
|
<em>sna/atom</em></p>
|
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<p>Compute <em>snav/atom</em> evaluates a per-atom array. The columns are
|
|
arranged into <em>ntypes</em> blocks, listed in order of atom type <em>I</em>. Each
|
|
block contains six sub-blocks corresponding to the <em>xx</em>, <em>yy</em>, <em>zz</em>,
|
|
<em>yz</em>, <em>xz</em>, and <em>xy</em> components of the virial tensor in Voigt
|
|
notation. Each of these sub-blocks contains one column for each
|
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bispectrum component, the same as for compute <em>sna/atom</em></p>
|
|
<p>These values can be accessed by any command that uses per-atom values
|
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from a compute as input. See <a class="reference internal" href="Section_howto.html#howto-15"><span class="std std-ref">Section 6.15</span></a> for an overview of LAMMPS output
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options.</p>
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</div>
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<div class="section" id="restrictions">
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<h2>Restrictions</h2>
|
|
<p>These computes are part of the SNAP package. They are only enabled if
|
|
LAMMPS was 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>
|
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</div>
|
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<div class="section" id="related-commands">
|
|
<h2>Related commands</h2>
|
|
<p><a class="reference internal" href="pair_snap.html"><span class="doc">pair_style snap</span></a></p>
|
|
</div>
|
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<div class="section" id="default">
|
|
<h2>Default</h2>
|
|
<p>The optional keyword defaults are <em>diagonal</em> = 0, <em>rmin0</em> = 0,
|
|
<em>switchflag</em> = 1.</p>
|
|
<hr class="docutils" />
|
|
<p id="thompson2014"><strong>(Thompson)</strong> Thompson, Swiler, Trott, Foiles, Tucker, under review, preprint
|
|
available at <a class="reference external" href="http://arxiv.org/abs/1409.3880">arXiv:1409.3880</a></p>
|
|
<p id="bartok2010"><strong>(Bartok)</strong> Bartok, Payne, Risi, Csanyi, Phys Rev Lett, 104, 136403 (2010).</p>
|
|
<p id="meremianin2006"><strong>(Meremianin)</strong> Meremianin, J. Phys. A, 39, 3099 (2006).</p>
|
|
<p id="varshalovich1987"><strong>(Varshalovich)</strong> Varshalovich, Moskalev, Khersonskii, Quantum Theory
|
|
of Angular Momentum, World Scientific, Singapore (1987).</p>
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