1.. index:: pair_style zbl 2.. index:: pair_style zbl/gpu 3.. index:: pair_style zbl/kk 4.. index:: pair_style zbl/omp 5 6pair_style zbl command 7====================== 8 9Accelerator Variants: *zbl/gpu*, *zbl/kk*, *zbl/omp* 10 11Syntax 12"""""" 13 14.. code-block:: LAMMPS 15 16 pair_style zbl inner outer 17 18* inner = distance where switching function begins 19* outer = global cutoff for ZBL interaction 20 21Examples 22"""""""" 23 24.. code-block:: LAMMPS 25 26 pair_style zbl 3.0 4.0 27 pair_coeff * * 73.0 73.0 28 pair_coeff 1 1 14.0 14.0 29 30Description 31""""""""""" 32 33Style *zbl* computes the Ziegler-Biersack-Littmark (ZBL) screened nuclear 34repulsion for describing high-energy collisions between atoms. 35:ref:`(Ziegler) <Ziegler>`. It includes an additional switching function 36that ramps the energy, force, and curvature smoothly to zero 37between an inner and outer cutoff. The potential 38energy due to a pair of atoms at a distance r_ij is given by: 39 40.. math:: 41 42 E^{ZBL}_{ij} & = \frac{1}{4\pi\epsilon_0} \frac{Z_i Z_j \,e^2}{r_{ij}} \phi(r_{ij}/a)+ S(r_{ij})\\ 43 a & = \frac{0.46850}{Z_{i}^{0.23} + Z_{j}^{0.23}}\\ 44 \phi(x) & = 0.18175e^{-3.19980x} + 0.50986e^{-0.94229x} + 0.28022e^{-0.40290x} + 0.02817e^{-0.20162x}\\ 45 46where *e* is the electron charge, :math:`\epsilon_0` is the electrical 47permittivity of vacuum, and :math:`Z_i` and :math:`Z_j` are the nuclear 48charges of the 49two atoms. The switching function :math:`S(r)` is identical to that used by 50:doc:`pair_style lj/gromacs <pair_gromacs>`. Here, the inner and outer 51cutoff are the same for all pairs of atom types. 52 53The following coefficients must be defined for each pair of atom types 54via the :doc:`pair_coeff <pair_coeff>` command as in the examples above, 55or in the LAMMPS data file. 56 57* :math:`Z_i` (atomic number for first atom type, e.g. 13.0 for aluminum) 58 59* :math:`Z_j` (ditto for second atom type) 60 61The values of :math:`Z_i` and :math:`Z_j` are normally equal to the atomic 62numbers of the two atom types. Thus, the user may optionally 63specify only the coefficients for each :math:`i==i` pair, and rely 64on the obvious mixing rule for cross interactions (see below). 65Note that when :math:`i==i` it is required that :math:`Z_i == Z_j`. 66When used with :doc:`hybrid/overlay <pair_hybrid>` and pairs are 67assigned 68to more than one sub-style, the mixing rule is not used and 69each pair of types interacting with the ZBL sub-style must 70be included in a pair_coeff command. 71 72.. note:: 73 74 The numerical values of the exponential decay constants in the 75 screening function depend on the unit of distance. In the above 76 equation they are given for units of angstroms. LAMMPS will 77 automatically convert these values to the distance unit of the 78 specified LAMMPS :doc:`units <units>` setting. The values of Z should 79 always be given as multiples of a proton's charge, e.g. 29.0 for 80 copper. 81 82---------- 83 84.. include:: accel_styles.rst 85 86---------- 87 88Mixing, shift, table, tail correction, restart, rRESPA info 89""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" 90 91For atom type pairs *i,j* and :math:`i \neq i`, the :math:`Z_i` and 92:math:`Z_j` coefficients 93can be mixed by taking :math:`Z_i` and :math:`Z_j` from the values 94specified for 95:math:`i == i` and :math:`j == j` cases. When used 96with :doc:`hybrid/overlay <pair_hybrid>` and pairs are assigned 97to more than one sub-style, the mixing rule is not used and 98each pair of types interacting with the ZBL sub-style 99must be included in a pair_coeff command. 100The :doc:`pair_modify <pair_modify>` mix option has no effect on 101the mixing behavior 102 103The ZBL pair style does not support the :doc:`pair_modify <pair_modify>` 104shift option, since the ZBL interaction is already smoothed to 0.0 at 105the cutoff. 106 107The :doc:`pair_modify <pair_modify>` table option is not relevant for 108this pair style. 109 110This pair style does not support the :doc:`pair_modify <pair_modify>` 111tail option for adding long-range tail corrections to energy and 112pressure, since there are no corrections for a potential that goes to 1130.0 at the cutoff. 114 115This pair style does not write information to :doc:`binary restart files <restart>`, so pair_style and pair_coeff commands must be 116specified in an input script that reads a restart file. 117 118This pair style can only be used via the *pair* keyword of the 119:doc:`run_style respa <run_style>` command. It does not support the 120*inner*, *middle*, *outer* keywords. 121 122---------- 123 124Restrictions 125"""""""""""" 126 none 127 128Related commands 129"""""""""""""""" 130 131:doc:`pair_coeff <pair_coeff>` 132 133Default 134""""""" 135 136none 137 138---------- 139 140.. _Ziegler: 141 142**(Ziegler)** J.F. Ziegler, J. P. Biersack and U. Littmark, "The 143Stopping and Range of Ions in Matter," Volume 1, Pergamon, 1985. 144