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