\(\renewcommand{\AA}{\text{Å}}\)

# pair_style e3b command

## Syntax

    pair_style e3b Otype

- Otype = atom type (numeric or type label) for oxygen

    pair_coeff * * keyword

- one or more keyword/value pairs must be appended.

- keyword = preset or Ea or Eb or Ec or E2 or K3 or K2 or Rs or Rc3 or Rc2 or bondL or neigh

- If the preset keyword is given, no others are needed. Otherwise, all are mandatory except for neigh. The neigh keyword is always optional.

    preset arg = 2011 or 2015 = which set of predefined parameters to use
             2011 = use the potential parameters from (Tainter 2011)
             2015 = use the potential parameters from (Tainter 2015)
    Ea arg = three-body energy for type A hydrogen bonding interactions (energy units)
    Eb arg = three-body energy for type B hydrogen bonding interactions (energy units)
    Ec arg = three-body energy for type C hydrogen bonding interactions (energy units)
    E2 arg = two-body energy correction (energy units)
    K3 arg = three-body exponential constant (inverse distance units)
    K2 arg = two-body exponential constant (inverse distance units)
    Rc3 arg = three-body cutoff (distance units)
    Rc2 arg = two-body cutoff (distance units)
    Rs arg = three-body switching function cutoff (distance units)
    bondL arg = intramolecular OH bond length (distance units)
    neigh arg = approximate integer number of molecules within Rc3 of an oxygen atom

## Examples

    pair_style e3b 1
    pair_coeff * * Ea 35.85 Eb -240.2 Ec 449.3 E2 108269.9 K3 1.907 K2 4.872 Rc3 5.2 Rc2 5.2 Rs 5.0 bondL 0.9572

    pair_style hybrid/overlay e3b 1 lj/cut/tip4p/long 1 2 1 1 0.15 8.5
    pair_coeff * * e3b preset 2011

    pair_style e3b OW
    labelmap atom 1 C 2 H 3 O 4 N 5 OW 6 HW
    pair_coeff * * Ea 35.85 Eb -240.2 Ec 449.3 E2 108269.9 K3 1.907 K2 4.872 Rc3 5.2 Rc2 5.2 Rs 5.0 bondL 0.9572

Used in example input script:

    examples/PACKAGES/e3b/in.e3b-tip4p2005

## Description

The e3b style computes an "explicit three-body" (E3B) potential for water (Kumar 2008).

\[\begin{split}E =& E_2 \sum_{i,j}e^{-k_2 r_{ij}} + E_A \sum_{\substack{i,j,k,\ell \\ \in \textrm{type A}}} f(r_{ij})f(r_{k\ell}) + E_B \sum_{\substack{i,j,k,\ell \\ \in \textrm{type B}}} f(r_{ij})f(r_{k\ell}) + E_C \sum_{\substack{i,j,k,\ell \\ \in \textrm{type C}}} f(r_{ij})f(r_{k\ell}) \\ f(r) =& e^{-k_3 r}s(r) \\ s(r) =& \begin{cases} 1 & r<R_s \\ \displaystyle\frac{(R_f-r)^2(R_f-3R_s+2r)}{(R_f-R_s)^3} & R_s\leq r\leq R_f \\ 0 & r>R_f\\ \end{cases}\end{split}\]

This potential was developed as a water model that includes the three-body cooperativity of hydrogen bonding explicitly. To use it in this way, it must be applied in conjunction with a conventional two-body water model, through pair style hybrid/overlay. The three body interactions are split into three types: A, B, and C. Type A corresponds to anti-cooperative double hydrogen bond donor interactions. Type B corresponds to the cooperative interaction of molecules that both donate and accept a hydrogen bond. Type C corresponds to anti-cooperative double hydrogen bond acceptor interactions. The three-body interactions are smoothly cutoff by the switching function s(r) between Rs and Rc3. The two-body interactions are designed to correct for the effective many-body interactions implicitly included in the conventional two-body potential. The two-body interactions are cut off sharply at Rc2, because K3 is typically significantly smaller than K2. See (Kumar 2008) for more details.

Only a single pair_coeff command is used with the e3b style and the first two arguments must be * *. The oxygen atom type for the pair style is passed as the only argument to the pair_style command, not in the pair_coeff command. The hydrogen atom type is inferred from the ordering of the atoms.

Note

Every atom of type Otype must be part of a water molecule. Each water molecule must have consecutive IDs with the oxygen first. This pair style does not test that this criteria is met.

Note

If using type labels, the type labels must be defined before calling the pair_coeff command.

The pair_coeff command must have at least one keyword/value pair, as described above. The preset keyword sets the potential parameters to the values used in (Tainter 2011) or (Tainter 2015). To use the water models defined in those references, the e3b style should always be used in conjunction with an lj/cut/tip4p/long style through pair_style hybrid/overlay, as demonstrated in the second example above. The preset 2011 option should be used with the TIP4P water model. The preset 2015 option should be used with the TIP4P/2005 water model. If the preset keyword is used, no other keyword is needed. Changes to the preset parameters can be made by specifying the preset keyword followed by the specific parameter to change, like Ea. Note that the other keywords must come after preset in the pair_style command. The e3b style can also be used to implement any three-body potential of the same form by specifying all the keywords except neigh: Ea, Eb, Ec, E2, K3, K2, Rc3, Rc2, Rs, and bondL. The keyword bondL specifies the intramolecular OH bond length of the water model being used. This is needed to include H atoms that are within the cutoff even when the attached oxygen atom is not.

This pair style allocates arrays sized according to the number of pairwise interactions within Rc3. To do this it needs an estimate for the number of water molecules within Rc3 of an oxygen atom. This estimate defaults to 10 and can be changed using the neigh keyword, which takes an integer as an argument. If the neigh setting is too small, the simulation will fail with the error “neigh is too small”. If the neigh setting is too large, the pair style will use more memory than necessary.

This pair style tallies a breakdown of the total E3B potential energy into sub-categories, which can be accessed via the compute pair command as a vector of values of length 4. The 4 values correspond to the terms in the first equation above: the E2 term, the Ea term, the Eb term, and the Ec term.

See the examples/PACKAGES/e3b directory for a complete example script.

## Mixing, shift, table, tail correction, restart, rRESPA info

This pair style does not support the pair_modify shift, table, and tail options.

This pair style does not write its information to binary restart files. Thus, you need to re-specify the pair_style and pair_coeff commands in an input script that reads a restart file.

This pair style is incompatible with respa.

## Restrictions

This pair style is part of the EXTRA-PAIR package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info.

This pair style requires the newton setting to be “on” for pair interactions.

This pair style requires a fixed number of atoms in the simulation, so it is incompatible with fixes like fix deposit. If the number of atoms changes between runs, this pair style must be re-initialized by calling the pair_style and pair_coeffs commands. This is not a fundamental limitation of the pair style, but the code currently does not support a variable number of atoms.

The preset keyword currently only works with real, metal, si, and cgs units.

## Related commands

pair_coeff, compute pair

## Default

The option default for the neigh keyword is 10.

(Kumar) Kumar and Skinner, J. Phys. Chem. B, 112, 8311 (2008)

(Tainter 2011) Tainter, Pieniazek, Lin, and Skinner, J. Chem. Phys., 134, 184501 (2011)

(Tainter 2015) Tainter, Shi, and Skinner, 11, 2268 (2015)