\(\renewcommand{\AA}{\text{Å}}\)

# pair_style smatb command

# pair_style smatb/single command

## Syntax

    pair_style style args

- style = smatb or smatb/single

- args = none

## Examples

    pair_style smatb
    pair_coeff 1 1 2.88 10.35 4.178 0.210 1.818 4.07293506 4.9883063257983666

    pair_style smatb/single
    pair_coeff 1 1 2.88 10.35 4.178 0.210 1.818 4.07293506 4.9883063257983666

## Description

Added in version 4May2022.

The smatb and smatb/single styles compute the Second Moment Approximation to the Tight Binding (Cyrot), (Gupta), (Rosato), given by

\[E_{i} = \sum_{j,R_{ij}\leq R_{c}} \alpha(R_{ij}) - \sqrt{\sum_{j,R_{ij}\leq R_{c}}\Xi^2(R_{ij})}\]

\(R_{ij}\) is the distance between the atom \(i\) and \(j\). And the two functions \(\alpha\left(r\right)\) and \(\Xi\left(r\right)\) are:

\[\begin{split}\alpha\left(r\right)=\left\lbrace\begin{array}{ll} A e^{-p \left(\frac{r}{R_{0}}-1\right)} & r < R_{sc}\\ a_3\left(r-R_{c}\right)^3+a_4\left(r-R_{c}\right)^4 +a_5\left(r-R_{c}\right)^5& R_{sc} < r < R_{c} \end{array} \right.\end{split}\]
\[\begin{split}\Xi\left(r\right)=\left\lbrace\begin{array}{ll} \xi e^{-q \left(\frac{r}{R_{0}}-1\right)} & r < R_{sc}\\ x_3\left(r-R_{c}\right)^3+x_4\left(r-R_{c}\right)^4 +x_5\left(r-R_{c}\right)^5& R_{sc} < r < R_{c} \end{array} \right.\end{split}\]

The polynomial coefficients \(a_3\), \(a_4\), \(a_5\), \(x_3\), \(x_4\), \(x_5\) are computed by LAMMPS: the two exponential terms and their first and second derivatives are smoothly reduced to zero, from the inner cutoff \(R_{sc}\) to the outer cutoff \(R_{c}\).

The smatb/single style is an optimization when using only a single atom type.

## Coefficients

The following coefficients must be defined for each pair of atoms types via the pair_coeff command as in the examples above, or in the data file or restart files read by the read_data or read_restart commands, or by mixing as described below:

- \(R_{0}\) (distance units)

- \(p\) (dimensionless)

- \(q\) (dimensionless)

- \(A\) (energy units)

- \(\xi\) (energy units)

- \(R_{cs}\) (distance units)

- \(R_{c}\) (distance units)

Note that: \(R_{0}\) is the nearest neighbor distance, usually coincides with the diameter of the atoms

See the run_style command for details.

## Mixing info

For atom type pairs I,J and I != J the coefficients are not automatically mixed.

## Restrictions

These pair styles are part of the SMTBQ package and are only enabled if LAMMPS is built with that package. See the Build package page for more info.

These pair styles require the newton setting to be “on” for pair interactions.

## Related commands

- pair_coeff

## Default

none

(Cyrot) Cyrot-Lackmann and Ducastelle, Phys Rev. B, 4, 2406-2412 (1971).

(Gupta) Gupta ,Phys Rev. B, 23, 6265-6270 (1981).

(Rosato) Rosato and Guillope and Legrand, Philosophical Magazine A, 59.2, 321-336 (1989).