\(\renewcommand{\AA}{\text{Å}}\)

# compute ti command

## Syntax

    compute ID group ti keyword args ...

- ID, group-ID are documented in compute command

- ti = style name of this compute command

- one or more attribute/arg pairs may be appended

- keyword = pair style (lj/cut, gauss, born, etc.) or tail or kspace

      pair style args = atype v_name1 v_name2
        atype = atom type (see asterisk form below)
        v_name1 = variable with name1 that is energy scale factor and function of lambda
        v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda
      tail args = atype v_name1 v_name2
        atype = atom type (see asterisk form below)
        v_name1 = variable with name1 that is energy tail correction scale factor and function of lambda
        v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda
      kspace args = atype v_name1 v_name2
        atype = atom type (see asterisk form below)
        v_name1 = variable with name1 that is K-Space scale factor and function of lambda
        v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda

## Examples

    compute 1 all ti lj/cut 1 v_lj v_dlj coul/long 2 v_c v_dc kspace 1 v_ks v_dks
    compute 1 all ti lj/cut 1*3 v_lj v_dlj coul/long * v_c v_dc kspace * v_ks v_dks

## Description

Define a computation that calculates the derivative of the interaction potential with respect to lambda, the coupling parameter used in a thermodynamic integration. This derivative can be used to infer a free energy difference resulting from an alchemical simulation, as described in Eike.

Typically this compute will be used in conjunction with the fix adapt command which can perform alchemical transformations by adjusting the strength of an interaction potential as a simulation runs, as defined by one or more pair_style or kspace_style commands. This scaling is done via a prefactor on the energy, forces, virial calculated by the pair or \(k\)-space style. The prefactor is often a function of a lambda parameter which may be adjusted from 0 to 1 (or vice versa) over the course of a run. The time-dependent adjustment is what the fix adapt command does.

Assume that the unscaled energy of a pair_style or kspace_style is given by \(U\). Then the scaled energy is

\[U_s = f(\lambda) U\]

where \(f\) is some function of \(\lambda\). What this compute calculates is

\[\frac{dU_s}{d\lambda} = U \frac{df(\lambda)}{d\lambda} = \frac{U_s}{f(\lambda)} \frac{df(\lambda)}{d\lambda},\]

which is the derivative of the system’s scaled potential energy \(U_s\) with respect to \(\lambda\).

To perform this calculation, you provide one or more atom types as atype. The variable atype can be specified in one of two ways. An explicit numeric value can be used, as in the first example above, or a wildcard asterisk can be used in place of or in conjunction with the atype argument to select multiple atom types. This takes the form “*” or “*n” or “m*” or “m*n”. If \(N\) is the number of atom types, then an asterisk with no numeric values means all types from 1 to \(N\). A leading asterisk means all types from 1 to n (inclusive). A trailing asterisk means all types from m to N (inclusive). A middle asterisk means all types from m to n (inclusive).

You also specify two functions, as equal-style variables. The first is specified as v_name1, where name1 is the name of the variable, and is \(f(\lambda)\) in the notation above. The second is specified as v_name2, where name2 is the name of the variable, and is \(df(\lambda)/d\lambda\) in the notation above (i.e., it is the analytic derivative of \(f\) with respect to \(\lambda\)). Note that the name1 variable is also typically given as an argument to the fix adapt command.

An alchemical simulation may use several pair potentials together, invoked via the pair_style hybrid or hybrid/overlay command. The total \(dU_s/d\lambda\) for the overall system is calculated as the sum of each contributing term as listed by the keywords in the compute ti command. Individual pair potentials can be listed, which will be sub-styles in the hybrid case. You can also include a \(k\)-space term via the kspace keyword. You can also include a pairwise long-range tail correction to the energy via the tail keyword.

For each term, you can specify a different (or the same) scale factor by the two variables that you list. Again, these will typically correspond toe the scale factors applied to these various potentials and the \(k\)-space contribution via the fix adapt command.

More details about the exact functional forms for the computation of \(du/dl\) can be found in the paper by Eike.

## Output info

This compute calculates a global scalar, namely \(dU_s/d\lambda\). This value can be used by any command that uses a global scalar value from a compute as input. See the Howto output doc page for an overview of LAMMPS output options.

The scalar value calculated by this compute is “extensive”.

The scalar value will be in energy units.

## Restrictions

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

## Related commands

fix adapt

## Default

none

(Eike) Eike and Maginn, Journal of Chemical Physics, 124, 164503 (2006).