# compute ti command

## Syntax

``` LAMMPS
compute ID group ti keyword args ...
```

-   ID, group-ID are documented in [compute](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

``` LAMMPS
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](Eike).

Typically this compute will be used in conjunction with the [fix
adapt](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](pair_style) or
[kspace_style](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](run). The time-dependent adjustment is what the [fix
adapt](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](variable).
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](fix_adapt) command.

An alchemical simulation may use several pair potentials together,
invoked via the [pair_style hybrid or hybrid/overlay](pair_hybrid)
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](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](fix_adapt) command.

More details about the exact functional forms for the computation of
$du/dl$ can be found in the paper by [Eike](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](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](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](Build_package) page for more info.

## Related commands

[fix adapt](fix_adapt)

## Default

none

------------------------------------------------------------------------

::: {#Eike}
**(Eike)** Eike and Maginn, Journal of Chemical Physics, 124, 164503
(2006).
:::