# compute temp/cs command

## Syntax

``` LAMMPS
compute ID group-ID temp/cs group1 group2
```

-   ID, group-ID are documented in [compute](compute) command
-   temp/cs = style name of this compute command
-   group1 = group-ID of either cores or shells
-   group2 = group-ID of either shells or cores

## Examples

``` LAMMPS
compute oxygen_c-s all temp/cs O_core O_shell
compute core_shells all temp/cs cores shells
```

## Description

Define a computation that calculates the temperature of a system based
on the center-of-mass velocity of atom pairs that are bonded to each
other. This compute is designed to be used with the adiabatic core/shell
model of [(Mitchell and Fincham)](MitchellFincham1). See the [Howto
coreshell](Howto_coreshell) page for an overview of the model as
implemented in LAMMPS. Specifically, this compute enables correct
temperature calculation and thermostatting of core/shell pairs where it
is desirable for the internal degrees of freedom of the core/shell pairs
to not be influenced by a thermostat. A compute of this style can be
used by any command that computes a temperature via
[fix_modify](fix_modify) (e.g., [fix temp/rescale](fix_temp_rescale),
[fix npt](fix_nh)).

Note that this compute does not require all ions to be polarized, hence
defined as core/shell pairs. One can mix core/shell pairs and ions
without a satellite particle if desired. The compute will consider the
non-polarized ions according to the physical system.

For this compute, core and shell particles are specified by two
respective group IDs, which can be defined using the [group](group)
command. The number of atoms in the two groups must be the same and
there should be one bond defined between a pair of atoms in the two
groups. Non-polarized ions which might also be included in the treated
system should not be included into either of these groups, they are
taken into account by the *group-ID* (second argument) of the compute.

The temperature is calculated by the formula

$$\text{KE} = \frac{\text{dim}}{2} N k_B T,$$

where KE is the total kinetic energy of the group of atoms (sum of
$\frac12 m v^2$), dim = 2 or 3 is the dimensionality of the simulation,
$N$ is the number of atoms in the group, $k_B$ is the Boltzmann
constant, and $T$ is the absolute temperature. Note that the velocity of
each core or shell atom used in the KE calculation is the velocity of
the center-of-mass (COM) of the core/shell pair the atom is part of.

A kinetic energy tensor, stored as a six-element vector, is also
calculated by this compute for use in the computation of a pressure
tensor. The formula for the components of the tensor is the same as the
above formula, except that $v^2$ is replaced by $v_x v_y$ for the $xy$
component, and so on. The six components of the vector are ordered $xx$,
$yy$, $zz$, $xy$, $xz$, $yz$. In contrast to the temperature, the
velocity of each core or shell atom is taken individually.

The change this fix makes to core/shell atom velocities is essentially
computing the temperature after a \"bias\" has been removed from the
velocity of the atoms. This \"bias\" is the velocity of the atom
relative to the center-of-mass velocity of the core/shell pair. If this
compute is used with a fix command that performs thermostatting then
this bias will be subtracted from each atom, thermostatting of the
remaining center-of-mass velocity will be performed, and the bias will
be added back in. This means the thermostatting will effectively be
performed on the core/shell pairs, instead of on the individual core and
shell atoms. Thermostatting fixes that work in this way include [fix
nvt](fix_nh), [fix temp/rescale](fix_temp_rescale), [fix
temp/berendsen](fix_temp_berendsen), and [fix langevin](fix_langevin).

The internal energy of core/shell pairs can be calculated by the
[compute temp/chunk](compute_temp_chunk) command, if chunks are defined
as core/shell pairs. See the [Howto coreshell](Howto_coreshell) doc page
for more discussion on how to do this.

## Output info

This compute calculates a global scalar (the temperature) and a global
vector of length 6 (KE tensor), which can be accessed by indices 1\--6.
These values can be used by any command that uses global scalar or
vector values from a compute as input.

The scalar value calculated by this compute is \"intensive\". The vector
values are \"extensive\".

The scalar value will be in temperature [units](units). The vector
values will be in energy [units](units).

## Restrictions

The number of core/shell pairs contributing to the temperature is
assumed to be constant for the duration of the run. No fixes should be
used which generate new molecules or atoms during a simulation.

## Related commands

[compute temp](compute_temp), [compute temp/chunk](compute_temp_chunk)

## Default

none

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

::: {#MitchellFincham1}
**(Mitchell and Fincham)** Mitchell, Fincham, J Phys Condensed Matter,
5, 1031-1038 (1993).
:::