\(\renewcommand{\AA}{\text{Å}}\)

# compute temp/cs command

## Syntax

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

ID, group-ID are documented in 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

```
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). See the 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 (e.g., fix temp/rescale, fix npt).

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 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

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 symmetric tensor, stored as a six-element vector, is also calculated by this compute for use in the computation of a pressure tensor by the compute pressue command. The formula for the components of the tensor is the same as the above expression for \(E_\mathrm{kin}\), except that the 1/2 factor is NOT included and the \(v_i^2\) is replaced by \(v_{i,x} v_{i,y}\) for the \(xy\) component, and so on. Note that because it lacks the 1/2 factor, these tensor components are twice those of the traditional kinetic energy tensor. The six components of the vector are ordered \(xx\), \(yy\), \(zz\), \(xy\), \(xz\), \(yz\).

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 temp/rescale, fix temp/berendsen, and fix langevin.

The internal energy of core/shell pairs can be calculated by the compute temp/chunk command, if chunks are defined as core/shell pairs. See the 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 (symmetric 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 is in temperature units. The vector values are in energy 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.

## Default

none

**(Mitchell and Fincham)** Mitchell, Fincham, J Phys Condensed Matter,
5, 1031-1038 (1993).