# Slow-growth approach

The free-energy profile along a geometric parameter can be scanned by an approximate slow-growth
approach^{[1]}.
In this method, the value of is linearly changed
from the value characteristic for the initial state (1) to that for
the final state (2) with a velocity of transformation
.
The resulting work needed to perform a transformation
can be computed as:

In the limit of infinitesimally small , the work
corresponds to the free-energy difference between the the final and initial state.
In the general case, is the irreversible work related
to the free energy via Jarzynski's identity^{[2]}:

Note that calculation of the free-energy via this equation requires
averaging of the term
over many realizations of the
transformation.
Detailed description of the simulation protocol that employs Jarzynski's identity
can be found in reference ^{[3]}.

## Anderson thermostat

- For a slow-growth simulation, one has to perform a calcualtion very similar to Constrained molecular dynamics but additionally the transformation velocity-related INCREM-tag for each geometric parameter with
`STATUS=0`has to be specified. For a slow-growth approach run with Andersen thermostat, one has to:

- Set the standard MD-related tags: IBRION=0, TEBEG, POTIM, and NSW
- Set MDALGO=1, and choose an appropriate setting for ANDERSEN_PROB
- Define geometric constraints in the ICONST-file, and set the STATUS parameter for the constrained coordinates to 0
- When the free-energy gradient is to be computed, set LBLUEOUT=.TRUE.

- Specify the transformation velocity-related INCREM-tag for each geometric parameter with
`STATUS=0`.

## Nose-Hoover thermostat

- For a slow-growth approach run with Nose-Hoover thermostat, one has to:

- Set the standard MD-related tags: IBRION=0, TEBEG, POTIM, and NSW
- Set MDALGO=2, and choose an appropriate setting for SMASS
- Define geometric constraints in the ICONST-file, and set the
`STATUS`parameter for the constrained coordinates to 0 - When the free-energy gradient is to be computed, set LBLUEOUT=.TRUE.

- Specify the transformation velocity-related INCREM-tag for each geometric parameter with
`STATUS=0`

VASP can handle multiple (even redundant) constraints. Note, however, that a too large number of constraints can cause problems with the stability of the SHAKE algorithm. In problematic cases, it is recommended to use a looser convergence criterion (see SHAKETOL) and to allow a larger number of iterations (see SHAKEMAXITER) in the SHAKE algorithm. Hard constraints may also be used in metadynamics simulations (see MDALGO=11 | 21). Information about the constraints is written onto the REPORT-file: check the lines following the string: `Const_coord`