When running FEP, the `alchOutFile` contains electrostatic and van der Waals energy
data calculated for `alchLambda` and `alchLambda2`, written every
`alchOutFreq` steps. The column `dE` is the energy
difference of the single configuration, `dE_avg` and `dG`
are the instantaneous ensemble average of the energy and the calculated
free energy at the time step specified in column 2, respectively.
The temperature is specified in the penultimate column. Upon completion
of `alchEquilSteps` steps, the calculation of `dE_avg` and
`dG` is restarted. The accumulated net free energy change is written
at each lambda value and at the end of the simulation.

Whereas the FEP module of NAMD supplies free energy differences determined from
equation (66), the wealth of information available in `alchOutFile` may be utilized profitably to explore different routes towards the
estimation of
. Both BAR and SOS methods, which combine
advantageously *direct* and *reverse* transformations to improve
convergence and accuracy of the calculation, represent relevant alternatives to
brute-force application of the FEP formula [50].

Within the SOS framework, the free energy difference between states and is expressed as:

and can be readily used with the statistical information provided by the forward and the backward runs.

When running TI free energy calculations, the `elec_dU/dl`,
`vdW_dU/dl`, and `bond_dU/dl` values reported in `alchOutFile`
are the derivatives of the internal energy with respect to the scaling factors
for each interaction type (*i.e.* electrostatics, etc.). `dU/dl` values are
locally averaged over the last `alchOutFreq` steps. Cumulative
averages for each component are reported alongside in the `_avg` columns.

The electrostatic, vdW, and bond values are separated following a partition
scheme -- that is, the ``appearing'' and the ``disappearing'' atoms are
accounted for separately. ``Partition 1'' contains those atoms whose
interactions are switched up as
increases -- *i.e.* flagged with
`1` in the `alchFile`. ``Partition 2'' represents those atoms whose
interactions are switched down as
increases -- *i.e.* flagged with
`-1`.
values for each component are obtained by integrating from
to
using the respective `ELEC / VDW / BOND LAMBDA` listed
for each partition after the title.

**New as of version 2.12:** The output in `alchOutFile` has been
extensively revised and now more closely matches the NAMD standard output.
Additional accounting for bonded term scaling is now also included.

The choice of values will depend on the application, but in general it is important to examine the shape of the curve to ensure that sampling is adequate to give a good estimate of the integral. In particular, it will be necessary to sample more finely towards the end points in order to accurately account for the strong repulsive van der Waals forces encountered when inserting particles into a system (see Figure 10).