Expanded ensemble (EE) mode can be used for calculations of solvation free energies by gradual removal or insertion of molecules in the system. The theory and computational details behind the expanded ensemble method are described in papers (J.Chem.Phys.96, 1776 (1992); Molec.Simulations , 18, 43 (1996)). Details of the current implementation are described in Jämbeck et all, J.Comput.Chem.,34,187 (2013).

The expanded ensemble methodology implemented in MDynaMix from v.5.2.3,
includes the Wang-Landau algorithm,
Wang F., Landau D. P., Phys. Rev. Lett. **86**, P. 2050-2053 (2001)),
for optimization of the balancing factors. Also, from v.5.2.5,
a different scheme of interaction change of the choosen solute molecule
with the rest of the system, based of soft core interaction potentials
(see e.g. L.Luder, R.Kjellander, J.Phys.Chem.B., 110, 15514 (2006)) ,
is implemented. Particularly, the interaction potentials
between all pairs of the solute and solvent atoms are changed with the insertion
parameter ,
according to:

The coupling parameter assumes a number of fixed values between 0 and 1, where ``1'' corresponds to the solute molecule properly inserted in the solvent, while value ``0'' correspons to the fully eliminated solute (which then can be considered as an a gas phase). The program computes probability distribution over subensembles with different values of , from which the free energy difference can be obtained. Additional bias for transition probabilities between subensembles is given by the balancing factors (biased potential over the insertion parameter), which need to be tuned in order to provide reasonable homogenious distribution of probabilities over subensembles. The Wang-Landau procedure is by default used for tuning of the balancing factors, but there is also possibility for manual tuning.

**Note:** Special care should be taken in MDEE simulations of molecules
having zero Lennard-Jones potential for hydrogen atoms (like SPC or TIP3P
water). Simulation may become unstable when repulsive potential between
oxygens becoms weeker while electrostatic attraction between hydrogen and
oxygen still present. It is advisable to prescribe some small Lennard-Jones
potential to such hydrogens.

The expanded ensemble is specified by the following keywords:

`MDEE <num_ensembles> <mode>`

Run expanded ensemble simulations with

`<num_ensembles>`

subensembles, Parameter`<mode>`

can be ```auto`

'' ( poins are set with equal separation between them within the [0:1] interval, and balancing factors are tuned automatically by ```WL`

'' ( points are specified by the user while balancing factors are optimized by the Wang-Landau procedure, or ```manual`

'' (manual setup of EE parameters).In the case of

`manual`

or`WL`

mode the`MDEE`

command should be followed by exactly`num_ensembles`

lines, with two number on each: the value of coupling parameter and balancing factor, corresponding to this subensemble. Values of balancing factors are given per inserted molecule in units of ``''.In the case of automatic setup of the expanded ensemble parameters, the set of coupling parameters is choosen uniformly in the range [0:1] (that is, where is the total number of subensembles

`<num_ensembles>`

.Default mode:

`auto`

In the case of automatic optimization of the balancing factors (mode

`auto`

or`WL`

), additional keywords can be used:`EE_typ <i_typ>`

Specifies that the molecules of type

`i_typ`

are those which are inserted/deleted in the EE procedure.**This keyword is required!**`Num_pass <value>`

Defines how many times the system should walk between the extreme subemsembles and back in order to complete one WL iteration. Default is 2.

`Num_WL <value>`

Defines the number of WL iterations. After this number of WL iterations is carried out, the optimization of balancing factors is completed, and the program proceeds with EE procedure with fixed balancing factors. Default is 10 iteration.

`WL_parameters <increment> <factor>`

Sets up initial increment in the Wang-Landau optimization of balancing factors, and scaling factor by which the increment is scaled after each WL iteration.

Default values:

`increment = 0.1`

,`factor = 0.5`

.In case of automatic WL tuning of the balancing factors (mode

`auto`

) the program starts expanded ensemble simulation with zero balancing factors. In case of mode`WL`

the initial values of the balancing factors are introduced from the input. After each attempt of visiting a subensemble, an increment is added to the corresponding balancing factor. After walking between extreme subensembles at least`Num_pass`

times, a WL series (sweep) finishes and the value of the increment is decreased by a factor (default value 0.5, see keyword`WL_parameters`

).**Notes:**1. If WL procedure has not performed necessary number of iterations (keyword

`Num_WL`

), the program gives warning in the output ``Expanded ensemble simulation not converged yet''. Then the computed free energy values may not be accurate or not relevant et all. It is always recommended to continue simulation long enough after the balancing factors are optimized.2. While evaluating results, ensure that the system has walked at least several times between the extreme subensembles (the first and the last). Look at the ``table of transition'' in the end of the output.

3. Pay attention at the acceptance ratios for transitions between subensembles, they can be found in the last two columns of the section ``Distribution over subensembles'' in the output. The acceptance ratios should not be too low. If they are too low (a few percent or less), the number of subensembles should be increased.

`EE_start-in <start_in>`

Start EE simulation in subensemble number

`<start_in>`

. Default: in the last subensemble (that is, with completely deleted EE molecule(s))`EE_freq <steps>`

Try EE transition after`steps`

MD steps.Default: 10

`EE_new`

Change balancing factors after restart (manual mode only). Otherwise the old values written in the restart file are used.

`EE_offset <b-value>`

Value of parameter in equation (12)

Default: .

`EE_power <w1> <w2>`

Values of parameters and in equation (12)

Default: ; .

`Probability_threshold <P_low>`

Assing value`P_low`

to computed subensembles probabilities which are lower than this numberDefault: 0.001