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Expanded Ensemble mode

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). Update 5.3.1 implements L2MC algorithm for Monte Carlo transitions between subensembles (Nikitin et al., J.Comp.Chem., 42, 787 (2021))

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 $\alpha$, $0 \le \alpha \le 1$ according to:


$\displaystyle V^{Ss}(\alpha,r)$ $\textstyle =$ $\displaystyle \alpha^{w1} \left[ 4 \varepsilon \left( \left(\frac{\sigma}{r+b(1... ...\right)^{12}- \left(\frac{\sigma}{r+b(1-\alpha^{w2})}\right)^6\right) + \right.$  
    $\displaystyle + \left. \frac{q_i q_j}{4 \pi \epsilon_0 (r+b(1-\alpha^{w2}))} \right]$ (12)

The coupling parameter $\alpha$ 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 $\alpha$, 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:

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