Do Keggin anions repulse each other in solution? The effect of solvent, counterions and ion representation investigated by free energy (PMF) simulations

Abstract

To investigate whether polyoxometallate a-PW 12 O 40 3À Keggin anions (noted PW 3À ) repulse each other in water, we calculated the changes in free energy DG(d) as a function of the P. . .P distance d (potential of mean force ''PMF'' calculations). As the anions approach each other, the free energy profiles are found to be quite flat, with a tiny minimum at ca. 11 A ˚, showing that the anions can form ''contact ion pairs'' in the presence of either H 3 O + , UO 2 2+ or Eu 3+ counterions. The results obtained with different methodological variants (water models, PW 3À charge models, sampling procedures) support our previous finding that PW 3À ions can form dimers or oligomers in water (A. Chaumont and G. Wipff (2008) [13]). The importance of stabilizing bridging water molecules and solute granularity is demonstrated by comparing PW 3À to S 3À spherical analogues and to PW 3+ cations (with all atomic charges of PW 3À inverted). With these analogues, a somewhat repulsive behavior (ca +2 to 3 kcal/mol) is observed at short distances. The role of water is further demonstrated by comparing PMFs in water and in methanol solution where there is no contact ion pair, but a free energy minimum at ca. 17 A ˚, corresponding to an ion separated pair PW 3À . . .Eu(MeOH) 9 3+. . .PW 3À . These findings are important for understanding processes like condensation and assembling of POMs and macro-ions in water or at aqueous interfaces.

Elucidating the Origin of the Attractive Force among Hydrophilic Macroions

“…Systems with macroions having less than six charged beads on the surface did not show any sign of big aggregates formation, though small aggregates such as dimers or trimers were observed as the number of charged beads on the surfaces of the macroions increased. Similar small size aggregates were also observed in atomistic MD simulations of the self-assembly of smaller size Keggin anions using Amber force field, in which the counterions were found to be distributed between Keggin anions in order to mediate the formation of small aggregates 22 23 . For those charge densities, the electrostatic forces on the macroions were several times larger than the van der Waals forces but were not strong enough to keep several macroions together.…”

“…Information on the self-assembly of macroions in solution is expected to come primarily from molecular dynamics (MD) simulations. However, very few MD simulations of macroions and their interactions with counterions and other macroions have been reported 18 19 20 21 22 23 . This is mainly due to the large and complex structures of the macroions, which makes the development of a force field for an all-atom MD simulation of the macroions very difficult.…”

Self‐Assembly of Subnanometer‐Scaled Polyhedral Oligomeric Silsesquioxane (POSS) Macroions in Dilute Solution

“…Moreover, the previous study proved the existence of water‐bridged hydrogen bonding as an auxiliary driving force for blackberry formation to strengthen the interaction between macroions 21. Wipff et al conducted detailed theoretical simulations on the changes in free energy as a function of the distance of the inter‐POM macroions and demonstrated the importance of stabilizing bridging water molecules by comparing the Keggin anion (PW 3– ) to its spherical analogues (S 3– ) and to Keggin cations (PW 3+ ) 22. The results showed that the specific water‐bridged hydrogen bonds in the dimer of Keggin anions were much stronger than the non‐specific ones in the dimer of S 3– .…”

Interactions between Keggin Anions in Water: The Higher Their Charge, the Higher Their Condensation? A Simulation Study

“…In a subsequent MD study, we calculated the change in free energy Δ G ( d ) upon anion association, i.e., as the P ··· P distance d is decreased from ca. 18 to 10 Å [potential of mean force (PMF) simulations] 20. In fact, the free energy profiles were quite flat, which indicates that the –3 charged anions can approach each other without energy penalty in water.…”