Modeling Kinetics and Thermodynamics of Guest Encapsulation into the [M4L6]12– Supramolecular Organometallic Cage

The encapsulation of molecular guests into supramolecular hosts is a complex molecular recognition process in which the guest displaces the solvent from the host cavity, while the host deforms to let the guest in. An atomistic description of the association would provide valuable insights on the physicochemical properties that guide it. This understanding may be used to design novel host assemblies with improved properties (i.e., affinities) toward a given class of guests. Molecular simulations may be conveniently used to model the association processes. It is thus of interest to establish efficient protocols to trace the encapsulation process and to predict the associated magnitudes ΔGbind and ΔGbind⧧. Here, we report the calculation of the Gibbs energy barrier and Gibbs binding energy by means of explicit solvent molecular simulations for the [Ga4L6]12– metallocage encapsulating a series of cationic molecules. The ΔGbind⧧ for encapsulation was estimated by means of umbrella sampling simulations. The steps involved were identified, including ion-pair formation and naphthalene rotation (from L ligands of the metallocage) during the guest’s entrance. The ΔGbind values were computed using the attach–pull–release method. The results reveal the sensitivity of the estimates on the force field parameters, in particular on atomic charges, showing that higher accuracy is obtained when charges are derived from implicit solvent quantum chemical calculations. Correlation analysis identified some indicators for the binding affinity trends. All computed magnitudes are in very good agreement with experimental observations. This work provides, on one side, a benchmarked way to computationally model a highly charged metallocage encapsulation process. This includes a nonstandard parameterization and charge derivation procedure. On the other hand, it gives specific mechanistic information on the binding processes of [Ga4L6]12– at the molecular level where key motions are depicted. Taken together, the study provides an interesting option for the future design of metal–organic cages.


Behavior of the metallocage 1 in solution
(a) (b) Figure S1. Optimized geometries of (a) metallocage, 1, and (b) NEt4 + encapsulated in the metallocage with implicit solvent. In both cases, 11 K + ions (purple spheres) were added explicitly in order to neutralize the system. Figure S2. The number of K + < 11 Å from the center of mass of the metallocage 1 during classical molecular dynamic simulation. Figure S3. Cavity volume of the 2  1 system in water solvent. Figure S4. Plot of the computed vs experimental binding Gibbs energies.

Correlations for binding energies
S4 Figure S5. Correlation between binding Gibbs energy and the cavity volume of the metallocage of the host-guest complexes.      Figure S9. Cavity volumes and packing coefficients of the metallocage during the encapsulation process. Figure S10. Snapshot of the most populated structure of the encapsulated state of 6  1 complex from APR simulations for binding free energy calculations Figure S11. Calculated ESP centers (yellow dots) obtained from QM ESP calculation.

APR simulation detail and setup
MD simulations in each APR window: 1. Minimizing 50000 cycles, 2. Running 1ps NVT at 10 K, 3. Heating the system from 10 K to 298.15 K in 100 ps, 4. Equilibrating the system under constant pressure, 50 NPT cycle, 5. NPT Production from 2.5 ns to 25 ns depending on the standard error of the mean (SEM) of the restraint forces, the SEM threshold is 0.100.
The cutoff for non-bonding interactions: 9 Å The approach employed for computing the electrostatic forces and potential: The Particle Mesh Ewald (PME) method The type of thermostat: Langevin The type of barostat: Monte Carlo The time step: 4 fs (hydrogen mass repartitioning was used) S9 Figure S12. Schematic representation of the APR simulations in this study. Table S3. Comparison between calculated binding Gibbs energies of the NEt4 + in the metallocage obtained using atomic charges derived with implicit solvent and without implicit solvent.

Charge derivation in implicit solvent vacuum
Calculated ∆G o bind -6.3 ± 0.6 2.7 ± 0.5 Experimental ∆G o bind -6.2 ± 0.01 Figure S13. The number of K + in less than 5 Å from the center of mass of the metallocage during 400 ns classical molecular dynamic simulation of the metallocage.

6.2%
The number of K + in < 5 Å from COM of metallocage S10 (a ) ( b ) Figure S14. The number of K + in less than 5 Å from the center of mass of the metallocage (a) during umbrella sampling simulations and (b) during the APR simulations.