Characterization of the Coordination and Solvation Dynamics of Solvated Systems—Implications for the Analysis of Molecular Interactions in Solutions and Pure H2O

The characterization of solvation shells of atoms, ions, and molecules in solution is essential to relate solvation properties to chemical phenomena such as complex formation and reactivity. Different definitions of the first-shell coordination sphere from simulation data can lead to potentially conflicting data on the structural properties and associated ligand exchange dynamics. The definition of a solvation shell is typically based on a given threshold distance determined from the respective solute–solvent pair distribution function g(r) (i.e., GC). Alternatively, a nearest neighbor (NN) assignment based on geometric properties of the coordination complex without the need for a predetermined cutoff criterion, such as the relative angular distance (RAD) or the modified Voronoi (MV) tessellation, can be applied. In this study, the effect of different NN algorithms on the coordination number and ligand exchange dynamics evaluated for a series of monatomic ions in aqueous solution, carbon dioxide in aqueous and dichloromethane solutions, and pure liquid water has been investigated. In the case of the monatomic ions, the RAD approach is superior in achieving a well separated definition of the first solvation layer. In contrast, the MV algorithm provides a better separation of the NNs from a molecular point of view, leading to better results in the case of solvated CO2. When analyzing the coordination environment in pure water, the cutoff-based GC framework was found to be the most reliable approach. By comparison of the number of ligand exchange reactions and the associated mean ligand residence times (MRTs) with the properties of the coordination number autocorrelation functions, it is shown that although the average coordination numbers are sensitive to the different definitions of the first solvation shell, highly consistent estimates for the associated MRT of the solvated system are obtained in the majority of cases.

1 Supporting Information           S4: Number of first shell ligand exchange events N 0.5 ex in ps −1 registered with minimum excursion time of t * = 0.5 ps per simulation time and the associated rate coefficient R ex determined for CO 2 in aqueous and DCM solution via the direct method [4]

Fig. S1 :
Fig. S1: Radial distribution functions of Li + -O H 2 O pairs considering the entire RDF (black) along with the respective segmentation into the first solvation shell (red) and the remaining solvent (blue) based on the a) GC, b) RAD, c) RAD open and d) MV nearest neighbour algorithms, respectively.To improve the visibility, the total RDF is displayed at an offset of +3.

Fig. S2 :
Fig. S2: Radial distribution functions of Na + -O H 2 O pairs considering the entire RDF (black) along with the respective segmentation into the first solvation shell (red) and the remaining solvent (blue) based on the a) GC, b) RAD, c) RAD open and d) MV nearest neighbour algorithms, respectively.To improve the visibility, the total RDF is displayed at an offset of +3.

Fig. S3 :
Fig. S3: Radial distribution functions of F − -O H 2 O pairs considering the entire RDF (black) along with the respective segmentation into the first solvation shell (red) and the remaining solvent (blue) based on the a) GC, b) RAD, c) RAD open and d) MV nearest neighbour algorithms, respectively.To improve the visibility, the total RDF is displayed at an offset of +3.

Fig. S4 :
Fig. S4: Radial distribution functions of Cl − -O H 2 O pairs considering the entire RDF (black) along with the respective segmentation into the first solvation shell (red) and the remaining solvent (blue) based on the a) GC, b) RAD, c) RAD open and d) MV nearest neighbour algorithms, respectively.To improve the visibility, the total RDF is displayed at an offset of +3.

Fig. S5 :
Fig. S5: Overlap area resulting from the segmented ion-O pair distribution functions as well as the cumulative overlap area (dashed lines) determined via trapezoidal integration for aqueous Li + , Na + , K + , F − , Cl − and Br − resulting from the RAD (black), RAD open (red) and MV (blue) nearest neighbour algorithm, respectively.

Fig. S6 :
Fig. S6: Coordination number autocorrelation function C CN (t) determined for a) F − b) Cl − c) Br − in aqueous solution and d) CO 2 in DCM obtained using the GC (black), RAD (red), RAD open (blue) and MV (green) nearest neighbour algorithm.

Fig. S7 :
Fig. S7: Example configuration taken from the MD simulation trajectory of aqueous CO 2 with five water molecules interacting with the positively charged central carbon atom via chargedipole interactions shown in red.When considering the water molecule in proximal position of CO 2(blue) at a distance of r ij , the five closer ligands are considered at distances labelled as r ik according to the RAD approach (see eq. 1 of the main manuscript).Depending on the angle θ jik , the proximal ligand may be excluded from the nearest neighbour assignment in the RAD algorithm due to the large difference between r 2 ij and r 2 ik .

Fig. S9 :
Fig. S9: Density profile of water resulting from the NPT-based MD simulation carried out at the DFTB3/3obwp level of theory (black) and the associated fit to a skewed normal distribution (red).The value for the experimental density 0.997 kg dm −3 is shown as the vertical line (green).

Fig. S10 :
Fig. S10: Average coordination number determined for each of the 250 water molecules in the system based on the GC (black), RAD (red), RAD open (blue) and MV (brown) nearest neighbour algorithm.The respective averages over all water molecules are shown as horizontal lines.

Table S1 :
Pearson and Spearman rank correlation coefficients determined for different combinations of the GC, RAD, RAD open and MV nearest neighbour algorithms in case of aqueous Li + , Na + , K + , F − , Cl − and Br − , respectively.Ion correlation coefficient GC-RAD GC-RAD open GC-MV RAD-RAD open RAD-MV RAD open -MV

Table S2 :
Cumulative area determined via trapezoidal integration of the overlap in the segmented ion-O pair distribution functions for aqueous Li + , Na + , K + , F − , Cl − and Br − resulting from the RAD, RAD open and MV nearest neighbour algorithm, respectively.Ion Area RAD Area RADopen Area MV

Table S3 :
Total number of first shell ligand exchange events N 0.0 ex in ps −1 for aqueous Li + , Na + , K + , F − , Cl − and Br − registered for t * = 0.0 per simulation time resulting from the GC, RAD, RAD open and MV nearest neighbour algorithm, respectively.

Table S5 :
resulting from the GC, RAD, RAD open and MV nearest neighbour algorithm, respectively.Total number of first shell ligand exchange events N 0.0 ex in ps −1 for CO 2 in aqueous and DCM solution as well as pure water registered for t * = 0.0 per simulation time resulting from the GC, RAD, RAD open and MV nearest neighbour algorithm, respectively.

Table S6 :
Relaxation time τ CN in ps obtained from the integration of the coordination number autocorrelation function of aqueous Li + , Na + , K + , F − , Cl − and Br − using the GC, RAD, RAD open and MV algorithm, respectively.

Table S7 :
Relaxation time τ CN in ps obtained from the integration of the coordination number autocorrelation function of CO 2 in H 2 O and DCM solution using the GC, RAD, RAD open and MV algorithm, respectively.CO 2 in H 2 O CO 2 in DCM

Table S8 :
Relaxation time τ CN in ps obtained from the integration of the coordination number autocorrelation function, pre-exponential fit factor N as well as short-time, long-time and effective decay constants τ s , τ l and τ ef f determined from the DFTB3 MD simulation of pure water using the GC, RAD, RAD open and MV algorithm, respectively.