Supporting information for: The solvation structure of Mg ions in ...
Supporting information for: The solvation structure of Mg ions in dichloro-complex solutions from first-principles molecular dynamics and simulated X-ray absorption spectra L. F. Wan∗ and David Prendergast Joint Center for Energy Storage Research (JCESR), The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 E-mail: [email protected]
Van der Waals interactions The impact of van der Waals dispersion forces on the solvation structure of Mg ions is examined using the vdW-DF2 functional, S1 as implemented in VASP. Here, we place a hexacoordinated Mg, in the form of MgCl2 ·4THF, in THF solution and perform a firstprinciples molecular dynamics (FPMD) simulation at 300 K. The initial structure is shown in Figure S1 (left). During equilibration, the Mg ion quickly sheds two of the coordinating THF molecules (within 0.3 ps) and remains tetracoordinated by two Cl− and two THFs for the rest of the 15 ps FPMD trajectory. The average bond lengths for Mg-Cl and Mg∗
To whom correspondence should be addressed
S1
O (THF) are approximately 2.3 and 2.0 ˚ A, respectively, which is in agreement with the solvation structure predicted by the PBE-GGA functional. Although van der Waals dispersion forces have negligible impact on the solvation structure of the Mg ion, they do enhance solvent-solvent interactions. In this work, the THF pairwise interactions are first estimated by considering the optimized isolated dimer structure (presented in Figure S2 for the vdW-DF2 functional). The obtained self-interaction energy is -0.13 eV/pair (-0.06 eV/pair) when using the vdW-DF2 (PBE) functional. In the solution phase, the self-interaction energy is estimated by considering the average potential energy difference per molecule between an FPMD snapshot comprising 25 THF molecules in a 15˚ A × 15˚ A × 15˚ A box, and an isolated THF molecule. The resulting self-interaction energy is -0.11 eV/THF (-0.05 eV/THF) for the vdW-DF2 (PBE) functional. Using either functional, the THF self-interaction energy is much weaker than the Mg-THF coordination energy, as discussed in the main text.
Figure S1: Initial (left) and equilibrated (right) MgCl2 /THF solvation structure, simulated using the vdW-DF2 functional. The black box indicates the periodic boundaries.
S2
Figure S2: DFT optimized structure for THF pair.
Equilibrated MgCl2/THF structure The energies to preserve six-fold coordination of Mg ion in MgCl2 · 4THF cluster is compared for three different DFT optimization scheme. In Figure S3 (a), the structure of MgCl2 · 4THF is fully optimized using the empirical Universal Force Field (UFF) model. The resulting molecular structure maintains octahedral coordination of Mg. The optimized UFF bond length for Mg-Cl is approximately 2.38 ˚ A and for Mg-O, it varies from 2.25 to 2.36 ˚ A. In Figure S3 (b), the octahedral symmetry of the central Mg ion is enforced by a symmetry constraint and the PBE total energy is minimized resulting in constrained-equilibrium bond lengths for Mg-Cl and Mg-O of 2.44 and 1.97 ˚ A, respectively. If this symmetry restriction is removed, further optimization causes one THF molecule to be pushed out of the first solvation shell so that the system can reach the lowest energy state, as shown in Figure S3 (c). The obtained Mg-Cl bond length is 2.33 ˚ A and 2.10 to 2.23 ˚ A for Mg-O, which is very similar to the optimized MgCl2 · 3THF structure. The corresponding PBE formation energy for each of these scenarios is calculated and compared in Figure S3. Not very surprisingly, the equilibrium UFF structure resides at a much higher energy compared to the PBE-GGA predicted minima (Figure S3 (b) and (c)), most likely due to the extended Mg-O bond lengths. Within PBE, the energy cost to preserve octahedral symmetry is ∼ 0.6 eV. Overall, in order to maintain the octahedral symmetry of Mg, all the ligands have to coordinate while simultaneously avoiding any overlap between their electronic orbitals. Using more sophisticated force field, such as optimized potentials for liquid simulations
S3
Figure S3: Structure of MgCl2 · 4THF using different optimization schemes: (a) Universal Force Field; (b) DFT with constraint octahedral symmetry; and (c) DFT with no symmetry constraint. Indicated relative energies with respect to (b) are computed using DFT-PBE all-atom force field (OPLS-AA), S2 also produce a six-fold coordination structure for Mg. Here, one MgCl2 ·THF cluster is embedded in 51 THF molecules and the system is equilibrated at 300 K using the LAMMPS code. S3 The obtained equilibrium structure is presented in Figure S4. In contrast to ab initio MD, the OPLS-AA classical force field results in a stable octahedral coordination of the Mg2+ ion. The Cl-Mg-Cl bond is almost linear and the average bond length is approximately 2.3 ˚ A. This bond length is similar to the DFT predicted value, although in DFT, the Cl-Mg-Cl bond angle is reduced to 140◦. The Mg-O bonds, on the other hand, are much longer compared to the DFT results. At this moment, it is not clear why the OPLS-AA force field fails to reproduce the DFT predicted Mg solvation structure or what essential physics are missing in the current OPLS-AA parameters. However, based on this preliminary study, we argue for caution and validation when studying such systems using classical force fields based on empirical interaction potentials and fixed electrostatic charges.
Ab initio MD simulation for [Mg2Cl3·6THF]+(AlCl3Et) A comparison of the experimental XRD-determined and FPMD-simulated [Mg2 Cl3 ·6THF]+ (AlCl3 Et) structure is given in Figure S5. The radial distribution function, g(r), is calculated and plot-
S4
Figure S4: Equilibrated MgCl2 /THF structure, simulated using the OPLS-AA force field. The black box indicates the periodic boundaries. There is only one Mg ion per unit cell. To visualize the integrity of the MgCl2 ·THF cluster, additional periodic images across the cell boundaries are also shown. The radial distribution function is averaged for 1.5 ns. ted in Figure S6 based on both structures. Compared to the static XRD structure, our MD simulated g(r) shows a significant broadening for both Mg-Cl and Mg-O peaks, while the center of the peak remains at the experimental value. In addition, the EXAFS spectra are simulated and averaged for 5 snapshots that are taken from our MD simulation (8 independent scattering event per snapshot). The k 3 weight χ(k) function is plotted in the inset of Figure S7 and the Fourier transformed k 3 χ(k) function is represented as the black line. The peak at R = 1.85 ˚ A corresponding to the nearest Mg-O distance, and the peak at R = 1.85 ˚ A is the Mg-Cl bond. Compared to the liquid phase, as shown in Figure 8 in the main text, the two peaks representing Mg-O and Mg-Cl bonds are clearly separated in this solid phase, whereas in the liquid MgCl2 /THF phase, these two peaks emerge into one. The peaks at R ≈ 3 and 4 ˚ A represents Mg-H and Mg-C distances.
S5
Figure S5: The crystal structure of [Mg2 Cl3 ·6THF]+ (AlCl3 Et). Side views of the experimentally identified [Mg2 Cl3 ·6THF]+ (AlCl3 Et) structure (a) along the a-axis and (b) b-axis. The Mg and Al cations are shown as orange and light blue spheres and Cl and O anions are marked in green and red, respectively, H atoms in off-white. (c) The obtained equilibrium structure from our MD simulation.
References (S1) Lee, K.; Murray, E. D.; Kong, L.; Lundqvist, B. I.; Langreth, D. C. Phys. Rev. B 2010, 82, 081101. (S2) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. J. Am. Chem. Soc. 1996, 118, 11225. (S3) Plimpton, S. J. Comp. Phys 1995, 117, 1.
S6
Figure S6: Radial distribution function for experimentally determined and MD simulated [Mg2 Cl3 ·6THF]+ (AlCl3 Et) crystals. The dashed lines indicate the integrated g(r) values from our MD simulations. An artificial broadening, 0.05 ˚ A, is provided for the XRD structural peaks.
Figure S7: Calculated Mg K-edge EXAFS spectrum for [Mg2 Cl3 ·6THF]+ (AlCl3 Et) crystal. The black curve is the total scattering for the atoms within 5.5 ˚ A distance from the absorbing 3 Mg atom. Inset is the k weighted χ(k) spectrum in k−space.
S7
Van der Waals interactions The impact of van der Waals dispersion forces on the solvation structure of Mg ions is examined using the vdW-DF2 functional, S1 as implemented in VASP. Here, we place a hexacoordinated Mg, in the form of MgCl2 ·4THF, in THF solution and perform a firstprinciples molecular dynamics (FPMD) simulation at 300 K. The initial structure is shown in Figure S1 (left). During equilibration, the Mg ion quickly sheds two of the coordinating THF molecules (within 0.3 ps) and remains tetracoordinated by two Cl− and two THFs for the rest of the 15 ps FPMD trajectory. The average bond lengths for Mg-Cl and Mg∗
To whom correspondence should be addressed
S1
O (THF) are approximately 2.3 and 2.0 ˚ A, respectively, which is in agreement with the solvation structure predicted by the PBE-GGA functional. Although van der Waals dispersion forces have negligible impact on the solvation structure of the Mg ion, they do enhance solvent-solvent interactions. In this work, the THF pairwise interactions are first estimated by considering the optimized isolated dimer structure (presented in Figure S2 for the vdW-DF2 functional). The obtained self-interaction energy is -0.13 eV/pair (-0.06 eV/pair) when using the vdW-DF2 (PBE) functional. In the solution phase, the self-interaction energy is estimated by considering the average potential energy difference per molecule between an FPMD snapshot comprising 25 THF molecules in a 15˚ A × 15˚ A × 15˚ A box, and an isolated THF molecule. The resulting self-interaction energy is -0.11 eV/THF (-0.05 eV/THF) for the vdW-DF2 (PBE) functional. Using either functional, the THF self-interaction energy is much weaker than the Mg-THF coordination energy, as discussed in the main text.
Figure S1: Initial (left) and equilibrated (right) MgCl2 /THF solvation structure, simulated using the vdW-DF2 functional. The black box indicates the periodic boundaries.
S2
Figure S2: DFT optimized structure for THF pair.
Equilibrated MgCl2/THF structure The energies to preserve six-fold coordination of Mg ion in MgCl2 · 4THF cluster is compared for three different DFT optimization scheme. In Figure S3 (a), the structure of MgCl2 · 4THF is fully optimized using the empirical Universal Force Field (UFF) model. The resulting molecular structure maintains octahedral coordination of Mg. The optimized UFF bond length for Mg-Cl is approximately 2.38 ˚ A and for Mg-O, it varies from 2.25 to 2.36 ˚ A. In Figure S3 (b), the octahedral symmetry of the central Mg ion is enforced by a symmetry constraint and the PBE total energy is minimized resulting in constrained-equilibrium bond lengths for Mg-Cl and Mg-O of 2.44 and 1.97 ˚ A, respectively. If this symmetry restriction is removed, further optimization causes one THF molecule to be pushed out of the first solvation shell so that the system can reach the lowest energy state, as shown in Figure S3 (c). The obtained Mg-Cl bond length is 2.33 ˚ A and 2.10 to 2.23 ˚ A for Mg-O, which is very similar to the optimized MgCl2 · 3THF structure. The corresponding PBE formation energy for each of these scenarios is calculated and compared in Figure S3. Not very surprisingly, the equilibrium UFF structure resides at a much higher energy compared to the PBE-GGA predicted minima (Figure S3 (b) and (c)), most likely due to the extended Mg-O bond lengths. Within PBE, the energy cost to preserve octahedral symmetry is ∼ 0.6 eV. Overall, in order to maintain the octahedral symmetry of Mg, all the ligands have to coordinate while simultaneously avoiding any overlap between their electronic orbitals. Using more sophisticated force field, such as optimized potentials for liquid simulations
S3
Figure S3: Structure of MgCl2 · 4THF using different optimization schemes: (a) Universal Force Field; (b) DFT with constraint octahedral symmetry; and (c) DFT with no symmetry constraint. Indicated relative energies with respect to (b) are computed using DFT-PBE all-atom force field (OPLS-AA), S2 also produce a six-fold coordination structure for Mg. Here, one MgCl2 ·THF cluster is embedded in 51 THF molecules and the system is equilibrated at 300 K using the LAMMPS code. S3 The obtained equilibrium structure is presented in Figure S4. In contrast to ab initio MD, the OPLS-AA classical force field results in a stable octahedral coordination of the Mg2+ ion. The Cl-Mg-Cl bond is almost linear and the average bond length is approximately 2.3 ˚ A. This bond length is similar to the DFT predicted value, although in DFT, the Cl-Mg-Cl bond angle is reduced to 140◦. The Mg-O bonds, on the other hand, are much longer compared to the DFT results. At this moment, it is not clear why the OPLS-AA force field fails to reproduce the DFT predicted Mg solvation structure or what essential physics are missing in the current OPLS-AA parameters. However, based on this preliminary study, we argue for caution and validation when studying such systems using classical force fields based on empirical interaction potentials and fixed electrostatic charges.
Ab initio MD simulation for [Mg2Cl3·6THF]+(AlCl3Et) A comparison of the experimental XRD-determined and FPMD-simulated [Mg2 Cl3 ·6THF]+ (AlCl3 Et) structure is given in Figure S5. The radial distribution function, g(r), is calculated and plot-
S4
Figure S4: Equilibrated MgCl2 /THF structure, simulated using the OPLS-AA force field. The black box indicates the periodic boundaries. There is only one Mg ion per unit cell. To visualize the integrity of the MgCl2 ·THF cluster, additional periodic images across the cell boundaries are also shown. The radial distribution function is averaged for 1.5 ns. ted in Figure S6 based on both structures. Compared to the static XRD structure, our MD simulated g(r) shows a significant broadening for both Mg-Cl and Mg-O peaks, while the center of the peak remains at the experimental value. In addition, the EXAFS spectra are simulated and averaged for 5 snapshots that are taken from our MD simulation (8 independent scattering event per snapshot). The k 3 weight χ(k) function is plotted in the inset of Figure S7 and the Fourier transformed k 3 χ(k) function is represented as the black line. The peak at R = 1.85 ˚ A corresponding to the nearest Mg-O distance, and the peak at R = 1.85 ˚ A is the Mg-Cl bond. Compared to the liquid phase, as shown in Figure 8 in the main text, the two peaks representing Mg-O and Mg-Cl bonds are clearly separated in this solid phase, whereas in the liquid MgCl2 /THF phase, these two peaks emerge into one. The peaks at R ≈ 3 and 4 ˚ A represents Mg-H and Mg-C distances.
S5
Figure S5: The crystal structure of [Mg2 Cl3 ·6THF]+ (AlCl3 Et). Side views of the experimentally identified [Mg2 Cl3 ·6THF]+ (AlCl3 Et) structure (a) along the a-axis and (b) b-axis. The Mg and Al cations are shown as orange and light blue spheres and Cl and O anions are marked in green and red, respectively, H atoms in off-white. (c) The obtained equilibrium structure from our MD simulation.
References (S1) Lee, K.; Murray, E. D.; Kong, L.; Lundqvist, B. I.; Langreth, D. C. Phys. Rev. B 2010, 82, 081101. (S2) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. J. Am. Chem. Soc. 1996, 118, 11225. (S3) Plimpton, S. J. Comp. Phys 1995, 117, 1.
S6
Figure S6: Radial distribution function for experimentally determined and MD simulated [Mg2 Cl3 ·6THF]+ (AlCl3 Et) crystals. The dashed lines indicate the integrated g(r) values from our MD simulations. An artificial broadening, 0.05 ˚ A, is provided for the XRD structural peaks.
Figure S7: Calculated Mg K-edge EXAFS spectrum for [Mg2 Cl3 ·6THF]+ (AlCl3 Et) crystal. The black curve is the total scattering for the atoms within 5.5 ˚ A distance from the absorbing 3 Mg atom. Inset is the k weighted χ(k) spectrum in k−space.
S7
