Supporting Information for âFrustrated Solvation Structures Can ...
Supporting Information for “Frustrated Solvation Structures Can Enhance Electron Transfer Rates” Richard C. Remsing,∗,†,¶ Ian G. McKendry,‡,¶ Daniel R. Strongin,‡,¶ Michael L. Klein,†,¶ and Michael J. Zdilla‡,¶ †Institute for Computational Molecular Science, Temple University, Philadelphia, PA 19122 ‡Department of Chemistry, Temple University, Philadelphia, PA 19122 ¶Center for the Computational Design of Functional Layered Materials, Temple University, Philadelphia, PA 19122 E-mail: [email protected]
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IR Spectra Experimentally determined infrared (IR) adsorption spectra are shown in Fig. S1A for bulk water and birnessite systems with average oxidation states (AOS) of 3.85 and 3.31. Signatures of the highly ordered, confined water molecules are observed in the high frequency O-H stretch region of the spectrum. In particular, the two peaks making up the O-H stretch region become more well defined, suggestive of increased ordering, and a shoulder develops at higher frequencies for the 3.85 AOS system. This shoulder is reminiscent of free O-Hlike species, resulting from water molecules that sacrifice water-water H-bonds in order to H-bond to the surface, or vice versa. Increasing water-surface interactions by lowering the AOS to 3.31 reduces this shoulder, and therefore the population of free O-H-like species, as expected for an increase in the ordering of the confined waters. The experimental results are corroborated by the simulated IR spectra shown in Fig. S1B,C for bulk water, and water confined between MnO2 sheets separated by distances of d = 7.52 Å and d = 7.42 Å, with the former corresponding to the system in the main text; both have an AOS of 3.75. The flexible water model used splits the broad O-H stretch peak into two peaks, but the qualitative changes that occur upon confining and increasing water ordering are still observed. The O-H stretch peaks sharpen, and a shoulder at high frequencies appears upon confinement in birnessite. Upon increasing the ordering of confined water molecules, here through decreasing the separation between MnO2 sheets, the high frequency shoulder disappears. The removal of this shoulder corresponds to a decrease in the population of waters that are not H-bonded well to the surface or other water molecules, illustrated by the decrease in the probability of observing waters with θD near 60◦ , shown in Fig. S1D. The increased ordering of confined waters is also evidenced by the change in the low frequency librational modes of the IR spectra. In particular, upon lowering d, the corresponding peak shifts to lower frequency, indicating slower dynamics of water molecules that one would expect to find when increasing the order in such a system.
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A
B
C
D
Figure S1: (A) Experimentally determined infrared (IR) absorption spectra for bulk water and birnessite with average oxidation states (AOS) of 3.85 and 3.31 show signatures of ordered water molecules in the high frequency region. Background effects have been removed by substracting a cubic polynomial from the spectra. (B) Simulated IR spectra show similar features in the high frequency region. (C) The low frequency part of the simulated spectra are also consistent with increased water ordering upon increasing confinement. (D) The probability distribution of the angle θD made by the dipole moment vector of water and the surface normal indicates that the changes in the spectra are largely due to a decrease in the population of water molecules that are not H-bonded well to either the surface or neighboring waters.
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Experimental Details Synthesis of high oxidation state birnessite Hydrochloric acid (4M, 50.0mL) was added drop wise via a syringe pump at 1 mL/min to a heated and stirred (80◦ C, 360 rpm) solution of potassium permanganate (0.200M, 250mL) in a 400mL beaker. Heating continued at 80◦ C for an additional 0.5h after addition was completed. The resulting 300mL solution was then covered to prevent excessive evaporation overnight and aged for 15h at 50◦ C before being washed via vacuum filtration with a fine frit five times to give the final birnessite product.
Synthesis of low oxidation state birnessite Hydrochloric acid (2M, 50.0mL) and MnCl2 (0.3M, 50mL) were added drop wise via a syringe pump at 1 mL/min to a heated and stirred (80◦ C, 360 rpm) solution of potassium permanganate (0.200M, 250mL) in a 400mL beaker. Heating continued at 80◦ C for an additional 0.5h after addition was completed. The resulting 300mL solution was then covered to prevent excessive evaporation overnight and aged for 15h at 50◦ C before being washed via vacuum filtration with a fine frit five times to give the final product.
Average oxidation state of Mn To determine total Mn content, 0.50g of birnessite was dissolved in hydroxylamine hydrochloride (0.25M, 20mL) and diluted to 250mL. Mn content was then determined by analysis of an aliquot of the diluted solution by ICP-OES. An oxalic acid-permangante back-titration 1 was used to determine the bulk AOS. First, Mn content was determined using the previous stated method. Second, a 0.50g sample of birnessite was completely dissolved in 5mL of 0.48M oxalic acid and 10.00mL H2 SO4 to reduce all Mn species to Mn2+ . The excess oxalate was determined by back-titration at 70◦ C with a KMnO4 (0.025M) solution. AOS was calculated according to both the titration result and the total amount of Mn. S4
Simulation of IR Spectra We compute IR adsoprtion spectra following previous work. 2,3 The IR spectrum is given by the real part of the Fourier transform of the autocorrelation function of the dipole moment of the simulation cell, Z
∞
hM(t) · M(0)i cos(ωt)dt,
I(ω) ∝
(S1)
0
where I(ω) is the spectral density, M(t) is the dipole moment vector of the cell at time t, ω is the vibrational frequency, and h· · · i indicates an ensemble average. Correlations between the system dipole moment often decay slowly, and hM(t) · M(0)i can be affected by artifacts due to periodic boundary conditions. Thus, it has been shown to be advantageous to recast the IR spectra in terms of the correlation between derivatives of the system dipole moment, 2,3 ∞
dM(t) dM(0) · I(ω) ∝ cos(ωt)dt dt dt 0 ! !+ Z ∞* X N N X qi vi (t) · qi vi (0) cos(ωt)dt. = Z
0
i=1
(S2) (S3)
i=1
Here, N is the number of atomic sites in the system, qi is the charge on site i, and vi (t) is velocity vector of site i at time t. We compute the IR spectra following Eq. S3. Prior to Fourier transform, we apply a standard Blackman window to the time correlation function in order to avoid artifacts due to finite time truncation. 4 All spectral densities are obtained from an average over twenty trajectories, each computed with a temporal resolution of 0.1 fs. We additionally smooth the resulting spectral densities with a windowing function that has a length of four data points. The simulation results presented in the main text were obtained with the rigid SPC/E model, but a flexible model is necessary to compute vibrational spectra. Therefore, we use the flexible SPC/Fw 5 model to compute IR adsorption spectra. This model accurately captures the liquid state properties of liquid water while giving a reasonable qualitative description of the vibrational spectra, and therefore the structure of SPC/Fw confined in S5
birnessite should be similar to SPC/E while allowing the study of vibrational properties. Additionally, the SPC model on which SPC/Fw is based is compatible with the force field we use to describe birnessite. Indeed, we find that the structure of SPC/Fw and SPC/E confined within birnessite are similar.
References (1) Zhao, W.; Cui, H.; Liu, F.; Tan, W.; Feng, X. Relationship Between Pb2+ Adsorption and Average Mn Oxidation State in Synthetic Birnessites. Clays and Clay Minerals 2009, 57, 513–520. (2) Praprotnik, M.; Janežič, D.; Mavri, J. Temperature Dependence of Water Vibrational Spectrum: A Molecular Dynamics Simulation Study. J. Phys. Chem. A 2004, 108, 11056–11062. (3) Praprotnik, M.; Janezic, D. Molecular Dynamics Integration and Molecular Vibrational Theory. III. The Infrared Spectrum of Water. J. Chem. Phys. 2005, 122, 174103. (4) Harris, F. J. On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform. Proc. IEEE 1978, 66, 51–83. (5) Wu, Y.; Tepper, H. L.; Voth, G. A. Flexible Simple Point-Charge Water Model with Improved Liquid-State Properties. J. Chem. Phys. 2006, 124, 024503.
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IR Spectra Experimentally determined infrared (IR) adsorption spectra are shown in Fig. S1A for bulk water and birnessite systems with average oxidation states (AOS) of 3.85 and 3.31. Signatures of the highly ordered, confined water molecules are observed in the high frequency O-H stretch region of the spectrum. In particular, the two peaks making up the O-H stretch region become more well defined, suggestive of increased ordering, and a shoulder develops at higher frequencies for the 3.85 AOS system. This shoulder is reminiscent of free O-Hlike species, resulting from water molecules that sacrifice water-water H-bonds in order to H-bond to the surface, or vice versa. Increasing water-surface interactions by lowering the AOS to 3.31 reduces this shoulder, and therefore the population of free O-H-like species, as expected for an increase in the ordering of the confined waters. The experimental results are corroborated by the simulated IR spectra shown in Fig. S1B,C for bulk water, and water confined between MnO2 sheets separated by distances of d = 7.52 Å and d = 7.42 Å, with the former corresponding to the system in the main text; both have an AOS of 3.75. The flexible water model used splits the broad O-H stretch peak into two peaks, but the qualitative changes that occur upon confining and increasing water ordering are still observed. The O-H stretch peaks sharpen, and a shoulder at high frequencies appears upon confinement in birnessite. Upon increasing the ordering of confined water molecules, here through decreasing the separation between MnO2 sheets, the high frequency shoulder disappears. The removal of this shoulder corresponds to a decrease in the population of waters that are not H-bonded well to the surface or other water molecules, illustrated by the decrease in the probability of observing waters with θD near 60◦ , shown in Fig. S1D. The increased ordering of confined waters is also evidenced by the change in the low frequency librational modes of the IR spectra. In particular, upon lowering d, the corresponding peak shifts to lower frequency, indicating slower dynamics of water molecules that one would expect to find when increasing the order in such a system.
S2
A
B
C
D
Figure S1: (A) Experimentally determined infrared (IR) absorption spectra for bulk water and birnessite with average oxidation states (AOS) of 3.85 and 3.31 show signatures of ordered water molecules in the high frequency region. Background effects have been removed by substracting a cubic polynomial from the spectra. (B) Simulated IR spectra show similar features in the high frequency region. (C) The low frequency part of the simulated spectra are also consistent with increased water ordering upon increasing confinement. (D) The probability distribution of the angle θD made by the dipole moment vector of water and the surface normal indicates that the changes in the spectra are largely due to a decrease in the population of water molecules that are not H-bonded well to either the surface or neighboring waters.
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Experimental Details Synthesis of high oxidation state birnessite Hydrochloric acid (4M, 50.0mL) was added drop wise via a syringe pump at 1 mL/min to a heated and stirred (80◦ C, 360 rpm) solution of potassium permanganate (0.200M, 250mL) in a 400mL beaker. Heating continued at 80◦ C for an additional 0.5h after addition was completed. The resulting 300mL solution was then covered to prevent excessive evaporation overnight and aged for 15h at 50◦ C before being washed via vacuum filtration with a fine frit five times to give the final birnessite product.
Synthesis of low oxidation state birnessite Hydrochloric acid (2M, 50.0mL) and MnCl2 (0.3M, 50mL) were added drop wise via a syringe pump at 1 mL/min to a heated and stirred (80◦ C, 360 rpm) solution of potassium permanganate (0.200M, 250mL) in a 400mL beaker. Heating continued at 80◦ C for an additional 0.5h after addition was completed. The resulting 300mL solution was then covered to prevent excessive evaporation overnight and aged for 15h at 50◦ C before being washed via vacuum filtration with a fine frit five times to give the final product.
Average oxidation state of Mn To determine total Mn content, 0.50g of birnessite was dissolved in hydroxylamine hydrochloride (0.25M, 20mL) and diluted to 250mL. Mn content was then determined by analysis of an aliquot of the diluted solution by ICP-OES. An oxalic acid-permangante back-titration 1 was used to determine the bulk AOS. First, Mn content was determined using the previous stated method. Second, a 0.50g sample of birnessite was completely dissolved in 5mL of 0.48M oxalic acid and 10.00mL H2 SO4 to reduce all Mn species to Mn2+ . The excess oxalate was determined by back-titration at 70◦ C with a KMnO4 (0.025M) solution. AOS was calculated according to both the titration result and the total amount of Mn. S4
Simulation of IR Spectra We compute IR adsoprtion spectra following previous work. 2,3 The IR spectrum is given by the real part of the Fourier transform of the autocorrelation function of the dipole moment of the simulation cell, Z
∞
hM(t) · M(0)i cos(ωt)dt,
I(ω) ∝
(S1)
0
where I(ω) is the spectral density, M(t) is the dipole moment vector of the cell at time t, ω is the vibrational frequency, and h· · · i indicates an ensemble average. Correlations between the system dipole moment often decay slowly, and hM(t) · M(0)i can be affected by artifacts due to periodic boundary conditions. Thus, it has been shown to be advantageous to recast the IR spectra in terms of the correlation between derivatives of the system dipole moment, 2,3 ∞
dM(t) dM(0) · I(ω) ∝ cos(ωt)dt dt dt 0 ! !+ Z ∞* X N N X qi vi (t) · qi vi (0) cos(ωt)dt. = Z
0
i=1
(S2) (S3)
i=1
Here, N is the number of atomic sites in the system, qi is the charge on site i, and vi (t) is velocity vector of site i at time t. We compute the IR spectra following Eq. S3. Prior to Fourier transform, we apply a standard Blackman window to the time correlation function in order to avoid artifacts due to finite time truncation. 4 All spectral densities are obtained from an average over twenty trajectories, each computed with a temporal resolution of 0.1 fs. We additionally smooth the resulting spectral densities with a windowing function that has a length of four data points. The simulation results presented in the main text were obtained with the rigid SPC/E model, but a flexible model is necessary to compute vibrational spectra. Therefore, we use the flexible SPC/Fw 5 model to compute IR adsorption spectra. This model accurately captures the liquid state properties of liquid water while giving a reasonable qualitative description of the vibrational spectra, and therefore the structure of SPC/Fw confined in S5
birnessite should be similar to SPC/E while allowing the study of vibrational properties. Additionally, the SPC model on which SPC/Fw is based is compatible with the force field we use to describe birnessite. Indeed, we find that the structure of SPC/Fw and SPC/E confined within birnessite are similar.
References (1) Zhao, W.; Cui, H.; Liu, F.; Tan, W.; Feng, X. Relationship Between Pb2+ Adsorption and Average Mn Oxidation State in Synthetic Birnessites. Clays and Clay Minerals 2009, 57, 513–520. (2) Praprotnik, M.; Janežič, D.; Mavri, J. Temperature Dependence of Water Vibrational Spectrum: A Molecular Dynamics Simulation Study. J. Phys. Chem. A 2004, 108, 11056–11062. (3) Praprotnik, M.; Janezic, D. Molecular Dynamics Integration and Molecular Vibrational Theory. III. The Infrared Spectrum of Water. J. Chem. Phys. 2005, 122, 174103. (4) Harris, F. J. On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform. Proc. IEEE 1978, 66, 51–83. (5) Wu, Y.; Tepper, H. L.; Voth, G. A. Flexible Simple Point-Charge Water Model with Improved Liquid-State Properties. J. Chem. Phys. 2006, 124, 024503.
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