Article pubs.acs.org/JPCC
A Comparative Theoretical Study of Proton-Coupled Hole Transfer for H2O and Small Organic Molecules (CH3OH, HCOOH, H2CO) on the Anatase TiO2(101) Surface Yongfei Ji,† Bing Wang,‡ and Yi Luo*,†,‡ †
Department of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, Stockholm SE-106 91, Sweden ‡ Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China ABSTRACT: The high oxidation power of the photogenerated hole in TiO2 has made it useful in many applications. It is of fundamental importance to understand how the hole transfers from the catalysis to adsorbates. We have performed a comparative study on the mechanism for the first proton-coupled hole transfer process in water, methanol, formic acid, and formaldehyde on the anatase TiO2(101) surface. Our results show that this process for all the molecules is concerted rather than sequential. Both the kinetic and thermodynamic effects need to be taken into account. The hole scavenging power for the four molecules under investigation is found to follow the order formaldehyde > formic acid > methanol > water, which agrees well with various experiments.
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INTRODUCTION TiO2 is a popular photocatalyst that has wide applications in the fields of energy and environment, such as wastewater treatment, air purification, self-cleaning, and antibacterial, just to name a few.1−3 One of the major reasons for its popularity is its high activity for the decomposition of molecules. This is because its valence band edge is well below the standard hydrogen electrode, which gives the photogenerated hole a high oxidation power. In general, the hole transfer process holds the key for understanding the mechanism of photocatalytic reactions and for the improvement of the performance of TiO2. Water (H2O) and other small organic molecules such as methanol (CH3OH), formic acid (HCOOH), and formaldehyde (H2CO) have been taken as model molecules in the study of the reaction between holes and molecules on TiO2 surfaces. For example, in a recent study,4 the hole transfer rate to formaldehyde was found to be much larger than that to methanol. The latter has widely been used as an efficient hole scavenger.5 Another transient adsorption experiment found that the transfer rate of the trapped hole to alcohol molecules follows the order methanol > ethanol > 2-propanol > water.6 The authors suggested that the transfer rate is determined by the reaction energy. However, early studies already showed that the rate is not necessarily correlated to the redox potential of the adsorbates, which in turn suggested that the kinetic effects may also play an important role.7 In other words, both the kinetics and thermodynamics of the hole need to be taken into account in describing the reactions. It should be mentioned that the reaction mechanism for the hole transfer is generally not well understood. One typical example is the first proton-coupled hole transfer process for RH-type molecules. This process could be concerted (reaction 1) or sequential. For the sequential process, there are two © 2014 American Chemical Society
possibilities: the hole transfer priors to the proton transfer (reactions 2 and 3) or vice versa (reactions 4 and 5). Moreover, the process for different molecules could be different, and it is difficult to be determined by experiments alone. In this context, it is highly desirable to carry out systematic theoretical studies to provide the underlying mechanism for the general photocatalytic reactions. RH + h+ → R• + H+
(1)
RH + h+ → (RH)+
(2)
(RH)+ → R• + H+
(3)
RH → R− + H+
(4)
R− + h+ → R•
(5)
However, theoretical calculations on photo-oxidation reactions are rare, the difficulties lie in the characterization of the nature of charge carriers and their roles in the reaction. It was suggested that the trapping of the photogenerated hole can occur within a picosecond after photoexcitation.8 Both the free and trapped holes can transfer to adsorbates, referred to as direct and indirect hole transfers,9−11 respectively. Previous experimental studies suggested that at least two types of trapped holes exist, the shallow hole and the deep hole.12,13 However, their exact natures are largely unknown. Theoretical calculations14,15 revealed that the under-coordinated surface oxygen atom is the most favorable trapping site for the hole on the bare rutile TiO2(110) and the anatase TiO2(101) surfaces. Received: June 12, 2014 Revised: August 11, 2014 Published: September 2, 2014 21457
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One reason for this is that the occupied states of the molecules are nearer to the top of the valence band on anatase than those on rutile (see below). This makes it easier for the hole to be trapped at them. Another reason is that the density of anatase is smaller than that of rutile, which means the average distance between atoms is shorter in anatase than that in rutile. The electron orbital in anatase then has larger tendency to be localized. In this case, the hybrid functional and DFT+U calculations may lead to the spontaneous trapping of the electron and the hole.15 Hence, we decide to use the GGA method to study the photo-oxidation of molecules by the free hole because it is easier to stabilize the free hole and computationally much cheaper. In our calculations, the free hole was presented by an unoccupied orbital at the top of the valence band. A slab model with one side relaxed and the other side fixed to mimic the bulk has been often used to model the surface. However, in our previous studies14,21 on the rutile TiO2(110) surface, such a surface model was found to introduce surface states right at the top of the valence band, which could lead to the artificial localization of the hole on the fixed side of the slab. We found that the anatase TiO2(101) surface has similar problems.20 Even saturation with dissociated water cannot remove the tendency for the free hole to localize on the fixed side of the slab.20 Thus, it is inappropriate to use it for the study of photocatalytic reactions involving the free hole. Instead, we used a five trilayer slab model with only the center layer fixed, and other atoms were allowed to relax.14,20,21 The hole was introduced by using the triplet state to mimic the singlet excited state.14,17,21,31 In this case, the hole was involved in the oxidation of the molecule with the excited electron kept in the bottom of the conduction band during the whole reaction. In our previous work,20 we managed to introduce only the hole by changing the stoichiometry of the system. The calculated potential energy surface and hole transfer along it are almost the same with those from the triplet calculation; this suggests that the effect of the excited electron on the reaction is very small.
The photo-oxidation of a water molecule by a trapped hole on these two surfaces has also been explored by first-principle calculations, which was found to be concerted on the rutile (110) surface14 and sequential on the anatase (101) surface.16 The hole scavenging power of several organic molecules has been investigated based on thermodynamic analysis.17 However, the molecular mechanism and the kinetics for the hole transfer to these molecules are still not well understood. On the other hand, the free hole and the shallow hole that is in thermal equilibrium with the free hole were suggested to react more efficiently with chemisorbed molecules and to have higher oxidation power than the deep holes.18,19 Therefore, it is a good starting point to study the reaction of the adsorbed molecules with the free hole. The free hole has been well characterized in our previous works.20−22 A higher reaction barrier and lower reaction energy can be expected for the oxidation of the molecules by the trapped hole because of the stabilization of the system via hole trapping.22 In this study, we perform first-principles calculations on the first proton-coupled hole (free) transfer process for four RHtype molecules: H2O, CH3OH, HCOOH, and H2CO. A concerted reaction is found for all of these four molecules. It is shown that both the kinetic and thermodynamic effects are important for the hole transfer. The scale of the hole scavenging ability for the molecules follows the order formaldehyde > formic acid > methanol > water, which is consistent with experimental findings.
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COMPUTATIONAL METHODS We performed spin-polarized calculations at generalized gradient approximation (GGA) with PBE23exchange-correlation functional implemented in VASP24−27 Ion−electron interaction was described by the PAW pseudopotential.28 An energy cutoff of 460 eV was applied for the plane-wave basis. The anatase TiO2(101) surface was described by a five trilayer slab model with a vacuum gap of 13 Å. A 3 × 1 supercell along the [010] and [101] directions with 180 atoms was used, and the calculations were performed at Γ point only. Structures were relaxed until all forces on the atoms were smaller than 0.02 eV/Å. The potential energy surfaces were calculated by the nudged elastic band method with climbing (CNEB).29 The minima energy path of the reaction can be obtained from this method. Then, we can trace the hole and proton transfer along it that in return will tell us whether the reaction is concerted or sequential:14,22 if it is a sequential reaction, there should be an intermediate state in which the molecule dissociates with the hole remaining delocalized22 (or the hole is transferred to the molecule that stays associative); otherwise, it is a concerted path in which the proton transfer and the hole transfer occur simultaneously.14 The photo-oxidation reaction of a RH-type molecule usually produces a R• radical at which the hole is localized. The selfinteraction error in density functional theory (DFT) has a tendency to over delocalize the orbital30 as we found on the rutile TiO2(110) surface.14,22 We adopted DFT+U14,22 or hybrid functional14 methods to overcome this tendency and to trap the hole. However, the calculations with the hybrid functional are extremely expensive, especially for the calculation of the transition state using the CNEB method because of the involvement of many images. The DFT+U method might face some uncertainties due to the choice of different U values. Fortunately, on the anatase (101) surface, we find that the hole can still be trapped by the R− groups even at the GGA level.
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RESULTS AND DISCUSSION Adsorption and Dissociation in the Ground State. The interaction of the anatase (101) surface with many small molecules has been investigated both theoretically and experimentally.32−41 The anatase (101) surface was found to be quite inertial; the molecules on the surface usually preferred to to be adsorbed associatively. For the four molecules included in this work, we have calculated the energy in molecular and dissociative adsorption geometry as well as the barrier for the dissociation. The results are shown in Figure 1. For water, the molecular adsorption is much more favorable (by 0.35 eV) than the dissociative adsorption, which agrees well with the scanning tunneling microscope experiment and previous theoretical calculations.34,35,38 The dissociation barrier is found to be 0.50 eV, which is also close to the result reported in other theoretical work.37 For methanol, the dissociative adsorption is only endothermic by 0.11 eV,32,36,37 and the dissociation barrier is almost the same as that of water. The adsorption of formic acid on the anatase (101) surface was first calculated by Vittadini et al.41 The most stable molecular adsorption is monodentate, whereas the dissociative adsorption is bidentate. In our calculations, the molecular adsorption of formic acid is nearly degenerated with the dissociative adsorption. More specifically, the dissociative 21458
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Figure 2. Partial density of states (PDOS) of the molecules in molecular and dissociative adsorption. (a−d) PDOS for H2O, CH3OH, HCOOH, H2CO. (e) PDOS for a Ti5f atom and an O2f atom. The energy of the top of the valence band Ev is taken as the energy zero, and a Gaussian smearing with a width of 0.05 eV is used.
without being trapped at the O2f atom first. For water, its HOMO is well below the top of the valence band34 in molecular adsorption, but in dissociative adsorption, its HOMO is even higher than that of the O2f atom, which explains why the OH group is a more favored hole trapping site over O2f.15 This is opposite to water on the rutile TiO2(110) surface.22 One reason might be that the top of the valence band of rutile is higher than that of anatase.45 Therefore, the PDOS of water is much nearer to the top of the valence band on the anatase than that on the rutile surface. Photo-oxidation of the Molecules: Proton-Coupled Hole Transfer. For the first proton-coupled hole transfer in the photo-oxidation of the molecules, the calculated potential energy surfaces and the structures for the initial, transition, and final states superimposed with the distribution of the hole orbital (the unoccupied orbital represents the hole) are shown in Figure 3. The initial states for the photo-oxidation reaction are obtained from the optimization of the ground-state structures in the triplet state. The structures of the reactant in the triplet state are almost the same as those in the ground state, and the hole orbitals (Figure 3b) are found to be delocalized over the whole slab. For the product, the hole is spontaneously localized mainly at the R groups for methanol and formaldehyde but shared by the R groups and a surface oxygen for water and formic acid. The hole orbital possesses the character of the antibonding orbital, resulting from the hybridization of the HOMO of the R− group and the p orbital of the surface oxygen. It should be mentioned that similar results were found for the oxidation of water on the rutile (110) surface.14,22 The potential energy surfaces calculated with the CNEB method are shown in Figure 3a. For water, the reaction is still endothermic, which agrees with a previous thermodynamic calculation.46 However, its barrier is lowered to 0.39 eV, and the product is more stable than that in the ground state. The
Figure 1. Dissociation of the molecules. (a) Potential energy surfaces. (b) Geometries of the initial state (left column), the transition state (TS), and the final state (right column) for the four molecules; from top to bottom each row corresponds to H2O, CH3OH, HCOOH, and H2CO; the red, gray, and white spheres represent the oxygen, titanium, and hydrogen atoms, respectively; for H2CO, the dissociative adsorption is unstable, and only the structure for molecular adsorption is shown.
adsorption is 0.05 eV higher than the molecular adsorption. It has been found that both molecularly and dissociatively adsorbed molecules exist on the surface.42 On a highly reduced anatase (101) surface, it was proposed that the molecules only adsorbed dissociatively.43 The dissociation of the molecule may be caused by the surface or subsurface defects. The dissociation barrier on a perfect surface is calculated to be 0.35 eV that is lower than those for both water and methanol. For formaldehyde, we find that the dissociative adsorption is not stable. The molecule is adsorbed with its O atom connected to the Ti atom and the H atom forming a hydrogen bond with a surface oxygen atom.44 The partial density of states (PDOS) of the molecules in the molecular and dissociative adsorption is shown in Figure 2. For all the molecules, we can see a significant upshift of the PDOS for the dissociative adsorption with respect to the associative one. This explains why the dissociative species of the molecules are usually more efficient hole scavengers.5,17 The PDOS of a 2fold coordinated oxygen (O2f) atom and a 5-fold coordinated Ti (Ti5f) atom is shown in Figure 2e. Except for water, the peak positions of the highest occupied molecular orbitals (HOMOs) of the molecules in molecular adsorption are already higher than that of the O2f atom. This indicates that all these organic molecules are efficient hole scavengers even when they are associatively adsorbed. The hole may directly transfer to them 21459
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surface, although the dissociation of the molecule also upshifts its HOMO significantly (Figure 2), the barrier is relatively high (0.50 eV), and the dissociation is endothermic (Figure 1). On the other hand, the HOMO of the molecularly adsorbed water on anatase is already quite near to the top of the valence band; therefore, the hole can transfer concertedly with the dissociation of the molecule, which also helps to lower the barrier of the reaction to 0.39 eV. Apparently, the concerted pathway is more favorable for the oxidation of the water by a free hole on the anatase (101) surface. However, for the oxidation of the adsorbed water by a trapped hole on the anatase (101) surface, it was found to be a sequential process in which the proton is transferred first followed by the hole transfer.16 This is similar to the oxidation of the adsorbed water by a trapped hole on the rutile (110) surface.22 The hole cannot transfer concertedly probably because of the energy and symmetry mismatching between the HOMO of the adsorbed molecule and the trapped hole orbital.14,22 For methanol, the reaction becomes exothermic, and the barrier is also lowered (to 0.35 eV) compared with that of the ground state. Because a much larger part of the hole is transferred to methanol in the transition state with respect to water, the oxidation barrier for methanol is even lower than that for water. It shows that methanol is a more efficient hole scavenger than water both thermodynamically and kinetically.4,6,48,49 The photo-oxidation of methanol on the rutile TiO2(110) has also been investigated by many experimental works.5,47,49−51 The existence of the transient dissociation state is also under debate.47 Although our results suggest that it is a one-step process on the anatase (101) surface, it is still not certain whether the same conclusion can be drawn for the rutile (110) surface. The oxidation of formic acid is quite similar to those of water and methanol. A decrease in the reaction energy and barrier and a concerted proton-coupled hole transfer process are observed. For formic acid, the reaction energy is lower than that of methanol; this agrees well with a thermodynamics analysis by Di Valentin et al.17 It is noted that methanol was suggested to be a stronger hole scavenger than formic acid.17 However, our calculation shows that the barrier for the oxidation of formic acid is much smaller than that of methanol. This indicates that, from a kinetic point of view, formic acid is a much more efficient hole scavenger that methanol. Previous experiments have shown that the oxidation rate of formic acid is higher than formate42 (HCOO−), and the hole accepting ability of formate was also found to be larger than that of methanol.7 These experimental facts suggest that formic acid should be a stronger hole acceptor than methanol. In this case, the kinetics plays a more important role. Among the four molecules in our study, the formaldehyde molecule is found to have the smallest barrier (0.05 eV) and the lowest reaction energy (−0.59 eV). It should be the most powerful hole scavenger. This finding also agrees well with a recent experimental result, which shows that the transfer rate of the hole to formaldehyde is much higher than that to methanol.4 Although there are no experimental results to compare the hole transfer rate of formaldehyde and formic acid, our calculations suggest that formaldehyde should be the most efficient hole scavenger. It is found that the hole is transferred via the O2f to formaldehyde (the hole orbital in the transition state is an antibonding orbital mainly from the hybridization of the HOMO of the molecule and the p orbital of O2f). This is very different from other molecules, to which the hole is
Figure 3. Oxidation of the molecules. (a) Potential energy surfaces. (b) Geometries of the initial state (left column), the transition state (TS), and the final state (right column) for the four molecules (from top to bottom each row corresponds to H2O, CH3OH, HCOOH, and H2CO); the red, gray, and white spheres represent the oxygen, titanium, and hydrogen atoms, respectively; the isosurface of the electron density for the hole orbital (green) in each state is superimposed on the structure; for the initial state, the isovalue is 0.001 e/Å3; for the transition state and the final state, the isovalue is 0.01 e/Å3.
potential energy surface shows that the reaction is a one-step process, suggesting that, in the oxidation of the molecule, the hole transfer is coupled with the proton transfer concertedly. This can also be directly seen from the hole orbital in the transition state in which the hole is mainly shared by the OH group and a surface oxygen atom. The partially transferred hole in the transition state weakens the binding of the proton by the O atom, leading to a lower barrier than that in the ground state. This is different from the photo-oxidation of water by a free hole on the rutile TiO 2(110) surface, 22 in which an intermediate transient dissociation state47 was found during the oxidation reaction. We attribute it to the difference in the electronic and chemical properties of the molecule on the rutile (110) and the anatase (101) surfaces. On the rutile (110) surface, the HOMO of the molecularly adsorbed water is well below the top of the valence band, but it upshifts a lot after dissociation by overcoming a small barrier.22 Therefore, the oxidation of the molecule is sequential. On the anatase (101) 21460
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(4) Dimitrijevic, N. M.; Shkrob, I. A.; Gosztola, D. J.; Rajh, T. Dynamics of Interfacial Charge Transfer to Formic Acid, Formaldehyde, and Methanol on the Surface of TiO2 Nanoparticles and Its Role in Methane Production. J. Phys. Chem. C 2012, 116, 878−885. (5) Shen, M.; Henderson, M. A. Identification of the Active Species in Photochemical Hole Scavenging Reactions of Methanol on TiO2. J. Phys. Chem. Lett. 2011, 2, 2707−2710. (6) Tamaki, Y.; Furube, A.; Murai, M.; Hara, K.; Katoh, R.; Tachiya, M. Direct Observation of Reactive Trapped Holes in TiO 2 Undergoing Photocatalytic Oxidation of Adsorbed Alcohols: Evaluation of the Reaction Rates and Yields. J. Am. Chem. Soc. 2006, 128, 416−417. (7) Byrne, J. A.; Eggins, B. R.; Dunlop, P. S. M.; Linquette-Mailley, S. The Effect of Hole Acceptors on the Photocurrent Response of Particulate TiO2 Anodes. Analyst 1998, 123, 2007−2012. (8) Tamaki, Y.; Furube, A.; Murai, M.; Hara, K.; Katoh, R.; Tachiya, M. Dynamics of Efficient Electron-Hole Separation in TiO2 Nanoparticles Revealed by Femtosecond Transient Absorption Spectroscopy under the Weak-Excitation Condition. Phys. Chem. Chem. Phys. 2007, 9, 1453−1460. (9) Berger, T.; Lana-Villarreal, T.; Monllor-Satoca, D.; Gomez, R. Thin Films of Rutile Quantum-Size Nanowires as Electrodes: Photoelectrochemical Studies. J. Phys. Chem. C 2008, 112, 15920− 15928. (10) Villarreal, T. L.; Gmez, R.; Neumann-Spallart, M.; AlonsoVante, N.; Salvador, P. Semiconductor Photooxidation of Pollutants Dissolved in Water: A Kinetic Model for Distinguishing between Direct and Indirect Interfacial Hole Transfer. I. Photoelectrochemical Experiments with Polycrystalline Anatase Electrodes under Current Doubling and Absence of Recombination. J. Phys. Chem. B 2004, 108, 15172−15181. (11) Villarreal, T. L.; Gmez, R.; Gonlez, M.; Salvador, P. A Kinetic Model for Distinguishing between Direct and Indirect Interfacial Hole Transfer in the Heterogeneous Photooxidation of Dissolved Organics on TiO2 Nanoparticle Suspensions. J. Phys. Chem. B 2004, 108, 20278−20290. (12) Yoshihara, T.; Katoh, R.; Furube, A.; Tamaki, Y.; Murai, M.; Hara, K.; Murata, S.; Arakawa, H.; Tachiya, M. Identification of Reactive Species in Photoexcited Nanocrystalline TiO2 Films by WideWavelength-Range (400−2500 nm) Transient Absorption Spectroscopy. J. Phys. Chem. B 2004, 108, 3817−3823. (13) Savory, D. M.; McQuillan, A. J. Influence of Formate Adsorption and Protons on Shallow Trap Infrared Absorption (STIRA) of Anatase TiO2 during Photocatalysis. J. Phys. Chem. C 2013, 117, 23645−23656. (14) Ji, Y.; Wang, B.; Luo, Y. Location of Trapped Hole on RutileTiO2(110) Surface and Its Role in Water Oxidation. J. Phys. Chem. C 2012, 116, 7863−7866. (15) Di Valentin, C.; Selloni, A. Bulk and Surface Polarons in Photoexcited Anatase TiO2. J. Phys. Chem. Lett. 2011, 2, 2223−2228. (16) Chen, J.; Li, Y.-F.; Sit, P.; Selloni, A. Chemical Dynamics of the First Proton-Coupled Electron Transfer of Water Oxidation on TiO2 Anatase. J. Am. Chem. Soc. 2013, 135, 18774−18777. (17) Di Valentin, C.; Fittipaldi, D. Hole Scavenging by Organic Adsorbates on the TiO2 Surface: A DFT Model Study. J. Phys. Chem. Lett. 2013, 4, 1901−1906. (18) Bahnemann, D. W.; Hilgendorff, M.; Memming, R. Charge Carrier Dynamics at TiO2 Particles: Reactivity of Free and Trapped Holes. J. Phys. Chem. B 1997, 101, 4265−4275. (19) Zhang, L. W.; Mohamed, H. H.; Dillert, R.; Bahnemann, D. Kinetics and Mechanisms of Charge Transfer Processes in Photocatalytic Systems: A Review. J. Photochem. Photobiol., C 2012, 13, 263− 276. (20) Ji, Y.; Luo, Y. First-Principles Study on the Mechanism of Photoselective Catalytic Reduction of NO by NH3 on Anatase TiO2(101) Surface. J. Phys. Chem. C 2014, 118, 6359−6364. (21) Ji, Y.; Wang, B.; Luo, Y. First Principles Study of O2 Adsorption on Reduced Rutile TiO2-(110) Surface under UV Illumination and Its Role on CO Oxidation. J. Phys. Chem. C 2013, 117, 956−961.
transferred via the 3-fold coordinated oxygen (O3f) atom. The HOMO of formaldehyde is a π orbital perpendicular to the molecular plane that matches the symmetry of the p orbital of O2f (the p orbital parallel to the O2f row). This again demonstrates the important role played by the symmetry in the hole transfer.14 Overall, our calculations strongly indicate that the protoncoupled hole transfer for the four molecules are all concerted and the order of transfer ability is as follows: formaldehyde > formic acid > methanol > water. It needs to be mentioned that our calculations correspond to the gas/solid interface. If the reaction takes place in solution, the proton may transfer to a solute molecule instead, but we believe that the proton-coupled hole transfer should still be concerted because the partially transferred hole in the transition state helps to lower the reaction barrier. However, the reaction in the liquid/solid interface could be much more complicated. For example, the reaction of molecules with the trapped hole might play an important role. A combination of molecular dynamics simulation and potential energy surface calculation could be a good method for the study of those reactions.16
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CONCLUSION In conclusion, we have performed a comparative study on the proton-coupled hole transfer process for water, methanol, formic acid, and formaldehyde on the anatase (101) surface. In the ground state, the molecules prefer to adsorb associatively on the surface. The fact that their electronic states (except the molecular water) are quite near the top of the valence band suggests that they are efficient hole scavengers. The calculated potential energy surfaces and the hole orbital along the oxidation pathway provide direct evidence that the first protoncoupled hole transfer process for these molecules is all concerted rather than sequential. Our results also demonstrate that the reaction energy is not necessarily correlated to the hole transfer rate. Both the kinetics and thermodynamics of the hole transfer should be considered. For the four molecules under the investigation, their scavenging efficiency for the free hole is found to follow the order formaldehyde > formic acid > methanol > water, which is in good agreement with existing experimental measurements.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by NBRP (grants 2010CB923300 and 2011CB921400) of China, and Gö ran Gustafsson Foundation for Research in Natural Sciences and Medicine. The Swedish National Infrastructure for Computing (SNIC) is acknowledged for computer time.
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dx.doi.org/10.1021/jp505854t | J. Phys. Chem. C 2014, 118, 21457−21462
