Article pubs.acs.org/JPCC
Ab Initio Study on Oxygen Doping of (5,4), (6,4), (6,5), and (8,6) Carbon Nanotubes Mari Ohfuchi* Fujitsu Laboratories Ltd., Atsugi 243-0197, Japan S Supporting Information *
ABSTRACT: Oxygen doping of single-wall carbon nanotubes (SWCNTs) exposed to ozone and light has attracted attention because of their greater luminescence quantum yield than that of pristine CNTs. The luminescence at E11*, which is red-shifted from E11 for pristine CNTs, originating from the oxidation appears to be also observed for small-diameter CNTs in chirality separation experiments without a particular oxidation treatment. To understand this phenomenon, we performed ab initio calculations for the adsorption of oxygen molecules (O2) onto realistic models of chiral CNTs. We found that the energy barrier from the physisorption of O2 to the chemisorption is lower than that of the reverse reaction for (6,4) nanotubes, whereas the relation is opposite for (8,6) nanotubes, consistent with the distinct luminescence peak at E11* observed for (6,4) nanotubes and with the lack of a pronounced luminescence peak for larger-diameter (8,6) nanotubes in the chirality separation experiments. As also proposed for ozone oxidation, one of the final products was found to be the isolated ether structure, whose ground state band gap is slightly narrower than that of pristine CNTs.
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INTRODUCTION Oxygen doping of single-wall carbon nanotubes (SWCNTs) has been reported to increase the luminescence quantum yield,1,2 showing promise for novel photonic devices such as near-infrared single-photon emitters. The oxygen atoms adsorbed onto the surface of SWCNTs are considered to function as luminescent centers, suppressing nonradiative exciton recombination due to collisions between excitons and quenching at defects and end sites of SWCNTs. In these studies, oxygen-doped CNTs were prepared by exposure of SWCNTs to ozone and light, whereas the luminescence originating from oxygen doping of SWCNTs appears to be observed for small-diameter CNTs separated into single chirality without a particular oxidation treatment.3 The distinct luminescence peak at E11* that is red-shifted from E11 for pristine CNTs can be observed for (6,4) and (6,5) nanotubes but not for (8,6) nanotubes or SWCNTs with larger diameters. From a theoretical point of view, for ozone oxidation, the ether structure perpendicular to the nanotube axis has been proposed as the most stable structure.1,4 The atomistic calculations, however, have been limited to semiempirical methods or highly symmetric models such as (8,8) nanotubes1,4−6 because ab initio studies of chiral CNTs, which have a larger unit cell, are challenging. On graphene flakes, it has been shown using density functional theory (DFT) that alignment of epoxy structures induces transforming into ether structures.7 With regards to the adsorption of oxygen molecules (O2), DFT has been used to study the reaction path from physisorption to chemisorption, including the formation of epoxy structures and carbon−carbon (C−C) bond breaking, © 2015 American Chemical Society
for zigzag or armchair CNTs with comparatively small unit cells.8−11 Ab initio studies of the reaction of O2 with realistic chiral CNTs appear to be important for understanding the experimental results related to oxygen doping of chiralityseparated CNTs. In this study, we performed DFT calculations to clarify the difference among (5,4), (6,4), (6,5), and (8,6) nanotubes.
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COMPUTATIONAL METHODS AND MODELS All DFT calculations in this study employed the OpenMX code,12−16 which uses pseudoatomic orbitals (PAOs) centered on atomic sites as the basis function set.12 This open-source software package provides the database of pseudopotentials and PAOs for an extensive list of elements. The data is wellbenchmarked even for molecular systems. The exchangecorrelation potential was treated with the Perdew−Burke− Ernzerhof generalized gradient approximation (GGA-PBE).17 The electron−ion interaction was described by normconserving pseudopotentials18 with partial core correction.19 We used the PAOs specified by C-s2p2d1 and O-s2p2d1, where C and O are atomic symbols for carbon and oxygen, respectively, and s2, for example, indicates the employment of two orbitals for the s component. For both atomic species, 7.0 Bohr was chosen as the cutoff radii of the PAOs. The energy band occupation was smeared by the Fermi distribution function (the temperature T = 300 K) to perform stable selfReceived: November 16, 2014 Revised: May 17, 2015 Published: May 21, 2015 13200
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configuration interaction study.23 The energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) was determined to be 2.37 eV for the triple state, which is consistent with that determined in a previous DFT investigation.24 Adsorption of O Atoms and O2 Molecules onto SWCNTs. The ratio of O to C atoms has been estimated to be one to a few thousands even for SWCNTs prepared by ozone and light.1 We modeled O atoms with low density by placing one O atom or O2 molecule in the large unit cells (244−364 C atoms), which are sufficient to describe the energetics and the energy band structures for separated O adsorption. The geometry optimization of SWCNTs adsorbed with O atoms or O2 molecules was executed while maintaining the unit length of the SWCNTs. The adsorption energy Ea for O atoms and O2 molecules is defined as follows:
consistent calculations. The convergence criterion of forces on atoms for all geometry optimizations was set to 0.1 eV/nm. SWCNTs. We examined (5,4), (6,4), (6,5), and (8,6) nanotubes. (The fundamental properties of SWCNTs are summarized in Supporting Information, Table S1 and Figure S1.) The unit cells of the SWCNTs used for the calculations of the stable and metastable adsorption structures are shown in Figure 1. The unit cell of the (6,4) nanotube is twice the size of
Ea = E(CNT + O) − E(CNT) −
1 3 E ( O2 ) 2
(1)
and Ea = E(CNT + 2O) − E(CNT) − E(3O2 )
(2)
respectively, where E(CNT + O) and E(CNT + 2O) are the total energies of the CNTs adsorbed with one or two O atoms per unit cell and E(CNT) and E(3O2) are those of the CNTs and the triplet O2, respectively. For calculations of the reaction path, the nudged elastic band (NEB) method25 was used. The spring constant for the NEB method was set to be 970 eV/nm2. To save the computational cost of the reaction path study, the (6,4) nanotubes were calculated using the primitive unit cell which is half of that used for the calculations of the stable adsorption structures. The number of sampling points for the reciprocal space integration was also reduced to one for both (6,4) and (8,6) nanotubes. The error in the adsorption energy caused by the reduction was less than 0.01 kcal/mol for the physisorption and 1 kcal/mol for the chemisorption.
Figure 1. Unit cells of single-wall carbon nanotubes (SWCNTs) for the calculations of the stable and metastable adsorption structures. Gray sticks represent carbon−carbon (C−C) bonds. (The band structures are shown in Supporting Information, Figure S2.)
the primitive unit cell in order to provide an adequate distance between adsorbed O atoms or O2 molecules. The sampling points for the reciprocal space integration was set to (0, 0, kz), where the number of kz is four, three, three, and five for (5,4), (6,4), (6,5), and (8,6) nanotubes, respectively. These k points can produce well converged results, where the error in the total energy is less than 0.0005 kcal/mol. The atomic structure of SWCNTs was fully relaxed using a 3 nm-square lateral unit cell, and the optimum unit length was determined. The obtained formation energy in units of kcal/mol can be expressed in the form 1.8/d2, where d (nm) is the diameter of SWCNTs, consistent with the previous detailed DFT investigation of chiral CNTs.20 The band gap Eg is smaller than the empirical value;21 Eg values obtained using DFT are well-known to be smaller than those determined experimentally. The ratios, however, range from 0.72 to 0.75, showing good qualitative agreement. Our data for Eg are also consistent with the previous DFT data.20 O2 Molecules. The atomic structure for O2 molecules was also optimized in a three-dimensional periodic boundary condition with a 3 nm cube. The triplet state of O2 is more stable than the singlet state by 27.19 kcal/mol. The O−O bond length is slightly shorter for the triplet state. The values are 0.1267 and 0.1271 nm for the triplet and singlet states, respectively. These energy difference and bond lengths are slightly larger than the experimentally determined values22 but are in good agreement with the results of a previous ab initio
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RESULTS AND DISCUSSION Stable and Metastable Adsorption Structures. We first discuss the atomic geometry and the adsorption energy for the stable or metastable adsorption structures. As shown in Figure 2a, the nanotube axis in the z-direction is tilted with respect to the six-membered ring because the SWCNTs are chiral. We defined bond “a” as the bond nearly perpendicular to the nanotube axis. Note that bonds “b” and “c” are similar but not equivalent. The schematic diagrams of the adsorption of O atoms and O2 molecules onto SWCNTs are shown in Figure 2b−d and Figure 2e−k, respectively. We start with the adsorption of isolated O atoms. The adsorption sites on bonds “a”, “b”, and “c” were examined. For all the SWCNTs, the epoxy structure was obtained only for bonds “b” and “c” (epoxy-b-O and epoxy-c-O, Figure 2b,c), and the ether structure was obtained only for bond “a” (ether-a-O, Figure 2d) (see also Supporting Information, Tables S3 and S4). The atomic structures for the counterparts (ether-b-O, ether-c-O, and epoxy-a-O, not shown in Figure 2) were not obtained probably because they do not have the local minimum in the potential energy surface. Similar results suggesting that exposure to ozone and light leaves the O atoms with the ether structure on SWCNTs after losing O2 molecules have been reported.1,4 For the epoxy-b-O and epoxy-c-O structures, the 13201
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Here, we consider the difference among the adsorption sites in the adsorption energy. We examined ethylene oxide and dimethyl ether molecules, which are considered to be strainfree epoxy and ether structures (see Supporting Information, Table S2). The formation energies and C−C bond lengths are −30.1 and −66.2 kcal/mol and 0.15 and 0.23 nm for ethylene oxide and dimethyl ether molecules, respectively. The energy difference between the epoxy and ether structures for (5,4) nanotubes is close to that of the strain-free structures. Bond “a” nearly perpendicular to the nanotube axis can stretch by increasing the facing C−C−C bond angles α (>120°) without changing the other bond lengths (Supporting Information, Table S4) and form the ether structure to lower the adsorption energy. The α, which increases with the diameter of the SWCNTs, is considered to further increase the strain energy. On the other hand, bonds “b” and “c” cannot stretch independently of the other bonds in the SWCNTs and keep the epoxy structure. The C−C−C bond angles facing bonds “b” and “c”, β and γ, are smaller than those of the pristine CNTs and approach them as the diameter of the SWCNTs increases (Supporting Information, Table S3). We move on to the adsorption of O2 molecules. The O2 molecules approaching SWCNTs physisorb onto the surface at a distance of approximately 0.31 nm (see also Supporting Information, Table S5 and Figure S6). As shown in Figure 2e,h, the physisorption of O2 onto bonds “a” and “b” was examined (physi-a and physi-b). For all the SWCNTs, the O−O distance remains that of an isolated O2 molecule. As shown in Figure 3b,c, the Ea values for the physisorption are small negative values and do not appear to depend either on the adsorption sites or on the chirality of the SWCNTs. The values are within the range from −2.4 to −2.8 kcal/mol. For all the SWCNTs, the energy bands of SWCNTs are not changed by the physisorption; however, two flat bands originating from O2 lie at approximately 0.15 eV with the same spin, demonstrating that the O2 molecule maintains its triplet state. If the smearing of band occupation is taken into consideration, this result also shows that a small amount of charge is transferred from the SWCNTs to the O2. Although the amount of charge transfer depends on the adsorption sites and on the chirality of the SWCNTs, the maximum value is 0.02e− per O2 molecule. Various values for the adsorption energy and for the amount of the charge transfer have been reported in the literature,8,26,27
Figure 2. Structures for the adsorption of isolated oxygen (O) atoms and O2 molecules onto the surface of single-wall carbon nanotubes (SWCNTs). (a) Definition of bonds “a”, “b”, and “c”. The nanotube axis in the z-direction is indicated by an arrow, which shows the example of (6,4) nanotubes. Schematic diagrams of adsorption structures (b) epoxy-b-O, (c) epoxy-c-O, (d) ether-a-O, (e) physi-a, (f) cyclo-a, (g) epoxy-c-O2, (h) physi-b, (i) cyclo-b, (j) epoxy-a-O2, and (k) ether-a-O2. Gray sticks and red spheres represent C−C bonds and O atoms, respectively. One O atom and two C atoms form triangular bonds in the case of the epoxy structure, whereas the O atom has broken the C−C bond in the case of the ether structure.
C−C bond length below the O atom dC−C was determined to be 0.15 nm for all the SWCNTs, which is slightly longer than that in the pristine CNTs. On the other hand, for the ether-a-O structure, the O atom has broken the bond between two connecting C atoms, and dC−C is extended to 0.21 nm for all the SWCNTs. The Ea values for the epoxy and ether structures differ significantly. The adsorption energies Ea are shown in Figure 3a. The Ea for epoxy-b-O and epoxy-c-O are positive and do not show a clear dependence on the diameter of SWCNTs. In contrast, the Ea for ether-a-O lies in the negative region and increases as the diameter of the SWCNTs becomes larger.
Figure 3. Adsorption energies of isolated O atoms and O2 molecules on SWCNTs. The structures are given in Figure 2. 13202
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Figure 4. Reaction path from (I) physi-b, (II) cyclo-b, and (III) epoxy-a-O2 to (IV) epoxy-b-O + ether-a-O (the structure is shown in (c)) for (a) (6,4) and (b) (8,6) nanotubes studied using the nudged elastic band (NEB) method. The adsorption energy, O−O distance, and spin moment are given as functions of the reaction coordinate, where the summation of the sum of the distances of the O atoms between the images used for the NEB method was normalized for each path. Adsorption energy for the reaction path from (V) ether-a-O to (VI) epoxy-b-O for (d) (6,4) and (e) (8,6) nanotubes.
ranging from −0.7 to −6 kcal/mol for the adsorption energy and from 0.01 to 0.1e− for the amount of charge. However, the results, including our data, qualitatively agree. Note that we have taken into account neither the van der Waals corrections28−30 nor the basis set super position error (BSSE) corrections,31 both of which are important to determine the physisorption energy. The BSSE is a well-known problem originating from localized orbital basis sets when applied to physisorption. The van der Waals corrections will decrease the physisorption energy; the BSSE corrections, on the contrary, will increase the physisorption energy. Our physisorption energies happened to be close to that of O2 onto graphene (−2.5 kcal/mol) calculated using a plane wave basis set and the van der Waals correction.28 These corrections will not significantly change the physisorption energies nor the reaction barriers. When the O2 molecules move closer to the SWCNTs, a cycloaddition product with an O−C distance of approximately 0.15 nm is obtained, as shown in Figure 2f,i (cyclo-a and cyclob) (see also Supporting Information, Table S6). For all the SWCNTs, the O atoms for the cyclo-a and cyclo-b structures have been moved slightly to the sides of bonds “c” and “a”, respectively, because of the chiral structure of the SWCNTs. The adsorption energy lies at approximately 10 kcal/mol, consistent with the results of previous studies.8−10 In general,
the Ea for the cyclo structure increases as the diameter of the SWCNTs becomes larger; however, it also appears to be affected by the chiral angle of the SWCNTs in the case of the cyclo-b structure. The chiral angles of (5,4) and (6,5) nanotubes are larger than those of (6,4) and (8,6) nanotubes (Supporting Information, Table S1). The formation of the cyclo-b structure is more endoergic for (5,4) and (6,5) nanotubes than for (6,4) and (8,6) nanotubes. For all the SWCNTs, the O2 molecule closer to the surface was dissociated and produced a two-epoxy structure (epoxy-cO2 and epoxy-a-O2, Figure 2g,j) (see also Supporting Information, Table S7). As previously described, the O atoms for the cyclo-a and cyclo-b structures were slightly shifted to the sides of bonds “c” and “a”, which led to the subsequent epoxyc-O2 and epoxy-a-O2 structures, respectively. Unlike the cyclo structure, the Ea values for the two adsorption sites of the twoepoxy structure differ significantly. The Ea for epoxy-c-O2 is positive and near that for epoxy-c-O; it appears to be affected by the chiral angle, although the aspect is the reverse of the cyclo-b structure. In contrast, the Ea for epoxy-a-O2 lies in the negative region and increases in a manner similar to Ea for the ether-a-O structure. For epoxy-c-O2, dC−C and γ were found to be approximately the same as those for epoxy-c-O for all the SWCNTs. On the other hand, for epoxy-a-O2, bond “a” that can stretch by increasing α plays an important role to lower the 13203
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Figure 5. Band gap of SWCNTs adsorbed by (a) O atoms or (b) O2 molecules. The adsorption structures are given in Figure 2.
with the fact that oxygen doping is normally not observed without a particular oxidation treatment. Under the experimental conditions that O2 molecules can overcome Eb from physi-b to cyclo-b, the O2 atoms are likely to form the epoxy-a-O2 structure for both CNTs, as shown in Figure 4a,b. We now consider the reverse reaction from the epoxy-a-O2 structure. For (6,4) nanotubes, the Eb from epoxya-O2 to cyclo-b was found to be 42.4 kcal/mol, which is higher than Eb from physi-b to cyclo-b. This indicates that under certain reaction conditions the dissociation of O2 can proceed on (6,4) nanotubes. In contrast, for (8,6) nanotubes, the Eb from epoxy-a-O2 to cyclo-b, which is 36.4 kcal/mol, is lower than Eb from physi-b to cyclo-b. For (8,6) nanotubes, the oxidation is likely to be suppressed because the cycloaddition product cannot be formed or the reverse reaction is faster. The O atoms that reached to the epoxy-a-O2 structure probably also proceed to the epoxy-b-O + ether-a-O structure for both CNTs, as shown in Figure 4a,b. While one of the O atoms on bond “a” moves onto bond “b” the other O atom transforms into the ether structure on the site. The Ea for epoxy-b-O + ether-a-O was found to be approximately equal to the sum of Ea for epoxy-b-O and ether-a-O for both CNTs, indicating that the epoxy-b-O and ether-a-O structures do not interact strongly with each other at a distance of 0.5 nm (Figure 4a,b, middle panels). Finally, we examined the reaction to escape from the ether-aO structure. The adsorption energy for the reaction path between ether-a-O and epoxy-b-O is shown in Figure 4d,e. The Eb values from ether-a-O to epoxy-b-O were found to be 43.4 and 36.3 kcal/mol for (6,4) and (8,6) nanotubes, respectively. For (6,4) nanotubes, the Eb from ether-a-O to epoxy-b-O is higher than Eb from physi-b to cyclo-b, which shows that under certain experimental conditions the ether-a-O structure can be one of the final products, as also proposed for ozone oxidation.1,4 On the other hand, for (8,6) nanotubes, the O atoms are unlikely to maintain the ether-a-O structure under the reaction conditions that O2 molecules overcome Eb from physi-b to cyclo-b. Thus, these results appear to be consistent with the chirality separation experiments where the distinct luminescence peak at E11* observed for (6,4) nanotubes and with the lack of a pronounced luminescence peak for (8,6) nanotubes. Note that the difference in Eb from physi-b to cyclob between (6,4) and (8,6) nanotubes (10.3 kcal/mol) is approximately equal to the difference in their Ea of cyclo-b, which may be important to understand the chirality dependence of the oxidation.
adsorption energy like the ether-a-O structure. For (5,4) nanotubes, dC−C and α are 0.17 nm and 121°, respectively. These dC−C and α, which are somewhat close to those of ethera-O, approach those of epoxy-c-O2 as the diameter of SWCNTs increases. When we moved the O atoms closer to the surface of the SWCNTs, a two-ether structure is obtained only on bond “a” for (5,4) nanotubes (ether-a-O2, Figure 2k) (see also Supporting Information, Table S8). The dC−C and α were found to be 0.21 nm and 127°, respectively. The same initial geometry for the ether structure finished with the epoxy structure after geometry optimization for the other adsorption sites and chirality of SWCNTs. The formation of the ether-aO2 structure is more endoergic than the epoxy-a-O2 structure for (5,4) nanotubes; however, for the other nanotubes, the Ea for two-ether structure may be substantially higher than that for the two-epoxy structure because α is much larger than 120° even for (5,4) nanotubes. Reaction Path from Physisorption to Chemisorption. We should consider not only the adsorption energy of the stable structure but also the reaction path to understand the degree of oxidation. The transformation from physi-b to the structure that is dissociated into epoxy-b-O and ether-a-O (epoxy-b-O + ether-a-O) through cyclo-b and epoxy-a-O2 was examined for (6,4) and (8,6) nanotubes using the NEB method considering the spin polarization. The adsorption energy Ea, O−O distance, and spin moment as functions of the reaction coordinate are given in Figure 4a,b. The schematic diagram for the epoxy-b-O + ether-a-O structure is shown in Figure 4c. For both CNTs, the physisorbed O2 molecule in the triplet state approaches the surface, maintaining the O−O distance but increasing the adsorption energy. The spin moment vanishes near the cycloaddition site, and the O−O distance increases. This transition of the spin state occurs through changes in the bonding character induced by the interaction with CNTs rather than the triplet−singlet transition in O2 molecules (see Supporting Information, Figures S12 and S13). Such magnetic transition induced by changes in the bonding character has been reported on graphitic materials and determined using the NEB method in the spin unrestricted formalism that we used in this study.32−34 The reaction barriers Eb for the formation of the cycloaddition product were found to be 29.0 and 39.3 kcal/ mol for (6,4) and (8,6) nanotubes, respectively. Assuming a standard value of 1013 s−1 as the prefactor, these Eb correspond to the reaction rate of 1.0 × 10−8 and 3.6 × 10−16 s−1, consistent 13204
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The Journal of Physical Chemistry C Band Gap. We finally discuss the band gap reduction in response to the red shift of the luminescence. The band gaps obtained for the adsorption structures Eg* are summarized in Figure 5a,b. For both adsorptions of isolated O atoms and O2 molecules, the Eg* for bond “a” lies relatively near Eg of pristine CNTs, whereas the Eg* for bonds “b” or “c” is further away and shows strong chiral angle dependence, although the aspect reverses between bonds “b” and “c.” In general, the reduction rate of the band gap, which is defined as (Eg − E*g )/Eg, is small for the adsorption structures with low adsorption energy and is increased and scattered as the adsorption energy increases (Supporting Information, Figure S14). The obtained reduction rate of the band gap for the ether-a-O structure that can be one of the final products is 2−3% for all the SWCNTs. Experimental studies of C60 and C70 fullerenes treated with ozone have demonstrated similar results.35,36 The electronic absorption spectra for the ether structure after losing O2 resemble those of the pristine fullerenes. It should be noticed that the electronic structures in our calculations are connected with the ground state. The exciton binding energy and oscillator strength are considered to be increased by localization.37,38 Indeed, a recent time-dependent DFT study39 has shown that the ether and epoxy structures on (6,5) nanotubes that reduce the ground state band gap by 3% and 14% are associated with the localized excitons that cause an 11% and 24% red shift of the E11, respectively. Although we should aim to study the excited states using methods such as time-dependent DFT to compare with the luminescence experiments, our results show that the red-shifted (approximately 10%) peaks of chirality-separated CNTs may be attributed to the ether-a-O structure and that further experiments may observe luminescence peaks with a different energy dependence on the chirality of SWCNTs.
physisorption to the cycloaddition product, and relation between the band gap reduction rate and the adsorption energy. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jp511472k.
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Corresponding Author
*E-mail:
[email protected]. Tel.: +81-46-250-8194. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The calculations were performed on the Fujitsu FX10 supercomputer system at the Information Technology Center, Nagoya University.
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REFERENCES
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CONCLUSION We performed ab initio calculations of chiral (5,4), (6,4), (6,5), and (8,6) carbon nanotubes (CNTs) adsorbed with isolated oxygen (O) atoms or O2 molecules. We found that the energy barrier from the physisorption of O2 to the dissociated twoepoxy structure through the cycloaddition product is lower than that of the reverse reaction for (6,4) nanotubes, whereas the relation is opposite for (8,6) nanotubes, consistent with the distinct luminescence peak at E11* observed for (6,4) nanotubes and with the lack of a pronounced luminescence peak for (8,6) nanotubes in chirality separation experiments. The adsorption energy of the physisorption of O2 does not depend on the chirality, whereas that of the cycloaddition product increases with increasing diameter of the CNTs. The energy difference between these two structures may be important to understand the chirality dependence of the oxidation with O2 molecules. One of the final products under the conditions that the oxidation occurs is the isolated ether structure, as also proposed for ozone oxidation. Unlike the other adsorption structures, the isolated ether structure reduces the ground state band gap by 2 to 3% for all the SWCNTs.
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AUTHOR INFORMATION
ASSOCIATED CONTENT
S Supporting Information *
Supplementary Tables S1−S8 and Figures S1−S14, showing fundamental properties of pristine CNTs, ethylene oxide and dimethyl ether molecules, adsorption energy values, some geometric data, and band diagrams for all of the adsorption structures, spin states in the reaction path from the 13205
DOI: 10.1021/jp511472k J. Phys. Chem. C 2015, 119, 13200−13206
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DOI: 10.1021/jp511472k J. Phys. Chem. C 2015, 119, 13200−13206
