Excited States of Metal-Adsorbed Dimethyl Disulfide: A TDDFT Study with Cluster Model.

The optical near field refers to a localized light field near a surface that can induce photochemical phenomena such as dipole-forbidden transitions. Recently, the photodissociation of the S-S bond of dimethyl disulfide (DMDS) was investigated using a scanning tunneling microscope with far- and near-field light. This reaction is thought to be initiated by the lowest-energy highest occupied molecular orbital (HOMO) to lowest unoccupied molecular orbital (LUMO) transition of the DMDS molecule under far-field light. In near-field light, photodissociation proceeds at lower photon energies than in far-field light. To gain insight into the underlying mechanism, we theoretically investigated the excited states of DMDS adsorbed on Cu and Ag surfaces modeled by a tetrahedral 20-atom cluster. The frontier orbitals of the molecule were delocalized by the interaction with the metal, resulting in narrowing of the HOMO-LUMO gap energy. The excited-state distribution was analyzed using the Mulliken population analysis, decomposing molecular orbitals into metal and DMDS fragments. The excited states of the intra-DMDS transitions were found over a wider energy range, but at low energies, their oscillator strengths were negligible, which is consistent with the experimental results. Sparse modeling analysis showed that typical electronic transitions differed between the higher and lower excited states. If these low-lying excited states are efficiently excited by near-field light with different selection rules, the S-S bond dissociation reaction can proceed.

Introduction

The optical near-field is a localized light field mostly discussed in the context of plasmons, a collective motion of free electrons in a metal.[1−3] Owing to its localization, the near-field is utilized in molecular spectroscopy and microscopy at nanoscale beyond the diffraction limit[3,4] such as surface- and tip-enhanced infrared spectroscopies[5,6] and Raman spectroscopies.[7−10] As the spatial variation of the near-field can be non-negligible, dipole-forbidden transitions can be excited owing to the field gradient.[11] Recently, the near-field has also been applied in photochemistry.[12−15]

Plasmonic materials are frequently used in near-field photochemistry. Charge injections from plasmonic materials to reactant molecules can also drive the chemical reactions.[16−19] For example, in the plasmon-induced water splitting reaction, a strontium titanate (SrTiO3) single-crystal substrate with metal nanoparticles as a photocatalysts is used as an optical antenna to collect and absorb visible light as a photoelectrode.[20] Similar experiments have been reported for ammonium synthesis.[21]

By contrast, the optical near-field can directly induce photoreactions. These photoreactions associate with surface-enhanced Raman measurements that have been known for a long time, although the mechanism remains unclear because an ensemble of molecules with various surface structures contributes to the SERS signal.[22,23] To study photoreactions in the near-field, it is necessary to obtain detailed information about the molecule, such as the adsorption structures and electronic states on the surface to disentangle various factors.[24]

Recent experiments have overcome this difficulty by combining scanning tunneling microscope (STM) and the near-field to study a single molecule photochemical reactions.[13,25−27] In these studies, weakly adsorbed molecules such as dimethyl disulfide (DMDS) on an Ag or Cu(111) surface undergo photolysis directly induced by the plasmon near-field,[13] whereas strongly interacting molecule such as O2 undergo photochemical reactions induced by direct/indirect charge transfer.[27,28]

In DMDS photolysis, S–S bond breaking occurs in both propagating far-field and near-field light.[13,25] For far-field light, photolysis is most effective at 450 nm for Ag(111) and for Cu(111). The reaction is attributed to transitions between the molecular orbitals originating from the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of DMDS. However, the near-field excitation can induce the reaction at energies lower than the far-field excitation, with maxima at 532 nm for Ag(111) and 670 nm for Cu(111). The possibility of vibrational excitation or charge transfer has been excluded by exhaustive experiments; however, the definitive mechanism remains unclear. Band calculations for DMDS/Ag and Cu(111) show that the HOMO and LUMO of DMDS are delocalized and the HOMO–LUMO gap energy is narrower than that of the pristine DMDS. Furthermore, the strong hybridization between the HOMO of DMDS and the metal surface as well as the weak hybridization between the LUMO of DMDS and the metal surface result in longer lifetimes of the intra-DMDS excited state, which is consistent with experimental results. However, no direct theoretical studies of such excited states have been performed to date.[13,25]

In this study, the excited states of free and adsorbed DMDS were investigated via quantum chemical calculations using a cluster model of the surface. The structural and electronic properties of the free and adsorbed DMDS were investigated in detail and compared. Particular attention will be paid to the excited states and oscillator strengths of the adsorbed DMDS to clarify the experimental findings that the photodissociation reaction occurs at different energy maxima.

Computational Details

First, free DMDS was examined, and then adsorbed DMDS was examined using a surface model of a tetrahedral 20-atom cluster (M20) with four (111) faces. Tetrahedral 20-atom clusters have been used to study the structural, vibrational, and electronic properties of adsorbates,[29−32] and Au20 has been reported to exist as a magic-numbered cluster.[33]

Spin-restricted density functional theory (DFT) calculations were used for the ground state, and time-dependent DFT (TDDFT) calculations were used for the excited states. Free DMDS was calculated using C2 symmetry and DMDS/M20 without symmetry constraints.

All electronic structure calculations were performed using TURBOMOLE[34,35] with def-SV(P) basis sets[36] and a relativistic effective core potential for Ag.[36] A range-separate functional of CAM-B3LYP[37] was used to account for the charge transfer nature of some excited states in DMDS/M20 (M = Cu, Ag). It is generally known that the excited state energies are 0.5 eV higher in CAM-B3LYP than B3LYP,[38,39] but the qualitative picture is unchanged.

Excited states were analyzed in detail by classifying molecular orbitals into fragments by Mulliken population analysis.[40] This method is explained in detail in our previous work.[41] Briefly, each MO was decomposed into contributions from the molecule (DMDS) and the metal (M20). The electronic transitions in each excited state are generally given by multiple occupied and unoccupied MO pairs. The fragmentation of MO allows electronic transitions in excited states to be divided into intramolecular, intermetallic, and metal–molecule transitions. Using this analysis, the nature of the excited states can be easily visualized. The excited states of up to 200 states for the Cu cluster and 100 states for the Ag cluster were calculated and analyzed in the energy range up to 300 nm.

While molecular orbital analysis is possible for the optical absorption spectrum of DMDS/M20, the large number of excited states and the complicated hybridization between DMDS frontier orbitals and metal orbitals hamper this analysis. To facilitate the analysis, a sparse modeling analysis was employed to extract the key pairs of occupied and unoccupied orbitals. First, the fractional oscillator strength of the transitions within the DMDS in all excited states was selected as the objective variable. Second, the fractional rates of intra-DMDS transitions for the lower excited states were used to clarify the differences in the nature of the excited states in the low- and high-energy regions. The descriptor is the rate of the occupied and unoccupied orbital pairs in each excited state.

For sparse modeling analysis, the least absolute shrinkage and selection operator (Lasso) is adopted.[42] The Lasso selects a few orbital pairs that contribute to simultaneously explaining the fractional oscillator-strength/rate of intra-DMDS transitions for all excited states. The Lasso solution is defined as the solution to the minimization problemwhere λ ≥ 0 denotes a constant. In the analysis, the N-vector y consists of the fractional oscillator strength/rate of intra-DMDS transitions, where N is the number of excited states. Matrix X of the descriptors is an N × p matrix, where p is the number of orbital pairs. The value of the (m, i)-element of X is the rate of the ith orbital pair to the mth excited state. Specifically, the values used in this study are as follows: Figure a, (N, p) = (200, 2542); Figure c, (N, p) = (100, 676); Figure a, (N, p) = (28, 2542); and Figure c, (N, p) = (51, 676).

Figure 6

Lasso results for partial oscillator strength vs the fractional contribution rate of orbital pairs for all the calculated excited states of (a) DMDS/Cu20 and (b) molecular orbital pairs (upper: unoccupied, lower: occupied) for largest contributions shown by the labels. (c and d) Same results but for DMDS/Ag20.

Figure 7

Same figures as for Figure but the objective variables here are the fraction rates for lower excited states, instead of the partial oscillator strength.

For large λ, the Lasso solution is a zero vector. For a moderately large λ, the Lasso solution is a sparse vector; that is, only a few elements of the solution are nonzero. The selected orbital pairs are expected to contribute mostly to the fractional oscillator-strength/rate of the intra-DMDS transitions of all excited states. The glmnet package in R was used for analysis.[43]

Results and Discussion

Free DMDS

Figure a shows the optimized structure of DMDS in two different directions. The lowest-energy conformer was cis, and optimization starting from the trans conformer (C–S–S–C dihedral angle ∼180°) resulted in a cis conformer (C–S–S–C ∼ 88°). Figure b shows the density of states (DOS), with green and red representing the contributions from S and CH3, respectively. The HOMO and HOMO–1 are degenerate, and the HOMO–LUMO gap energy is 9.19 eV. Figure d shows the relative total energies and C–S–S-C dihedral angles; the two minima correspond to the cis conformer. The lower maximum corresponds to the trans conformer, whereas the higher maximum corresponds to the overlapping orientation of the two CH3 groups. The corresponding rotation barriers are 0.34 and 0.62 eV. These barrier heights are larger than ethane and smaller than ethine, suggesting that the S–S bond is stronger than a normal single bond (∼0.1 eV) and weaker than a double bond (∼2.8 eV).[44] The frontier orbitals shown in Figure c suggest that the HOMO and HOMO–1 contribute to the weak π bonding, in addition to the σ bonding orbital of HOMO–2.

Figure 1

(a) Optimized structures from different directions and the dihedral angle and length of the S–S bond, (b) the density of states where green and red bars show the contribution from S and CH3, respectively, (c) frontier orbitals, and (d) the energy profile along the dihedral angle related to the rotation about the S–S bond of the isolated DMDS.

Figure a shows the calculated absorption spectrum of the free DMDS. The green solid and dashed bars below the x-axis indicate the positions of the singlet and triplet excited states, respectively. The blue bars indicate the oscillator strength, and the red curves are obtained by convoluting the Lorentz function for all oscillator strengths. The lowest singlet and triplet excited states are observed at 244 and 295 nm, respectively. Thus, no absorption peaks are found in the region >400 nm. The calculated absorption spectrum is consistent with the experiment,[45] where the first peak is centered around 265 nm and whose onset is estimated to be around 335 nm. The excitation energy is slightly overestimated in our calculations, as in our previous studies using CAM-B3LYP functional.[46] The two lowest-energy singlet and triplet states are assigned to HOMO–1 and HOMO–LUMO transitions. The S1 state has a large oscillator strength, whereas the S2 state has a very small oscillator strength but is not forbidden. The transition dipole moments from the ground state to the S1 and S2 states are parallel and normal to the C2 axis, respectively. As shown in Figure c, the LUMO is antibonding in nature. Both S1 and S2 excited states are directly related to the photolysis. Excitation to S1 or other higher lying excited states relaxed to the lowest energy states causes dissociation of the S–S bond.

Figure 2

(a) Absorption spectrum of free DMDS. Green solid and dashed bars, blue bar, and red lines show the position of the singlet and triplet excited states, oscillator strength, and absorption curve obtained by convoluting the oscillator strength with a Lorentz function. (b–e) Excited state energy profile plotted against the S–S bond length. Black horizontal lines in the right show the position of eigenstates of the same spin multiplicity and S0 at the bottom, calculated at the final step (S1, S2) and 1/2 steps from the last (T1/T2) of the optimization. T1 and T2 optimizations are terminated by the SCF convergence problem in the S0 state due to the smaller HOMO–LUMO gap energies. S1 and S2 optimizations are finished at a S–S bond length of about 2.5 Å.

Parts b–e of Figure plot the energy change in the process of geometry optimization in the excited states after vertical excitation from the ground state equilibrium structure as a function of S–S bond length. The horizontal bars on the right-hand side indicate the positions of the S0 and excited states with the same spin multiplicity as the optimized one. The geometry optimizations of the T1 and T2 states stopped due to convergence problems because of the small HOMO–LUMO gap energy in the S0 state. In such cases, one or two steps before the final state can be used to show the S0 and excited states. Geometry optimizations for the S1 and S2 states end around the S–S bond length of 2.5 Å. In these states, the S–S bond is elongated and can be dissociated by excitation. After the optimizations, the S2 and T2 states become the S1 and T1 states, respectively. No such changes in the energy orderings are found for S1 and T1 optimizations. In TURBOMOLE, only one symmetry can be selected in the geometry optimization of the excited states, and other states with different symmetries cannot be calculated simultaneously.

In the singlet-excited-state geometry optimization, the S–S bond was elongated and slightly shortened at the end. This differs from previous studies that used CASSCF/CASPT2 for the S1–S4 states.[47] However, the previous study calculated the excited-state energies only by stretching the S–S distance and did not perform a full optimization. Therefore, there is no substantial contradiction in the present results. The properties of the S1 and S2 states, such as symmetry and electron configuration, are the same as those reported in previous studies. This guaranteed the accuracy of the calculations. As for the energies of the excited states, our results are approximately 1 eV smaller than the previous ones, but the qualitative features are the same, and the following discussion is reliable.

DMDS/M20

Hereafter, the structural and electronic properties of the adsorbed DMDS are studied using 20-atom tetrahedral clusters as substrates. Although the size of the cluster should ideally be larger than 2 nm in radius as the density of states of the cluster is close to its bulk counterpart,[48] this requires us to treat more then 300 atoms, which is heavily demanding for performing excited state calculations and analysis. The use of a small-size cluster may overestimate the HOMO–LUMO gap energy (while this also depends on the density functional), the sparse density of state of cluster may induce rather inhomogeneous interactions with an adsorbate, and existence of edges can affect the adsorption geometry. Nevertheless, the 20-atom cluster used here gives a rather reasonable adsorption geometry, while sparse but substantial interactions with the adsorbate broaden its HOMO and LUMO. On the other hand, the HOMO–LUMO gap energy is surely overestimated, but the qualitative picture and main conclusions should be intact.

Geometric Structure

Geometry optimization was performed on several initial structures, and the two lowest energy optimized structures obtained are shown in Figure , along with their relative energies and representative bond lengths. The optimized structures shown in parts a and b of Figure correspond to the experimentally resolved structures of DMDS adsorbed on Cu and Ag surfaces, respectively,[25] in which the two S atoms are on the surface metal atoms. By contrast, parts c and d of Figure show different adsorption structures of DMDS/Cu20 and DMDS/Ag20, respectively, where one S atom is located on the metal atom and the other on the bridge site. The latter structure has a lower energy, but the energy difference with the former structure is almost the same, that is, less than 0.06 eV. Similar structures were obtained using functionals other than CAM-B3LYP. Because the energy difference is negligible, the present cluster model can be used for analysis. The structures shown in parts a and b of Figure were used to study the excited states. The two S–M distances are different for the structures in parts a and b of Figure ; however, this is due to the use of finite-size clusters as the surface model. Calculations using the slab model yielded the same S–M distances for the Cu and Ag surfaces.[25]

Figure 3

Optimized structures of (a, c) DMDS/Cu20 and (b, d) DMDS/Ag20 with different adsorption sites, viewed from different directions, along with relative total energies in eV and representative bond lengths in Å.

For future reference, the IR and Raman spectra of free DMDS and DMDS/Cu20 and DMDS/Ag20 are given in the Figure S1 in the Supporting Information. The frequencies of the S–S stretching mode are 510, 486, and 503 cm–1 for the free molecule and that adsorbed on Cu and Ag, respectively. The frequencies suggest that the S–S bond is weakened upon the adsorption and the Cu is better to activate the S–S bond.

Electronic Structure

Figure shows the DOS and several Kohn–Sham orbitals of DMDS/Cu20, DMDS/Ag20, and DMDS. Figure a shows the total DOS of DMDS/Cu20, below which the partial DOS (PDOS) of DMDS in DMDS/Cu20 is plotted. Blue, green, and red indicate contributions from Cu, S, and CH3 groups, respectively, from the Mulliken population analysis.[40]Figure b depicts the same DOS for DMDS/Ag20. For comparison, the DOS of the free DMDS is shown in Figure c. Focusing on the PDOS of DMDS, it can be seen that the HOMO, HOMO–1, and LUMO of free DMDS are delocalized owing to interactions with the metal atoms. The effective HOMO–LUMO energy gap of DMDS, estimated using the edge of the PDOS of DMDS, is significantly reduced from 9.2 eV to about 4 eV by adsorption.

Figure 4

Total and projected density of states for (a) DMDS/Cu20, (b) DMDS/Ag20, and (c) DMDS. Representative KS orbitals for (d) DMDS/Cu20 and (e) DMDS/Ag20.

Let us compare the Cu and Ag substrates. The 3d band edge of Cu is located near −8 eV, close to the HOMO of free DMDS, and has a higher energy than the 4d band edge of Ag (−9 eV). Because the 3d band is energetically closer to the HOMO of free DMDS, the interaction is stronger, and the distribution of the PDOS of DMDS is wider on Cu than on Ag. By contrast, the HOMO of DMDS is slightly localized on the Ag substrate. This difference in the HOMO distribution affects the structures of the excited states.

Parts d and e of Figure show representative Kohn–Sham orbitals of DMDS/M20 where the large contribution of DMDS is indicated by the DOS. HOMO–5 and LUMO+7 of DMDS/Cu20 and HOMO–7 and LUMO+11 of DMDS/Ag20 appear to be derived from the HOMO and LUMO of free DMDS.

Excited States

Figure shows the results of the analysis of the excited states and the calculated absorption spectrum of DMDS/Cu20 is shown in Figure a. Each excited state was fragmented, as explained in the computational section. The fraction of excited states is shown in Figure b, where each column is labeled and divided into intrametal (green), metal to molecule (red), molecule to metal (blue), and intramolecular (purple) transitions. Finally, each fraction was multiplied by the oscillator strength to obtain the absorption fractions, as shown in Figure c. The same is true for Ag20, as shown in Figures d–f. In the present model, the transitions within the metal make the largest contribution; however, this amount depends on the cluster size and geometry of the model. Notably, the intramolecular transitions, shown in purple, were thoroughly investigated and found to be the origin of the photodissociation of the S–S bond.[25]

Figure 5

(a) Absorption spectrum, (b) transition fractions, and (c) transition fractions with oscillator strength (i.e., the absorption fractions) of DMDS/Cu20. (d–f) Corresponding properties for DMDS/Ag20.

From the results for DMDS/Cu20, the excited states originating from intramolecular transitions exist with negligibly small oscillator strengths of approximately 500 nm. The experimental findings showed that the largest S–S dissociation rate of near-field excitation was approximately 100 nm shorter wavelength than the propagating light excitation. The present computational results are consistent with these results. The excited states localized to molecule exists in the lower-energy region, but their oscillator strength is small. The oscillator strength is the absorption rate of the propagating far-field light. With near-field light, the selection rule can change, and thus, there is a possibility of strongly exciting these lower-energy excited states than the higher-energy regions. It should be noted that the plasmonic absorption spectra simulated for the nanogap between the STM tip and surface have maxima in the lower-energy regions, coinciding with the photodissociation rate maxima with the near-field.

This observation is clearer for Ag substrate. From Figure d–f around 400 nm, the excited states localized to DMDS exist, but the oscillator strength is very small.

Experiments showed that the maximum photodissociation rate of Ag is energetically higher than that of Cu, and the peak is sharper.[13] In other words, the Cu is more useful for lowering excitation energy for the photolysis. This behavior is also observed in the present calculations. This difference can be attributed to the d-band edge. As discussed above, the top of the 3d-band is energetically close to the HOMO of the free DMDS, so the interaction between the HOMO of the molecule and the 3d band becomes stronger and the distribution of the HOMO of the molecule widens, as shown in Figure . This broadening is reflected in the excited-state distribution and the absorption spectrum, as shown in Figure .

To gain further understanding of the intra-DMDS contributions in the excited states, we performed a sparse modeling analysis (Lasso in this study) to determine the governing occupied and unoccupied orbital pairs. First, the oscillator strength in all computed excited states is used as an objective variable, the results of which are shown in Figure . Second, for the lower energy region, where the oscillator strengths are small, the fractional rate is used as an objective variable, as shown in Figure . For Cu and Ag, S1–S28 (>440 nm) and S1–S51 (>359 nm) were used for the later analysis, chosen to be the lower-energy region.

Parts a and c of Figures and 7 are called the path diagrams, which show the Lasso solutions for various values of λ. The horizontal axis is the L1 norm, the length of the vector |β| = ∑|β|, which is determined by fixing λ There is one-to-one correspondence between the Lasso solution {β} and λ, while not direct/inverse proportion. The vertical axis is the value of each β. The unit of β is determined by y/X. In the present case, y is the fractional oscillator strength or rate of intramolecular transitions, while X is the contribution rate of the orbital pairs. As both y and X are kind of unitless, given by the arbitrary unit, β can also be unitless. The quantitative comparison of β among different path diagrams is difficult or even meaningless as the dimension of the vectors can change, while qualitative comparisons can be made. A path diagram shows how large an element of a solution is among all the elements of the solution. Roughly speaking, a large value of β implies the relative importance of the ith orbital pair. In the analysis, Lasso can perform unstably for too small λ because the number of rows is smaller than that of the columns of the matrix X. Therefore, the path diagrams were trimmed to focus on important solutions corresponding to large and moderate values of λ. The solution to the right corresponds to the smaller λ. In the following, the coefficients of negative values or of exponential increase are considered to be ill-behavior.

Figure shows the Lasso results for the chosen L1 norm range for DMDS/Cu20 and DMDS/Ag20. For DMDS/Cu20, shown in Figure a, the three prominent contributions are extracted, and the orbital pairs are shown in Figure b, where unoccupied and occupied orbitals are shown in the upper and lower parts. While the occupied orbitals are not clearly localized to DMDS, the unoccupied orbitals for α and γ show the LUMO nature of DMDS. However, the stronger hybridization between the DMDS and Cu20 orbitals makes this less clear. For DMDS/Ag20, the Lasso result is much simpler and one of the three major contributions, α has the clear HOMO–LUMO nature of DMDS. These orbital pairs are the origin of the optical transition localized in the DMDS. As the main orbital pairs found by the Lasso include the transitions to the LUMO of DMDS (α and γ for Cu20, and α for Ag20 substrates in Figure ), which is an antibonding nature for S–S bond, the intramolecular transitions with substantial oscillator strength can trigger the photolysis.

Let us consider the lower-energy region, where the partial oscillator strengths are small. Based on the comparisons between Figures and 7, the dominant orbital pairs were changed, though α of DMDS/Cu20 looks similar. To interpret this, electronic transitions to the molecular LUMO disappear from the selected orbital pairs, except for α of DMDS/Cu20, which may cause weaker interactions with far-field light. While transition dipole moments are smaller for lower lying excited states, the quadrupole and further multipole interactions may be possible if a near-field is used. This should be addressed in the future studies.

Before concluding this work, it is worth mentioning that we optimized the geometry of some of the selected excited states of DMDS/M20. During the optimization process, we observed an elongation of the S–S bond; however, as shown in Figure , the high density of excited states in the high-energy region caused frequent switching of excited states, which hindered the convergence. To solve this problem, it is necessary to develop a theoretical method that can simultaneously handle the high-density excited states for structural relaxation.

Conclusions

In this study, we investigated the excited states of free and adsorbed DMDS molecules on a 20-atom tetrahedral cluster model substrate to clarify the mechanism of photolysis induced by far- and near-field light, showing energy differences of approximately 100 nm lower for the near-field than for the far-field. Using the TDDFT method, excited states corresponding to intramolecular transitions that may trigger the photolysis were found over a wider energy range. However, there is a large difference in the oscillator strength. Excited states in the low-energy region are mostly forbidden in the far-field, whereas they are allowed in the high-energy region. In the experiment, the near-field was stronger in the low-energy region than in the high-energy region. The selection rules may be different for far- and near-field light. A low-energy region is allowed and may be strongly excited in the near field, but this also needs to be proven theoretically. In the future, we would like to study the near-field excitation of the DMDS to obtain direct evidence.