Transition in the Molecular Orientation of Phenol Adsorbates on the

Mar 16, 2012 - Department of Chemical Engineering, Stanford University, 381 North-South Mall, Stanford, California 94305, United States. •S Supporti...
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Transition in the Molecular Orientation of Phenol Adsorbates on the Ge(100)-2 × 1 Surface Bonggeun Shong and Stacey F. Bent* Department of Chemical Engineering, Stanford University, 381 North-South Mall, Stanford, California 94305, United States S Supporting Information *

ABSTRACT: The coverage-dependent adsorption behavior of phenol on the germanium (100) surface was studied with multiple internal reflection Fourier transform infrared (IR) spectroscopy and density functional theory (DFT) calculations. Phenol chemisorbs via O−H dissociation to form adsorbed phenoxy. A transition between two adsorption configurations as a function of phenol exposure is found. Polarized IR results indicate that the surface phenoxy group lies flat in the low-exposure regime and stands upright upon higher exposures. DFT calculations also support the lying down to standing up transition through both simulated IR shifts and calculated adsorption energies. A π-complex between the phenyl ring and the surface Ge dimer is formed for the lying down configuration, causing a decrease of surface reactivity and necessitating large exposures to form the standing up orientation. neighboring surface dimer.19 In another example, phenylthiol molecules adsorbed on Ge(100) were found to form a mixture of lying down and standing up configurations.20 Understanding molecular orientation in aromatic adsorbate systems is important since orientation plays a critical role in the performance of organic electronic devices and is in many cases determined by the surface functionalization of the substrate.21,22 In this study, we explore the coverage-dependent adsorption behavior of phenol on the Ge(100)-2 × 1 surfaces, by a combination of Fourier transform infrared (FTIR) spectroscopy experiments with density functional theory (DFT) calculations. Our results show that phenol is adsorbed by O−H dissociation on Ge(100). At low exposure, the phenyl ring of the surface phenoxy group is lying down with its ring interacting with the surface. With further exposure, a structural transition to the standing up configuration occurs. The molecular orientations of the adsorbates are quantitatively determined by analysis of polarized IR spectra.

1. INTRODUCTION Direct organic functionalization of semiconductor surfaces has gained increasing interest in recent years.1−4 The (100) surfaces of Ge and Si are reconstructed under vacuum to form dimers that possess both double bond and zwitterionic character,1 allowing reactions similar to those found in organic chemistry such as cycloadditions5 and acid−base reactions.6 Germanium, in particular, has excellent electronic properties, making it an attractive alternative material for electronic devices7 as well as high Li+ diffusivity, which makes it of interest for Li-ion battery anodes.8 However, unlike SiO2, the native Ge oxide is chemically unstable and thus proper surface treatment is required for future applications.1,7 Reactions on a clean Ge surface are more controllable than those on Si surfaces because of its lower reactivity;1,2 for instance, benzene can only physisorb on Ge(100)9 while it chemisorbs on Si(100).10 Adsorption of aromatic molecules on a semiconductor surface provides possibilities for tuning of the surface properties for applications in nano- or opto-electronics.11−13 On Si or Ge surfaces, substituted benzene derivatives often show selective reactions toward preserving their aromaticity.5,14 Phenol is an aromatic molecule that can be attached to a semiconductor surface through its hydroxyl group. A previous experimental study showed that the phenol is adsorbed on Si(100) via O−H dissociation,15 while theoretical studies considered formation of covalent Si−C bonds as possible further interaction of the phenyl group with the surface.16−18 Even if no covalent bond is formed between a carbon atom and the surface, the aromatic rings can still be involved in long-range interactions with the surface if the adsorbate is anchored by another moiety. For example, the phenyl group of styrene adsorbed on Ge(100) was found to lie down close to the electrophilic down atom of a © 2012 American Chemical Society

2. EXPERIMENTAL AND COMPUTATIONAL METHODS FTIR spectroscopy experiments were conducted in a previously described ultrahigh vacuum (UHV) chamber6 with a base pressure of less than 1 × 10−10 Torr. Briefly, the surface of a trapezoidal Ge(100) crystal (Harrick Scientific, 19 × 14 × 1 mm, 45° beveled edges) was cleaned via two cycles of Ar+ sputtering and annealing. Cleanliness of the sample was confirmed with Auger electron spectroscopy, and the 2 × 1 Received: January 31, 2012 Revised: March 5, 2012 Published: March 16, 2012 7925

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reconstruction was confirmed by low-energy electron diffraction (LEED). IR spectra were collected in multiple internal reflection (MIR) geometry by a BioRad FTS-60A spectrometer equipped with a liquid nitrogen cooled HgCdTe detector. All spectra were manually corrected for baseline sloping. Absorption by the CaF2 viewports resulted in a low-frequency cutoff of ∼1050 cm−1. A wire grid polarizer (Cambridge Physical Sciences IGP-225) was placed in the beam path for the polarized spectra. Phenol (>99%, Acros Organics) was purified by repeated freeze−pump−thaw cycles. The molecular identity and purity of the reactant were confirmed with an in situ quadrupole mass spectrometer. Phenol vapor was exposed to the Ge crystal through a variable leak valve. Surface exposures are reported in langmuirs (1 L = 10−6 Torr·s). Pressures were not corrected for ionization gauge sensitivity. Density functional theory calculations were performed using the Gaussian03 software package23 with B3LYP, B3PW91, PBE0, BP86, and TPSSh exchange-correlation (XC) functionals. A Ge23H24 two-dimer trench cluster whose top two Ge layers were allowed to relax from the ideal Ge crystal positions was used to model the Ge(100) surface. The adsorbate molecules and the Ge dimer atoms were modeled with a 6311++G(d,p) basis set, and a LANL2DZ pseudopotential was used for the subsurface Ge atoms. The terminating H atoms were modeled with a 6-31G(d) basis set. In vibrational frequency calculations, these hydrogen atoms were assigned a mass of 74.0 amu to match the atomic mass of Ge. Relative IR absorption intensities are calculated by analytically determining dipole moment derivatives. Lorenzian lineshapes with a fwhm of 10 cm−1 and relative calculated intensities were used to represent IR bands. The transition states were initially guessed and then confirmed after optimization to have an imaginary vibrational frequency along the reaction coordinate. All reported energies were zero-point corrected. The default convergence criteria of Gaussian03 were used in all geometry optimizations, which include an energetic change of 1 × 10−6 Hartree (6.3 × 10−4 kcal/mol) per step.

Figure 1. IR spectra of phenol on Ge(100)-2 × 1. (a) Physisorbed multilayer at 130 K (scaled); (b−f) chemisorption spectra at 310 K with exposures in the range of 10−104 L; and (g) DFT calculated spectra of an O−H dissociated phenol (dashed line, standing up; solid line, lying down).

with the phenoxy moiety lying down (LD) and the other with phenoxy standing up (SU) relative to the surface. Thus, we assign the lower exposure and higher exposure features in the IR spectra to LD and SU configurations, respectively. The Ge− H stretching mode at 1980 cm−1 did not show a frequency change with exposure; peaks at 1230 and 1240 cm−1 were assigned to different modes for LD and SU according to the calculated absorption intensities in each structures. The full assignment of the IR spectra is summarized in Table 1. The frequency shifts, Δν̃, listed in the table are defined as Δν̃ = ν̃SU − ν̃LD. Table 1. IR Assignments for Phenol on Ge(100)-2 × 1a

3. RESULTS 3.1. IR Spectroscopy Results. Figure 1 shows the IR spectra of phenol adsorbed on Ge(100) with varying exposures. The low-temperature physisorption spectrum (a) matches well with the IR spectra of phenol in the literature.24,25 The chemisorbed spectra (b−f) differ from that of the multilayer but match well with the calculated spectra of O−H dissociated phenol (g). In these B3LYP-simulated spectra, the frequencies were scaled by a factor of 0.97.26 IR spectra showing the frequency range of 1050−3500 cm−1 are given in the Supporting Information (Figure S1). Two states of adsorption are observed in the chemisorption IR spectra, which will be identified by the following analysis as lying down in the low-dose regime and standing up in the highdose regime. First, under the low dosages of 10 and 40 L (b, c), the shapes and the positions of the peaks are constant, while the intensity increases with dosage. Next, under the highexposure regime of 102 L to 104 L (d−f), a transition can be seen manifested in the growing shoulders of a second adsorption state, identified as the standing up configuration. Even with an exposure of 104 L (f), trace vibrations corresponding to the first state are still present. These frequency shifts closely parallel those found in the calculated spectra of two different configurations of adsorbed phenol: one

a

mode (cm−1)

ML

CC stretching 1 C−H bending 1 C−H bending 2 C−O stretching O−H bending 1 C−H bending 3 CC stretching 2 O−H bending 2 ring stretching 1 ring stretching 2 ring stretching 3 ring stretching 4 Ge−H stretching O−H stretching

1073 1154 1169 1227 1240

LD

SU

Δν̃

1158 1228

1161 1214

3 −14

1230 1240 1378 1477 1500 1597 1607

1476 1574

1484 1588

8 14

1980

1980

0

3253

The assignments for multilayer (ML) are based on refs 24 and 25.

To help understand the coverage dependent spectral transition during phenol adsorption, the Ge surface with phenol exposures of 102 L, 103 L, and 104 L was probed with polarized IR spectroscopy. Polarized spectra after 103 L phenol exposure are presented in Figure 2. The features assigned to SU consistently show smaller intensities in the s-polarized 7926

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of phenol molecules and Ge clusters isolated from each other but fixed at LD and SU geometries are compared. The adsorbate and the cluster undergo structural deformation upon interaction. Therefore, the separated cluster and the adsorbate fixed at the chemisorption geometries are less stable than that of their respective fully optimized structures, with the degree of destabilization reflecting the degree of deformation. Assuming the Ge−O and the Ge−H bond strengths are independent of the configuration, the separated cluster and molecule with LD geometries are 2.5 kcal/mol less stable than that of their SU counterparts. This supports the theory that the LD configuration is largely stabilized through interactions of phenyl with the empty Ge dimer but not other structural change during the transition such as deformation of the cluster itself. The magnitude of the π-interaction, E(π), is defined as E(π) = ΔE + ΔE(separated), where ΔE(separated) is the energetic difference between the separated cluster and molecules with LD and SU geometries. In previous studies, similar calculations were shown to predict differences in experimental adsorption energies on the group IV semiconductor surfaces within 1−2 kcal/mol.6,28,29 However, B3LYP is known to underestimate dispersion interactions,30 which can partly account for the phenyl−dimer interaction. Therefore, we employed four other popular XC functionals, including two hybrid (B3PW91 and PBE0), one GGA (BP86), and one hybrid meta-GGA (TPSSh) to more accurately capture the transition between LD and SU. All these functionals consistently gave positive ΔE values that are larger than the B3LYP result, implying that the calculated energetic difference between the LD and SU states is significant. When averaged over the values from the 5 optimized geometries, the tilt angles of the optimized structures from the surface normal are 77 ± 1° and 40 ± 2° for the LD and SU, respectively; the molecular axis is azimuthally rotated 15 ± 1° from the direction of the next surface dimer in LD (Figure 4). Moreover, as shown

Figure 2. p- and s-polarized IR spectra of 103 L phenol adsorbed on Ge(100)-2 × 1 at 310 K.

spectrum, while the intensities of LD peaks slightly increase. Similar variations in peak intensity between s- and ppolarization were observed for all exposures studied. The dichroic ratio D is defined by D = As/Ap, where As and Ap are the integrated absorbance of each peak in the s- and ppolarized spectra, respectively. The areas below the ring stretching modes 2 and 3 were used in the calculation of D because they do not overlap significantly with other modes, and their signals are well above the noise level. A purely Gaussian line shape was used for deconvolution of each IR peak. The average D values for LD and SU configurations were determined to be DLD = 1.06 ± 0.11 and DSU = 0.76 ± 0.08. 3.2. DFT Calculation Results. Figure 3 shows energies of critical points along the reaction pathway of phenol on

Figure 3. Reaction coordinate diagram for phenol on Ge(100). The O-dative bonded intermediate state, O−H dissociation transition state, O−H dissociated lying down state, and OH dissociated standing up state are marked as IS, TS, LD, and SU, respectively.

Ge(100), calculated with the B3LYP functional. O−H dissociation can readily happen, similar to the reactions of aliphatic alcohols on Ge(100).27,28 The kinetic barrier from the intermediate (IS) to the transition state (TS) of 10.5 kcal/mol is smaller than that for the reaction of ethanol (15.8 kcal/mol) calculated at the same level of theory,28 which can be explained by the higher acidity of phenol. However, unlike methanol or ethanol, two distinct local energy minima (LD and SU) were found for the O−H dissociated product. In the LD geometry, the phenoxy moiety is inclined toward the surface, allowing a πinteraction between the phenyl ring and the adjacent empty Ge dimer. However, in the SU geometry, the adsorbate is separated from the dimer and the π−π interaction is lost. The energetic difference between two configurations (ΔE = E(SU) − E(LD)) was calculated as 2.0 kcal/mol, which is much smaller than the adsorption energy itself but large enough to hold the adsorbate on the surface by suppressing vibrational or rotational motions. To clarify whether the energetic difference originates from the formation of the π-complex or from other changes accompanying the transition, the sum of the calculated energies

Figure 4. Top view of phenol adsorbed on the Ge cluster in LD configuration. Green, Ge; red, O; gray, C; white, H; and blue, the neighboring down Ge atom.

in Figure 1a for B3LYP as an example, frequency shifts of phenol adsorbates were observed in DFT simulations of the IR spectra with the above functionals. Scaling factors of 0.97, 0.97, 0.96, 1.0, and 1.0 were used for the frequencies calculated with B3LYP, B3PW91, PBE0, BP86, and TPSSh, respectively.26 The calculated IR shifts, energetic differences, and magnitudes of πinteraction are summarized in Table 2.

4. DISCUSSION 4.1. Orientation of the Adsorbate at Each Configuration. The p-polarized light in our MIR setup nearly equally probes vibrations with dipole moments parallel and perpendicular to the surface.31,32 Thus, the p-polarized spectrum in Figure 2 is similar to the unpolarized spectrum in Figure 1e except for a lower signal-to-noise ratio. However, the s7927

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LD configuration, while in the SU configuration, the adsorbate stands up further from the surface. These tilt angles are close to the calculated values within errors (γLD = 77 ± 1° and γSU = 40 ± 2°). 4.2. Formation of Phenyl−Dimer π-Complex. The azimuthal rotation of the molecular axis in the LD configuration causes the C3C4 double bond to be located close to the electrophilic down atom, where the π* orbital of the surface dimer is localized. A π-complex is formed by interaction between the adsorbate HOMO and the surface LUMO. This noncovalently bound structure is considered as an intermediate for [2 + 2] cycloaddition reactions of unsaturated hydrocarbons on the Si or Ge surfaces.39,40 The calculated E(π) values in the range of 4.5−9.5 kcal/mol are comparable to the estimated πcomplex binding energy of ethylene on Ge(100) of 5.1−9.2 kcal/mol.40 Moreover, the rotation of the adsorbate in the calculated geometry moves the more negatively charged C4 atom41 and the aromatic ring itself farther from the positively charged down atom, suggesting that the formation of a πcomplex is more important than electrostatic interaction between the ring and the down atom in stabilizing the LD configuration. The features of the phenoxy adsorbates in the chemisorption IR spectra show blue- or red-shifts upon transition from LD to SU. These shifts are also explained by the π-complex formation. In the LD configuration, the π electron density of the phenyl ring is donated to the down atom as they come in proximity to each other. The decrease in electron density of the aromatic ring causes red-shifts of the ring stretching modes.42 At the same time, the movements of C atoms during C−O stretching are restricted as the ring becomes bound to the surface. This additional strain results in a blue-shift of ν(C−O). The reverse shifts are found at the LD to SU transition as the π-interaction is lost. While the directions of the frequency shifts found in the calculations were the same with the experiments, the magnitudes of the shifts varied according to the XC functional used. Functionals that estimated stronger π−π interactions and thus larger ΔE values tended to predict larger Δν̃ values, especially for the ring stretching modes. The ring stretching modes involve significant potential energy distributed on CC vibrations compared to other modes,25 so the stronger the πcomplex formed, the larger the shifts that are found. Therefore, it is concluded that the π-complex formation cause the shifts in the IR spectra. 4.3. Decrease in the Surface Reactivity after LD Saturation. It is notable that the sticking probability of phenol decreases significantly after the surface is covered with LD adsorbates. From the IR spectra (Figure 1), the LD saturation occurs at exposure of 40 L, while SU saturation is not achieved until an exposure of 104 L. Thus, the reactivity of the surface during the spectral transition after LD saturation is at least 250-fold smaller than the reactivity during LD adsorption on the bare surface. Since the LD adsorbate covers the down atom of the adjacent dimer, only the electron-rich up atom of the dimer is exposed to the reactant molecules. It is generally accepted that proton transfer reactions on the (100)-2 × 1 surfaces of Si or Ge proceed through a precursor state in which the O or N atom of the reactant molecule is dative bonded to the down atom.6 The dimer, once it forms a π-complex with already adsorbed phenol, would have both a smaller effective area for collision and a lower electron affinity. Therefore, we expect that

Table 2. IR Shifts, Energetic Differences between SU and LD Configurations, and Magnitudes of π-Interaction Calculated with Each XC Functional Δν̃ (cm−1)

B3LYP

B3PW91

PBE0

BP86

TPSSh

C−H bending 2 C−O stretching ring stretching 2 ring stretching 3 ΔE (kcal/mol) E(π) (kcal/mol)

4.9 −4.5 3.3 13.2 2.0 4.5

4.5 −5.0 4.4 16.1 3.3 6.9

5.0 −5.0 5.8 17.0 5.5 9.5

3.6 −2.8 3.6 16.5 3.2 7.1

2.8 −3.7 4.3 16.4 3.3 6.8

polarized light has an electric field component entirely parallel to the surface plane, so that only the parallel components of the vibrations are probed.31,32 Therefore, the selective decrease in the intensities of SU peaks in the s-polarized spectra suggests that the adsorbate vibrations in the SU configuration have more significant perpendicular components, while in the LD configuration the vibrations are more parallel to the surface. From the experimental dichroic ratio, we can estimate the molecular orientation of the phenol adsorbate in the LD and SU configurations. For an internal reflection geometry, the electric field amplitude components of the IR light in each direction are given by eqs 1−3 where the x, y, and z axes, respectively, are along, across, and perpendicular to the surface plane.33 Ex =

Ey =

Ez =

2(cos θ)[sin 2 θ − n313])1/2 (1 − n312)1/2 [(1 + n312) sin 2 θ − n312]1/2

(1)

2 cos θ [1 − n312]1/2

(2)

2(cos θ sin θ)n32 2 (1 − n312)1/2 [(1 + n312) sin 2 θ − n312]1/2

(3)

Here, θ is equal to 45° for our trapezoidal crystal, and nab = na/ nb. The refractive indices in the 1100−1800 cm−1 region are n1 = 4.01 for Ge,34 and n3 = 1 for vacuum by definition. The refractive index of phenol of 1.542 is adopted for n2 of the adsorbate.35,36 Inserting all these parameters into eqs 1−3, we obtain Ex = 1.41, Ey = 1.46, and Ez = 0.634. In the case of the surface phenoxy adsorbates, the transition dipole moments of the ring stretching modes are all nearly parallel to the molecular axis, i.e., the direction of the C−O bond. Assuming that each LD and SU structure is uniaxially oriented around the surface normal,37 the dichroic ratio D is given as a function of the tilt angle, γ, by38 D=

Ey 2 sin 2 γ Ex 2 sin 2 γ + 2Ez 2 cos2 γ

(4)

which can be rearranged to yield γ from D ⎡

⎤ ⎥ γ = tan ⎢ 2 2⎥ − E DE y x ⎦ ⎣ −1⎢

2DEz 2

(5)

By inserting the dichroic ratios for each configurations along with Ex, Ey, and Ez into eq 5, we get the tilt angles of phenol adsorbate at each configurations of γLD = 82 (+ 8, − 21)° and γSU = 45 (+ 6, − 5)°. These values are consistent with the conclusion that the adsorbate leans toward the surface in the 7928

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Notes

an LD adsorbate-covered dimer loses reactivity upon dissociative adsorption of phenol, whereas the uncovered dimers can participate in further reaction. However, if the system is in thermal equilibrium, some fraction of the adsorbates take the SU configuration, releasing the phenyl-covered dimer and enabling further reaction. Assuming a Boltzmann distribution for LD and SU states, ΔE of 3.4 kcal/mol corresponds to a fraction of 1/250 of SU at 310 K. Decreasing the fraction of SU to 1/1000 yields ΔE of 4.3 kcal/mol. These energies match well with the DFT-calculated ΔE between 2.0 to 5.5 kcal/mol. With these estimates, less than 0.5% of the adsorbates would be expected to be in the SU configuration at saturation of LD. This small fraction would not be easily discernible in the IR spectra, which is consistent with our observations of a single adsorption regime at low dose. Therefore, the low reaction probability of phenol on the LDsaturated surface is attributed to the small fraction of uncovered Ge dimers. However, at higher doses, two phenol molecules may be adsorbed adjacent to each other. Then, there would be no empty down atom that can form the π-complex with the phenyl rings, so that the adsorbates would only be present in the SU configuration. Carbone et al. found that the activation barrier for O−H dissociation of phenol on Si(100) is almost independent of the coverage.17 We expect this to hold on Ge(100), too, as the larger lattice constant of Ge may decrease adsorbate−adsorbate interactions. Hence, once a phenol molecule encounters an uncovered Ge dimer, the reaction would proceed as it does on a bare surface whether a SU adsorbate exists next to the dimer or not. Furthermore, the adsorption energy per phenol molecule on Si(100) becomes higher approaching saturation because of dispersive attraction between the adsorbates.18 Thus, energetically, it would always be more favorable to adsorb another molecule until the surface is saturated.

The authors declare no competing financial interest.



ACKNOWLEDGMENTS This work was supported by the National Science Foundation (CHE-0910717). B.S. acknowledges the Samsung Scholarship for the fellowship support. Scientific discussions with K. T. Wong and S. M. Herron were highly appreciated.



5. CONCLUSIONS Phenol chemisorbs on the Ge(100)-2 × 1 surface by O−H dissociation to form a phenoxy adsorbate. Chemisorbed phenol undergoes a structural transition from lying down to standing up with increasing exposure. The molecular orientations of the adsorbates were quantitatively verified by polarized IR experiments and theoretical calculations. In the lying down configuration, adsorbates lean toward an adjacent empty Ge dimer and form a noncovalent π-complex. In this geometry, the surface active site, or Ge dimer, loses its reactivity upon being covered by the phenyl ring. At high coverage, phenoxy adsorbates stand up closer to the surface normal. Our study provides fundamental knowledge toward molecular scale control over the adsorbate orientation of a functional aromatic moiety at the organic−inorganic interface.



ASSOCIATED CONTENT

* Supporting Information S

Complete ref 23 and IR spectra of phenol adsorbed on Ge(100)-2 × 1 showing the full range of frequencies of interest. This material is available free of charge via the Internet at http://pubs.acs.org.



REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*Phone: 650-723-0385. Fax: 650-723-9780. E-mail: sbent@ stanford.edu. 7929

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(32) Wang, G. T.; Mui, C.; Musgrave, C. B.; Bent, S. F. J. Phys. Chem. B 1999, 103, 6803. (33) Haller, G. L.; Rice, R. W. J. Phys. Chem. 1970, 74, 4386. (34) Potter, R. F. Germanium (Ge). In Handbook of Optical Constants of Solids; Palik, E. D., Ed.; Academic Press: London, U.K., 1998; Vol. 1, p 465. (35) Wohlfarth, C. Refractive Index of Phenol. In SpringerMaterials: The Landolt-Börnstein Database; Lechner, M. D., Ed.; Springer-Verlag: Heidelberg, Germany, 2008; Vol. 47. (36) In this three-layer model, the adsorbate orientation is dependent on the choice of the refractive index of the adsorbate layer, which is controversial in the literature. By choosing n2 = 1, it reduces to the two-layer model and gives unphysical values of γLD = 87° and γSU = 67°. With n2 = 1.4, γLD = 83° and γSU = 50°; n2 = 1.7 gives γLD = 80° and γSU = 39°. (37) In other words, the adsorbates are assumed to have a preferred tilt angle from the surface normal but be azimuthally isotropic. The SU state would have a low barrier for rotation about the Ge−O bond, so it can be estimated as uniaxial. For the LD state, 8 energetically degenerate adsorbate orientations each tilted ± 15° from the x and y axes of the crystal exist, considering that steps on the Ge(100) surface allow two perpendicular reconstruction domains. Although the system is not truly azimuthally isotropic, the large number (8) of orientations sampled by the adsorbates, in addition to the angle averaging to 0 at a macroscopic scale, allow us to approximate it as isotropic. Therefore, we believe that the uniaxial assumption is reasonably valid also for LD. (38) Ahn, D. J.; Franses, E. I. J. Phys. Chem. 1992, 96, 9952. (39) Nagao, M.; Umeyama, H.; Mukai, K.; Yamashita, Y.; Yoshinobu, J.; Akagi, K.; Tsuneyuki, S. J. Am. Chem. Soc. 2004, 126, 9922. (40) Fan, X. L.; Sun, C. C.; Zhang, Y. F.; Lau, W. M. J. Phys. Chem. C 2010, 114, 2200. (41) Olson, R. M.; Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theory Comput. 2007, 3, 2046. (42) Van Duyne, R. P.; Cape, T. W.; Suchanski, M. R.; Siedle, A. R. J. Phys. Chem. 1986, 90, 739.

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