S1

Supporting Information Distinct Binding of Rhenium Catalysts on

Nanostructured and Single Crystalline TiO2 Surfaces Revealed by Two-Dimensional Sum

Frequency Generation Spectroscopy Heather Vanselous,1,° Pablo E. Videla,2,° Victor S. Batista,2,* and Poul B. Petersen1,*

° H.V. and P.E.V. contributed equally.

1)Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, United States; 2)Department of Chemistry and Energy Sciences Institute, Yale University, 225 Prospect St., New Haven, Connecticut 06520, United States

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1. Euler Transformation between Laboratory Coordinate Frame and Molecular Coordinate Frame.

As shown in Figure 1 of the main text, in the molecular frame the a-c plane is defined as the plane of the bipyridine ring, whereas the b axis is perpendicular to it. The laboratory frame is defined with the Z axis along the normal of the surface and the X axis in the incidence plane perpendicular to Z. The relation between the XYZ and abc frames is described through the Euler angles q, y, and f. The ZXZ rotation matrix formalism is used for all rotations, as described in Equation S1.1 Note that using this convention, a twist angle y of 0° correspond to the molecule bonded in a bidentate mode to crystalline TiO2, a binding motif that is energetically favored in crystalline TiO2 surfaces.2-4

𝑅(𝜙, 𝜃, 𝜓) = )cos(𝜙) −sin(𝜙) 0sin(𝜙) cos(𝜙) 00 0 1

3)1 0 00 cos(𝜃) −sin(𝜃)0 sin(𝜃) cos(𝜃)

3 )cos(𝜓) −sin(𝜓) 0sin(𝜓) cos(𝜓) 00 0 1

3

(S1)

2. Feynman diagram of 2D SFG Spectroscopy

Figure S1. Feynman diagram of 2D SFG spectroscopy for coupled oscillators. p and q represent fundamental states, r represent overtones and combination bands, and the capital letter represent virtual electronic state.

000qp qp 0P000

E1

E3

E2

Evis

Esig

R1

000q00p 0P000

R2

000qp qrqR qq q

R3

00q 0qpq0Q 000

E1

E3

E2

Evis

Esig

R4

00q 00 0p0P 000

R5

00q 0qprpRppp

R6

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3. Calculation of Molecular Hyperpolarizability Tensor Elements.

Energy and geometry optimization of the gas phase Re(CO)3 complex was perform using the Gaussian 09, Revision D.01, software package, 5 employing the B3LYP hybrid functional6 and the SDD7 basis sets for Re and the 6-311+G(d) basis set for all nonmetal atoms. We employ “tight” optimization criteria and ultrafine grid integration to obtain accurate results. Dipoles derivatives 𝜕𝜇

𝜕𝑄78 and polarizabilities derivatives 𝜕𝛼 𝜕𝑄7: for each vibrational mode were obtain using the

keyword ‘raman’ and ‘iop(7/33=1)’ and are listed below. We employ the harmonic approximation to obtain the transition parameters between the first- and second-excited state, i.e. the ground to first-excited state transition parameters are multiplied by √2.

Mode 86 (A’(2)): 1962 cm-1

Dipole derivatives: 6.70373D-02 3.33912D+01 5.16706D+00 Polarizability derivatives: -0.224872D+01 -0.130229D-02 -0.670367D-03 -0.130229D-02 0.249790D+01 -0.162034D+01 -0.670367D-03 -0.162034D+01 -0.377469D+01

Mode 87 (A’’): 1989 cm-1

Dipole derivatives: 3.35373D+01 -5.07018D-02 -1.36907D-03 Polarizability derivatives: -0.255403D-02 -0.784744D+00 -0.205916D+01 -0.784744D+00 -0.257025D-02 0.893207D-02 -0.205916D+01 0.893207D-02 -0.477596D-02

Mode 88 (A’(1)): 2058 cm-1

Dipole derivatives: 2.91217D-03 4.87486D+00 -3.76001D+01 Polarizability derivatives: -0.148131D+01 0.609132D-03 0.117327D-02 0.609132D-03 0.121826D+01 0.189366D+00 0.117327D-02 0.189366D+00 -0.518718D+01

4. Coordinates of the optimized structure of gas-phase Re(CO)3

0 1 O 0.00000000 0.00000000 0.00000000 O 6.08445000 0.00000000 0.00000000 C 5.71586900 0.00000000 4.74207900 N 4.37313600 0.01342900 4.67285300 H 7.60506500 -0.02071400 3.71702800

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C 5.92711900 -0.00795800 2.36138000 H 4.06433900 0.01341400 1.31189800 C 6.52697100 -0.01283400 3.62048900 C 4.53873400 0.00637100 2.28213700 H 2.02011000 0.01342000 1.31189800 C 3.78018100 0.01743800 3.45324400 H 6.14219400 0.00560000 5.73589800 C 1.54571600 0.00636600 2.28213600 C 2.30426900 0.01743200 3.45324300 C 0.15733100 -0.00797700 2.36137900 N 1.71131300 0.01341100 4.67285300 C -0.44252100 -0.01286600 3.62048800 C 0.36858000 -0.00003200 4.74207900 H -1.52061400 -0.02075900 3.71702700 Re 3.04222300 0.19652200 6.42793500 C 4.41212200 0.50420500 7.77806200 H -0.05774400 0.00555900 5.73589700 O 5.24843500 0.69264200 8.54595100 C 1.67231900 0.50418100 7.77806100 C 3.04223900 -1.70500100 6.80905400 O 3.04224800 -2.83994200 7.03089600 O 0.83600700 0.69261100 8.54595400 Cl 3.04220400 2.63120400 5.79156900 C -0.71326000 -0.01697100 1.14797800 C 6.79771100 -0.01695200 1.14797900

5. Fresnel factors coefficients

The Fresnel factors8-9 listed in Table S1 were calculated using 𝑛>?@ = 1, 𝑛A?BC = 2.52,10-11 and 𝑛?FGH@I = 1.62 9 and the experimental incident beam angles 𝛾LM,N = 𝛾LM,O = 55°, 𝛾LM,Q = 65° and 𝛾R?S = 60°.

TABLE S1. Fresnel prefactor coefficients for ppppp polarization.

Element Value Element Value Element Value Element Value ZZZZZ 7.48 XZZZX -10.09 ZZXXZ 9.65 XZXXX -13.01 XXZZZ -9.48 ZXXZZ 9.06 ZZXZX 9.65 XXZXX -13.70 XZXZZ -9.00 ZXZXZ 10.16 ZZZXX 10.82 XXXZX -12.22 XZZXZ -10.09 ZXZZX 10.16 ZXXXX 13.10 XXXXZ -12.22

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6. Influence of surface on dipole and polarizability tensor.

To test the influence of the surface on the dipole and polarizability tensors of the Re(CO)3 complex we compute the changes in dipole derivatives and polarizability derivatives for each vibrational mode as a function of the tilt angle of a Re(CO)3 molecule bound to a TiO2 surface. The bound system was taken from a previous study4 and consist of the Re(CO)3 complex on a Rutile(110) surface along the [-110] axis. This structure represents the most stable conformation of the molecule bonded in a bidentate mode to crystalline TiO2, with an equilibrium tilt angle of q»-10°.4 Starting from this configuration, and keeping the TiO2 slab frozen, a new set of configurations where the Re(CO)3 molecule present different tilt angles was generated by applying the Euler rotation matrix to the catalyst’s atoms. For each of these new configurations a single-point frequency calculation was carried out to obtain the dipole and polarizabilities derivatives. For these calculations the wb97xd hybrid functional12 was employed with the LANL2DZ13 basis sets for Re and Ti atoms and the 6-31G(d) basis set for all other atoms.

The influence of the surface on the dipole and polarizability derivatives tensors is presented in Figure S2. The results are presented as fractional errors defined as

𝜎(𝜃; 𝒑) =W𝒑(X)Y𝒑Z[\(X)W]

‖𝒑(X)‖] (S2)

where ‖‖_ represents a Frobenius norm and 𝒑 is either the dipole derivative 𝜕𝝁 𝜕𝑄78 or the

polarizability derivatives 𝜕𝜶 𝜕𝑄7: . The reference is taken to be the equilibrium orientation (with

qeq»-10°) but with the dipole/polarizability tensor rotated to the actual tilt angle q. Hence, small values of the metric 𝜎(𝜃; 𝒑) indicate that the effect of the surface is small whereas big values represent a modulation of dipole/polarizability tensors by surface-interactions.

As can be appreciated from Figure S2, for orientations close to the equilibrium one (b𝜃 − 𝜃H7b < 20-30°) the fractional error for both dipole and polarizability derivatives is within 5-7% of the reference configuration. We estimate that an error of this order is inherent to the methodology used (we estimate this error by performing similar calculations for a Re(CO)3 in the absence of a surface). Hence, for orientations of the complex normal to the surface the surface does not exert a significant influence on the transition dipole and polarizability tensors, in agreement with suggestions done on previous studies 3-4, 14-15 and the fact that the carbonyl groups do not have direct contact with TiO2 in those configurations. On the other hand, for configurations in which the complex is in direct contact with the surface (q»±50°) the fractional error is 15-25%, suggesting some modulation of the response of the molecule through electronic coupling to the surface. For the crystalline surfaces investigated in this work, previous SFG studies suggested that the Re(CO)3 complex (and analogous ones) binds to crystalline TiO2 surfaces roughly normal perpendicular, with a tilt angle q ranging from 0 to 30°.2, 4 Although we cannot discard the presence of configurations with the catalyst in close contact with the surface for the heterogenous nanocrystalline TiO2 interface, these results presented in this section allow to primary ascribe the changes in intensity between the symmetric and antisymmetric modes observed in the SFG spectra only to changes in relative angle of the catalyst relative to the surface.

S6

Note, however, that the results presented in Figure S2 should be interpreted with caution. The different configurations of the Re(CO)3 catalyst on TiO2 are obtained by applying a constraint in the tilt angle of the molecule and, hence, do not correspond to true minima (stationary points) of the potential energy surface. In this regard, the use of normal modes to compute the dipoles and polarizability derivatives may introduce some errors in the calculation. Taking into consideration this caveat, the results of Figure S2 provides only a qualitative description of the effect of the surface on dipole and polarizability tensors. Future work in this area will be needed to provide a quantitative answer.

Figure S2. Fractional error of the dipole derivatives (top panel) and polarizability derivatives (bottom panel) with respect to the equilibrium reference configuration for A’(2) (black circles), A’’ (red circles) and A’(1) (blue circles) CO stretching modes of Re(CO)3 on TiO2. Dotted lines are guides for the eye.

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7. Additional DFT-based 2D SFG spectra

Figures S3 and S4 show additional 2D SFG as a function of the tilt angle q for different orientations of the Re(CO)3 complex anchored to the surface through both carboxylate groups (y=0°). Figure S3 shows results for azimuthally-average ab initio SFG, where the top panels correspond to average spectra over configuration lying 45° apart (Df=45°), consistent with the symmetry of the rutile (001) surface, whereas the bottom panels correspond to averages performed over configurations that are 90° apart (Df=90°), consistent with rutile (110). In Figure S4 we present SFG spectra for fixed azimuthal angle of f=0° or f= 45°, where a d-distribution is assumed. For a description of the features observed in the spectra the reader is referred to the main text.

Figure S3. Ab initio 2D SFG spectra for the Re(CO)3 complex as a function of tilt angle q for a bidentate binding motif (y=0°) and two different azimuthally-averaged distribution of the azimuthal angle f. Spectra correspond to zero waiting time and are normalized for clarity. Contours are evenly spaced with blue indicating negative values and red indicating positive values.

S8

Figure S4. Ab initio 2D SFG spectra for the Re(CO)3 complex as a function of tilt angle q for a bidentate binding motif (y=0°) and two different delta distributions of the azimuthal angle f. Spectra correspond to zero waiting time and are normalized for clarity. Contours are evenly spaced with blue indicating negative values and red indicating positive values.

8. Additional References

1. Yan, E. C. Y.; Fu, L.; Wang, Z.; Liu, W., Biological Macromolecules at Interfaces Probed by Chiral Vibrational Sum Frequency Generation Spectroscopy. Chem. Rev. 2014, 114 (17), 8471-8498. 2. Anfuso, C. L.; Snoeberger, R. C.; Ricks, A. M.; Liu, W.; Xiao, D.; Batista, V. S.; Lian, T., Covalent Attachment of a Rhenium Bipyridyl CO2 Reduction Catalyst to Rutile TiO2. J. Am. Chem. Soc. 2011, 133 (18), 6922-6925. 3. Anfuso, C. L.; Xiao, D.; Ricks, A. M.; Negre, C. F. A.; Batista, V. S.; Lian, T., Orientation of a Series of CO2 Reduction Catalysts on Single Crystal TiO2 Probed by Phase-Sensitive Vibrational Sum Frequency Generation Spectroscopy ( PS-VSFG ). J. Phys. Chem. C 2012, 116, 24107-24114. 4. Ge, A.; Rudshteyn, B.; Psciuk, B. T.; Xiao, D.; Song, J.; Anfuso, C. L.; Ricks, A. M.; Batista, V. S.; Lian, T., Surface-Induced Anisotropic Binding of a Rhenium CO2-Reduction Catalyst on Rutile TiO2 (110) Surfaces. J. Phys. Chem. C 2016, 120, 20970-20977.

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5. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, Ö.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, Revision D.01; Wallingford CT, 2016. 6. Becke, A. D., Density-Functional Thermochemistry.III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98 (7), 5648-5648. 7. Andrae, D.; Häußermann, U.; Dolg, M.; Stoll, H.; Preuß, H. T., Energy-Adjusted Ab Initio Pseudopotentials for the Second and Third Row Transition Elements. Theor. Chim. Acta 1990, 77 (2), 123-141. 8. Wang, H.-F.; Gan, W.; Lu, R.; Rao, Y.; Wu, B.-H., Quantitative Spectral and Orientational Analysis in Surface Sum Frequency Generation Vibrational Spectroscopy (SFG-VS). Int. Rev. Phys. Chem. 2005, 24 (2), 191-256. 9. Zhuang, X.; Miranda, P.; Kim, D.; Shen, Y., Mapping Molecular Orientation and Conformation at Interfaces by Surface Nonlinear Optics. Phys. Rev. B 1999, 59 (19), 12632-12640. 10. Rams, J.; Tejeda, A.; Cabrera, J. M., Refractive Indices of Rutile as a Function of Temperature and Wavelength. Journal of Applied Physics 1997, 82 (3), 994-994. 11. Devore, J. R., Refractive Indices of Rutile and Sphalerite. Journal of the Optical Society of America 1951, 41, 416-419. 12. Chai, J.-D.; Head-Gordon, M., Long-Range Corrected Hybrid Density Functionals with Damped Atom–Atom Dispersion Corrections. Phys. Chem. Chem. Phys. 2008, 10 (44), 6615-6620. 13. Hay, P. J.; Wadt, W. R., Ab Initio Effective Core Potentials for Molecular Calculations. Potentials for K to Au Including the Outermost Core Orbitals. J. Chem. Phys. 1985, 82 (1), 299-310. 14. Clark, M. L.; Rudshteyn, B.; Ge, A.; Chabolla, S. A.; MacHan, C. W.; Psciuk, B. T.; Song, J.; Canzi, G.; Lian, T.; Batista, V. S.; Kubiak, C. P., Orientation of Cyano-Substituted Bipyridine Re(I) Fac-Tricarbonyl Electrocatalysts Bound to Conducting Au Surfaces. J. Phys. Chem. C 2016, 120 (3), 1657-1665. 15. Laaser, J. E.; Christianson, J. R.; Oudenhoven, T. A.; Joo, Y.; Gopalan, P.; Schmidt, J. R.; Zanni, M. T., Dye Self-Association Identified by Intermolecular Couplings between Vibrational Modes As Revealed by Infrared Spectroscopy, and Implications for Electron Injection. J. Phys. Chem. C 2014, 118 (11), 5854-5861.