Supporting Information

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1 Supporting Information The Journal of Physical Chemistry A Determination of Binding Strengths of a Host-Guest Complex Using Resonance Raman Scattering Edward H. Witlicki, Stinne W. Hansen, Martin Christensen, Thomas S. Hansen, Sune D. Nygaard, Jan O. Jeppesen, Eric W. Wong, Lasse Jensen, Amar H. Flood Table of Contents S1. Determination of the Spectral and the Resonance Raman Enhancement Factors S2. Computational Details and Results S3. Calculated Absolute and Relative Experimental Raman Intensities of TTF and CBPQT 4+ S4. Experimental and Calculated Spectra ( cm 1 ) S5. Selected Normal Modes S6. Coordinates of the Optimized Geometries S7. References S1

2 S1. Determination of the Spectral and the Resonance Raman Enhancement Factors The spectral enhancement factors (SEFs) were calculated using the final solutions of the titration (MeCN) containing the complex compared to a 34 mm solution (MeCN) of CBPQT 4+ or a 11 mm solution (MeCN) of TTF by reference to the MeCN solvent bands. The background counts were subtracted from the signal counts for each vibrational band of interest, including those of the solvent. Each of the Raman band intensities obtained from the sample at 100% complexation was then normalized to that of a solvent band chosen for its proximal frequency in order to minimize self-absorption effects. The SEFs were obtained by taking the ratio of the concentration and solvent-scaled, resonance-enhanced Raman bands at the end of the titration to those of the normal Raman bands of the 34 mm CBPQT 4+ solution (for CBPQT 4+ -based vibrations in the complex) or the 11 mm TTF solution (for TTF-based vibrations in the complex). Resonance Raman enhancement factors (RREFs) were calculated from spectra of the same solution (5 mm CBPQT 4+, 10 mm TTF, MeCN, 298 K) using two different excitation wavelengths (785 and nm) and with the same set of optics, obviating the need to normalize to concentration and solid angle. The background subtracted signal counts were normalized to irradiation time and laser power before taking the ratio of resonantly-enhanced (785 nm excitation) to normal Raman (514.5 nm excitation) signal intensity. S2. Computational Details and Results All calculations presented in this work have been done using a local version of the Amsterdam Density Functional (ADF) program package. S1 The Becke-Perdew (BP86) XC-potential and a triple-ζ-polarized Slater type (TZP) basis set from the ADF basis set library have been used. The 1s core has been kept frozen for C, N, and O atoms, and the 1s-2p core for S. The vibrational frequencies and normal modes were calculated within the harmonic approximation. We have successfully used this functional and basis set in earlier studies of RRS spectra. S2 The binding energy of the complex is analyzed using the extended transition state method developed by Ziegler and Rauk. S3 Basis set superposition errors (BSSE) have not been accounted for, but is expected to be small for weakly interaction systems with the TZP basis set. Full geometry optimization, excitation energies and frequency calculations have been performed prior to the polarizability calculations. The polarizability derivatives are then calculated by numerical 3-point differentiation with respect to the normal mode displacements as described in detail in Ref. S4. This allows us to selectively study the Raman intensities of the normal modes associated with the frequency range cm 1. The electronic polarizability both on and off resonance is calculated by including the finite lifetime of the electronic excited states in the timedependent density functional theory (TDDFT) calculation. S4 The finite lifetime is included phenomenologically using a common damping parameter which describes relaxation and dephasing of the excited state. A value of Γ = Hartree (~800 cm 1 ) was used, which is what we have found previously to be reasonable for other molecules. S4 Absolute Raman intensities are presented here as the differential Raman scattering cross section (dσ/dω) as S2

3 (1) where ν in and ν p are the frequency of the incident light and of the p'th vibrational mode, respectively, and T = 298 K. and are the isotropic and anisotropic polarizability derivatives with respect to vibrational mode p. For the normal Raman spectra the polarizability derivatives needed in eq (1) were calculated at zero frequency; however a wavelength of nm was assumed for calculations of the Raman differential cross section. The charge-transfer (CT) transition for the complex was calculated using TDDFT to be at ev, which severely underestimate the experimental result of ev. To match the experimental situation in which the excitation is on the blue side of the CT maximum, we calculated the resonance Raman spectra at ev, slightly blue of the CT transition. However, in the calculations of the cross-sections we used a wavelength of 850 nm. To assist with the vibrational assignment of the normal modes of the complex we calculate the overlap between the normal modes of the complex (i) and those of the free TTF and CBPQT 4+ (jth modes). The overlap (O ij ) is calculated as the normalized scalar product of the normal modes (2) where and are the mass weighted Cartesian normal modes for the complex and the uncomplexed units, respectively. The contribution of each normal mode is then calculated as the square of the overlap. Before calculating the overlap the molecules are aligned in space using the quaternion method as described in ref. [S5]. Table S1. Percentage contributions of the normal modes of TTF (D 2h ) and CBPQT 4+ to the normal modes of the complex calculated using eq.(2). TTF* and CBPQT 4+ * indicate normal modes calculated from the individual molecules based on the structure they adopt within the complex. CBPQT TTF CBPQT % 63% % % 73% % CBPQT 4+ * TTF CBPQT % 86% % % 83% % S3

4 TTF (D 2h ) TTF CBPQT % 78% TTF* 1537 TTF CBPQT % In one trivial example, the CBPQT 4+ -based 1602 cm 1 band of the complex corresponds to (a) 92% of the 1613 cm 1 band of the geometry-optimized free CBPQT 4+, or (b) 97% of the 1615 cm 1 band of the CBPQT 4+ excised from the complex. This is trivial because the normal mode description remains relatively unchanged following the changes in structure, conformation and symmetry upon complexation. S3. Calculated Absolute and Relative Experimental Raman Intensities of TTF and CBPQT 4+ The calculated absolute Raman cross sections indicate that the CBPQT 4+ is a stronger scatterer than TTF. On the basis of comparison between the intensities of the two strongest bands of CBPQT 4+ (1613 cm 1 ) and TTF (1508 cm 1 ), the ratio is six. Experimentally, the ratio was determined by reference to MeCN solvent bands using the same bands to be a factor of two-fold more intense for CBPQT 4+. S4. Experimental and Calculated RRS Spectra ( cm 1 ) S4

5 Notes: Experimental (left) and calculated (right) Raman spectra for TTF (green; expt: solid state; calc: gas phase, D 2h ), CBPQT 4+ (blue; expt: 4PF 6 salt in solid state; calc: gas phase) and the TTF CBPQT 4+ complex (black; expt: 11.5 mm, MeCN; calc: gas phase). All experimental spectra were obtained at room temperature. S.5 Selected Normal Modes S5

6 S6

7 S6. Coordinates of the Optimized Geometries Table S2. Cartesian coordinates of TTF in Ångstrom using TZP/BP86. TTF X Y Z S C S C C C S C C S H H H H Table S3. Cartesian coordinates of CBPQT 4+ in Ångstrom using TZP/BP86. CBPQT 4+ X Y Z C C C N S7

8 C C C C C C C C C C N C C C C C H H H H H H H H H H H H H H H H C C C C C C H N H H C C H C C H C S8

9 H C H H N H H C C C C H C H C H H H H Table S4. Cartesian coordinates of TTF CBPQT 4+ in Ångstrom using TZP/BP86. TTF CBPQT 4+ X Y Z C C C C C C C N C C C C C C C C N C C C C C C S9

10 C C C C N C C C C C C C C N C C C S C S C C C S C C S H H H H H H H H H H H H H H H H H H H H H H S10

11 H H H H H H H H H H H H H H S7. References (S1) (a) te Velde, G.; Bickelhaupt, F. M.; van Gisbergen, S. J. A.; Fonseca Guerra, C.; Baerends, E. J.; Snijders, J. G.; Ziegler, T. J. Comput. Chem 2001, 22, (b) ADF, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands, Local modified version. (S2) (a) Jensen, L.; Zhao, L.; Autschbach, J.; Schatz, G. C. J. Chem. Phys. 2005, 123, (b) Jensen, L.; Schatz, G. C. J. Phys. Chem. A, 2006, 110, (S3) (a) Zeigler, T.; Rauk, A. Theor. Chim. Acta 1977, 46, (b) Ziegler, T.; Rauk, A. Inorg. Chem. 1979, 18, (c) Ziegler, T.; Rauk, A. Inorg. Chem. 1979, 18, (S4) Reiher, M.; Neugebauer, J.; Hess, B. A. Z. Phys. Chem. 2003, 217, (S5) Heisterberg, D. J. 1990, A program to superimpose atoms of two molecules by the quaternion method. S11