Supporting Information

Transcription

1 Supporting Information Unraveling the Key Features of the Reactive State of Decatungstate Anion in Hydrogen Atom Transfer (HAT) Photocatalysis Vincent De Waele, Olivier Poizat, Maurizio Fagnoni, Alessandro Bagno, ǁ, Davide Ravelli,* Université de Lille, CNRS, UMR 8516, LASIR, Laboratoire de Spectrochimie et Raman, F59000 Lille, France PhotoGreen Lab, Department of Chemistry, University of Pavia, viale Taramelli 12, Pavia, Italy. Fax: ; Tel: ǁ Department of Chemistry, University of Padova, via Marzolo 1, Padova, Italy Deceased March 23, 2015 OPTIMIZED GEOMETRIES DARK STATES ANALYSIS for [W 10 O 32 ] 4- CALCULATED SPECTRUM of TRIPLET [W 10 O 32 ] 4- (wo) REFERENCES p. S2 p. S3 p. S6 p. S8 S1

2 1. OPTIMIZED GEOMETRIES All calculations were carried out with the ADF program. S1 The following geometries were optimized at the COSMO-BP86/TZ2P (All Electron basis set) level, including the parameters of acetonitrile as solvent ( = 37.5, radius = 2.76 Å); relativistic effects were included by means of the ZORA approximation at the Scalar Level (ZSC). The triplet state has been treated using with a spinunrestricted formalism. These structures were then employed throughout the rest of this study. Table S1. Optimized parameters for the structures used in the study. [W 10 O 32 ] 4- - D 4h symmetry a Triplet [W 10 O 32 ] 4- (wo) - D 4h symmetry 1. O O O O O O O O O O O O O O O O W W W W W O O O O O O O O O O O O O O O O W W W W W O O O O O O O O O O O O O O O O W W W W W O O O O O O O O O O O O O O O O W W W W W a The same structure has already been reported in previous works by our group. S2,S3 S2

3 2. DARK STATES ANALYSIS for [W 10 O 32 ] 4- All TD-DFT calculations reported here have been carried out at the PBE0/TZP (Frozen Core basis set) level, including the solvation effects (COSMO model, solvent acetonitrile) and the solvent response (CSMRSP option). The calculations were carried out both on allowed and forbidden transitions, using the Davidson algorithm. The output provided the energy of the transition (E) in ev and oscillator strengths (f). The first parameter was then converted to wavelength by means of the relationship [nm] = / E [ev]. The given f values have been multiplied by the degree of degeneracy of the irreducible representation to which the transition belongs, as recommended in the ADF documentation. S1 The spin-orbit coupling term has been introduced by exploiting two different approaches. In the first one, the spin-orbit coupling was included self-consistently in the ground state calculation (ZSO method), S4 while in the second the spin-orbit coupling term was introduced as perturbation to a scalar relativistic calculation of excitation energies (SOPERT method). S5 S3

4 Table S2. Full list of dark states at the ZSO level of theory. energy [ev] energy [nm] Calculated f Symmetry block Real f [sec] E-35 A 1u 8.35E E-05 E u 1.24E E E+00 B 1u 0.00E E+00 B 2u 0.00E E-05 E u 7.05E E E-04 A 2u 1.05E E E-36 A 1u 2.25E E+00 B 2g 0.00E E+00 B 1g 0.00E E+00 E g 0.00E E+00 A 1g 0.00E E+00 A 2g 0.00E E-05 E u 2.82E E E-04 A 2u 5.98E E E+00 B 2u 0.00E E-06 E u 5.86E E E-36 A 1u 1.41E E+00 E g 0.00E E+00 A 1g 0.00E E+00 B 1u 0.00E E+00 A 2g 0.00E E+00 B 2g 0.00E E+00 B 1g 0.00E E+00 E g 0.00E E+00 E g 0.00E E+00 A 1g 0.00E E-03 E u 3.08E E E+00 A 2g 0.00E E+00 E g 0.00E E+00 B 1u 0.00E E+00 B 2u 0.00E E-04 E u 1.06E E E-02 A 2u 1.39E E E-36 A 1u 4.09E E+00 E g 0.00E E+00 A 2g 0.00E a E-01 A 2u 3.38E E-09 a This is the transition responsible for the well known absorption band of the decatungstate anion and its energy has been taken as the upper limit for the selection of the dark states to be considered. S3 S4

5 Table S3. Full list of dark states at the SOPERT level of theory. energy [ev] energy [nm] Calculated f Symmetry block Real f Single group excitation contributions a E+00 A 1u 0.00E+00 1 st Triplet A 2u (99.90%) E-06 E u 3.43E-06 1 st Triplet A 2u (99.93%) E-41 B 2u 6.12E-41 1 st Triplet E u (99.69%) E+00 B 1u 0.00E+00 1 st Triplet E u (99.77%) E-06 E u 1.01E-05 1 st Triplet E u (95.10%) E-06 A 2u 2.52E-06 1st Triplet E u (87.09%) 1 st Triplet A 1u (12.90%) E+00 A 1u 0.00E+00 1st Triplet E u (94.13%) 1 st Singlet A 1u (5.78%) E+00 B 1g 0.00E+00 1 st Triplet E g (99.77%) E+00 B 2g 0.00E+00 1 st Triplet E g (99.76%) E+00 E g 0.00E+00 1 st Triplet E g (97.03%) E+00 A 1g 0.00E+00 1 st Triplet E g (93.82%) E+00 A 2g 0.00E+00 1 st Triplet E g (98.07%) E-05 E u 5.48E-05 1 st Triplet A 1u (94.07%) E-06 A 2u 3.38E-06 1st Triplet A 1u (86.43%) 1 st Triplet E u (12.77%) E-07 E u 8.51E-07 1 st Triplet B 1u (99.68%) E-40 B 2u 7.26E-40 1 st Triplet B 1u (99.81%) E+00 A 1u 0.00E+00 1st Singlet A 1u (93.44%) 1 st Triplet E u (5.67%) E+00 E g 0.00E+00 1 st Triplet A 2g (91.28%) 1 st Triplet A 2g (86.85%) E+00 A 1g 0.00E+00 2 nd Triplet E g (7.09%) 1 st Triplet E g (5.90%) E+00 B 1u 0.00E+00 1 st Singlet B 1u (99.87%) E+00 A 2g 0.00E+00 1st Singlet A 2g (85.91%) 2 nd Triplet E g (12.35%) E+00 B 1g 0.00E+00 2 nd Triplet E g (99.68%) E+00 B 2g 0.00E+00 2 nd Triplet E g (99.68%) 2 nd Triplet E g (74.76%) E+00 E g 0.00E+00 2 nd Singlet E g (16.94%) 1 st Singlet E g (7.36%) E+00 E g 0.00E+00 1st Singlet E g (90.91%) 2 nd Singlet E g (5.28%) E-03 E u 3.33E-03 1st Singlet E u (84.14%) 2 nd Triplet E u (14.63%) E+00 A 1g 0.00E+00 2nd Triplet E g (92.75%) 1 st Triplet A 2g (6.74%) E+00 A 2g 0.00E+00 2nd Triplet E g (87.44%) 1 st Singlet A 2g (11.88%) E+00 E g 0.00E+00 2nd Singlet E g (75.34%) 2 nd Triplet E g (18.30%) E+00 B 1u 0.00E+00 2 nd Triplet E u (99.70%) E-39 B 2u 6.15E-39 2 nd Triplet E u (99.71%) E-04 E u 9.54E-04 2nd Triplet E u (83.82%) 1 st Singlet E u (14.19%) E-03 A 2u 7.09E-03 2 nd Triplet E u (97.16%) E+00 A 1u 0.00E+00 2 nd Triplet E u (99.01%) 35 b E-01 A 2u 3.48E-01 1 st Singlet A 2u (98.00%) a Only contributions > 5% have been shown. b This is the transition responsible for the well known absorption band of the decatungstate anion and its energy has been taken as the upper limit for the selection of the dark states to be considered. S3 S5

6 3. CALCULATED SPECTRUM of TRIPLET [W 10 O 32 ] 4- (wo) The spectrum reported in Figure 5 has been obtained as described below. All TD-DFT calculations reported here have been carried out at the PBE0/TZP (Frozen Core basis set) level with adoption of the Tamm-Dancoff approximation (TDA), S6 also including the solvation effects (COSMO model, solvent acetonitrile) and the solvent response (CSMRSP option). Relativistic effects were included by means of the ZORA approximation at the Scalar Level (ZSC). In this case, a spin-unrestricted formalism has been adopted. The calculations were carried out only on the allowed transitions, using the Davidson algorithm. The output provided the energy of the transition (E) in ev and oscillator strengths (f). The first parameter was then converted to wavelength by means of the relationship [nm] = / E [ev]. The given f values have been multiplied by the degree of degeneracy of the irreducible representation to which the transition belongs, as recommended in the ADF documentation. S1 Calculated spectra were obtained by convolution of Gaussian curves. S7 reported below: The equation used is M W f exp W cm out Where: () [M -1 cm -1 ] is the molar extinction coefficient at the considered wavelength ; W [cm -1 ] is the full width at half maximum of each Gaussian curve (the only parameter required to the user, in this case arbitrarily fixed at 6000 cm -1, in accordance with previous works by our group); S2,S3 f is the oscillator strength given by the output (multiplied by the appropriate factor as stated above); out [cm -1 ] is the energy of the transition given in the output. S6

7 Table S4. [W 10 O 32 ] 4-30 lowest allowed transitions (ZSC-COSMO-PBE0/TZP-FC level). energy [ev] energy [nm] Calculated f Symmetry block Real f E-05 E u 2.38E E-05 E u 4.40E E-02 A 2u 3.04E E-03 E u 2.11E E-04 E u 1.83E E-03 A 2u 6.18E E-03 E u 4.72E E-02 E u 1.27E E-03 E u 3.58E E-02 A 2u 7.84E E-01 A 2u 1.66E E-04 E u 2.33E E-02 A 2u 6.26E E-02 A 2u 1.82E E-03 E u 3.03E E-02 A 2u 5.02E E-05 E u 7.89E E-03 E u 3.17E E-02 A 2u 2.23E E-04 E u 7.79E E-05 E u 1.15E E-01 A 2u 1.81E E-03 E u 9.43E E-02 A 2u 3.77E E-04 E u 1.09E E-03 E u 3.44E E-03 A 2u 3.68E E-05 E u 1.05E E-03 E u 1.38E E-02 A 2u 5.47E-02 S7

8 4. REFERENCES (S1) te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. J. Comput. Chem. 2001, 22, Documentation available online at: (S2) Ravelli, D.; Dondi, D.; Fagnoni, M.; Albini, A.; Bagno, A. J. Comput. Chem. 2011, 32, (S3) Ravelli, D.; Dondi, D.; Fagnoni, M.; Albini, A.; Bagno, A. Phys. Chem. Chem. Phys. 2013, 15, (S4) Wang, F.; Ziegler, T.; van Lenthe, E.; van Gisbergen, S. J. A.; Baerends, E. J. J. Chem. Phys. 2005, 122, (S5) Wang F.; Ziegler, T. J. Chem. Phys. 2005, 123, (S6) Hirata S.; Head-Gordon, M. Chem. Phys. Lett. 1999, 314, (S7) O Boyle, N. M.; Tenderholt, A. L.; Langner, K. M. J. Comput. Chem. 2008, 29, S8