Department of Chemistry, Faculty of Science, King Khalid University, Abha 61413, P.O. Box 9004, Saudi Arabia b

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1 Supporting information The effect of anchoring groups on the electro-optical and charge injection in triphenylamine 6 O 12 Ahmad Irfan a, Shabbir Muhammad b, Abdullah G. Al-Sehemi a,c,d, M.S. Al-Assiri e,f, Abul Kalam a, Aijaz Rasool Chaudhry b,g a Department of Chemistry, Faculty of Science, King Khalid University, Abha 61413, P.O. Box 9004, Saudi Arabia b Department of Physics, Faculty of Science, King Khalid University, Abha 61413, P.O. Box 9004, Saudi Arabia c Unit of Science and technology, Faculty of Science, King Khalid University, Abha 61413, P.O. Box 9004, Saudi Arabia d Research Center for Advanced Materials Science, King Khalid University, Abha 61413, P.O. Box 9004, Saudi Arabia. e Department of Physics, Faculty of Sciences and Arts, Najran University, P.O. Box 1988, Najran 11001, Saudi Arabia f Promising Centre for Sensors and lectronic Devices (PCSD), Najran University, P.O. Box 1988, Najran 11001, Saudi Arabia g Physics Department, Faculty of Science, Universiti Teknologi Malaysia, Johor Bahru, Malaysia Detail Methodology The description of the electron transfer from a to a semiconductor, the rate of the charge transfer process can be derived from the general classical Marcus theory 1-5, k inject. = V RP 2 /h (π/λk B T ) 1/2 exp[ (ΔG inject. + λ) 2 /4λk B T ] (1) In eq. (1), k inject. is the rate constant (in S -1 ) of the electron injection from to TiO 2, k BT is the Boltzmann thermal energy, h the Planck constant, - ΔG inject. the free energy of injection and λ is the reorganization energy of the system, V RP is the coupling constant between the reagent and the product potential curves. q (1) revealed that larger V RP leads to higher rate constant which would result better sensitizer. The value of V RP defines the adiabatic or non-adiabatic character of the electron transfer. The use of the Generalized Mulliken-Hush formalism (GMH) allows evaluating V RP for a photoinduced charge transfer 2,3. The Hsu et al. explained that V RP can be evaluated as 3. V RP = Δ RP /2 (2) The injection driving force can be formally expressed within Koopmans Corresponding author: Ahmad Irfan -mail: irfaahmad@gmail.com Tel.: Fax:

2 approximation as Δ RP = [ + 2 LUMO ] - [ HOMO + LUMO determine + HOMO ] (3) is the conduction band edge. It is often difficult to accurately because it is highly sensitive to the conditions, e.g. the ph of the solution. Thus we used experimental value corresponding to conditions the semiconductor is in contact with aqueous redox electrolytes of fixed ph 7.0, i.e., = -4.0 ev 6-8. More quantitatively for a closed-shell system reduction potential of the ( potential of first oxidation (i. e., - Δ RP = [ - HOMO ] = - [ The eq (4) can be rewritten as Δ RP = - [ RD corresponds to the LUMO ), as the HOMO energy is related to the = HOMO + + RD entropy change during the light absorption process can be neglected. For the second model, one assumes that electron injection occurs after relaxation. Given this 2 ). As a result eq. (3) becomes, ] (4) ] (5) We propose to establish a reliable theoretical scheme to evaluate the s excited state oxidation potential and quantify the electron injection onto a titanium dioxide (TiO 2 ) surface. The free energy change (in electron volts, ev) for the electron injection can be expressed as 7. ΔG inject = * - (6) * is the oxidation potential of the in the excited state and is the reduction potential of the semiconductor conduction band. Two models can be used for the evaluation of * 9,10. The first implies that the electron injection occurs from the unrelaxed excited state. For this reaction path, the excited state oxidation potential can be extracted from the redox potential of the ground state, vertical transition energy corresponding to the photoinduced, * = - (7) and the is the energy of the. Note that this relation is only valid if the

3 condition, * is expressed as 10 : * = (8) 0 0 is the 0-0 transition energy between the ground state and the excited state. To estimate the 0-0 absorption line, we need both the S 0 (singlet ground state) and the S 1 (first singlet excited state) equilibrium geometries, Q S0 and Q S1, respectively. Though electron injection from unrelaxed excited states has been observed in TiO 2 11 and SnO 2 12, the relative contribution of an ultrafast injection path is not clear, and the most experimental groups assume that the electron injection dominantly occurs after relaxation. Preat et al. concluded that the absolute difference between the relaxed and unrelaxed ΔG inject. is constant, and is of the same order of magnitude than the * and * have been evaluated using qs. (6) and (7). mean average error (MA) 13. The ΔG inject and The LH of the has to be as high as possible to imize the photocurrent response. The LH can be expressed as 14 : (9) A (ƒ) is the absorption (oscillator strength) of the associated to the. The oscillator strength is directly derived from the TDDFT calculations as follow: (10) is the dipolar transition moment associated to the electronic excitation. In order to imize ƒ, both and must be large 15,16. Fig. S1. The methanol interaction with the anchoring group of TPA-PT1 (left) and TPA-PT2 (right) sensitizers. 3

4 Table S1 The ΔG inject., ΔG r inject., oxidation potentials, light harvesting efficiencies (LH), V RP, absorption (λ a ) in nm, oscillator strengths (f), electronic excitation energy ( transitions of investigated s at B3LYP/6-31G** and TD-CAM-B3LYP/6-31G** (PCM, in methanol) level of theories. System ΔG inject. inject. ƒ LH ΔG r V RP λ a Transition * TC4 a H -> L b TPA-PT (-2.49) 1.65 (1.51) 3.53 (3.67) (0.999) (0.900) 1.37 (1.46) (1.245) 351 (338) H -> L (H -> L) TPA-PT (-2.53) 1.58 (1.47) 3.60 (3.71) (1.041) (0.909) 1.42 (1.48) (1.265) 344 (334) H -> L (H -> L) ΔG inject. r = relative electron injection ΔG inject. ()/ ΔG inject. (TC4) a,b Details can be found in reference 21,26 ) and Values in parentheses are in gas phase In present case no effect of solute-solvent interaction has been noticed on the absorption wavelengths but the influence has been observed on the oscillator strengths, see Table S2. No doubt the solute-solvent interaction affect the absorption wavelength but in this study, we have attached just one methanol at the anchoring side so no effect was observed (This data has been given in supporting information). But the H-bonding of the optimized geometry after solute-solvent interaction revealed that methanol would be favorable to deprotonate the H ultimately oxygens of anchoring group which would bind with the TiO 2 cluster. Table S2 The absorption wavelengths (λ a ) in nm, oscillator strengths (f), electronic excitation energy ( ) and transitions of investigated s (TPA-PT1-methanol and TPA-PT2-methanol) at TD-CAM-B3LYP/6-31G** and TD-CAM-B3LYP/6-31G** (PCM, in methanol) level of theories. System ƒ λ a Transition TPA-PT1 (3.53) a (3.68) b (1.096) a (1.045) b (351) a (337) b (H -> L) a (H -> L) b TPA-PT2 (3.71) a (3.60) b (1.059) a (1.153) b (334) a (344) b (H -> L) a (H -> L) b a The values have been calculated in methanol by considering the bulk solvation effect b The values have been calculated in gas phase 4

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