Supporting information for: Ultrafast Transient Absorption Spectroscopy of. the Sunscreen Constituent Ethylhexyl Triazone

Transcription

1 Supporting information for: Ultrafast Transient Absorption Spectroscopy of the Sunscreen Constituent Ethylhexyl Triazone Lewis A. Baker,,, Sarah L. Clark, Scott Habershon,, and Vasilios G. Stavros, Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, United Kingdom Centre for Scientific Computing, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, United Kingdom S1

2 Global fit residuals and error analysis A global fitting procedure was employed to determine a set of optimised parameters for the entire TAS, as described in the main text, which is subject to the minimisation of the sum of squares between the modelled TAS and the experimental TAS. The residuals of the globally fitted TAS and the experimental TAS are given in Figure S1. In general the residuals are small (ca. 2 m OD) compared to the maximum signal of 100 m OD, but there are a few regions where the global fit over- and under-estimates the TAS which is not unexpected in such global analysis procedures. m OD m OD nm 400 nm 450 nm 500 nm 550 nm (A) (C) Wavelength / nm Wavelength / nm m OD (B) (D) Figure S1: A selection of kinetic traces (solid lines) with corresponding global fit (dashed lines), for EHT-dioxane (A) and EHT-methanol (C). The residual between the experimental TAS and the globally fitted TAS for EHT-dioxane (B) and EHT-methanol (D). S2

3 Uncertainties at the 95% level are assigned to the determined lifetimes using an asymptotic standard error (ASE) technique. S1 Briefly, for each TAS the goodness-of-fit for the set of optimised parameters determined by the global fit is calculated, denoted by. Subsequently, the value of one lifetime τ is varied in a systematic manner whilst keeping all other lifetimes fixed. The global fit optimisation proceeds as before and a new goodness-of-fit is calculated denoted by χ 2 (τ). A 95% confidence interval for the value of the lifetime τ is then defined by: χ 2 (τ) = 1 + p ν F 1 (0.95, p, ν), (1) where p denotes the total number of parameters in the global fit, ν the number of degrees of freedom and F 1 is the inverse-f cumulative distribution function. Thus, for each value τ is fixed to, the goodness-of-fit ratio χ2 (τ) is calculated until Equation 1 is no longer satisfied. The uncertainty reported is that which deviates maximally from the globally fitted lifetime and satisfies Equation 1. This procedure is repeated for all lifetimes which correspond to dynamical processes, shown in Figure S2. S3

4 χ 2 (A) (B) (C) χ (D) Time delay / fs (E) (F) Figure S2: Asymptotic standard error for each lifetime, as quoted in the manuscript. Following the procedure given in the text, the largest deviation from the global minimum value to the value which intercepts the line χ2 = 4 is taken to be the uncertainty (horizontal line). (A) (C) EHT-dioxane, τ 1, τ 2 and τ 3 respectively. (D) (F) EHT-methanol, τ 1, τ 2 and τ 3 respectively. S4

5 Electronic structure calculations All electronic structure calculations were performed using the TURBOMOLE package. S2,S3 Density functional theory and time-dependent density functional theory were used with the BP-86 functional, S4 the augmented Dunning aug-cc-pvdz basis set, S5,S6 and the resolution of the identity S7 and multipole accelerated resolution of the identity approximations, S8 with the corresponding auxiliary basis set. S9 For all calculations, default convergence criteria were used, except for the geometry optimisation of the S1 geometry where a relaxed criteria of 10 4 Hartrees in energy was used due to convergence difficulties. The first thirty excited states and their corresponding oscillator strengths are given for the initial photoexcitation, see Table S1. The main text shows a representative example of the initial excitation (n = 15) but we note there are a two other transitions which might realistically be accessed by the pump wavelengths used, namely the n = 14 and n = 16 transitions, see Figure S3. To calculate the absorption spectra, given in Figure 4 of the main text, EHT is optimised n = 14 n = 15 n = 16 Figure S3: The likely initial photoexcitation(s) which all display 1 ππ character. n = 15 was given in the main text. S5

6 Table S1: The first 30 singlet excited states calculated at the ground state geometry. Those in bold correspond to those considered in Figure S3. n Wavelength / nm Oscillator Strength in either the S 1 state or the T 1 state. From this geometry, oscillator strengths are calculated for each transition (λ 0 ). These oscillator strengths, f(λ 0 ) are then convoluted ( ) with a S6

7 Gaussian function across all wavelengths (λ): I(λ) = f (λ0 ) e (λ λ0 )2 2σ 2 (2) A value of σ = 15 nm is used which broadens the spectra similar to the broadening observed in the experimental data (Figure 4 of the main text). This methodology is extended to investigate how the absorption profile changes along the S1 potential energy surface. Linearly interpolated coordinates are used between the initial geometry and the optimised S1 geometry, see Figure S Norm. absorbance Wavelength / nm Figure S4: The evolution of the absorption profile of EHT along the S1 potential energy surface. Linearly interpolated coordinates are used between the initial geometry ( 1) and the optimised S1 geometry ( 5). Trajectories are equally spaced in their interpolations. S7

8 Solvent effects All calculations have been performed in the gas-phase to qualitatively inform on the experimental solution-phase results. To confirm the structures discussed in this work are sensible, we initially performed the ground state optimisation of EHT with and without an implicit methanol field using the COSMO model, S10 see Figure S5. Very little difference between the Figure S5: The ground state optimised geometry of EHT with (opaque) and without (translucent green) an implicit methanol solvent field. two geometries are seen. The largest differences are observed in the tails of EHT, which we have shown are not involved in the photodynamics (discussed in the main text), thus the gas-phase calculations are reasonable representation of the likely lowest energy conformer of EHT. References (S1) Lakowicz, J. R. Principles of Fluorescence Spectroscopy, 3rd ed.; Springer Science+Business Media, S8

9 (S2) TURBOMOLE V , A development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, , TURBOMOLE GmbH, since 2007; available from (S3) von Arnim, M.; Ahlrichs, R. J. Comput. Chem. 1998, 19, (S4) Perdew, J. P. Phys. Rev. B 1986, 33, (S5) Dunning, T. H. J. Chem. Phys. 1989, 90, (S6) Kendall, R. A.; Thom H. Dunning, J.; Harrison, R. J. J. Chem. Phys. 1992, 96, (S7) Eichkorn, K.; Treutler, O.; Öhm, H.; Häser, M.; Ahlrichs, R. Chem. Phys. Lett. 1995, 240, (S8) Sierka, M.; Hogekamp, A.; Ahlrichs, R. J. Chem. Phys. 2003, 118, (S9) Eichkorn, K.; Weigend, F.; Treutler, O.; Ahlrichs, R. Theor. Chem. Acc. 1997, 97, (S10) Klamt, A.; Schüürmann, G. J. Chem. Soc., Perkin Trans , 2, S9