Limits of the Nuclear Ensemble Method for Electronic Spectra Simulations: Temperature Dependence of the (E)-Azobenzene Spectrum.

We explore the range of applicability of the nuclear ensemble method (NEM) for quantitative simulations of absorption spectra and their temperature variations. We formulate a "good practice" for the NEM based on statistical theory. Special attention is paid to proper treatment of uncertainty estimation including the convergence with the number of samples, which is often neglected in the field. As a testbed, we have selected a well-known chromophore, (E)-azobenzene. We measured its temperature difference UV-vis absorption spectra in methanol, which displayed two dominant features: a moderate increase in the intensity of the nπ* band and a pronounced decrease in intensity of the low-energy part of the ππ* band. We attributed both features to increasing non-Condon effects with temperature. We show that the NEM based on the path integral molecular dynamics combined with range-separated hybrid functionals provides quantitatively accurate spectra and their differences. Experimentally, the depletion of the absorption in the ππ* band showed a characteristic vibrational progression that cannot be reproduced with the NEM. We show that hundreds of thousands of samples are necessary to achieve an accuracy sufficient for the unambiguous explanation of the observed temperature effects. We provide a detailed analysis of the temperature effects on the spectrum based on the harmonic model of the system combined with the NEM. We also rationalize the vibrational structure of the spectrum using the Franck-Condon principle.

Azobenzene photoisomerization quantum yields in methanol redetermined.

The quantum yields of azobenzene photoisomerization in methanol solution were redetermined using newly obtained molar absorption coefficients of its cis- and trans-isomers. The results differ substantially from those published previously, especially in the range of the nπ* absorption band. Besides actinometry, these findings are relevant for applications of azobenzene derivatives in optical switching.

The absorption spectrum of cis-azobenzene.

Azobenzene is a prototypical photochromic molecule existing in two isomeric forms, which has numerous photochemical applications that rely on a precise knowledge of the molar absorption coefficients (ε). Careful analysis revealed that the previously reported absorption spectra of the "pure" isomers were in fact mutually contaminated by small amounts of the other isomer. Therefore, the absorption spectra of both trans- and cis-azobenzene in methanol were re-determined at temperatures of 5-45 °C. The thermodynamically more stable trans-azobenzene was prepared by warming the solution in the dark. To obtain the spectrum of cis-azobenzene three methods were used, which gave consistent results within the limits of error. The method based on the subtraction of derivative spectra coupled with a global analysis of the spectra recorded during thermal cis-trans isomerization is shown to give slightly more reliable results than the method using isomeric ratios determined by 1H-NMR. The described methods are readily generalizable to other azobenzene derivatives and to other photochromic systems. The practical implication of the re-determined ε values is demonstrated by a very high precision of spectrophotometric species analysis in azobenzene isomeric mixtures. The new ε values imply that the previously reported quantum yields must be revised.