Statistics within UV-Visible Absorption Spectrum of Ethanolic Azobenzene

TL;DR

The study addresses how local liquid structure modulates the UV–visible absorption spectrum of trans-azobenzene in ethanol. It combines extensive MD sampling with TD-DFT spectra in explicit solvent and applies emulator-based component analysis (ECA) on LMBTR descriptors to identify a small set of latent structural variables that govern spectral ROI variance, notably linking a S2 blueshift to weaker solvent hydrogen bonding and bond contractions. The findings show that, despite broad structural diversity, a low-dimensional subspace largely explains spectral variation, with robust conclusions across B3LYP and PBE functionals and implications for post-excitation photodynamics in liquids. Data and scripts are publicly available, highlighting the method’s potential for interpreting structure–spectra relationships in complex liquids and guiding pump–probe experiments.

Abstract

We report a statistical simulation of the UV--visible absorption spectrum of {\it trans}-azobenzene in ethanol solution. Due to intermolecular interactions, the used explicit solvent environment necessitates accounting for numerous transitions for a spectrum covering the two energetically lowest lines, S$_1$ and S$_2$. Furthermore, the spectrum manifests vast variation as a function of the underlying local structure, in conjunction with previous observations for spectra of liquids in the X-ray regime. We disentangle the complex structure--spectrum relationship using a machine learning-based method known as the emulator-based component analysis. This structural decomposition outperforms commonly used principal component analysis in explained spectral variation and reveals a small subset of latent structural variables responsible for the total spectral variance. Among other structural characteristics, blueshifting of the S$_2$ peak occurs with fewer hydrogen bonds with the ethanol solvent, and a contracted N=N bond within the C--N=N--C bridge. The observed structural dependence of the absorption spectrum thus implies an overrepresentation of certain structural classes after a photoexcitation, potentially significant for the subsequent nuclear dynamics, photophysics, and photochemistry.

Figures (13)

• Figure 1: Results of the spectrum calculations and variance captured by different dimensionality reduction techniques. a: Simulated ensemble average UV--visible absorption spectrum for trans-azobenzene in ethanol, together with an experiment reproduced from Ref. Nägele1997. The blue-shaded area depicts the standard deviation of the data set, indicating significant statistical variation. The gray-shaded areas depict the two regions of interest (ROIs I and II) defined for the subsequent analysis. Computational results have been shifted to match the experiment. Additionally, the figure presents an example local structure prepared with Jmol jmol. b: Spectral R$^2$ score as a function of the rank of emulator-based component analysis (ECA) and principal component analysis (PCA), evaluated using the neural network emulator after the respective dimensionality reduction. The first two ECA components explain a large portion of the spectral ROI variance, while the higher components show rapidly diminishing R$^2$ score gains. Structural decomposition by PCA covers significantly less spectral variance for the same rank. c: Structural R$^2$ score as a function of decomposition rank. The ECA vectors cover a small fraction of the structural variance compared to structural PCA. The result indicates that explaining structural variation alone does not explain the spectral variation.
• Figure 2: The relationship between spectral properties and the latent coordinates from ECA using the test set with the corresponding Pearson's correlation coefficients $r$. a: The difference between the two ROI values is highly correlated with the spectrally most significant structural variable $t_1$. b: The correlation between ROI value difference and the second most significant structural variable $t_2$ is negligible. c: The total ROI value sum is weakly correlated with $t_1$, but d: highly correlated with $t_2$. For details, see text.
• Figure 3: Element-wise change in radial number density ($\Delta$RND) implied by a ten-unit rise of latent coordinate $t_1$ associated with ROI value difference from a: the nitrogen atoms, and from b: carbon atoms of the C-N=N-C bridge. We denote regions corresponding to the weakening of the hydrogen bonding and possible rotation of the ethanol molecules with an asterisk (*). Additionally, the triangles ($\triangledown$) denote regions indicating shortening of N=N or C$_\mathrm{N=N}$--C bonds, and the square ($\Box$) denotes a region indicating an increase in the length of the N--C bond. The curves shown are an average for the two N atoms or the two C$_\mathrm{N=N}$ atoms.
• Figure 4: Validation of the ECA results evaluated over the whole data set. a: The mean spectra of structures with N=N bond length above and below the average value. b: The mean spectra for structures with a given number of hydrogen bonds accepted by the azo group, calculated with criteria described in Ref. Niskanen2017. The inspection is motivated by ECA first finding these characteristics.
• Figure 5: Autocorrelation functions of the production run at intervals of 10 fs. a: The curves for z-score standardized data which was used in the analysis. Spectral data is represented by the two regions of interest values (ROIs) and the structural data is represented by the local many-body tensor representation (LMBTR) vectors derived from the xyz-coordinates and atomic number of each nucleus. b Corresponding curves for data that has not been z-score standardized. Additionally, we show the autocorrelation of the full spectra.