Reconstruction of Nuclear Ensemble Approach Electronic Spectra Using Probabilistic Machine Learning

Abstract

The theoretical prediction of molecular electronic spectra by means of quantum mechanical (QM) computations is fundamental to gain a deep insight into many photophysical and photochemical processes. A computational strategy that is attracting significant attention is the so-called Nuclear Ensemble Approach (NEA), that relies on generating a representative ensemble of nuclear geometries around the equilibrium structure and computing the vertical excitation energies (Δ E ) and oscillator strengths ( f ) and phenomenologically broadening each transition with a line-shaped function with empirical full-width δ. Frequently, the choice of δ is carried out by visually finding the trade-off between artificial vibronic features (small δ) and over-smoothing of electronic signatures (large δ). Nevertheless, this approach is not satisfactory, as it relies on a subjective perception and may lead to spectral inaccuracies overall when the number of sampled configurations is limited due to an excessive computational burden (high-level QM methods, complex systems, solvent effects, etc.). In this work, we have developed and tested a new approach to reconstruct NEA spectra, dubbed GMM-NEA, based on the use of Gaussian Mixture Models (GMMs), a probabilistic machine learning algorithm, that circumvents the phenomenological broadening assumption and, in turn, the use of δ altogether. We show that GMM-NEA systematically outperforms other data-driven models to automatically select δ overall for small datasets. In addition, we report the use of an algorithm to detect anomalous QM computations (outliers) that can affect the overall shape and uncertainty of the NEA spectra. Finally, we apply GMM-NEA to predict the photolysis rate for HgBrOOH, a compound involved in Earth’s atmospheric chemistry.

The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry

“…The absorption at these bands could play a role in the photolysis reaction of this compound, as they overlap with a region of strong solar radiation in the troposphere. In contrast, the GMM-NEA spectrum is, as expected, significantly smoother and, whereas there is indeed absorbance around 2 to 3 eV, the bands are not as resolved as previously predicted. The GMM-NEA absorption spectrum can be now used, for instance, to determine the photolysis rate ( J ) as J = prefix∫ ϕ ( λ , T ) σ normala normalb normals ( λ ) scriptI ( θ , λ ) normald λ , where ϕ(λ, T ) is the photolysis quantum yield as a function of wavelength and temperature, σ abs (λ) is the absorption cross section spectrum, and scriptI ( θ , λ ) is the solar spectral actinic flux (in quanta s –1 cm –2 nm –1 ) at the altitude of interest as a function of solar zenith angle θ and wavelength.…”

“…The GMM-NEA absorption spectrum can be now used, for instance, to determine the photolysis rate ( J ) as J = prefix∫ ϕ ( λ , T ) σ normala normalb normals ( λ ) scriptI ( θ , λ ) normald λ , where ϕ(λ, T ) is the photolysis quantum yield as a function of wavelength and temperature, σ abs (λ) is the absorption cross section spectrum, and scriptI ( θ , λ ) is the solar spectral actinic flux (in quanta s –1 cm –2 nm –1 ) at the altitude of interest as a function of solar zenith angle θ and wavelength. A value for J of 0.025 s –1 is obtained in such manner for HgBrOOH (see details in ref ). This type of computations allows to evaluate the implications of solar light chemistry in the atmospheric cycle of Hg. − …”

“…To circumvent its use and, in turn, the selection of a bandwidth δ altogether, a novel approach based on the use of Gaussian mixture models (GMM), an unsupervised ML algorithm commonly used for clustering, classification, and density estimation tasks, was reported recently. 441 The key for this approach is to mathematically transform the conventional equation for the reconstruction of NEA spectra to express it in terms of the GMM parameters that model the distribution of the 411 The total number of iterations, obtained by summing up all the products of number of iterations times number of points, is 3730 for RS-RFO and 1993 for RVO. pairs .., s for each transition.…”

“…Naturally, as it relies on a nonsatisfactory subjective perception, there is a growing interest in applying machine learning (ML) techniques (i.e., objective criteria) to adequately reconstruct the electronic NEA spectra for small data sets. ,,,, Whereas these approaches lead to broadly satisfactory results, all the models reported to date still rely on the use of the phenomenological broadening underpinning the NEA formalism. To circumvent its use and, in turn, the selection of a bandwidth δ altogether, a novel approach based on the use of Gaussian mixture models (GMM), an unsupervised ML algorithm commonly used for clustering, classification, and density estimation tasks, was reported recently . The key for this approach is to mathematically transform the conventional equation for the reconstruction of NEA spectra to express it in terms of the GMM parameters that model the distribution of the pairs false{ normalΔ E i , f i false} i = 1 , ... , N normals for each transition.…”

Benchmarking Computational Approaches to Predict the UV-Vis Spectra of Organic Photocatalysts

“…[13][14][15] This functional dependence is an issue even in elaborate multiscale ensemble modelling approaches, where most of the other factors (e.g., solvent, temperature, nuclear quantum effects) affecting the spectral line shape are treated accurately. [16][17][18][19][20][21][22][23] As there is no way of telling which functional will yield the best prediction for the molecules in hand, looking up benchmark studies is the proper way to start an investigation. 24 These benchmarks most commonly use high level ab initio reference calculations, called theoretical best estimates (TBEs), and thus disclose which functionals perform as e.g., EOM-CCSD(T) at the complete basis set (CBS) limit would perform for a given set of molecule types.…”