Cost-Effective Simulations of Vibrationally-Resolved Absorption Spectra of Fluorophores with Machine-Learning-Based Inhomogeneous Broadening

Abstract

The results of electronic and vibrational structure simulations are an invaluable support for interpreting experimental absorption/emission spectra, which stimulates the development of reliable and cost-effective computational protocols. In this work, we contribute to these efforts and propose an efficient first-principle protocol for simulating vibrationally-resolved absorption spectra, including nonempirical estimations of the inhomogeneous broadening. To this end, we analyze three key aspects: (i) a metric-based selection of density functional approximation (DFA) so to benefit from the computational efficiency of time-dependent density function theory (TD-DFT) while safeguarding the accuracy of the vibrationally-resolved spectra, (ii) an assessment of two vibrational structure schemes (vertical gradient and adiabatic Hessian) to compute the Franck–Condon factors, and (iii) the use of machine learning to speed up nonempirical estimations of the inhomogeneous broadening. In more detail, we predict the absorption band shapes for a set of 20 medium-sized fluorescent dyes, focusing on the bright ππ ★ S0 → S1 transition and using experimental results as references. We demonstrate that, for the studied 20-dye set which includes structures with large structural variability, the preselection of DFAs based on an easily accessible metric ensures accurate band shapes with respect to the reference approach and that range-separated functionals show the best performance when combined with the vertical gradient model. As far as band widths are concerned, we propose a new machine-learning-based approach for determining the inhomogeneous broadening induced by the solvent microenvironment. This approach is shown to be very robust offering inhomogeneous broadenings with errors as small as 2 cm–1 with respect to genuine electronic-structure calculations, with a total CPU time reduced by 98%.

Elucidating the Role of Hydrogen Bonding in the Optical Spectroscopy of the Solvated Green Fluorescent Protein Chromophore: Using Machine Learning to Establish the Importance of High-Level Electronic Structure

“…We then show how this initial low-level ML model that qualitatively captures the character of the electronic excitations, such as which nuclear motions couple most strongly to the electronic excitation, can be enhanced to achieve quantitative accuracy by transfer learning using only hundreds of high-level energies. The data efficiency of this approach allows us to train ML models to high-level electronic structure with the solvation environment explicitly included, expanding on other recent studies which have trained ML models to high-level electronic structure calculations in the gas phase , or with implicit solvation , or to lower-level electronic structure methods such as TDDFT. ,− In particular, here we demonstrate that one can develop an accurate ML model of electronic excitations at the level of EOM-CCSD embedded in DFT by starting from either a TDDFT or a configuration interaction singles (CIS) , low-level treatment of the excited-state electronic structure using only 400 embedded EOM-CCSD energy calculations.…”

“…Due to these challenges, a vast majority of previous studies that sample chromophore-environment excitation energies have used time-dependent density functional theory (TDDFT) , to treat the electronic excitations since it serves as a practical compromise between computational efficiency and accuracy. However, although for a range of chromophores in solution TDDFT has been shown to produce accurate linear spectra, − in particular when combined with approaches that account for vibronic effects that are not present in ensemble methods, ,− challenging cases remain where a higher-level treatment of the electronic structure is essential.…”

Delta Machine Learning for Predicting Dielectric Properties and Raman Spectra

“…Both symmetry-adapted kernel-based methods − and neural-network approaches − have been used for this, as well as a physical based small parametric model . In addition, ML methods have also been applied to compute aspects of Raman spectra directly, without explicit consideration of polarizabilities. − Delta ML (Δ-ML) is a combined approach to predicting physical quantities: a computationally inexpensive approximation is used as a first step and ML methods are then applied to learn only the differences between first-step predictions and true values . The challenge in any Δ-ML method is the search for a physical model to achieve sound first-step predictions that can be seamlessly combined with the proceeding ML method.…”

How does theory compare to experiment for oscillator strengths in electronic spectra? Proposing range-separated hybrids with reliable accountability

“…In this regard, it is difficult to disregard the role of computational quantum chemistry. Given the rich collection of references in the context of predicting the position of the bands in the electronic spectra, 12–24 theoretical explorations on the absorption intensities remain relatively limited and have proven to be challenging. As a matter of fact, contrary to excitation energies for which a large number of highly accurate benchmark sets are available, 12–24 obtaining the reference values of oscillator strengths is not an easy task, as differences between various high-correlated wave function-based approaches cannot be negligible.…”