Machine Learning Approach to Vertical Energy Gap in Redox Processes

A straightforward approach to calculating the free energy change (ΔG) and reorganization energy of a redox process is linear response approximation (LRA). However, accurate prediction of redox properties is still challenging due to difficulties in conformational sampling and vertical energy-gap sampling. Expensive hybrid quantum mechanical/molecular mechanical (QM/MM) calculations are typically employed in sampling energy gaps using conformations from simulations. To alleviate the computational cost associated with the expensive QM method in the QM/MM calculation, we propose machine learning (ML) methods to predict the vertical energy gaps (VEGs). We tested several ML models to predict the VEGs and observed that simple models like linear regression show excellent performance (mean absolute error ∼0.1 eV) in predicting VEGs in all test systems, even when using features extracted from cheaper semiempirical methods. Our best ML model (extra trees regressor) shows a mean absolute error of around 0.1 eV while using features from the cheapest QM method. We anticipate our approach can be generalized to larger macromolecular systems with more complex redox centers.

How Does Mg2+(aq) Interact with ATP(aq)? Biomolecular Structure through the Lens of Liquid-Jet Photoemission Spectroscopy

Liquid-jet photoemission spectroscopy (LJ-PES) allows for a direct probing of electronic structure in aqueous solutions. We show the applicability of the approach to biomolecules in a complex environment, exploring site-specific information on the interaction of adenosine triphosphate in the aqueous phase (ATP(aq)) with magnesium (Mg2+(aq)), highlighting the synergy brought about by the simultaneous analysis of different regions in the photoelectron spectrum. In particular, we demonstrate intermolecular Coulombic decay (ICD) spectroscopy as a new and powerful addition to the arsenal of techniques for biomolecular structure investigation. We apply LJ-PES assisted by electronic-structure calculations to study ATP(aq) solutions with and without dissolved Mg2+. Valence photoelectron data reveal spectral changes in the phosphate and adenine features of ATP(aq) due to interactions with the divalent cation. Chemical shifts in Mg 2p, Mg 2s, P 2p, and P 2s core-level spectra as a function of the Mg2+/ATP concentration ratio are correlated to the formation of [Mg(ATP) 2]6-(aq), [MgATP]2-(aq), and [Mg2ATP](aq) complexes, demonstrating the element sensitivity of the technique to Mg2+-phosphate interactions. The most direct probe of the intermolecular interactions between ATP(aq) and Mg2+(aq) is delivered by the emerging ICD electrons following ionization of Mg 1s electrons. ICD spectra are shown to sensitively probe ligand exchange in the Mg2+-ATP(aq) coordination environment. In addition, we report and compare P 2s data from ATP(aq) and adenosine mono- and diphosphate (AMP(aq) and ADP(aq), respectively) solutions, probing the electronic structure of the phosphate chain and the local environment of individual phosphate units in ATP(aq). Our results provide a comprehensive view of the electronic structure of ATP(aq) and Mg2+-ATP(aq) complexes relevant to phosphorylation and dephosphorylation reactions that are central to bioenergetics in living organisms.

Unraveling the Photoionization Dynamics of Indole in Aqueous and Ethanol Solutions

The photoionization dynamics of indole, the ultraviolet-B chromophore of tryptophan, were explored in water and ethanol using ultrafast transient absorption spectroscopy with 292, 268, and 200 nm excitation. By studying the femtosecond-to-nanosecond dynamics of indole in two different solvents, a new photophysical model has been generated that explains many previously unsolved facets of indole's complex solution phase photochemistry. Photoionization is only an active pathway for indole in aqueous solution, leading to a reduction in the fluorescence quantum yield in water-rich environments, which is frequently used in biophysical experiments as a key signature of the protein-folded state. Photoionization of indole in aqueous solution was observed for all three pump wavelengths but via two different mechanisms. For 200 nm excitation, electrons are ballistically ejected directly into the bulk solvent. Conversely, 292 and 268 nm excitation populates an admixture of two 1ππ* states, which form a dynamic equilibrium with a tightly bound indole cation and electron-ion pair. The ion pair dissociates on a nanosecond time scale, generating separated solvated electrons and indole cations. The charged species serve as important precursors to triplet indole production and greatly enhance the overall intersystem crossing rate. Our proposed photophysical model for indole in aqueous solution is the most appropriate for describing photoinduced dynamics of tryptophan in polypeptide sequences; tryptophan in aqueous pH 7 solution is zwitterionic, unlike in peptides, and resultantly has a competitive excited state proton transfer pathway that quenches the tryptophan fluorescence.

Excited state hydrogen or proton transfer pathways in microsolvated n-cyanoindole fluorescent probes

The sensitivity of the fluorescence properties of n-cyanoindole (n-CNI) fluorescent probes to the microenvironment makes them potential reporters of protein conformation and hydration. The fluorescence intensity of 5-CNI, 6-CNI, and 7-CNI is quenched when exposed to water solvent whereas substitution on position 4 of indoles dramatically increases it. A potential mechanism for this sensitivity to water may be similar to that found in indole. The fluorescence of indole is found to be quenched when interacting with water and ammonia solvent molecules via radiationless decay through an S1 (πσ*)/S0 conical intersection caused by excited state proton or hydrogen transfer to the solvent molecules. In this study we examine this fluorescence quenching mechanism along the N-H bond stretch of n-CNI probes using water cluster models and quantum mechanical calculations of the excited states. We find that n-CNI-(H2O)1-2 clusters form cyclic or non-cyclic structures via hydrogen bonds which lead to different photochemical reaction paths that can potentially quench the fluorescence by undergoing internal conversion from S1 to S0. However, the existence of a high energy barrier along the potential energy surface of the S1 state in most cases prevents this from occurring. We show that substitution on position 4 leads to the highest energy barrier that prevents the fluorophore from accessing these non-radiative channels, in agreement with its high intensity. We also find that the energy barrier in the S1 state of non-cyclic 5-CNI-(H2O)1-2 excited complexes decreases as the number of water molecules increases, which suggests great sensitivity of the fluorescence quenching on the aqueous environment.

Specific versus Nonspecific Solvent Interactions of a Biomolecule in Water

Solvent interactions, particularly hydration, are vital in chemical and biochemical systems. Model systems reveal microscopic details of such interactions. We uncover a specific hydrogen-bonding motif of the biomolecular building block indole (C8H7N), tryptophan's chromophore, in water: a strong localized N-H···OH2 hydrogen bond, alongside unstructured solvent interactions. This insight is revealed from a combined experimental and theoretical analysis of the electronic structure of indole in aqueous solution. We recorded the complete X-ray photoemission and Auger spectrum of aqueous-phase indole, quantitatively explaining all peaks through ab initio modeling. The efficient and accurate technique for modeling valence and core photoemission spectra involves the maximum-overlap method and the nonequilibrium polarizable-continuum model. A two-hole electron-population analysis quantitatively describes the Auger spectra. Core-electron binding energies for nitrogen and carbon highlight the specific interaction with a hydrogen-bonded water molecule at the N-H group and otherwise nonspecific solvent interactions.

Influence of H-bonds on the photoionization of aromatic chromophores in water: The aniline molecule

We have conducted time-resolved experiments (pump-probe and pump-repump-probe) on a model aromatic chromophore, aniline, after excitation in water at 267 nm. In the initial spectra recorded, in addition to the absorption corresponding to the bright ππ* excitation, the fingerprint of a transient state with the electron located on the solvent molecule is identified. We postulate that the latter corresponds to the πσ* state along the N-H bond, whose complete relaxation with a ∼500 ps lifetime results in the formation of the fully solvated electron and cation. This ionization process occurs in parallel with the ππ* photophysical channel that yields the characteristic ∼1 ns fluorescence lifetime. The observed branched pathway is rationalized in terms of the different H-bonds that the water establishes with the amino group. The proposed mechanism could be common for aromatics in water containing N-H or O-H bonds and would allow the formation of separated charges after excitation at the threshold of their electronic absorptions.

UV Photoelectron Spectroscopy of Aqueous Solutions

Knowledge of the electronic structure of an aqueous solution is a prerequisite to understanding its chemical and biological reactivity and its response to light. One of the most direct ways of determining electronic structure is to use photoelectron spectroscopy to measure electron binding energies. Initially, photoelectron spectroscopy was restricted to the gas or solid phases due to the requirement for high vacuum to minimize inelastic scattering of the emitted electrons. The introduction of liquid-jets and their combination with intense X-ray sources at synchrotrons in the late 1990s expanded the scope of photoelectron spectroscopy to include liquids. Liquid-jet photoelectron spectroscopy is now an active research field involving a growing number of research groups. A limitation of X-ray photoelectron spectroscopy of aqueous solutions is the requirement to use solutes with reasonably high concentrations in order to obtain photoelectron spectra with adequate signal-to-noise after subtracting the spectrum of water. This has excluded most studies of organic molecules, which tend to be only weakly soluble. A solution to this problem is to use resonance-enhanced photoelectron spectroscopy with ultraviolet (UV) light pulses (hν ≲ 6 eV). However, the development of UV liquid-jet photoelectron spectroscopy has been hampered by a lack of quantitative understanding of inelastic scattering of low kinetic energy electrons (≲5 eV) and the impact on spectral lineshapes and positions.In this Account, we describe the key steps involved in the measurement of UV photoelectron spectra of aqueous solutions: photoionization/detachment, electron transport of low kinetic energy electrons through the conduction band, transmission through the water-vacuum interface, and transport through the spectrometer. We also explain the steps we take to record accurate UV photoelectron spectra of liquids with excellent signal-to-noise. We then describe how we have combined Monte Carlo simulations of electron scattering and spectral inversion with molecular dynamics simulations of depth profiles of organic solutes in aqueous solution to develop an efficient and widely applicable method for retrieving true UV photoelectron spectra of aqueous solutions. The huge potential of our experimental and spectral retrieval methods is illustrated using three examples. The first is a measurement of the vertical detachment energy of the green fluorescent protein chromophore, a sparingly soluble organic anion whose electronic structure underpins its fluorescence and photooxidation properties. The second is a measurement of the vertical ionization energy of liquid water, which has been the subject of discussion since the first X-ray photoelectron spectroscopy measurement in 1997. The third is a UV photoelectron spectroscopy study of the vertical ionization energy of aqueous phenol which demonstrates the possibility of retrieving true photoelectron spectra from measurements with contributions from components with different concentration profiles.

Conical Intersections in Solution with Polarizable Embedding: Integral-Exact Direct Reaction Field

A common strategy to exploring the properties and reactivity of complex systems is to use quantum mechanics/molecular mechanics (QM/MM) embedding, wherein a QM region is defined and treated with electronic structure theory, and the remainder of the system is treated with a force field. Important to the description of electronic excited states, especially those of charge-transfer character, is the treatment of the coupling between the QM and MM subsystems. The state of the art is to use a polarizable force field for the MM region and mutually couple the QM wavefunction and MM induced dipoles, in addition to the usual electrostatic embedding, yielding a polarizable embedding (QM/MM-Pol) approach. However, we showed previously that current popular QM/MM-Pol approaches exhibit issues of root flipping and/or incorrect descriptions of electronic crossings in multistate calculations [J. Chem. Theory Comput. 14, 2137 (2018)]. Here, we demonstrate a solution to these problems with an integral-exact reformulation of the direct reaction field approach of Thole and Van Duijnen (QM/MM-IEDRF). The resulting embedding potential includes one- and two-electron operators and many-body dipole-induced dipole interactions and thus includes a natural description of the screening of electron-electron interactions by the MM induced dipoles. Pauli repulsion from the environment is mimicked by effective core potentials on the MM atoms. Inherent to the DRF approach is the assumption that MM dipoles respond instantaneously to the positions of the QM electrons; therefore, dispersion interactions are captured approximately. All electronic states are eigenfunctions of the same Hamiltonian, while the polarization induced in the environment and the associated energetic stabilization are unique to each state. This allows for a consistent definition of transition properties and state crossings. We demonstrate QM/MM-IEDRF by exploring the influence of a (polarizable) inert xenon matrix environment on the conical intersection underlying the photoisomerization of ethylene.

All-Atom Nonadiabatic Semiclassical Mapping Dynamics for Photoinduced Charge Transfer of Organic Photovoltaic Molecules in Explicit Solvents

Direct all-atom simulation of nonadiabatic dynamics in disordered condensed phases like liquid solutions and amorphous solids has been challenging. The first all-atom simulation of the photoinduced charge-transfer dynamics of a prototypical organic photovoltaic carotenoid-porphyrin-C₆₀ molecular triad in explicit tetrahydrofuran is presented. Based on the Meyer-Miller mapping Hamiltonian, various semiclassical and mixed quantum-classical dynamics are employed, including the linearized semiclassical, symmetrical quasiclassical, mean-field Ehrenfest, classical mapping model, and spin-mapping model approaches. The all-atom nonadiabatic dynamics were compared to multi-state harmonic models with a globally shared bath, and the models built using the ensemble averages on the initial electronic state could reproduce the all-atom results. The solvent effect was found to be critical for the photoinduced charge transfer, and the time-dependent solute-solvent radial distribution functions revealed that only the nonadiabatic dynamics started with the effective forces on the initial electronic state could capture the correct nuclear dynamics. The proposed strategy for modeling condensed-phase nonadiabatic dynamics with atomistic details is readily applied to complex condensed-phase systems.

Accurate Vertical Ionization Energy of Water and Retrieval of True Ultraviolet Photoelectron Spectra of Aqueous Solutions

Ultraviolet (UV) photoelectron spectroscopy provides a direct way of measuring valence electronic structure; however, its application to aqueous solutions has been hampered by a lack of quantitative understanding of how inelastic scattering of low-energy (<5 eV) electrons in liquid water distorts the measured electron kinetic energy distributions. Here, we present an efficient and widely applicable method for retrieving true UV photoelectron spectra of aqueous solutions. Our method combines Monte Carlo simulations of electron scattering and spectral inversion, with molecular dynamics simulations of depth profiles of organic solutes in aqueous solution. Its application is demonstrated for both liquid water, and aqueous solutions of phenol and phenolate, which are ubiquitous biologically relevant structural motifs.

Environment-Driven Coherent Population Transfer Governs the Ultrafast Photophysics of Tryptophan

By combining UV transient absorption spectroscopy with sub-30-fs temporal resolution and CASPT2/MM calculations, we present a complete description of the primary photoinduced processes in solvated tryptophan. Our results shed new light on the role of the solvent in the relaxation dynamics of tryptophan. We unveil two consecutive coherent population transfer events involving the lowest two singlet excited states: a sub-50-fs nonadiabatic L_a → L_b transfer through a conical intersection and a subsequent 220 fs reverse L_b → L_a transfer due to solvent-assisted adiabatic stabilization of the L_a state. Vibrational fingerprints in the transient absorption spectra provide compelling evidence of a vibronic coherence established between the two excited states from the earliest times after photoexcitation and lasting until the back-transfer to L_a is complete. The demonstration of response to the environment as a driver of coherent population dynamics among the excited states of tryptophan closes the long debate on its solvent-assisted relaxation mechanisms and extends its application as a local probe of protein dynamics to the ultrafast time scales.

Investigating the Ultrafast Dynamics and Long-Term Photostability of an Isomer Pair, Usujirene and Palythene, from the Mycosporine-like Amino Acid Family

Mycosporine-like amino acids are a prevalent form of photoprotection in micro- and macro-organisms. Using a combination of natural product extraction/purification and femtosecond transient absorption spectroscopy, we studied the relaxation pathway for a common mycosporine-like amino acid pair, usujirene and its geometric isomer palythene, in the first few nanoseconds following photoexcitation. Our studies show that the electronic excited state lifetimes of these molecules persist for only a few hundred femtoseconds before the excited state population is funneled through an energetically accessible conical intersection with subsequent vibrational energy transfer to the solvent. We found that a minor portion of the isomer pair did not recover to their original state within 3 ns after photoexcitation. We investigated the long-term photostability using continuous irradiation at a single wavelength and with a solar simulator to mimic a more real-life environment; high levels of photostability were observed in both experiments. Finally, we employed computational methods to elucidate the photochemical and photophysical properties of usujirene and palythene as well as to reconcile the photoprotective mechanism.

Modeling solvation effects on absorption and fluorescence spectra of indole in aqueous solution

Modeling the optical spectra of molecules in solution presents a challenge, so it is important to understand which of the solvation effects (i.e., electrostatics, mutual polarization, and hydrogen bonding interactions between solute and solvent molecules) are crucial in reproducing the various features of the absorption and fluorescence spectra and to identify a sufficient theoretical model that accurately captures these effects with minimal computational cost. In this study, we use various implicit and explicit solvation models, such as molecular dynamics coupled with non-polarizable and polarizable force fields, as well as Car-Parrinello molecular dynamics, to model the absorption and fluorescence spectra of indole in aqueous solution. The excited states are computed using the equation of motion coupled cluster with single and double excitations combined with the effective fragment potential to represent water molecules, which we found to be a computationally efficient approach for modeling large solute-solvent clusters at a high level of quantum theory. We find that modeling mutual polarization, compared to other solvation effects, is a dominating factor for accurately reproducing the position of the peaks and spectral line shape of the absorption spectrum of indole in solution. We present an in-depth analysis of the influence that different solvation models have on the electronic excited states responsible for the features of the absorption spectra. Modeling fluorescence is more challenging since it is hard to reproduce even the correct emitting state, and force field parameters need to be re-evaluated.

Ionization Energy of Liquid Water Revisited

The ionization energy of liquid water is one of its most fundamental properties, an important benchmark for first-principles electronic-structure calculations and a crucial reference in the growing field of liquid-phase photoelectron spectroscopy. Despite this significance, a consensus on its value appears to be missing in the literature. Therefore, we use a monochromatized high-harmonic light source to perform detailed measurements of the ionization energy of liquid water in the presence of a tunable bias voltage applied to the liquid jet. Our results suggest that this simple method is sufficient to simultaneously compensate the effects of the streaming potential and that of the vacuum-level offset between the liquid and the photoelectron spectrometer. Our measurements yield corrected values of the vertical and adiabatic ionization energies of the 1b₁ band of bulk liquid water of 11.67(15) and 10.12(15) eV, respectively. Our method is broadly applicable and is likely to result in corrections to the measured ionization energies of solvated species as well.

An experimental and computational study of the effect of aqueous solution on the multiphoton ionisation photoelectron spectrum of phenol

We revisit the photoelectron spectroscopy of aqueous phenol in an effort to improve our understanding of the impact of inhomogeneous broadening and inelastic scattering on solution-phase photoelectron spectra.

Design and characterization of a recirculating liquid-microjet photoelectron spectrometer for multiphoton ultraviolet photoelectron spectroscopy

A new recirculating liquid-microjet photoelectron spectrometer for multiphoton ultraviolet photoelectron spectroscopy is described. A recirculating system is essential for studying samples that are only available in relatively small quantities. The reduction in background pressure when using the recirculating system compared to a liquid-nitrogen cold-trap results in a significant improvement in the quality of the photoelectron spectra. Moreover, the recirculating system results in a negligible streaming potential. The instrument design, operation, and characterization are described in detail, and its performance is illustrated by comparing a photoelectron spectrum of aqueous phenol recorded using the recirculating system with one recorded using a liquid nitrogen cold-trap.

Magic Numbers for the Photoelectron Anisotropy in Li-Doped Dimethyl Ether Clusters

Photoelectron velocity map imaging of Li(CH₃OCH₃)_n clusters (1 ≤ n ≤ 175) is used to search for magic numbers related to the photoelectron anisotropy. Comparison with density functional calculations reveals magic numbers at n = 4, 5, and 6, resulting from the symmetric charge distribution with high s-character of the highest occupied molecular orbital. Since each of these three cluster sizes correspond to the completion of a first coordination shell, they can be considered as “isomeric motifs of the first coordination shell”. Differences in the photoelectron anisotropy, the vertical ionization energies and the enthalpies of vaporization between Li(CH₃OCH₃)_n and Na(CH₃OCH₃)_n can be rationalized in terms of differences in their solvation shells, atomic ionization energies, polarizabilities, metal–oxygen bonds, ligand–ligand interactions and by cooperative effects.