Optimal Representation of the Nuclear Ensemble: Application to Electronic Spectroscopy

Legion: A Platform for Gaussian Wavepacket Nonadiabatic Dynamics

Nonadiabatic molecular dynamics is crucial in investigating the time evolution of excited states in molecular systems. Among the various methods for performing such dynamics, those employing frozen Gaussian wavepacket propagation, particularly the multiple spawning approach, offer a favorable balance between computational cost and reliability. It propagates on-the-fly trajectories used to build and propagate the nuclear wavepacket. Despite its potential, efficient, flexible, and easily accessible software for Gaussian wavepacket propagation is less common compared to other methods, such as surface hopping. To address this, we present Legion, a software that facilitates the development and application of classical-trajectory-guided quantum wavepacket methods. The version presented here already contains a highly flexible and fully functional ab initio multiple spawning implementation, with different strategies to improve efficiency. Legion is written in Python for data management and NumPy/Fortran for numerical operations. It is created under the umbrella of the Newton-X platform and inherits all of its electronic structure interfaces beyond other direct interfaces. It also contains new approximations that allow it to circumvent the computation of the nonadiabatic coupling, extending the electronic structure methods that can be used for multiple spawning dynamics. We test, validate, and demonstrate Legion's functionalities through multiple spawning dynamics of fulvene (CASSCF and CASPT2) and DMABN (TDDFT).

Evaluating the Importance of Conformers for Understanding the Vacuum-Ultraviolet Spectra of Oxiranes: Experiment and Theory

Vacuum-ultraviolet (VUV) absorption spectroscopy enables electronic transitions that offer the unambiguous identification of molecules. As target molecules become more complex, multifunctional species present a great challenge to both experimental and computational spectroscopy. This research reports both experimental and theoretical studies of oxiranes. Computationally, the nuclear ensemble approach has been used to accurately predict experimental spectra for a variety of molecules. However, this approach incurs great computational cost, as ensembles generally consist of thousands of geometries. The present study aims to drastically reduce the ensemble by evaluating the significance of the conformers to the predicted spectra. This approach was applied to 11 substituted oxiranes using the Conformer Rotamer Ensemble Sampling Tool (CREST) of Grimme to generate an ensemble of unique conformers determined by their Boltzmann populations. Five TD-DFT functionals (BMK, CAM-B3LYP, M06-2X, MN15, ωB97X-D) and EOM-CCSD were used to simulate the spectrum of each substituted oxirane ensemble. Computed spectra were then compared to the experiment using both qualitative and quantitative metrics. Based on these metrics, it was observed that certain conformers may not be necessary to characterize this set of oxiranes despite the temperature (323 K) of the experiment. A single conformer can then be used with TD-DFT and EOM-CCSD to replicate the experimental spectra of these medium-sized combustion species.

AtmoSpec-A Tool to Calculate Photoabsorption Cross-Sections for Atmospheric Volatile Organic Compounds

Characterizing the photolysis processes undergone by transient volatile organic compounds (VOCs) in the troposphere requires the knowledge of their photoabsorption cross-section-quantities often challenging to determine experimentally, particularly due to the reactivity of these molecules. We present a computational tool coined AtmoSpec, which can predict a quantitative photoabsorption cross-section for volatile organic compounds by using computational photochemistry. The user enters the molecule of interest as a SMILES code and, after selecting a level of theory for the electronic structure (and waiting for the calculations to take place), is presented with a photoabsorption cross-section for the low-energy conformers and an estimate of the photolysis rate coefficient for different standardized actinic fluxes. More specifically, AtmoSpec is an automated workflow for the nuclear ensemble approach, an efficient technique to approximate the absolute intensities and excitation wavelengths of a photoabsorption cross-section for a molecule in the gas phase of interest in atmospheric chemistry and astrochemistry. This work provides background information on the nuclear ensemble approach, a guided example of a typical AtmoSpec calculation, details about the architecture of the code, and the current limitations and future developments of this tool.

Calculating absorption and fluorescence spectra for chromophores in solution with ensemble Franck-Condon methods

Accurately modeling absorption and fluorescence spectra for molecules in solution poses a challenge due to the need to incorporate both vibronic and environmental effects, as well as the necessity of accurate excited state electronic structure calculations. Nuclear ensemble approaches capture explicit environmental effects, Franck-Condon methods capture vibronic effects, and recently introduced ensemble-Franck-Condon approaches combine the advantages of both methods. In this study, we present and analyze simulated absorption and fluorescence spectra generated with combined ensemble-Franck-Condon approaches for three chromophore-solvent systems and compare them to standard ensemble and Franck-Condon spectra, as well as to the experiment. Employing configurations obtained from ground and excited state ab initio molecular dynamics, three combined ensemble-Franck-Condon approaches are directly compared to each other to assess the accuracy and relative computational time. We find that the approach employing an average finite-temperature Franck-Condon line shape generates spectra nearly identical to the direct summation of an ensemble of Franck-Condon spectra at one-fourth of the computational cost. We analyze how the spectral simulation method, as well as the level of electronic structure theory, affects spectral line shapes and associated Stokes shifts for 7-nitrobenz-2-oxa-1,3-diazol-4-yl and Nile red in dimethyl sulfoxide and 7-methoxy coumarin-4-acetic acid in methanol. For the first time, our studies show the capability of combined ensemble-Franck-Condon methods for both absorption and fluorescence spectroscopy and provide a powerful tool for simulating linear optical spectra.

Liquid-jet photoemission spectroscopy as a structural tool: site-specific acid-base chemistry of vitamin C

Liquid-jet photoemission spectroscopy (LJ-PES) directly probes the electronic structure of solutes and solvents. It also emerges as a novel tool to explore chemical structure in aqueous solutions, yet the scope of the approach has to be examined. Here, we present a pH-dependent liquid-jet photoelectron spectroscopic investigation of ascorbic acid (vitamin C). We combine core-level photoelectron spectroscopy and ab initio calculations, allowing us to site-specifically explore the acid-base chemistry of the biomolecule. For the first time, we demonstrate the capability of the method to simultaneously assign two deprotonation sites within the molecule. We show that a large change in chemical shift appears even for atoms distant several bonds from the chemically modified group. Furthermore, we present a highly efficient and accurate computational protocol based on a single structure using the maximum-overlap method for modeling core-level photoelectron spectra in aqueous environments. This work poses a broader question: to what extent can LJ-PES complement established structural techniques such as nuclear magnetic resonance? Answering this question is highly relevant in view of the large number of incorrect molecular structures published.

MLatom Software Ecosystem for Surface Hopping Dynamics in Python with Quantum Mechanical and Machine Learning Methods

We present an open-source MLatom@XACS software ecosystem for on-the-fly surface hopping nonadiabatic dynamics based on the Landau-Zener-Belyaev-Lebedev algorithm. The dynamics can be performed via Python API with a wide range of quantum mechanical (QM) and machine learning (ML) methods, including ab initio QM (CASSCF and ADC(2)), semiempirical QM methods (e.g., AM1, PM3, OMx, and ODMx), and many types of ML potentials (e.g., KREG, ANI, and MACE). Combinations of QM and ML methods can also be used. While the user can build their own combinations, we provide AIQM1, which is based on Δ-learning and can be used out-of-the-box. We showcase how AIQM1 reproduces the isomerization quantum yield of trans-azobenzene at a low cost. We provide example scripts that, in dozens of lines, enable the user to obtain the final population plots by simply providing the initial geometry of a molecule. Thus, those scripts perform geometry optimization, normal mode calculations, initial condition sampling, parallel trajectories propagation, population analysis, and final result plotting. Given the capabilities of MLatom to be used for training different ML models, this ecosystem can be seamlessly integrated into the protocols building ML models for nonadiabatic dynamics. In the future, a deeper and more efficient integration of MLatom with Newton-X will enable a vast range of functionalities for surface hopping dynamics, such as fewest-switches surface hopping, to facilitate similar workflows via the Python API.

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.

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

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

Excitation and fragmentation of the dielectric gas C4F7N: Electrons vs photons

C₄F₇N is a promising candidate for the replacement of sulfur hexafluoride as an insulating medium, and it is important to understand the chemical changes initiated in the molecule by collision with free electrons, specifically the formation of neutral fragments. The first step of neutral fragmentation is electronic excitation, yet neither the absorption spectrum in the vacuum ultraviolet (VUV) region nor the electron energy loss spectrum have previously been reported. Here, we experimentally probed the excited states by VUV photoabsorption spectroscopy and electron energy loss spectroscopy (EELS). We found that the distribution of states populated upon electron impact with low-energy electrons is significantly different from that following photoabsorption. This difference was confirmed and interpreted with ab initio modeling of both VUV and EELS spectra. We propose here a new computational protocol for the simulation of EELS spectra combining the Born approximation with approximate forms of correlated wave functions, which allows us to calculate the (usually very expensive) scattering cross sections at a cost similar to the calculation of oscillator strengths. Finally, we perform semi-classical non-adiabatic dynamics simulations to investigate the possible neutral fragments of the molecule formed through electron-induced neutral dissociation. We show that the product distribution is highly non-statistical.

Newton-X Platform: New Software Developments for Surface Hopping and Nuclear Ensembles

Newton-X is an open-source computational platform to perform nonadiabatic molecular dynamics based on surface hopping and spectrum simulations using the nuclear ensemble approach. Both are among the most common methodologies in computational chemistry for photophysical and photochemical investigations. This paper describes the main features of these methods and how they are implemented in Newton-X. It emphasizes the newest developments, including zero-point-energy leakage correction, dynamics on complex-valued potential energy surfaces, dynamics induced by incoherent light, dynamics based on machine-learning potentials, exciton dynamics of multiple chromophores, and supervised and unsupervised machine learning techniques. Newton-X is interfaced with several third-party quantum-chemistry programs, spanning a broad spectrum of electronic structure methods.

Applicability of the Thawed Gaussian Wavepacket Dynamics to the Calculation of Vibronic Spectra of Molecules with Double-Well Potential Energy Surfaces

Simulating vibrationally resolved electronic spectra of anharmonic systems, especially those involving double-well potential energy surfaces, often requires expensive quantum dynamics methods. Here, we explore the applicability and limitations of the recently proposed single-Hessian thawed Gaussian approximation for the simulation of spectra of systems with double-well potentials, including 1,2,4,5-tetrafluorobenzene, ammonia, phosphine, and arsine. This semiclassical wavepacket approach is shown to be more robust and to provide more accurate spectra than the conventional harmonic approximation. Specifically, we identify two cases in which the Gaussian wavepacket method is especially useful due to the breakdown of the harmonic approximation: (i) when the nuclear wavepacket is initially at the top of the potential barrier but delocalized over both wells, e.g., along a low-frequency mode, and (ii) when the wavepacket has enough energy to classically go over the low potential energy barrier connecting the two wells. The method is efficient and requires only a single classical ab initio molecular dynamics trajectory, in addition to the data required to compute the harmonic spectra. We also present an improved algorithm for computing the wavepacket autocorrelation function, which guarantees that the evaluated correlation function is continuous for arbitrary size of the time step.

Reconstruction of Nuclear Ensemble Approach Electronic Spectra Using Probabilistic Machine Learning

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 (ΔE) 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.

Calculating Photoabsorption Cross-Sections for Atmospheric Volatile Organic Compounds

Characterizing the photochemical reactivity of transient volatile organic compounds (VOCs) in our atmosphere begins with a proper understanding of their abilities to absorb sunlight. Unfortunately, the photoabsorption cross-sections for a large number of transient VOCs remain unavailable experimentally due to their short lifetime or high reactivity. While structure-activity relationships (SARs) have been successfully employed to estimate the unknown photoabsorption cross-sections of VOCs, computational photochemistry offers another promising strategy to predict not only the vertical electronic transitions of a given molecule but also the width and shape of the bands forming its absorption spectrum. In this work, we focus on the use of the nuclear ensemble approach (NEA) to determine the photoabsorption cross-section of four exemplary VOCs, namely, acrolein, methylhydroperoxide, 2-hydroperoxy-propanal, and (microsolvated) pyruvic acid. More specifically, we analyze the influence that different strategies for sampling the ground-state nuclear density-Wigner sampling and ab initio molecular dynamics with a quantum thermostat-can have on the simulated absorption spectra. We highlight the potential shortcomings of using uncoupled harmonic modes within Wigner sampling of nuclear density to describe flexible or microsolvated VOCs and some limitations of SARs for multichromophoric VOCs. Our results suggest that the NEA could constitute a powerful tool for the atmospheric community to predict the photoabsorption cross-section for transient VOCs.