Communication: Extended multi-state complete active space second-order perturbation theory: Energy and nuclear gradients

Photoisomerization pathways of trans-resveratrol

Resveratrol is well-known for promoting health benefits due to its antioxidant, anti-aging, anti-carcinogenic, and other beneficial activities. Understanding the photophysics of resveratrol is essential for determining its applicability to pharmaceutical innovations. In the present work, we used an explore-then-assess strategy to map the internal conversion pathways of trans-resveratrol. This strategy consists of exploring the multidimensional configurational space with nonadiabatic dynamics simulations based on a semiempirical multireference method, followed by a feasibility assessment of reduced-dimensionality pathways at a high ab initio theoretical level. The exploration step revealed that internal conversion to the ground state may occur near five distinct conical intersections. The assessment step showed that the main photoisomerization pathway involves a twisted-pyramidalized S1/S0 conical intersection, yielding either trans or cis isomers. However, a secondary path was identified, where cis-trans isomerization happens in the excited state and internal conversion occurs at a cyclic conical intersection, yielding a closed-ring resveratrol derivative. This derivative, which can be formed through this direct path or an indirect photoexcitation, may be connected to the production of oxygen-reactive species previously reported and have implications in photodynamic therapy.

Excited state electronic structure of dimethyl disulfide involved in photodissociation at ∼200 nm

Dimethyl disulfide (DMDS), one of the smallest organic molecules with an S-S bond, serves as a model system for understanding photofragmentation in polypeptides and proteins. Prior studies of DMDS photodissociation excited at ∼266 nm and ∼248 nm have elucidated the mechanisms of S-S and C-S bond cleavage, which involve the lowest excited electronic states S1 and S2. Far less is known about the dissociation mechanisms and electronic structure of relevant excited states of DMDS excited at ∼200 nm. Herein we present calculations of the electronic structure and properties of electronic states S1-S6 accessed when DMDS is excited at ∼200 nm. Our analysis includes a comparison of theoretical and experimental UV spectra, as well as theoretically predicted one-dimensional cuts through the singlet and triplet potential energy surfaces along the S-S and C-S bond dissociation coordinates. Finally, we present calculations of spin-orbit coupling constants at the Franck-Condon geometry to assess the likelihood of ultrafast intersystem crossing. We show that choosing an accurate yet computationally efficient electronic structure method for calculating the S0-S6 potential energy surfaces along relevant dissociation coordinates is challenging due to excited states with doubly excited character and/or mixed Rydberg-valence character. Our findings demonstrate that the extended multi-state complete active space second-order perturbation theory (XMS-CASPT2) balances this computational efficiency and accuracy, as it captures both the Rydberg character of states in the Franck-Condon region and multiconfigurational character toward the bond-dissociation limits. We compare the performance of XMS-CASPT2 to a new variant of equation of motion coupled cluster theory with single, double, and perturbative triple corrections, EOM-CCSD(T)(a)*, finding that EOM-CCSD(T)(a)* significantly improves the treatment of doubly excited states compared to EOM-CCSD, but struggles to quantitatively capture asymptotic energies along bond dissociation coordinates for these states.

Simulation of the non-adiabatic dynamics of an enone-Lewis acid complex in an explicit solvent

Unlocking the full potential of Lewis acid catalysis for photochemical transformations requires a comprehensive understanding of the ultrafast dynamics of substrate-Lewis acid complexes. In a previous article [Peschel et al., Angew. Chem. Int. Ed., 2021, 60, 10155], time-resolved spectroscopy supported by static calculations revealed that the Lewis acid remains attached during the relaxation of the model complex cyclohexenone-BF3. In contrast to the experimental observation, surface-hopping dynamics in the gas phase predicted ultrafast heterolytic dissociation. We attributed the discrepancy to missing solvent interactions. Thus, in this work, we present an interface between the SHARC and FermiONs++ program packages, which enables us to investigate the ultrafast dynamics of cyclohexenone-BF3 in an explicit solvent environment. Our simulations demonstrate that the solvent prevents the dissociation of the complex, leading to an intriguing dissociation-reassociation mechanism. Comparing the dynamics with and without triplet states highlights their role in the relaxation process and shows that the Lewis acid inhibits intersystem crossing. These findings provide a clear picture of the relaxation process, which may aid in designing future Lewis acid catalysts for photochemical applications. They underscore that an explicit solvent model is required to describe relaxation processes in weakly bound states, as energy transfer to the solvent is crucial for the system to reach its minimum geometries.

Ab Initio Multiple Spawning Nonadiabatic Dynamics with Different CASPT2 Flavors: A Fully Open-Source PySpawn/OpenMolcas Interface

We introduce an interface between PySpawn, a simulation package to run ab initio multiple spawning (AIMS) nonadiabatic dynamics, and OpenMolcas, a software package to perform multiconfigurational perturbations theory (CASPT2) electronic structure calculations. Our interface allows us to exploit all the functionalities of the two codes: the modular and efficient Python implementation of the AIMS algorithm and the extensive analysis tools offered by PySpawn, with the cutting-edge implementation of CASPT2 equations in OpenMolcas, including the recently introduced analytical gradients and different flavors. Both are fully open-source and free of charge, making the following implementation unique in the current plethora of software for nonadiabatic dynamics. This represents an important step toward a wider application of AIMS-based nonadiabatic dynamics combined with high-accuracy excited-state calculations. The importance and the need for such an implementation are demonstrated by application to the ultrafast relaxation of fulvene from S1 to S0, which is drastically affected by the potential energy surface on which the nuclear wavepacket is propagated. Additionally, the decay is influenced by the CASPT2 flavor adopted, posing interesting questions in the choice of one over the other and opening the door to deeper studies on the effect of CASPT2 formulations in nonadiabatic dynamics.

Dynamics of NO Release and Linkage Isomer Formation from S-Nitroso-Mercaptoethanol in Aqueous Solutions: Insights from Femtosecond Infrared Spectroscopy

Understanding the photodynamics of S-nitroso-thiol (RSNO), an effective NO transporter in biological systems, is essential for its photochemical applications. S-nitroso-mercaptoethanol (MceSNO), a simple water-soluble RSNO, facilitates high-level quantum calculations. We investigated the photoexcitation dynamics of MceSNO in an aqueous solution, focusing on NO dissociation, recombination, and linkage isomerization using quantum calculations and femtosecond infrared spectroscopy. Upon excitation at 320 nm, MceSNO rapidly dissociates into NO and MceS radicals. Approximately 31 ± 3% of MceS reacts with unexcited MceSNO molecules, forming MceSSMce and releasing additional NO. The remaining MceS undergoes geminate recombination with NO, forming either MceSNO (41 ± 4%) or MceSON (28 ± 3%), the latter being a sulfur-ON linkage isomer observed for the first time in a room-temperature solution. MceSON isomerizes back to MceSNO in 470 ± 30 ps. The formation mechanism of MceSON was verified through a potential energy surface constructed at the CASPT2D(16,11)/cc-pVTZ level. The isomerization barrier was determined to be 3.3 ± 1.2 kcal/mol in water.

Electronic Structure Methods for Simulating Flavin's Spectroscopy and Photophysics: Comparison of Multi-reference, TD-DFT, and Single-Reference Wave Function Methods

The use of flavins and flavoproteins in photocatalytic, sensing, and biotechnological applications has led to a growing interest in computationally modeling the excited-state electronic structure and photophysics of flavin. However, there is limited consensus regarding which computational methods are appropriate for modeling flavin's photophysics. We compare the energies of low-lying excited states of flavin computed with time-dependent density functional theory (TD-DFT), equation-of-motion coupled cluster (EOM-EE-CCSD), scaled opposite-spin configuration interaction [SOS-CIS(D)], multiconfiguration pair-density functional theory (MC-PDFT), and several multireference perturbation theory (MR-PT2) methods. In the first part, we focus on excitation energies of the first singlet excited state (S1) of five different redox and protonation states of flavin, with the goal of finding a suitable active space for MR-PT2 calculations. In the second part, we construct two sets of one-dimensional potential energy surfaces connecting the S0 and S1 equilibrium geometries (S0-S1 path) and the S1 (π,π*) and S2 (n,π*) equilibrium geometries (S1-S2 path). The first path therefore follows a Franck-Condon active mode of flavin while the second path maps crossings points between low-lying singlet and triplet states in flavin. We discuss the similarities and differences in the TD-DFT, EOM-EE-CCSD, SOS-CIS(D), MC-PDFT and MR-PT2 energy profiles along these paths. We find that (TD-)DFT methods are suitable for applications such as simulating the spectra of flavins but are inconsistent with several other methods when used for some geometry optimizations and when describing the energetics of dark (n,π*) states. MR-PT2 methods show promise for the simulation of flavin's low-lying excited states, but the selection of orbitals for the active space and the number of roots used for state averaging must be done carefully to avoid artifacts. Some properties, such as the intersystem crossing geometry and energy between the S1 (π,π*) and T2 (n,π*) states, may require additional benchmarking before they can be determined quantitatively.

Triplet-Singlet Emission of d-Block Metal Complexes Characterized by Spin-Orbit Natural Transition Orbitals

Spin-orbit natural transition orbital (SO-NTO) methodology, recently developed in our group for complete and restricted active space (CAS/RAS) wavefunction calculations, is applied to analyze triplet-to-singlet emission in transition metal complexes. The lowest-energy (longest-wavelength) spin-forbidden transitionT 1 → S 0 ${{{\rm T}}_{1}\to {{\rm S}}_{0}}$ is studied for for [Ir(pbt)2(acac)] and [Re(CO)4(pbt)] and the complexes [W(CO)4(bpy)] and [Mo(CO)4(bpy)]. For the latter complexes, spin-forbidden transitions from higher spin-triplet levels are additionally analyzed. SO-NTOs are compared with spin-free NTOs for the transitions under consideration. The major assignment of a spin-forbidden transition is obtained from the spin-free NTO analysis, while the source of intensity of the electronic transition is revealed by the SO-NTOs.

A Polarizable QM/MM Model That Combines the State-Averaged CASSCF and AMOEBA Force Field for Photoreactions in Proteins

This study presents the polarizable quantum mechanics/molecular mechanics (QM/MM) embedding of the state-averaged complete active space self-consistent field (SA-CASSCF) in the atomic multipole optimized energetics for biomolecular applications (AMOEBA) force field for the purpose of studying photoreactions in protein environments. We describe two extensions of our previous work that combine SA-CASSCF with AMOEBA water models, allowing it to be generalized to AMOEBA models for proteins and other macromolecules. First, we discuss how our QM/MM model accounts for the discrepancy between the direct and polarization electric fields that arises in the AMOEBA description of intramolecular polarization. A second improvement is the incorporation of link atom schemes to treat instances in which the QM/MM boundary goes through covalent bonds. A single-link atom scheme and double-link atom scheme are considered in this work, and we will discuss how electrostatic interaction, van der Waals interaction, and various kinds of valence terms are treated across the boundary. To test the accuracy of the link atom scheme, we will compare QM/MM with full QM calculations and study how the errors in ground state properties, excited state properties, and excitation energies change when tuning the parameters in the link atom scheme. We will also test the new SA-CASSCF/AMOEBA method on an elementary reaction step in NanoLuc, an artificial bioluminescence luciferase. We will show how the reaction mechanism is different when calculated in the gas phase, in polarizable continuum medium (PCM), versus in protein AMOEBA models.

Excited-State Intramolecular Proton Transfer toward Conical Intersections in Indigo, Epindolidione, and Indirubin

Indigo exhibits a high degree of photostability, experimentally supported by observations such as quenching of fluorescence and an exceptionally short excited-state lifetime. Epindolidione, a structural isomer of indigo, is highly fluorescent in contrast to indigo, while indirubin, another structural isomer, exhibits weak fluorescence similar to that of indigo. To elucidate the origin of the difference in photophysical and photochemical behavior, potential energy profiles of the excited-state intramolecular proton transfer in indigo, epindolidione, and indirubin are computationally studied by quantum chemical calculations using the TDDFT and extended MS-CASPT2 (XMS-CASPT2) methods. As a result, it is found that indigo and indirubin exhibit little energy barrier for the single proton transfer (SPT) in the S1(ππ*) state from the diketo to keto-enol form and low energy of the S1/S0 conical intersection (CI) in the latter form with a planar molecular structure. Epindolidione, on the other hand, exhibits much higher barriers for SPT and access to CI. These results suggest that the excited-state SPT and subsequent nonradiative deactivation via CI are more likely to occur in indigo and indirubin than in epindolidione, which is consistent with the experimental observations described above. For indigo and epindolidione, the deactivation channels via the second SPT from the keto-enol to dienol form are also compared.

Ultrafast Photoinduced Dynamics in 1,3-Cyclohexadiene: A Comparison of Trajectory Surface Hopping Schemes†

Photoinduced nonadiabatic processes play a crucial role in a wide range of disciplines, from fundamental steps in biology to modern applications in advanced materials science. A theoretical understanding of these processes is highly desirable, and trajectory surface hopping (TSH) has proven to be a well-suited framework for a wide range of systems. In this work, we present a comprehensive comparison between two TSH algorithms, the conventional Tully's fewest switches surface hopping (FSSH) scheme and the Landau-Zener surface hopping (LZSH), to study the photoinduced ring-opening of 1,3-cyclohexadiene (CHD) to 1,3,5-hexatriene at the spin-flip time-dependent density functional theory (SF-TDDFT) level of theory. Additionally, we compare our results with a literature study at the extended multistate complete active space second-order perturbation theory method (XMS-CASPT2) level of theory. Our results show that the average population and lifetimes estimated with LZSH using SF-TDDFT are closer to the literature (using multireference methods) than those estimated with FSSH using SF-TDDFT. The latter speaks in favor of applying LZSH in combination with the SF-TDDFT method to study larger and more complex systems such as molecular photoswitches where the CHD molecule acts as a backbone. In addition, we present an implementation of Tully's FSSH algorithm as an extension to the PySurf software package.

Perturbation theory in the complete degenerate active space (CDAS-PT2)

Methods based on the multireference perturbation theory (MRPT) with the one-electron zeroth-order Hamiltonian are widely used for the description of excited states, for example, due to their relatively low computational cost. However, current methods have a common drawback-use of a model space with low size. In this article, we propose the MRPT method with the model space extended to the complete active space. The one-electron zeroth-order Hamiltonian suitable for this extension is formulated. The proposed method was applied to common models, such as LiF, ethylene, and trans-butadiene. It was shown to have accuracy superior to XMCQDPT2 in most cases, especially in the case of the small active space.

Non-adiabatic dynamics of photoexcited cyclobutanone: Predicting structural measurements from trajectory surface hopping with XMS-CASPT2 simulations

Over the years, theoretical calculations and scalable computer simulations have complemented ultrafast experiments, as they offer the advantage of overcoming experimental restrictions and having access to the whole dynamics. This synergy between theory and experiment promises to yield a deeper understanding of photochemical processes, offering valuable insights into the behavior of complex systems at the molecular level. However, the ability of theoretical models to predict ultrafast experimental outcomes has remained largely unexplored. In this work, we aim to predict the electron diffraction signals of an upcoming ultrafast photochemical experiment using high-level electronic structure calculations and non-adiabatic dynamics simulations. In particular, we perform trajectory surface hopping with extended multi-state complete active space with second order perturbation simulations for understanding the photodissociation of cyclobutanone (CB) upon excitation at 200 nm. Spin-orbit couplings are considered for investigating the role of triplet states. Our simulations capture the bond cleavage after ultrafast relaxation from the 3s Rydberg state, leading to the formation of the previously observed primary photoproducts: CO + cyclopropane/propene (C3 products), ketene, and ethene (C2 products). The ratio of the C3:C2 products is found to be about 1:1. Within 700 fs, the majority of trajectories transition to their electronic ground state, with a small fraction conserving the initial cyclobutanone ring structure. We found a minimal influence of triplet states during the early stages of the dynamics, with their significance increasing at later times. We simulate MeV-ultrafast electron diffraction (UED) patterns from our trajectory results, linking the observed features with specific photoproducts and the underlying structural dynamics. Our analysis reveals highly intense features in the UED signals corresponding to the photochemical processes of CB. These features offer valuable insights into the experimental monitoring of ring opening dynamics and the formation of C3 and C2 photoproducts.

Complex potential energy surfaces with projected CAP technique: Vibrational excitation of N2

The projected complex absorbing potential (CAP) technique is one of the methods that allow one to extend the bound state methods for computing resonances' energies and widths. Here, we explore the accuracy of the potential energy curves generated with different electronic structure theory methods in combination with the projected CAP technique by considering resonant vibrational excitation (RVE) of N2 by electron impact as a model process. We report RVE cross sections computed using the boomerang model with potential energy curves obtained with CAP-based extended multistate complete active space perturbation theory (XMS-CASPT2) and equation of motion coupled-cluster method for electron attachment with single and double substitution (EOM-EA-CCSD) methods. We also compare potential energy curves computed with several electronic structure methods, including XMS-CASPT2, EOM-EA-CCSD, multireference configuration interaction with singles (MR-CIS) and singles and doubles (MR-CISD). A good agreement is observed between the experiment and simulated RVE cross sections obtained with the potential energy curves generated with XMS-CASPT2 and EOM-EA-CCSD methods, thus highlighting the potential of the projected CAP technique combined with accurate electronic structure methods for dynamical simulations of the processes that proceed through metastable electronic states.

Reference Energies for Double Excitations: Improvement and Extension

In the realm of photochemistry, the significance of double excitations (also known as doubly excited states), where two electrons are concurrently elevated to higher energy levels, lies in their involvement in key electronic transitions essential in light-induced chemical reactions as well as their challenging nature from the computational theoretical chemistry point of view. Based on state-of-the-art electronic structure methods (such as high-order coupled-cluster, selected configuration interaction, and multiconfigurational methods), we improve and expand our prior set of accurate reference excitation energies for electronic states exhibiting a substantial amount of double excitations [Loos et al. J. Chem. Theory Comput. 2019, 15, 1939]. This extended collection encompasses 47 electronic transitions across 26 molecular systems that we separate into two distinct subsets: (i) 28 "genuine" doubly excited states where the transitions almost exclusively involve doubly excited configurations and (ii) 19 "partial" doubly excited states which exhibit a more balanced character between singly and doubly excited configurations. For each subset, we assess the performance of high-order coupled-cluster (CC3, CCSDT, CC4, and CCSDTQ) and multiconfigurational methods (CASPT2, CASPT3, PC-NEVPT2, and SC-NEVPT2). Using as a probe the percentage of single excitations involved in a given transition (%T1) computed at the CC3 level, we also propose a simple correction that reduces the errors of CC3 by a factor of 3, for both sets of excitations. We hope that this more complete and diverse compilation of double excitations will help future developments of electronic excited-state methodologies.

Core-Hole Coherent Spectroscopy in Molecules

We study the ultrafast dynamics initiated by a coherent superposition of core-excited states of nitrous oxide molecule. Using high-level ab initio methods, we show that the decoherence caused by the electronic decay and the nuclear dynamics is substantially slower than the induced ultrafast quantum beatings, allowing the system to undergo several oscillations before it dephases. We propose a proof-of-concept experiment using the harmonic up-conversion scheme available at x-ray free-electron laser facilities to trace the evolution of the created core-excited-state coherence through a time-resolved x-ray photoelectron spectroscopy.

Gaussian Process Regression for State-to-State Integral Cross Sections: The Case of the O + O2 Collision Dissociation Reactions

Research on hypersonic vehicles has become increasingly important worldwide in recent years. However, accurately simulating the dynamics of the nonequilibrium high-temperature reactions that are in the hypersonic flow around the vehicles presents a significant challenge as a large number of states and transitions are accessible even for the smallest atom-diatom reaction systems. It is quite difficult, sometimes even impossible, to exhaustively investigate all relevant combinations or determine high-dimensional analytical representations for the state-to-state reaction probabilities. In this study, we used Gaussian process regression (GPR) to fit a model based on only 807 QCT data for training. The confidence interval of the GPR prediction and the Kullback-Leibler (KL) divergence were used to help minimize the sampling amount of data for fitting the converged GPR model. The model aims to predict the state-to-state integral cross section (ICS) of the O + O2 → 3O dissociation reaction under random initial conditions (Et, v, j). In total, it took almost a month to obtain this converged GPR model, but it took only a few seconds to predict the ICS value for any initial condition. For 330 initial conditions not included in the training set, the mean-square error (MSE) between the QCT-calculated ICSs and the GPR-predicted ones is only 0.08 Å2 and the R2 is 0.9986, indicating that the GPR model can replace the direct expensive QCT calculation with high accuracy. Finally, we calculated the equilibrium dissociation rate coefficients based on the StS ICS values predicted by the GPR model, and the results were in good agreement with available experimental and theoretical results. Thus, this study provides an effective and accurate approach to the extensive direct state-to-state reaction dynamic calculations.

Global Potential Energy Surfaces by Compressed-State Multistate Pair-Density Functional Theory for Hyperthermal Collisions in the O2+O2 System

Interactions between oxygen molecules play an important role in atmospheric chemistry and hypersonic flow chemistry in atmospheric entries. Recently, high-quality ab initio potential energy surface (PES) of the quintet O4 was reported by Paukku et al. [J. Chem. Phys. 147, 034301 (2017)]. 10543 configurations were sampled and calculated at the level of MS-CASPT2/maug-cc-pVTZ with scaled external correlation. The PES was fitted to a many-body (MB) form with the many-body part described by the permutationally invariant polynomial approach (MB-PIP). In this work, the PIP-Neural Network (PIP-NN) and MB-PIP-NN methods were used to refit the PES based on the same data by Paukku et al. Three PESs were compared. It was found that the performances differ significantly in the O+O3 region as well as in the long-range region. Therefore, additional 1300 points were sampled, and the efficient compressed-state multistate pair-density functional theory (CMS-PDFT) was used to calculate the electronic structure of these 1300 points and 10543 points by Paukku et al. Then, a completely new quintet PES was fitted using the MB-PIP-NN method. Based on this PES, the quasi-classical trajectory (QCT) approach was used to reveal all possible reaction channels for hyperthermal O2-O2 collisions.

The photodissociation dynamics and ultrafast electron diffraction image of cyclobutanone from the surface hopping dynamics simulation

The comprehension of nonadiabatic dynamics in polyatomic systems relies heavily on the simultaneous advancements in theoretical and experimental domains. The gas-phase ultrafast electron diffraction (UED) technique has attracted significant attention as a unique tool for monitoring photochemical and photophysical processes at the all-atomic level with high temporal and spatial resolutions. In this work, we simulate the UED spectra of cyclobutanone using the trajectory surface hopping method at the extended multi-state complete active space second order perturbation theory (XMS-CASPT2) level and thereby predict the results of the upcoming UED experiments in the Stanford Linear Accelerator Laboratory. The simulated results demonstrate that a few pathways, including the C2 and C3 dissociation channels, as well as the ring opening channel, play important roles in the nonadiabatic reactions of cyclobutanone. We demonstrate that the simulated UED signal can be directly interpreted in terms of atomic motions, which provides a unique way of monitoring the evolution of the molecular structure in real time. Our work not only provides numerical data that help to determine the accuracy of the well-known surface hopping dynamics at the high XMS-CASPT2 electronic-structure level but also facilitates the understanding of the microscopic mechanisms of the photoinduced reactions in cyclobutanone.

WFOT: A Wave Function Overlap Tool between Single- and Multi-Reference Electronic Structure Methods for Spectroscopy Simulation

We report the development of a novel diagnostic tool, named wave function overlap tool (WFOT), designed to evaluate the overlap between wave functions computed at single-reference [i.e., time-dependent density functional theory or configuration interaction singles (CIS)] and multireference (i.e., CASSCF/CASPT2) electronic structure levels of theory. It relies on truncating the single- and multireference WFs to CIS-like expansions spanning the same configurational space and maximizing the molecular orbital overlap by means of a unitary transformation. To demonstrate the functionality of the tool, we calculate the transient spectrum of acetylacetone by evaluating excited state absorption signals with multireference quality on top of single-reference on-the-fly dynamics simulations. Semiautomatic spectra generation is facilitated by interfacing the tool with the COBRAMM package, which also allows one to use WFOT with several quantum chemistry codes such as Gaussian, NWChem, and OpenMolcas. Other exciting possibilities for the utilization of the code beyond the simulation of transient absorption spectroscopy are eventually discussed.

Generalized Semiclassical Ehrenfest Method: A Route to Wave Function-Free Photochemistry and Nonadiabatic Dynamics with Only Potential Energies and Gradients

We reconsider recent methods by which direct dynamics calculations of electronically nonadiabatic processes can be carried out while requiring only adiabatic potential energies and their gradients. We show that these methods can be understood in terms of a new generalization of the well-known semiclassical Ehrenfest method. This is convenient because it eliminates the need to evaluate electronic wave functions and their matrix elements along the mixed quantum-classical trajectories. The new approximations and procedures enabling this advance are the curvature-driven approximation to the time-derivative coupling, the generalized semiclassical Ehrenfest method, and a new gradient correction scheme called the time-derivative matrix (TDM) scheme. When spin-orbit coupling is present, one can carry out dynamics calculations in the fully adiabatic basis using potential energies and gradients calculated without spin-orbit coupling plus the spin-orbit coupling matrix elements. Even when spin-orbit coupling is neglected, the method is useful because it allows calculations by electronic structure methods for which nonadiabatic coupling vectors are unavailable. In order to place the new considerations in context, the article starts out with a review of background material on trajectory surface hopping, the semiclassical Ehrenfest scheme, and methods for incorporating decoherence. We consider both internal conversion and intersystem crossing. We also review several examples from our group of successful applications of the curvature-driven approximation.

Sub-100-fs energy transfer in coenzyme NADH is a coherent process assisted by a charge-transfer state

Excitation energy transfer (EET) is a key photoinduced process in biological chromophoric assemblies. Here we investigate the factors which can drive EET into efficient ultrafast sub-ps regimes. We demonstrate how a coherent transport of electronic population could facilitate this in water solvated NADH coenzyme and uncover the role of an intermediate dark charge-transfer state. High temporal resolution ultrafast optical spectroscopy gives a 54±11 fs time constant for the EET process. Nonadiabatic quantum dynamical simulations computed through the time-evolution of multidimensional wavepackets suggest that the population transfer is mediated by photoexcited molecular vibrations due to strong coupling between the electronic states. The polar aqueous solvent environment leads to the active participation of a dark charge transfer state, accelerating the vibronically coherent EET process in favorably stacked conformers and solvent cavities. Our work demonstrates how the interplay of structural and environmental factors leads to diverse pathways for the EET process in flexible heterodimers and provides general insights relevant for coherent EET processes in stacked multichromophoric aggregates like DNA strands.

Using a multistate mapping approach to surface hopping to predict the ultrafast electron diffraction signal of gas-phase cyclobutanone

Using the recently developed multistate mapping approach to surface hopping (multistate MASH) method combined with SA(3)-CASSCF(12,12)/aug-cc-pVDZ electronic structure calculations, the gas-phase isotropic ultrafast electron diffraction (UED) of cyclobutanone is predicted and analyzed. After excitation into the n-3s Rydberg state (S2), cyclobutanone can relax through two S2/S1 conical intersections, one characterized by compression of the CO bond and the other by dissociation of the α-CC bond. Subsequent transfer into the ground state (S0) is then achieved via two additional S1/S0 conical intersections that lead to three reaction pathways: α ring-opening, ethene/ketene production, and CO liberation. The isotropic gas-phase UED signal is predicted from the multistate MASH simulations, allowing for a direct comparison to the experimental data. This work, which is a contribution to the cyclobutanone prediction challenge, facilitates the identification of the main photoproducts in the UED signal and thereby emphasizes the importance of dynamics simulations for the interpretation of ultrafast experiments.

Spin-Restricted Descriptions of Singlet Oxygen Reactions from XMS-CASPT2 Benchmarks

Reactions of singlet oxygen are numerous, some of which are desired but many are unwanted. Therefore, the ability to correctly predict and interpret this reactivity for complex molecular systems is essential to our understanding of singlet oxygen reactions. DFT is widely used for predicting many reactions but is not suited to degenerate electronic structures; application to isolated singlet oxygen often uses the spin-unrestricted formalism, which results in severe spin contamination. In this work, we demonstrate that spin-restricted DFT can correctly describe the reaction pathway for four prototypical singlet oxygen reactions. By careful benchmarking with XMS-CASPT2, we show that, from the first transition state onward, the degeneracy of the 1Δg state is broken due to differing interactions of the (degenerate) π* orbitals with the organic substrate; this result is well replicated with DFT. These findings demonstrate the utility of using spin-restricted DFT to explore reactions, opening the way to confidently use this computationally efficient method for molecular systems of medium to large organic molecules.

Ultrafast photochemistry and electron-diffraction spectra in n → (3s) Rydberg excited cyclobutanone resolved at the multireference perturbative level

We study the ultrafast time evolution of cyclobutanone excited to the singlet n → Rydberg state through non-adiabatic surface-hopping simulationsperformed at extended multi-state complete active space second-order perturbation (XMS-CASPT2) level of theory. These dynamics predict relaxation to the ground-state with a timescale of 822 ± 45 fs with minimal involvement of the triplets. The major relaxation path to the ground-state involves a three-state degeneracy region and leads to a variety of fragmented photoproducts. We simulate the resulting time-resolved electron-diffraction spectra, which track the relaxation of the excited state and the formation of various photoproducts in the ground state.

Revisiting fulgide photochromism: Mechanistic decoding and electron transport from computational exploration

The photochromic behavior of the fulgide molecule relies on ring-closure and ring-opening processes involving conical intersections during excited state transformation between isomers. The precise location and topography of these conical intersections significantly shape the decay process and fluorescence phenomena inherent to the molecule. This work combines electronic structure theory calculations using the density functional theory and wavefunction methods, as well as surface hopping simulation to analyze the photochemical behavior of an experimentally synthesized fulgide molecule, (E)-p-methylacetophenylisopropylidenesuccinic anhydride (1E). Our study reveals the conical intersection between the first excited state (S1) and the ground electronic state (S0), which emerges beyond the S1 minimum of 1E to the ring-closing side. The distinctive topography of this conical intersection appears to be sloped. These findings suggest a reduced quantum yield for the formation of the closed isomer, indicating a higher likelihood of reformation of the open isomer(s). The surface hopping simulation further supports this observation, revealing a mere ∼8% quantum yield for the formation of the closed isomer. In addition, the photoisomerization of the fulgide molecule initiates a cascade of conduction switching and holds great potential for applications in molecular electronics. Delving into the realm of molecular electronics, we have further examined the electron transport properties, disclosing the higher conductivity of the closed isomer.

Air-Stable Dinuclear Complexes of Four-Coordinate ZnII and NiII Ions with a Radical Bridge: A Detailed Look at Redox Activity and Antiferromagnetic Coupling

Air-stable dinuclear complexes [(bmsab)NiII(tmsab)NiII(bmsab)]3- and [(bmsab)ZnII(tmsab)ZnII(bmsab)]3- (bmsab = bis(methanesulfoneamido)benzene, tmsab = tetra(methanesulfonamido)benzene) were prepared via a synthetic route based on heteroleptic precursor complexes. The new complexes combine a distorted tetrahedral coordination environment with an open-shell bridging ligand. The ZnII species was subjected to a detailed investigation of the (spectro-)electrochemical processes. The NiII species is a rare example of a complex that combines strong exchange coupling (J > 440 cm-1) with pronounced positive zero-field splitting (D = +72 cm-1). Combining SQUID magnetometry and (HF)EPR spectroscopy with ab initio calculations allowed for accurate quantification of the exchange interaction.

New physical insights into the supporting subspace factorization of XMS-CASPT2 and generalization to multiple spin states via spin-free formulation

This paper introduces a spin-free formulation of the supporting subspace factorization [C. Song and T. J. Martínez, J. Chem. Phys. 149, 044108 (2018)], enabling a reduction in the computational scaling of the extended multi-state complete active space second-order perturbation (XMS-CASPT2) method for arbitrary spins. Compared to the original formulation that is defined in the spin orbitals and is limited to singlet states, the spin-free formulation in this work treats different spin states equivalently, thus naturally generalizing the idea beyond singlet states. In addition, we will present a new way of deriving the supporting subspace factorization with the purpose of understanding its physical interpretation. In this new derivation, we separate the sources that make CASPT2 difficult into the "same-site interactions" and "inter-site interactions." We will first show how the Kronecker sum can be used to remove the same-site interactions in the absence of inter-site interactions, leading to MP2 energy in dressed orbitals. We will then show how the inter-site interactions can be exactly recovered using Löwdin partition, where the supporting subspace concept will naturally arise. The new spin-free formulation maintains the main advantage of the supporting subspace factorization, i.e., allowing XMS-CASPT2 energies to be computed using highly optimized MP2 energy codes and Fock build codes, thus reducing the scaling of XMS-CASPT2 to the same scaling as MP2. We will present and discuss results that benchmark the accuracy and performance of the new method. To demonstrate how the new method can be useful in studying real photochemical systems, the supporting subspace XMS-CASPT2 is applied to a photoreaction sensitive to magnetic field effects. The new spin-free formulation makes it possible to calculate the doublet and quartet states required in this particular photoreaction mechanism.

Deciphering the Internal Conversion Processes Involved in the Photochemical Ring-Opening of 1,3-Cyclohexadiene by Symmetric sp2-Carbon Substitutions

Chemical substituents hold the potential to markedly influence the photochemical behavior in molecular systems and assist in gaining a comprehensive understanding of nonadiabatic phenomena. In this study, we have conducted a comparative analysis of the influence of chemical substituents on the photochemical ring-opening of 1,3-cyclohexadiene (CHD), considering four systems: CHD, 2,3-dimethylcyclohexadiene (CHD-Me2-1), 1,4-dimethylcyclohexadiene (CHD-Me2-2), and 1,2,3,4-tetramethylcyclohexadiene (CHD-Me4), using electronic structure theory calculations and nonadiabatic molecular dynamics simulations. Employing extended multistate complete active space second-order perturbation (XMS-CASPT2) theory, we optimized reactants, S1 states, conical intersections (CIns), and products, revealing structural and energetic variations consistent with prior research. Nonadiabatic molecular dynamics simulation was used to gain insights into photochemical dynamics at state-averaged complete active space self-consistent field (SA-CASSCF) theory. CHD-Me4 exhibited reduced carbon-carbon single bond rupture rates, responsible for ring-opening, due to substituent proximity. Further, CHD-Me2-2 and CHD-Me4 displayed prolonged excited-state relaxation times, highlighting notable substituents' impact. Analysis of kinetic energy profiles of specific carbon atoms also revealed restrained atomic displacements, particularly in CHD-Me2-2 and CHD-Me4. These findings advance our understanding of how substituents modulate photochemical reactions in cyclohexadiene derivatives, guiding new molecular design and future research.

Minimum-Energy Conical Intersections by Compressed Multistate Pair-Density Functional Theory

Compressed multistate pair-density functional theory (CMS-PDFT) is a multistate version of multiconfiguration pair-density functional theory that can capture the correct topology of coupled potential energy surfaces (PESs) around conical intersections. In this work, we develop interstate coupling vectors (ISCs) for CMS-PDFT in the OpenMolcas and PySCF/mrh electronic structure packages. Yet, the main focus of this work is using ISCs to calculate minimum-energy conical intersections (MECIs) by CMS-PDFT. This is performed using the projected constrained optimization method in OpenMolcas, which uses ISCs to restrain the iterations to the conical intersection seam. We optimize the S1/S0 MECIs for ethylene, butadiene, and benzene and show that CMS-PDFT gives smooth PESs in the vicinities of the MECIs. Furthermore, the CMS-PDFT MECIs are in good agreement with the MECI calculated by the more expensive XMS-CASPT2 method.

Unexpected and delayed fragmentation dynamics of the organometallic ferrocene induced by ion-collision

We have investigated the fragmentation dynamics of the organometallic ferrocene molecule after interaction with multiply charged ions using multicoincidence mass spectrometry and quantum chemistry calculations. We observed unexpected fragmentation dynamics of the two-body breakup channels from ferrocene dications revealing a charge screening effect from the iron atom and delayed fragmentation dynamics. These observations are rationalized through the population of a specific long-lived excited state, where one positive charge is located on each cyclopentadienyl ring.

Impact of isoelectronic substitution on the excited state processes in polycyclic aromatic hydrocarbons: a joint experimental and theoretical study of 4a,8a-azaboranaphthalene

Substituting CC with the isoelectronic BN units is a promising approach to modify the optoelectronic properties of polycyclic aromatic hydrocarbons. While computational studies have already addressed trends in the electronic structure of the various isosteres, experimental data are still scarce. Here, the excited state spectroscopy and dynamics of 4a,8a-azaboranaphthalene were studied by picosecond time-resolved photoionization in a supersonic jet and analyzed with the aid of XMS-CASPT2 and time-dependent DFT calculations. A resonance-enhanced multiphoton ionization spectrum (REMPI) reveals the S1 origin at  = 33 830 ± 12 cm-1. Several vibrational bands were resolved and assigned by comparison with the computations. A [1+1] photoelectron spectrum via the S1 origin yielded an adiabatic ionization energy of 8.27 eV. Selected vibrational bands were subsequently investigated by pump-probe photoionization. While the origin as well as several low-lying vibronic states exhibit lifetimes in the ns-range, a monoexponential decay is observed at higher excitation energies, ranging from 400 ps at +1710 cm-1 to 13 ps at +3360 cm-1. The deactivation is attributed to an internal conversion of the optically excited S1 state via a barrier that gives access to a conical intersection (CI) to the S0 state. The doping significantly changes the energetic ordering of CIs and lowers the corresponding energy barrier for the associated deactivation pathway, as revealed by nudged elastic band (NEB) calculations.

Parametrically Managed Activation Functions for Improved Global Potential Energy Surfaces for Six Coupled 5A' States and Fourteen Coupled 3A' States of O + O2

We report new potential energy surfaces for six coupled 5A' states and 14 coupled 3A' states of O3. The new surfaces are created by parametrically managed diabatization by deep neural network (PM-DDNN). The PM-DDNN method uses calculated adiabatic potential energy surfaces to discover and fit an underlying adiabatic-equivalent set of diabatic surfaces and their couplings and obtains the fit to the adiabatic surfaces by diagonalization of the diabatic potential energy matrix (DPEM). The procedure yields the adiabatic surfaces and their gradients, as well as the DPEM and its gradient. If desired one can also compute the nonadiabatic coupling due to the transformation. The present work improves on previous work by using a new coordinate to guide the decay of the neural network contribution to the many-body fit to the whole DPEM. The main objective was to obtain smoother potentials than the previous ones with better suitability for dynamics calculations, and this was achieved. Furthermore, we obtained suitably small deviations from the input reference data. For the six coupled 5A' surfaces, the 60,366 data below 10 eV are fit with a mean unsigned error (MUE) of 49 meV, and for the 14 coupled 3A' surfaces, the 76,733 data below 10 eV are fit with an MUE of 28 meV. The data below 5 eV fit even more accurately with MUEs of 37 meV (5A') and 20 meV (3A').

A Theoretical Perspective on the Photochemistry of Boron-Nitrogen Lewis Adducts

Boron-Nitrogen (B-N) Lewis adducts form a versatile family of compounds with numerous applications in functional molecules. Despite the growing interest in this family of compounds for optoelectronic applications, little is currently known about their photophysics and photochemistry. Even the electronic absorption spectrum of ammonia borane, the textbook example of a B-N Lewis adduct, is unavailable. Given the versatility of the light-induced processes exhibited by these molecules, we propose in this work a detailed theoretical study of the photochemistry and photophysics of simple B-N Lewis adducts. We used advanced techniques in computational photochemistry to identify and characterize the possible photochemical pathways followed by ammonia borane and extended this knowledge to the substituted B-N Lewis adducts pyridine-borane and pyridine-boric acid. The photochemistry observed for this series of molecules allows us to extract qualitative rules to rationalize the light-induced behavior of more complex B-N-containing molecules.

Photo-oxidation of methanol in complexes with pyrido[2,3-b]pyrazine: a nonadiabatic molecular dynamics study

Excited-state Proton-Coupled Electron Transfer (PCET) constitutes a key step in the photo-oxidation of small, electron-rich systems possessing acidic hydrogen atoms, such as water or alcohols, which can play a vital role in green hydrogen production. In this contribution, we employ ab initio quantum-chemical methods and on-the-fly nonadiabatic molecular dynamics simulations to study the mechanism and the photodynamics of PCET in 1 : 1 pyrido[2,3-b]pyrazine complexes with methanol. We find the process to be ultrafast and efficient when the intramolecular hydrogen bond is formed with one of the β-positioned nitrogen atoms. The complex exhibiting a hydrogen bond with an isolated nitrogen site, on the contrary, shows much lower reactivity. We explain this effect with the stabilization of the reactive ππ* charge-transfer electronic state in the former case.

Chemical control of excited-state reactivity of the anionic green fluorescent protein chromophore

Controlling excited-state reactivity is a long-standing challenge in photochemistry, as a desired pathway may be inaccessible or compete with other unwanted channels. An important example is internal conversion of the anionic green fluorescent protein (GFP) chromophore where non-selective progress along two competing torsional modes (P: phenolate and I: imidazolinone) impairs and enables Z-to-E photoisomerization, respectively. Developing strategies to promote photoisomerization could drive new areas of applications of GFP-like proteins. Motivated by the charge-transfer dichotomy of the torsional modes, we explore chemical substitution on the P-ring of the chromophore as a way to control excited-state pathways and improve photoisomerization. As demonstrated by methoxylation, selective P-twisting appears difficult to achieve because the electron-donating potential effects of the substituents are counteracted by inertial effects that directly retard the motion. Conversely, these effects act in concert to promote I-twisting when introducing electron-withdrawing groups. Specifically, 2,3,5-trifluorination leads to both pathway selectivity and a more direct approach to the I-twisted intersection which, in turn, doubles the photoisomerization quantum yield. Our results suggest P-ring engineering as an effective approach to boost photoisomerization of the anionic GFP chromophore.

Hybrid Density Functional Valence Bond Method with Multistate Treatment

Recently, a hybrid density functional valence bond (VB) method, λ-DFVB(U), has been proposed and shown to give accuracy that is comparable to that of CASPT2 in calculations of atomization energies, atomic excitation energies, and reaction barriers, while its computational cost is approximately the same as the valence bond self-consistent-field (VBSCF) method. However, the interaction between electronic states is not included in λ-DFVB(U) since the last step of λ-DFVB(U) is not a diagonalization of the Hamiltonian matrix on the electronic state basis. Therefore, λ-DFVB(U) gives the wrong topology of the potential energy surfaces (PESs) near the conical intersection region. In the present paper, we propose a novel hybrid density functional VB method with multistate treatment, named λ-DFVB(MS), in which an effective Hamiltonian matrix is constructed on the basis of the diabatic states obtained by the valence-bond-based compression approach for the diabatization scheme, and the interaction between electronic states can be included through the diagonalization of the effective Hamiltonian matrix. Test calculations show that λ-DFVB(MS) gives the correct topology of the PESs near the conical intersection region. We also show that the VBSCF wave function with selected VB structures can be applied as a reference in λ-DFVB(MS).

A Complete Unveiling of the Mechanism and Chirality in Photoisomerization of Arylazopyrazole 3pzH: Combined Electronic Structure Calculations and AIMS Dynamic Simulations

The arylazopyrazole 3pzH as a novel photoswitch exhibits quantitative switching and high thermal stability. In this work, combined electronic structure calculations and ab initio multiple spawning (AIMS) dynamic simulations were performed to systemically investigate the cis ↔ trans photoisomerization mechanism and the chiral preference after photoexcitation of 3pzH to the first excited singlet state (S1). Unlike most of the azoheteroarene photoswitches reported previously, many twisted and T-shaped cis isomers were found to be stable for 3pzH in the S0 state, owing to the moderate interaction between the hydrogen atom and π electrons of the aromatic ring. Two twisted cis isomers with different chirality ((M)-Z1 and (P)-Z1), the most stable T-shaped cis isomer ((T)-Z2), and the most stable planar trans isomer (E2) were selected as the initial structures to carry out the AIMS nonadiabatic dynamic simulations. Following excitation to the S1 state, all of the cis isomers decayed to conical intersection (CI) regions via the same bicycle pedal mechanism, while the evolution of the trans isomers to their CI regions was achieved via rotation around the N═N bond. More importantly, chiral preferences were found for the twisted cis isomers in the S1 state through the AIMS dynamic simulations due to the steric effect and static electronic repulsion. Notably, chirality was also observed in S1 isomerization starting from the planar E2 isomer because of the dynamic effect. After the nonadiabatic transition to the S0 state, the bicycle pedal mechanism was found to play a crucial role in cis ↔ trans photoisomerization. The simulated photoisomerization productivities were generally consistent with past experimental observations. Our calculations not only uncover the underlying reason for the excellent photoswitching properties of 3pzH but also enrich the knowledge of photoisomerization for azoheteroarene photoswitches, which will surely benefit their rational design.

Which Electronic Structure Method to Choose in Trajectory Surface Hopping Dynamics Simulations? Azomethane as a Case Study

Nonadiabatic dynamics simulations have become a standard approach to explore photochemical reactions. Such simulations require underlying potential energy surfaces and couplings between them, calculated at a chosen level of theory, yet this aspect is rarely assessed. Here, in combination with the popular trajectory surface hopping dynamics method, we use a high-accuracy XMS-CASPT2 electronic structure level as a benchmark for assessing the performances of various post-Hartree-Fock methods (namely, CIS, ADC(2), CC2, and CASSCF) and exchange-correlation functionals (PBE, PBE0, and CAM-B3LYP) in a TD-DFT/TDA context, using the isomerization around a double bond as test case. Different relaxation pathways are identified, and the ability of the different methods to reproduce their relative importance and time scale is discussed. The results show that multireference electronic structure methods should be preferred, when studying nonadiabatic decay between excited and ground states. If not affordable, TD-DFT with TDA and hybrid functionals and ADC(2) are efficient alternatives but overestimate the nonradiative decay yield and thus may miss deexcitation pathways.

Capturing the generation and structural transformations of molecular ions

Molecular ions are ubiquitous and play pivotal roles1-3 in many reactions, particularly in the context of atmospheric and interstellar chemistry4-6. However, their structures and conformational transitions7,8, particularly in the gas phase, are less explored than those of neutral molecules owing to experimental difficulties. A case in point is the halonium ions9-11, whose highly reactive nature and ring strain make them short-lived intermediates that are readily attacked even by weak nucleophiles and thus challenging to isolate or capture before they undergo further reaction. Here we show that mega-electronvolt ultrafast electron diffraction (MeV-UED)12-14, used in conjunction with resonance-enhanced multiphoton ionization, can monitor the formation of 1,3-dibromopropane (DBP) cations and their subsequent structural dynamics forming a halonium ion. We find that the DBP+ cation remains for a substantial duration of 3.6 ps in aptly named 'dark states' that are structurally indistinguishable from the DBP electronic ground state. The structural data, supported by surface-hopping simulations15 and ab initio calculations16, reveal that the cation subsequently decays to iso-DBP+, an unusual intermediate with a four-membered ring containing a loosely bound17,18 bromine atom, and eventually loses the bromine atom and forms a bromonium ion with a three-membered-ring structure19. We anticipate that the approach used here can also be applied to examine the structural dynamics of other molecular ions and thereby deepen our understanding of ion chemistry.

Multiconfigurational Calculations and Experimental Resonant Raman/SERRS of a Donor-Acceptor Thiadiazole Dye

The resonant Raman (RR) and resonant SERS spectra of the thiadiazole-based dye dibromobenzo[c]-1,2,5-thiadiazole (DBTD) were studied through multiconfigurational XMS-CASPT2/CASSCF and experimental methods in solution. The results indicate that the S1 excited state of DBTD is described by π → π* with internal CT from the benzene ring to the thiadizole. In resonance conditions at 364 nm, the RR spectrum shows intensifications in modes that describe extensive geometrical changes at both the benzene ring and the thiadiazole region, indicating an internal CT character to the S1. The SERS spectra observed on gold and silver nanoparticles indicate different adsorption geometries, which leads to distinct enhancement patterns on the spectra with varying excitation energy. It evidences the major contribution of the chemical enhancement mechanism on the spectra from a metal → DBTD CT state, as confirmed by the simulated spectra. This theoretical approach proved strong in the prediction of the main features of the observed experimental resonant Raman and SERS spectra indicating a potential for adequate description of the chemical mechanism of SERS.

On the description of conical intersections between excited electronic states with LR-TDDFT and ADC(2)

Conical intersections constitute the conceptual bedrock of our working understanding of ultrafast, nonadiabatic processes within photochemistry (and photophysics). Accurate calculation of potential energy surfaces within the vicinity of conical intersections, however, still poses a serious challenge to many popular electronic structure methods. Multiple works have reported on the deficiency of methods like linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) or algebraic diagrammatic construction to second-order [ADC(2)]-approaches often used in excited-state molecular dynamics simulations-to describe conical intersections between the ground and excited electronic states. In the present study, we focus our attention on conical intersections between excited electronic states and probe the ability of AA LR-TDDFT and ADC(2) to describe their topology and topography, using protonated formaldimine and pyrazine as two exemplar molecules. We also take the opportunity to revisit the performance of these methods in describing conical intersections involving the ground electronic state in protonated formaldimine-highlighting in particular how the intersection ring exhibited by AA LR-TDDFT can be perceived either as a (near-to-linear) seam of intersection or two interpenetrating cones, depending on the magnitude of molecular distortions within the branching space.

Assessment of the Electron Correlation Treatment on the Quantum-Classical Dynamics of Retinal Protonated Schiff Base Models: XMS-CASPT2, RMS-CASPT2, and REKS Methods

We compare the performance of three different multiconfigurational wave function-based electronic structure methods and two implementations of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method. The study is characterized by three features: (i) it uses a small set of quantum-classical trajectories rather than potential energy surface mapping, (ii) it focuses, exclusively, on the photoisomerization of retinal protonated Schiff base models, and (iii) it probes the effect of both methyl substitution and the increase in length of the conjugate π-system. For each tested method, the corresponding analytical gradients are used to drive the quantum-classical (Tully's FSSH method) trajectory propagation, including the recent multistate XMS-CASPT2 and RMS-CASPT2 gradients. It is shown that while CASSCF, XMS-CASPT2, and RMS-CASPT2 yield consistent photoisomerization dynamics descriptions, REKS produces, in some of these systems, qualitatively different behavior that is attributed to a flatter and topographically different excited state potential energy surface. The origin of this behavior can be traced back to the effect of the employed density functional approximation. The above studies are further expanded by benchmarking, at the CASSCF and REKS levels, the electronic structure methods using a QM/MM model of the visual pigment rhodopsin.

What Controls the Quality of Photodynamical Simulations? Electronic Structure Versus Nonadiabatic Algorithm

The field of nonadiabatic dynamics has matured over the last decade with a range of algorithms and electronic structure methods available at the moment. While the community currently focuses more on developing and benchmarking new nonadiabatic dynamics algorithms, the underlying electronic structure controls the outcome of nonadiabatic simulations. Yet, the electronic-structure sensitivity analysis is typically neglected. In this work, we present a sensitivity analysis of the nonadiabatic dynamics of cyclopropanone to electronic structure methods and nonadiabatic dynamics algorithms. In particular, we compare wave function-based CASSCF, FOMO-CASCI, MS- and XMS-CASPT2, density-functional REKS, and semiempirical MRCI-OM3 electronic structure methods with the Landau-Zener surface hopping, fewest switches surface hopping, and ab initio multiple spawning with informed stochastic selection algorithms. The results clearly demonstrate that the electronic structure choice significantly influences the accuracy of nonadiabatic dynamics for cyclopropanone even when the potential energy surfaces exhibit qualitative and quantitative similarities. Thus, selecting the electronic structure solely on the basis of the mapping of potential energy surfaces can be misleading. Conversely, we observe no discernible differences in the performance of the nonadiabatic dynamics algorithms across the various methods. Based on the above results, we discuss the present-day practice in computational photodynamics.

Following the Nonadiabatic Ultrafast Dynamics of Uracil via Simulated X-ray Absorption Spectra

The nucleobase uracil exhibits high photostability due to ultrafast relaxation processes mediated by conical intersections (CoIns), where the interplay between nuclear and electron dynamics becomes crucial. In our previous study, we observed seemingly long-lived traces of electronic coherence for the relaxation process through the S2/S1 CoIn by applying our ansatz for coupled nuclear and electron dynamics in molecules (NEMol). In this work, we theoretically investigate how time-dependent transient X-ray absorption spectroscopy can be used to observe this ultrafast dynamics. Therefore, we calculated X-ray absorption spectra (XAS) for the oxygen K-edge, using a multireference protocol in combination with NEMol dynamics. Thus, we have access to both the transient XAS based on the nuclear wavepacket dynamics and the modulation of the signals caused by the electronic coherence induced by the excitation process and the presence of a CoIn seam. In both cases, we were able to qualitatively predict its influence on the resulting XAS.

Theoretical Insight into the Effect of Phosphorus Oxygenation on Nonradiative Decays: Comparative Analysis of P-Bridged Stilbene Analogs

Incorporation of the phosphorus element into a π-conjugated skeleton offers valuable prospects for adjusting the electronic structure of the resulting functional π-electron systems. Trivalent phosphorus has the potential to decrease the LUMO level through σ*-π* interaction, which is further enhanced by its oxygenation to the pentavalent P center. This study shows that utilizing our computational analysis to examine excited-state dynamics based on radiative/nonradiative rate constants and fluorescence quantum yield (ΦF) is effective for analyzing the photophysical properties of P-containing organic dyes. We theoretically investigate how the trivalent phosphanyl group and pentavalent phosphine oxide moieties affect radiative and nonradiative decay processes. We evaluate four variations of P-bridged stilbene analogs. Our analysis reveals that the primary decay pathway for photoexcited bis-phosphanyl-bridged stilbene is the intersystem crossing (ISC) to the triplet state and nonradiative. The oxidation of the phosphine moiety, however, suppresses the ISC due to the relative destabilization of the triplet states. The calculated rate constants match an increase in experimental ΦF from 0.07 to 0.98, as simulated from 0.23 to 0.94. The reduced HOMO-LUMO gap supports a red shift in the fluorescence spectra relative to the phosphine analog. The thiophene-fused variant with the nonoxidized trivalent P center exhibits intense emission with a high ΦF, 0.95. Our prediction indicates that the ISC transfer is obstructed owing to the relatively destabilized triplet state induced by the thiophene substitution. Conversely, the thiophene-fused analog with the phosphine oxide moieties triggers a high-rate internal conversion mediated by conical intersection, leading to a decreased ΦF.

Multiconfigurational photodynamics simulations reveal the mechanism of photodecarbonylations of cyclopropenones in explicit aqueous environments

Gas-evolving photochemical reactions use light and mild conditions to access strained organic compounds irreversibly. Cyclopropenones are a class of light-responsive molecules used in bioorthogonal photoclick reactions; their excited-state decarbonylation reaction mechanisms are misunderstood due to their ultrafast (<100 femtosecond) lifetimes. We have combined multiconfigurational quantum mechanical (QM) calculations and non-adiabatic molecular dynamics (NAMD) simulations to uncover the excited-state mechanism of cyclopropenone and a photoprotected cyclooctyne-(COT)-precursor in gaseous and explicit aqueous environments. We explore the role of H-bonding with fully quantum mechanical explicitly solvated NAMD simulations for the decarbonylation reaction. The cyclopropenones pass through asynchronous conical intersections and have dynamically concerted photodecarbonylation mechanisms. The COT-precursor has a higher quantum yield of 55% than cyclopropenone (28%) because these trajectories prefer to break a σCC bond to avoid the strained trans-cyclooctene geometries. Our solvated simulations show an increased quantum yield (58%) for the systems studied here.

On the Wavelength-Dependent Photochemistry of the Atmospheric Molecule CF3COCl

The wavelength control of photochemistry usually results from ultrafast dynamics following the excitation of different electronic states. Here, we investigate the CF3COCl molecule, exhibiting wavelength-dependent photochemistry both via (i) depositing increasing internal energy into a single state and (ii) populating different electronic states. We reveal the mechanism behind the photon-energy dependence by combining nonadiabatic ab initio molecular dynamics techniques with the velocity map imaging experiment. We describe a consecutive mechanism of photodissociation where an immediate release of Cl taking place in an excited electronic state is followed by a slower ground-state dissociation of the CO fragment. The CO release is subject to an activation barrier and is controlled by excess internal energy via the excitation wavelength. Therefore, a selective release of CO along with Cl can be achieved. The mechanism is fully supported by both the measured kinetic energy distributions and anisotropies of the angular distributions. Interestingly, the kinetic energy of the released Cl atom is sensitively modified by accounting for spin-orbit coupling. Given the atmospheric importance of CF3COCl, we discuss the consequences of our findings for atmospheric photochemistry.

Stability and Reactivity of the Phenalene and Olympicene Isomers

The phenalene (triangulene) and olympicene molecules belong to the polycyclic aromatic hydrocarbon class, which have attracted substantial technological interest due to their unique electronic properties. Electronic structure calculations serve as a valuable tool in investigating the stability and reactivity of these molecular systems. In the present work, the multireference calculations, namely, the complete active space second-order perturbation theory and multireference averaged quadratic coupled cluster (MR-AQCC), were employed to study the reactivity and stability of phenalene and olympicene isomers, as well as their modified structures where the sp3-carbon at the borders were removed. The harmonic oscillator model of aromaticity (HOMA) and the nucleus-independent chemical shift as geometric and magnetic indexes calculated with density functional theory were utilized to assess the aromaticity of the studied molecules. These indexes were compared with properties such as the excitation energy and natural orbitals occupation. The reactivity analyzed using the HOMA index combined with MR-AQCC revealed the radical character of certain structures as well as the weakening of their aromaticity. Moreover, the results suggest that the removal of sp3-carbon atoms and the addition of hydrogen atoms did not alter the π network and the excitation energies of the phenalene molecules.

When Is a Bond Broken? The Polarizability Perspective

The question of when a chemical bond can be said to be broken is of fundamental chemical interest but has not been widely studied. Herein we propose that the maxima of static polarizability along bond dissociation coordinates naturally define cutoff points for bond rupture, as they represent the onset of localization of shared electron density into constituent fragments. Examples of computed polarizability maxima over the course of bond cleavage in main-group and transition metal compounds are provided, across covalent, dative and charge-shift bonds. The behavior along reaction paths is also considered. Overall, the static polarizability is found to be a sensitive reporter of electronic structure reorganization associated with bond stretching, and thus can serve as a metric for describing bond cleavage (or diagnose the absence of a chemical bond).

Multiconfiguration Pair-Density Functional Theory for Vertical Excitation Energies in Actinide Molecules

Modeling actinides with electronic structure theories is challenging because these systems present a strong ligand field and metal-ligand covalency. We systematically investigate the effectiveness of pair-density functional theory (PDFT) for the calculation of vertical excitation energies in An(III), [AnIIICl6]3-, and [AnVIO2]2+ (An = U, Np, Pu, and Am). We compare the performance of PDFT, hybrid PDFT, and multistate PDFT with traditional active-space methods followed by perturbation theory, like multistate CASPT2, and with experimental data. Overall, multistate PDFT gives quantitative agreement with multistate CASPT2 at a significantly reduced computational cost.