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Organic nitrates (RONO2) are secondary compounds whose fate is closely related to the transport and removal of NOx in the atmosphere. Despite their ubiquitous presence in submicron aerosols, the photochemistry of RONO2 has only been investigated in the gas phase, leaving their reactivity in condensed phases poorly explored. This work aims to address this gap by investigating, for the first time, the reaction products and the mechanisms of aqueous-phase photolysis of four RONO2 (i.e., isopropyl nitrate, isobutyl nitrate, α-nitrooxy acetone, and 1-nitrooxy-2-propanol). The results show that the reactivity of RONO2 in the aqueous phase differs significantly from that in the gas phase. In contrast to the gas phase, where RONO2 release NOx upon photolysis, the aqueous-phase photolysis of RONO2 leads primarily to the direct formation of nitrous acid (HONO or HNO2), which was confirmed by quantum chemistry calculations. Hence, the aqueous-phase photolysis of RONO2 represents both a NOx sink and a source of atmospheric nitrous acid, a significant precursor of ⋅ OH and ⋅ NO. These secondary radicals (⋅ OH and ⋅ NO) are efficiently trapped in the aqueous phase, leading to the formation of HNO3 and functionalized RONO2. This reactivity can thus potentially contribute to the aging of secondary organic aerosol (SOA) and serves as an additional source of aqueous-phase SOA.

Light-induced excited spin-state trapping reactions in iron pyridinic complexes allow the iron's low-to-high spin transition in a sub-picosecond timescale. Employing a recently developed model for [Fe(2,2'-bipyridine) 3 ] 2+ photochemical spin-crossover reaction in conjunction with quantum wavepacket dynamics, we explore the possibility of controlling the reaction through external electromagnetic fields, aiming at stabilizing the initial metal-to-ligand charge transfer states. We show that simple Gaussian-shaped electromagnetic fields have a minor effect on the population kinetics. However, introducing vibrationally excited initial wavepacket representations allows for maintaining the population trapped in the metal-to-ligand charge transfer states. Using optimal control theory, we propose an electromagnetic field shape that increases the lifetime of metal-to-ligand charge transfer states. These results open the route for controlling the iron photochemistry through the action of external electric fields., (© 2024 The Authors. ChemPhysChem published by Wiley-VCH GmbH.)

Optimizing exchange-correlation functionals for both core/valence ionization potentials (cIPs/vIPs) and valence excitation energies (VEEs) at the same time in the framework of MRSF-TDDFT is self-contradictory. To overcome the challenge, within the previous "adaptive exact exchange" or double-tuning strategy on Coulomb-attenuating XC functionals (CAM), a new XC functional specifically for cIPs and vIPs was first developed by enhancing exact exchange to both short- and long-range regions. The resulting DTCAM-XI functional achieved remarkably high accuracy in its predictions with errors of less than half eV. An additional concept of "valence attenuation", where the amount of exact exchange for the frontier orbital regions is selectively suppressed, was introduced to consistently predict both VEEs and IPs at the same time. The second functional, DTCAM-XIV, exhibits consistent overall prediction accuracy at ∼0.64 eV. By preferentially optimizing VEEs within the same "valence attenuation" concept, a third functional, DTCAM-VAEE, was obtained, which exhibits improved performance as compared to that of the previous DTCAM-VEE and DTCAM-AEE in the prediction of VEEs, making it an attractive alternative to BH&HLYP. As the combination of "adaptive exchange" and "valence attenuation" is operative, it would be exciting to explore its potential with a more tunable framework in the future.

Long-range electrostatic effects are fundamental for describing chemical reactivity in the condensed phase. Here, we present the methodology of an efficient quantum mechanical/molecular mechanical (QM/MM) model in periodic boundary conditions (PBC) compatible with QM/MM boundaries at chemical bonds. The method combines electrostatic potential fitted charge operators and electrostatic potentials derived from the smooth particle-mesh Ewald (PME) sum approach. The total energy and its analytic first derivatives with respect to QM, MM, and lattice vectors allow QM/MM molecular dynamics (MD) in the most common thermodynamic ensembles. We demonstrate the robustness of the method by performing a QM/MM MD equilibration of methanol in water. We simulate the cis/trans isomerization free-energy profiles in water of proline amino acid and a proline-containing oligopeptide, showing a correct description of the reaction barrier. Our PBC-compatible QM/MM model can efficiently be used to study the chemical reactivity in the condensed phase and enzymatic catalysis.

High-intensity femtosecond pulses from an X-ray free-electron laser enable pump-probe experiments for the investigation of electronic and nuclear changes during light-induced reactions. On timescales ranging from femtoseconds to milliseconds and for a variety of biological systems, time-resolved serial femtosecond crystallography (TR-SFX) has provided detailed structural data for light-induced isomerization, breakage or formation of chemical bonds and electron transfer 1,2 . However, all ultrafast TR-SFX studies to date have employed such high pump laser energies that nominally several photons were absorbed per chromophore 3-17 . As multiphoton absorption may force the protein response into non-physiological pathways, it is of great concern 18,19 whether this experimental approach 20 allows valid conclusions to be drawn vis-à-vis biologically relevant single-photon-induced reactions 18,19 . Here we describe ultrafast pump-probe SFX experiments on the photodissociation of carboxymyoglobin, showing that different pump laser fluences yield markedly different results. In particular, the dynamics of structural changes and observed indicators of the mechanistically important coherent oscillations of the Fe-CO bond distance (predicted by recent quantum wavepacket dynamics 21 ) are seen to depend strongly on pump laser energy, in line with quantum chemical analysis. Our results confirm both the feasibility and necessity of performing ultrafast TR-SFX pump-probe experiments in the linear photoexcitation regime. We consider this to be a starting point for reassessing both the design and the interpretation of ultrafast TR-SFX pump-probe experiments 20 such that mechanistically relevant insight emerges., (© 2024. The Author(s).)

The tuning mechanism of pH can be extremely challenging to model computationally in complex biological systems, especially with respect to the photochemical properties. This article reports a protocol aimed at modeling pH-dependent photodynamics using a combination of constant-pH molecular dynamics and semiclassical nonadiabatic molecular dynamics simulations. With retinal photoisomerization in Anabaena sensory rhodopsin (ASR) as a testbed, we show that our protocol produces pH-dependent photochemical properties, such as the isomerization quantum yield or decay rates. We decompose our results into single-titrated residue contributions, identifying some key tuning amino acids. Additionally, we assess the validity of the single protonation state picture to represent the system at a given pH and propose the most populated protein charge state as a compromise between cost and accuracy.

The accurate description of solvent effects on X-ray absorption spectra (XAS) is fundamental for comparing the simulated spectra with experiments in solution. Currently, few protocols exist that can efficiently reproduce the effects of the solute/solvent interactions on XAS. Here, we develop an efficient and accurate theoretical protocol for simulating the solvent effects on XAS. The protocol combines electrostatic embedding QM/MM based on electrostatic potential fitted operators for describing the solute/solvent interactions and mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) for simulating accurate XAS spectra. To demonstrate the capabilities of our protocol, we compute the X-ray absorption of neutral proline in the gas phase and ionic proline in water in all relevant K-edges, showing excellent agreement with experiments. We show that states represented by core to π* transitions are almost unaffected by the interaction with water, whereas the core to σ* transitions are more impacted by the fluctuation of proline structure and the electrostatic interaction with the solvent. Finally, we reconstruct the pH-dependent XAS of proline in solution, determining that the N K-edge can be used to distinguish its three protonation states.

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.

It is demonstrated that significant accuracy improvements in MRSF-TDDFT can be achieved by introducing two different exchange-correlation (XC) functionals for the reference Kohn-Sham DFT and the response part of the calculations, respectively. Accordingly, two new XC functionals of doubly tuned Coulomb attenuated method-vertical excitation energy (DTCAM-VEE) and DTCAM-AEE were developed on the basis of the "adaptive exact exchange (AEE)" concept in the framework of the Coulomb-attenuating XC functionals. The values by DTCAM-VEE are in excellent agreement with those of Thiel's set [mean absolute errors (MAEs) and the interquartile range (IQR) values of 0.218 and 0.327 eV, respectively]. On the other hand, DTCAM-AEE faithfully reproduced the qualitative aspects of conical intersections (CIs) of trans -butadiene and thymine and the nonadiabatic molecular dynamics (NAMD) simulations on thymine. The latter functional also remarkably exhibited the exact 1/ R asymptotic behavior of the charge-transfer state of an ethylene-tetrafluoroethylene dimer and the accurate potential energy surfaces (PESs) along the two torsional angles of retinal protonated Schiff base model with six double bonds (rPSB6). Overall, DTCAM-AEE generally performs well, as its MAE (0.237) and IQR (0.41 eV) are much improved as compared to BH&HLYP. The current idea can also be applied to other XC functionals as well as other variants of linear response theories, opening a new way of developing XC functionals.

Automatic Rhodopsin Modeling (ARM) is a simulation protocol providing QM/MM models of rhodopsins capable of reproducing experimental electronic absorption and emission trends. Currently, ARM is restricted to a single protonation microstate for each rhodopsin model. Herein, we incorporate an extension of the minimal electrostatic model (MEM) into the ARM protocol to account for all relevant protonation microstates at a given pH. The new ARM+MEM protocol determines the most important microstates contributing to the description of the absorption spectrum. As a test case, we have applied this methodology to simulate the pH-dependent absorption spectrum of a toy model, showing that the single-microstate picture breaks down at certain pH values. Subsequently, we applied ARM+MEM to Anabaena sensory rhodopsin, confirming an improved description of its absorption spectrum when the titration of several key residues is considered.

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.

Photoexcitation of [Fe II (2,2'-bipyridine) 3 ] 2+ induces a subpicosecond spin crossover transformation from a low-spin singlet to a high-spin quintet state. The mechanism involves metal-centered (MC) and metal-ligand charge transfer (MLCT) triplet intermediates, but their individual contributions to this efficient intersystem crossing have been object of debate. Employing quantum wavepacket dynamics, we show that MC triplets are catalyzing the transfer to the high-spin state. This photochemical pathway is made possible thanks to bipyridine stretching vibrations, facilitating the conversion between the MLCT bands to such MC triplets. We show that the lifetime of the MLCT states can be increased to tens of picoseconds by breaking the conjugation between pyridine units, which increases the energetic gap between MLCT and MC states. This opens the route for the design of new chelating ligands inducing long-lived MLCT states in iron complexes.

Hybrid quantum mechanics/molecular mechanics (QM/MM) models are successful at describing the properties and reactivity of biological macromolecules. Combining ab initio QM/MM methods and periodic boundary conditions (PBC) is currently the optimal approach for modeling chemical processes in an infinite environment, but frequently, these models are too time-consuming for general applicability to biological systems in a solution. Here, we define a simple and efficient electrostatic embedding QM/MM model in PBC, combining the benefits of electrostatic potential fitted atomic charges and particle-mesh Ewald sums, which can efficiently treat systems of an arbitrary size at a reasonable computational cost. To illustrate this, we apply our scheme to extract the lowest singlet excitation energies from a model for Arabidopsis thaliana cryptochrome 1 containing circa 93 000 atoms, accurately reproducing the experimental absorption maximum.

The photochemistry of nucleobases, important for their role as building blocks of DNA, is largely affected by the electrostatic environment in which they are soaked. For example, despite the numerous studies of thymine in solution and DNA, there is still a debate on the photochemical deactivation pathways after UV absorption. Many theoretical models are oversimplified due to the lack of computationally accurate and efficient electronic structure methodologies that capture excited state electron correlation effects when nucleobases are embedded in large electrostatic media. Here, we combine mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) with electrostatic embedding QM/MM using electrostatic potential fittingfitted (ESPF) atomic charges, as a strategy to accurately and efficiently describe the electronic structure of chromophores polarized by an electrostatic medium. In particular, we develop analytic expressions for the energy and gradient of MRSF/MM based on the ESPF coupling using atom-centered grids and total charge conservation. We apply this methodology to the study of solvation effects on thymine photochemistry in water and thymine dimers in DNA. In the former, the combination of trajectory surface hopping (TSH) nonadiabatic molecular dynamics (NAMD) with MRSF/MM remarkably revealed accelerated deactivation decay pathways, which is consistent with the experimental decay time of ∼400 fs. The enhanced hopping rate can be explained by the preferential stabilization of corresponding conical interactions due to their increased dipole moments. Structurally, it is a consequence of characteristic methyl puckered geometries near the conical intersection region. For the thymine dimer in B-DNA, we found new photochemical pathways through conical intersections that could explain the formation of cyclobutadiene dimers and 6-4 photoproducts.

The lack of a theory capable of connecting the amino acid sequence of a light-absorbing protein with its fluorescence brightness is hampering the development of tools for understanding neuronal communications. Here we demonstrate that a theory can be established by constructing quantum chemical models of a set of Archaerhodopsin reporters in their electronically excited state. We found that the experimentally observed increase in fluorescence quantum yield is proportional to the computed decrease in energy difference between the fluorescent state and a nearby photoisomerization channel leading to an exotic diradical of the protein chromophore. This finding will ultimately support the development of technologies for searching novel fluorescent rhodopsin variants and unveil electrostatic changes that make light emission brighter and brighter., (© 2022. The Author(s).)

The rational engineering of photoresponsive materials, e.g., light-driven molecular motors, is a challenging task. Here, we use structure-related design rules to prepare a prototype molecular rotary motor capable of completing an entire revolution using, exclusively, the sequential absorption of two photons; i.e., a photon-only two-stroke motor. The mechanism of rotation is then characterised using a combination of non-adiabatic dynamics simulations and transient absorption spectroscopy measurements. The results show that the rotor moiety rotates axially relative to the stator and produces, within a few picoseconds at ambient T, an intermediate with the same helicity as the starting structure. We discuss how such properties, that include a 0.25 quantum efficiency, can help overcome the operational limitations of the classical overcrowded alkene designs., (© 2022. The Author(s).)

It is demonstrated that the challenging core-hole particle (CHP) orbital relaxation for core electron spectra can be readily achieved by the mixed-reference spin-flip (MRSF)-time-dependent density functional theory (TDDFT). With the additional scalar relativistic effects on K-edge excitation energies of 24 second- and 17 third-row molecules, the particular ΔCHP-MRSF(R) exhibited near perfect predictions with RMSE ∼0.5 eV, featuring a median value of 0.3 and an interquartile range of 0.4. Overall, the CHP effect is 2-4 times stronger than relativistic ones, contributing more than 20 eV in the cases of sulfur and chlorine third-row atoms. Such high precision allows to explain the splitting and spectral shapes of O, N, and C atom K-edges in the ground state of thymine with atom as well as orbital specific accuracy. The same protocol with a double hole particle relaxation also produced remarkably accurate K-edge spectra of core to valence hole excitation energies from the first ( n O8 π*) and second (ππ*) excited states of thymine, confirming the assignment of 1s → n excitation for the experimentally observed 526.4 eV peak. Regarding both accuracy and practicality, therefore, MRSF-TDDFT provides a promising protocol for core electron spectra of both ground and excited electronic states alike.

First row transition metal complexes with d 4 to d 7 electronic configurations exhibit spin-crossover (SCO), which can be induced by external stimuli, such as temperature, pressure and light. The low-spin to high-spin transition has been widely studied, but very little is known about the reverse process. Here, we present a theoretical study of thermal and light-induced high-to-low spin crossover in prototypical Fe(II) complexes. The lifetime of the high-spin state in the thermal process is determined using Fermi's golden rule. With this methodology, we have accurately computed the transfer rate of the HS state thermal relaxation at several time scales (from sub-nanosecond to a few seconds) in two different iron complexes. The use of quasi-degenerate perturbation theory (QDPT2) in the analysis of the LS-HS spin-orbit coupling has allowed us to identify 3 T 1 as the main intermediate state coupling the LS and HS states. The light-induced process has been studied using wavepacket quantum dynamics along the main vibrational coordinates (one symmetric and two asymmetric Fe-N stretchings). The study suggests that after the initial excitation from the 5 T 2g to the 5 E g state, the population is transferred back to a vibrationally hot 5 T 2g state, from which a small amount of the population is transferred to the 1 A 1g state via the intermediate 3 T 1g . Most of the population remains trapped in the HS state at the time scale of the simulation.

Three anthraquinone-based chromophores (9,10-anthraquinone, alizarin, purpurin) are compared from the point of view of their experimental and computed NMR and UV-visible light absorption spectra. Using a hybrid (explicit/implicit) solvent model, each proton chemical shift can be reproduced with an error of less than 7%, even when such protons are engaged in inter-molecular hydrogen bonds with the solvent or when the analyzed sample contains a significant amount of impurities, for instance, 9,10-anthraquinone in purpurin. All the steady-state UV-visible absorption spectra feature a significant vibrational progression in the first absorption band. The shape of the corresponding computed spectra, including vibronic couplings obtained with the adiabatic Hessian approach and the Franck-Condon and Herzberg-Teller approximation of the transition dipole, are in excellent agreement with the experimental ones. The importance and the nature of the vibronic couplings are different for the three molecules, even if they only differ by the number of hydroxyl groups.

Most aromatic ketones containing first-row elements undergo unexpectedly fast intersystem crossing in a few tens of picoseconds and a quantum yield close to unity. Among them, xanthone (9 H -xanthen-9-one) possesses one of the fastest singlet-triplet rates of only ∼1.5 ps. The exact mechanism of this unusually fast transition is still under debate. Here, we perform wavepacket dynamics of the photochemistry of xanthone in the gas phase and in polar solvents. We show that xanthone follows El-Sayed's rule for intersystem crossing. From the second singlet excited state, the mechanism is sequential: (i) an internal conversion between singlets 1 ππ* → 1 nπ* (85 fs), (ii) an intersystem crossing 1 nπ* → 3 ππ* (2.0 ps), and (iii) an internal conversion between triplets 3 ππ* → 3 nπ* (602 fs). Each transfer finds its origin in a barrierless access to electronic state intersections. These intersections are close to minimum energy structures, allowing for efficient transitions from the initial singlet state to the triplets.

Thymine photochemistry is important for understanding DNA photodamage. In the gas phase, thymine undergoes a fast non-radiative decay from S2 to S1. In the S1 state, it gets trapped for several picoseconds until returning to the ground-state S0. Here, we explore the electrostatic effects of nanomeric droplets of methanol and water on the excited states of thymine. For this purpose, we develop and implement an electrostatic embedding TD-DFT/MM method based on a QM/MM coupling defined through electrostatic potential fitting charges. We show that both in methanol and water, the mechanism is similar to the gas phase. The solvent molecules participate in defining the branching plane of S0/S1 intersection and have a negligible effect on the S1/S2 intersection. Despite the wrong topology of the ground/excited state intersections, electrostatic embedding TD-DFT/MM allows for a fast exploration of the potential energy surfaces and a qualitative picture of the photophysics of thymine in solvent droplets.

Non-radiative relaxation of the photoexcited thymine in the gas phase shows an unusually long excited-state lifetime, and, over the years, a number of models, i.e., S 1 -trapping, S 2 -trapping, and S 1 &S 2 -trapping, have been put forward to explain its mechanism. Here, we investigate this mechanism using non-adiabatic molecular dynamics (NAMD) simulations in connection with the recently developed mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) method. We show that the previously predicted S 2 -trapping model was due to an artifact caused by an insufficient account of the dynamic electron correlation. The current work supports the S 1 -trapping mechanism with two lifetimes, τ 1 = 30 ± 1 fs and τ 2 = 6.1 ± 0.035 ps, quantitatively consistent with the recent time-resolved experiments. Upon excitation to the S 2 (ππ*) state, thymine undergoes an ultrafast (ca. 30 fs) S 2 →S 1 internal conversion and resides around the minimum on the S 1 (n O π*) surface, slowly decaying to the ground state (ca. 6.1 ps). While the S 2 →S 1 internal conversion is mediated by fast bond length alternation distortion, the subsequent S 1 →S 0 occurs through several conical intersections, involving a slow puckering motion.

Infrared (IR) spectroscopy is an undoubtedly valuable tool for analyzing vibrations, conformational changes, and chemical reactions of biological macromolecules. Currently, there is a lack of theoretical methods to create a model successfully and efficiently simulate and interpret the origin of the spectral signatures, which are often complex to analyze. Here, we develop a new method for IR vibrational spectroscopy based on analytic second derivatives of electrostatic embedding QM/MM energy, the computation of electric dipole moments with respect to nuclear perturbations and the localization of normal modes. In addition to the IR spectrum, the method can provide the origin of each peak from clearly identified molecular motions of constituent fragments. As a proof of concept, we analyze the IR spectra of flavin adenine dinucleotides in water and in Arabidopsis thaliana cryptochrome proteins for four redox forms, in addition to the difference IR spectra before and after illumination with blue light. We show that the main peaks in the difference spectrum are due to N-H hydrogen out-of-plane motions and hydrogen bendings.

The electrostatic potential fitting method (ESPF) is a powerful way of defining atomic charges derived from quantum density matrices fitted to reproduce a quantum mechanical charge distribution in the presence of an external electrostatic potential. These can be used in the Hamiltonian to define a robust and efficient electrostatic embedding QM/MM method. The original formulation of ESPF QM/MM was based on two main approximations, namely, neglecting the grid derivatives and nonconserving of the total QM charge. Here, we present a new ESPF atomic charge operator, which overcomes these drawbacks at virtually no extra computational cost. The new charge operators employ atom-centered grids and conserve the total charge when traced with the density matrix. We present an efficient and easy-to-implement analytic form for the energy, gradient, and hessian that scales linearly with the MM subsystem size. We show that grid derivatives and charge conservation are fundamental to preserve the translational invariance properties of energies and their derivatives and exact conditions to be satisfied by the atomic charge derivatives. As proof of concept, we compute the transition state that leads to the formation of hydrogen peroxide during cryptochrome's reoxidation reaction. Last, we show that the construction of the full QM/MM hessian scales linearly with the MM subsystem size.

Cryptochromes are a class of flavoproteins proposed as candidates to explain magnetoreception of animals, plants and bacteria. The main hypothesis is that a biradical is formed upon blue-light absorption by flavin adenine dinucleotide (FAD). In a protein milieu, the oxidized form of FAD can be reduced, leading to four redox derivative forms: anionic and neutral semi-reduced radicals, and anionic and neutral fully reduced forms. All these forms have a characteristic electronic absorption spectrum, with a strong vibrational resolution. Here, we carried out a normal mode analysis at the electrostatic embedding QM/MM level of theory to compute the vibrationally resolved absorption spectra of the five redox forms of FAD embedded in a plant cryptochrome. We show that explicitly accounting for vibrational broadening contributions to electronic transitions is essential to reproduce the experimental spectra. In the case of the neutral radical form of FAD, the absorption spectrum is reproduced only if the presence of a tryptophan radical is considered.

Analytic second derivatives of electrostatic embedding (EE) quantum mechanics/molecular mechanics (QM/MM) energy are important for performing vibrational analysis and simulating vibrational spectra of quantum systems interacting with an environment represented as a classical electrostatic potential. The main bottleneck of EE-QM/MM second derivatives is the solution of coupled perturbed equations for each MM atom perturbation. Here, we exploit the Q-vector method [ J. Chem. Phys ., 2019 , 151 , 041102] to workaround this bottleneck. We derive the full analytic second derivative of the EE-QM/MM energy, which allows us to compute QM, MM, and QM-MM Hessian blocks in an efficient and easy to implement manner. To show the capabilities of our method, we compute the normal modes for the full Arabidopsis thaliana plant cryptochrome. We show that the flavin adenine dinucleotide vibrations (QM subsystem) strongly mix with protein modes. We compute approximate vibronic couplings for the lowest bright transition, from which we extract spectral densities and the homogeneous broadening of FAD absorption spectrum in protein using vibrationally resolved electronic spectrum simulations.

In electrostatic embedding mixed quantum and molecular mechanics (QM/MM) approaches, the QM charge distribution is polarized by the electrostatic interaction with the MM environment. Analytic derivatives of expectation values of operators are required to extract properties such as vibrational spectra. These derivatives usually require solving a set of coupled perturbed equations for each nucleus/atom in the system, thus becoming prohibitive when the MM subsystem contains thousands of atoms. In the context of Electrostatic Potential Fitting (ESPF) QM/MM, we can easily overcome this bottleneck by defining a set of auxiliary coupled perturbed equations called the Q-vector equations. The Q-vector method scales only with the size of the QM subsystem, producing an effective charge tensor that leads to the atomic charge derivative after contraction with the MM electrostatic potential gradient. As an example, we use the charge derivatives as an analysis tool to identify the most important chromophore-polarizing amino-acids in plant cryptochrome. This finding opens up the route of defining polarizable force fields and simulating vibrational spectroscopy using ESPF QM/MM electrostatic embedding at an affordable computational cost.

Cryptochrome is a blue-light absorbing flavoprotein containing a flavin adenine dinucleotide (FAD) cofactor. FAD can accept up to two electrons and two protons, which can be subsequently transferred to substrates present in the binding pocket. It is well known that reactive oxygen species are generated when triplet molecular oxygen is present in the cavity. Here, we investigate the formation and stability of radical oxygen species in Drosophila melanogaster cryptochrome using molecular dynamics simulations and electronic structure calculations. We find that the superoxide and hydroxyl radicals in doublet spin states are stabilized in the pocket due to the attractive electrostatic interactions and hydrogen bonding with partially reduced FAD. These findings validate from a molecular dynamics perspective that [FAD˙--HO2˙] or [FADH˙-O2˙-] can be alternative radical pairs at the origin of magnetoreception.

Light absorption of myoglobin triggers diatomic ligand photolysis and a spin crossover transition of iron(II) that initiate protein conformational change. The photolysis and spin crossover reactions happen concurrently on a femtosecond timescale. The microscopic origin of these reactions remains controversial. Here, we apply quantum wavepacket dynamics to elucidate the ultrafast photochemical mechanism for a heme-carbon monoxide (heme-CO) complex. We observe coherent oscillations of the Fe-CO bond distance with a period of 42 fs and an amplitude of ∼1 Å. These nuclear motions induce pronounced geometric reorganization, which makes the CO dissociation irreversible. The reaction is initially dominated by symmetry breaking vibrations inducing an electron transfer from porphyrin to iron. Subsequently, the wavepacket relaxes to the triplet manifold in ∼75 fs and to the quintet manifold in ∼430 fs. Our results highlight the central role of nuclear vibrations at the origin of the ultrafast photodynamics of organometallic complexes.

When a chromophore interacts with several titratable molecular sites, the modeling of its photophysical properties requires to take into account all their possible protonation states. We have developed a multi-scale protocol, based on constant-pH molecular dynamics simulations coupled to QM/MM excitation energy calculations, aimed at sampling both the phase space and protonation state space of a short polypeptide featuring a tyrosine-tryptophan dyad interacting with two aspartic acid residues. We show that such a protocol is accurate enough to help in the interpretation of the experimental tyrosine UV absorption spectrum at both acidic and basic pH. Moreover, it is confirmed that radical tryptophan probably contributes to the peptide spectrum, thanks to a UV-induced electron transfer from tyrosine to tryptophan, ultimately shedding light on the complex pH-dependent behavior of the peptide spectrum.

We examine the mechanism of ultrafast internal conversion between the B band (Soret band) and the Q band in porphine (H2P), the prototypical free-base porphyrin, using electronic structure studies and on-the-fly surface-hopping nonadiabatic dynamics. Our study highlights the crucial role of dark states within the N band which are found to mediate B/Q state transfer, necessitating a treatment beyond Gouterman's classic four-orbital model. The sequential B → N → Q pathway dominates largely over the direct B → Q pathway which is found to be energetically unfavorable. Potential energy surface cuts and conical intersections between excited states are determined by TDDFT and validated by CASSCF/CASPT2 and XMCQDPT2 calculations. Both the static analysis and on-the-fly surface-hopping calculations suggest a pathway which involves minor structural deformations via in-plane vibrations. The B → N conversion is a barrierless adiabatic process occurring within ∼20 fs, while the subsequent N → Q conversion occurs via a conical intersection within ∼100 fs, in agreement with time-resolved experiments for porphine and related free base porphyrins. Furthermore, evidence for both sequential and direct transfer to the Qx and Qy states is obtained.

Normal mode analysis is nowadays routinely performed in most quantum chemistry codes as a valuable tool for studying molecular motions. In systems formed by several molecular units, such as noncovalently bound donor-acceptor systems, normal modes are frequently delocalized over the whole structure, leading to a complicated interpretation of vibrations. Here, we propose a simple procedure to localize normal modes, based on the definition of fragment Hessian submatrices that lead to legitimate local fragment modes. These fragment modes can be defined for any arbitrary number of atoms and fragments and form in general a complete basis that can be used to expand the total normal modes. We use this fragment basis to explore the molecular origin of the normal modes of benzene, and several peaks in the infrared spectrum of tetraalanine. Additionally, we propose a criteria to define breathing modes in noncovalently bound systems, based on the fact that motions of the center of mass of fragments are not translational and rotational invariant with respect to the total center of mass of the system. By using the Sayvetz-Eckart conditions of fragments, we can quantify the contribution of rotation and translation of the fragments center of mass on the normal modes of the total system.

The electronic excited states populated upon absorption of UV photons by DNA are extensively studied in relation to the UV-induced damage to the genetic code. Here, we report a new unexpected relaxation pathway in adenine-thymine double-stranded structures (AT)n . Fluorescence measurements on (AT)n hairpins (six and ten base pairs) and duplexes (20 and 2000 base pairs) reveal the existence of an emission band peaking at approximately 320 nm and decaying on the nanosecond time scale. Time-dependent (TD)-DFT calculations, performed for two base pairs and exploring various relaxation pathways, allow the assignment of this emission band to excited states resulting from mixing between Frenkel excitons and adenine-to-thymine charge-transfer states. Emission from such high-energy long-lived mixed (HELM) states is in agreement with their fluorescence anisotropy (0.03), which is lower than that expected for π-π* states (≥0.1). An increase in the size of the system quenches π-π* fluorescence while enhancing HELM fluorescence. The latter process varies linearly with the hypochromism of the absorption spectra, both depending on the coupling between π-π* and charge-transfer states. Subsequently, we identify the common features between the HELM states of (AT)n structures with those reported previously for alternating (GC)n : high emission energy, low fluorescence anisotropy, nanosecond lifetimes, and sensitivity to conformational disorder. These features are also detected for calf thymus DNA in which HELM states could evolve toward reactive π-π* states, giving rise to delayed fluorescence., (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Conical intersections are perhaps the most significant mechanistic features of chemical reactions occurring through excited states. By providing funnels for efficient non-adiabatic population transfer, conical intersections govern the branching ratio of products of such reactions, similar to what the transition states do for ground-state reactivity. In this regard, intersections between the ground and the lowest excited states play a special role, and the correct description of the potential energy surfaces in their vicinity is crucial for understanding the mechanism and dynamics of excited-state reactions. The methods of density functional theory, such as time-dependent density functional theory, are widely used to describe the excited states of large molecules. However, are these methods suitable for describing the conical intersections or do they lead to artifacts and, consequently, to erroneous description of reaction dynamics? Here we address the first part of this question and analyze the ability of several density functional approaches, including the linear-response time-dependent approach as well as the spin-flip and ensemble formalisms, to provide the correct description of conical intersections and the potential energy surfaces in their vicinity. It is demonstrated that the commonly used linear-response time-dependent theory does not yield a proper description of these features and that one should instead use alternative computational approaches.

In their famous paper, Kohn and Sham formulated a formally exact density-functional theory (DFT) for the ground-state energy and density of a system of N interacting electrons, albeit limited at the time by certain troubling representability questions. As no practical exact form of the exchange-correlation (xc) energy functional was known, the xc-functional had to be approximated, ideally by a local or semilocal functional. Nowadays, however, the realization that Nature is not always so nearsighted has driven us up Perdew's Jacob's ladder to find increasingly nonlocal density/wavefunction hybrid functionals. Time-dependent (TD-) DFT is a younger development which allows DFT concepts to be used to describe the temporal evolution of the density in the presence of a perturbing field. Linear response (LR) theory then allows spectra and other information about excited states to be extracted from TD-DFT. Once again the exact TD-DFT xc-functional must be approximated in practical calculations and this has historically been done using the TD-DFT adiabatic approximation (AA) which is to TD-DFT very similar to what the local density approximation (LDA) is to conventional ground-state DFT. Although some of the recent advances in TD-DFT focus on what can be done within the AA, others explore ways around the AA. After giving an overview of DFT, TD-DFT, and LR-TD-DFT, this chapter focuses on many-body corrections to LR-TD-DFT as one way to build hybrid density-functional/wavefunction methodology for incorporating aspects of nonlocality in time not present in the AA.

Singlet excitons in π-stacked molecular crystals can split into two triplet excitons in a process called singlet fission that opens a route to carrier multiplication in photovoltaics. To resolve controversies about the mechanism of singlet fission, we have developed a first principles nonadiabatic quantum dynamical model that reveals the critical role of molecular stacking symmetry and provides a unified picture of coherent versus thermally activated singlet fission mechanisms in different acenes. The slip-stacked equilibrium packing structure of pentacene derivatives is found to enhance ultrafast singlet fission mediated by a coherent superexchange mechanism via higher-lying charge transfer states. By contrast, the electronic couplings for singlet fission strictly vanish at the C(2h) symmetric equilibrium π stacking of rubrene. In this case, singlet fission is driven by excitations of symmetry-breaking intermolecular vibrations, rationalizing the experimentally observed temperature dependence. Design rules for optimal singlet fission materials therefore need to account for the interplay of molecular π-stacking symmetry and phonon-induced coherent or thermally activated mechanisms.

The photoreactive pathways that may lead to DNA damage depend crucially upon the nature of the excited electronic states. The study of alternating guanine-cytosine duplexes by fluorescence spectroscopy and quantum mechanical calculations identifies a novel type of excited states that can be populated following UVB excitation. These states, denoted High-energy Emitting Long-lived Mixed (HELM) states, extend across both strands and arise from mixing between cytosine Frenkel excitons and guanine-to-cytosine charge transfer states. They emit at energies higher than ππ* states localized on single bases, survive for several nanoseconds, are sensitive to the ionic strength of the solution, and are strongly affected by the structural transition from the B form to the Z form. Their impact on the formation of lesions of the genetic code needs to be assessed.

State-averaged (SA) variants of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method, SA-REKS and state-interaction (SI)-SA-REKS, implement ensemble density functional theory for variationally obtaining excitation energies of molecular systems. In this work, the currently existing version of the SA-REKS method, which included only one excited state into the ensemble averaging, is extended by adding more excited states to the averaged energy functional. A general strategy for extension of the REKS-type methods to larger ensembles of ground and excited states is outlined and implemented in extended versions of the SA-REKS and SI-SA-REKS methods. The newly developed methods are tested in the calculation of several excited states of ground-state multi-reference systems, such as dissociating hydrogen molecule, and excited states of donor-acceptor molecular systems. For hydrogen molecule, the new method correctly reproduces the distance dependence of the lowest excited state energies and describes an avoided crossing between the doubly excited and singly excited states. For bithiophene-perylenediimide stacked complex, the SI-SA-REKS method correctly describes crossing between the locally excited state and the charge transfer excited state and yields vertical excitation energies in good agreement with the ab initio wavefunction methods.

Quantum-dynamical simulations are used to investigate the interplay of exciton delocalization and vibronically induced internal conversion processes in the elementary charge separation steps at regioregular donor-acceptor heterojunctions. Ultrafast internal conversion leads to efficient deexcitation within the excitonic and charge transfer manifolds, thus modifying the charge separation dynamics. We address a model donor-acceptor junction representative of regioregular P3HT-PCBM, using high-dimensional quantum dynamics simulations by multiconfigurational methods. While partial trapping into an interfacial charge separated state occurs, long-range charge-separated states are accessed as previously demonstrated in the work of Tamura and Burghardt [J. Am. Chem. Soc. 2013, 135, 16364]. For an H-aggregate type, stacked donor species, the initial bright state undergoes ultrafast internal conversion within the excitonic manifold, creating multiple charge transfer pathways before reaching the lowest-energy dark exciton, which is uncoupled from the charge transfer manifold. This process profoundly affects the charge separation mechanism and efficiency. For small energetic offsets between the interfacial excitonic and charge transfer states, a delocalized initial bright state proves less prone to electron-hole capture by the interfacial trap than a localized, vibronic wavepacket close to the interface. For both delocalized and localized initial states, a comparable yield of free carriers is obtained, which is found to be optimal for energetic offsets of the order of the Coulomb barrier to charge separation. Interfacial trapping is significantly reduced as the barrier height decreases with fullerene aggregation. Despite the high-dimensional nature of the system, charge separation is an ultrafast coherent quantum process exhibiting oscillatory features as observed in recent experiments.

Deoxyribonucleic acid photosensitization, i.e. the photoinduced electron- or energy-transfer of chromophores interacting with DNA, is a crucial phenomenon that triggers important DNA lesions such as pyrimidine dimerization, even upon absorption of relatively low-energy radiation. Oxidative lesions may also be produced via the photoinduced production of reactive oxygen species. Aromatic ketones, and acetophenone in particular, are well known for their sensitization effects. In this contribution we model the structural and dynamical properties of the acetophenone/DNA aggregates as well as their spectroscopic and photophysical properties using high-level hybrid quantum mechanics/molecular mechanics methods. We show that the key steps of the photochemistry of acetophenone in gas phase are conserved in the macromolecular environment and thus an ultrafast singlet-triplet conversion of acetophenone is expected prior to the transfer to DNA., (© 2014 The American Society of Photobiology.)

Quantum-chemical computational methods are benchmarked for their ability to describe conical intersections in a series of organic molecules and models of biological chromophores. Reference results for the geometries, relative energies, and branching planes of conical intersections are obtained using ab initio multireference configuration interaction with single and double excitations (MRCISD). They are compared with the results from more approximate methods, namely, the state-interaction state-averaged restricted ensemble-referenced Kohn-Sham method, spin-flip time-dependent density functional theory, and a semiempirical MRCISD approach using an orthogonalization-corrected model. It is demonstrated that these approximate methods reproduce the ab initio reference data very well, with root-mean-square deviations in the optimized geometries of the order of 0.1 Å or less and with reasonable agreement in the computed relative energies. A detailed analysis of the branching plane vectors shows that all currently applied methods yield similar nuclear displacements for escaping the strong non-adiabatic coupling region near the conical intersections. Our comparisons support the use of the tested quantum-chemical methods for modeling the photochemistry of large organic and biological systems.

We report and characterize ground-state and excited-state potential energy profiles using a variety of electronic structure methods along a loop lying on the branching plane associated with a conical intersection (CI) of a reduced retinal model, the penta-2,4-dieniminium cation (PSB3). Whereas the performance of the equation-of-motion coupled-cluster, density functional theory, and multireference methods had been tested along the excited- and ground-state paths of PSB3 in our earlier work, the ability of these methods to correctly describe the potential energy surface shape along a CI branching plane has not yet been investigated. This is the focus of the present contribution. We find, in agreement with earlier studies by others, that standard time-dependent DFT (TDDFT) does not yield the correct two-dimensional (i.e., conical) crossing along the branching plane but rather a one-dimensional (i.e., linear) crossing along the same plane. The same type of behavior is found for SS-CASPT2(IPEA=0), SS-CASPT2(IPEA=0.25), spin-projected SF-TDDFT, EOM-SF-CCSD, and, finally, for the reference MRCISD+Q method. In contrast, we found that MRCISD, CASSCF, MS-CASPT2(IPEA=0), MS-CASPT2(IPEA=0.25), XMCQDPT2, QD-NEVPT2, non-spin-projected SF-TDDFT, and SI-SA-REKS yield the expected conical crossing. To assess the effect of the different crossing topologies (i.e., linear or conical) on the PSB3 photoisomerization efficiency, we discuss the results of 100 semiclassical trajectories computed by CASSCF and SS-CASPT2(IPEA=0.25) for a PSB3 derivative. We show that for the same initial conditions, the two methods yield similar dynamics leading to isomerization quantum yields that differ by only a few percent.

Computational investigation of the longest wavelength excitations in a series of cyanines and linear n-acenes is undertaken with the use of standard spin-conserving linear response time-dependent density functional theory (TD-DFT) as well as its spin-flip variant and a ΔSCF method based on the ensemble DFT. The spin-conserving linear response TD-DFT fails to accurately reproduce the lowest excitation energy in these π-conjugated systems by strongly overestimating the excitation energies of cyanines and underestimating the excitation energies of n-acenes. The spin-flip TD-DFT is capable of correcting the underestimation of excitation energies of n-acenes by bringing in the non-dynamic electron correlation into the ground state; however, it does not fully correct for the overestimation of the excitation energies of cyanines, for which the non-dynamic correlation does not seem to play a role. The ensemble DFT method employed in this work is capable of correcting for the effect of missing non-dynamic correlation in the ground state of n-acenes and for the deficient description of differential correlation effects between the ground and excited states of cyanines and yields the excitation energies of both types of extended π-conjugated systems with the accuracy matching high-level ab initio multireference calculations.

Nitroxide-mediated photopolymerization (NMP(2)) is a promising novel route to initiate radical polymerization. In NMP(2), alkoxyamines bounded to a monomer are attached to a chromophore. Upon light absorption, the excitation energy is transferred from the chromophore to the alkoxyamine moiety, inducing the cleavage of the oxygen-carbon bond and thus initiating the polymerization. The NMP(2) mechanism depends strongly on several factors like the type of chromophore, the monomer, the connectivity pattern, etc. This complexity makes it difficult to design new NMP(2) initiators with increased polymerization efficiency and selectivity. In the present article, we characterize by means of quantum mechanical calculations the main steps of the NMP(2) initiation for alkoxyamines attached to aromatic ketones. We show how the excitation energy can be transferred from the chromophore to the alkoxyamine moiety, and present two easily computed parameters which can account for the selectivity of the O-C bond photocleaveage. Finally, using results obtained for a series of isomers, we give some rules that may help the design of more efficient NMP(2) initiators.

Even though time-dependent density-functional theory (TDDFT) works generally well for describing excited states energies and properties in the Franck-Condon region, it can dramatically fail in predicting photochemistry, notably when electronic state crossings occur. Here, we assess the ability of TDDFT to describe the photochemistry of an important class of triplet sensitizers, namely, aromatic ketones. We take acetophenone as a test molecule, for which accurate ab initio results exist in the literature. Triplet acetophenone is generated thanks to an exotic three-state crossing involving one singlet and two triplets states (i.e., a simultaneous intersystem crossing and triplet conical intersection), thus being a stringent test for approximate TDDFT. We show that most exchange-correlation functionals can only give a semi-qualitative picture of the overall photochemistry, in which the three-state crossing is rather represented as a triplet conical intersection separated from the intersystem crossing. The best result overall is given by the double hybrid functional mPW2PLYP, which is even able to reproduce quantitatively the three-state crossing region. We rationalize this results by noting that double hybrid functionals include a larger portion of double excitation character to the excited states.

Acetophenone has a rich photochemistry, which strongly depends on the absorbing state. For example, the excitation to the lowest singlet excited state (S1) leads to a triplet population with a phosphorescence quantum yield of one, while the excitation to S2 leads to photocleavage reactions. Here, we rationalize the photochemistry of acetophenone after being absorbed into the S1, S2 and S3 states by performing a systematic study of all the singlet and triplet minimum energy structures and state crossings between the relevant electronic states. We calculate these structures at the complete-active space self-consistent field (CASSCF) level of theory and at the correlated extended second-order quasi-degenerate multi-reference perturbation theory (XMCQDPT2), emphasizing the importance of correlation effects in the determination of structures.

In the quest for a cost-effective level of theory able to describe a large portion of the ground and excited potential energy surfaces of large chromophores, promising approaches are rooted in various approximations to the exact density functional theory (DFT). In the present work, we investigate how generalized Kohn-Sham DFT (GKS-DFT), time-dependent DFT (TDDFT), and spin-restricted ensemble-DFT (REKS) methods perform along three important paths characterizing a model retinal chromophore (the penta-2,4-dieniminium cation) in a region of near-degeneracy (close to a conical intersection) with respect to reference high-level multiconfigurational wave function methods. If GKS-DFT correctly describes the closed-shell charge transfer state, only TDDFT and REKS approaches give access to the open-shell diradical, one which sometimes corresponds to the electronic ground state. It is demonstrated that the main drawback of the usual DFT-based methods lies in the absence of interactions between the charge transfer and the diradicaloid configurations. Hence, we test a new computational scheme based on the State-averaged REKS (SA-REKS) approach, which explicitly includes these interactions into account. The State-Interaction SA-REKS (SI-SA-REKS) method significantly improves on the REKS and the SA-REKS results for the target system. The similarities and differences between DFT and wave function-based approaches are analyzed according to (1) the active space dimensions of the wave function-based methods and (2) the relative electronegativities of the allyl and protonated Schiff base moieties.