Influence of pump laser fluence on ultrafast myoglobin structural dynamics.

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 transfer1,2. However, all ultrafast TR-SFX studies to date have employed such high pump laser energies that nominally several photons were absorbed per chromophore3-17. As multiphoton absorption may force the protein response into non-physiological pathways, it is of great concern18,19 whether this experimental approach20 allows valid conclusions to be drawn vis-à-vis biologically relevant single-photon-induced reactions18,19. 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 dynamics21) 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 experiments20 such that mechanistically relevant insight emerges.

Automatic Rhodopsin Modeling with Multiple Protonation Microstates.

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 toAnabaenasensory rhodopsin, confirming an improved description of its absorption spectrum when the titration of several key residues is considered.

Solvent Effects and pH Dependence of the X-ray Absorption Spectra of Proline from Electrostatic Embedding Quantum Mechanics/Molecular Mechanics and Mixed-Reference Spin-Flip Time-dependent Density-Functional Theory.

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.

An efficient electrostatic embedding QM/MM method using periodic boundary conditions based on particle-mesh Ewald sums and electrostatic potential fitted charge operators.

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.

Quantum dynamics simulations of the thermal and light-induced high-spin to low-spin relaxation in Fe(bpy)3 and Fe(mtz)6.

First row transition metal complexes with d4 to d7 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 3T1 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 5T2g to the 5Eg state, the population is transferred back to a vibrationally hot 5T2g state, from which a small amount of the population is transferred to the 1A1g state via the intermediate 3T1g. Most of the population remains trapped in the HS state at the time scale of the simulation.

Stressing the differences in alizarin and purpurin dyes through UV-visible light absorption and 1H-NMR spectroscopies.

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.

Ultrafast Intersystem Crossing in Xanthone from Wavepacket Dynamics.

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 (9H-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 1ππ* → 1nπ* (85 fs), (ii) an intersystem crossing 1nπ* → 3ππ* (2.0 ps), and (iii) an internal conversion between triplets 3ππ* → 3nπ* (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.

Infrared spectroscopy from electrostatic embedding QM/MM: local normal mode analysis of infrared spectra of arabidopsis thaliana plant cryptochrome.

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.

Photochemistry of Thymine in Protic Polar Nanomeric Droplets Using Electrostatic Embeding TD-DFT/MM.

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.

UV-visible absorption spectrum of FAD and its reduced forms embedded in a cryptochrome protein.

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.

Theoretical insights into the formation and stability of radical oxygen species in cryptochromes.

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.

Analytic QM/MM atomic charge derivatives avoiding the scaling of coupled perturbed equations with the MM subsystem size.

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.

Sampling the protonation states: the pH-dependent UV absorption spectrum of a polypeptide dyad.

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.

Ultrafast photochemistry of free-base porphyrin: a theoretical investigation of B → Q internal conversion mediated by dark states.

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.

Many-Body Perturbation Theory (MBPT) and Time-Dependent Density-Functional Theory (TD-DFT): MBPT Insights About What Is Missing In, and Corrections To, the TD-DFT Adiabatic Approximation.

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.

Description of Conical Intersections with Density Functional Methods.

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.

High-Energy Long-Lived Mixed Frenkel-Charge-Transfer Excitons: From Double Stranded (AT)n to Natural DNA.

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.

First-Principles Quantum Dynamics of Singlet Fission: Coherent versus Thermally Activated Mechanisms Governed by Molecular π Stacking.

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.

Ensemble density functional theory method correctly describes bond dissociation, excited state electron transfer, and double excitations.

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.

Theoretical study of the photochemical initiation in nitroxide-mediated photopolymerization.

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.