Time-Dependent Resonant Inelastic X-ray Scattering of Pyrazine at the Nitrogen K-Edge: A Quantum Dynamics Approach.

We calculate resonant inelastic X-ray scattering spectra of pyrazine at the nitrogen K-edge in the time domain including wavepacket dynamics in both the valence and core-excited state manifolds. Upon resonant excitation, we observe ultrafast non-adiabatic population transfer between core-excited states within the core-hole lifetime, leading to molecular symmetry distortions. Importantly, our time-domain approach inherently contains the ability to manipulate the dynamics of this process by detuning the excitation energy, which effectively shortens the scattering duration. We also explore the impact of pulsed incident X-ray radiation, which provides a foundation for state-of-the-art time-resolved experiments with coherent pulsed light sources.

Coupling Molecular Systems with Plasmonic Nanocavities: A Quantum Dynamics Approach.

Plasmonic nanoparticles have the capacity to confine electromagnetic fields to the subwavelength regime and provide strong coupling with few or even a single emitter at room temperature. The photophysical properties of the emitters are highly dependent on the relative distance and orientation between them and the nanocavity. Therefore, there is a need for accurate and general light-matter interaction models capable of guiding their design in application-oriented devices. In this work, we present a Hermitian formalism within the framework of quantum dynamics and based on first-principles electronic structure calculations. Our vibronic approach considers the quantum nature of the plasmonic excitations and the dynamics of nonradiative channels to model plasmonic nanocavities and their dipolar coupling to molecular electronic states. Thus, the quantized and dissipative nature of the nanocavity is fully addressed.

Optimal Mode Combination in the Multiconfiguration Time-Dependent Hartree Method through Multivariate Statistics: Factor Analysis and Hierarchical Clustering.

The multiconfiguration time-dependent Hartree (MCTDH) method and its multilayer extension (ML-MCTDH) are powerful algorithms for the efficient computation of nuclear quantum dynamics in high-dimensional systems. By providing time-dependent variational orbitals and an optimal choice of layered effective degrees of freedom, one is able to reduce the computational cost to an amenable number of configurations. However, choices related to selecting properly the mode grouping and tensor tree are strongly system dependent and, thus far, subjectively based on intuition and/or experience. Therefore, herein we detail a new protocol based on multivariate statistics─more specifically, factor analysis and hierarchical clustering─for a reliable and convenient guiding in the optimal design of such complex "system-of-systems" tensor-network decompositions. The advantages of employing the new algorithm and its applicability are tested on water and two floppy protonated water clusters with large amplitude motions.

Rational Design of Phe-BODIPY Amino Acids as Fluorogenic Building Blocks for Peptide-Based Detection of Urinary Tract Candida Infections.

Fungal infections caused by Candida species are among the most prevalent in hospitalized patients. However, current methods for the detection of Candida fungal cells in clinical samples rely on time-consuming assays that hamper rapid and reliable diagnosis. Herein, we describe the rational development of new Phe-BODIPY amino acids as small fluorogenic building blocks and their application to generate fluorescent antimicrobial peptides for rapid labelling of Candida cells in urine. We have used computational methods to analyse the fluorogenic behaviour of BODIPY-substituted aromatic amino acids and performed bioactivity and confocal microscopy experiments in different strains to confirm the utility and versatility of peptides incorporating Phe-BODIPYs. Finally, we have designed a simple and sensitive fluorescence-based assay for the detection of Candida albicans in human urine samples.

Regularizing the MCTDH equations of motion through an optimal choice on-the-fly (i.e., spawning) of unoccupied single-particle functions.

The multi-configuration time-dependent Hartree method is a general algorithm to solve the time-dependent Schrödinger equation, in which the wavefunction is expanded in a direct product of self-adapting time-dependent Single-Particle Functions (SPFs) that are propagated in time according to the Dirac-Frenkel variational principle. In the current version of this approach, the size of the SPF basis is fixed at the outset so that singularities in the working equations resulting from unoccupied functions have to be removed by a regularization procedure. Here, an alternative protocol is presented, in which we gradually increase the number of unoccupied SPFs on-the-fly (i.e., spawning) and optimize their shape by variationally minimizing the error made by the finite size of the basis. An initial estimate for the respective new expansion coefficients is also computed, thus avoiding the need to regularize the equations of motion. The advantages of employing the new algorithm are tested and discussed in some illustrative examples.

Multidimensional Quantum Mechanical Modeling of Electron Transfer and Electronic Coherence in Plant Cryptochromes: The Role of Initial Bath Conditions.

A multidimensional quantum mechanical protocol is used to describe the photoinduced electron transfer and electronic coherence in plant cryptochromes without any semiempirical, e.g., experimentally obtained, parameters. Starting from a two-level spin-boson Hamiltonian we look at the effect that the initial photoinduced nuclear bath distribution has on an intermediate step of this biological electron transfer cascade for two idealized cases. The first assumes a slow equilibration of the nuclear bath with respect to the previous electron transfer step that leads to an ultrafast decay with little temperature dependence; while the second assumes a prior fast bath equilibration on the donor potential energy surface leading to a much slower decay, which contrarily displays a high temperature dependence and a better agreement with previous theoretical and experimental results. Beyond Marcus and semiclassical pictures these results unravel the strong impact that the presence or not of equilibrium initial conditions has on the electronic population and coherence dynamics at the quantum dynamics level in this and conceivably in other biological electron transfer cascades.

Accidental degeneracy in the spiropyran radical cation: charge transfer between two orthogonal rings inducing ultra-efficient reactivity.

Photochromism of the spiropyran radical cation to the corresponding merocyanine form is investigated by a combination of electrochemical oxidation, UV/vis absorption spectroscopy, spectroelectrochemistry and first-principles calculations (TD-DFT, CAS-SCF and CAS-PT2). First, we demonstrate that the ring-opening of mono-spiropyrans occurs upon one-electron oxidation and that it can be driven photochemically as well as thermally, with trapping of the merocyanine by protonation. Second, in order to explain this experimentally observed spectroelectrochemical behaviour we suggest a theoretical mechanism based on the reactivity of the two lowest electronic excited-states, which promotes effective electron transfer from the indoline (nitrogen-ring) to the pyran (oxygen-ring) moieties (and vice versa) through a conical intersection seam of degeneracy. Characterisation of the minimum energy conical intersection on this crossing revealed that it presents a rare diabatic trapping topology. The excited state molecule cannot escape from crossing the intersection seam due to the presence of only one degeneracy-lifting coordinate that efficiently channels into the formation of the merocyanine photoproduct, so giving rise to a "kitchen sink" funnel-like effect. Therefore, assuming rapid relaxation after vertical excitation to a higher electronic state, photoconversion cannot be avoided in the D1 electronic state, which rationalises the remarkably efficient visible light driven excited-state reactivity observed experimentally.

Quantum effects in ultrafast electron transfers within cryptochromes.

Cryptochromes and photolyases are flavoproteins that may undergo ultrafast charge separation upon electronic excitation of their flavin cofactors. Charge separation involves chains of three or four tryptophan residues depending on the protein of interest. The molecular mechanisms of these processes are not completely clear. In the present work we investigate the relevance of quantum effects like the occurrence of nuclear tunneling and of coherences upon charge transfer in Arabidopsis thaliana cryptochromes. The possible breakdown of the Condon approximation is also investigated. We have devised a simulation protocol based on the realization of molecular dynamics simulations on diabatic potential energy surfaces defined at the hybrid constrained density functional theory/molecular mechanics level. The outcomes of the simulations are analyzed through various dedicated kinetics schemes related to the Marcus theory that account for the aforementioned quantum effects. MD simulations also provide a basic material to define realistic model Hamiltonians for subsequent quantum dissipative dynamics. To carry out quantum simulations, we have implemented an algorithm based on the Hierarchical Equations of Motion. With this new tool in hand we have been able to model the electron transfer chain considering either two- or three-state models. Kinetic models and quantum simulations converge to the conclusion that quantum effects have a significant impact on the rate of charge separation. Nuclear tunneling involving atoms of the tryptophan redox cofactors as well as of the environment (protein atoms and water molecules) is significant. On the other hand non-Condon effects are negligible in most simulations. Taken together, the results of the present work provide new insights into the molecular mechanisms controlling charge separation in this family of flavoproteins.

Electron dynamics upon ionization: control of the timescale through chemical substitution and effect of nuclear motion.

Photoionization can generate a non-stationary electronic state, which leads to coupled electron-nuclear dynamics in molecules. In this article, we choose benzene cation as a prototype because vertical ionization of the neutral species leads to a Jahn-Teller degeneracy between ground and first excited states of the cation. Starting with equal populations of ground and first excited states, there is no electron dynamics in this case. However, if we add methyl substituents that break symmetry but do not radically alter the electronic structure, we see charge migration: oscillations in the spin density that we can correlate with particular localized electronic structures, with a period depending on the gap between the states initially populated. We have also investigated the effect of nuclear motion on electron dynamics using a complete active space self-consistent field (CASSCF) implementation of the Ehrenfest method, most previous theoretical studies of electron dynamics having been carried out with fixed nuclei. In toluene cation for instance, simulations where the nuclei are allowed to move show significant differences in the electron dynamics after 3 fs, compared to simulations with fixed nuclei.

N-confused porphyrin tautomers: lessons from density functional theory.

Using first-principle calculations, we characterize the properties of N-confused porphyrins (NCP), with a focus on the differences between the 2H and 3H tautomers. We find that NCP-3H is almost as strongly aromatic as porphyrin, and about twice as aromatic, i.e., remarkably more stable, than NCP-2H, due to the less efficient π-conjugation in the latter form. The deprotonation of the NH-group at the external side of the inverted ring of NCP-2H, adds a lone pair to the π-system, which restores a strong aromaticity, while methylation has no significant effect. Investigating the impact of solvation using a continuum model, we find quite stable solvation energies with a relative dielectric constant, εr, in the 5-40 range, for both tautomers. NCP-3H presents a slightly lower energy than its NCP-2H counterpart in all solvents. However, the energy differences between the two species are of the order of the error margin of the method, hence too small to discuss the experimentally observed stabilization of NCP-3H in dichloromethane (DCM, a poorly polar solvent) and NCP-2H in N,N-dimethylformamide (DMF, a strongly polar solvent) or to extract the population ratios between the two forms in the different solvents. Therefore, the vibronic absorption spectra are also investigated in an effort to rationalize the complex absorption profiles of these NCP derivatives. We find very distinct spectra for the 2H and 3H forms in DMF and DCM, respectively, each fairly reproducing the experiment. We also find that, in the same solvent, the two species exhibit very different signatures, which allows us to conclude that the 2H and 3H tautomers are largely dominant in DMF and DCM, respectively. Interestingly, the vibrational motions that strongly participate in the shoulder of the Soret band and the multiple maxima of the Q-bands largely differ in the two tautomers.

A curve-crossing model to rationalize and optimize diarylethene dyads.

Going from photochromic compounds presenting a single switchable function to multi-addressable photochromic multimers remains an extremely difficult task notably because the interactions of several photochromic units through a linker generally result in a substantial loss of photoactivity. Due to their size and the intrinsic complexity of their electronic structure, coupled photochromes also constitute a fundamental challenge for theoretical chemistry. We present here an effective curve-crossing model that, used in connection with easily accessible ab initio data, allows a first understanding of the difficulty to obtain efficient multiphotochromes. Indeed, we demonstrate that extra crossing points, specific to multiphotochromes, have to be passed to ensure reactivity. In addition, the proposed approach allows the definition of an intuitive tilt criterion that can be used to screen a large number of substitution patterns and hence help in the design of new compounds, an aspect that is also developed here. The compatibility of this tilt criterion with previously proposed static Franck-Condon parameters is discussed as well.

Electronic control of initial nuclear dynamics adjacent to a conical intersection.

Photoionization can create a nonstationary electronic state and therefore initiates coupled electron-nuclear dynamics in molecules. Using a CASSCF implementation of the Ehrenfest method, we study the nuclear dynamics following vertical ionization of toluene, starting close to the conical intersection between ground and first excited states of its cation. The results show how the initial nuclear dynamics is controlled by the nonstationary electronic state character. In particular, ionization of this system leading to an equal superposition of the two lowest energy states can initiate nuclear dynamics in an orthogonal direction in the branching space to dynamics on the ground or first excited state potential energy surfaces alone.

New insights into the by-product fatigue mechanism of the photo-induced ring-opening in diarylethenes.

The photochromic properties of diarylethenes, some of the most studied class of molecular switches, are known to be controlled by non-adiabatic decay at a conical intersection seam. Nevertheless, as their fatigue-reaction mechanism - leading to non-photochromic products - is yet to be understood, we investigate the photo-chemical formation of the so-called by-product isomer using three complementary computational methods (MMVB, CASSCF and CASPT2) on three model systems of increasing complexity. We show that for the ring-opening reaction a transition state on S1(2A) involving bond breaking of the penta-ring leads to a low energy S1(2A)/S0(1A) conical intersection seam, which lies above one of the transition states leading to the by-product isomer on the ground state. Therefore, radiationless decay and subsequent side-product formation can take place explaining the photo-degradation responsible for the by-product generation in diarylethene-type molecules. The effect of dynamic electron correlation and the possible role of inter-system crossing along the penta-ring opening coordinate are discussed as well.

Coupled electron-nuclear dynamics: charge migration and charge transfer initiated near a conical intersection.

Coupled electron-nuclear dynamics, implemented using the Ehrenfest method, has been used to study charge migration with fixed nuclei, together with charge transfer when nuclei are allowed to move. Simulations were initiated at reference geometries of neutral benzene and 2-phenylethylamine (PEA), and at geometries close to potential energy surface crossings in the cations. Cationic eigenstates, and the so-called sudden approximation, involving removal of an electron from a correlated ground-state wavefunction for the neutral species, were used as initial conditions. Charge migration without coupled nuclear motion could be observed if the Ehrenfest simulation, using the sudden approximation, was started near a conical intersection where the states were both strongly coupled and quasi-degenerate. Further, the main features associated with charge migration were still recognizable when the nuclear motion was allowed to couple. In the benzene radical cation, starting from the reference neutral geometry with the sudden approximation, one could observe sub-femtosecond charge migration with a small amplitude, which results from weak interaction with higher electronic states. However, we were able to engineer large amplitude charge migration, with a period between 10 and 100 fs, corresponding to oscillation of the electronic structure between the quinoid and anti-quinoid cationic electronic configurations, by distorting the geometry along the derivative coupling vector from the D6h Jahn-Teller crossing to lower symmetry where the states are not degenerate. When the nuclear motion becomes coupled, the period changes only slightly. In PEA, in an Ehrenfest trajectory starting from the D2 eigenstate and reference geometry, a partial charge transfer occurs after about 12 fs near the first crossing between D1, D2 (N(+)-Phenyl, N-Phenyl(+)). If the Ehrenfest propagation is started near this point, using the sudden approximation without coupled nuclear motion, one observes an oscillation of the spin density--charge migration--between the N atom and the phenyl ring with a period of 4 fs. When the nuclear motion becomes coupled, this oscillation persists in a damped form, followed by an effective charge transfer after 30 fs.

How the conical intersection seam controls chemical selectivity in the photocycloaddition of ethylene and benzene.

The photocycloaddition reaction of benzene with ethylene has been studied at the CASSCF level, including the characterization of an extended conical intersection seam. We show that the chemical selectivity is, in part, controlled by this extended conical intersection seam and that the shape of the conical intersection seam can be understood in terms of simple VB arguments. Further, the shape and energetics of the asynchronous segment of the conical intersection seam suggest that 1,2 (ortho) and 1,3 (meta) will be the preferred chemical products with similar weight. The 1,4 (para) point on the conical intersection is higher in energy and corresponds to a local maximum on the seam. VB analysis shows that the pairs of VB structures along this asynchronous seam are the same and thus the shape will be determined mainly by steric effects. Synchronous structures on the seam are higher in energy and belong to a different branch of the seam separated by a saddle point on the seam. On S1 we have documented three mechanistic pathways corresponding to transition states (with low barriers) between the reactants and the conical intersection seam: a mixed asynchronous/synchronous [1,2] ortho path, an asynchronous [1,3] meta path, and a synchronous [1,3] meta path.

Towards converging non-adiabatic direct dynamics calculations using frozen-width variational gaussian product basis functions.

In this article, we investigate the convergence of quantum dynamics calculations with coupled variationally optimized gaussian product basis functions, describing wavepacket motion on regions of molecular potential energy surfaces calculated on the fly. As a benchmark system, we model the radiationless decay of fulvene from its first electronic excited state through an extended S(1)∕S(0) conical intersection seam and monitor two associated properties: the spatial extent to which the conical intersection seam is sampled and the timescale and stepwise nature of the population transfer. We suggest that the fully variational description reviewed here (direct dynamics-variational multi-configuration gaussian) provides a way to balance accuracy against computational cost for molecules of comparable sizes by choosing the number of coupled gaussian product basis functions and a middle way forward between grid based and trajectory surface hopping approaches to non-adiabatic molecular quantum dynamics calculations.

Nonequilibrium Fermi golden rule for electronic transitions through conical intersections.

We consider photoinduced electronic transitions through conical intersections in large molecules. Starting from the linear vibronic model Hamiltonian and treating linear diabatic couplings within the second order cumulant expansion, we have developed a simple analytical expression for the time evolution of electronic populations at finite temperature. The derived expression can be seen as a nonequilibrium generalization of the Fermi golden rule due to a nonequilibrium character of the initial photoinduced nuclear distribution. All parameters in our model are obtained from electronic structure calculations followed by a diabatization procedure. The results of our model are found to agree well with those of quantum dynamics for a test set of systems: fulvene molecule, 2,6-bis(methylene) adamantyl cation, and its dimethyl derivative.

Controlling the mechanism of fulvene S(1)/S(0) decay: switching off the stepwise population transfer.

Direct quantum dynamics simulations were performed to model the radiationless decay of the first excited state S(1) of fulvene. The full space of thirty normal mode nuclear coordinates was explicitly considered. By default, ultrafast internal conversion takes place centred on the higher-energy planar region of the S(1)/S(0) conical intersection seam, giving the stepwise population transfer characteristic of a sloped surface crossing, and leading back to the ground state reactant. Two possible schemes for controlling whether stepwise population transfer occurs or not-either altering the initial geometry distribution or the initial momentum composition of the photo-excited wavepacket-were explored. In both cases, decay was successfully induced to occur in the lower-energy twisted/peaked region of the crossing seam, switching off the stepwise population transfer. This absence of re-crossing is a direct consequence of the change in the position on the intersection at which decay occurs (our target for control), and its consequences should provide an experimentally observable fingerprint of this system.

Fluorescence of the perylene radical cation and an inaccessible D(0)/D(1) conical intersection: An MMVB, RASSCF, and TD-DFT computational study.

The photophysics of the perylene radical cation (Pe(+)) was studied using the molecular mechanics-valence bond (MMVB) hybrid force field. Potential energy surfaces of the first three electronic states were investigated. Geometry optimizations of critical points-including conical intersections between the relevant electronic states-were performed using the MMVB analytical energy gradient for cations. No accessible planar conical intersection between the D(0) and D(1) states of Pe(+) was found; this is consistent with the experimentally observed D(1) lifetimes and the observation of D(1) emission from this cation in the condensed phase. Benchmark RASSCF and TD-DFT calculations support the reliability of the MMVB results.