Coherent Mixing of Singlet and Triplet States in Acrolein and Ketene: A Computational Strategy for Simulating the Electron-Nuclear Dynamics of Intersystem Crossing.

We present a theoretical study of intersystem crossing (ISC) in acrolein and ketene with the Ehrenfest method that can describe a superposition of singlet and triplet states. Our simulations illustrate a new mechanistic effect of ISC, namely, that a superposition of singlets and triplets yields nonadiabatic dynamics characteristic of that superposition rather than the constituent state potential energy surfaces. This effect is particularly significant in ketene, where mixing of singlet and triplet states along the approach to a singlet/singlet conical intersection occurs, with the spin-orbit coupling (SOC) remaining small throughout. In both cases, the effects require many recrossings of the singlet/triplet state crossing seam, consistent with the textbook treatment of ISC.

3-Methylation alters excited state decay in photoionised uracil.

UV and VUV-induced processes in DNA/RNA nucleobases are central to understand photo-damaging and photo-protecting mechanisms in our genetic material. Here we model the events following photoionisation and electronic excitation in uracil, methylated in the 1' and 3' positions, using the correlated XMS-CASPT2 method. We compare our results against those for uracil and 5-methyl-uracil (thymine) previously published. We find 3-methylation, an epigenetic modification in non-negligible amounts, shows the largest differences in photoionised decay of all three derivatives studied compared to uracil itself. At the S0 minimum, 3-methyl-uracil (3mUra) shows almost degenerate excited cation states. Upon populating the cation manifold, a crossing is predicted featuring different topography compared to other methylated uracil species in this study. We find an effective 3-state conical intersection accessible for 3mUra+, which points towards an additional pathway for radiationless decay. 3-Methylation reduces the potential energy barrier mediating decay to the cation ground state, making it vanish and leading to a pathway that we expect will contribute to the fastest radiationless decay amongst all methylated uracil species studied to date. 1- and 5-methylation, on the other hand, give differences from uracil in detail only: ionisation potentials are slightly red-shifted and the potential energy barrier mediating decay to the cation ground state is small but almost unchanged. By comparing against CASSCF calculations, we establish XMS-CASPT2 is essential to correctly describe conical intersections for 3mUra+. Our calculations show how a chemical modification that seems relatively small electronically can nevertheless have a significant impact on the behaviour of electronic excited states: a single methylation in the 3' position alters the behaviour of the RNA base uracil and appears to open an additional pathway for radiationless decay following ionisation and electronic excitation.

How electronic superpositions drive nuclear motion following the creation of a localized hole in the glycine radical cation.

In this work, we have studied the nuclear and electron dynamics in the glycine cation starting from localized hole states using the quantum Ehrenfest method. The nuclear dynamics is controlled both by the initial gradient and by the instantaneous gradient that results from the oscillatory electron dynamics (charge migration). We have used the Fourier transform (FT) of the spin densities to identify the "normal modes" of the electron dynamics. We observe an isomorphic relationship between the electron dynamics normal modes and the nuclear dynamics, seen in the vibrational normal modes. The FT spectra obtained this way show bands that are characteristic of the energy differences between the adiabatic hole states. These bands contain individual peaks that are in one-to-one correspondence with atom pair (+·) ↔ (·+) resonances, which, in turn, stimulate nuclear motion involving the atom pair. With such understanding, we anticipate "designer" coherent superpositions that can drive nuclear motion in a particular direction.

Molecular excited state calculations with adaptive wavefunctions on a quantum eigensolver emulation: reducing circuit depth and separating spin states.

Ab initio electronic excited state calculations are necessary for the quantitative study of photochemical reactions, but their accurate computation on classical computers is plagued by prohibitive resource scaling. The Variational Quantum Deflation (VQD) is an extension of the quantum-classical Variational Quantum Eigensolver (VQE) algorithm for calculating electronic excited state energies, and has the potential to address some of these scaling challenges using quantum computers. However, quantum computers available in the near term can only support a limited number of quantum circuit operations, so reducing the quantum computational cost in VQD methods is critical to their realisation. In this work, we investigate the use of adaptive quantum circuit growth (ADAPT-VQE) in excited state VQD calculations, a strategy that has been successful previously in reducing the resources required for ground state energy VQE calculations. We also invoke spin restrictions to separate the recovery of eigenstates with different spin symmetry to reduce the number of calculations and accumulation of errors in computing excited states. We created a quantum eigensolver emulation package - Quantum Eigensolver Building on Achievements of Both quantum computing and quantum chemistry (QEBAB) - for testing the proposed adaptive procedure against two existing VQD methods that use fixed-length quantum circuits: UCCGSD-VQD and k-UpCCGSD-VQD. For a lithium hydride test case we found that the spin-restricted adaptive growth variant of VQD uses the most compact circuits out of the tested methods by far, consistently recovers adequate electron correlation energy for different nuclear geometries and eigenstates while isolating the singlet and triplet manifold. This work is a further step towards developing techniques which improve the efficiency of hybrid quantum algorithms for excited state quantum chemistry, opening up the possibility of exploiting real quantum computers for electronic excited state calculations sooner than previously anticipated.

Modelling Photoionisation in Isocytosine: Potential Formation of Longer-Lived Excited State Cations in its Keto Form.

The front cover artwork is provided by Dr. Javier Segarra-Martí (University of Valencia, Spain) and Prof. Michael J. Bearpark (Imperial College London, UK). The image shows the ultrafast photoionisation of DNA canonical nucleobase cytosine and the slower ionization process in non-canonical base isocytosine embedded within a DNA backbone. Read the full text of the Article at 10.1002/cphc.202100402.

Modelling Photoionisation in Isocytosine: Potential Formation of Longer-Lived Excited State Cations in its Keto Form.

Studying the effects of UV and VUV radiation on non-canonical DNA/RNA nucleobases allows us to compare how they release excess energy following absorption with respect to their canonical counterparts. This has attracted much research attention in recent years because of its likely influence on the origin of our genetic lexicon in prebiotic times. Here we present a CASSCF and XMS-CASPT2 theoretical study of the photoionisation of non-canonical pyrimidine nucleobase isocytosine in both its keto and enol tautomeric forms. We analyse their lowest energy cationic excited states including 2π+ , 2nO+ and 2nN+ and compare these to the corresponding electronic states in cytosine. Investigating lower-energy decay pathways we find - unexpectedly - that keto-isocytosine+ presents a sizeable energy barrier potentially inhibiting decay to its cationic ground state, whereas enol-isocytosine+ features a barrierless and consequently ultrafast pathway analogous to the one previously found for the canonical (keto) form of cytosine+ . Dynamic electron correlation reduces the energy barrier in the keto form substantially (by ∼1 eV) but it is nevertheless still present. We additionally compute the UV/Vis absorption signals of the structures encountered along these decay channels to provide spectroscopic fingerprints to assist future experiments in monitoring these intricate photo-processes.

Radical-Triggered Reaction Mechanism of the Green-to-Red Photoconversion of EosFP.

Reaction intermediates in the green-to-red photoconversion of the photochromic fluorescent protein EosFP have been observed using high-intensity continuous blue illumination. An intermediate was identified through light-induced accumulation that continues to convert the green form in subsequent darkness, putatively containing a tyrosyl radical, albeit with anomalously shifted features in both the electronic and FTIR spectra. Lowering the pH to 5.5 significantly delays the decay of this tyrosyl intermediate, which is accompanied by Stark-shifted features in the electronic spectra of reactants and products. Vibrational mode assignments for the high-frequency and fingerprint FTIR spectral regions of the reaction intermediates support a proposed sequence of events where the newly formed Cα═Cß ethylenic bond precedes modifications on the His-62 imidazole ring and confirms a C═O(NH2) product group on Phe-61. We propose a reaction mechanism that involves tyrosyl generation via singlet excited-state-mediated oxidation which subsequently triggers the covalent reactions by oxidation of the green chromophore.

Modeling multidimensional spectral lineshapes from first principles: application to water-solvated adenine.

In this discussion we present a methodology to describe spectral lineshape from first principles, providing insight into the solvent-solute molecular interactions in terms of static and dynamic disorder and how these shape the signals recorded experimentally in linear and nonlinear optical spectroscopies, including two-dimensional electronic spectroscopy (2DES). Two different strategies for simulating the lineshape are compared: both rely on the same evaluation of the coupling between the electronic states and the intra-molecular vibrations, while they differ in describing the influence exerted by the diverse water configurations attained along a molecular dynamics (MD) simulation. The first method accounts for such water arrangements as first order perturbations on the adenine energies computed for a single reference (gas phase) quantum calculation. The second method requires computation of the manifold of excited states explicitly at each simulation snapshot, employing a hybrid quantum mechanics/molecular mechanics (QM/MM) scheme. Both approaches are applied to a large number of states of the adenine singlet excited manifold (chosen because of its biological role), and compared with available experimental data. They give comparable results but the first approach is two orders of magnitude faster. We show how the various contributions (static/dynamic disorder, intra-/inter-molecular interactions) sum up to build the total broadening observed in experiments.

Molecular Vertical Excitation Energies Studied with First-Order RASSCF (RAS[1,1]): Balancing Covalent and Ionic Excited States.

RASSCF calculations of vertical excitation energies were carried out on a benchmark set of 19 organic molecules studied by Thiel and co-workers [ J. Chem. Phys. 2008 , 128 , 134110 ]. The best results, in comparison with the MS-CASPT2 results of Thiel, were obtained using a RASSCF space that contains at most one hole and one particle in the RAS1 and RAS3 spaces, respectively, which we denote as RAS[1,1]. This subset of configurations recovers mainly the effect of polarization and semi-internal electronic correlation that is only included in CASSCF in an averaged way. Adding all-external correlation by allowing double excitations from RAS1 and RAS2 into RAS3 did not improve the results, and indeed, they were slightly worse. The accuracy of the first-order RASSCF computations is demonstrated to be a function of whether the state of interest can be classified as covalent or ionic in the space of configurations built from orbitals localized onto atomic sites. For covalent states, polarization and semi-internal correlation effects are negligible (RAS[1,1]), while for ionic states, these effects are large (because of inherent diffusiveness of these states compared to the covalent states) and, thus, an acceptable agreement with MS-CASPT2 can be obtained using first-order RASSCF with the extra basis set involving 3p orbitals in most cases. However, for those ionic states that are quasi-degenerate with a Rydberg state or for nonlocal nπ* states, there remains a significant error resulting from all external correlation effects.

Ultrafast and radiationless electronic excited state decay of uracil and thymine cations: computing the effects of dynamic electron correlation.

In this article we characterise the radiationless decay of the first few electronic excited states of the cations of DNA/RNA nucleobases uracil and thymine, including the effects of dynamic electron correlation on energies and geometries (optimised with XMS-CASPT2). In both systems, we find that one state of 2n and another two of 2π+ character can be populated following photoionisation, and their different minima and interstate crossings are located. We find strong similarities between uracil and thymine cations: with accessible conical intersections suggesting that depopulation of their electronic excited states takes place on ultrafast timescales in both systems, suggesting that they are photostable in agreement with previous theoretical (uracil+) evidence. We find that dynamic electron correlation separates the energy levels of the "3-state" conical intersection (D2/D1/D0)CI previously located with CASSCF for uracil+, which will therefore have a different geometry and higher energy. Simulating the electronic and vibrational absorptions allows us to characterise spectral fingerprints that could be used to monitor these cation photo-processes experimentally.

Electron Dynamics upon Ionization of Polyatomic Molecules: Coupling to Quantum Nuclear Motion and Decoherence.

Knowledge about the electronic motion in molecules is essential for our understanding of chemical reactions and biological processes. The advent of attosecond techniques opens up the possibility to induce electronic motion, observe it in real time, and potentially steer it. A fundamental question remains the factors influencing electronic decoherence and the role played by nuclear motion in this process. Here, we simulate the dynamics upon ionization of the polyatomic molecules paraxylene and modified bismethylene-adamantane, with a quantum mechanical treatment of both electron and nuclear dynamics using the direct dynamics variational multiconfigurational Gaussian method. Our simulations give new important physical insights about the expected decoherence process. We have shown that the decoherence of electron dynamics happens on the time scale of a few femtoseconds, with the interplay of different mechanisms: the dephasing is responsible for the fast decoherence while the nuclear overlap decay may actually help maintain it and is responsible for small revivals.

Charge migration in polycyclic norbornadiene cations: Winning the race against decoherence.

The observation of electronic motion remains a key target in the development of the field of attoscience. However, systems in which long-lived oscillatory charge migration may be observed must be selected carefully, particularly because it has been shown that nuclear spatial delocalization leads to a loss of coherent electron density oscillations. Here we demonstrate electron dynamics in norbornadiene and extended systems where the hole density migrates between two identical chromophores. By studying the effect of nuclear motion and delocalization in these example systems, we present the physical properties that must be considered in candidate molecules in which to observe electron dynamics. Furthermore, we also show a key contribution to nuclear delocalization arises from motion in the branching plane of the cation. For the systems studied, the dephasing time increases with system size while the energy gap between states, and therefore the frequency of the density oscillation, decreases with size (obeying a simple exponential dependence on the inter-chromophore distance). We present a system that balances these two effects and shows several complete oscillations in the spin density before dephasing occurs.

Electron and nuclear dynamics following ionisation of modified bismethylene-adamantane.

We have simulated the coupled electron and nuclear dynamics using the Ehrenfest method upon valence ionisation of modified bismethylene-adamantane (BMA) molecules where there is an electron transfer between the two π bonds. We have shown that the nuclear motion significantly affects the electron dynamics after a few fs when the electronic states involved are close in energy. We have also demonstrated how the non-stationary electronic wave packet determines the nuclear motion, more precisely the asymmetric stretching of the two π bonds, illustrating "charge-directed reactivity". Taking into account the nuclear wave packet width results in the dephasing of electron dynamics with a half-life of 8 fs; this eventually leads to the equal delocalisation of the hole density over the two methylene groups and thus symmetric bond lengths.

Excited-State Decay in the Photoisomerisation of Azobenzene: A New Balance between Mechanisms.

The mechanism of the photoisomerisation of azobenzene has been studied by means of multiconfigurational ab initio calculations. Our results show that it is necessary to account for the dynamic electron correlation in the location of the critical points (CASPT2 optimizations) to obtain a correct description of the topography of the potential energy surfaces of the low energy singlet excited states. By using this methodology, we have found that the state populated by the initial excitation is the S2 (ππ*) state, which decays very efficiently to the S1 (nπ*) state at a pedal-like non-rotated geometry. In the S1 state, relaxation leads to a rotated geometry where the system decays to the ground state, in which further relaxation can lead to either the trans or cis geometries. However, the S1 /S0 conical intersection seam also extends to planar geometries, so this reaction path is also accessible for rotation-constrained systems. Our results explain the experimental observations satisfactorily.

Nuclear spatial delocalization silences electron density oscillations in 2-phenyl-ethyl-amine (PEA) and 2-phenylethyl-N,N-dimethylamine (PENNA) cations.

We simulate electron dynamics following ionization in 2-phenyl-ethyl-amine and 2-phenylethyl-N,N-dimethylamine as examples of systems where 3 coupled cationic states are involved. We study two nuclear effects on electron dynamics: (i) coupled electron-nuclear motion and (ii) nuclear spatial delocalization as a result of the zero-point energy in the neutral molecule. Within the Ehrenfest approximation, our calculations show that the coherent electron dynamics in these molecules is not lost as a result of coupled electron-nuclear motion. In contrast, as a result of nuclear spatial delocalization, dephasing of the oscillations occurs on a time scale of only a few fs, long before any significant nuclear motion can occur. The results have been rationalized using a semi-quantitative model based upon the gradients of the potential energy surfaces.

Geometric Rotation of the Nuclear Gradient at a Conical Intersection: Extension to Complex Rotation of Diabatic States.

Nonadiabatic dynamics in the vicinity of conical intersections is of essential importance in photochemistry. It is well known that if the branching space is represented in polar coordinates, then for a geometry represented by angle θ, the corresponding adiabatic states are obtained from the diabatic states with the mixing angle θ/2. In an equivalent way, one can study the relation between the real rotation of diabatic states and the resulting nuclear gradient. In this work, we extend the concept to allow a complex rotation of diabatic states to form a nonstationary superposition of electronic states. Our main result is that this leads to an elliptical transformation of the effective potential energy surfaces; i.e., the magnitude of the initial nuclear gradient changes as well as its direction. We fully explore gradient changes that result from varying both θ and ϕ (the complex rotation angle) as a way of electronically controlling nuclear motion, through Ehrenfest dynamics simulations for benzene cation.

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.

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.

Non-adiabatic dynamics close to conical intersections and the surface hopping perspective.

Conical intersections play a major role in the current understanding of electronic de-excitation in polyatomic molecules, and thus in the description of photochemistry and photophysics of molecular systems. This article reviews aspects of the basic theory underlying the description of non-adiabatic transitions at conical intersections, with particular emphasis on the important case when the dynamics of the nuclei are treated classically. Within this classical nuclear motion framework, the main aspects of the surface hopping methodology in the conical intersection context are presented. The emerging picture from this treatment is that of electronic transitions around conical intersections dominated by the interplay of the nuclear velocity and the derivative non-adiabatic coupling vector field.