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Nitroaromatic compounds are found in brown carbon aerosols emitted to the Earth's atmosphere by biomass burning, and are important organic chromophores for the absorption of solar radiation. Here, transient absorption spectroscopy spanning 100 fs-8 μs is used to explore the pH-dependent photochemical pathways for aqueous solutions of p -nitrophenol, chosen as a representative nitroaromatic compound. Broadband ultrafast UV-visible and infrared probes are used to characterize the excited states and intermediate species involved in the multistep photochemistry, and to determine their lifetimes under different pH conditions. The assignment of absorption bands, and the dynamical interpretation of our experimental measurements are supported by computational calculations. After 320 nm photoexcitation to the first bright state, which has 1 ππ* character in the Franck-Condon region, and ultrafast (∼200 fs) structural relaxation in the adiabatic S 1 state to a region with 1 nπ* electronic character, the S 1 p -nitrophenol population decays on a time scale of ∼12 ps. This decay involves competition between direct internal conversion to the S 0 state (∼40%) and rapid intersystem crossing to the triplet manifold (∼60%). Population in the T 1 -state decays by excited-state proton transfer (ESPT) to the surrounding water and relaxation of the resulting triplet-state p -nitrophenolate anion to its S 0 electronic ground state in ∼5 ns. Reprotonation of the S 0 -state p -nitrophenolate anion recovers p -nitrophenol in its electronic ground state. Overall recovery of the S 0 state of aqueous p -nitrophenol via these competing pathways is close to 100% efficient. The experimental observations help to explain why nitroaromatic compounds such as p -nitrophenol resist photo-oxidative degradation in the environment.

Thiophene is a prototype for the excited state photophysics that lies at the heart of many technologies within the field of organic electronics. Here, we report a multiphoton ionisation photoelectron imaging study of gas-phase thiophene using a range of photon energies to excite transitions from the ground electronic state to the first two electronically excited singlet states, from the onset of absorption to the absorption maximum. Analysis of the photoelectron spectra and angular distributions reveal features arising from direct photoionisation from the ground electronic state, and resonance-enhanced photoionisation via the electronically excited singlet states. The first two ionisation energies from the ground electronic state were confirmed to be 8.8 eV (adiabatic) and 9.6 eV (vertical). The ionisation energies from the first two electronically excited singlet states were found to be 3.7 eV (adiabatic) and 4.4 eV (vertical).

The static gas-phase ("simple") ultraviolet absorption spectrum of thiophene is investigated using a combination of a vibronic coupling model Hamiltonian with multi-configuration time-dependent Hartree quantum dynamics simulations. The model includes five states and all 21 vibrations, with potential surfaces calculated at the complete active space with second-order perturbation level of theory. The model includes terms up to eighth-order to describe the diabatic potentials. The resulting spectrum is in excellent agreement with the experimentally measured spectrum of Holland et al. [Phys. Chem. Chem. Phys. 16, 21629 (2014)]. The, until now not understood, spectral features are assigned, with a combination of strongly coupled vibrations and vibronic coupling between the states giving rise to a progression of triplets on the rising edge of the broad spectrum. The analysis of the underlying dynamics indicates that population transfer between all states takes place on a sub-100 fs timescale, with ring-opening occurring at longer times. The model thus provides a starting point for further investigations into the complicated photo-excited dynamics of this key hetero-aromatic molecule., (© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).)

A comprehensive computational study of the gas-phase photodissociation dynamics of methanol is presented. Using a multiconfigurational active space based method (RASSCF) to obtain multidimensional potential energy surfaces (PESs) on-the-fly, direct quantum dynamics simulations were run using the variational multi-configurational Gaussian method (DD-vMCG). Different initial excitation energies were simulated to investigate the dependence of the branching ratios on the electronic state being populated. A detailed mechanistic explanation is provided for the observed differences with respect to the excitation energy. Population of the lowest lying excited state of methanol leads to rapid hydroxyl hydrogen loss as the main dissociation channel. This is rationalized by the strongly dissociative nature of the PES cut along the O-H stretching coordinate, confirmed by the broad feature in the absorption spectrum. In contrast, more energetic excitations lead mainly to C-O bond breaking. Again, analysis of the diabatic surfaces offers a clear explanation in terms of the nature of the electronic states involved and the coupling between them. The type of calculations presented, as well as the subsequent analysis of the results, should be seen as a general workflow for the modeling of photochemical reactions.

We report a protocol for the implementation of "reaction path following" from a transition state through a conical intersection, including both the path curvature induced by the derivative coupling and the corresponding induced electronic coherences. This protocol focuses on the "central" Gaussian wavepacket (initially unexcited) in the quantum Ehrenfest (QuEh) method. Like the reaction path following, the normal mode corresponding to the imaginary frequency at the transition state is given an initial momentum. The protocol is applied to the "channel 3" radiationless decay of benzene. We also demonstrate that one can enhance the effect of the derivative coupling and the electronic coherence with an IR pulse.

Quantum dynamics simulations are becoming a standard tool for simulating photo-excited molecular systems involving a manifold of coupled states, known as non-adiabatic dynamics. While these simulations have had many successes in explaining experiments and giving details of non-adiabatic transitions, the question remains as to their predictive power. In this work, we present a set of quantum dynamics simulations on cyclobutanone using both grid-based multi-configuration time-dependent Hartree and direct dynamics variational multi-configuration Gaussian methods. The former used a parameterized vibronic coupling model Hamiltonian, and the latter generated the potential energy surfaces on the fly. The results give a picture of the non-adiabatic behavior of this molecule and were used to calculate the signal from a gas-phase ultrafast electron diffraction (GUED) experiment. Corresponding experimental results will be obtained and presented at a later stage for comparison to test the predictive power of the methods. The results show that over the first 500 fs after photo-excitation to the S2 state, cyclobutanone relaxes quickly to the S1 state, but only a small population relaxes further to the S0 state. No significant transfer of population to the triplet manifold is found. It is predicted that the GUED experiments over this time scale will see signals related mostly to the C-O stretch motion and elongation of the molecular ring along the C-C-O axis., (© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).)

Quantum dynamics simulations are becoming a powerful tool for understanding photo-excited molecules. Their poor scaling, however, means that it is hard to study molecules with more than a few atoms accurately, and a major challenge at the moment is the inclusion of the molecular environment. Here, we present a proof of principle for a way to break the two bottlenecks preventing large but accurate simulations. First, the problem of providing the potential energy surfaces for a general system is addressed by parameterizing a standard force field to reproduce the potential surfaces of the molecule's excited-states, including the all-important vibronic coupling. While not shown here, this would trivially enable the use of an explicit solvent. Second, to help the scaling of the nuclear dynamics propagation, a hierarchy of approximations is introduced to the variational multi-configurational Gaussian method that retains the variational quantum wavepacket description of the key quantum degrees of freedom and uses classical trajectories for the remaining in a quantum mechanics/molecular mechanics like approach. The method is referred to as force field quantum dynamics (FF-QD), and a two-state ππ*/nπ* model of uracil, excited to its lowest bright ππ* state, is used as a test case., (© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).)

Nitroaromatic compounds are major constituents of the brown carbon aerosol particles in the troposphere that absorb near-ultraviolet (UV) and visible solar radiation and have a profound effect on the Earth's climate. The primary sources of brown carbon include biomass burning, forest fires, and residential burning of biofuels, and an important secondary source is photochemistry in aqueous cloud and fog droplets. Nitrobenzene is the smallest nitroaromatic molecule and a model for the photochemical behavior of larger nitroaromatic compounds. Despite the obvious importance of its droplet photochemistry to the atmospheric environment, there have not been any detailed studies of the ultrafast photochemical dynamics of nitrobenzene in aqueous solution. Here, we combine femtosecond transient absorption spectroscopy, time-resolved infrared spectroscopy, and quantum chemistry calculations to investigate the primary steps following the near-UV (λ ≥ 340 nm) photoexcitation of aqueous nitrobenzene. To understand the role of the surrounding water molecules in the photochemical dynamics of nitrobenzene, we compare the results of these investigations with analogous measurements in solutions of methanol, acetonitrile, and cyclohexane. We find that vibrational energy transfer to the aqueous environment quenches internal excitation, and therefore, unlike the gas phase, we do not observe any evidence for formation of photoproducts on timescales up to 500 ns. We also find that hydrogen bonding between nitrobenzene and surrounding water molecules slows the S 1 /S 0 internal conversion process.

Despite the fact that NO 2 is considered to be the main photoproduct of nitrobenzene photochemistry, no mechanism has ever been proposed to rationalize its formation. NO photorelease is instead a more studied process, probably due to its application in the drug delivery sector and the study of roaming mechanisms. In this contribution, a photoinduced mechanism accounting for the formation of NO 2 in nitrobenzene is theorized based on CASPT2, CASSCF, and DFT electronic structure calculations and CASSCF classical dynamics. A triplet nπ* state is shown to evolve toward C-NO 2 dissociation, being, in fact, the only low-lying excited state favoring such a deformation. Along the triplet dissociation path, the possibility to decay to the singlet ground state results in the frustration of the dissociation and in the recombination of the fragments, either back to the nitro or the nitrite isomer. The thermal decomposition of the latter to NO constitutes globally a roaming mechanism of NO formation.

Photoexcitation of green fluorescent protein (GFP) triggers long-range proton transfer along a "wire" of neighboring protein residues, which, in turn, activates its characteristic green fluorescence. The GFP proton wire is one of the simplest, most well-characterized models of biological proton transfer but remains challenging to simulate due to the sensitivity of its energetics to the surrounding protein conformation and the possibility of non-classical behavior associated with the movement of lightweight protons. Using a direct dynamics variational multiconfigurational Gaussian wavepacket method to provide a fully quantum description of both electrons and nuclei, we explore the mechanism of excited state proton transfer in a high-dimensional model of the GFP chromophore cluster over the first two picoseconds following excitation. During our simulation, we observe the sequential starts of two of the three proton transfers along the wire, confirming the predictions of previous studies that the overall process starts from the end of the wire furthest from the fluorescent chromophore and proceeds in a concerted but asynchronous manner. Furthermore, by comparing the full quantum dynamics to a set of classical trajectories, we provide unambiguous evidence that tunneling plays a critical role in facilitating the leading proton transfer., (© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).)

The phenol molecule is a prototype for non-adiabatic dynamics and the excited-state photochemistry of biomolecules. In this article, we report a joint theoretical and experimental investigation on the resonance enhanced multiphoton ionisation photoelectron (REMPI) spectra of the two lowest ionisation bands of phenol. The focus is on the theoretical interpretation of the measured spectra using quantum dynamics simulations. These were performed by numerically solving the time-dependent Schrödinger equation using the multi-layer variant of the multiconfiguration time-dependent Hartree algorithm together with a vibronic coupling Hamiltonian model. The ionising laser pulse is modelled explicitly within the ionisation continuum model to simulate experimental femtosecond 1+1 REMPI photoelectron spectra. These measured spectra are sensitive to very short lived electronically excited states, providing a rigorous benchmark for our theoretical methods. The match between experiment and theory allows for an interpretation of the features of the spectra at different wavelengths and shows that there are features due to both 'direct' and 'indirect' ionisation, resulting from non-resonant and resonant excitation by the pump pulse.

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.

Nitroaromatic compounds can photorelease nitric oxide after UV absorption. The efficiency of the photoreaction depends on the molecular structure, and two features have been pointed out as particularly important for the yield of the process: the presence of methyl groups at the ortho position with respect to the nitro group and the degree of conjugation of the molecule. In this paper, we provide a theoretical characterization at the CASPT2//CASSCF (complete active space second-order perturbation theory//complete active space self-consistent field) level of theory of the photorelease of NO for four molecules derived from nitrobenzene through the addition of ortho methyl groups and/or the elongation of the conjugation. Our previously described mechanism obtained for the photorelease of NO in nitrobenzene has been adopted as a model for the process. According to this model, the process proceeds through a reactive singlet-triplet crossing (STC) region that the system can reach from the triplet 3 (π O π*) minimum. The energy barrier that must be surmounted in order to populate the reactive STC can be associated with the efficiency of the photoreaction. Here, the obtained results display clear differences in the efficiency of the photoreaction in the studied systems and can be correlated with experimental results. Thus, the model proves its ability to highlight the differences in the photoreaction efficiency for the nitroaromatic compounds studied here.

The creation and dynamical fate of a coherent superposition of electronic states generated in a polyatomic molecule by broadband ionization with extreme ultraviolet pulses is studied using the multiconfiguration time-dependent Hartree method together with an ionization continuum model Hamiltonian. The electronic coherence between the hole states usually lasts until the nuclear dynamics leads to decoherence. A key goal of attosecond science is to control the electronic motion and design laser control schemes to retain this coherence for longer timescales. Here, we investigate this possibility using time-delayed pulses and show how this opens up the prospect of coherent control of charge migration phenomenon.

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.

Three methods for non-adiabatic dynamics are compared to highlight their capabilities. Multi-configurational time-dependent Hartree is a full grid-based solution to the time-dependent Schrödinger equation, variational multi-configurational Gaussian (vMCG) uses a less flexible but unrestricted Gaussian wavepacket basis, and trajectory surface hopping (TSH) replaces the nuclear wavepacket with a swarm of classical trajectories. Calculations with all methods using a model Hamiltonian were performed. The vMCG and TSH were also then run in a direct dynamics mode, with the potential energy surfaces calculated on-the-fly using quantum chemistry calculations. All dynamics calculations used the Quantics package, with the TSH calculations using a new interface to a surface hopping code. A novel approach to calculate adiabatic populations from grid-based quantum dynamics using a time-dependent discrete variable representation is presented, allowing a proper comparison of methods. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

In this work, we report a complete analysis by theoretical and spectroscopic methods of the short-time behaviour of 4-(dimethylamino)benzonitrile (DMABN) in the gas phase as well as in cyclohexane, tetrahydrofuran, acetonitrile, and water solution, after excitation to the La state. The spectroscopic properties of DMABN were investigated experimentally using UV absorption and fluorescence emission spectroscopy. The computational study was developed at different electronic structure levels and using the Polarisable Continuum Model (PCM) and explicit solvent molecules to reproduce the solvent environment. Additionally, excited state quantum dynamics simulations in the diabatic picture using the direct dynamics variational multiconfigurational Gaussian (DD-vMCG) method were performed, the largest quantum dynamics "on-the-fly" simulations performed with this method until now. The comparison with fully converged multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) dynamics on parametrised linear vibronic coupling (LVC) potentials show very similar population decays and evolution of the nuclear wavepacket. The ring C=C stretching and three methyl tilting modes are identified as the responsible motions for the internal conversion from the La to the Lb states. No major differences are observed in the ultrafast initial decay in different solvents, but we show that this effect depends strongly on the level of electronic structure used.

Gaussian wavepacket methods are becoming popular for the investigation of nonadiabatic molecular dynamics. In the present work, a recently developed efficient algorithm for the Direct Dynamics variational Multi-Configurational Gaussian (DD-vMCG) method has been used to describe the multidimensional photodissociation dynamics of phenol including all degrees of freedom. Full-dimensional quantum dynamic calculations including for the first time six electronic states ( 1 ππ, 1 1 ππ*, 1 1 πσ*, 2 1 πσ*, 2 1 ππ*, 3 1 ππ*), along with a comparison to an existing analytical 4-state model for the potential energy surfaces are presented. Including the fifth singlet excited state is shown to have a significant effect on the nonadiabatic photodissociation of phenol to the phenoxyl radical and hydrogen atom. State population and flux analysis from the DD-vMCG simulations of phenol provided further insights into the decay mechanism, confirming the idea of rapid relaxation to the ground state through the 1 ππ/1 1 πσ* conical intersection.

The primary event occurring during the E-to-Z photoisomerization reaction of retinal protonated Schiff base (rPSB) is single-to-double bond inversion. In this work we examine the nuclear dynamics that occurs when the initial excited state is a superposition of the S 1 and S 2 electronic excited states that might be created in a laser experiment. The nuclear dynamics is dominated by double bond inversion that is parallel to the derivative coupling vector of S 1 and S 2 . Thus, the molecule behaves as if it were at a conical intersection even if the states are nondegenerate.

We report on first applications of the Multi-Layer Gaussian-based Multi-Configuration Time-Dependent Hartree (ML-GMCTDH) method [Römer et al., J. Chem. Phys. 138, 064106 (2013)] beyond its basic two-layer variant. The ML-GMCTDH scheme provides an embedding of a variationally evolving Gaussian wavepacket basis into a hierarchical tensor representation of the wavefunction. A first-principles parameterized model Hamiltonian for ultrafast non-adiabatic dynamics in an oligothiophene-fullerene charge transfer complex is employed, relying on a two-state linear vibronic coupling model that combines a distribution of tuning type modes with an intermolecular coordinate that also modulates the electronic coupling. Efficient ML-GMCTDH simulations are carried out for up to 300 vibrational modes using an implementation within the QUANTICS program. Excellent agreement with reference ML-MCTDH calculations is obtained.

The study of coupled electron-nuclear dynamics driven by coherent superpositions of electronic states is now possible in attosecond science experiments. The objective is to understand the electronic control of chemical reactivity. In this work we report coherent 8-state non-adiabatic electron-nuclear dynamics simulations of the benzene radical cation. The computations were inspired by the extreme ultraviolet (XUV) experimental results in which all 8 electronic states were prepared with significant population. Our objective was to study the nuclear dynamics using various bespoke coherent electronic state superpositions as initial conditions in the Quantum-Ehrenfest method. The original XUV measurements were supported by Multi-configuration time-dependent Hartree (MCTDH) simulations, which suggested a model of successive passage through conical intersections. The present computations support a complementary model where non-adiabatic events are seen far from a conical intersection and are controlled by electron dynamics involving non-adjacent adiabatic states. It proves to be possible to identify two superpositions that can be linked with two possible fragmentation paths., (© 2021. The Author(s).)

The Direct Dynamics variational Multi-Configurational Gaussian (DD-vMCG) method provides a fully quantum mechanical solution to the time-dependent Schrödinger equation for the time evolution of nuclei with potential surfaces calculated on-the-fly using a quantum chemistry program. Initial studies have shown its potential for flexible and accurate simulations of non-adiabatic excited-state molecular dynamics. In this paper, we present developments to the DD-vMCG algorithm that improve both its accuracy and efficiency. First, a new, efficient parallel algorithm to control the DD-vMCG database of quantum chemistry points is presented along with improvements to the Shepard interpolation scheme. Second, the use of symmetry in describing the potential surfaces is introduced along with a new phase convention in the propagation diabatization. Benchmark calculations on the allene radical cation including all degrees of freedom then show that the new scheme is able to produce a consistent non-adiabatic coupling vector field. This new DD-vMCG version thus opens the route for effectively and accurately treating complex chemical systems using quantum dynamics simulations.

The first two excitation bands below 7 eV in the electronic absorption spectrum of maleimide are investigated using a model Hamiltonian including four low-lying singlet excited states within the manifold of 24 vibrational modes. The role of non-adiabatic effects is studied and shines light on both the broad, inter-state coupling-dominated spectral band as well as the fine-structured, not-so-strong coupled band. Calculations have been performed using the Multiconfigurational Time-Dependent Hartree (MCTDH) wavepacket propagation method as well as its multilayer version (ML-MCTDH) using a quadratic vibronic coupling (QVC) Hamiltonian model where parameters are obtained from fitting adiabatic potential energy surfaces computed by ab initio methods. The quantum dynamics calculations provide information on the relaxation dynamics and the vibrational modes involved. Already with a low-order vibronic coupling model and only a few modes being considered, a quantitative agreement with the experimental spectrum is obtained. However, it is found that all modes need to be considered to get a full picture of the photo-excited relaxation dynamics of this molecule.

Firefly bioluminescence is exploited widely in imaging in the biochemical and biomedical sciences; however, our fundamental understanding of the electronic structure and relaxation processes of the oxyluciferin that emits the light is still rudimentary. Here, we employ photoelectron spectroscopy and quantum chemistry calculations to investigate the electronic structure and relaxation of a series of model oxyluciferin anions. We find that changing the deprotonation site has a dramatic influence on the relaxation pathway following photoexcitation of higher lying electronically excited states. The keto form of the oxyluciferin anion is found to undergo internal conversion to the fluorescent S 1 state, whereas we find evidence to suggest that the enol and enolate forms undergo internal conversion to a dipole bound state, possibly via the fluorescent S 1 state. Partially resolved vibrational structure points towards the involvement of out-of-plane torsional motions in internal conversion to the dipole bound state, emphasising the combined electronic and structural role that the microenvironment plays in controlling the electronic relaxation pathway in the enzyme.

At low excitation energies nitrobenzene photoreleases NO with low translational and rotational energy, while at higher excitation energies NO is photoreleased with both low and high translational and rotational energy. The fast products are formed through a singlet-triplet crossing (STC) region featuring an oxaziridine ring, while a ground state roaming mechanism was suggested to produce the slow molecules. Computing translational and rotational energies performing CASSCF classical dynamics, we here prove how the same oxaziridine STC can account for both fast and slow photoproducts, depending on the region of the seam through which the ground state is populated. A roaming-type STC/CI has also been characterized, from which slow NO molecules can also be formed through a roaming photodegradation mechanism, here in the excited state. The higher accessibility of the oxaziridine STC mechanism, 1.53 eV lower in energy than the roaming path, questions the contribution of roaming in nitrobenzene NO photoproduction.

We describe the implementation of a laser control pulse in the quantum-Ehrenfest method, a molecular quantum dynamics method that solves the time-dependent Schrödinger equation for both electrons and nuclei. The oscillating electric field-dipole interaction is incorporated directly in the one-electron Hamiltonian of the electronic structure part of the algorithm. We then use the coupled electron-nuclear dynamics of the π-system in the allene radical cation (•CH 2 =C=CH 2 ) + as a simple model of a pump-control experiment. We start (pump) with a two-state superposition of two cationic states. The resulting electron dynamics corresponds to the rapid oscillation of the unpaired electron between the two terminal methylenes. This electron dynamics is, in turn, coupled to the torsional motion of the terminal methylenes. There is a conical intersection at 90° twist, where the electron dynamics collapses because the adiabatic states become degenerate. After passing the conical intersection, the electron dynamics revives. The IR pulse (control) in our simulations is timed to have its maximum at the conical intersection. Our simulations show that the effect of the (control) pulse is to change the electron dynamics at the conical intersection and, as a consequence, the concomitant nuclear dynamics, which is dominated by the change in the torsional angle.

Solving the time-dependent Schrödinger equation (TDSE) for large molecular systems is a complicated task due to the inherent exponential scaling of the problem. One of the most successful and versatile methods for obtaining numerically converged solutions for small to medium-sized systems is multiconfiguration time-dependent Hartree (MCTDH). In a recent publication [ J. Chem. Phys. 2020 , 152 , 084101] we introduced a hierarchy of approximations to the MCTDH method which mitigate the exponential scaling by truncating the configuration space based on a maximum excitation level w.r.t. a selected reference configuration. The MCTDH[ n ] methods are able to treat large systems, but the single-reference Ansatz is not optimal in cases where one (or a few) degrees of freedom are special. Examples could be double-well systems, intramolecular vibrational-energy redistribution (IVR) calculations, or nonadiabatic dynamics. In this work we introduce a multireference (MR) extension to the MCTDH[ n ] methods where selected higher-order excitations for the special degrees of freedom can be introduced in a simple but flexible way. The resulting MR-MCTDH[ n ] methods allow for, for example, treating nonadiabatic dynamics within the single-set formalism with the wave packets on each electronic surface described using the same level of approximation. Example calculations are performed on formyl fluoride (IVR), salicylaldimine (double well), and pyrazine (nonadiabatic dynamics). The results show that fast convergence is achieved by extending the configuration space in the special modes that govern the quantum dynamics.

The low quantum yield of photoformation of cyclobutane pyrimidine dimers and pyrimidine-pyrimidone (6-4) adducts in DNA bases is usually associated with the presence of more favorable nonreactive decay paths and with the unlikeliness of exciting the system in a favorable conformation. Here, we prove that the ability of the reactive conical intersection to bring the system either back to the absorbing conformation or to the photoproduct must be considered as a fundamental factor in the low quantum yields of the mentioned photodamage. In support of the proposed model, the one order of magnitude difference in the quantum yield of formation of the cyclobutane thymine dimer with respect to the thymine-thymine (6-4) adduct is rationalized here by comparing the reactive ability of the seam of intersections leading respectively to the cyclobutane thymine dimer and the oxetane precursor of the thymine-thymine (6-4) adduct at the CASPT2 level of theory.

The multiconfiguration time-dependent Hartree (MCTDH) method is a powerful method for solving the time-dependent Schrödinger equation in quantum molecular dynamics. It is, however, hampered by the so-called curse of dimensionality which results in exponential scaling with respect to the number of degrees of freedom in the system and, thus, limits its applicability to small- and medium-sized molecules. To avoid this scaling, we derive equations of motion for a series of truncated MCTDH methods using a many-mode second-quantization formulation where the configuration space is restricted based on mode-combination levels as also done in the vibrational configuration interaction and vibrational coupled cluster methods for solving the time-independent Schrödinger equation. The full MCTDH wave function is invariant with respect to the choice of constraint (or gauge) operators, but restricting the configuration space removes this invariance. We, thus, analyze the remaining redundancies and derive equations for variationally optimizing the non-redundant matrix elements of the constraint operators. As an alternative, we also present a constraint that keeps the density matrices block diagonal during the propagation and the two choices are compared. Example calculations are performed on formyl fluoride and a series of high-dimensional Henon-Heiles potentials. The results show that the MCTDH[n] methods can be applied to large systems and that an optimal choice of constraint operators is key to obtaining the correct physical behavior of the wave function.

Following on from previous experimental and theoretical work [Neville et al., Nat. Commun. 7, 11357 (2016)], we report the results of a combined electronic structure theory and quantum dynamics study of the excited state dynamics of the pyrrole dimer following excitation to its first two excited states. Employing an exciton-based analysis of the Ã(π3s/σ * ) and B̃(π3s/3p/σ * ) states, we identify an excited-state electron transfer pathway involving the coupling of the Ã(π3s/σ * ) and B̃(π3s/3p/σ * ) states and driven by N-H dissociation in the B̃(π3s/3p/σ * ) state. This electron transfer mechanism is found to be mediated by vibronic coupling of the B̃ state, which has a mixed π3s/3p Rydberg character at the Franck-Condon point, to a high-lying charge transfer state of the πσ * character by the N-H stretch coordinate. Motivated by these results, quantum dynamics simulations of the excited-state dynamics of the pyrrole dimer are performed using the multiconfigurational time-dependent Hartree method and a newly developed model Hamiltonian. It is predicted that the newly identified electron transfer pathway will be open following excitation to both the Ã(π3s/σ * ) and B̃(π3s/3p/σ * ) states and may be the dominant relaxation pathway in the latter case.

In a seminal work the photodissociation of IBr has been controlled using a strong non-resonant IR pulse [Sussman et al., Science, 2006, 314, 274], changing the branching ratio of products in different final states via the relative timing of pump and control pulses. In this paper, we revisit the control of this molecule. Potential surfaces for the complete spin-orbit manifold of IBr states dissociating into the ground and first excited states of the constituent atoms have been calculated at the multi-reference configuration interaction (MRCI) level of theory as a function of applied field. Both the strength and direction of field have been taken into account and it is seen how the avoided crossing between the states thought to be key in the control mechanism shift as a function of field strength. These surfaces will enable full calculations of the molecule in the pump-control field. Preliminary dynamics calculations with the field placed along the molecular axis show that a Hamiltonian including all 36-states agrees with earlier results and is able to model the basic features of the control. However, just like earlier results, this restricted model is not able to reproduce the timescale of the control.

The photophysics of nitroaromatic compounds is characterized by an ultrafast decay into the triplet manifold and by significant triplet quantum yields. The latter quantity changes drastically depending on the system, as shown for 2-nitronaphthalene, 1-nitronaphthalene, and 2-methyl-1-nitronaphthalene, whose triplet quantum yields have been previously measured to be 0.93 ± 0.15, 0.64 ± 0.12, and 0.33 ± 0.05, respectively (J. Phys. Chem. A, 2013, 117, 14100). In this study, we rationalize the reported trend of the triplet quantum yield on the basis of the different abilities of the excited S 1 state to reach a previously unreported conical intersection with the ground state. This path is in competition with the path leading to the triplet state, which appears to be equally favorable in the three systems. The energy barriers from the S 1 CASPT2//CASSCF minima to a CASPT2 minimum-energy-crossing-point of the S 1 /S 0 conical intersection have been computed to follow the same trend as the triplet quantum yields of the nitroaromatic systems under analysis. The path has also been characterized for nitrobenzene; an energy barrier was obtained that nicely fits the derived model and is in agreement with its triplet quantum yield value (>0.8). The ability of the present model to not only rationalize the experimental data of a single molecule but also to reproduce a trend for four slightly different systems demonstrates its reliability.

Quantum dynamics simulations are an important tool to evaluate molecular behaviour including the, often key, quantum nature of the system. In this paper we present an algorithm that is able to simulate the time evolution of a molecule after photo-excitation into a manifold of states. The direct dynamics variational multi-configurational Gaussian (DD-vMCG) method circumvents the computational bottleneck problems of traditional grid-based methods by computing the potential energy functions on-the-fly, i.e. only where required. Unlike other commonly used direct dynamics methods, DD-vMCG is fully quantum mechanical. Here, the method is combined with a novel on-the-fly diabatisation scheme to simulate the short-time dynamics of the key molecule formamide and its acid analogue formimidic acid. This is a challenging test system due to the nature and large number of excited states, and eight coupled states are included in the calculations. It is shown that the method is able to provide unbiased information on the product channels open after excitation at different energies and demonstrates the potential to be a practical scheme, limited mainly by the quality of the quantum chemistry used to describe the excited states.

An algorithm is described for quantum dynamics where an Ehrenfest potential is combined with fully quantum nuclear motion (Quantum-Ehrenfest, Qu-Eh). The method is related to the single-set variational multi-configuration Gaussian approach (vMCG) but has the advantage that only a single quantum chemistry computation is required at each time step since there is only a single time-dependent potential surface. Also shown is the close relationship to the "exact factorization method." The quantum Ehrenfest method is compared with vMCG for study of electron dynamics in a modified bismethylene-adamantane cation system. Illustrative examples of electron-nuclear dynamics are presented for a distorted allene system and for HCCI + where one has a degenerate Π system.

Water is the predominant medium for chemistry and biology, yet its role in determining how molecules respond to ultraviolet light is not well understood at the molecular level. Here, we combine gas-phase and liquid-microjet photoelectron spectroscopy to investigate how an aqueous environment influences the electronic structure and relaxation dynamics of phenol, a ubiquitous motif in many biologically relevant chromophores. The vertical ionization energies of electronically excited states are important quantities that govern the rates of charge-transfer reactions, and, in phenol, the vertical ionization energy of the first electronically excited state is found to be lowered by around 0.8 eV in aqueous solution. The initial relaxation dynamics following photoexcitation with ultraviolet light appear to be remarkably similar in the gas-phase and aqueous solution; however, in aqueous solution, we find evidence to suggest that solvated electrons are formed on an ultrafast time scale following photoexcitation just above the conical intersection between the first two excited electronic states.

Time-resolved photoelectron spectroscopy measurements combined with quantum chemistry and dynamics calculations allow unprecedented insight into the electronic relaxation mechanisms of photoexcited molecules in the gas-phase. In this Tutorial Review, we explain the essential concepts linking photoelectron spectroscopy measurements with electronic structure and how key features on the potential energy landscape are identified using quantum chemistry and quantum dynamics calculations. We illustrate how time-resolved photoelectron spectroscopy and theory work together using examples ranging in complexity from the prototypical organic molecule benzene to a pyrrole dimer bound by a weak N-Hπ interaction and the green fluorescent protein chromophore.

A ten singlet state vibronic coupling Hamiltonian was constructed describing the seven internal coordinates of acetylene. A Σ symmetry-adapted polynomial expansion of the nuclear coordinates over diabatic elements was used to fit adiabatic energies obtained from ab initio calculations. The fitted vibronic Hamiltonian was subsequently used to model vibrationally mediated photo-dissociation (VMD) experiments. The model suggests that some control over dissociation channels might be achieved by choosing different ranges of pre-excitation and UV-excitation energies.

The electronic structure and excited-state dynamics of the ubiquitous bioluminescent probe luciferin and its furthest red-shifted analogue infraluciferin have been investigated using photoelectron spectroscopy and quantum chemistry calculations. In our electrospray ionization source, the deprotonated anions are formed predominantly in their phenolate forms and are directly relevant to studies of luciferin and infraluciferin as models for their unstable oxyluciferin and oxyinfraluciferin emitters. Following photoexcitation in the range 357-230 nm, we find that internal conversion from high-lying excited states to the S 1 (1ππ*) state competes efficiently with electron detachment. In infraluciferin, we find that decarboxylation also competes with direct electron detachment and internal conversion. This detailed spectroscopic and computational study defines the electronic structure and electronic relaxation processes of luciferin and infraluciferin and will inform the design of new bioluminescent systems and applications.

Nitrobenzene is the simplest nitroaromatic compound and yet is characterized by a challenging and rich photophysics and photochemistry. In the present contribution, the main decay paths undertaken by the system after UV absorption from both the brightest 1 (L a ππ*) and the lowest 1 (n A π*) singlet excited states have been characterized by means of CASPT2//CASSCF computations. The obtained results match with the main photophysical properties experimentally reported: the lack of fluorescence and phosphorescence emission is justified by the presence of accessible conical intersections and intersystem crossing regions between, respectively, the 1 (n A π*) and 3 (n A π*) states and the ground state, while the high triplet quantum yield is attributable to the strong coupling between the 1 (n A π*) and 3 (π O π*) states along the main decay path of the former. Two not previously reported singlet-triplet crossing regions, termed (T1/S0) stc-NO and (T1/S0) stc-ep , have been here documented, from which the ground state can decay toward NO and phenoxy radical production and toward the formation of an epoxide ring structure, respectively. A possible mechanism leading to the photoisomerization of the nitro into the nitrite group, believed to be a key step in the photodegradation of nitrobenzene, has been proposed, based on the geometrical deformation recorded along the decay path leading from the 1 (n A π*) state back to the original ground state through a conical intersection characterized by a significant shortening of the carbon-nitrogen bond.

Green fluorescent protein (GFP) continues to play an important role in the biological and biochemical sciences as an efficient fluorescent probe and is also known to undergo light-induced redox transformations. Here, we employ photoelectron spectroscopy and quantum chemistry calculations to investigate how the phenoxide moiety controls the competition between electron emission and internal conversion in the isolated GFP chromophore anion, following photoexcitation with ultraviolet light in the range 400-230 nm. We find that moving the phenoxide group from the para position to the ortho position enhances internal conversion back to the ground electronic state but that adding an additional OH group to the para chromophore, at the ortho position, impedes internal conversion. Guided by quantum chemistry calculations, we interpret these observations in terms of torsions around the C-C-C bridge being enhanced by electrostatic repulsions or impeded by the formation of a hydrogen-bonded seven-membered ring. We also find that moving the phenoxide group from the para position to the ortho position reduces the energy required for detachment processes, whereas adding an additional OH group to the para chromophore at the ortho position increases the energy required for detachment processes. These results have potential applications in tuning light-induced redox processes of this biologically and technologically important fluorescent protein.

Photoinduced electron transfer is central to many biological processes and technological applications, such as the harvesting of solar energy and molecular electronics. The electron donor and acceptor units involved in electron transfer are often held in place by covalent bonds, π-π interactions or hydrogen bonds. Here, using time-resolved photoelectron spectroscopy and ab initio calculations, we reveal the existence of a new, low-energy, photoinduced electron-transfer mechanism in molecules held together by an NH⋯π bond. Specifically, we capture the electron-transfer process in a pyrrole dimer, from the excited π-system of the donor pyrrole to a Rydberg orbital localized on the N-atom of the acceptor pyrrole, mediated by an N-H stretch on the acceptor molecule. The resulting charge-transfer state is surprisingly long lived and leads to efficient electronic relaxation. We propose that this relaxation pathway plays an important role in biological and technological systems containing the pyrrole building block.

The dynamics of N-methylpyrrole following excitation at wavelengths in the range 241.5-217.0 nm were studied using a combination of time-resolved photoelectron spectroscopy (TRPES), ab initio quantum dynamics calculations using the multi-layer multi-configurational time-dependent Hartree method, as well as high-level photoionization cross section calculations. Excitation at 241.5 and 236.2 nm results in population of the A2(πσ(∗)) state, in agreement with previous studies. Excitation at 217.0 nm prepares the previously neglected B1(π3py) Rydberg state, followed by prompt internal conversion to the A2(πσ(∗)) state. In contrast with the photoinduced dynamics of pyrrole, the lifetime of the wavepacket in the A2(πσ(∗)) state was found to vary with excitation wavelength, decreasing by one order of magnitude upon tuning from 241.5 nm to 236.2 nm and by more than three orders of magnitude when excited at 217.0 nm. The order of magnitude difference in lifetimes measured at the longer excitation wavelengths is attributed to vibrational excitation in the A2(πσ(∗)) state, facilitating wavepacket motion around the potential barrier in the N-CH3 dissociation coordinate.

A method for diabatising multiple electronic states on-the-fly within the direct dynamics variational multi-configuration Gaussian method for calculating quantum nuclear dynamics is presented. The method is based upon the propagation of the adiabatic-diabatic transformation matrix along the paths followed by the Gaussian basis functions that constitute the nuclear wave function, by use of a well-known differential equation relating the matrix and the nonadiabatic vector coupling terms between the electronic states. The implementation of the method is described, and test calculations are presented using the ground and first-excited states of the butatriene cation as an example, allowing comparison to the earlier regularisation diabatisation scheme as well as to full nuclear dynamics on a precomputed potential energy surface. The new scheme is termed propagation diabatisation.

We demonstrate here conclusively that the variational multiconfiguration Gaussian (vMCG) method converges to the grid based full quantum dynamics multiconfiguration time-dependent Hartree result for a tunnelling problem in many dimensions, using the intramolecular proton transfer in salicylaldimine as a model system. The 13-dimensional model potential energy surface was obtained from Hartree Fock energies with the 6-31G* basis set and the expectation value of the flux operator along the transition mode was used as a benchmark characteristic. As well as showing excellent convergence of the vMCG method on the model surface using a local harmonic approximation and a moderate number of basis functions, we show that the direct dynamics version of the vMCG also performs very well, usually needs the same number of Gaussians to converge, and converges to exact results if those are obtained on an accurately fitted surface. Finally, we make an important observation that the width of the Gaussian basis functions must be chosen very carefully to obtain accurate results with the use of the frozen-width approximation.

The dynamics of pyrrole excited at wavelengths in the range 242-217 nm are studied using a combination of time-resolved photoelectron spectroscopy and wavepacket propagations performed using the multi-configurational time-dependent Hartree method. Excitation close to the origin of pyrrole's electronic spectrum, at 242 and 236 nm, is found to result in an ultrafast decay of the system from the ionization window on a single timescale of less than 20 fs. This behaviour is explained fully by assuming the system to be excited to the A2(πσ(∗)) state, in accord with previous experimental and theoretical studies. Excitation at shorter wavelengths has previously been assumed to result predominantly in population of the bright A1(ππ(∗)) and B2(ππ(∗)) states. We here present time-resolved photoelectron spectra at a pump wavelength of 217 nm alongside detailed quantum dynamics calculations that, together with a recent reinterpretation of pyrrole's electronic spectrum [S. P. Neville and G. A. Worth, J. Chem. Phys. 140, 034317 (2014)], suggest that population of the B1(πσ(∗)) state (hitherto assumed to be optically dark) may occur directly when pyrrole is excited at energies in the near UV part of its electronic spectrum. The B1(πσ(∗)) state is found to decay on a timescale of less than 20 fs by both N-H dissociation and internal conversion to the A2(πσ(∗)) state.

A theoretical study of the intra-molecular vibrational-energy redistribution of toluene using time-resolved photo-electron spectra calculated using nuclear quantum dynamics and a simple, two-mode model is presented. Calculations have been carried out using the multi-configuration time-dependent Hartree method, using three levels of approximation for the calculation of the spectra. The first is a full quantum dynamics simulation with a discretisation of the continuum wavefunction of the ejected electron, whilst the second uses first-order perturbation theory to calculate the wavefunction of the ion. Both methods rely on the explicit inclusion of both the pump and probe laser pulses. The third method includes only the pump pulse and generates the photo-electron spectrum by projection of the pumped wavepacket onto the ion potential energy surface, followed by evaluation of the Fourier transform of the autocorrelation function of the subsequently propagated wavepacket. The calculations performed have been used to study the periodic population flow between the 6a and 10b16b modes in the S1 excited state, and compared to recent experimental data. We obtain results in excellent agreement with the experiment and note the efficiency of the perturbation method.

A model Hamiltonian based on the vibronic coupling model is developed to describe the excited state dynamics of 3-pyrroline. With the use of the method of improved relaxation in conjunction with the MCTDH wavepacket propagation algorithm, vibrational eigenstates corresponding to both the axial and equatorial conformers of 3-pyrroline are calculated and subsequently used in a conformer-resolved study of the photodissociation of 3-pyrroline following excitation to its S1(3s/πσ*) and S2(3px) states. In analogy with ammonia, the excited state dynamics of both conformers of 3-pyrroline are found to be dominated by the (quasi-) planarization of the molecule in its electronically excited states and predominantly diabatic behavior of dissociation mediated by a conical intersection between the S1 and S0 states.

The first band in the electronic spectrum of pyrrole is calculated from wavepacket propagations performed using the MCTDH method. To do so, two model Hamiltonians are constructed to describe seven low-lying excited electronic states of pyrrole. These Hamiltonians are based on the vibronic coupling model, and are parameterised via fitting to extensive CASPT2 and EOM-CCSD calculations. A detailed analysis of the structure of pyrrole's electronic spectrum in the range 5.5 to 6.5 eV is made. The role of intensity borrowing from transitions to ππ(*) states by lower-lying 3s and 3p Rydberg states is assessed, and reassignments of much of the spectrum are subsequently made which indicate that most of the states in the spectrum are predominantly Rydberg in character. The resulting conclusions drawn serve to highlight the limitations of assignments based on the matching of calculated vertical excitation energies and the positions of peak maxima observed in electronic spectra.

A model Hamiltonian based on the quadratic vibronic coupling model is developed to describe the photoinduced dynamics of aniline excited to the manifold of states comprising its first six singlet electronic states. The model Hamiltonian is parametrized by fitting to the results of extensive EOM-CCSD calculations and its validity tested through the calculation of the first two bands in the electronic absorption spectrum of aniline. It is found that two previously neglected 3p Rydberg states play an important role in the dynamics of aniline following excitation into the first two (1)ππ* states. Assignments of the vibrational structure seen in the experimental spectrum is made, and the role played by the Herzberg-Teller effect in excitation to the first (1)ππ* state is analyzed.