Gravitationally-induced wave function collapse time for molecules.

The Diósi-Penrose model states that the wave function collapse ending a quantum superposition occurs due to the instability of coexisting gravitational potentials created by distinct geometric conformations of the system in different states. The Heisenberg time-energy principle can be invoked to estimate the collapse time for the energy associated with this instability, the gravitational self-energy. This paper develops atomistic models to calculate the Diósi-Penrose collapse time. It applies them to a range of systems, from small molecules to large biological structures and macroscopic systems. An experiment is suggested to test the Diósi-Penrose hypothesis, and we critically examine the model, highlighting challenges from an atomistic perspective, such as gravitational self-energy saturation and limited extensivity.

Photoisomerization pathways of trans-resveratrol.

Resveratrol is well-known for promoting health benefits due to its antioxidant, anti-aging, anti-carcinogenic, and other beneficial activities. Understanding the photophysics of resveratrol is essential for determining its applicability to pharmaceutical innovations. In the present work, we used an explore-then-assess strategy to map the internal conversion pathways of trans-resveratrol. This strategy consists of exploring the multidimensional configurational space with nonadiabatic dynamics simulations based on a semiempirical multireference method, followed by a feasibility assessment of reduced-dimensionality pathways at a high ab initio theoretical level. The exploration step revealed that internal conversion to the ground state may occur near five distinct conical intersections. The assessment step showed that the main photoisomerization pathway involves a twisted-pyramidalized S1/S0 conical intersection, yielding either trans or cis isomers. However, a secondary path was identified, where cis-trans isomerization happens in the excited state and internal conversion occurs at a cyclic conical intersection, yielding a closed-ring resveratrol derivative. This derivative, which can be formed through this direct path or an indirect photoexcitation, may be connected to the production of oxygen-reactive species previously reported and have implications in photodynamic therapy.

Unexpected longer T1 lifetime of 6-sulfur guanine than 6-selenium guanine: the solvent effect of hydrogen bonds to brake the triplet decay.

The decay of the T1 state to the ground state is an essential property of photosensitizers because it decides the lifetime of excited states and, thus, the time window for sensitization. The sulfur/selenium substitution of carbonyl groups can red-shift absorption spectra and enhance the triplet yield because of the large spin-orbit coupling, modifying nucleobases to potential photosensitizers for various applications. However, replacing sulfur with selenium will also cause a much shorter T1 lifetime. Experimental studies found that the triplet decay rate of 6-seleno guanine (6SeGua) is 835 times faster than that of 6-thio guanine (6tGua) in aqueous solution. In this work, we reveal the mechanism of the T1 decay difference between 6SeGua and 6tGua by computing the activation energy and spin-orbit coupling for rate calculation. The solvent effect of water is treated with explicit microsolvation and implicit solvent models. We find that the hydrogen bond between the sulfur atom of 6tGua and the water molecule can brake the triplet decay, which is weaker in 6SeGua. This difference is crucial to explain the relatively long T1 lifetime of 6tGua in an aqueous solution. This insight emphasizes the role of solvents in modulating the excited state dynamics and the efficiency of photosensitizers, particularly in aqueous environments.

Auger-Meitner and X-ray Absorption Spectra of Ethylene Cation: Insight into Conical Intersection Dynamics.

We present a theoretical investigation of the near-edge X-ray absorption fine structure and the Auger-Meitner decay spectra of ethylene and its cation. Herein, we demonstrate that our method, coupled with the nuclear ensemble approach, successfully reproduces the natural bandwidth structure of the experimental resonant Auger-Meitner decay spectra of ethylene, which is not very well reproduced within the Franck-Condon approximation. Furthermore, we analyze the Auger-Meitner decay spectra of the ethylene cation in light of minimum energy conical intersection structures involving the two lowest cationic states (D1 and D0), providing valuable insights into the ultrafast D1/D0 relaxation dynamics. Our results suggest that Auger-Meitner electron spectroscopy can help elucidate the mechanism behind the initial 20 fs of the relaxation dynamics.

A simple approach to rotationally invariant machine learning of a vector quantity.

Unlike with the energy, which is a scalar property, machine learning (ML) prediction of vector or tensor properties poses the additional challenge of achieving proper invariance (covariance) with respect to molecular rotation. For the energy gradients needed in molecular dynamics (MD), this symmetry is automatically fulfilled when taking analytic derivative of the energy, which is a scalar invariant (using properly invariant molecular descriptors). However, if the properties cannot be obtained by differentiation, other appropriate methods should be applied to retain the covariance. Several approaches have been suggested to properly treat this issue. For nonadiabatic couplings and polarizabilities, for example, it was possible to construct virtual quantities from which the above tensorial properties are obtained by differentiation and thus guarantee the covariance. Another possible solution is to build the rotational equivariance into the design of a neural network employed in the model. Here, we propose a simpler alternative technique, which does not require construction of auxiliary properties or application of special equivariant ML techniques. We suggest a three-step approach, using the molecular tensor of inertia. In the first step, the molecule is rotated using the eigenvectors of this tensor to its principal axes. In the second step, the ML procedure predicts the vector property relative to this orientation, based on a training set where all vector properties were in this same coordinate system. As the third step, it remains to transform the ML estimate of the vector property back to the original orientation. This rotate-predict-rotate (RPR) procedure should thus guarantee proper covariance of a vector property and is trivially extensible also to tensors such as polarizability. The RPR procedure has an advantage that the accurate models can be trained very fast for thousands of molecular configurations, which might be beneficial where many training sets are required (e.g., in active learning). We have implemented the RPR technique, using the MLatom and Newton-X programs for ML and MD, and performed its assessment on the dipole moment along MD trajectories of 1,2-dichloroethane.

Prediction Challenge: Simulating Rydberg photoexcited cyclobutanone with surface hopping dynamics based on different electronic structure methods.

This research examines the nonadiabatic dynamics of cyclobutanone after excitation into the n → 3s Rydberg S2 state. It stems from our contribution to the Special Topic of the Journal of Chemical Physics to test the predictive capability of computational chemistry against unseen experimental data. Decoherence-corrected fewest-switches surface hopping was used to simulate nonadiabatic dynamics with full and approximated nonadiabatic couplings. Several simulation sets were computed with different electronic structure methods, including a multiconfigurational wavefunction [multiconfigurational self-consistent field (MCSCF)] specially built to describe dissociative channels, multireference semiempirical approach, time-dependent density functional theory, algebraic diagrammatic construction, and coupled cluster. MCSCF dynamics predicts a slow deactivation of the S2 state (10 ps), followed by an ultrafast population transfer from S1 to S0 (<100 fs). CO elimination (C3 channel) dominates over C2H4 formation (C2 channel). These findings radically differ from the other methods, which predicted S2 lifetimes 10-250 times shorter and C2 channel predominance. These results suggest that routine electronic structure methods may hold low predictive power for the outcome of nonadiabatic dynamics.

Temperature effects on the internal conversion of excited adenine and adenosine.

This work aims to elucidate the dependence of the excited-state lifetime of adenine and adenosine on temperature. So far, it has been experimentally shown that while adenine's lifetime is unaffected by temperature, adenosine's lifetime strongly depends on it. However, the non-Arrhenius temperature dependence has posed a challenge in explaining this phenomenon. We used surface hopping to simulate the dynamics of adenine and adenosine in the gas phase at 0 and 400 K. The temperature effects were observed under the initial conditions via Wigner sampling with thermal corrections. Our results confirm that adenine's excited-state lifetime does not depend on temperature, while adenosine's lifetime does. Adenosine's dependency is due to intramolecular vibrational energy transfer from adenine to the ribose group. At 0 K, this transfer reduced the mean kinetic energy of adenine's moiety so much that internal conversion is inhibited, and the lifetime elongated by a factor of 2.3 compared to that at 400 K. The modeling also definitively ruled out the influence of viscosity, which was proposed as an alternative explanation previously.

Surface hopping modeling of charge and energy transfer in active environments.

An active environment is any atomic or molecular system changing a chromophore's nonadiabatic dynamics compared to the isolated molecule. The action of the environment on the chromophore occurs by changing the potential energy landscape and triggering new energy and charge flows unavailable in the vacuum. Surface hopping is a mixed quantum-classical approach whose extreme flexibility has made it the primary platform for implementing novel methodologies to investigate the nonadiabatic dynamics of a chromophore in active environments. This Perspective paper surveys the latest developments in the field, focusing on charge and energy transfer processes.

Simulations of molecular photodynamics in long timescales.

Nonadiabatic dynamics simulations in the long timescale (much longer than 10 ps) are the next challenge in computational photochemistry. This paper delimits the scope of what we expect from methods to run such simulations: they should work in full nuclear dimensionality, be general enough to tackle any type of molecule and not require unrealistic computational resources. We examine the main methodological challenges we should venture to advance the field, including the computational costs of the electronic structure calculations, stability of the integration methods, accuracy of the nonadiabatic dynamics algorithms and software optimization. Based on simulations designed to shed light on each of these issues, we show how machine learning may be a crucial element for long time-scale dynamics, either as a surrogate for electronic structure calculations or aiding the parameterization of model Hamiltonians. We show that conventional methods for integrating classical equations should be adequate to extended simulations up to 1 ns and that surface hopping agrees semiquantitatively with wave packet propagation in the weak-coupling regime. We also describe our optimization of the Newton-X program to reduce computational overheads in data processing and storage. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Using diketopyrrolopyrroles to stabilize double excitation and control internal conversion.

Diketopyrrolopyrrole (DPP) is a pivotal functional group to tune the physicochemical properties of novel organic photoelectronic materials. Among multiple uses, DPP-thiophene derivatives forming a dimer through a vinyl linker were recently shown to quench the fluorescence observed in their isolated monomers. Here, we explain this fluorescence quenching using computational chemistry. The DPP-thiophene dimer has a low-lying doubly excited state that is not energetically accessible for the monomer. This state delays the fluorescence allowing internal conversion to occur first. We characterize the doubly excited state wavefunction by systematically changing the derivatives to tune the π-scaffold size and the acceptor and donor characters. The origin of this state's stabilization is related to the increase in the π-system and not to the charge-transfer features. This analysis delivers core conceptual information on the electronic properties of organic chromophores arranged symmetrically around a vinyl linker, opening new ways to control the balance between luminescence and internal conversion.

Pre-Dewar structure modulates protonated azaindole photodynamics.

Recent experimental work revealed that the lifetime of the S3 state of protonated 7-azaindole is about ten times longer than that of protonated 6-azaindole. We simulated the nonradiative decay pathways of these molecules using trajectory surface hopping dynamics after photoexcitation into S3 to elucidate the reason for this difference. Both isomers mainly follow a common ππ* relaxation pathway involving multiple state crossings while coming down from S3 to S1 in the subpicosecond time scale. However, the simulations reveal that the excited-state topographies are such that while the 6-isomer can easily access the region of nonadiabatic transitions, the internal conversion of the 7-isomer is delayed by a pre-Dewar bond formation with a boat conformation.

Correction: Modeling the heating and cooling of a chromophore after photoexcitation.

Correction for 'Modeling the heating and cooling of a chromophore after photoexcitation' by Elizete Ventura et al., Phys. Chem. Chem. Phys., 2022, 24, 9403-9410, https://doi.org/10.1039/D2CP00686C.

Modeling the heating and cooling of a chromophore after photoexcitation.

The heating of a chromophore due to internal conversion and its cooling down due to energy dissipation to the solvent are crucial phenomena to characterize molecular photoprocesses. In this work, we simulated the ab initio nonadiabatic dynamics of cytosine, a prototypical chromophore undergoing ultrafast internal conversion, in three solvents-argon matrix, benzene, and water-spanning an extensive range of interactions. We implemented an analytical energy-transfer model to analyze these data and extract heating and cooling times. The model accounts for nonadiabatic effects, and excited- and ground-state energy transfer, and can analyze data from any dataset containing kinetic energy as a function of time. Cytosine heats up in the subpicosecond scale and cools down within 25, 4, and 1.3 ps in argon, benzene, and water, respectively. The time constants reveal that a significant fraction of the benzene and water heating occurs while cytosine is still electronically excited.

Probing the electronic structure and photophysics of thiophene-diketopyrrolopyrrole derivatives in solution.

Diketopyrrolopyrroles are a popular class of electron-withdrawing unit in optoelectronic materials. When combined with electron donating side-chain functional groups such as thiophenes, they form a very broad class of donor-acceptor molecules: thiophene-diketopyrrolopyrroles (TDPPs). Despite their widescale use in biosensors and photovoltaic materials, studies have yet to establish the important link between the electronic structure of the specific TDPP and the critical optical properties. To bridge this gap, ultrafast transient absorption with 22 fs time resolution has been used to explore the photophysics of three prototypical TDPP molecules: a monomer, dimer and polymer in solution. Interpretation of experimental data was assisted by a recent high-level theoretical study, and additional density functional theory calculations. These studies show that the photophysics of these molecular prototypes under visible photoexcitation are determined by just two excited electronic states, having very different electronic characters (one is optically bright, the other dark), their relative energetic ordering and the timescales for internal conversion from one to the other and/or to the ground state. The underlying difference in electronic structure alters the branching between these excited states and their associated dynamics. In turn, these factors dictate the fluorescence quantum yields, which are shown to vary by ∼1-2 orders of magnitude across the TDPP prototypes investigated here. The fast non-radiative transfer of molecules from the bright to dark states is mediated by conical intersections. Remarkably, wavepacket signals in the measured transient absorption data carry signatures of the nuclear motions that enable mixing of the electronic-nuclear wavefunction and facilitate non-adiabatic coupling between the bright and dark states.

Electron delocalisation in conjugated sulfur heterocycles probed by resonant Auger spectroscopy.

We propose a novel approach for an indirect probing of conjugation and hyperconjugation in core-excited molecules using resonant Auger spectroscopy. Our work demonstrates that the changes in the electronic structure of thiophene (C4H4S) and thiazole (C3H3NS), occurring in the process of resonant sulfur K-shell excitation and Auger decay, affect the stabilisation energy resulting from π-conjugation and hyperconjugation. The variations in the stabilisation energy manifest themselves in the resonant S KL2,3L2,3 Auger spectra of thiophene and thiazole. The comparison of the results obtained for the conjugated molecules and for thiolane (C4H8S), the saturated analogue of thiophene, has been performed. The experimental observations are interpreted using high-level quantum-mechanical calculations and the natural bond orbital analysis.

Trajectory Surface Hopping for a Polarizable Embedding QM/MM Formulation.

We present the implementation of trajectory surface-hopping nonadiabatic dynamics for a polarizable embedding QM/MM formulation. Time-dependent density functional theory was used at the quantum mechanical level of theory, whereas the molecular mechanics description involved the polarizable AMOEBA force field. This implementation has been obtained by integrating the surface-hopping program Newton-X NS with an interface between the Gaussian 16 and the Tinker suites of codes to calculate QM/AMOEBA energies and forces. The implementation has been tested on a photoinduced electron-driven proton-transfer reaction involving pyrimidine and a hydrogen-bonded water surrounded by a small cluster of water molecules and within a large water droplet.

Defining the temperature of an isolated molecule.

The microcanonical temperature of an isolated molecule is derived in terms of Boltzmann and Gibbs volume entropies within the quantum harmonic vibrational and equivalent degenerated model approximations. The effects of the entropy functional choice and various approximations are examined. The difference between Boltzmann and Gibbs volume temperatures is negligible for molecules bigger than ten atoms. However, it is significant for smaller systems, opening a way to probe them experimentally. A simple, analytical expression of the temperature as a function of the vibrational energy is provided, allowing predictions with a ±3% margin of error compared to the exact harmonic estimate. The microcanonical temperature is discussed and exemplified with polycyclic aromatic hydrocarbon molecules and other molecules of astrophysical interest.

Non-Kasha fluorescence of pyrene emerges from a dynamic equilibrium between excited states.

Pyrene fluorescence after a high-energy electronic excitation exhibits a prominent band shoulder not present after excitation at low energies. The standard assignment of this shoulder as a non-Kasha emission from the second-excited state (S2) has been recently questioned. To elucidate this issue, we simulated the fluorescence of pyrene using two different theoretical approaches based on vertical convolution and nonadiabatic dynamics with nuclear ensembles. To conduct the necessary nonadiabatic dynamics simulations with high-lying electronic states and deal with fluorescence timescales of about 100 ns of this large molecule, we developed new computational protocols. The results from both approaches confirm that the band shoulder is, in fact, due to S2 emission. We show that the non-Kasha behavior is a dynamic-equilibrium effect not caused by a metastable S2 minimum. However, it requires considerable vibrational energy, which can only be achieved in collisionless regimes after transitions into highly excited states. This strict condition explains why the S2 emission was not observed in some experiments.

Mechanistic Aspects of the Photophysics of UVA Filters Based on Meldrum Derivatives.

Skin photoprotection against UVA radiation is crucial, but it is hindered by the sparsity of approved commercial UVA filters. Sinapoyl malate (SM) derivatives are promising candidates for a new class of UVA filters. They have been previously identified as an efficient photoprotective sunscreen in plants due to their fast nonradiative energy dissipation. Combining experimental and computational results, in our previous letter (J. Phys. Chem. Lett. 2021, 12, 337-344) we showed that coumaryl Meldrum (CMe) and sinapoyl Meldrum (SMe) are outstanding candidates for UVA filters in sunscreen formulations. Here, we deliver a comprehensive computational characterization of the excited-state dynamics of these molecules. Using reaction pathways and excited-state dynamics simulations, we could elucidate the photodeactivation mechanism of these molecules. Upon photoexcitation, they follow a two-step logistic decay. First, an ultrafast and efficient relaxation stabilizes the excited state alongside a 90° twisting around the allylic double bond, giving rise to a minimum with a twisted intramolecular excited-state (TICT) character. From this minimum, internal conversion to the ground state occurs after overcoming a 0.2 eV barrier. Minor differences in the nonradiative decay and fluorescence of CMe and SMe are associated with an additional minimum present only in the latter.

Excitonic and charge transfer interactions in tetracene stacked and T-shaped dimers.

Extended quantum chemical calculations were performed for the tetracene dimer to provide benchmark results, analyze the excimer survival process, and explore the possibility of using long-range-corrected (LC) time-dependent second-order density functional tight-biding (DFTB2) for this system. Ground- and first-excited-state optimized geometries, vertical excitations at relevant minima, and intermonomer displacement potential energy curves (PECs) were calculated for these purposes. Ground-state geometries were optimized with the scaled-opposite-spin (SOS) second-order Møller-Plesset perturbation (MP2) theory and LC-DFT (density functional theory) and LC-DFTB2 levels. Excited-state geometries were optimized with SOS-ADC(2) (algebraic diagrammatic construction to second-order) and the time-dependent approaches for the latter two methods. Vertical excitations and PECs were compared to multireference configuration interaction DFT (DFT/MRCI). All methods predict the lowest-energy S0 conformer to have monomers parallel and rotated relative to each other and the lowest S1 conformer to be of a displaced-stacked type. LC-DFTB2, however, presents some relevant differences regarding other conformers for S0. Despite some state-order inversions, overall good agreement between methods was observed in the spectral shape, state character, and PECs. Nevertheless, DFT/MRCI predicts that the S1 state should acquire a doubly excited-state character relevant to the excimer survival process and, therefore, cannot be completely described by the single reference methods used in this work. PECs also revealed an interesting relation between dissociation energies and the intermonomer charge-transfer interactions for some states.