Ultrafast non-adiabatic dynamics of ethylene including Rydberg states

SHARC meets TEQUILA: mixed quantum-classical dynamics on a quantum computer using a hybrid quantum-classical algorithm

Recent developments in quantum computing are highly promising, particularly in the realm of quantum chemistry. Due to the noisy nature of currently available quantum hardware, hybrid quantum-classical algorithms have emerged as a reliable option for near-term simulations. Mixed quantum-classical dynamics methods effectively capture nonadiabatic effects by integrating classical nuclear dynamics with quantum chemical computations of the electronic properties. However, these methods face challenges due to the high computational cost of the quantum chemistry part. To mitigate the computational demand, we propose a method where the required electronic properties are computed through a hybrid quantum-classical approach that combines classical and quantum hardware. This framework employs the variational quantum eigensolver and variational quantum deflation algorithms to obtain ground and excited state energies, gradients, nonadiabatic coupling vectors, and transition dipole moments. These quantities are used to propagate the nonadiabatic molecular dynamics using the Tully's fewest switches surface hopping method, although the implementation is also compatible with other molecular dynamics approaches. The approach, implemented by integrating the molecular dynamics program package SHARC with the TEQUILA quantum computing framework, is validated by studying the cis-trans photoisomerization of methanimine and the electronic relaxation of ethylene. The results show qualitatively accurate molecular dynamics that align with experimental findings and other computational studies. This work is expected to mark a significant step towards achieving a "quantum advantage" for realistic chemical simulations.

Deuterium Isotope Effect on Internal Conversion of Ethylene Studied by Time-Resolved Photoelectron Spectroscopy

The effect of deuterium isotopes on the internal conversion of ethylene is studied by using extreme ultraviolet time-resolved photoelectron spectroscopy. For deuterium-labeled ethylene, the time scale for ultrafast internal conversion is increased by a factor of approximately √2, in agreement with the results of ab initio multiple spawning calculations, indicating the essential role played by hydrogen motion in the conversion process. Following internal conversion, a metastable species with an electron binding energy of ∼9 eV is produced, and it decays with a time constant similar to that for both isotopologues.

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.

Scoring molecular wires subject to an ultrafast laser pulse for molecular electronic devices

A nonionizing ultrafast laser pulse of 20-fs duration with a peak amplitude electric-field ±E = 200 × 10^-4 a.u. was simulated. It was applied to the ethene molecule to consider its effect on the electron dynamics, both during the application of the laser pulse and for up to 100 fs after the pulse was switched off. Four laser pulse frequencies ω = 0.2692, 0.2808, 0.2830, and 0.2900 a.u. were chosen to correspond to excitation energies mid-way between the (S₁ ,S₂ ), (S₂ ,S₃ ), (S₃ ,S₄ ) and (S₄ ,S₅ ) electronic states, respectively. Scalar quantum theory of atoms in molecules (QTAIM) was used to quantify the shifts of the C1C2 bond critical points (BCPs). Depending on the frequencies ω selected, the C1C2 BCP shifts were up to 5.8 times higher after the pulse was switched off compared with a static E-field with the same magnitude. Next generation QTAIM (NG-QTAIM) was used to visualize and quantify the directional chemical character. In particular, polarization effects and bond strengths, in the form of bond-rigidity vs. bond-flexibility, were found, for some laser pulse frequencies, to increase after the laser pulse was switched off. Our analysis demonstrates that NG-QTAIM, in partnership with ultrafast laser irradiation, is useful as a tool in the emerging field of ultrafast electron dynamics, which will be essential for the design, and control of molecular electronic devices.

Ultrafast Photoisomerization of Ethylene Studied Using Time-Resolved Extreme Ultraviolet Photoelectron Spectroscopy

The photoisomerization of isolated ethylene (ethene) was observed in real time from the Franck-Condon region in the ¹ππ* state to ground-state products using time-resolved photoelectron spectroscopy with extreme ultraviolet (EUV, 21.7 eV) probe pulses. A combination of filamentation four-wave mixing and high-order harmonic generation was employed to obtain a temporal resolution of 31 ± 2 fs. The nuclear wave packet created by a 160 nm pump pulse accesses C═C twisted geometries within 10 fs, and the population transfer from the excited to the ground state occurs within the next 20-30 fs. Formation of vibrationally highly excited ground-state molecules was observed in less than 45 fs, and they decayed with two time constants of 0.87 and >5 ps. The interpretation of the photoelectron spectra is supported by vertical ionization energies calculated using XMS-CASPT2 along geodesically interpolated reaction paths from the Franck-Condon region to the products.

Fewest switches surface hopping with Baeck-An couplings

In the Baeck-An (BA) approximation, first-order nonadiabatic coupling vectors are given in terms of adiabatic energy gaps and the second derivative of the gaps with respect to the coupling coordinate. In this paper, a time-dependent (TD) BA approximation is derived, where the couplings are computed from the energy gaps and their second time-derivatives. TD-BA couplings can be directly used in fewest switches surface hopping, enabling nonadiabatic dynamics with any electronic structure methods able to provide excitation energies and energy gradients. Test results of surface hopping with TD-BA couplings for ethylene and fulvene show that the TD-BA approximation delivers a qualitatively correct picture of the dynamics and a semiquantitative agreement with reference data computed with exact couplings. Nevertheless, TD-BA does not perform well in situations conjugating strong couplings and small velocities. Considered the uncertainties in the method, TD-BA couplings could be a competitive approach for inexpensive, exploratory dynamics with a small trajectories ensemble. We also assessed the potential use of TD-BA couplings for surface hopping dynamics with time-dependent density functional theory (TDDFT), but the results are not encouraging due to singlet instabilities near the crossing seam with the ground state.

Fewest switches surface hopping with Baeck-An couplings

In the Baeck-An (BA) approximation, first-order nonadiabatic coupling vectors are given in terms of adiabatic energy gaps and the second derivative of the gaps with respect to the coupling coordinate. In this paper, a time-dependent (TD) BA approximation is derived, where the couplings are computed from the energy gaps and their second time-derivatives. TD-BA couplings can be directly used in fewest switches surface hopping, enabling nonadiabatic dynamics with any electronic structure methods able to provide excitation energies and energy gradients. Test results of surface hopping with TD-BA couplings for ethylene and fulvene show that the TD-BA approximation delivers a qualitatively correct picture of the dynamics and a semiquantitative agreement with reference data computed with exact couplings. Nevertheless, TD-BA does not perform well in situations conjugating strong couplings and small velocities. Considered the uncertainties in the method, TD-BA couplings could be a competitive approach for inexpensive, exploratory dynamics with a small trajectories ensemble. We also assessed the potential use of TD-BA couplings for surface hopping dynamics with time-dependent density functional theory (TDDFT), but the results are not encouraging due to singlet instabilities near the crossing seam with the ground state.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

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.

Velocity Adjustment in Surface Hopping: Ethylene as a Case Study of the Maximum Error Caused by Direction Choice

The most common surface hopping dynamics algorithms require velocity adjustment after hopping to ensure total-energy conservation. Based on the semiclassical analysis, this adjustment must be made parallel to the nonadiabatic coupling vector's direction. Nevertheless, this direction is not always known, and the common practice has been to adjust the velocity in either the linear momentum or velocity directions. This paper benchmarks surface hopping dynamics of photoexcited ethylene with velocity adjustment in several directions, including those of the nonadiabatic coupling vector, the momentum, and the energy gradient difference. It is shown that differences in time constants and structural evolution fall within the statistical uncertainty of the method considering up to 500 trajectories in each dynamics set, rendering the three approaches statistically equivalent. For larger ensembles beyond 1000 trajectories, significant differences between the results arise, limiting the validity of adjustment in alternative directions. Other possible adjustment directions (velocity, single-state gradients, angular momentum) are evaluated as well. Given the small size of ethylene, the results reported in this paper should be considered an upper limit for the error caused by the choice of the velocity-adjustment direction on surface hopping dynamics.

The generality of the GUGA MRCI approach in COLUMBUS for treating complex quantum chemistry

The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calculations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of diabatization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully variational uncontracted spin-orbit MRCI, COLUMBUS provides a unique possibility of performing high-level calculations on compounds containing heavy atoms up to lanthanides and actinides. Crucial for carrying out all of these calculations effectively is the availability of an efficient parallel code for the CI step. Configuration spaces of several billion in size now can be treated quite routinely on standard parallel computer clusters. Emerging developments in COLUMBUS, including the all configuration mean energy multiconfiguration self-consistent field method and the graphically contracted function method, promise to allow practically unlimited configuration space dimensions. Spin density based on the GUGA approach, analytic spin-orbit energy gradients, possibilities for local electron correlation MR calculations, development of general interfaces for nonadiabatic dynamics, and MRCI linear vibronic coupling models conclude this overview.

A molecular perspective on Tully models for nonadiabatic dynamics

We present a series of standardized molecular tests for nonadiabatic dynamics, reminiscent of the one-dimensional Tully models proposed in 1990.

The 3s Rydberg state as a doorway state in the ultrafast dynamics of 1,1-difluoroethylene

The deactivation dynamics of 1,1-difluoroethylene after light excitation is studied within the surface hopping formalism in the presence of 3s and 3p Rydberg states using multi-state second order perturbation theory (MS-CASPT2).

Photoinduced C–H bond fission in prototypical organic molecules and radicals

We survey and assess current knowledge regarding the primary photochemistry of hydrocarbon molecules and radicals.

Non-adiabatic molecular dynamics with ΔSCF excited states

Accurate modelling of nonadiabatic transitions and electron-phonon interactions in extended systems is essential for understanding the charge and energy transfer in photovoltaic and photocatalytic materials. The extensive computational costs of the advanced excited state methods have stimulated the development of many approximations to study the nonadiabatic molecular dynamics (NA-MD) in solid-state and molecular materials. In this work, we present a novel ▵SCF-NA-MD methodology that aims to account for electron-hole interactions and electron-phonon back-reaction critical in modelling photoinduced nuclear dynamics. The excited states dynamics is described using the delta self-consistent field (▵SCF) technique within the density functional formalism and the trajectory surface hopping. The technique is implemented in the open-source Libra-X package freely available on the Internet (https://github.com/Quantum-Dynamics-Hub/Libra-X). This work illustrates the general utility of the developed ▵SCF-NA-MD methodology by characterizing the excited state energies and lifetimes, reorganization energies, photoisomerization quantum yields, and by providing the mechanistic details of reactive processes in a number of organic molecules.

On the possibility to accelerate the thermal isomerizations of overcrowded alkene-based rotary molecular motors with electron-donating or electron-withdrawing substituents

We employ computational methods to investigate the possibility of using electron-donating or electron-withdrawing substituents to reduce the free-energy barriers of the thermal isomerizations that limit the rotational frequencies achievable by synthetic overcrowded alkene-based molecular motors. Choosing as reference systems one of the fastest motors known to date and two variants thereof, we consider six new motors obtained by introducing electron-donating methoxy and dimethylamino or electron-withdrawing nitro and cyano substituents in conjugation with the central olefinic bond connecting the two (stator and rotator) motor halves. Performing density functional theory calculations, we then show that electron-donating (but not electron-withdrawing) groups at the stator are able to reduce the already small barriers of the reference motors by up to 18 kJ mol(-1). This result outlines a possible strategy for improving the rotational frequencies of motors of this kind. Furthermore, exploring the origin of the catalytic effect, it is found that electron-donating groups exert a favorable steric influence on the thermal isomerizations, which is not manifested by electron-withdrawing groups. This finding suggests a new mechanism for controlling the critical steric interactions of these motors. Graphical Abstract The introduction of electron-donating groups in one of the fastest rotary molecular motors known to date is found to reduce the free-energy barriers of the thermal steps that limit the rotational frequencies by up to 18 kJ mol(-1).

How does tetraphenylethylene relax from its excited states?

Photocyclization play a key role in the deactivation mechanism of tetraphenylethylene.

A multireference configuration interaction study of the photodynamics of nitroethylene

Extended multireference configuration interaction with singles and doubles (MR-CISD) calculations of nitroethylene (H₂C=CHNO₂) were carried out to investigate the photodynamical deactivation paths to the ground state. The ground (S₀) and the first five valence excited electronic states (S₁–S₅) were investigated. In the first step, vertical excitations and potential energy curves for CH₂ and NO₂ torsions and CH₂ out-of-plane bending starting from the ground state geometry were computed. Afterward, five conical intersections, one between each pair of adjacent states, were located. The vertical calculations mostly confirm the previous assignment of experimental spectrum and theoretical results using lower-level calculations. The conical intersections have as main features the torsion of the CH₂ moiety, different distortions of the NO₂ group and CC, CN, and NO bond stretchings. In these conical intersections, the NO₂ group plays an important role, also seen in excited state investigations of other nitro molecules. Based on the conical intersections found, a photochemical nonradiative deactivation process after a π–π* excitation to the bright S₅ state is proposed. In particular, the possibility of NO₂ release in the ground state, an important property in nitro explosives, was found to be possible.

Photochemistry and photophysics at extended seams of conical intersection

The role of extended seams of conical intersection in excited-state mechanisms is reviewed. Seams are crossings of the potential energy surface in many dimensions where the decay from the excited to the ground state can occur, and the extended seam is composed of different segments lying along a reaction coordinate. Every segment is associated with a different primary photoproduct, which gives rise to competing pathways. This idea is first illustrated for fulvene and ethylene, and then it is used to explain more complex cases such as the dependence of the isomerisation of retinal chromophore isomers on the protein environment, the dependence of the efficiency of the azobenzene photochemical switch on the wavelength of irradiation and the direction of the isomerisation, and the coexistence of different mechanisms in the photo-induced Wolff rearrangement of diazonaphthoquinone. The role of extended seams in the photophysics of the DNA nucleobases and the relationship between two-state seams and three-state crossings is also discussed. As an outlook, the design of optical control strategies based on the passage of the excited molecule through the seam is considered, and it is shown how the excited-state lifetime of fulvene can be modulated by shaping the energy of the seam.

Conical intersections and low-lying electronic states of tetrafluoroethylene

The low-lying electronic states of tetrafluoroethylene (C2 F4 ) are characterized theoretically for the first time using equation-of-motion coupled cluster theory (EOM-CCSD), and complete active space self-consistent field (CASSCF) and second-order perturbation theory (CASPT2). Computations are performed for vertical excitation energies, equilibrium geometries, minimum-energy conical intersections, and potential energy curves along three geometric coordinates: 1) twisting of the FCCF dihedral angle, 2) pyramidalization of the CF2 group, and 3) migration of a fluorine atom resulting in an ethylidene-like (CF3 CF) structure. The results suggest two relaxation pathways from the Rydberg-3s excited electronic state to the ground state. These relaxation pathways are discussed in conjunction with the femtosecond photoionization spectroscopy results of Trushin et al. [ChemPhysChem- 2004, 5, 1389].

Molecular mechanism of diaminomaleonitrile to diaminofumaronitrile photoisomerization: an intermediate step in the prebiotic formation of purine nucleobases

The photoinduced isomerization of diaminomaleonitrile (DAMN) to diaminofumaronitrile (DAFN) was suggested to play a key role in the prebiotically plausible formation of purine nucleobases and nucleotides. In this work we analyze two competitive photoisomerization mechanisms on the basis of state-of-the-art quantum-chemical calculations. Even though it was suggested that this process might occur on the triplet potential-energy surface, our results indicate that the singlet reaction channel should not be disregarded either. In fact, the peaked topography of the S1 /S0 conical intersection suggests that the deexcitation should most likely occur on a sub-picosecond timescale and the singlet photoisomerization mechanism might effectively compete even with a very efficient intersystem crossing. Such a scenario is further supported by the relatively small spin-orbit coupling of the S1 and T2 states in the Franck-Condon region, which does not indicate a very effective triplet bypass for this photoreaction. Therefore, we conclude that the triplet reaction channel in DAMN might not be as prominent as was previously thought.

Hexamethylcyclopentadiene: time-resolved photoelectron spectroscopy and ab initio multiple spawning simulations

Time-resolved photoelectron spectroscopy and ab initio multiple spawning dynamical simulations of hexamethylcyclopentadiene reveal wavepacket evolution in a distinct degree of freedom.