Quantum dynamics study of fulvene double bond photoisomerization: the role of intramolecular vibrational energy redistribution and excitation energy

Recommendations for Velocity Adjustment in Surface Hopping

This study investigates velocity adjustment directions after hopping in surface hopping dynamics. Using fulvene and a protonated Schiff base (PSB4) as case studies, we investigate the population decay and reaction yields of different sets of dynamics with the velocity adjusted in either the nonadiabatic coupling, gradient difference, or momentum directions. For the latter, in addition to the conventional algorithm, we investigated the performance of a reduced kinetic energy reservoir approach recently proposed. Our evaluation also considered velocity adjustment in the directions of approximate nonadiabatic coupling vectors. While results for fulvene are susceptible to the adjustment approach, PSB4 is not. We correlated this dependence to the topography near the conical intersections. When nonadiabatic coupling vectors are unavailable, the gradient difference direction is the best adjustment option. If the gradient difference is also unavailable, a semiempirical vector direction or the momentum direction with a reduced kinetic energy reservoir becomes an excellent option to prevent an artificial excess of back hoppings. The precise velocity adjustment direction is less crucial for describing the nonadiabatic dynamics than the kinetic energy reservoir's size.

Benchmarking non-adiabatic quantum dynamics using the molecular Tully models

On-the-fly non-adiabatic dynamics methods are becoming more important as tools to characterise the time evolution of a system after absorbing light. These methods, which calculate quantities such as state energies, gradients and interstate couplings at every time step, circumvent the requirement for pre-computed potential energy surfaces. There are a number of different algorithms used, the most common being Tully Surface Hopping (TSH), but all are approximate solutions to the time-dependent Schrödinger equation and benchmarking is required to understand their accuracy and performance. For this, a common set of systems and observables are required to compare them. In this work, we validate the on-the-fly direct dynamics variational multi-configuration Gaussian (DD-vMCG) method using three molecular systems recently suggested by Ibele and Curchod as molecular versions of the Tully model systems used to test one-dimensional non-adiabatic behaviour [Ibele et al., Phys. Chem. Chem. Phys. 2020, 22, 15183-15196]. Parametrised linear vibronic potential energy surfaces for each of the systems were also tested and compared to on-the-fly results. The molecules, which we term the Ibele-Curchod models, are ethene, DMABN and fulvene and the authors used them to test and compare several versions of the Ab Initio Multiple Spawning (AIMS) method alongside TSH. The three systems present different deactivation pathways after excitation to their ππ* bright states. When comparing DD-vMCG to AIMS and TSH, we obtain crucial differences in some cases, for which an explanation is provided by the classical nature and the chosen initial conditions of the TSH simulations.

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.

An overview of the cycloaddition chemistry of fulvenes and emerging applications

The unusual electronic properties and unique reactivity of fulvenes have interested researchers for over a century. The propensity to form dipolar structures at relatively low temperatures and to participate as various components in cycloaddition reactions, often highly selectively, makes them ideal for the synthesis of complex polycyclic carbon scaffolds. As a result, fulvene cycloaddition chemistry has been employed extensively for the synthesis of natural products. More recently, fulvene cycloaddition chemistry has also found application to other areas including materials chemistry and dynamic combinatorial chemistry. This highlight article discusses the unusual properties of fulvenes and their varied cycloaddition chemistry, focussing on applications in organic and natural synthesis, dynamic combinatorial chemistry and materials chemistry, including dynamers, hydrogels and charge transfer complexes. Tables providing comprehensive directories of fulvene cycloaddition chemistry are provided, including fulvene intramolecular and intermolecular cycloadditions complete with reactant partners and their resulting cyclic adducts, which provide a useful reference source for synthetic chemists working with fulvenes and complex polycyclic scaffolds.

Torsional Potentials of Glyoxal, Oxalyl Halides, and Their Thiocarbonyl Derivatives: Challenges for Popular Density Functional Approximations

The reliability of popular density functionals was studied for the description of torsional profiles of 36 molecules: glyoxal, oxalyl halides, and their thiocarbonyl derivatives. HF and 18 functionals of varying complexity, from local density to range-separated hybrid approximations and double-hybrid, have been considered and benchmarked against CCSD(T)-level rotational profiles. For molecules containing heavy halogens, most functionals fail to reproduce barrier heights accurately and a number of functionals introduce spurious minima. Dispersion corrections show no improvement. Calibrated torsion-corrected atom-centered potentials rectify the shortcomings of PBE and also improve on σ-hole based intermolecular binding in dimers and crystals.

Early events in the photochemistry of 5-diazo Meldrum's acid: formation of a product manifold in C–N bound and pre-dissociated intersection seam regions

Photolysis of 5-diazo Meldrum's acid yields three different primary products in a sub-ps scale. High-level computations show that this is due to the presence of an extended seam of intersection associated to different reaction paths.

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.

The response of the electronic structure to electronic excitation and double bond torsion in fulvene: a combined QTAIM, stress tensor and MO perspective

New insights into the double bond isomerization of fulvene in the ground and excited electronic states are provided by newly developed QTAIM and stress tensor tools. The S0 and S1 states follow the 'biradical' torsion model, but the double bond is stiffer in the S0 state; by contrast, the S2 state follows the 'zwitterionic' torsion. Differences are explained in terms of the ellipticity and bond critical point (BCP) stiffness for both QTAIM and the stress tensor. Overall, the wave-function based analysis is found to be in agreement with the work of Bonačić-Koutecký and Michl that the bond-twisted species can have biradical or zwitterionic character, depending on the state. Using QTAIM and the stress tensor a new understanding of bond torsion is revealed; the electronic charge density around the twisted bond is found not to rotate in concert with the nuclei of the rotated -CH2 methylene group. The ability to visualize how the bond stiffness varies between individual electronic states and how this correlates with the QTAIM and stress tensor bond stiffness is highlighted. In addition, the most and least preferred morphologies of bond-path torsion are visualized. Briefly we discuss the prospects for using this new QTAIM and stress tensor analysis for excited state chemistry.

Photophysics of fulvene under the non-resonant stark effect. Shaping the conical intersection seam

We introduce a mechanistic strategy to control the excited state lifetime of fulvene based on shaping the topography of an extended seam of intersection with the non-resonant dynamic Stark effect. Fulvene has a very short excited state lifetime due to an energetically accessible seam of intersection which lies along the methylene torsion coordinate, and the initial decay occurs at the seam segment around the planar conical intersection structure. We have followed a three-step approach to simulate the control. First, we have calculated the effect of a non-resonant electric field on the potential energy surface at the ab initio level, including the field in a self-consistent way. The relative energy of the planar segment of the seam is increased by the non-resonant field. In the second step we simulate the control carrying out MCTDH quantum dynamics propagations under a static non-resonant field to derive the main control mechanisms. At moderately intense fields (epsilon < or = 0.03 a.u.) the decay is faster as compared to the field free case because the vibrational overlap between the excited and ground state vibrational functions is increased. However, at more intense fields (epsilon = 0.04 a.u.) the planar conical intersection is energetically inaccessible and the decay occurs at a slower time scale, at the segment of the seam with more twisted geometries. In the third step, the control over the dynamics is exerted with a non-resonant dynamic field. The acceleration of the decay due to the improved vibrational overlap does not occur, but the decay can be made slower with a dynamic field of 0.08 a.u. The results show the viability of our approach to control the photophysics shaping the topology of the conical intersection seam, and they prove that the extended nature of the seam is crucial for simulating and understanding the control.

Evaluation of the importance of spin-orbit couplings in the nonadiabatic quantum dynamics with quantum fidelity and with its efficient "on-the-fly" ab initio semiclassical approximation

We propose to measure the importance of spin-orbit couplings (SOCs) in the nonadiabatic molecular quantum dynamics rigorously with quantum fidelity. To make the criterion practical, quantum fidelity is estimated efficiently with the multiple-surface dephasing representation (MSDR). The MSDR is a semiclassical method that includes nuclear quantum effects through interference of mixed quantum-classical trajectories without the need for the Hessian of potential energy surfaces. Two variants of the MSDR are studied, in which the nuclei are propagated either with the fewest-switches surface hopping or with the locally mean field dynamics. The fidelity criterion and MSDR are first tested on one-dimensional model systems amenable to numerically exact quantum dynamics. Then, the MSDR is combined with "on-the-fly" computed electronic structure to measure the importance of SOCs and nonadiabatic couplings in the photoisomerization dynamics of CH(2)NH(2)(+) considering 20 electronic states and in the collision of F + H(2) considering six electronic states.

Wave Packet Dynamics at an Extended Seam of Conical Intersection: Mechanism of the Light-Induced Wolff Rearrangement

Quantum dynamics calculations on a model surface based on CASPT2//CASSCF calculations are carried out to probe the traversal of a wave packet through an extended seam of conical intersection during the light-induced Wolff rearrangement of diazonaphtoquinone. The reaction is applied in the fabrication of integrated circuits. It consists of nitrogen elimination and ring rearrangement to yield a ketene. After excitation, the wave packet relaxes and reaches the extended seam. A fraction of the wave packet decays to the ground state at a region of the seam connected to a carbene intermediate, while the remaining part decays at a region leading to the ketene. The passage of the wave packet through the extended seam explains the competition between concerted ketene formation and a stepwise mechanism involving a carbene. The two primary photoproducts are formed in the first 100 fs of the simulation, in agreement with recent ultrafast spectroscopy measurements.