Conical intersection seams in spin-orbit coupled systems with an even number of electrons: A numerical study based on neural network fit surfaces

On the Topological Phase around Conical Intersections with Tamm-Dancoff Linear-Response Time-Dependent Density Functional Theory

Regions of nuclear-configuration space away from the Franck-Condon geometry can prove problematic for some electronic structure methods, given the propensity of such regions to possess conical intersections, i.e., (highly connected) points of degeneracy between potential energy surfaces. With the likelihood (perhaps even inevitability) for nonadiabatic dynamics simulations to explore molecular geometries in close proximity to conical intersections, it is vital that the performance of electronic structure methods is routinely examined in this context. In a recent paper [Taylor, J. T. J. Chem. Phys. 2023, 159, 214115.], the ability of linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) to provide a proper description of conical intersections, in terms of their topology and topography, was investigated, with particular attention paid to conical intersections between two excited electronic states. For the same prototypical molecules, protonated formaldimine and pyrazine, we herein consider whether AA LR-TDDFT can correctly reproduce the topological phase accumulated by the adiabatic electronic wave function upon traversing a closed path around an excited-to-excited state conical intersection despite not using the appropriate quadratic-response nonadiabatic coupling vectors. Equally, we probe the ability of the ground-to-excited state intersection ring exhibited by AA LR-TDDFT in protonated formaldimine to give rise to a similar topological phase in spite of its incorrect dimensionality.

Development of Parallel On-the-Fly Algorithm for Global Exploration of Conical Intersection Seam Space

Conical intersection (CI) seams are configuration spaces of a molecular system where two or more (spin) adiabatic electronic states are degenerate in energy. They play essential roles in photochemistry because nonradiative decays often occur near the minima of the seam, i.e., the minimum energy CIs (MECIs). Thus, it is important to explore the CI seams and discover the MECIs. Although various approaches exist for CI seam exploration, most of them are local in nature, requiring reasonable initial guesses of geometries and nuclear gradients during the search. Global search algorithms, on the other hand, are powerful because they can fully sample the configurational space and locate important MECIs missed by local algorithms. However, global algorithms are often computationally expensive for large systems due to their poor scalability with respect to the number of degrees of freedom. To overcome this challenge, we develop the parallel on-the-fly Crystal algorithm to globally explore the CI seam space, taking advantage of its superior scaling behavior. Specifically, Crystal is coupled with on-the-fly evaluations of the excited and ground state energies using multireference electronic structure methods. Meanwhile, the algorithm is parallelized to further boost its computational efficiency. The effectiveness of this new algorithm is tested for three types of molecular photoswitches of significant importance in material and biomedical sciences: photostatin (PST), stilbene, and butadiene. A rudimentary implementation of the algorithm is applied to PST and stilbene, resulting in the discovery of all previously identified MECIs and several new ones. A refined version of the algorithm, combined with a systematic clustering technique, is applied to butadiene, resulting in the identification of an unprecedented number of energetically accessible MECIs. The results demonstrate that the parallel on-the-fly Crystal algorithm is a powerful tool for automated global CI seam exploration.

Quantum simulation of conical intersections

We explore the simulation of conical intersections (CIs) on quantum devices, setting the groundwork for potential applications in nonadiabatic quantum dynamics within molecular systems. The intersecting potential energy surfaces of H3+ are computed from a variance-based contracted quantum eigensolver. We show how the CIs can be correctly described on quantum devices using wavefunctions generated by the anti-Hermitian contracted Schrödinger equation ansatz, which is a unitary transformation of wavefunctions that preserves the topography of CIs. A hybrid quantum-classical procedure is used to locate the seam of CIs. Additionally, we discuss the quantum implementation of the adiabatic to diabatic transformation and its relation to the geometric phase effect. Results on noisy intermediate-scale quantum devices showcase the potential of quantum computers in dealing with problems in nonadiabatic chemistry.

From a one-mode to a multi-mode understanding of conical intersection mediated ultrafast organic photochemical reactions

This review discusses how ultrafast organic photochemical reactions are controlled by conical intersections, highlighting that decay to the ground-state at multiple points of the intersection space results in their multi-mode character.

Internal conversion and intersystem crossing dynamics based on coupled potential energy surfaces with full geometry-dependent spin-orbit and derivative couplings. Nonadiabatic photodissociation dynamics of NH3(A) leading to the NH(X3Σ-, a1Δ) + H2 channel

We simulate the photodissociation of NH₃ originating from its first excited singlet state S₁ into the NH₂ + H (radical) and NH + H₂ (molecular) channels. The states considered are the ground singlet state S₀, the first excited singlet state S₁ and the lowest-lying triplet state T₁, which permit for the first time a uniform treatment of the internal conversion and intersystem crossing. The simulations are based on a diabatic potential energy matrix (DPEM) of S₀, S₁ coupled by a conical intersection seam, as well as a potential energy surface (PES) for T₁ coupled by spin-orbit coupling (SOC) to the two singlet states. The DPEM and PES are fitted to ab initio electronic structure data (ESD) including energies, energy gradients, and derivative couplings. The DPEM also defines an adiabatic to diabatic state (AtD) transformation, which is used to transform the singular adiabatic SOC into a smooth function of the nuclear coordinates in the diabatic representation, allowing the diabatic SOC to be fit to an analytical functional form. ESD and SOC data obtained from these surfaces can serve as input for either quantum or semi-classical characterization of the nonadiabatic dynamics. Using the SHARC suite of programs, nonadiabatic simulations based on over 40 000 semi-classical trajectories assess the convergence of our results. The production of NH + H₂ is not direct, but is only achieved through a quasi-statistical dissociation mechanism after internal conversion to the ground electronic state. This leads to a much lower yield comparing with the main NH₂ + H channel. The NH(X³Σ^_) radical produced through the intersystem crossing from S₀ to T₁ is rare (∼0.2%) compared to NH(a¹Δ) due to the process being spin forbidden.

Intersystem Crossings in Late-Row Elements: A Perspective

Intersystem crossing (ISC), a vital component of the electronic and nuclear transitions that compose photophysics, has been successfully simulated in light elements and transition metal complexes. Derived from the Z-dependent spin-orbit coupling (SOC), ISC is expected to be of greater importance in heavier elements, but few attempts have been made at the simulation of ISC in lanthanides or actinides. In this work, we explore several of the challenges that will need to be overcome in order to treat ISC in late-row elements, including the loss of spin as a good quantum number, the need to include SOC variationally via two- or four-component electronic structure, and the high density of states present in late-row complexes. Density functional theory (DFT) calculations are used to illustrate several of these effects, while a model Hamiltonian is used to illustrate the importance of momentum rescaling in surface hopping simulations of strongly coupled states.