Electronic and nuclear flux dynamics at a conical intersection

Spin current in the early stage of radical reactions and its mechanisms

We study the electronic spin flux (atomic-scale flow of the spin density in molecules) by a perturbation analysis and ab initio nonadiabatic calculations. We derive a general perturbative expression of the charge and spin fluxes and identify the driving perturbation of the fluxes to be the time derivative of the electron-nucleus interaction term in the Hamiltonian. We then expand the expression in molecular orbitals so as to identify relevant components of the fluxes. Our perturbation theory describes the electronic fluxes in the early stage of reactions in an intuitively clear manner. The perturbation theory is then applied to an analysis of the spin flux obtained in ab initio calculations of the radical reaction of O2 and CH3· starting from three distinct spin configurations; (a) CH3· and triplet O2 with total spin of the system set Stot=1/2 (b) CH3· and singlet O2, Stot=1/2, and (c) CH3· and triplet O2, Stot=3/2. Further analysis of the time-dependent behaviors of the spin flux in these numerical simulations reveals (i) the spin flux induces rearrangement of the local spin structure, such as reduction of the spin polarization arising from the triplet O2 and (ii) the spin flux flows from O2 to CH3· in the reaction starting from spin configuration (a) and from CH3· to O2 in that starting from configuration (b), whereas no major intermolecular spin flux was observed in that starting from configuration (c). Our study thus establishes the mechanism of the spin flux that rearranges the local spin structures associated with chemical bonds.

Electronic-state chaos, intramolecular electronic energy redistribution, and chemical bonding in persisting multidimensional nonadiabatic systems

We study the chaotic, huge fluctuation of electronic state, resultant intramolecular energy redistribution, and strong chemical bonding surviving the fluctuation with exceedingly long lifetimes of highly excited boron clusters. Those excited states constitute densely quasi-degenerate state manifolds. The huge fluctuation is induced by persisting multidimensional nonadiabatic transitions among the states in the manifold. We clarify the mechanism of their coexistence and its physical significance. In doing so, we concentrate on two theoretical aspects. One is quantum chaos and energy randomization, which are to be directly extracted from the properties of the total electronic wavefunctions. The present dynamical chaos takes place through frequent transitions from adiabatic states to others, thereby making it very rare for the system to find dissociation channels. This phenomenon leads to the concept of what we call intramolecular nonadiabatic electronic-energy redistribution, which is an electronic-state generaliztion of the notion of intramolecular vibrational energy redistribution. The other aspect is about the peculiar chemical bonding. We investigate it with the energy natural orbitals (ENOs) to see what kind of theoretical structures lie behind the huge fluctuation. The ENO energy levels representing the highly excited states under study appear to have four robust layers. We show that the energy layers responsible for chaotic dynamics and those for chemical bonding are widely separated from each other, and only when an event of what we call "inter-layer crossing" happens to burst can the destruction of these robust energy layers occur, resulting in molecular dissociation. This crossing event happens only rarely because of the large energy gaps between the ENO layers. It is shown that the layers of high energy composed of complex-valued ENOs induce the turbulent flow of electrons and electronic-energy in the cluster. In addition, the random and fast time-oscillations of those high energy ENOs serve as a random force on the nuclear dynamics, which can work to prevent a concentration of high nuclear kinetic energy in the dissociation channels.

Energy natural orbital characterization of nonadiabatic electron wavepackets in the densely quasi-degenerate electronic state manifold

Dynamics and energetic structure of largely fluctuating nonadiabatic electron wavepackets are studied in terms of Energy Natural Orbitals (ENOs) [K. Takatsuka and Y. Arasaki, J. Chem. Phys. 154, 094103 (2021)]. Such huge fluctuating states are sampled from the highly excited states of clusters of 12 boron atoms (B₁₂), which have densely quasi-degenerate electronic excited-state manifold, each adiabatic state of which gets promptly mixed with other states through the frequent and enduring nonadiabatic interactions within the manifold. Yet, the wavepacket states are expected to be of very long lifetimes. This excited-state electronic wavepacket dynamics is extremely interesting but very hard to analyze since they are usually represented in large time-dependent configuration interaction wavefunctions and/or in some other complicated forms. We have found that ENO gives an invariant energy orbital picture to characterize not only the static highly correlated electronic wavefunctions but also those time-dependent electronic wavefunctions. Hence, we first demonstrate how the ENO representation works for some general cases, choosing proton transfer in water dimer and electron-deficient multicenter chemical bonding in diborane in the ground state. We then penetrate with ENO deep into the analysis of the essential nature of nonadiabatic electron wavepacket dynamics in the excited states and show the mechanism of the coexistence of huge electronic fluctuation and rather strong chemical bonds under very random electron flows within the molecule. To quantify the intra-molecular energy flow associated with the huge electronic-state fluctuation, we define and numerically demonstrate what we call the electronic energy flux.

Real-time electronic energy current and quantum energy flux in molecules

Intra- and inter-molecular electronic energy current is formulated by defining the probability current of electronic energy, called the energy flux. Among vast possible applications to electronic energy transfer phenomena, including chemical reaction dynamics, here we present a first numerical example from highly excited nonadiabatic electron wavepacket dynamics of a boron cluster B₁₂.

Nuclear–Electron Correlation Effects and Their Photoelectron Imprint in Molecular XUV Ionisation

The ionisation of molecules by attosecond XUV pulses is accompanied by complex correlated dynamics, such as the creation of coherent electron wave packets in the parent ion, their interplay with nuclear wave packets, and a correlated photoelectron moving in a multi-centred potential. Additionally, these processes are influenced by the dynamics prior to and during the ionisation. To fully understand and subsequently control the ionisation process on different time scales, a profound understanding of electron and nuclear correlation is needed. Here, we investigate the effect of nuclear–electron correlation in a correlated two-electron and one-nucleus quantum model system. Solving the time-dependent Schrödinger equation allows to monitor the correlation impact pre, during, and post-XUV ionisation. We show how an initial nuclear wave packet displaced from equilibrium influences the post-ionisation dynamics by means of momentum conservation between the target and parent ion, whilst the attosecond electron population remains largely unaffected. We calculate time-resolved photoelectron spectra and their asymmetries and demonstrate how the coupled electron–nuclear dynamics are imprinted on top of electron–electron correlation on the photoelectron properties. Finally, our findings give guidelines towards when correlation resulting effects have to be incorporated and in which instances the exact correlation treatment can be neglected.

Quantum flux densities for electronic-nuclear motion: exact versus Born-Oppenheimer dynamics

We study the coupled electronic-nuclear dynamics in a model system to compare numerically exact calculations of electronic and nuclear flux densities with those obtained from the Born-Oppenheimer (BO) approximation. Within the adiabatic expansion of the total wave function, we identify the terms which contribute to the flux densities. It is found that only off-diagonal elements that involve the interaction between different electronic states contribute to the electronic flux whereas in the nuclear case the major contribution belongs to the BO electronic state. New flux densities are introduced where in both, the electronic and the nuclear case, the main contribution is contained in the component corresponding to the BO state. As a consequence, they can be determined within the BO approximation, and an excellent agreement with the exact results is found. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

High-order geometric integrators for representation-free Ehrenfest dynamics

Ehrenfest dynamics is a useful approximation for ab initio mixed quantum-classical molecular dynamics that can treat electronically nonadiabatic effects. Although a severe approximation to the exact solution of the molecular time-dependent Schrödinger equation, Ehrenfest dynamics is symplectic, is time-reversible, and conserves exactly the total molecular energy as well as the norm of the electronic wavefunction. Here, we surpass apparent complications due to the coupling of classical nuclear and quantum electronic motions and present efficient geometric integrators for "representation-free" Ehrenfest dynamics, which do not rely on a diabatic or adiabatic representation of electronic states and are of arbitrary even orders of accuracy in the time step. These numerical integrators, obtained by symmetrically composing the second-order splitting method and exactly solving the kinetic and potential propagation steps, are norm-conserving, symplectic, and time-reversible regardless of the time step used. Using a nonadiabatic simulation in the region of a conical intersection as an example, we demonstrate that these integrators preserve the geometric properties exactly and, if highly accurate solutions are desired, can be even more efficient than the most popular non-geometric integrators.