On the molecular electronic flux: Role of nonadiabaticity and violation of conservation

A basis-free phase space electronic Hamiltonian that recovers beyond Born-Oppenheimer electronic momentum and current density

We present a phase-space electronic Hamiltonian ĤPS (parameterized by both nuclear position X and momentum P) that boosts each electron into the moving frame of the nuclei that are closest in real space. The final form for the phase space Hamiltonian does not assume the existence of an atomic orbital basis, and relative to standard Born-Oppenheimer theory, the newly proposed one-electron operators can be expressed directly as functions of electronic and nuclear positions and momentum. We show that (i) quantum-classical dynamics along such a Hamiltonian maintains momentum conservation and that (ii) diagonalizing such a Hamiltonian can recover the electronic momentum and electronic current density reasonably well. In conjunction with other reports in the literature that such a phase-space approach can also recover vibrational circular dichroism spectra, we submit that the present phase-space approach offers a testable and powerful approach to post-BO electronic structure theory. Moreover, the approach is inexpensive and can be immediately applied to simulations of chiral induced spin selectivity experiments (where the transfer of angular momentum between nuclei and electrons is considered critical).

An electronic phase-space Hamiltonian approach for electronic current density and vibrational circular dichroism

The Born-Oppenheimer framework stipulates that chemistry and physics occur on potential energy surfaces VBO(X) parameterized by a nuclear coordinate X, which are built by diagonalizing a BO Hamiltonian ĤBO(X). However, such a framework cannot recover many measurable chemical and physical features, including vibrational circular dichroism spectra. In this article, we show that a phase-space electronic Hamiltonian ĤPS(X,P), parameterized by both nuclear position X and momentum P, with a similar computational cost as solving ĤBO(X), can recover not just experimental vibrational circular dichroism signals but also a meaningful electronic current density that explains the features of the vibrational circular dichroism rotational strengths. Combined with earlier demonstrations that such Hamiltonians can also recover qualitatively correct electronic momenta with electronic densities that approximately satisfy a continuity equation, the data would suggest that, if one looks closely enough, chemistry in fact occurs on potential energy surfaces parameterized by both X and P, EPS(X, P). While the dynamical implications of such a phase-space electronic Hamiltonian are not yet known, we hypothesize that, by offering classical trajectories that explicitly offer nonzero electronic momentum while also conserving the total angular momentum (unlike Born-Oppenheimer theory), this new phase-space electronic structure Hamiltonian may well explain some fraction of the chiral-induced spin selectivity effect.

Angular Momentum Transfer between a Molecular System and a Continuous Circularly Polarized Light Field within a Semiclassical Born-Oppenheimer Surface Hopping Framework

We simulate semiclassically angular momentum transfer for a molecular system subject to a circularly polarized light (CPL) field either moving along a single Born-Oppenheimer (BO) surface or moving along multiple BO surfaces. Both sets of simulations are able to conserve the total angular momentum around the propagation direction of the CPL field, the former requiring a Berry force and the latter requiring a surface parametrized by both nuclear position and momentum (a so-called phase-space approach). Our results provide new insight into the nature of semiclassical nonadiabatic dynamics methods and further demonstrate the power of such methods to capture angular momentum transfer between different media, highlighting the need for accurate algorithms that conserve the total angular momentum.

Practical phase-space electronic Hamiltonians for ab initio dynamics

Modern electronic structure theory is built around the Born-Oppenheimer approximation and the construction of an electronic Hamiltonian Ĥel(X) that depends on the nuclear position X (and not the nuclear momentum P). In this article, using the well-known theory of electron translation (Γ') and rotational (Γ″) factors to couple electronic transitions to nuclear motion, we construct a practical phase-space electronic Hamiltonian that depends on both nuclear position and momentum, ĤPS(X,P). While classical Born-Oppenheimer dynamics that run along the eigensurfaces of the operator Ĥel(X) can recover many nuclear properties correctly, we present some evidence that motion along the eigensurfaces of ĤPS(X,P) can better capture both nuclear and electronic properties (including the elusive electronic momentum studied by Nafie). Moreover, only the latter (as opposed to the former) conserves the total linear and angular momentum in general.

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.

Adiabatic electronic flux in molecules and in condensed matter

The theory of adiabatic electron transport in a correlated condensed-matter system is rooted in a seminal paper by Niu and Thouless [J. Phys A {\bf 17}, 2453 (1984)]; I adopt here an analogous logic in order to { retrieve the known expression for the adiabatic electronic flux in a molecular system [L. A. Nafie, J. Chem. Phys. {\bf 79}, 4950 (1983)]. Its derivation here is considerably simpler than those available in the current quantum-chemistry literature; it also explicitly identifies the adiabaticity parameter, in terms of which the adiabatic flux and the electron density are both exact to first order. It is shown that continuity equation is conserved to the same order. For the sake of completeness,} I also briefly outline the relevance of the macroscopic electronic flux to the physics of solids and liquids.