Multidirectional Angular Electronic Flux during Adiabatic Attosecond Charge Migration in Excited Benzene.

Recently, adiabatic attosecond charge migration (AACM) has been monitored and simulated for the first time, with application to the oriented iodoacetylene cation where AACM starts from the initial superposition of the ground state (φ0) and an electronic excited state (φ1). Here, we develop the theory for electronic fluxes during AACM in ring-shaped molecules, with application to oriented benzene prepared in the superposition of the ground and first excited singlet states. The initial state and its time evolution are analogous to coherent tunneling where φ0 and φ1 have different meanings; however, they denote the wave functions of the lowest tunneling doublet. This analogy suggests to transfer the theory of electronic fluxes during coherent tunneling to AACM, with suitable modifications which account for (i) the different time scales and (ii) the different electronic states, and which make use of (iii) the preparation of the initial state for AACM by a linearly polarized laser pulse. Application to benzene yields the multidirectional angular electronic flux with a pincer-motion type pattern during AACM: this unequivocal result confirms a previous working hypothesis. Moreover, the theory of AACM allows quantification of the electronic flux; that is, the maximum number of electrons (out of 42) which flow concertedly during AACM in benzene is 6 × 0.08 = 0.48.

Quantum theory of concerted electronic and nuclear fluxes associated with adiabatic intramolecular processes.

An elementary molecular process can be characterized by the flow of particles (i.e., electrons and nuclei) that compose the system. The flow, in turn, is quantitatively described by the flux (i.e., the time-sequence of maps of the rate of flow of particles though specified surfaces of observation) or, in more detail, by the flux density. The quantum theory of concerted electronic and nuclear fluxes (CENFs) associated with electronically adiabatic intramolecular processes is presented. In particular, it is emphasized how the electronic continuity equation can be employed to circumvent the failure of the Born-Oppenheimer approximation, which always predicts a vanishing electronic flux density (EFD). It is also shown that all CENFs accompanying coherent tunnelling between equivalent "reactant" and "product" configurations of isolated molecules are synchronous. The theory is applied to three systems of increasing complexity. The first application is to vibrating, aligned H2(+)((2)Σg(+)), or vibrating and dissociating H2(+)((2)Σg(+), J = 0, M = 0). The EFD maps manifest a rich and surprising structure in this simplest of systems; for example, they show that the EFD is not necessarily synchronous with the nuclear flux density and can alternate in direction several times over the length of the molecule. The second application is to coherent tunnelling isomerization in the model inorganic system B4, in which all CENFs are synchronous. The contributions of core and valence electrons to the EFD are separately computed and it is found that core electrons flow with the nuclei, whereas the valence electrons flow obliquely to the core electrons in distinctive patterns. The third application is to the Cope rearrangement of semibullvalene, which also involves coherent tunnelling. An especially interesting discovery is that the so-called "pericyclic" electrons do not behave in the manner typically portrayed by the traditional Lewis structures with appended arrows. Indeed, it is found that only about 3 pericyclic electrons flow, in contrast to the 6 predicted by the Lewis picture. It is remarkable that the time scales of these three processes vary by 18 orders of magnitude: femtoseconds (H2(+)((2)Σg(+))); picoseconds (B4); kilosceconds (semibullvalene). It is emphasized that results presented herein are appearing in the literature for the first time.

Imaging the Ultrafast Photoelectron Transfer Process in Alizarin-TiO2.

In this work, we adopt a quantum mechanical approach based on time-dependent density functional theory (TDDFT) to study the optical and electronic properties of alizarin supported on TiO2 nano-crystallites, as a prototypical dye-sensitized solar cell. To ensure proper alignment of the donor (alizarin) and acceptor (TiO2 nano-crystallite) levels, static optical excitation spectra are simulated using time-dependent density functional theory in response. The ultrafast photoelectron transfer from the dye to the cluster is simulated using an explicitly time-dependent, one-electron TDDFT ansatz. The model considers the δ-pulse excitation of a single active electron localized in the dye to the complete set of energetically accessible, delocalized molecular orbitals of the dye/nano-crystallite complex. A set of quantum mechanical tools derived from the transition electronic flux density is introduced to visualize and analyze the process in real time. The evolution of the created wave packet subject to absorbing boundary conditions at the borders of the cluster reveal that, while the electrons of the aromatic rings of alizarin are heavily involved in an ultrafast charge redistribution between the carbonyl groups of the dye molecule, they do not contribute positively to the electron injection and, overall, they delay the process.

Dissociating H2⁺(²Σg⁺,JM=00) ion as an exploding quantum bubble.

The nuclear and electronic probability and flux densities for a vibrating and dissociating H2(+) molecular ion in the electronic and rotational ground state (corresponding to the quantum numbers ²Σ(g)⁺,JM=00) are calculated. As a consequence of the isotropy of the scenario, the vibrating H2(+) appears as a pulsating quantum bubble, while the dissociating H2(+) appears as an exploding quantum bubble. The dissociating part is represented by a discretization of the continuum through use of £2 integrable B-spline basis set. It is shown that the vibrating part (the pulsating quantum bubble) interferes with the dissociating part (the exploding quantum bubble) and that the interference is much more noticeable in the probability density than in the flux density.

Vibrating H2(+)((2)Σg(+), JM = 00) ion as a pulsating quantum bubble in the laboratory frame.

We present quantum dynamics simulations of the concerted nuclear and electronic densities and flux densities of the vibrating H2(+) ion with quantum numbers (2)Σg(+), JM = 00 corresponding to the electronic and rotational ground state, in the laboratory frame. The underlying theory is derived using the nonrelativistic and Born­Oppenheimer approximations. It is well-known that the nuclear density of the nonrotating ion (JM = 00) is isotropic. We show that the electronic density is isotropic as well, confirming intuition. As a consequence, the nuclear and electronic flux densities have radial symmetry. They are related to the corresponding densities by radial continuity equations with proper boundary conditions. The time evolutions of all four observables, i.e., the nuclear and electronic densities and flux densities, are illustrated by means of characteristic snapshots. As an example, we consider the scenario with initial condition corresponding to preparation of H2(+) by near-resonant weak field one-photon-photoionization of the H2 molecule in its ground state, (1)Σg(+), vJM = 000. Accordingly, the vibrating, nonrotating H2(+) ion appears as pulsating quantum bubble in the laboratory frame, quite different from traditional considerations of vibrating H2+ in the molecular frame, or of the familiar alternative scenario of aligned vibrating H2(+) in the laboratory frame.

Nuclear fluxes in diatomic molecules deduced from pump-probe spectra with spatiotemporal resolutions down to 5 pm and 200 asec.

When molecules move, their nuclei flow. The corresponding quantum observable, i.e., the nuclear flux density, was introduced by Schrödinger in 1926, but until now, it has not been measured. Here the first experimental results are deduced from high-resolution pump-probe measurements of the time-dependent nuclear densities in a vibrating diatomic molecule or molecular ion. The nuclear densities are converted to flux densities by means of the continuity equation. The flux densities are much more sensitive to time-dependent quantum effects than the densities. Applications to the sodium molecule and the deuterium molecular ion unravel four new effects; e.g., at the turns from bond stretch to compression, the flux of the nuclei exhibits multiple changes of directions, from small to large bond lengths, a phenomenon that we call the "quantum accordion."