Jhon Fredy Pérez-Torres

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.

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.

Vibrating H2+(2Σg+, 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 Born–Oppenheimer 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.

Computation of the Electronic Flux Density in the Born−Oppenheimer Approximation

A molecule in the electronic ground state described in the Born–Oppenheimer approximation (BOA) by the wave function ΨBO = Φ0χ0 (where Φ0 is the time-independent electronic energy eigenfunction and χ0 is a time-dependent nuclear wave packet) exhibits a nonzero nuclear flux density, whereas it always displays zero electronic flux density (EFD), because the electrons are in a stationary state. A hierarchical approach to the computation of the EFD within the context of the BOA, which utilizes only standard techniques of quantum chemistry (to obtain Φ0) and quantum dynamics (to describe the evolution of χ0 on the ground-state potential energy surface), provides a resolution of this puzzling, nonintuitive result. The procedure is applied to H2(+) oriented parallel with the z-axis and vibrating in the ground state (2)Σg(+). First, Φ0 and χ0 are combined by the coupled-channels technique to give the normally dominant z-component of the EFD. Imposition of the constraints of electronic continuity, cylindrical symmetry of Φ0 and two boundary conditions on the EFD through a scaling procedure yields an improved z-component, which is then used to compute the complementary orthogonal ρ-component. The resulting EFD agrees with its highly accurate counterpart furnished by a non-BOA treatment of the system.

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.