B-Spline Solution of the Two-Center Dirac Equation in the Electronic Continuum for Relativistic Molecular Photoionization

In this work, the two-center Dirac equation is solved numerically using an extension of an adapted B-spline basis set method previously implemented in relativistic atomic calculations (Fischer, C. F.; Zatsarinny, O. Comput. Phys. Commun. 2009, 180, 879). The robustness of the chosen numerical method, which avoids the appearance of spurious states common in other approaches, allows us to investigate molecular photoionization within a relativistic framework by simply adapting those methods already available in the nonrelativistic case (Brosolo, M.; Decleva, P. Chem. Phys. 1992, 159, 185; Brosolo, M.; Decleva, P.; Lisini, A. Mol. Opt. Phys. 1992, 25, 3345). First, light diatomic molecules (i.e., H2+ and HeH2+) are investigated with the purpose of testing the validity and efficiency of the method. Then, a series of one-electron molecular hydrides (i.e., HF9+, HCl17+ and HI53+) is explored by computing the total photoionization cross sections, asymmetry β-parameters and partial phase shifts. The present methodology can be easily extended to treat N-electron molecules following previous approaches in nonrelativistic calculations (Plesiat, E.; Decleva, P.; Martin, F. Phys. Chem. Chem. Phys. 2012, 14, 10853). The inclusion of a second photon can be also accomplished just like in atomic investigations aiming at reproducing pump-probe experiments capable to extract the photoionization time-delays (Vinbladh, J.; Dahlstrom, J. M.; Lindroth, E. Phys. Rev A 2019, 100, 043424; Vinblach, J.; Dahlstrom, J. M.; Lindroth, E. Atoms 2022, 10, 80).

Simulating Real-Time Molecular Electron Dynamics Efficiently Using the Time-Dependent Density Matrix Renormalization Group

Compared to ground-state electronic structure optimizations, accurate simulations of molecular real-time electron dynamics are usually much more difficult to perform. To simulate electron dynamics, the time-dependent density matrix renormalization group (TDDMRG) has been shown to offer an attractive compromise between accuracy and cost. However, many simulation parameters significantly affect the quality and efficiency of a TDDMRG simulation. So far, it is unclear whether common wisdom from ground-state DMRG carries over to the TDDMRG, and a guideline on how to choose these parameters is missing. Here, in order to establish such a guideline, we investigate the convergence behavior of the main TDDMRG simulation parameters, such as time integrator, the choice of orbitals, and the choice of matrix-product-state representation for complex-valued nonsinglet states. In addition, we propose a method to select orbitals that are tailored to optimize the dynamics. Lastly, we showcase the TDDMRG by applying it to charge migration ionization dynamics in furfural, where we reveal a rapid conversion from an ionized state with a σ character to one with a π character within less than a femtosecond.

Molecular-Frame Photoelectron Angular Distributions of CO in the Vicinity of Feshbach Resonances: An XCHEM Approach

The advent of ultrashort XUV pulses is pushing for the development of accurate theoretical calculations to describe ionization of molecules in regions where electron correlation plays a significant role. Here, we present an extension of the XCHEM methodology to evaluate laboratory- and molecular-frame photoelectron angular distributions in the region where Feshbach resonances are expected to appear. The performance of the method is demonstrated in the CO molecule, for which information on Feshbach resonances is very scarce. We show that photoelectron angular distributions are dramatically affected by the presence of resonances, to the point that they can completely reverse the preferred electron emission direction observed in direct nonresonant photoionization. This is the consequence of significant changes in the electronic structure of the molecule when resonances decay, an effect that is mostly driven by electron correlation in the ionization continuum. The present methodology can thus be helpful for the interpretation of angularly resolved photoionization time delays in this and more complex molecules.

Potential Energy Curves of Molecular Nitrogen for Singly and Doubly Ionized States with Core and Valence Holes

Theoretical description of potential energy curves (PECs) of molecular ions is essential for interpretation and prediction of coupled electron-nuclear dynamics following ionization of parent molecule. However, an accurate representation of these PECs for core or inner valence ionized state is nontrivial, especially at stretched geometries for double- or triple-bonded systems. In this work, we report PECs of singly and doubly ionized states of molecular nitrogen using state-of-the-art quantum chemical methods. The valence, inner valence, and core ionized states have been computed. A double-loop optimization scheme that separates the treatment of the core and the valence orbitals during the orbital optimization step of the multiconfiguration self-consistent field method has been implemented. This technique allows the energy to be converged to any desired ionized state with any number of core or inner-shell holes. The present work also compares the PECs obtained using both delocalized and localized sets of orbitals for the core hole states. The PECs of a number of singly and doubly ionized valence states have also been computed and compared with previous studies. The computed PECs reported here are expected to be of importance for future studies to understand the interplay between photoionization and Auger spectra during the breakup of molecular nitrogen when interacting with intense free electron lasers.

Attosecond timing of electron emission from a molecular shape resonance

Shape resonances in physics and chemistry arise from the spatial confinement of a particle by a potential barrier. In molecular photoionization, these barriers prevent the electron from escaping instantaneously, so that nuclei may move and modify the potential, thereby affecting the ionization process. By using an attosecond two-color interferometric approach in combination with high spectral resolution, we have captured the changes induced by the nuclear motion on the centrifugal barrier that sustains the well-known shape resonance in valence-ionized N2. We show that despite the nuclear motion altering the bond length by only 2%, which leads to tiny changes in the potential barrier, the corresponding change in the ionization time can be as large as 200 attoseconds. This result poses limits to the concept of instantaneous electronic transitions in molecules, which is at the basis of the Franck-Condon principle of molecular spectroscopy.

Full-dimensional theoretical description of vibrationally resolved valence-shell photoionization of H2O

We have performed a full-dimensional theoretical study of vibrationally resolved photoelectron emission from the valence shell of the water molecule by using an extension of the static-exchange density functional theory that accounts for ionization as well as for vibrational motion in the symmetric stretching, antisymmetric stretching, and bending modes. At variance with previous studies performed in centrosymmetric molecules, where vibrationally resolved spectra are mostly dominated by the symmetric stretching mode, in the present case, all three modes contribute to the calculated spectra, including intermode couplings. We have found that diffraction of the ejected electron by the various atomic centers is barely visible in the ratios between vibrationally resolved photoelectron spectra corresponding to different vibrational states of the remaining H2O+ cation (the so-called v-ratios), in contrast to the prominent oscillations observed in K-shell ionization of centrosymmetric molecules, including those that only contain hydrogen atoms around the central atoms, e.g., CH4. To validate the conclusions of our work, we have carried out synchrotron radiation experiments at the SOLEIL synchrotron and determined photoelectron spectra and v-ratios for H2O in a wide range of photon energies, from threshold up to 150 eV. The agreement with the theoretical predictions is good.

Exploring coherent electron excitation and migration dynamics by electron diffraction with ultrashort X-ray pulses

Exploring ultrafast charge migration is of great importance in biological and chemical reactions.

Angular momentum sensitive two-center interference

In quantum mechanics the Young-type double-slit experiment can be performed with electrons either traveling through a double slit or being coherently emitted from two inversion symmetric molecular sites. In the latter one the valence photoionization cross sections of homonuclear diatomic molecules were predicted to oscillate over kinetic energy almost 50 years ago. Beyond the direct proof of the oscillatory behavior of these photoionization cross sections σ, we show that the angular distribution of the emitted electrons reveals hitherto unexplored information on the relative phase shift between the corresponding partial waves through two-center interference patterns.