In nonrelativistic physics, the concepts of geometry and topology are usually applied to characterize spatial structures or structures in momentum space. We introduce the concept of temporal geometry, which encompasses the geometric and topological properties of temporal shapes, i.e., trajectories traced by the tip of a time-dependent vector. We apply it to electric field polarizations controlling ultrafast electron currents or induced polarization in chiral molecules. The central concepts of temporal geometry-Berry curvature and Berry connection-emerge as ubiquitous features of photoexcited, nonequilibrium, chiral electron dynamics. We demonstrate that the Berry curvature and Berry connection (1) rely on the polarization properties of light pulses, (2) can be introduced for multiphoton processes, and (3) control enantiosensitive geometric observables via nonequilibrium electronic dynamics excited by tailored laser fields. Our findings may open a way to ultrafast, topologically nontrivial, and enantiosensitive chemical dynamics.

We here describe a procedure for the calculation of photoelectron spectra in solution, including vibrational and dynamical solvent effect. Steady state vibronic spectra are computed in harmonic approximation including the...

We have theoretically investigated the ultrafast intramolecular hydrogen transfer in the glycine molecule after ionization, as observed by Castrovilli et al., J. Phys. Chem. Lett. 9, 6012-6016 (2018), following excitation of the molecule with an XUV attosecond pulse train of 1.5 fs duration. In this experiment, the interaction of the glycine molecule with the XUV pulse creates a superposition of electronic states, whose dynamics is coupled to the nuclear one. We employed the static exchange restricted active space density functional theory correlated approach, as implemented in the Tiresia code [Decleva et al., Molecules, 27(6), 2026 (2022)], to evaluate ionization probabilities. Coherence effects were studied through quantum dynamics simulations using the multi-layer multi-configuration time-dependent Hartree method on a vibronic coupling Hamiltonian model. Our findings indicate that, for the pulses used in the Castrovilli et al. experiment, electronic coherence dissipates very rapidly, in less than 3 fs. Consequently, we performed simulations starting from single electronic state. In addition, we described the long-term coupled electron-nuclear dynamics using the trajectory surface hopping method. Our results reveal that hydrogen transfer predominantly occurs when the active state reaches the cationic ground state. Charge analysis confirms that this process corresponds to a proton transfer.

Ultrafast time-resolved photoelectron spectra are reported for the vacuum-ultraviolet (VUV) photoionization of acetylene following excitation to the Ã1Au state via UV absorption at 200 nm. The excitation energy lies above the lowest dissociation threshold to C2H X̃2Σ+ + H, as well as above the threshold for adiabatic dissociation of the Ã1Au state to form C2H (Ã2Π) + H. The time-dependent mass spectra and photoelectron spectra provide insight into the intramolecular decay processes of the Ã1Au state. In addition, photoelectron spectra of the Ã1Au state with VUV light access both the X̃2Πu and Ã2Σg+ states of the ion, as well as the predicted, but previously unobserved, 1 2Πg state, which corresponds to a two-hole, one-particle configuration that lies in close proximity to the Ã2Σg+ state. The 1 2Πg state is split into 2A2 + 2B2 and 2Ag + 2Bg states in the cis and trans configurations, respectively. Electronic structure calculations, along with trajectory calculations, reproduce the principal features of the experimental data and confirm the assignment of the 1 2Πg state.

Tracking the multifarious ultrafast electronic and structural changes occurring in a molecule during a photochemical transformation is a challenging endeavor that benefits from recent experimental and computational progress in time-resolved techniques. Measurements of valence electronic states, which provide a global picture of the bonding structure of the molecule, and core electronic states, which provide insight into the local environment, traditionally require different approaches and are often studied separately. Here, we demonstrate that X-ray pulses from a seeded free-electron laser (FEL) enable the measurement of high-resolution, time-resolved X-ray photoelectron spectra (XPS) that capture weak satellite states resulting from shake-down processes in a valence-excited molecule. This approach effectively combines the advantages of both valence- and core-state investigations. We applied this method to investigate photoexcited CS_2 molecules, where the role of internal conversion (IC) and intersystem crossing (ISC) in determining the pre-dissociation dynamics is controversial. We present XPS spectra from photoexcited CS_2, obtained at the FERMI FEL. High-resolution measurements, compared to the corresponding spectra obtained from accurate multireference quantum chemical calculations, reveal that shake-down satellite channels are highly sensitive to both valence electronic and geometric changes. Previous studies of the pre-dissociation dynamics have led to uncertain assignments of the branching between singlet and triplet excited states. We derive a propensity rule that demonstrates the spin-selectivity of the shake-downs. This selectivity allows us to unequivocally assign contributions from the bright and dark singlet excited states, with populations tracked along the pre-dissociation dynamic pathway.

In this article the recent developments of the open-source OpenMolcas chemistry software environment, since spring 2020, are described, with the main focus on novel functionalities that are accessible in the stable branch of the package and/or via interfaces with other packages. These community developments span a wide range of topics in computational chemistry, and are presented in thematic sections associated with electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report represents a useful summary of these developments, and it offers a solid overview of the chemical phenomena and processes that OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

Chiroptical effects using circularly polarized light produce signals that change sign when switching either molecular handedness (enantiosensitivity) or the light helicity (circular dichroism). Here, we break this enantiosensitive-and-dichroic paradigm by measuring a new type of chiroptical signal which is enantiosensitive but not dichroic. We photoionize chiral molecules using a strong laser field and detect the three-dimensional photoelectron momentum distribution. The non-dichroic, enantiosensitive asymmetry is encoded in octupolar and higher multipolar terms in the photoelectron angular distribution, which appear in multiphoton ionization with elliptically polarized fields or cross polarized two-color fields. The robustness of the enantiosensitivity with respect to the relative phase between the vectorial components of the ionizing field represents an example of symmetry protection, and opens unexplored opportunities for imaging ultrafast dynamics in chiral molecules, such as enantiosensitive photoelectron spectroscopy with bright squeezed vacuum states.

Reconstruction of attosecond beatings by two-photon interferences (RABBIT) has amply been used to retrieve photoionization delays from photoelectron spectra measured in atoms and, more recently, in molecules. For the latter, the molecular orientation and multicenter nature of the potential felt by the escaping electron often makes the extraction of these delays problematic. One of the complications comes from the fact that the energy separation between the states of the resulting molecular cation is of the order of the photon energy of the driving infrared (IR) field, so that, during the ionization process, the IR field may induce resonant transitions between such states. This adds a third ionization path to the standard two-path ionization scheme of RABBIT. Here we present a detailed theoretical study of RABBIT in the acetylene molecule in which we have explicitly evaluated time-resolved photoelectron spectra as those recorded in actual experiments. We do so for both random and well-defined orientations of the molecule, and for photoelectron spectra integrated over and resolved in the photoelectron emission angle. We show that the presence of this additional third path can strongly affect the values and physical meaning of photoionization delays extracted from fits based on the commonly used two-path interference scheme. This is indeed the case for acetylene molecules parallel to the light polarization direction, where the extracted delays strongly depend on the IR frequency, while for molecules perpendicular to the polarization direction the standard two-path RABBIT conditions are fulfilled.

We report a study of the electronic and nuclear relaxation dynamics of the photoexcited RNA base uracil in the gas phase using time-resolved core-level photoelectron spectroscopy together with high-level calculations. The dynamics was investigated by trajectory surface hopping calculations, and the core ionization energies were calculated for geometries sampled from these. The molecule was excited by a UV laser and dynamics probed on the oxygen, nitrogen, and carbon sites by core electron spectroscopy. We find that the main de-excitation channel of the initially excited S2(ππ*) state involves internal conversion to the S1(nπ*) state with a time constant of 17 ± 4 fs, while a portion of S2(ππ*) population returns directly to the ground state by internal conversion. We find no evidence that the S1(nπ*) state decays to the ground state; instead, it decays to triplet states with a time constant of 1.6 ± 0.4 ps. Oscillations of the S1(nπ*) state O 1s intensity as a function of time correlate with those of calculated C4═O8 and C5═C6 bond lengths, which undergo a sudden expansion following the initial π → π* excitation. Our calculations support our interpretation of the data and provide detailed insight into the relaxation processes of uracil.

We show that the photoelectron angular distributions produced by elliptical and cross-polarized two-color laser fields interacting with randomly oriented chiral molecules decompose into four irreducible representations of the D_2h point group. One of these (A_u) corresponds to a non-dichroic enantiosensitive (NoDES) contribution. This NoDES contribution has opposite sign for opposite enantiomers but remains invariant under reversal of the field ellipticity, enabling chirality detection that is robust against variations of the relative phase between orthogonal field components. We propose a protocol to isolate this component using only two velocity-map imaging projections and validate it through numerical simulations. Our calculations, performed in the two-photon resonantly-enhanced ionization, multi-photon, and strong-field ionization regimes with cross-polarized two-color fields show that the NoDES signal reaches about 1% of the energy-resolved ionization yield, comparable to photoelectron circular dichroism and much larger than standard magnetic-dipole chiroptical effects. NoDES spectroscopy thus provides a symmetry-protected and phase-robust route to probe molecular chirality on the ultrafast time scale. The experimental confirmation of our theory is presented in the companion paper [L. Fede et al., arXiv (2025)].

We create a beam of chiral topological light - light that displays temporal local chirality with an azimuthally varying handedness characterized by an integer topological charge. We apply this new type of light to detect molecular chirality via High Harmonic Generation spectroscopy and demonstrate that its topology is imprinted onto the molecular response, leading to enantiosensitive observables that are robust against common experimental noise.

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 beta-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).

The topological response of matter to electromagnetic fields is a highly demanded property in materials design and metrology due to its robustness against noise and decoherence, stimulating recent advances in ultrafast photonics. Embedding topological properties into the enantiosensitive optical response of chiral molecules could therefore enhance the efficiency and robustness of chiral optical discrimination. Here we achieve such a topological embedding by introducing the concept of chiral topological light—a light beam which displays chirality locally, with an azimuthal distribution of its handedness described globally by a topological charge. The topological charge is mapped onto the azimuthal intensity modulation of the non-linear optical response, where enantiosensitivity is encoded into its spatial rotation. The spatial rotation is robust against intensity fluctuations and imperfect local polarization states of the driving field. Our theoretical results show that chiral topological light enables detection of percentage-level enantiomeric excesses in randomly oriented mixtures of chiral molecules, opening a way to new, extremely sensitive and robust chiro-optical spectroscopies with attosecond time resolution.

We present a thorough theoretical and experimental investigation of photoionization time delays in the N2O molecule. Our theory provides actual XUV+IR time-resolved photoelectron spectra as measured in real reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) experiments. This requires not only accounting for the interaction between the XUV field and the neutral molecule, but also between the IR field and the ejected electron, which is only possible through explicit evaluation of a large number of dipole couplings between molecular electronic continuum states. To compare with the results of these calculations we have performed RABBIT experiments in which the ejected electron and the resulting ionic fragments are measured in coincidence, thus allowing us to obtain photoionization delays for a particular orientation of the molecule with respect to the polarization of the XUV and IR fields. We have found very good agreement between calculated and measured RABBIT spectra for both nondissociative and dissociative ionization channels. In particular, we unambiguously show a photoionization delay of about 60 as in the vicinity of a well-known shape resonance of N2O in the nondissociative ionization channel. More importantly, we show a dramatic effect of the IR field in the orientation-resolved ionization delays in the whole photon energy range investigated in this paper (18-40 eV), even at the level of relative ionization delays (i.e., delays referred to an internal reference delay) where the effect of the IR field is generally assumed to cancel out. Finally, we explicitly show that the problem of spectral congestion inherent to most molecular systems, which usually prevents extraction of photoionization delays, is substantially alleviated by resolving the molecular orientation or, ideally, by resolving both the molecular orientation and the electron emission angle, where access to perfectly isolated ionization channels is possible at specific angles.

The photodissociation dynamics of UV excited CS2 are investigated using time-resolved Auger-Meitner (AM) spectroscopy. AM decay is initiated by inner-shell ionisation with a femtosecond duration x-ray (179.9 eV) probe generated by the FERMI free electron laser. The time-delayed x-ray probe removes an electron from the S(2p) orbital leading to secondary emission of a high energy electron through AM decay. We monitor the electron kinetic energy of the AM emission as a function of pump-probe delay and observe time-dependent changes in the spectrum that correlate with the formation of bound, excited-state CS2 molecules at early times, and CS + S fragments on the picosecond timescale. The results are analysed based on a simplified kinetic scheme that provides a time constant for dissociation of approximately 1.2 ps, in agreement with previous time-resolved x-ray photoelectron spectroscopy measurements.

Photoionization as a half-scattering process is not instantaneous. Usually, time delays in photoionization are on the order of tens of attoseconds. In going from a single atom to a nano-object, one can expect the delay to increase, since the photoelectron scatters over a larger distance. Here we show that this intuition is not correct when comparing three-dimensional and planar molecules. Using attosecond interferometry, we find that the time delays in two-dimensional (2D) carbon-based molecules can be significantly shorter than those of three-dimensional counterparts. The measured time delay carries the signature of the spatial distribution of the 2D hole created in the residual molecular cation, allowing us to obtain its dimensions with angstrom accuracy. Our results demonstrate that the photoionization delay depends on the symmetry and shape of the created hole, as we show by identifying a quadrupole contribution in the measured delay of 2D molecules. Attosecond interferometry measurements of photoionization delays in planar carbon-based molecules can provide information on the dimension and shape of the two-dimensional hole generated in the process.

The Tiresia program [1] provides access to numerically accurate solutions of the one-particle Schrodinger equation for highly excited states of complex polyatomic molecules, both bound and continuum, that cannot be described by conventional Quantum Chemistry approaches. It is based on an expansion of the required solution in a local multicentric basis set, with primitive functions built as products of a radial B-spline times a real spherical harmonic. In conjunction with Density Functional Theory (DFT), it has been extensively employed in a large variety of photoionization studies, also for rather large systems. Highly excited bound states as well as wavepacket propagation can also be accurately described. In fact, the flexibility of the basis essentially allows accurate solutions of linear operator equations, like Poisson or inhomogeneous perturbative equations, which are employed in the code. The program is parallelized with standard MPI-I instructions and makes extensive use of the Scalapack linear algebra library. Ancillary programs are available for the evaluation of photoionization cross sections and angular distributions from randomly to fully oriented molecules.Program summaryProgram Title: TiresiaCPC Library link to program files: https://doi .org /10 .17632 /fcrjxwgjxh .1Licensing provisions: GPLv3 Programming language: Fortran77, Fortran90, MPI Supplementary material: Program manual documentNature of problem: Accurate solutions for highly excited and continuum electronic states in complex polyatomic molecules. Molecular photoionization cross sections and angular distributions under high energy, high intensity radiation pulses from Synchrotron radiation and laser sources, photoelectron imaging in pump-probe experiments, basis for electronic wavepackets under ultrafast or nonperturbative excitation.Solution method: Solution of the Schrodinger and similar linear operator equations in a finite domain is obtained via basis set expansion. Flexible basis set, that may approach practical completeness within the domain, is obtained as a multicenter set of B-spline radial functions times spherical harmonics. Accurate numerical integration is employed for the evaluation of matrix elements, and conventional diagonalization for bound states, or Galerkin approach for the full multichannel solution in the continuum. Full hamiltonian and dipole matrices in the spectral basis are available for time propagation. DFT many-body description is available, and strong correlations in the bound states may be incorporated via Dyson orbitals.Additional comments including restrictions and unusual features: The code is noted for computational efficiency, which allows fast yet reasonably accurate photoionization calculations for medium-sized molecules, allowing, e.g., calculations at many molecular geometries as required to describe time-resolved photoelectron spectra in pump-probe experiments.

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

Calculations of the photoionization cross section of C60 including all valence and core subshells have been carried out for photon energies up to 1 keV using density functional theory (DFT) and time-dependent DFT (TDDFT) within the framework of a fully molecular model. The high-energy valence subshell cross sections behave rather differently than the results from model potentials where the cross section falls far too rapidly with energy. This unphysical behavior of the model calculations is traced to smearing out of the carbon nuclei in the model potentials which makes it difficult for momentum to be conserved at the higher energies. Comparison with 60 times carbon atomic cross section sheds light on similarities and differences. The high energy behavior of individual valence cross sections reflects the amount of C 2s/2p mixing in the molecular orbitals.

The K-edge photoelectron and KLL Auger-Meitner decay spectra of Argon have been investigated computationally at the restricted active space perturbation theory to the second order level using biorthonormally transformed orbital sets. Binding energies were computed for the Ar 1s primary ionization, as well as for satellite states originated from shake-up and shake-off processes. Based on our calculations, the contributions of shake-up and shake-off states to the KLL Auger-Meitner spectra of Argon have been completely elucidated. Our results are compared with recent state-of-the-art experimental measurements on Argon.