Hybrid-Basis Close-Coupling Interface to Quantum Chemistry Packages for the Treatment of Ionization Problems

Developing interoperable, accessible software via the atomic, molecular, and optical sciences gateway: A case study of the B-spline atomic R-matrix code graphical user interface

The Atomic, Molecular, and Optical Science (AMOS) Gateway is a comprehensive cyberinfrastructure for research and educational activities in computational AMO science. The B-Spline atomic R-Matrix (BSR) suite of programs is one of several computer programs currently available on the gateway. It is an excellent example of the gateway's potential to increase the scientific productivity of AMOS users. While the suite is available to be used in batch mode, its complexity does not make it well-suited to the approach taken in the gateway's default setup. The complexity originates from the need to execute many different computations and to construct generally complex workflows, requiring numerous input files that must be used in a specific sequence. The BSR graphical user interface described in this paper was developed to considerably simplify employing the BSR codes on the gateway, making BSR available to a large group of researchers and students interested in AMO science.

An energy-modified quantum defect method for the analysis of Rydberg spectra: Application to 2-butyne

The high resolution Rydberg absorption spectrum of 2-butyne C4H6 recorded previously at the SOLEIL synchrotron facility has been interpreted using multichannel quantum defect theory (MQDT). The calculations are based on the continuum scattering calculations of Xu et al., J. Chem. Phys. 136, 154303 (2012) and of Jacovella et al., J. Phys. Chem. A 119, 12339 (2015) pertaining to the dipole-allowed excited state symmetries in absorption from the ground state. In contrast to the traditional approach of calculating low-lying electronic states first and then attempting to extend the calculations to ever higher energy, here the analysis proceeds through the extension of these detailed calculations of the electronic continuum scattering down into the discrete region of the spectrum. The continuum reaction matrices and dipole transition moments are adapted to the discrete Rydberg region via the use of an energy-modified formulation of MQDT theory and associated energy dependences of the quantum defects. The analysis reproduces more than 40 Rydberg states from n ≈ 10 down to the 3d and 4s levels with an rms error of better than 20 cm-1. These belong to five Rydberg series with three different molecular symmetries. While the approach predicts many additional series, most of these are calculated and observed to carry only little oscillator strength. The analysis shows that the Rydberg spectrum is dominated by the excitation of an e″ symmetry electron of fδ and gπ type, in line with what previous studies of the above-threshold shape resonance of 2-butyne have shown. The present study is intended to serve as an example showing how first principles continuum calculations may be useful for the interpretation of highly bound discrete states in a range that poses problems for the standard ab initio techniques. The quantitative treatment of the dipole absorption cross sections is deferred to a future paper.

Nonadiabatic dynamics with classical trajectories: The problem of an initial coherent superposition of electronic states

Advances in coherent light sources and development of pump-probe techniques in recent decades have opened the way to study electronic motion in its natural time scale. When an ultrashort laser pulse interacts with a molecular target, a coherent superposition of electronic states is created and the triggered electron dynamics is coupled to the nuclear motion. A natural and computationally efficient choice to simulate this correlated dynamics is a trajectory-based method where the quantum-mechanical electronic evolution is coupled to a classical-like nuclear dynamics. These methods must approximate the initial correlated electron-nuclear state by associating an initial electronic wavefunction to each classical trajectory in the ensemble. Different possibilities exist that reproduce the initial populations of the exact molecular wavefunction when represented in a basis. We show that different choices yield different dynamics and explore the effect of this choice in Ehrenfest, surface hopping, and exact-factorization-based coupled-trajectory schemes in a one-dimensional two-electronic-state model system that can be solved numerically exactly. This work aims to clarify the problems that standard trajectory-based techniques might have when a coherent superposition of electronic states is created to initialize the dynamics, to discuss what properties and observables are affected by different choices of electronic initial conditions and to point out the importance of quantum-momentum-induced electronic transitions in coupled-trajectory schemes.

Resonant Photoionization of CO2 up to the Fourth Ionization Threshold

We present a comprehensive theoretical study of valence-shell photoionization of the CO2 molecule by using the XCHEM methodology. This method makes use of a fully correlated molecular electronic continuum at a level comparable to that provided by state-of-the-art quantum chemistry packages in bound-state calculations. The calculated total and angularly resolved photoionization cross sections are presented and discussed, with particular emphasis on the series of autoionizing resonances that appear between the first and the fourth ionization thresholds. Ten series of Rydberg autoionizing states are identified, including some not previously reported in the literature, and their energy positions and widths are provided. This is relevant in the context of ongoing experimental and theoretical efforts aimed at observing in real-time (attosecond time scale) the autoionization dynamics in molecules.

Computing Decay Widths of Autoionizing Rydberg States with Complex-Variable Coupled-Cluster Theory

We compute autoionization widths of various Rydberg states of neon and N2 by equation-of-motion coupled-cluster theory combined with complex scaling and complex basis functions. This represents the first time that complex-variable methods are applied to Rydberg states represented in Gaussian basis sets. A new computational protocol based on Kaufmann basis functions is designed to make these methods applicable to atomic and molecular Rydberg states. As a first step, we apply our protocol to the neon atom and compute widths of the 3s, 3p, 4p and 3d Rydberg states. We then proceed to compute the widths of the 3sσg, 3dσg, and 3dπg Rydberg states of N2, which belong to the Hopfield series. Our results demonstrate a decrease in the decay width for increasing angular momentum and principal quantum number within both Rydberg series.

Attosecond photoionization delays in the vicinity of molecular Feshbach resonances

Temporal delays extracted from photoionization phases are currently determined with attosecond resolution by using interferometric methods. Such methods require special care when photoionization occurs near Feshbach resonances due to the interference between direct ionization and autoionization. Although theory can accurately handle these interferences in atoms, in molecules, it has to face an additional, so far insurmountable problem: Autoionization is slow, and nuclei move substantially while it happens, i.e., electronic and nuclear motions are coupled. Here, we present a theoretical framework to account for this effect and apply it to evaluate time-resolved and vibrationally resolved photoelectron spectra and photoionization phases of N₂ irradiated by a combination of an extreme ultraviolet (XUV) attosecond pulse train and an infrared pulse. We show that Feshbach resonances lead to unusual non-Franck-Condon vibrational progressions and to ionization phases that strongly vary with photoelectron energy irrespective of the vibrational state of the remaining molecular cation.

Photoionization of the water molecule with XCHEM

We have evaluated total and partial photoionization cross sections, β asymmetry parameters, and molecular frame photoelectron angular distributions (MFPADs) of the water molecule by using the XCHEM methodology. This method accounts for electron correlation in the electronic continuum, which is crucial to describe Feshbach resonances and their autoionization decay. We have identified a large number of Feshbach resonances, some of them previously unknown, in the region between 12.2 and 18.7 eV, for which we provide energy positions and widths. Many of these resonances lead to pronounced peaks in the photoionization spectra, some of them remarkably wide (up to 0.2 eV, for resonances converging to the third ionization threshold), which should be observable in high-energy resolution experiments. We show that, in the vicinity of these peaks, both asymmetry parameters and MFPADs vary very rapidly with photoelectron energy, which, as in atoms and simpler molecules, reflects the interference between direct ionization and autoionization, which is mostly driven by electron correlation.

Quantum coherence in molecular photoionization

The study of onset and decay, as well as control of ultrafast quantum coherence in many-electron systems is in the focus of interest of attosecond physics. Interpretation of attosecond experiments detecting the ultrafast quantum coherence requires application of advanced theoretical and computational tools combining many-electron theory, description of the electronic continuum, including in the strong laser field scenario, as well as nuclear dynamics theory. This perspective reviews the recent theoretical advances in understanding the attosecond dynamics of quantum coherence in photoionized molecular systems and outlines possible future directions of theoretical and experimental study of coherence and entanglement in the attosecond regime.

Continuum Electronic States: The Tiresia Code

A multicenter (LCAO) B-spline basis is described in detail, and its capabilities concerning affording convergent solutions for electronic continuum states and wavepacket propagation are presented. It forms the core of the Tiresia code, which implements static-DFT and TDDFT hamiltonians, as well as single channel Dyson-DFT and Dyson-TDDFT descriptions to include correlation in the bound states. Together they afford accurate and computationally efficient descriptions of photoionization properties of complex systems, both in the single photon and strong field environments. A number of examples are provided.

Multi-electron excitation contributions towards primary and satellite states in the photoelectron spectrum

The computation of Dyson orbitals and corresponding ionization energies has been implemented within the Equation of Motion Coupled Cluster Singles, Doubles and Perturbative Triples (EOM-CC3) method. Coupled to an accurate...

Trends in angle-resolved molecular photoelectron spectroscopy

In this perspective article, main trends of angle-resolved molecular photoelectron spectroscopy in the laboratory up to the molecular frame, in different regimes of light-matter interactions, are highlighted with emphasis on foundations and most recent applications.

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.

Capturing Correlation Effects on Photoionization Dynamics

A highly correlated combination of the equation-of-motion coupled cluster (EOM-CC) Dyson orbital and the multicentric B-spline time-dependent density functional theory (TDDFT)-based approach is proposed and implemented within the single-channel approximation to describe molecular photoionization processes. The twofold objective of the approach is to capture interchannel coupling effects, missing in the B-spline DFT treatment, and to explore the response of Dyson orbitals to strong correlation effects and its influence on the photoionization observables. We validate our scheme by computing partial cross sections, branching ratios, asymmetry parameters, and molecular frame photoelectron angular distributions of simple molecules. Finally, the method has been applied to the study of photoelectron spectra of the Ni(C₃H₅)₂ molecule, where giant correlation effects completely destroy the Koopmans picture.

Dialogue on analytical and ab initio methods in attoscience

The perceived dichotomy between analytical and ab initio approaches to theory in attosecond science is often seen as a source of tension and misconceptions. This Topical Review compiles the discussions held during a round-table panel at the 'Quantum Battles in Attoscience' cecam virtual workshop, to explore the sources of tension and attempt to dispel them. We survey the main theoretical tools of attoscience-covering both analytical and numerical methods-and we examine common misconceptions, including the relationship between ab initio approaches and the broader numerical methods, as well as the role of numerical methods in 'analytical' techniques. We also evaluate the relative advantages and disadvantages of analytical as well as numerical and ab initio methods, together with their role in scientific discovery, told through the case studies of two representative attosecond processes: non-sequential double ionisation and resonant high-harmonic generation. We present the discussion in the form of a dialogue between two hypothetical theoreticians, a numericist and an analytician, who introduce and challenge the broader opinions expressed in the attoscience community.

Molecular fragmentation as a way to reveal early electron dynamics induced by attosecond pulses

We present a theoretical study of the electron and nuclear dynamics that would arise in an attosecond two-color XUV-pump/XUV-probe experiment in glycine. In this scheme, the broadband pump pulse suddenly ionizes the molecule and creates an electronic wave packet that subsequently evolves under the influence of the nuclear motion until it is finally probed by the second XUV pulse. To describe the different steps of such an experiment, we have combined a multi-reference static-exchange scattering method with a trajectory surface hopping approach. We show that by changing the central frequency of the pump pulse, i.e., by engineering the initial electronic wave packet with the pump pulse, one can drive the cation dynamics into a specific fragmentation pathway. Reminiscence of this early electron dynamics can be observed in specific fragmentation channels (not all of them) as a function of the pump-probe delay and in time-resolved photoelectron spectra at specific photoelectron energies. The optimum conditions to visualize the initial electronic coherence in photoelectron and photo-ion spectra depend very much on the characteristics of the pump pulse as well as on the electronic structure of the molecule under study.

First-Principles Simulations of Biological Molecules Subjected to Ionizing Radiation

Ionizing rays cause damage to genomes, proteins, and signaling pathways that normally regulate cell activity, with harmful consequences such as accelerated aging, tumors, and cancers but also with beneficial effects in the context of radiotherapies. While the great pace of research in the twentieth century led to the identification of the molecular mechanisms for chemical lesions on the building blocks of biomacromolecules, the last two decades have brought renewed questions, for example, regarding the formation of clustered damage or the rich chemistry involving the secondary electrons produced by radiolysis. Radiation chemistry is now meeting attosecond science, providing extraordinary opportunities to unravel the very first stages of biological matter radiolysis. This review provides an overview of the recent progress made in this direction, focusing mainly on the atto- to femto- to picosecond timescales. We review promising applications of time-dependent density functional theory in this context.

Accurate Description of Photoionization Dynamical Parameters

Calculation of dynamical parameters for photoionization requires an accurate description of the initial and final states of the system, as well as of the outgoing electron. We show that using a linear combination of atomic orbitals B-spline density functional theory (DFT) method to describe the outgoing electron, in combination with correlated equation of motion coupled cluster singles and double Dyson orbitals, gives good agreement with experiment and outperforms other simpler approaches, like plane and Coulomb waves, used to describe the photoelectron. Results are presented for cross-sections, angular distributions, and dichroic parameters in chiral molecules, as well as for photoionization from excited states. We also present a comparison with the results obtained using Hartree-Fock and DFT molecular orbitals selected according to Koopmans' theorem for the bound states.

The physical stage of radiolysis of solvated DNA by high-energy-transfer particles: insights from new first principles simulations

Electron dynamics simulations based on density functional theory are carried out on nanometric molecular systems to decipher the primary processes following irradiation of bio-macromolecules by high energy transfer charged particles.

Resonant photoionization of O2 up to the fourth ionization threshold

We present a detailed theoretical study of valence-shell photoionization of the oxygen molecule by using the recently proposed XCHEM method. This method makes use of a hybrid Gaussian and B-spline basis in the framework of a close-coupling approach to describe electron correlation in the molecular electronic continuum at a level comparable to that provided by multi-reference configuration interaction methods in bound state calculations. The computed total and partial photoionization cross sections are presented and discussed, with emphasis on the series of autoionizing resonances that appear between the first and the fourth ionization thresholds, i.e., photon energies between 12 and 18 eV. More than fifty autoionizing states are identified, including series not previously reported in the literature, and their energy positions and widths are provided. The present results illustrate the potential of the XCHEM approach to accurately describe molecular autoionization, which is mostly due to electron correlation. This is relevant in view of current experimental efforts aimed at providing real-time (attosecond) imaging of autoionization dynamics in molecules.

Disentangling Spectral Phases of Interfering Autoionizing States from Attosecond Interferometric Measurements

We have determined spectral phases of Ne autoionizing states from extreme ultraviolet and midinfrared attosecond interferometric measurements and ab initio full-electron time-dependent theoretical calculations in an energy interval where several of these states are coherently populated. The retrieved phases exhibit a complex behavior as a function of photon energy, which is the consequence of the interference between paths involving various resonances. In spite of this complexity, we show that phases for individual resonances can still be obtained from experiment by using an extension of the Fano model of atomic resonances. As simultaneous excitation of several resonances is a common scenario in many-electron systems, the present work paves the way to reconstruct electron wave packets coherently generated by attosecond pulses in systems larger than helium.

Restricted Correlation Space B-Spline ADC Approach to Molecular Ionization: Theory and Applications to Total Photoionization Cross-Sections

Herein is presented a new approach to the ab initio algebraic diagrammatic construction (ADC) schemes for the polarization propagator, which is explicitly designed to accurately and efficiently describe molecular ionization. The restricted correlation space (RCS) version of the ADC methods up to second order of perturbation theory is derived via the intermediate state representation (ISR) and implemented in the multicenter B-spline basis set for the electronic continuum. Remarkably a general close-coupling structure of the RCS-ADC many-electron wave function, connecting the N-particle to the ( N - 1)-particle ADC intermediate states, emerges naturally as a nontrivial result of the RCS ansatz. Moreover, the introduced RCS-ADC schemes prove to be particularly manageable from a computational point of view, overcoming the practical limitations of the conventional ADC approaches. The quality of the new RCS-ADC( n) approaches is verified by performing a series of total photoionization cross-section calculations on a test set of molecules. The excellent agreement of the results with existing accurate benchmarks demonstrates that the RCS versions of the ADC schemes are optimal and quantitatively accurate methods for studying multichannel molecular photoionization.

Optimal Basis Set for Electron Dynamics in Strong Laser Fields: The case of Molecular Ion H2. J Chem Theory Comput 2018;14:5846-5858. [PMID: 30247900 PMCID: PMC6255052 DOI: 10.1021/acs.jctc.8b00656]

A clear understanding of the mechanisms that control the electron dynamics in a strong laser field is still a challenge that requires interpretation by advanced theory. Development of accurate theoretical and computational methods, able to provide a precise treatment of the fundamental processes generated in the strong field regime, is therefore crucial. A central aspect is the choice of the basis for the wave function expansion. Accuracy in describing multiphoton processes is strictly related to the intrinsic properties of the basis, such as numerical convergence, computational cost, and representation of the continuum. By explicitly solving the 1D and 3D time-dependent Schrödinger equation for H2+ in the presence of an intense electric field, we explore the numerical performance of using a real-space grid, a B-spline basis, and a Gaussian basis (improved by optimal Gaussian functions for the continuum). We analyze the performance of the three bases for high-harmonic generation and above-threshold ionization for H2+. In particular, for high-harmonic generation, the capability of the basis to reproduce the two-center interference and the hyper-Raman phenomena is investigated.

Electron Correlation in the Ionization Continuum of Molecules: Photoionization of N2 in the Vicinity of the Hopfield Series of Autoionizing States

Direct measurement of autoionization lifetimes by using time-resolved experimental techniques is a promising approach when energy-resolved spectroscopic methods do not work. Attosecond time-resolved experiments have recently provided the first quantitative determination of autoionization lifetimes of the lowest members of the well-known Hopfield series of resonances in N₂. In this work, we have used the recently developed XCHEM approach to study photoionization of the N₂ molecule in the vicinity of these resonances. The XCHEM approach allows us to describe electron correlation in the molecular electronic continuum at a level similar to that provided by multireference configuration interaction methods in bound state calculations, a necessary condition to accurately describe autoionization, shakeup, and interchannel couplings occurring in this range of photon energies. Our results show that electron correlation leading to interchannel mixing is the main factor that determines the magnitude and shape of the N₂ photoionization cross sections, as well as the lifetimes of the Hopfield resonances. At variance with recent speculations, nonadiabatic effects do not seem to play a significant role. These conclusions are supported by the very good agreement between the calculated cross sections and those determined in synchrotron radiation and attosecond experiments.

Application of the complex Kohn variational method to attosecond spectroscopy

The complex Kohn variational method is extended to compute light-driven electronic transitions between continuum wave functions in atomic and molecular systems. This development enables the study of multiphoton processes in the perturbative regime for arbitrary light polarization. As a proof of principle, we apply the method to compute the photoelectron spectrum arising from the pump-probe two-photon ionization of helium induced by a sequence of extreme ultraviolet and infrared light pulses. We compare several two-photon ionization pump-probe spectra, resonant with the (2s2p) 1P 1 o Feshbach resonance, with independent simulations based on the atomic B-spline close-coupling STOCK code, and find good agreement between the two approaches. This finite-pulse perturbative approach is a step towards the ab initio study of weak-field attosecond processes in polyelectronic molecules.