Full-dimensional treatment of short-time vibronic dynamics in molecular high-harmonics generation process in methane

We present derivation and implementation of the Multi-Configurational Strong-Field Approximation with Gaussian nuclear Wave Packets (MC-SFA-GWP) -- a version of the molecular strong-field approximation which treats all electronic and nuclear degrees of freedom, including their correlations, quantum-mechanically. The technique allows, for the first time, realistic simulation of high-harmonic emission in polyatomic molecules without invoking reduced-dimensionality models for the nuclear motion or the electronic structure. We use MC-SFA-GWP to model isotope effects in high-harmonics generation (HHG) spectroscopy of methane. The HHG emission in this molecule transiently involves strongly vibronically-coupled $^2F_2$ electronic state of the $\rm CH_4^+$ cation. We show that the isotopic HHG ratio in methane contains signatures of: a) field-free vibronic dynamics at the conical intersection (CI); b) resonant features in the recombination cross-sections; c) laser-driven bound-state dynamics; as well as d) the well-known short-time Gaussian decay of the emission. We assign the intrinsic vibronic feature (a) to a relatively long-lived ($\ge4$ fs) vibronic wave packet of the singly-excited $\nu_4$ ($t_2$) and $\nu_2$ ($e$) vibrational modes, strongly coupled to the components of the $^2F_2$ electronic state. We demonstrate that these physical effects differ in their dependence on the wavelength, intensity, and duration of the driving pulse, allowing them to be disentangled. We thus show that HHG spectroscopy provides a versatile tool for exploring both conical intersections and resonant features in photorecombination matrix elements in the regime not easily accessible with other techniques

Conserving GW scheme for nonequilibrium quantum transport in molecular contacts

We give a detailed presentation of our recent scheme to include correlation effects in molecular transport calculations using the GW approximation within the non-equilibrium Keldysh formalism. We restrict the GW self-energy to the central region, and describe the leads by density functional theory (DFT). A minimal basis of maximally localized Wannier functions is applied both in the central GW region and the leads. The importance of using a conserving, i.e. fully self-consistent, GW self-energy is demonstrated both analytically and by numerical examples. We introduce an effective spin-dependent interaction which automatically reduces self-interaction errors to all orders in the interaction. The scheme is applied to the Anderson model in- and out of equilibrium. In equilibrium at zero temperature we find that GW describes the Kondo resonance fairly well for intermediate interaction strengths. Out of equilibrium we demonstrate that the one-shot G0W0 approximation can produce severe errors, in particular at high bias. Finally, we consider a benzene molecule between featureless leads. It is found that the molecule's HOMO-LUMO gap as calculated in GW is significantly reduced as the coupling to the leads is increased, reflecting the more efficient screening in the strongly coupled junction. For the IV characteristics of the junction we find that HF and G0W0[G_HF] yield results closer to GW than does DFT and G0W0[G_DFT]. This is explained in terms of self-interaction effects and life-time reduction due to electron-electron interactions.Comment: 23 pages, 16 figure

Development and Implementation of High-Level Propagator Methods for the Description of Electronically Stable and Unstable States

Interactions of atoms or molecules with electromagnetic radiation or free electrons can induce a variety of transformations. Apart from elastic scattering processes, in which the quantum states of the involved particles are preserved, inelastic scattering may occur. The distribution of product states depends on the kind of the interacting particles and the energy transferred in the scattering process. Among the possible transformations are electronic excitation, photoionization and the formation of electronic resonances, i.e., metastable electronic states which undergo subse quent decay by emission of an electron. The latter states can evolve in electronic excitation processes or as a result of electron attachment. In this dissertation, the implementation and application of quantum chemical propagator methods for the description of the above-mentioned processes are presented. More specifically, a number of perturbation theoretical methods based on the algebraic diagrammatic construction (ADC) schemes for the electron propagator and the polarization propagator are considered. In the framework of these methods, one-electron properties are available via the intermediate state representation (ISR) approach, which enables the computation of the explicit form of the respective wave functions. The third-order static self-energy Σ(3) appearing in the third-order ADC(3) equations can thereby be replaced by an improved fourth-order quantity resulting from the so-called Σ(4+)-procedure, and this option has been explored in the context of ADC for ionization potentials (IP-ADC), electron affinities (EA-ADC) and, for the first time, excitation energies (PP-ADC). In the first part of this dissertation, photoionization processes are considered, whose theoretical treatment is possible using IP-ADC(3). In the course of this work, the existing implementation of IP-ADC(3) in the Q-Chem quantum chemical program package has been extended by the possibility to compute photoelectron intensities, and therefore, to simulate photoelectron spectra. Other newly implemented features enable the interpretation of ionization transitions by means of visualization of Dyson orbitals and one-particle density matrix-based quantities as, e.g., detachment and attachment densities, which are available via the second-order ISR(2) approach. The accuracy of the IP-ADC(3)/ISR(2) methodology with respect to ionization potentials and one-particle properties of electron-detached states has been evaluated in a subsequent benchmark study. Therein, the results obtained for 44 electronic states of small molecules are compared to high-level configuration interaction results. For this set of transitions, ionization potentials exhibit a mean absolute error of |∆| ≈ 0.2 eV. For dipole moments, a relative error of |∆| = 19 % is found. In a second IP-ADC(3) study, the applicability of the newly implemented density matrix-based analyses for the interpretation of photoelectron spectra is demonstrated using the example of the galvinoxyl free radical. In the second part of this dissertation, electronic resonances are addressed. Due to the unbound nature of the involved electronic states, their theoretical treatment is challenging. Different theoretical approaches for their description within the framework of standard quantum chemical methods have been devised, two of which are considered in this work. First, the efficient implementation of the Fano-Stieltjes-ADC method in the Q-Chem program is presented. For the first time, the third-order PP-ADC(3) scheme as well as various unrestricted PP-ADC schemes have been combined with the Fano-Stieltjes formalism. The applicability of the implementation for the description of resonances in medium-sized organic molecules is demonstrated in a study of a Feshbach resonance in the naphthalene molecule. As a second option for the theoretical treatment of electronic resonances, the combination of the subspace-projected complex absorbing potential (CAP) method with PP- ADC(3) and EA-ADC(3) is considered. Results obtained using the novel CAP-EA-ADC and CAP-PP-ADC methods as implemented in the Q-Chem quantum chemical program package show an excellent agreement with theoretical best estimates and experimental data in studies of π* shape resonances in unsaturated molecules. Among the studied resonance states are the ²Πg resonance of the dinitrogen anion as well as the lowest π* resonances of the anions of the non-conjugated organic dienes norbornadiene and 1,4-cyclohexadiene. CAP-EA-ADC(3) calculations are in line with previous findings and show that a strong through-bond interaction mechanism reverses the natural ordering of the π* molecular orbitals in 1,4-cyclohexadiene

General Time-Dependent Configuration-Interaction Singles I: The Molecular Case

We present a grid-based implementation of the time-dependent configuration-interaction singles method suitable for computing the strong-field ionization of small gas-phase molecules. After outlining the general equations of motion used in our treatment of this method, we present example calculations of strong-field ionization of He, LiH, H2O, and C2H4 that demonstrate the utility of our implementation. The following paper [S. Carlström et al., following paper, Phys. Rev. A 106, 042806 (2022)] specializes to the case of spherical symmetry, which is applied to various atoms

Electron dynamics in complex time and complex space

This thesis investigates the dynamics of electrons ionized by strong low frequency laser fields, from a semiclassical perspective, developing a trajectory-based formalism to describe the interactions of the outgoing electron with the remaining ion. Trajectory models for photoionization generally arise in the regime known as optical tunnelling, where the atom is subjected to a strong, slow field, which tilts the potential landscape around the ion, forming a potential energy barrier that electrons can then tunnel through. There are multiple approaches that enable the description of the ionized electron, but they are generally limited or models derived by analogy, and the status of the trajectories is unclear. This thesis analyses this trajectory language in the context of the Analytical R-Matrix theory of photoionization, deriving a trajectory model from the fundamentals, and showing that this requires both the time and the position of the trajectory to be complex. I analyse this complex component of the position and I show that it requires careful handling: of the potentials where it appears, and of the paths in the complex plane that the trajectory is taken through. In this connection, I show that the Coulomb potential of the ion induces branch cuts in the complex time plane that the integration path needs to avoid, and I show how to navigate these branch cuts. I then use this formalism to uncover a kinematic mechanism for the recently discovered (Near-)Zero Energy Structures of above-threshold ionization. In addition, I analyse the generation of high-order harmonics of the driving laser that are emitted when the photoelectron recollides with the ion, using a pair of counter-rotating circularly polarized pulses to drive the emission, both in the context of the conservation of spin angular momentum and as a probe of the long-wavelength breakdown of the dipole approximation.Open Acces

Ionization of pyridine: interplay of orbital relaxation and electron correlation

The valence shell ionization spectrum of pyridine was studied using the third-order algebraic-diagrammatic construction approximation scheme for the one-particle Green’s function and the outer-valence Green’s function method. The results were used to interpret angle resolved photoelectron spectra recorded with synchrotron radiation in the photon energy range of 17–120 eV. The lowest four states of the pyridine radical cation, namely, 2A2 (1a 2 −1 1a2−1 ), 2A1(7a 1 −1 7a1−1), 2B1(2b 1 −1 2b1−1), and 2B2(5b 2 −1 5b2−1), were studied in detail using various high-level electronic structure calculation methods. The vertical ionization energies were established using the equation-of-motion coupled-cluster approach with single, double, and triple excitations (EOM-IP-CCSDT) and the complete basis set extrapolation technique. Further interpretation of the electronic structure results was accomplished using Dyson orbitals, electron density difference plots, and a second-order perturbation theory treatment for the relaxation energy. Strong orbital relaxation and electron correlation effects were shown to accompany ionization of the 7a1 orbital, which formally represents the nonbonding σ-type nitrogen lone-pair (nσ) orbital. The theoretical work establishes the important roles of the π-system (π-π* excitations) in the screening of the nσ-hole and of the relaxation of the molecular orbitals in the formation of the 7a1(nσ)−1 state. Equilibrium geometric parameters were computed using the MP2 (second-order Møller-Plesset perturbation theory) and CCSD methods, and the harmonic vibrational frequencies were obtained at the MP2 level of theory for the lowest three cation states. The results were used to estimate the adiabatic 0-0 ionization energies, which were then compared to the available experimental and theoretical data. Photoelectron anisotropy parameters and photoionization partial cross sections, derived from the experimental spectra, were compared to predictions obtained with the continuum multiple scattering approach

Software for the frontiers of quantum chemistry : An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange–correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear–electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an “open teamware” model and an increasingly modular design.This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.Peer reviewe