Molecular ionization energies and ground- and ionic-state properties using a non-Dyson electron propagator approach

Analytical Gradients for Electron-Attached and Ionized States for the Algebraic-Diagrammatic Construction Scheme for the Electron Propagator up to Third Order

The derivation and implementation of analytical gradients for methods based on the non-Dyson algebraic diagrammatic construction for the electron propagator, IP-ADC and EA-ADC, up to the third order is presented. Using nuclear gradients, ground-state equilibrium structures for small open-shell systems are calculated. In addition, we investigated the performance of IP/EA-ADC methods for the calculation of adiabatic ionization potentials and electron affinities for medium-sized organic molecules.

Fourth-Order Algebraic Diagrammatic Construction for Electron Detachment and Attachment: The IP- and EA-ADC(4) Methods

We present a non-Dyson fourth-order algebraic diagrammatic construction formulation of the electron propagator, featuring the distinct IP- and EA-ADC(4) schemes for the treatment of ionization and electron attachment processes. The algebraic expressions have been derived automatically using the intermediate state representation approach and implemented in the Q-Chem quantum-chemical program package. The performance of the novel methods is assessed with respect to high-level reference data for ionization potentials and electron affinities of closed- and open-shell systems. While only minor improvements over the corresponding third-order methods are observed for one-hole ionization and one-particle electron attachment processes from closed-shell systems (MAEIP-ADC(4) = 0.27 eV and MAEEA-ADC(4) = 0.05 eV), a significantly enhanced performance is found in case of open-shell reference states (MAEIP-ADC(4) = 0.11 eV and MAEEA-ADC(4) = 0.02 eV). A particularly appealing feature of the novel methods is their accurate treatment of satellite transitions. For closed-shell reference states, we obtain accuracies of MAEIP-ADC(4) = 0.81 eV and MAEEA-ADC(4) = 0.27 eV, while in case of open-shell reference states, mean absolute errors of MAEIP-ADC(4) = 0.15 eV and MAEEA-ADC(4) = 0.27 eV are found.

Reference Energies for Valence Ionizations and Satellite Transitions

Upon ionization of an atom or a molecule, another electron (or more) can be simultaneously excited. These concurrently generated states are called "satellites" (or shakeup transitions) as they appear in ionization spectra as higher-energy peaks with weaker intensity and larger width than the main peaks associated with single-particle ionizations. Satellites, which correspond to electronically excited states of the cationic species, are notoriously challenging to model using conventional single-reference methods due to their high excitation degree compared to the neutral reference state. This work reports 42 satellite transition energies and 58 valence ionization potentials (IPs) of full configuration interaction quality computed in small molecular systems. Following the protocol developed for the quest database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; and Loos, P.-F. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], these reference energies are computed using the configuration interaction using a perturbative selection made iteratively (CIPSI) method. In addition, the accuracy of the well-known coupled-cluster (CC) hierarchy (CC2, CCSD, CC3, CCSDT, CC4, and CCSDTQ) is gauged against these new accurate references. The performances of various approximations based on many-body Green's functions (GW, GF2, and T-matrix) for IPs are also analyzed. Their limitations in correctly modeling satellite transitions are discussed.

Dense-sparse quantum Monte Carlo algebraic diagrammatic construction and importance ranking

Quantum Monte Carlo Algebraic Diagrammatic Construction (QMCADC) has been proposed as a reformulation of the second-order ADC scheme for the polarization propagator within the projection quantum Monte Carlo formalism. Dense-sparse partitioning and importance ranking filtering strategies are now exploited to accelerate its convergence and to alleviate the sign problem inherent in such calculations. By splitting the configuration space into dense and sparse subsets, the corresponding projection operator is decomposed into four distinct blocks. Deterministic calculations handle the dense-to-dense and sparse-to-dense blocks, while the remaining blocks, dense-to-sparse and sparse-to-sparse, are stochastically evaluated. The dense set is efficiently stored in a fixed-size array, and the sparse set is represented through conventional floating random Monte Carlo walks. The stochastic projection is further refined through importance ranking criteria, enabling a reduction in the required number of walkers with a controllable bias. Our results demonstrate the integration of dense-sparse partitioning with importance ranking filtering to significantly enhance the efficiency of QMCADC, enabling large-scale molecular excited-state calculations. Furthermore, this novel approach maximizes the utilization of the sparsity of ADC(2), transforming QMCADC into a tailored framework for ADC calculations.

New-Generation Electron-Propagator Methods for Calculations of Electron Affinities and Ionization Energies: Tests on Organic Photovoltaic Molecules

A new generation of ab initio electron-propagator self-energies recently superseded its antecedents' accuracy and computational efficiency in calculating vertical ionization energies (VIEs) of closed-shell molecules. (See J. Chem. Phys. 2021, 155, 204107, J. Chem. Theory Comput. 2022, 18, 4927, J. Chem. Phys. 2023, 159, 124109.) No adjustable parameters were introduced in the generation of reference orbitals or in the construction of self-energies. The same approach has been extended in this work to vertical electron affinities (VEAs). Calculations were performed on 24 conjugated, organic photovoltaic molecules with diverse functional groups. These molecules are considerably larger than those studied in previous tests on VIEs. Several new-generation self-energies produce mean absolute errors (MAEs) below 0.1 eV versus ΔCCSD(T) (i.e., total energy differences from the coupled-cluster singles, doubles, and perturbative triples method) VIEs and VEAs obtained with identical basis sets. A composite model employs cubically and quintically scaling algorithms and power-law basis-set extrapolations based on augmented double-triple or triple-quadruple ζ data. Its MAEs are near 0.05 eV versus benchmark values, with 0.03 eV error bars for the lowest VIE and the highest VEA of each molecule. A more efficient and equally accurate composite model for calculating VIEs avoids full transformations of electron repulsion integrals to the molecular orbital basis. High probability factors support the diagonal self-energy approximation, wherein Dyson orbitals are proportional to canonical, Hartree-Fock orbitals.

A new generation of non-diagonal, renormalized self-energies for calculation of electron removal energies

A new generation of diagonal self-energies for the calculation of electron removal energies of molecules and molecular ions that has superseded its predecessors with respect to accuracy, efficiency, and interpretability is extended to include non-diagonal self-energies that permit Dyson orbitals to be expressed as linear combinations of canonical Hartree-Fock orbitals. In addition, an improved algorithm for renormalized methods eliminates the convergence difficulties encountered in the first studies of the new, diagonal self-energies. A dataset of outer-valence, vertical ionization energies with almost full-configuration-interaction quality serves as a standard of comparison in numerical tests. The new non-diagonal, renormalized methods are slightly more accurate than their diagonal counterparts, with mean absolute errors between 0.10 and 0.06 eV for outer-valence final states. This advantage is procured at the cost of an increase in the scaling of arithmetic bottlenecks that accompany the inclusion of non-diagonal self-energy terms. The new, non-diagonal, renormalized self-energies are also more accurate and efficient than their non-diagonal predecessors.

State-specific frozen natural orbital for reduced-cost algebraic diagrammatic construction calculations: The application to ionization problem

We have developed a reduced-cost algebraic diagrammatic construction (ADC) method based on state-specific frozen natural orbital and natural auxiliary functions. The newly developed method has been benchmarked on the GW100 test set for the ionization problem. The use of state-specific natural orbitals drastically reduces the size of the virtual space with a systematically controllable accuracy and offers a significant speedup over the standard ionization potential (IP)-ADC(3) method. The accuracy of the method can be controlled by two thresholds and nearly a black box to use. The inclusion of the perturbative correction significantly improves the accuracy of the calculated IP values, and the efficiency of the method has been demonstrated by calculating the IP of a molecule with 60 atoms and more than 2216 basis functions.

Algebraic Diagrammatic Construction Schemes Employing the Intermediate State Formalism: Theory, Capabilities, and Interpretation

Algebraic diagrammatic construction (ADC) schemes represent a family of ab initio methods for the calculation of excited electronic states and electron-detached and -attached states. All ADC methods have been demonstrated to possess great potential for molecular applications, e.g., for the calculation of absorption or photoelectron spectra or electron attachment processes. ADC originates from Green's function or propagator theory; however, most recent ADC developments heavily rely on the intermediate state representation or effective Liouvillian formalisms, which comprise new ADC methods and computational schemes for high-order properties. The different approaches for the calculation of excitation energies, ionization potentials, and electron affinities are intimately related, and they provide a coherent description of these quantities at equivalent levels of theory and with comparable errors. Most quantum chemical program packages contain ADC methods; however, the most complete ADC suite of methods can be found in the recent release of Q-Chem.

Vertical Ionization Potentials and Electron Affinities at the Double-Hybrid Density Functional Level

The double-hybrid (DH) time-dependent density functional theory is extended to vertical ionization potentials (VIPs) and electron affinities (VEAs). Utilizing the density fitting approximation, efficient implementations are presented for the genuine DH ansatz relying on the perturbative second-order correction, while an iterative analogue is also elaborated using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH approach. The favorable computational requirements of the present schemes are discussed in detail. The performance of the recently proposed spin-component-scaled and spin-opposite-scaled (SOS) range-separated (RS) and long-range corrected (LC) DH functionals is comprehensively assessed, while popular hybrid and global DH approaches are also discussed. For the benchmark calculations, up-to-date test sets are selected with high-level coupled-cluster references. Our results show that the ADC(2)-based SOS-RS-PBE-P86 approach is the most accurate and robust functional. This method consistently outperforms the excellent SOS-ADC(2) approach for VIPs, although the results are somewhat less satisfactory for VEAs. Among the genuine DH functionals, the SOS-ωPBEPP86 approach is also recommended for describing ionization processes, but its performance is even less reliable for electron-attached states. In addition, surprisingly good results are attained by the LC hybrid ωB97X-D functional, where the corresponding occupied (unoccupied) orbital energies are retrieved as VIPs (VEAs) within the present formalism.

Algebraic Diagrammatic Construction Theory for Simulating Charged Excited States and Photoelectron Spectra

Charged excitations are electronic transitions that involve a change in the total charge of a molecule or material. Understanding the properties and reactivity of charged species requires insights from theoretical calculations that can accurately describe orbital relaxation and electron correlation effects in open-shell electronic states. In this Review, we describe the current state of algebraic diagrammatic construction (ADC) theory for simulating charged excitations and its recent developments. We start with a short overview of ADC formalism for the one-particle Green's function, including its single- and multireference formulations and extension to periodic systems. Next, we focus on the capabilities of ADC methods and discuss recent findings about their accuracy for calculating a wide range of excited-state properties. We conclude our Review by outlining possible directions for future developments of this theoretical approach.

The Multistate Quantum Monte Carlo Algebraic Diagrammatic Construction Method

A multistate formulation of the recently developed quantum Monte Carlo (QMC) algebraic diagrammatic construction (ADC) method, QMCADC, is presented. QMCADC solves the Hermitian eigenvalue problem of the second-order ADC scheme for the polarization propagator stochastically by combining ADC schemes with projector quantum Monte Carlo (PQMC). It allows for massively parallel distributed computing and exploits the sparsity of the effective ADC matrix, thereby relaxing memory and processing requirements of ADC methods significantly. Here, the theory and implementation of the multistate variant of QMCADC are described, and our first proof-of-principle calculations for various molecular systems are shown. Indeed, multistate QMCADC enables sampling of an arbitrary number of low-lying excited states and can reproduce their vertical excitation energies with a marginal controllable error. The performance of multistate QMCADC is examined in terms of state-wise and overall accuracy as well as with respect to the balance in the treatments of excited states relatively to each other. The results are very promising as they show bias and imbalances among excited states to diminish as the number of sampling points increases. Furthermore, the impact of the quality of trial wave functions on the vertical excitation energies is investigated. A black-box approach for the generation of high quality trial wave functions internally is given.

Non-Dyson Algebraic Diagrammatic Construction Theory for Charged Excitations in Solids

We present the first implementation and applications of non-Dyson algebraic diagrammatic construction theory for charged excitations in three-dimensional periodic solids (EA/IP-ADC). The EA/IP-ADC approach has a computational cost similar to the ground-state Møller-Plesset perturbation theory, enabling efficient calculations of a variety of crystalline excited-state properties (e.g., band structure, band gap, density of states) sampled in the Brillouin zone. We use EA/IP-ADC to compute the quasiparticle band structures and band gaps of several materials (from large-gap atomic and ionic solids to small-gap semiconductors) and analyze the errors of EA/IP-ADC approximations up to the third order in perturbation theory. Our work also reports the first-ever calculations of ground-state properties (equation-of-state and lattice constants) of three-dimensional crystalline systems using a periodic implementation of third-order Møller-Plesset perturbation theory (MP3).

Electron Propagator Self-Energies versus Improved GW100 Vertical Ionization Energies

Ab initio electron propagator (EP) methods that are free of adjustable parameters in their self-energy formulae and in the generation of their orbital bases have been applied to the calculation of the lowest vertical ionization energies (VIEs) of the GW100 set. An improved set of standard results accompanied by irreducible representation assignments has been produced indirectly with coupled-cluster singles and doubles plus perturbative triples, i.e., CCSD(T), total energy differences at initial-state geometries reoptimized (in 28 cases) with the largest applicable point groups. The best compromises of accuracy and efficiency belong to a new generation of EP self-energies, several members of which may be derived from an intermediately normalized, Hermitized super-operator metric. The following diagonal self-energy methods are optimal: opposite-spin non-Dyson second order (os-nD-D2), approximately renormalized partial third order (P3+), approximately renormalized quasiparticle third order (Q3+), and non-Dyson approximately renormalized linear third order version B (nD-L3+B). Their mean absolute errors (MAEs) in electron volts and arithmetic scaling factors expressed in terms of occupied (O) and virtual (V) orbital dimensions are, respectively, (0.18, OV²), (0.14, O²V³), (0.15, O²V³), and (0.11, OV⁴). The 0.06 eV MAE for the non-diagonal, sixth-power (O²V⁴) Brueckner doubles, triple-field operator (BD-T1) EP method is exceeded by the 0.1 eV MAE with respect to experiments in seventh-power, ΔCCSD(T) calculations and indicates that BD-T1 may serve as a direct, spin-symmetry-conserving alternative in the generation of standard results for VIEs of larger, closed-shell molecules.

Interferometry of Quantum Revivals

It has recently been shown that an interferometric approach can be used to obtain Auger lifetimes in molecules in certain point groups. Here, we extend this concept to those molecular states for which Auger decay is energetically forbidden and which exhibit initial quasi-exponential decay followed by quantum revivals. We demonstrate that this allows us to extract the quasi-exponential decay rate and the revival timescale. We solve analytically a model containing a state coupled to the idealised Bixon-Jortner quasicontinuum, and we obtain an interferometric signature of revival which can be easily generalised to realistic systems. Moreover, we analyse how this revival signature is influenced by the system parameters, and we suggest optimal conditions for its observation. We therefore show that our new approach allows population revivals of a molecular state to be detected interferometrically.

Benchmarking CASPT3 Vertical Excitation Energies

Based on 280 reference vertical transition energies of various natures (singlet, triplet, valence, Rydberg, n → π∗, π → π∗, and double excitations) extracted from the QUEST database, we assess the accuracy of third-order multireference perturbation theory, CASPT3, in the context of molecular excited states. When one applies the disputable ionization- potential-electron-affinity (IPEA) shift, we show that CASPT3 provides a similar accuracy as its second-order counterpart, CASPT2, with the same mean absolute error of 0.11 eV. However, as already reported, we also observe that the accuracy of CASPT3 is almost insensitive to the IPEA shift, irrespective of the transition type and system size, with a small reduction of the mean absolute error to 0.09 eV when the IPEA shift is switched off.

Exploring the accuracy and usefulness of semi-empirically scaled ADC schemes by blending second and third order terms

Different approaches to mixed-order algebraic-diagrammatic construction (ADC) schemes are investigated. The performance of two different strategies for scaling third-order contributions to the ADC secular matrix is evaluated. Both considered schemes employ a single tuning parameter and conserve general properties inherent to all ADC methods such as hermiticity and size-consistency.The first approach, scaled-matrix ADC[(2)+x(3)], scales all contributions first occurring in ADC(3) equally and leads to an improvement of the accuracy of excitation energies compared to ADC(3) for x=0.4-0.5. However, with respect to excited state dipole moments this method provides lower accuracy than ADC(3). The second scaling approach, MP[(1)+x(2)]-ISR(3), scales the second order contributions of the ground-state wavefunction and derives a rigorous ADC scheme via the intermediate state representation (ISR) formalism. Although the error in excitation energies is not improved, this method provides insight into the relevance of the individual terms of the ADC(3) matrix and indicates, that the MP(2) wavefunction is indeed the optimal reference wavefunction for deriving a third-order single-reference ADC scheme.

Photoionization Observables from Multi-Reference Dyson Orbitals Coupled to B-Spline DFT and TD-DFT Continuum

We present a theoretical model to compute the accurate photoionization dynamical parameters (cross-sections, asymmetry parameters and orbital, or cross-section, ratios) from Dyson orbitals obtained with the multi-state complete active space perturbation theory to the second order (MS-CASPT2) method. Our new implementation of Dyson orbitals in OpenMolcas takes advantage of the full Abelian symmetry point group and has the corrected normalization. The Dyson orbitals are coupled to an accurate description of the electronic continuum obtained with a multicentric B-spline basis at the DFT and TD-DFT levels. Two prototype diatomic molecules, i.e., CS and SiS, have been chosen due to their smallness, which hides important correlation effects. These effects manifest themselves in the appearance of well-characterized isolated satellite bands in the middle of the valence region. The rich satellite structures make CS and SiS the perfect candidates for a computational study based on our highly accurate MS-CASPT2/B-spline TD-DFT protocol.

Ultrafast temporal evolution of interatomic Coulombic decay in NeKr dimers

We investigate interatomic Coulombic decay in NeKr dimers after neon inner-valence photoionization [Ne⁺(2s^-1)] using a synchrotron light source. We measure with high energy resolution the two singly charged ions of the Coulomb-exploding dimer dication and the photoelectron in coincidence. By carefully tracing the post-collision interaction between the photoelectron and the emitted ICD electron we are able to probe the temporal evolution of the state as it decays. Although the ionizing light pulses are 80 picoseconds long, we determine the lifetime of the intermediate dimer cation state and visualize the contraction of the nuclear structure on the femtosecond time scale.

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...

A new generation of diagonal self-energies for the calculation of electron removal energies

A new generation of diagonal self-energy approximations in ab initio electron propagator theory for the calculation of electron removal energies of molecules and molecular ions has been derived from an intermediately normalized, Hermitized super-operator metric. These methods and widely used antecedents such as the outer valence Green's function and the approximately renormalized partial third order method are tested with respect to a dataset of vertical ionization energies generated with a valence, triple-ζ, correlation-consistent basis set and a converged series of many-body calculations whose accuracy approaches that of full configuration interaction. Several modifications of the diagonal second-order self-energy, a version of G₀W₀ theory based on Tamm-Dancoff excitations and several non-diagonal self-energies are also included in the tests. All new methods employ canonical Hartree-Fock orbitals. No adjustable or empirical parameters appear. A hierarchy of methods with optimal accuracy for a given level of computational efficiency is established. Several widely used diagonal self-energy methods are rendered obsolete by the new hierarchy whose members, in order of increasing accuracy, are (1) the opposite-spin non-Dyson diagonal second-order or os-nD-D2, (2) the approximately renormalized third-order quasiparticle or Q3+, (3) the renormalized third-order quasiparticle or RQ3, (4) the approximately renormalized linear third-order or L3+, and (5) the renormalized linear third-order or RL3 self-energies.

Multireference Algebraic Diagrammatic Construction Theory for Excited States: Extended Second-Order Implementation and Benchmark

We present an implementation and benchmark of new approximations in multireference algebraic diagrammatic construction theory for simulations of neutral electronic excitations and UV/vis spectra of strongly correlated molecular systems (MR-ADC). Following our work on the first-order MR-ADC approximation [J. Chem. Phys. 2018, 149, 204113], we report the strict and extended second-order MR-ADC methods (MR-ADC(2) and MR-ADC(2)-X) that combine the description of static and dynamic electron correlation in the ground and excited electronic states without relying on state-averaged reference wave functions. We present an extensive benchmark of the new MR-ADC methods for excited states in several small molecules, including the carbon dimer, ethylene, and butadiene. Our results demonstrate that, for weakly correlated electronic states, the MR-ADC(2) and MR-ADC(2)-X methods outperform the third-order single-reference ADC approximation and are competitive with the results from equation-of-motion coupled cluster theory. For states with multireference character, the performance of the MR-ADC methods is similar to that of an N-electron valence perturbation theory. In contrast to conventional multireference perturbation theories, the MR-ADC methods have many attractive features, such as a straightforward and efficient calculation of excited-state properties and a direct access to excitations outside of the frontier (active) orbitals.

Core-Valence Attosecond Transient Absorption Spectroscopy of Polyatomic Molecules

Tracing ultrafast processes induced by interaction of light with matter is often very challenging. In molecular systems, the initially created electronic coherence becomes damped by the slow nuclear rearrangement on a femtosecond timescale which makes real-time observations of electron dynamics in molecules particularly difficult. In this work, we report an extension of the theory underlying the attosecond transient absorption spectroscopy (ATAS) for the case of molecules, including a full account for the coupled electron-nuclear dynamics in the initially created wave packet, and apply it to probe the oscillations of the positive charge created after outer-valence ionization of the propiolic acid molecule. By taking advantage of element-specific core-to-valence transitions induced by x-ray radiation, we show that the resolution of ATAS makes it possible to trace the dynamics of electron density with atomic spatial resolution.

Valence shell photoelectron angular distributions and vibrationally resolved spectra of imidazole: A combined experimental-theoretical study

Linearly polarized synchrotron radiation has been used to record polarization dependent valence shell photoelectron spectra of imidazole in the photon energy range 21-100 eV. These have allowed the photoelectron angular distributions, as characterized by the anisotropy parameter β, and the electronic state intensity branching ratios to be determined. Complementing these experimental data, theoretical photoionization partial cross sections and β-parameters have been calculated for the outer valence shell orbitals. The assignment of the structure appearing in the experimental photoelectron spectra has been guided by vertical ionization energies and spectral intensities calculated by various theoretical methods that incorporate electron correlation and orbital relaxation. Strong orbital relaxation effects have been found for the 15a', nitrogen lone-pair orbital. The calculations also predict that configuration mixing leads to the formation of several low-lying satellite states. The vibrational structure associated with ionization out of a particular orbital has been simulated within the Franck-Condon model using harmonic vibrational modes. The adiabatic approximation appears to be valid for the X ²A″ state, with the β-parameter for this state being independent of the level of vibrational excitation. However, for all the other outer valence ionic states, a disparity occurs between the observed and the simulated vibrational structure, and the measured β-parameters are at variance with the behavior expected at the level of the Franck-Condon approximation. These inconsistencies suggest that the excited electronic states may be interacting vibronically such that the nuclear dynamics occur over coupled potential energy surfaces.

CAP/EA-ADC method for metastable anions: Computational aspects and application to π* resonances of norbornadiene and 1,4-cyclohexadiene

The second- and third-order algebraic-diagrammatic construction schemes for the electron propagator for studies of electron attachment processes [EA-ADC(2) and EA-ADC(3)] have been extended to include the complex absorbing potential (CAP) method for the treatment of electronic resonances. Theoretical and conceptual aspects of the new CAP/EA-ADC methodology are studied in detail at the example of the well-known ²Π_g resonance of the nitrogen anion N₂ ^-. The methodology is further applied to π* shape resonances, for which ethylene is considered as a prototype. Furthermore, the first many-body treatment of the π₊ ^* and π_- ^* resonances of norbornadiene and 1,4-cyclohexadiene is provided, which have served as model systems for the concept of through-space and through-bond interactions for a long time.

Intermediate state representation approach to physical properties of molecular electron-attached states: Theory, implementation, and benchmarking

Computational schemes for comprehensive studies of molecular electron-attached states and the calculation of electron affinities (EAs) are formulated and implemented employing the intermediate state representation (ISR) formalism and the algebraic-diagrammatic construction approximation for the electron propagator (EA-ADC). These EA-ADC(n)/ISR(m) schemes allow for a consistent treatment of not only electron affinities and pole strengths up to third-order of perturbation theory (n = 3) but also one-electron properties of electron-attached states up to second order (m = 2). The EA-ADC/ISR equations were implemented in the Q-Chem program for Ŝ_z-adapted intermediate states, allowing also open-shell systems to be studied using unrestricted Hartree-Fock references. For benchmarking of the EA-(U)ADC/ISR schemes, EAs and dipole moments of various electron-attached states of small closed- and open-shell molecules were computed and compared to full configuration interaction data. As an illustrative example, EA-ADC(3)/ISR(2) has been applied to the thymine-thymine (6-4) DNA photolesion.

Time-resolved pump-probe spectroscopy with spectral domain ghost imaging

An atomic-level picture of molecular and bulk processes, such as chemical bonding and charge transfer, necessitates an understanding of the dynamical evolution of these systems. On the ultrafast timescales associated with nuclear and electronic motion, the temporal behaviour of a system is often interrogated in a 'pump-probe' scheme. Here, an initial 'pump' pulse triggers dynamics through photoexcitation, and after a carefully controlled delay a 'probe' pulse initiates projection of the instantaneous state of the evolving system onto an informative measurable quantity, such as electron binding energy. In this paper, we apply spectral ghost imaging to a pump-probe time-resolved experiment at an X-ray free-electron laser (XFEL) facility, where the observable is spectral absorption in the X-ray regime. By exploiting the correlation present in the shot-to-shot fluctuations in the incoming X-ray pulses and measured electron kinetic energies, we show that spectral ghost imaging can be applied to time-resolved pump-probe measurements. In the experiment presented, interpretation of the measurement is simplified because spectral ghost imaging separates the overlapping contributions to the photoelectron spectrum from the pump and probe pulse.

Efficient implementation of the single-reference algebraic diagrammatic construction theory for charged excitations: Applications to the TEMPO radical and DNA base pairs

We present an efficient implementation of the second- and third-order single-reference algebraic diagrammatic construction (ADC) theory for electron attachment and ionization energies and spectra [EA/IP-ADC(n), n = 2, 3]. Our new EA/IP-ADC program features spin adaptation for closed-shell systems, density fitting for efficient handling of the two-electron integral tensors, and vectorized and parallel implementation of tensor contractions. We demonstrate capabilities of our efficient implementation by applying the EA/IP-ADC(n) (n = 2, 3) methods to compute the photoelectron spectrum of the (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO) radical, as well as the vertical and adiabatic electron affinities of TEMPO and two DNA base pairs (guanine-cytosine and adenine-thymine). The spectra and electron affinities computed using large diffuse basis sets with up to 1028 molecular orbitals are found to be in good agreement with the best available results from the experiment and theoretical simulations.

Effect of spin-orbit coupling on decay widths of electronic decay processes

Auger-Meitner processes are electronic decay processes of energetically low-lying vacancies. In these processes, the vacancy is filled by an electron of an energetically higher lying orbital, while another electron is simultaneously emitted to the continuum. In low-lying orbitals, relativistic effects can not, even for light elements, be neglected. At the same time, lifetime calculations are computationally expensive. In this context, we investigate which effect spin-orbit coupling has on Auger-Meitner decay widths and aim for a rule of thumb for the relative decay widths of initial states split by spin-orbit coupling. We base this rule of thumb on Auger-Meitner decay widths of Sr4p^-1 and Ra6p^-1 obtained by relativistic FanoADC-Stieltjes calculations and validate it against Auger-Meitner decay widths from the literature.

Fano-ADC(2,2) method for electronic decay rates

Fano-ADC is a family of ab initio methods for the prediction of electronic decay widths in excited, singly and doubly ionized systems. It has been particularly successful in elucidating the geometry dependence of the inter-atomic decay widths in clusters and facilitated the prediction of new electronic decay phenomena. However, the available Fano-ADC schemes are limited to the second-order treatment of the initial state and the first-order treatment of the final states of the decay. This confines the applicability of the Fano-ADC approach to first-order decay processes, e.g., normal but not double Auger decay (DAD), and compromises the numerical accuracy of the schemes through the unbalanced treatment of electronic correlation. Here, we introduce the ADC(2,2) approximation for singly ionized states, which describes both initial and final states of the decay up to second order. We use the new scheme to construct the Fano-ADC(2,2) approximation for the decay widths and show that it provides superior accuracy for the decay widths of a series of processes. Moreover, the Fano-ADC(2,2) method provides access to second-order decay processes, such as DAD, which are qualitatively beyond the reach of the previously available Fano-ADC implementations.

Asymmetric Density Fitting with Modified Cholesky Decomposition Applied to Second-Order Electron Propagator

Computation of molecular orbital electron repulsion integrals (MO-ERIs) as a transformation from atomic orbital ERIs (AO-ERIs) is the bottleneck of second-order electron propagator calculations when a single orbital is studied. In this contribution, asymmetric density fitting is combined with modified Cholesky decomposition to generate efficiently the required MO-ERIs. The key point of the presented algorithms is to keep track of integrals through partial contractions performed on three-center AO-ERIs; these contractions are stored in RAM instead of the AO-ERIs. Two implementations are provided, an in-core, which reduces the arithmetic and memory scaling factors as compared to the four-center AO-ERIs contraction method, and a semidirect, which overcomes memory limitations by evaluating antisymmetrized MO-ERIs in batches. On the numerical side, the proposed approach is fast and stable. The bad effects due to ill conditioning, namely, several negative and close to zero eigenvalues due to machine round off errors of the matrix associated with the density fitting process, are effectively controlled by means of a modified Cholesky factorization that avoids the matrix inversion needed to perform the asymmetrical density fitting implementation. The numerical experience presented shows that the in-core implementation is highly competitive to perform calculations on medium and large basis sets, while the semidirect implementation has small variations in time by changes in the available memory. The general applicability is illustrated on a set of selected relatively large-size molecules.

Onset of ionic coherence and ultrafast charge dynamics in attosecond molecular ionisation

Here is presented a fully ab initio theoretical framework for simulating the correlated many-electron dynamics occurring during and emerging from molecular ionisation by attosecond laser pulses. This is based on the time-dependent (TD) version of the B-spline restricted correlation space (RCS)-algebraic diagrammatic construction (ADC) method, with the full description of the photoelectron and inclusion of electron correlation effects, such as shakeup processes and inter-channel couplings. The nature of the ultrafast charge dynamics in the molecular ion is elucidated by quantitatively predicting the degree of electronic coherence and eigenstate content of the prepared molecular cationic state, beyond the commonly used sudden approximation. The results presented here for the acetylene and ethylene molecules show that even in the high photon energy regime the simulated hole dynamics is quantitatively different from the prediction of the sudden approximation. Moreover, for high-bandwidth ionising pulse, the residual interaction between the cation, in highly-excited shake-up states, and the emitted slow photoelectron gives rise to a loss of coherence in the ionic system which can persist for the first few femtoseconds after ionisation.

Molecular Auger Interferometry

We introduce and present a theory of interferometric measurement of a normal Auger decay lifetime in molecules. Molecular Auger interferometry is based on the coherent phase control of Auger dynamics in a two-color (ω/2ω) laser field. We show that, in contrast to atoms, in oriented molecules of certain point groups the relative ω/2ω phase modulates the total ionization yield. A simple analytical formula is derived for the extraction of the lifetimes of Auger-active states from a molecular Auger interferogram, circumventing the need in either high-resolution or attosecond spectroscopy. We demonstrate the principle of the interferometric Auger lifetime measurement using inner-valence decay in CH_{3}F.

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.

Electron correlation effects in the photoionization of CO and isoelectronic diatomic molecules

This paper investigates the first sigma satellite band, which is by far the most prominent, in the valence photoelectron spectra for a set of isoelectronic diatomic molecules: carbon monoxide, carbon monosulfide, carbon monoselenide, silicon monoxide and boron monofluoride. In particular, we analyze the effect of the electronic structure, with the change of the atomic pair along the row and column of the periodic table on the position of the satellite peak as well as on the related dynamical observables profiles. For this investigation, highly correlated calculations have been performed on the primary ionic states and the satellite band for all the molecules considered. Cross sections for the primary ionic states, calculated using Dyson orbitals, have been compared with those obtained with Hartree-Fock and Density Functional Theory to probe the impact of the correlation in the bound states on the photoionization observables. Limitations of a simple intensity borrowing mechanism clearly result from the analysis of the satellite state, characterized by different features with respect to the relevant primary states.

Green's function coupled cluster formulations utilizing extended inner excitations

In this paper, we analyze new approximations of the Green's function coupled cluster (GFCC) method where locations of poles are improved by extending the excitation level of inner auxiliary operators. These new GFCC approximations can be categorized as the GFCC-i(n, m) method, where the excitation level of the inner auxiliary operators (m) used to describe the ionization potential and electron affinity effects in the N - 1 and N + 1 particle spaces is higher than the excitation level (n) used to correlate the ground-state coupled cluster wave function for the N-electron system. Furthermore, we reveal the so-called "n + 1" rule in this category [or the GFCC-i(n, n + 1) method], which states that in order to maintain size-extensivity of the Green's function matrix elements, the excitation level of inner auxiliary operators X _p (ω) and Y _q (ω) cannot exceed n + 1. We also discuss the role of the moments of coupled cluster equations that in a natural way assures these properties. Our implementation in the present study is focused on the first approximation in this GFCC category, i.e., the GFCC-i(2,3) method. As our first practice, we use the GFCC-i(2,3) method to compute the spectral functions for the N₂ and CO molecules in the inner and outer valence regimes. In comparison with the Green's function coupled cluster singles, doubles results, the computed spectral functions from the GFCC-i(2,3) method exhibit better agreement with the experimental results and other theoretical results, particularly in terms of providing higher resolution of satellite peaks and more accurate relative positions of these satellite peaks with respect to the main peak positions.