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Vacancies in the L 1 shell of atoms and molecules can decay non-radiatively via Coster-Kronig decay whereby the vacancy is filled by an electron from the L 2,3 shell while a second electron is emitted into the ionization continuum. This process is akin to Auger decay, but in contrast to Auger electrons, Coster-Kronig electrons have rather low kinetic energies of less than 50 eV. In the present work, we extend recently introduced methods for the construction of molecular Auger spectra that are based on complex-scaled equation-of-motion coupled-cluster theory to Coster-Kronig decay. We compute ionization energies as well as total and partial decay widths for the 2s -1 states of argon and hydrogen sulfide and construct the L 1 L 2,3 M Coster-Kronig and L 1 MM Auger spectra of these species. Whereas our final spectra are in good agreement with the available experimental and theoretical data, substantial disagreements are found for various branching ratios suggesting that spin-orbit coupling makes a major impact on Coster-Kronig decay already in the third period of the periodic table.

We investigate the reliability of two cost-effective coupled-cluster methods for computing spin-state energetics and spin-related properties of a set of open-shell transition-metal complexes. Specifically, we employ the second-order approximate coupled-cluster singles and doubles (CC2) method and projection-based embedding that combines equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) with density functional theory (DFT). The performance of CC2 and EOM-CCSD-in-DFT is assessed against EOM-CCSD. The chosen test set includes two hexaaqua transition-metal complexes containing Fe(II) and Fe(III), and a large Co(II)-based single-molecule magnet with a non-aufbau ground state. We find that CC2 describes the excited states more accurately, reproducing EOM-CCSD excitation energies within 0.05 eV. However, EOM-CCSD-in-DFT excels in describing transition orbital angular momenta and spin-orbit couplings. Moreover, for the Co(II) molecular magnet, using EOM-CCSD-in-DFT eigenstates and spin-orbit couplings, we compute spin-reversal energy barriers, as well as temperature-dependent and field-dependent magnetizations and magnetic susceptibilities that closely match experimental values within spectroscopic accuracy. These results underscore the efficiency of CC2 in computing state energies of multi-configurational, open-shell systems and highlight the utility of the more cost-efficient EOM-CCSD-in-DFT for computing spin-orbit couplings and magnetic properties of complex and large molecular magnets.

We report the first coupled-cluster study of Auger decay in heavy metals. The zinc atom is used as a case study due to its relevance to the Auger emission properties of the 67 Ga radionuclide. Coupled-cluster theory combined with complex basis functions is used to describe the transient nature of the core-ionized zinc atom. We also introduce second-order Møller-Plesset perturbation theory as an alternative method for computing partial Auger decay widths. Scalar-relativistic effects are included in our approach for computing Auger electron energies by means of the spin-free exact two-component one-electron Hamiltonian, while spin-orbit coupling is treated by means of perturbation theory. We center our attention on the K-edge Auger decay of zinc dividing the spectrum into three parts (K-LL, K-LM, and K-MM) according to the shells involved in the decay. The computed Auger spectra are in good agreement with experimental results. The most intense peak is found at an Auger electron energy of 7432 eV, which corresponds to a 1 D 2 final state arising from K-L 2 L 3 transitions. Our results highlight the importance of relativistic effects for describing Auger decay in heavier nuclei. Furthermore, the effect of a first solvation shell is studied by modeling Auger decay in the hexaaqua-zinc(II) complex. We find that K-edge Auger decay is slightly enhanced by the presence of the water molecules as compared to the bare atom.

We compute EOM-EA-CCSD and EOM-EA-CCSDT potential energy curves and one-electron properties of several anions at bond lengths close to where these states become unbound. We compare the anions of HCl and pyrrole, which are associated with s-wave scattering, with N 2 and H 2 , which correspond to resonances. For HCl and pyrrole, we observe, on inclusion of diffuse basis functions, a pronounced bending effect in the anionic potential energy curves near the crossing points with their corresponding neutral molecules. Additionally, we observe that the Dyson orbital and second moment of the electron density become extremely large in this region; for HCl, the size of the latter becomes 5 orders of magnitude larger over a range of 5 pm. This behaviour is not observed in H 2 or N 2 . Our work thus shows that bound state electronic-structure methods can distinguish between anions that turn into electronic resonances and those associated with s-wave scattering states.

Computational study of electronic resonances is still a very challenging topic, with the phenomenon of dissociative electron attachment (DEA) being one of the multiple features worth investigating. Recently, we extended the charge stabilization method from energies to properties of conceptual density functional theory and applied this to metastable anionic states of ethene and chlorinated ethene derivatives to study the DEA mechanism present in these compounds. We now present an extension to spatial functions, namely, the electronic Fukui function and the electron localization function. The results of our analysis show that extrapolated spatial functions are relevant and useful for more precise localization of the unbound electron. Furthermore, we report for the first time the combination of the electron localization function with Berlin's binding function for these challenging electronic states. This promising methodology allows for accurate predictions of when and where DEA will happen in the molecules studied and provides more insight into the process., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Complex absorbing potentials (CAPs) are artificial potentials added to electronic Hamiltonians to make the wave function of metastable electronic states square-integrable. This makes the electronic-structure theory of resonances comparable to that of bound states, thus reducing the complexity of the problem. However, the most often used box and Voronoi CAPs depend on several parameters that have a substantial impact on the numerical results. Among these parameters are the CAP strength and a set of spatial parameters that define the onset of the CAP. It has been a common practice to minimize the perturbation of the resonance states due to the CAP by optimizing the strength parameter while fixing the onset parameters, although the performance of this approach strongly depends on the chosen onset. Here, we introduce a more general approach that allows one to optimize not only the CAP strength but also the spatial parameters. We show that fixing the CAP strength and optimizing the spatial parameters is a reliable way to minimize CAP perturbations. We illustrate the performance of this new approach by computing resonance energies and widths of the temporary anions of dinitrogen, ethylene, and formic acid. This is done at the Hartree-Fock and equation-of-motion coupled-cluster singles and doubles levels of theory using full and projected box and Voronoi CAPs.

We compute autoionization widths of various Rydberg states of neon and N 2 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 3sσ g , 3dσ g , and 3dπ g Rydberg states of N 2 , 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.

We present the theory for the evaluation of nonadiabatic couplings (NACs) involving resonance states within the complex absorbing potential equation-of-motion coupled-cluster (CAP-EOM-CC) framework implemented within the singles and doubles approximation. Resonance states are embedded in the continuum and undergo rapid decay through autodetachment. In addition, nuclear motion can facilitate transitions between different resonances and between resonances and bound states. These nonadiabatic transitions affect the chemical fate of resonances and have distinct spectroscopic signatures. The NAC vector is a central quantity needed to model such effects. In the CAP-EOM-CC framework, resonance states are treated on the same footing as bound states. Using the example of fumaronitrile, which supports a bound radical anion and several anionic resonances, we analyze the NAC between bound states and pseudocontinuum states, between bound states and resonances, and between two resonances. We find that the NAC between a bound state and a resonance is nearly independent of the CAP strength and thus straightforward to evaluate, whereas the NAC between two resonance states or between a bound state and a pseudocontinuum state is more difficult to evaluate.

When a vacancy is created in an inner-valence orbital of a dimer of atoms or molecules, the resulting species can undergo interatomic/intermolecular Coulombic decay (ICD): the hole is filled through a relaxation process that leads to a doubly ionized cluster with two positively charged atoms or molecules. Since they are subject to electronic decay, inner-valence ionized states are not bound states but electronic resonances whose transient nature can only be described with special quantum-chemical methods. In this work, we explore the capacity of equation-of-motion coupled-cluster theory with two techniques from non-Hermitian quantum mechanics, complex basis functions and Feshbach-Fano projection with a plane wave description of the outgoing electron, to describe ICD. To this end, we compute the decay rates of several dimers: Ne2, NeAr, NeMg, and (HF)2, among which the energy of the outgoing electron varies between 0.3 and 16 eV. We observe that both methods deliver better results when the outgoing electron is fast, but the characteristic R-6 distance dependence of the ICD width is captured much better with complex basis functions., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

We present an ab initio computational study of the Auger spectra of methane, ethane, ethylene, and acetylene. Auger spectroscopy is an established technique to probe the electronic structure of molecules and exploits the Auger-Meitner effect that core-ionized states undergo. We compute partial decay widths using coupled-cluster theory with single and double substitutions (CCSD) and equation-of-motion CCSD theory combined with complex-scaled basis functions and Feshbach-Fano projection. We generate Auger spectra from these partial widths and draw conclusions about the strength of particular decay channels and trends among the four molecules. A connection to experimental results about fragmentation pathways of the electronic states produced by Auger decay is also made.

We present an ab initio computational study of the Auger electron spectrum of benzene. Auger electron spectroscopy exploits the Auger-Meitner effect, and although it is established as an analytic technique, the theoretical modeling of molecular Auger spectra from first principles remains challenging. Here, we use coupled-cluster theory and equation-of-motion coupled-cluster theory combined with two approaches to describe the decaying nature of core-ionized states: (i) Feshbach-Fano resonance theory and (ii) the method of complex basis functions. The spectra computed with these two approaches are in excellent agreement with each other and also agree well with experimental Auger spectra of benzene. The Auger spectrum of benzene features two well-resolved peaks at Auger electron energies above 260 eV, which correspond to final states with two electrons removed from the 1e 1g and 3e 2g highest occupied molecular orbitals. At lower Auger electron energies, the spectrum is less well resolved, and the peaks comprise multiple final states of the benzene dication. In line with theoretical considerations, singlet decay channels contribute more to the total Auger intensity than the corresponding triplet decay channels.

The charge stabilization method has often been used before for obtaining energies of temporary anions. Herein, we combine this method for the first time with conceptual density functional theory (DFT) and quantum theory of atoms in molecules by extending it to the study of nuclear Fukui functions, atom-condensed electronic Fukui functions, and bond critical points. This is applied to temporary anions of ethene and chlorinated ethene compounds, which are known to undergo dissociative electron attachment (DEA). It appears that the method is able to detect multiple valence resonance states in the same molecule, namely, a Π and a Σ state. The obtained nuclear and atom-condensed electronic Fukui functions are interpreted as nuclear forces and electron distributions, respectively, and show clear differences between the Π and Σ states. This enables a more profound characterization and understanding of how the DEA process proceeds. The conclusions are in line with findings from earlier publications, proving that the combination of conceptual DFT with the charge stabilization method yields reasonable results at rather low computational cost.

Dissociative electron attachment, that is, the cleavage of chemical bonds induced by low-energy electrons, is difficult to model with standard quantum-chemical methods because the involved anions are not bound but subject to autodetachment. We present here a new computational development for simulating the dynamics of temporary anions on complex-valued potential energy surfaces. The imaginary part of these surfaces describes electron loss, whereas the gradient of the real part represents the force on the nuclei. In our method, the forces are computed analytically based on Hartree-Fock theory with a complex absorbing potential. Ab initio molecular dynamics simulations for the temporary anions of dinitrogen, ethylene, chloroethane, and the five mono- to tetrachlorinated ethylenes show qualitative agreement with experiments and offer mechanistic insights into dissociative electron attachments. The results also demonstrate how our method evenhandedly deals with molecules that may undergo dissociation upon electron attachment and those which only undergo autodetachment.

Electronic resonances are states that are unstable towards loss of electrons. They play critical roles in high-energy environments across chemistry, physics, and biology but are also relevant to processes under ambient conditions that involve unbound electrons. This feature article focuses on complex-variable techniques such as complex scaling and complex absorbing potentials that afford a treatment of electronic resonances in terms of discrete square-integrable eigenstates of non-Hermitian Hamiltonians with complex energy. Fundamental aspects of these techniques as well as their integration into molecular electronic-structure theory are discussed and an overview of some recent developments is given: analytic gradient theory for electronic resonances, the application of rank-reduction techniques and quantum embedding to them, as well as approaches for evaluating partial decay widths.

The emission of an Auger electron is the predominant relaxation mechanism of core-vacant states in molecules composed of light nuclei. In this non-radiative decay process, one valence electron fills the core vacancy, while a second valence electron is emitted into the ionization continuum. Because of this coupling to the continuum, core-vacant states represent electronic resonances that can be tackled with standard quantum-chemical methods only if they are approximated as bound states, meaning that Auger decay is neglected. Here, we present an approach to compute Auger decay rates of core-vacant states from coupled-cluster and equation-of-motion coupled-cluster wave functions combined with complex scaling of the Hamiltonian or, alternatively, complex-scaled basis functions. Through energy decomposition analysis, we illustrate how complex-scaled methods are capable of describing the coupling to the ionization continuum without the need to model the wave function of the Auger electron explicitly. In addition, we introduce in this work several approaches for the determination of partial decay widths and Auger branching ratios from complex-scaled coupled-cluster wave functions. We demonstrate the capabilities of our new approach by computations on core-ionized states of neon, water, dinitrogen, and benzene. Coupled-cluster and equation-of-motion coupled-cluster theory in the singles and doubles approximation both deliver excellent results for total decay widths, whereas we find partial widths more straightforward to evaluate with the former method.

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.

Readily accessible tetraorganoborate salts undergo selective coupling reactions under blue light irradiation in the presence of catalytic amounts of transition-metal-free acridinium photocatalysts to furnish unsymmetrical biaryls, heterobiaryls and arylated olefins. This represents an interesting conceptual approach to forge C-C bonds between aryl, heteroaryl and alkenyl groups under smooth photochemical conditions. Computational studies were conducted to investigate the mechanism of the transformation., (© 2020 The Authors. Published by Wiley-VCH GmbH.)

Optical cycling, a continuous photon scattering off atoms or molecules, plays a central role in the quantum information science. While optical cycling has been experimentally achieved for many neutral species, few molecular ions have been investigated. We present a systematic theoretical search for diatomic molecular ions suitable for optical cycling using equation-of-motion coupled-cluster methods. Inspired by the electronic structure patterns of laser-cooled neutral molecules, we establish the design principles for molecular ions and explore various possible cationic molecular frameworks. The results show that finding a perfect molecular ion for optical cycling is challenging, yet possible. Among various possible diatomic molecules we suggest several candidates, which require further attention from both theory and experiment: YF+, SiO+, PN+, SiBr+, and BO+.

Conventional methods carrying out C(sp 2 )-C(sp 2 ) bond formations are typically mediated by transition-metal-based catalysts. Herein, we conceptualize a complementary avenue to access such bonds by exploiting the potential of electrochemistry in combination with organoboron chemistry. We demonstrate a transition metal catalyst-free electrocoupling between (hetero)aryls and alkenes through readily available alkenyl-tri(hetero)aryl borate salts (ATBs) in a stereoconvergent fashion. This unprecedented transformation was investigated theoretically and experimentally and led to a library of functionalized alkenes. The concept was then carried further and applied to the synthesis of the natural product pinosylvin and the derivatization of the steroidal dehydroepiandrosterone (DHEA) scaffold., (© 2020 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.)

An up-to-date overview of the CFOUR program system is given. After providing a brief outline of the evolution of the program since its inception in 1989, a comprehensive presentation is given of its well-known capabilities for high-level coupled-cluster theory and its application to molecular properties. Subsequent to this generally well-known background information, much of the remaining content focuses on lesser-known capabilities of CFOUR, most of which have become available to the public only recently or will become available in the near future. Each of these new features is illustrated by a representative example, with additional discussion targeted to educating users as to classes of applications that are now enabled by these capabilities. Finally, some speculation about future directions is given, and the mode of distribution and support for CFOUR are outlined.

We study the performance of the resolution-of-the-identity (RI) approximation for complex basis functions that we recently introduced [M. Hernández Vera and T.-C. Jagau, J. Chem. Phys. 151, 111101 (2019)] for second-order Møller-Plesset (MP2) perturbation theory as well as for the Coulomb and exchange contributions in Hartree-Fock theory. The sensitivity of this new RI-MP2 method toward the basis set and the auxiliary basis set is investigated, and computation times are analyzed. We show that the auxiliary basis set can be chosen purely real, that is, no complex-scaled functions need to be included. This approximation enables a further speedup of the method without compromising accuracy. We illustrate the application range of our implementation by computing static-field ionization rates of several polyacenes up to pentacene (C 22 H 18 ) at the RI-MP2 level of theory. Pronounced anisotropies are observed for the ionization rates of these molecules.

We report herein versatile, transition metal-free and additive-free (hetero)aryl-aryl coupling reactions promoted by the oxidative electrocoupling of unsymmetrical tetra(hetero)arylborates (TABs) prepared from ligand-exchange reactions on potassium trifluoroarylborates. Exploiting the power of electrochemical oxidations, this method complements the existing organoboron toolbox. We demonstrate the broad scope, scalability, and robustness of this unconventional catalyst-free transformation, leading to functionalized biaryls and ultimately furnishing drug-like small molecules, as well as late stage derivatization of natural compounds. In addition, the observed selectivity of the oxidative coupling reaction is related to the electronic structure of the TABs through quantum-chemical calculations and experimental investigations.

Anionic states of benzonitrile are investigated by high-level electronic structure methods. The calculations using equation-of-motion coupled-cluster theory for electron-attached states confirm earlier conclusions drawn from the photodetachment experiments wherein the ground state of the anion is the valence 2B1 state, while the dipole bound state lies adiabatically ∼0.1 eV above. Inclusion of triple excitations and zero-point vibrational energies is important for recovering relative state correct ordering. The computed Franck-Condon factors and photodetachment cross-sections further confirm that the observed photodetachment spectrum originates from the valence anion. The valence anion is electronically bound at its equilibrium geometry, but it is metastable at the equilibrium geometry of the neutral. The dipole-bound state, which is the only bound anionic state at the neutral equilibrium geometry, may serve as a gateway state for capturing the electron. Thus, the emerging mechanistic picture entails electron capture via a dipole bound state, followed by non-adiabatic relaxation forming valence anions.

A generalization of the Schwarz bound employed to reduce the scaling of quantum-chemical calculations is introduced in the context of non-Hermitian methods employing complex-scaled basis functions. Non-Hermitian methods offer a treatment of molecular metastable states in terms of L 2 -integrable wave functions with complex energies, but until now, an efficient upper bound for the resulting electron-repulsion integrals has been unavailable due to the complications from non-Hermiticity. Our newly formulated bound allows us to inexpensively and rigorously estimate the sparsity in the complex-scaled two-electron integral tensor, providing the basis for efficient integral screening procedures. We have incorporated a screening algorithm based on the new Schwarz bound into the state-of-the-art complex basis function integral code by White, Head-Gordon, and McCurdy [J. Chem. Phys. 142, 054103 (2015)]. The effectiveness of the screening is demonstrated through non-Hermitian Hartree-Fock calculations of the static field ionization of the 2-pyridoxine 2-aminopyridine molecular complex.

A resolution-of-the-identity (RI) approximation for two-electron integrals over Gaussian basis functions with a complex-scaled exponent is presented. Such functions are used in non-Hermitian quantum mechanics to represent electronic resonances by L 2 integrable wave functions with complex energies. We have implemented this new RI approximation for second-order Møller-Plesset perturbation (MP2) theory as well as for the Coulomb and exchange contributions in Hartree-Fock (HF) theory. We discuss the differences to the standard RI approximation of Hermitian quantum mechanics and demonstrate the utility of the non-Hermitian RI-MP2 and RI-HF methods by computations of the orientation-dependent ionization rates of CO, C 6 H 6 , and C 10 H 8 in static electric fields. Our results illustrate that RI-MP2 correctly describes correlation effects in molecular electronic resonances while the computational cost is low enough to allow for investigations of medium-sized molecules.

Despite their small size, C2 species pose big challenges to electronic structure methods, owing to extensive electronic degeneracies and multi-configurational wave functions, which lead to a dense manifold of electronic states. We present detailed electronic structure calculations of C2, C2-, and C22-, emphasizing spectroscopically relevant properties. We employ the double ionization potential (DIP) and ionization potential (IP) variants of the equation-of-motion coupled-cluster method with single and double substitutions (EOM-CCSD) and a dianionic reference state. We show that EOM-CCSD is capable of describing multiple interacting states in C2 and C2- in an accurate, robust, and effective way. We also characterize the electronic structure of C22-, which is metastable with respect to electron detachment.

Photoelectron angular distributions determined in small energy increments between 3.522 and 3.650 eV reveal distinctly different detachment mechanisms within the CuF 2 - (X 1 Σ) → linear CuF 2 (X 2 Σ) + e - band. Certain channels also display non-Franck-Condon behaviour, the action spectra of which reveal rich structure. The behaviour reflects excitation to an electronically unbound anion state (at the linear geometry). The effects of the intermediate state are observed in the detachment behaviour at photon energies down to the X 1 Σ→ X 2 Σ threshold. Adiabatic CAP-EOM-CCSD (equation of motion coupled cluster singles and doubles, including a complex absorbing potential) energy curves are presented along the bending coordinate, showing the complexity of anion and neutral states for this system. The photodetachment action spectra represent a spectroscopic probe of the vibronic state energies in the vertical excitation region and highlight the need for treatment of vibronic coupling in systems involving the loss of an electron.

We present a method for locating non-Hermitian degeneracies, called exceptional points (EPs), and minimum-energy EPs between molecular resonances using the complex absorbing potential equation-of-motion coupled-cluster (CAP-EOM-CC) method. EPs are the complex-valued analogue of conical intersections (CIs) and have a similar impact on nonadiabatic processes between resonances as CIs have on nonradiative transitions between bound states. We demonstrate that the CAP-EOM-CC method in the singles and doubles approximation (CAP-EOM-CCSD) yields crossings of the correct dimensionality. The use of analytic gradients enables applications to multidimensional problems. Results are presented for hydrogen cyanide and chloroethylene, for which the location of the crossings of anionic resonances is crucial for understanding the dissociative electron attachment process.

Photoelectron spectra of 63 CuF 2 - are reported at wavelengths 310 nm, 346.6 nm, and 350.1 nm, obtained via velocity map imaging. The photoelectron angular distributions allow for the unambiguous assignment of a 2 Σ g + neutral CuF 2 ground state. Vibrational analysis of the direct detachment transitions in the spectra enables accurate determination of the anion and neutral bond length difference (0.073 Å), adiabatic electron affinity of CuF 2 (3.494 eV) and symmetric stretching (500 cm -1 , anion, and 630 cm -1 , neutral) and antisymmetric stretching (610 cm -1 , anion, and 782 cm -1 neutral) frequencies of the ground electronic states. Strongly photon energy dependent intensities are also observed for select transitions. Equation-of-motion coupled-cluster singles and doubles calculations augmented by a complex absorbing potential reveal a metastable 1 Π g anion state which is optically accessible due to Renner-Teller coupling. Mediation of the detachment process by this state allows measurement of the bending frequencies (177 cm -1 , anion, and 200 cm -1 , neutral) completing the inventory of experimentally measured vibrational properties of the ground electronic states.

The equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) method with and without a complex absorbing potential (CAP) is applied for the study of the complex potential energy surfaces (CPES) of temporary anions and their parent neutral molecules. Crossings between the anionic state and the neutral state can be connected to the emission of nearly zero-energy electrons, which is demonstrated by the examples of acrylonitrile and methacrylonitrile. We show that the location of the minimum-energy crossing point (MECP) relative to the equilibrium structures of the neutral molecule and the anion can explain experimentally observed peaks on the threshold line of two-dimensional electron-energy loss spectra. The location and energy of the MECP is also crucial in dissociative electron attachment as we illustrate for chloro-substituted ethylenes. It is demonstrated that both the metastable region of the anionic CPES and the crossing with the neutral PES need to be considered to explain trends in the chloride ion formation cross sections of dichloroethylenes.

We determine equilibrium structures, adiabatic electron affinities, and resonance widths of various temporary anions to benchmark the complex absorbing potential equation-of-motion coupled-cluster (CAP-EOM-CC) method. The second-order approximation to CAP-EOM-CC with singles and doubles (SD) excitations is found to yield slightly lower resonance positions and widths than full CAP-EOM-CCSD. The basis set dependence of adiabatic resonance positions and widths is similar to that of the vertical quantities. We demonstrate the usefulness of structure optimizations of temporary anions by two examples. For the anions of acrylonitrile and methacrylonitrile, we observe good agreement for the adiabatic electron affinities and structural changes between our theoretical results and two-dimensional electron-energy loss spectra. For the unsaturated hydrocarbons ethylene, 1,3-butadiene, and cis- and trans-1,3,5-hexatriene, the agreement between theory and electron transmission spectroscopy is good for the lower-lying π* resonances, while our results for the 3π* resonance of trans-hexatriene suggest a shortcoming of the method or reinterpretation of the corresponding electron transmission spectrum. The experimentally determined difference between the electron affinities of the 2π* resonances of the cis isomer and the trans isomer of hexatriene are reproduced well by CAP-EOM-EA-CCSD and CAP-EOM-EA-CCSD(2).

Ionization rates and Stark shifts of H 2 , CO, O 2 , H 2 O, and CH 4 in static electric fields have been computed with coupled-cluster methods in a basis set of atom-centered Gaussian functions with a complex-scaled exponent. Consideration of electron correlation is found to be of great importance even for a qualitatively correct description of the dependence of ionization rates and Stark shifts on the strength and orientation of the external field. The analysis of the second moments of the molecular charge distribution suggests a simple criterion for distinguishing tunnel and barrier suppression ionization in polyatomic molecules.

The impact of residual electron correlation beyond the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) approximation on positions and widths of electronic resonances is investigated. To establish a method that accomplishes this task in an economical manner, several approaches proposed for the approximate treatment of triple excitations are reviewed with respect to their performance in the electron attachment (EA) variant of EOM-CC theory. The recently introduced EOM-CCSD(T)(a)* method [D. A. Matthews and J. F. Stanton, J. Chem. Phys. 145, 124102 (2016)], which includes non-iterative corrections to the reference and the target states, reliably reproduces vertical attachment energies from EOM-EA-CC calculations with single, double, and full triple excitations in contrast to schemes in which non-iterative corrections are applied only to the target states. Applications of EOM-EA-CCSD(T)(a)* augmented by a complex absorbing potential (CAP) to several temporary anions illustrate that shape resonances are well described by EOM-EA-CCSD, but that residual electron correlation often makes a non-negligible impact on their positions and widths. The positions of Feshbach resonances, on the other hand, are significantly improved when going from CAP-EOM-EA-CCSD to CAP-EOM-EA-CCSD(T)(a)*, but the correct energetic order of the relevant electronic states is still not achieved.

Electronic resonances are metastable states with finite lifetime embedded in the ionization or detachment continuum. They are ubiquitous in chemistry, physics, and biology. Resonances play a central role in processes as diverse as DNA radiolysis, plasmonic catalysis, and attosecond spectroscopy. This review describes novel equation-of-motion coupled-cluster (EOM-CC) methods designed to treat resonances and bound states on an equal footing. Built on complex-variable techniques such as complex scaling and complex absorbing potentials that allow resonances to be associated with a single eigenstate of the molecular Hamiltonian rather than several continuum eigenstates, these methods extend electronic-structure tools developed for bound states to electronic resonances. Selected examples emphasize the formal advantages as well as the numerical accuracy of EOM-CC in the treatment of electronic resonances. Connections to experimental observables such as spectra and cross sections, as well as practical aspects of implementing complex-valued approaches, are also discussed.

The general theory of analytic energy gradients is presented for the complex absorbing potential equation-of-motion coupled-cluster (CAP-EOM-CC) method together with an implementation within the singles and doubles approximation. Expressions for the CAP-EOM-CC energy gradient are derived based on a Lagrangian formalism with a special focus on the extra terms arising from the presence of the CAP. Our implementation allows for locating minima on high-dimensional complex-valued potential energy surfaces and thus enables geometry optimizations of resonance states of polyatomic molecules. The applicability of our CAP-EOM-CC gradients is illustrated by computations of the equilibrium structures and adiabatic electron affinities of the temporary anions of formaldehyde, formic acid, and ethylene. The results are compared to those obtained from standard EOM-CC calculations and the advantages of CAP methods are emphasized.

The theory and implementation of the complex-scaled coupled-cluster method with singles and doubles excitations (cs-CCSD) for studying resonances induced by static electric fields are presented. Within this framework, Stark shifts and ionization rates are obtained directly from the real and imaginary parts of the complex energy. The method is applied to the ground states of hydrogen, helium, lithium, beryllium, neon, argon, and carbon at varying field strengths. Complex-scaled Hartree-Fock, second-order many-body perturbation theory, and CCSD results are reported and analyzed with a focus on the impact of electron correlation on the ionization process. cs-CCSD calculations with suitably augmented standard Gaussian basis sets are found to deliver accurate strong-field ionization rates over a range of six orders of magnitude. The field-induced resonances are characterized beyond energy and ionization rate through their dipole moments, second moments, as well as Dyson orbitals and comparisons are drawn to autoionizing and autodetaching resonances. Marked differences are found between the tunneling and above-barrier regimes allowing for a clear distinction of the two mechanisms.

The theoretical description of electronic resonances is extended beyond calculations of energies and lifetimes. We present the formalism for calculating Dyson orbitals and transition dipole moments within the equation-of-motion coupled-cluster singles and doubles method for electron-attached states augmented by a complex absorbing potential (CAP-EOM-EA-CCSD). The capabilities of the new methodology are illustrated by calculations of Dyson orbitals of various transient anions. We also present calculations of transition dipole moments between transient and stable anionic states as well as between different transient states. Dyson orbitals characterize the differences between the initial neutral and final electron-attached states without invoking the mean-field approximation. By extending the molecular-orbital description to correlated many-electron wave functions, they deliver qualitative insights into the character of resonance states. Dyson orbitals and transition moments are also needed for calculating experimental observables such as spectra and cross sections. Physically meaningful results for those quantities are obtained only in the framework of non-Hermitian quantum mechanics, e.g., in the presence of a complex absorbing potential (CAP), when studying resonances. We investigate the dependence of Dyson orbitals and transition moments on the CAP strength and illustrate how Dyson orbitals help understand the properties of metastable species and how they are affected by replacing the usual scalar product by the so-called c-product.

Electron attachment to closed-shell molecules is a gateway to various important processes in the gas and condensed phases. The properties of an electron-attached state, such as its energy and lifetime as well as the character of the molecular orbital to which the electron is attached, determine the fate of the anion. In this experimental and theoretical study of copper and silver fluoride anions, we introduce a new type of metastable anionic state. Abrupt changes in photoelectron angular distributions point to the existence of autodetaching states. Equation-of-motion coupled-cluster singles and doubles calculations augmented by a complex absorbing potential identify some of these states as Σ and Π dipole-stabilized resonances, a new type of shape resonance. In addition, these molecules support valence and dipole-bound states and a Σ resonance of charge-transfer character. By featuring five different types of anionic states, they provide a vehicle for studying fundamental properties of anions and for validating new theoretical approaches for metastable states.

A production-level implementation of equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) for electron attachment and excitation energies augmented by a complex absorbing potential (CAP) is presented. The new method enables the treatment of metastable states within the EOM-CC formalism in a similar manner as bound states. The numeric performance of the method and the sensitivity of resonance positions and lifetimes to the CAP parameters and the choice of one-electron basis set are investigated. A protocol for studying molecular shape resonances based on the use of standard basis sets and a universal criterion for choosing the CAP parameters are presented. Our results for a variety of π(*) shape resonances of small to medium-size molecules demonstrate that CAP-augmented EOM-CCSD is competitive relative to other theoretical approaches for the treatment of resonances and is often able to reproduce experimental results.

A new strategy of using complex absorbing potentials (CAPs) within electronic structure calculations of metastable electronic states, which are ubiquitous in chemistry and physics, is presented. The stumbling block in numerical applications of CAPs is the necessity to optimize the CAP strength for each system, state, and one-electron basis set, while there is no clear metric to assess the quality of the results and no simple algorithm of achieving numerical convergence. By analyzing the behavior of resonance wave functions, we found that robust results can be obtained when considering fully stabilized resonance states characterized by constant density at large η (parameter determining the CAP strength). Then the perturbation due to the finite-strength CAP can be removed by a simple energy correction derived from energy decomposition analysis and response theory. The utility of this approach is illustrated by CAP-augmented calculations of several shape resonances using EOM-EA-CCSD with standard Gaussian basis sets.

The general theory required for the calculation of analytic third energy derivatives at the coupled-cluster level of theory is presented and connected to preceding special formulations for hyperpolarizabilities and polarizability gradients. Based on our theory, we have implemented a scheme for calculating the dipole Hessian matrix in a fully analytical manner within the coupled-cluster singles and doubles approximation. The dipole Hessian matrix is the second geometrical derivative of the dipole moment and thus a third derivative of the energy. It plays a crucial role in IR spectroscopy when taking into account anharmonic effects and is also essential for computing vibrational corrections to dipole moments. The superior accuracy of the analytic evaluation of third energy derivatives as compared to numerical differentiation schemes is demonstrated in some pilot calculations.

The formalism of response theory is applied to derive expressions for static and dynamic polarizabilities within the state-specific multireference coupled-cluster theory suggested by Mukherjee and co-workers (Mk-MRCC) [J. Chem. Phys. 110, 6171 (1998)]. We show that the redundancy problem inherent to Mk-MRCC theory gives rise to spurious poles in the Mk-MRCC response functions, which hampers the reliable calculation of dynamic polarizabilities. Furthermore, we demonstrate that in the case of a symmetry-breaking perturbation a working response theory is obtained only if certain internal excitations are included in the responses of the cluster amplitudes. Exemplary calculations within the singles and doubles approximation (Mk-MRCCSD) are carried out on aryne compounds to illustrate the impact of a multireference ansatz on the polarizability.

The recently presented linear-response function for Mukherjee's multireference coupled-cluster method (Mk-MRCC) [T.-C. Jagau and J. Gauss, J. Chem. Phys. 137, 044115 (2012)] is employed to determine vertical excitation energies within the singles and doubles approximation (Mk-MRCCSD-LR) for ozone as well as for o-benzyne, m-benzyne, and p-benzyne, which display increasing multireference character in their ground states. In order to assess the impact of a multireference ground-state wavefunction on excitation energies, we compare all our results to those obtained at the single-reference coupled-cluster level of theory within the singles and doubles as well as within the singles, doubles, and triples approximation. Special attention is paid to the artificial splitting of certain excited states which arises from the redundancy intrinsic to Mk-MRCC theory and hinders the straightforward application of the Mk-MRCC-LR method.

Analytic gradients for the state-specific multireference coupled-cluster method suggested by Mahapatra et al. [Mol. Phys. 94, 157 (1998)] (Mk-MRCC) are reported within the singles and doubles approximation using two-configurational self-consistent field (TCSCF) orbitals. The present implementation extends our previous work on Mk-MRCC gradients [E. Prochnow et al., J. Chem. Phys. 131, 064109 (2009)] which is based on restricted Hartree-Fock orbitals and consequently the main focus of the present paper is on the treatment of orbital relaxation at the TCSCF level using coupled-perturbed TCSCF theory. Geometry optimizations on m-arynes and nitrenes are presented to illustrate the influence of the orbitals on the computed equilibrium structures. The results are compared to those obtained at the single-reference coupled-cluster singles and doubles and at the Mk-MRCC singles and doubles level of theory when using restricted Hartree-Fock orbitals.

Single crystals of Ln(4)Na(2)K(2)M(2)O(13) (Ln = Nd, Sm, Eu, Gd; M = Nb, Ta) were grown out of a reactive high temperature hydroxide melt. The structures were determined by single crystal X-ray diffraction. Ln(4)Na(2)K(2)M(2)O(13) crystallizes in the monoclinic space group C2/c in which niobium and tantalum are located in a rare 5-coordinate, square pyramidal coordination environment. Optical band gaps were estimated from diffuse reflectance UV/vis spectra. The magnetic susceptibility data were measured, and the intense room temperature photoluminescence of the europium containing compounds was studied.