Ab Initio Computation of Auger Decay in Heavy Metals: Zinc about It.

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 67Ga 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 1D2 final state arising from K-L2L3 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.

Signatures of s-wave scattering in bound electronic states.

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 N2 and H2, 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 H2 or N2. 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.

Combining extrapolated electron localization functions and Berlin's binding functions for the prediction of dissociative electron attachment.

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.

A New Strategy to Optimize Complex Absorbing Potentials for the Computation of Resonance Energies and Widths.

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.

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

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

Interatomic and intermolecular Coulombic decay rates from equation-of-motion coupled-cluster theory with complex basis functions.

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.

Analytic Evaluation of Nonadiabatic Couplings within the Complex Absorbing Potential Equation-of-Motion Coupled-Cluster Method.

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.

Ab Initio Investigation of the Auger Spectra of Methane, Ethane, Ethylene, and Acetylene.

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.

The Auger spectrum of benzene.

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 1e1g and 3e2g 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.

Conceptual density functional theory for temporary anions stabilized by scaled nuclear charges.

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.

Ab Initio Molecular Dynamics of Temporary Anions Using Complex Absorbing Potentials.

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.

Theory of electronic resonances: fundamental aspects and recent advances.

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.

Molecular Auger decay rates from complex-variable coupled-cluster theory.

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.

Photocatalyzed Transition-Metal-Free Oxidative Cross-Coupling Reactions of Tetraorganoborates*.

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.

In search of molecular ions for optical cycling: a difficult road.

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+.

Coupled-cluster techniques for computational chemistry: The CFOUR program package.

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.

Resolution-of-the-identity second-order Møller-Plesset perturbation theory with complex basis functions: Benchmark calculations and applications to strong-field ionization of polyacenes.

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 (C22H18) at the RI-MP2 level of theory. Pronounced anisotropies are observed for the ionization rates of these molecules.

Electro-Olefination-A Catalyst Free Stereoconvergent Strategy for the Functionalization of Alkenes.

Conventional methods carrying out C(sp2 )-C(sp2 ) 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.

The quest to uncover the nature of benzonitrile anion.

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.

Electrochemical Synthesis of Biaryls via Oxidative Intramolecular Coupling of Tetra(hetero)arylborates.

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.