Coupled-cluster treatment of complex open-shell systems: the case of single-molecule magnets.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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+.

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.

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.

Spectroscopy of temporary anion states: Renner-Teller coupling and electronic autodetachment in copper difluoride anion.

Photoelectron angular distributions determined in small energy increments between 3.522 and 3.650 eV reveal distinctly different detachment mechanisms within the CuF2-(X 1Σ) → linear CuF2(X 2Σ) + 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 1Σ→ X 2Σ 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.

EOM-CC guide to Fock-space travel: the C2 edition.

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.

Resolution-of-the-identity approximation for complex-scaled basis functions.

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 L2 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, C6H6, and C10H8 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.

A Schwarz inequality for complex basis function methods in non-Hermitian quantum chemistry.

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 L2-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.