While the periodic equation-of-motion coupled-cluster (EOM-CC) method promises systematic improvement of electronic band gap calculations in solids, its practical application at the singles and doubles level (EOMCCSD) is hindered by severe finite-size errors in feasible simulation cells. We present a hybrid approach combining EOM-CCSD with the computationally less demanding GW approximation to estimate thermodynamic limit band gaps for several insulators and semiconductors. Our method substantially reduces required cell sizes while maintaining accuracy. Comparisons with experimental gaps and self-consistent GW calculations reveal that deviations in EOM-CCSD predictions correlate with reduced single excitation character of the excited many-electron states. Our work not only provides a computationally tractable approach to EOM-CC calculations in solids but also reveals fundamental insights into the role of single excitations in electronic-structure theory.

We investigate the convergence of quasiparticle energies for periodic systems to the thermodynamic limit using increasingly large simulation cells corresponding to increasingly dense integration meshes in reciprocal space. The quasiparticle energies are computed at the level of equation-of-motion coupled-cluster theory for ionization (IP-EOM-CC) and electron attachment processes (EA-EOM-CC). By introducing an electronic correlation structure factor, the expected asymptotic convergence rates for systems with different dimensionality are formally derived. We rigorously test these derivations through numerical simulations for trans-polyacetylene using IP/EA-EOM-CCSD and the G0W0@HF approximation, which confirm the predicted convergence behavior. Our findings provide a solid foundation for efficient schemes to correct finite-size errors in IP/EA-EOM-CCSD calculations.

In the molecular quantum chemistry community, coupled-cluster (CC) methods are well-recognized for their systematic convergence and reliability. The extension of the theory to extended systems has been comparably recent, so that developments and studies of periodic CC methods for both the ground-state and for excited states are still active fields of research and provide valuable benchmark data when the reliability of density functional approximations is questionable. In this contribution we describe the CC-aims interface between the FHI-aims and the Cc4s software packages. This linkage makes a variety of correlated wave function-based ground-state methods including M\o ller-Plesset perturbation theory (MP2), the random-phase approximation (RPA) and the gold-standard of quantum chemistry CCSD(T) method for both molecular and periodic applications accessible. This contribution discusses these ground-state methods for clusters and molecules, as well as for periodic systems. In particular, we discuss recent advancements and the implementation of the equation-of-motion CC method for the calculation of ionization (IP-EOM-CCSD) and electron attachment (EA-EOM-CCSD) processes. Open questions and routes to solutions are discussed as well.

A major part of computational materials science and computational chemistry concerns calculations of total energy differences and electronic excitations of poly-atomic systems. Currently, the most prevalent method for such computations is density-functional theory (Hohenberg & Kohn, 1964) (DFT) based on the Kohn-Sham formalism (Kohn & Sham, 1965) (KS) together with one of the numerous exchange-correlation (xc) approximations (Civalleri et al., 2012; Sousa et al., 2007). The trade-off between comparably low computational cost and often reliably accurate results render it the dominant method in the field. Often, however, the accuracy of the xc approximations is not sufficent and uncertain, in particular when electronic correlations play a decisive role (Savin & Johnson, 2014; Zhang et al., 2016; Zhang & Grüneis, 2019). Coupled-cluster (CC) methods (Čı́žek, 1966), while substantially more computationally expensive have proven to be significantly more accurate and reliable, at least for molecules and non-metallic solids. On these grounds, they allow for a systematic accuracy benchmark of other methods. Indeed, in molecular quantum chemistry the CC approach is considered the gold standard for a theoretical description of binding energies and electronic properties (Chan, 2019). It is typically used (at least) for benchmark studies. While the original CC methodology allows one to calculate the ground-state total energy of a system, it is also possible to compute properties of excited states using the equation-of-motion formalism of CC (EOM-CC) with comparable accuracy and reliability (Stanton & Bartlett, 1993). The conventional CC approach is limited, however, to systems with about 50 electrons (Feller & Dixon, 2001; Gyevi-Nagy et al., 2019). By employing approximations, which exploit the locality of electronic correlation, materials with a couple of hundreds of electrons have been calculated via local natural orbital CC (LNO-CC) (Nagy & Kállay, 2019) and explicitly correlated pair natural orbital CC (PNO-CC-F12) (Ma & Werner, 2021). The extension of CC to periodic systems (Hirata et al., 2004) has been explored to a great degree by the research groups of Andreas Grüneis and Garnet Chan.

Iron–sulfur clusters serve unique roles in biochemistry, geochemistry, and renewable energy technologies. However, a full theoretical understanding of their structures and properties is still lacking. To facilitate large-scale reactive molecular dynamics simulations of iron–sulfur clusters in aqueous environments, a ReaxFF reactive force field is developed, based on an extensive set of quantum chemical calculations. This force field compares favorably with the reference calculations on gas-phase species and significantly improves on a previous ReaxFF parametrization. We employ the new potential to study the stability and reactivity of iron–sulfur clusters in explicit water with constant-temperature reactive molecular dynamics. The aqueous species exhibit a dynamic, temperature-dependent behavior, in good agreement with previous much more costly ab initio simulations.

Four established ReaxFF force fields, trained on biochemical systems, have been systematically benchmarked on 20 proteinogenic amino acids and 11 dipeptides. The force fields were compared with respect to geometries, energetics, and atomic charges of conformers for the amino acids. To assess the performance with respect to reactivity, the condensation reactions for the formation of dipeptides were investigated by calculating the reaction energetics and pathways. We found systematic errors in the torsion angles for the amino acids, with deviations over 100°, and a generally incorrect account of relative energies for amino acid conformers. In describing the reactivity, only one of the force fields could reproduce the reaction energies of amino acid condensations quantitatively. All four force fields predict unphysical mechanisms for these reactions, involving highly unstable intermediate structures, proton transfers involving aliphatic protons, and even five-coordinate carbon atoms. The corresponding energy landscapes exhibit fluctuations on small length scales and artificial minima.

Compliance with the Lieb-Oxford bound for the indirect Coulomb energy and for the exchange-correlation energy is investigated for a number of density-functional methods methods based on the adiabatic-connection fluctuation-dissipation (ACFD) theorem to treat correlation. Furthermore, the correlation contribution to the pair density resulting from these methods is compared with highly accurate reference values for the helium atom and the hydrogen molecule at several bond distances. For molecules the Lieb-Oxford bound is obeyed by all considered methods. For the homogeneous electron gas it is violated by all methods for low electron densities. The simplest considered ACFD method, the direct random phase approximation (dRPA), violates the Lieb-Oxford bound much earlier than more advanced ACFD methods that, in addition to the simple Hartree kernel, take into account the exchange kernel and an approximate correlation kernel in the calculation of the correlation energy. While the dRPA yields quite poor correlation contributions to the pair density, those from more advanced ACFD methods are physically reasonable but still leave room for improvements in particular in the case of the stretched hydrogen molecule.

Compliance with the Lieb-Oxford bound for the indirect Coulomb energy and for the exchange-correlation energy is investigated for a number of density-functional methods based on the adiabatic-connection fluctuation-dissipation (ACFD) theorem to treat correlation. Furthermore, the correlation contribution to the pair density resulting from these methods is compared with highly accurate reference values for the helium atom and for the hydrogen molecule at several bond distances. For molecules, the Lieb-Oxford bound is obeyed by all considered methods. For the homogeneous electron gas, it is violated by all methods for low electron densities. The simplest considered ACFD method, the direct random phase approximation (dRPA), violates the Lieb-Oxford bound much earlier than more advanced ACFD methods that, in addition to the simple Hartree kernel, take into account the exchange kernel and an approximate correlation kernel in the calculation of the correlation energy. While the dRPA yields quite poor correlation contributions to the pair density, those from more advanced ACFD methods are physically reasonable but still leave room for improvements, particularly in the case of the stretched hydrogen molecule.