Communication: Random-phase approximation excitation energies from approximate equation-of-motion coupled-cluster doubles

Reference Energies for Valence Ionizations and Satellite Transitions

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

Modeling of High-Harmonic Generation in the C60 Fullerene Using Ab Initio, DFT-Based, and Semiempirical Methods

We report calculations of the high-harmonic generation spectra of the C60 fullerene molecule carried out by employing a diverse set of real-time time-dependent quantum chemical methods. All methodologies involve expanding the propagated electronic wave function in bases consisting of the ground and singly excited time-independent eigenstates obtained through the solution of the corresponding linear-response equations. We identify the correlation and exchange effect in the spectra by comparing the results from methods relying on the Hartree-Fock reference determinant with those obtained using approaches based on the density functional theory with different exchange-correlation functionals. The effect of the full random-phase approximation treatment of the excited electronic states is also analyzed and compared with the configuration interaction singles and the Tamm-Dancoff approximation. We also showcase the fact that the real-time extension of the semiempirical method INDO/S can be effectively applied for an approximate description of laser-driven dynamics in large systems.

Exact relationships between the GW approximation and equation-of-motion coupled-cluster theories through the quasi-boson formalism

We describe the relationship between the GW approximation and various equation-of-motion (EOM) coupled-cluster (CC) theories. We demonstrate the exact equivalence of the G₀W₀ approximation and the propagator theory for an electron-boson problem in a particular excitation basis. From there, we establish equivalence within the quasi-boson picture to the IP+EA-EOM unitary CC propagator. We analyze the incomplete description of screening provided by the standard similarity-transformed IP+EA-EOM-CC and the recently introduced G₀W₀ Tamm-Dancoff approximation. We further consider the approximate decoupling of IP and EA sectors in EOM-CC treatments and devise the analogous particle-hole decoupling approach for the G₀W₀ approximation. Finally, we numerically demonstrate the exact relationships and magnitude of the approximations in the calculations of a set of molecular ionization potentials and electron affinities.

Connections between many-body perturbation and coupled-cluster theories

Here, we build on the works of Scuseria et al. [J. Chem. Phys. 129, 231101 (2008)] and Berkelbach [J. Chem. Phys. 149, 041103 (2018)] to show connections between the Bethe-Salpeter equation (BSE) formalism combined with the GW approximation from many-body perturbation theory and coupled-cluster (CC) theory at the ground- and excited-state levels. In particular, we show how to recast the GW and Bethe-Salpeter equations as non-linear CC-like equations. Similitudes between BSE@GW and the similarity-transformed equation-of-motion CC method are also put forward. The present work allows us to easily transfer key developments and the general knowledge gathered in CC theory to many-body perturbation theory. In particular, it may provide a path for the computation of ground- and excited-state properties (such as nuclear gradients) within the GW and BSE frameworks.

Absorption Spectra of Solids from Periodic Equation-of-Motion Coupled-Cluster Theory

We present ab initio absorption spectra of six three-dimensional semiconductors and insulators calculated using Gaussian-based periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD). The spectra are calculated efficiently by solving a system of linear equations at each frequency, giving access to an energy range of tens of electronvolts without explicit enumeration of excited states. We assess the impact of cost-saving approximations associated with Brillouin zone sampling, frozen orbitals, and the partitioned EOM-CCSD approximation. Although our most converged spectra exhibit line shapes that are in good agreement with experimental spectra, they are uniformly shifted to higher energies by about 1 eV, which is not explained by the remaining finite-size errors. We tentatively attribute this discrepancy to a combination of vibrational effects and the remaining electron correlation, i.e., triple excitations and above.

Ab Initio Lifetime and Concomitant Double-Excitation Character of Plasmons at Metallic Densities

The accurate calculation of excited state properties of interacting electrons in the condensed phase is an immense challenge in computational physics. Here, we use state-of-the-art equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD) to calculate the dynamic structure factor, which can be experimentally measured by inelastic x-ray and electron scattering. Our calculations are performed on the uniform electron gas at densities corresponding to Wigner-Seitz radii of r_{s}=5, 4, and 3 corresponding to the valence electron densities of common metals. We compare our results to those obtained using the random-phase approximation (RPA), which is known to provide a reasonable description of the collective plasmon excitation and which resums only a small subset of the polarizability diagrams included in EOM-CCSD. We find that EOM-CCSD, instead of providing a perturbative improvement on the RPA plasmon, predicts a many-state plasmon resonance, where each contributing state has a double-excitation character of 80% or more. This finding amounts to an ab initio treatment of the plasmon linewidth, which is in good quantitative agreement with previous diagrammatic calculations, and highlights the strongly correlated nature of lifetime effects in condensed-phase electronic structure theory.