Automated Generation of Optimized Auxiliary Basis Sets for Long-Range-Corrected TDDFT Using the Cholesky Decomposition

Response properties from frozen-density embedding approximate second-order coupled-cluster theory

We present an implementation of the coupled frozen-density embedding (FDEc) formalism for the calculation of ground-state and excited-state properties, linear-response properties, and transition moments with the coupled cluster with the singles and approximate doubles (CC2) model. Following the general strategy introduced by Höfener and Visscher [J. Chem. Theory Comput.12, 549-557 (2016)], we derive the working equations needed for the evaluation of these properties and describe their implementation into our open-source quantum chemistry program, Serenity. Our implementation comprises both projection-based embedding as well as embedding based on non-additive kinetic-energy functionals and the corresponding potentials. It makes use of the resolution-of-the-identity technique and features-in addition to CC2-the algebraic diagrammatic construction scheme of second order, ADC(2), as well as spin-component-scaled and scaled-opposite spin versions of CC2 and ADC(2). We demonstrate the capabilities of this FDEc framework by analyzing excitation energies, singlet and triplet excitation-energy splittings as well as oscillator strengths of excitonically coupled dimers, the excited-state/difference dipole moment of a formaldehyde⋯water system, and the optical rotatory dispersion of a microsolvated organic chromophore. In the latter case, we reconsider the case of (P)-dimethylallene· (H2O)2, for which uncoupled CC2-based frozen-density embedding fails, while FDEc-time-dependent density-functional theory showed promising results in earlier work. Here, we can confirm that the inclusion of system-environment response couplings leads to agreement with supermolecular CC2 results, highlighting the importance of inter-subsystem couplings in response-property calculations for molecular aggregates.

Accelerating Analytic-Continuation GW Calculations with a Laplace Transform and Natural Auxiliary Functions

We present a simple and accurate GW implementation based on a combination of a Laplace transform (LT) and other acceleration techniques used in post-self-consistent field quantum chemistry, namely, natural auxiliary functions and the frozen-core approximation. The LT-GW approach combines three major benefits: (a) a small prefactor for computational scaling, (b) easy integration into existing molecular GW implementations, and (c) significant performance improvements for a wide range of possible applications. Illustrating these advantages for systems consisting of up to 352 atoms and 7412 basis functions, we further demonstrate the benefits of this approach combined with an efficient implementation of the Bethe-Salpeter equation.

Automatic Generation of Auxiliary Basis Sets in Spherical Representation Using the Cholesky Decomposition

Density fitting techniques that use automatically generated auxiliary basis sets generally rely on the formation of basis function products. Recently, Lehtola [ J. Chem. Theory Comput. 2021, 17, 6886-6900] presented a procedure making use of a purely spherical representation by adding auxiliary basis functions coupled to the required angular momentum quantum numbers for the product of spherical harmonics and then removing linear dependencies by means of a Cholesky decomposition. In this work, we extend this idea by making use of the explicit equations for the product of two spherical harmonics in the angular part of the basis function product. Some of the resulting terms are not directly accessible when popular standard integral libraries are used, which could prevent the widespread use of the exact product form. For these terms, we introduce four approximations of increasing sophistication that require integrals involving only standard Gaussian-type orbitals and thus can be computed with standard libraries. We assess the accuracy of the different schemes in the context of the aCD for the reconstruction of the electron repulsion integral matrix and absolute and relative single point energies and in the framework of optimally tuned range-separated hybrid functionals.

Minimal Auxiliary Basis Set Approach for the Electronic Excitation Spectra of Organic Molecules

We report a minimal auxiliary basis model for time-dependent density functional theory (TDDFT) with hybrid density functionals that can accurately reproduce excitation energies and absorption spectra from TDDFT while reducing cost by about 2 orders of magnitude. Our method, dubbed TDDFT-ris, employs the resolution-of-the-identity technique with just one s-type auxiliary basis function per atom for the linear response operator, where the Gaussian exponents are parametrized across the periodic table using tabulated atomic radii with a single global scaling factor. By tuning on a small test set, we determine a single functional-independent scale factor that balances errors in excitation energies and absorption spectra. Benchmarked on organic molecules and compared to standard TDDFT, TDDFT-ris has an average energy error of only 0.06 eV and yields absorption spectra in close agreement with TDDFT. Thus, TDDFT-ris enables simulation of realistic absorption spectra in large molecules that would be inaccessible from standard TDDFT.