An assessment of orbital energy corrections for the direct random phase approximation and explicit σ -functionals

σ-Functionals belong to the class of Kohn−Sham (KS) correlation functionals based on the adiabatic-connection fluctuation−dissipation theorem and are technically closely related to the random phase approximation (RPA). They have the same computational demand as the latter, with the computational effort of an energy evaluation for both methods being lower than that of a preceding hybrid DFT calculation for typical systems but yield much higher accuracy, reaching chemical accuracy of 1 kcal/mol for quantities such as reactions and transition energies in main group chemistry. In previous work on σ-functionals, rather large Gaussian basis sets have been used. Here, we investigate the actual basis set requirements of σ-functionals and present three setups that employ smaller Gaussian basis sets ranging from quadruple-ζ (QZ) to tripleζ (TZ) quality and represent a good compromise between accuracy and computational efficiency. Furthermore, we introduce an implementation of σ-functionals based on Slater-type basis sets and present two setups of QZ and TZ quality for this implementation. We test the accuracy of these setups on a large database of various physical properties and types of reactions, as well as equilibrium geometries and vibrational frequencies. As expected, the accuracy of σ-functional calculations becomes somewhat lower with a decreasing basis set size. However, for all setups considered here, calculations with σ-functionals are clearly more accurate than those within the RPA and even more so than those of the conventional KS methods. For the smallest setup using Gaussian-type basis functions and Slater-type basis functions, we introduce a reparametrization that reduces the loss in accuracy due to the basis set error to some extent. A comparison with the range-separated hybrid ωB97X-V and the double hybrid DSD-BLYP-D3 shows that σ functionals outperform in accuracy both of these accurate and, for their class, representative functionals.

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…Furthermore, low-scaling RPA implementations exist, [53][54][55][56][57][58][59][60]108,120 which have been already applied to σfunctionals. 48,66…”

Section: Geometriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Basis Set Requirements of σ-Functionals for Gaussian- and Slater-Type Basis Functions and Comparison with Range-Separated Hybrid and Double Hybrid Functionals

Fauser,

Förster,

Redeker

et al. 2024

“…Most notably, RPA is able to describe noncovalent interactions exceptionally well without the need to introduce semiempirical corrections, which makes it stand out from empirical dispersion correction methods. − Furthermore, it is able to describe systems with vanishing electronic gaps, where methods such as MP2 fail. In addition, the recently developed RPA-like σ-functionals − introduced by the Görling group look especially promising in that regard. Much progress has been made in terms of the computational efficiency of RPA since it was first proposed by Bohm and Pines in 1953 .…”

Section: Introductionmentioning

confidence: 99%

Efficient Method for the Computation of Frozen-Core Nuclear Gradients within the Random Phase Approximation

Drontschenko

Gräf

Laqua

et al. 2022

Self Cite

A method for the evaluation of analytical frozencore gradients within the random phase approximation is presented. We outline an efficient way to evaluate the response of the density of active electrons arising only when introducing the frozen-core approximation and constituting the main difficulty, together with the response of the standard Kohn−Sham density. The general framework allows to extend the outlined procedure to related electron correlation methods in the atomic orbital basis that require the evaluation of density responses, such as second-order Møller−Plesset perturbation theory or coupled cluster variants. By using Cholesky decomposed densities�which reintroduce the occupied index in the time-determining steps�we are able to achieve speedups of 20−30% (depending on the size of the basis set) by using the frozen-core approximation, which is of similar magnitude as for molecular orbital formulations. We further show that the errors introduced by the frozen-core approximation are practically insignificant for molecular geometries.

A Constraint-Based Orbital-Optimized Excited State Method (COOX)

Kussmann,

Lemke,

Weinbrenner

et al. 2024

In this work, we present a novel method to directly calculate targeted electronic excited states within a self-consistent field calculation based on constrained density functional theory (cDFT). The constraint is constructed from the static occupied-occupied and virtualvirtual parts of the excited state difference density from (simplified) linear-response time-dependent density functional theory calculations (LR-TDDFT). Our new method shows a stable convergence behavior, provides an accurate excited state density adhering to the Aufbau principle, and can be solved within a restricted SCF for singlet excitations to avoid spin contamination. This also allows the straightforward application of post-SCF electron-correlation methods like MP2 or direct RPA methods. We present the details of our constraint-based orbitaloptimized excited state method (COOX) and compare it to similar schemes. The accuracy of excitation energies will be analyzed for a benchmark of systems, while the quality of the resulting excited state densities is investigated by evaluating excited state nuclear forces and excited state structure optimizations. We also investigate the performance of the proposed COOX method for long-range charge transfer excitations and conical intersections with the ground-state.