Charge transfer excitations from particle-particle random phase approximation—Opportunities and challenges arising from two-electron deficient systems

Abstract

The particle-particle random phase approximation (pp-RPA) is a promising method for studying charge transfer(CT) excitations. Through a detailed analysis on two-electron deficient systems, we show that the pp-RPA is always able to recover the long-distance asymptotic -1/R trend for CT excitations as a result of the concerted effect between orbital energies and the pp-RPA kernel. We also provide quantitative results for systems with relatively short donor-acceptor distances. With conventional hybrid or range-separated functionals, the pp-RPA performs much better than time-dependent density functional theory (TDDFT), although it still gives underestimated results which are not as good as TDDFT with system-dependent tuned functionals. For pp-RPA, there remain three great challenges in dealing with CT excitations. First, the delocalized frontier orbitals in strongly correlated systems often lead to difficulty with self-consistent field convergence as well as an incorrect picture with about half an electron transferred. Second, the commonly used density functionals often underestimate the energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (LUMO) for the two-electron deficient species, resulting in systems with delocalized orbitals. Third, the performance of pp-RPA greatly depends on the energy difference between the LUMO and a higher virtual orbital. However, the meaning of the orbital energies for higher virtual orbitals is still not clear. We also discuss the performance of an approximate pp-RPA scheme that uses density functional tight binding (pp-DFTB) as reference and demonstrate that the aforementioned challenges can be overcome by adopting suitable range-separated hybrid functionals. The pp-RPA and pp-DFTB are thus promising general approaches for describing charge transfer excitations.

Hole–hole Tamm–Dancoff-approximated density functional theory: A highly efficient electronic structure method incorporating dynamic and static correlation

“…36,41 Weitao Yang and coworkers also highlighted pp-RPA and its Tamm-Dancoff approximated pp-TDA variant as effective methods to compute electronic ground and excited state energies. [43][44][45][46][47][48][49][50][51][52] Starting from a doubly cationic (N-2)-electron reference, the N-electron ground state and excited states generated by excitations from the highest occupied molecular orbital (HOMO) are recovered by performing two-electron attachments. 45,[49][50] This allows the treatment of the N-electron ground and excited states on equal footing (derived as simultaneous eigenvalues of a common Hamiltonian) at a computational cost comparable to the simplest excited state methods, e.g., TDDFT/ph-RPA and configuration interaction singles (CIS).…”

“…This (N+2)-electron pp-RPA scheme and its corresponding hole-hole (hh) Tamm-Dancoff approximation (hh-TDA) were first presented by Yang and coworkers. 49 Although the pp-RPA and pp-TDA methods based on an (N-2)-electron reference have now become quite established, [43][44][45][46][47][48][49][50][51][52][53] less attention has been paid to the hh-TDA method based on an (N+2)-electron reference. Yang and coworkers applied the hh-TDA method to oxygen and sulfur atoms 49 (noting "relatively large errors" in the results), but we have found no published reports of further developments or applications of hh-TDA to molecules.…”

Charge transfer excitation energies from ground state density functional theory calculations

“…41 It has been shown to produce good CT results, as well as excellent description of the asymptotically correct 1/R trend. 42 Building beyond the framework of DFT, there are other methods successfully developed to describe CT excitations. The many-body perturbation theory at GW level and Bethe-Salpeter approach (BSE) 43,44 can yield results of similar accuracy as TDDFT from the best range-separated functional.…”

Benchmarking DFTB+ on the first singlet vertical excitation energy of small organic molecules

“…DFTB+ is a popular and open source scientific software package that offers a fast and scalable implementation of the density functional based tight binding (DFTB) method [1]. Among the many implemented features, which are being actively developed [2] by its vast community of users, there is available a set of methods for simulating the photo-absorption spectroscopy of molecular systems; namely, the timedependent DFTB method (TD-DFTB) and the DFTBapproximate particle-particle random phase approximation (ppRPA) [3]. In DFTB+, TD-DFTB exists as two distinct but equivalent implementations: one is based on Casida's linear response (LR) approach [4] and the other is a real-time implementation based on the semi-classical Ehrenfest method for nuclear-electronic dynamics [5].…”

“…Thus, we have decided to include brief overviews of the methods revised in this work, which will aid the reader in the discussion of the results. However, we strongly recommend the readers to refer to the original publications for the respective implementations of DFTB [2], TD-DFTB (DFTB-Casida) [11] and pp-DFTB (DFTB-ppRPA) [3]. We also want to recommend a pedagogical introduction to those who are completely new to DFTB [17].…”