Reference Energies for Double Excitations

Abstract

Excited states exhibiting double excitation character are notoriously di cult to model using conventional singlereference methods, such as adiabatic time-dependent density-functional theory (TD-DFT) or equation-of-motion coupled cluster (EOM-CC). In addition, these states are typical experimentally "dark" making their detection in photo-absorption spectra very challenging. Nonetheless, they play a key role in the faithful description of many physical, chemical, and biological processes. In the present work, we provide accurate reference excitation energies for transitions involving a substantial amount of double excitation using a series of increasingly large di use-containing atomic basis sets. Our set gathers 20 vertical transitions from 14 small-and medium-size molecules (acrolein, benzene, beryllium atom, butadiene, carbon dimer and trimer, ethylene, formaldehyde, glyoxal, hexatriene, nitrosomethane, nitroxyl, pyrazine, and tetrazine). Depending on the size of the molecule, selected con guration interaction (sCI) and/or multicon gurational (CASSCF, CASPT2, (X)MS-CASPT2 and NEVPT2) calculations are performed in order to obtain reliable estimates of the vertical transition energies. In addition, coupled cluster approaches including at least contributions from iterative triples (such as CC3, CCSDT, CCSDTQ, and CCSDTQP) are assessed. Our results clearly evidence that the error in CC methods is intimately related to the amount of double excitation character of the transition. For "pure" double excitations (i.e. for transitions which do not mix with single excitations), the error in CC3 can easily reach 1 eV, while it goes down to few tenths of an eV for more common transitions (like in trans-butadiene) involving a signi cant amount of singles. As expected, CC approaches including quadruples yield highly accurate results for any type of transitions. e quality of the excitation energies obtained with multicon gurational methods is harder to predict. We have found that the overall accuracy of these methods is highly dependent of both the system and the selected active space. e inclusion of the σ and σ orbitals in the active space, even for transitions involving mostly π and π orbitals, is mandatory in order to reach high accuracy. A theoretical best estimate (TBE) is reported for each transition. We believe that these reference data will be valuable for future methodological developments aiming at accurately describing double excitations. TOC graphical abstract arXiv:1811.12861v1 [physics.chem-ph] 30 Nov 2018

The Quest for Highly Accurate Excitation Energies: A Computational Perspective

“…For all the transitions of the QUEST#3 set, we reported at least CCSDT/aug-cc-pVTZ (sometimes with basis set extrapolation) and CC3/aug-cc-pVQZ transition energies as well as CC3/aug-cc-pVTZ oscillator strengths for each dipole-allowed transition. Pursuing our previous benchmarking efforts, 47,50 we confirmed that CC3 almost systematically delivers transition energies in agreement with higher-level theoretical models (±0.04 eV) except for transitions presenting a dominant double excitation character (see Fig. 3).…”

“…It is also noteworthy that CCSDT and CC3 are also able to detect the presence of double excitations, a feature that is absent from both CCSD and CC2. 50 It is also important to mention the recent rejuvenation of the second-and third-order algebraic diagrammatic construction [ADC (2) 51 and ADC(3) 52,53 ] methods that scale as N 5 and N 6 , respectively. These methods are related to the older second-and third-order polarization propagator approaches (SOPPA and TOPPA).…”

A Mountaineering Strategy to Excited States: Highly Accurate Energies and Benchmarks for Medium Sized Molecules

“…Recently, we have developed two sets of theoretical best estimates (TBEs) of FCI quality for the vertical transition energies of small closed-shell compounds. 20,21 (See Ref. 24 for a recent review.)…”

Pros and Cons of the Bethe–Salpeter Formalism for Ground-State Energies

“…24,43 However, similar to adiabatic TD-DFT, [44][45][46][47] the static version of BSE cannot describe multiple excitations. [48][49][50] A significant limitation of the BSE formalism, as compared to TD-DFT, lies in the lack of analytical nuclear gradients (i.e., the first derivatives of the energy with respect to the nu-clear displacements) for both the ground and excited states, 51 preventing efficient studies of excited-state processes (e.g., chemoluminescence and fluorescence) associated with geometric relaxation of ground and excited states, and structural changes upon electronic excitation. [52][53][54][55] While calculations of the GW quasiparticle energy ionic gradients is becoming increasingly popular, [56][57][58][59][60][61] only one pioneering study of the excited-state BSE gradients has been published so far.…”