Excitation energies of polycylic aromatic hydrocarbons by double-hybrid functionals: Assessing the PBE0-DH and PBE-QIDH models and their range-separated versions.

A family of non-empirical double-hybrid (DH) density functionals, such as Perdew-Burke-Ernzerhof (PBE)0-DH, PBE-QIDH, and their range-separated exchange (RSX) versions RSX-0DH and RSX-QIDH, all using Perdew-Burke-Ernzerhof(PBE) exchange and correlationfunctionals, is applied here to calculate the excitation energies for increasingly longer linear and cyclic acenes as part of their intense benchmarking for excited states of all types. The energies for the two lowest-lying singlet 1La and 1Lb states of linear oligoacenes as well as the triplet 3La and 3Lb states, are calculated and compared with experimental results. These functionals clearly outperform the results obtained from hybrid functionals and favorably compare with other double-hybrid expressions also tested here, such as B2-PLYP, B2GP-PLYP, ωB2-PLYP, and ωB2GP-PLYP. The study is complemented by the computation of adiabatic S0-T1 singlet-triplet energy difference for linear acenes as well as the extension of the study to strained cyclic oligomers, showing how the family of non-empirical expressions robustly leads to competitive results.

Assessment of the nonempirical r2SCAN-QIDH double-hybrid density functional against large and diverse datasets.

We update the Quadratic Integrand Double-Hybrid (QIDH) model [J. Chem. Phys. 141, 031101 (2014)] by incorporating the nonempirical restored-regularized Strongly Constrained and Appropriately Normed (r2SCAN) meta-generalized gradient approximation exchange-correlation functional, thus devising a robust density functional approximation free of any empirical parameter and incorporating all the constraints so far known for the exchange-correlation kernel. We assessed the new r2SCAN-QIDH expression on the GMTKN55 database and further extend its application to various types of non-covalent interactions (e.g., S66 × 8, O24 × 5). The assessment done shows that the model becomes very competitive in accuracy with respect to parent exchange-correlation functionals of any type, but without relying on any fitted parameter or numerical training.

Stability of the polyynic form of C18, C22, C26, and C30 nanorings: a challenge tackled by range-separated double-hybrid density functionals.

We calculate the relative energy between the cumulene and polyyne structures of a set of C4k+2 (k = 4-7) rings (C18, C22, C26, and C30 prompted by the recent synthesis of the cyclo[18]carbon (or simply C18) compounds. Reference results were obtained by a costly Quantum Monte-Carlo (QMC) approach, providing thus very accurate values allowing to systematically compare the performance of a variety of wavefunction methods [(i.e., MP2, SCS-MP2, SOS-MP2, DLPNO-CCSD, and DLPNO-CCSD(T)] as well as DFT approaches, applying for the latter a diversity of density functionals covering global and range-separated hybrid and double-hybrid models. The influence of the use of a range-separation scheme for density functionals, for both hybrid and double-hybrid expressions, is discussed according to its key role. Overall, range-separated double-hybrid functionals (e.g., RSX-QIDH) behave very accurately and provide competitive results compared with DLPNO-CCSD(T), at a more reasonable computational cost.

Violation of Hund's rule in molecules: Predicting the excited-state energy inversion by TD-DFT with double-hybrid methods.

The energy difference (ΔEST) between the lowest singlet (S1) state and the triplet (T1) excited state of a set of azaphenalene compounds, which is theoretically and experimentally known to violate Hund's rule, giving rise to the inversion of the order of those states, is calculated here with a family of double-hybrid density functionals. That excited-state inversion is known to be very challenging to reproduce for time-dependent density functional theory employing common functionals, e.g., hybrid or range-separated expressions, but not for wavefunction methods due to the inclusion of higher-than-single excitations. Therefore, we explore here if the last developed family of density functional expressions (i.e., double-hybrid models) is able to provide not only the right excited-state energy order but also accurate ΔEST values, thanks to the approximate inclusion of double excitations within these models. We herein employ standard double-hybrid (B2-PLYP, PBE-QIDH, and PBE0-2), range-separated (ωB2-PLYP and RSX-QIDH), spin-scaled (SCS/SOS-B2PLYP21, SCS-PBE-QIDH, and SOS-PBE-QIDH), and range-separated spin-scaled (SCS/SOS-ωB2-PLYP, SCS-RSX-QIDH, and SOS-RSX-QIDH) expressions to systematically assess the influence of the ingredients entering into the formulation while concomitantly providing insights for their accuracy.

Communication: Accurate description of interaction energies and three-body effects in weakly bound molecular complexes by PBE-QIDH models.

We apply a recently developed parameter-free double-hybrid density functional belonging to the quadratic-integrand double-hybrid model to calculate association energies (ΔE) and three-body effects (Δ3E) arising from intermolecular interactions in weakly bound supramolecular complexes (i.e., the dataset 3B-69). The model behaves very accurately for trimer association energies and is found to outperform widely used density functional approximations while approaching the accuracy of more costly ab initio methods for three-body effects. The results are further improved when we add some specific corrections for the remaining dispersion interactions, D3(BJ) or VV10 for two-body effects and Axilrod-Teller-Muto for three-body effects, leading to marginal deviations (less than 1 kcal/mol for ΔE and around 0.03-0.04 kcal/mol for Δ3E) with respect to benchmark results.

Partnering dispersion corrections with modern parameter-free double-hybrid density functionals.

The PBE-QIDH and SOS1-PBE-QIDH double-hybrid density functionals are merged with a pair of dispersion corrections, namely the pairwise additive D3(BJ) and the non-local correlation functional VV10, leading to the corresponding dispersion-corrected models. The parameters adjusting each of the dispersion corrections to the functionals are obtained by fitting to well-established energy datasets (e.g. S130) used as a benchmark, giving rise to functionals spanning covalent and non-covalent binding forces. The application of the models to challenging systems out of the training set, like those comprising the L7 database of large supramolecular complexes, or the S66x8 dataset of stretched and elongated intermolecular distances, reveals the high accuracy of the coupling.

Importance of Orbital Optimization for Double-Hybrid Density Functionals: Application of the OO-PBE-QIDH Model for Closed- and Open-Shell Systems.

We assess here the reliability of orbital optimization for modern double-hybrid density functionals such as the parameter-free PBE-QIDH model. We select for that purpose a set of closed- and open-shell strongly and weakly bound systems, including some standard and widely used data sets, to show that orbital optimization improves the results with respect to standard models, notably for electronically complicated systems, and through first-order properties obtained as derivatives of the energy.