A comparison of density functional theory (DFT) methods for estimating the singlet–triplet (S0–T1) excitation energies of benzene and polyacenes

Effect of Benzo-Annelation on Triplet State Energies in Polycyclic Conjugated Hydrocarbons

In a series of earlier studies, the effect of benzo-annelation was found to be a useful tool for tuning the aromaticity in polycyclic conjugated compounds to desired level. In this work we studied the (anti)aromaticity of benzo-annelated derivatives of three conjugated hydrocarbons (anthracene, fluoranthene and biphenylene) in their lowest lying singlet (S0) and triplet (T1) states by means of the energy effect (ef), harmonic oscillator model of aromaticity (HOMA), multicentre delocalization indices (MCI), magnetically induced current densities (MICDs) and nucleus independent chemical shifts (NICS). We showed that benzo-annelation is a topology-based effect which can be used to modify the T1 state excitation energies (E(T1)). A quantitative model was established being able to accurately predict the E(T1) based only on the numbers of angularly, linearly and geminally annelated benzene rings. In addition, it was demonstrated that the E(T1) can be directly related to the (anti)aromatic character of the central ring in the studied molecules in their S0 state.

Chemically accurate singlet-triplet gaps of organic chromophores and linear acenes by the random phase approximation and σ-functionals

Predicting the energy differences between different spin-states is challenging for many widely used ab initio electronic structure methods. We here assess the ability of the direct random phase approximation (dRPA), dRPA plus two different screened second-order exchange (SOX) corrections, and σ-functionals to predict adiabatic singlet-triplet gaps. With mean absolute deviations of below 0.1 eV to experimental reference values, independent of the Kohn-Sham starting point, dRPA and σ-functionals accurately predict singlet-triplet gaps of 18 organic chromophores. The addition of SOX corrections to dRPA considerably worsens agreement with experiment, adding to the mounting evidence that dRPA+SOX methods are not generally applicable beyond-RPA methods. Also for a series of linear acene chains with up to ten fused rings, dRPA, and σ-functionals are in excellent agreement with coupled-cluster single double triple reference data. In agreement with advanced multi-reference methods, dRPA@PBE and σ-functional@PBE predict a singlet ground state for all chain lengths, while dRPA@PBE0 and σ-functional@PBE0 predict a triplet ground state for longer acenes. Our work shows dRPA and σ-functionals to be reliable methods for calculating singlet-triplet gaps in aromatic molecules.

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 ¹L_a and ¹L_b states of linear oligoacenes as well as the triplet ³L_a and ³L_b 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.

Communication: Proper use of broken-symmetry calculations in antiferromagnetic polyradicals

The present comment formulates some recommendations regarding the use of broken-symmetry Unrestricted Density Functional Theory (UDFT) solutions in those polyradical architectures predicted to be of ground-state singlet character according to Ovchinnikov's rule. It proposes a procedure to identify the number of open shells, to reach the relevant Ms = 0 solution, and to estimate the low-energy spectrum of the states which keeps this number of open shells.

Benchmarking semiempirical, Hartree–Fock, DFT, and MP2 methods against the ionization energies and electron affinities of short- through long-chain [n]acenes and [n]phenacenes

Vertical and adiabatic ionization energies (IEs) and electron affinities (EAs) were calculated for the n = 1–10 [n]acenes using a wide range of semiempirical, Hartree–Fock, density functional, and second-order Moller–Plesset perturbation theory model chemistries. None of the model chemistries examined was able to accurately predict the IEs or EAs for both short- through long-chain [n]acenes, as well as for extrapolations to the polymeric limit, when compared to available experimental and benchmark theoretical data. Except for 6-31G(d), the choice of the basis set does not affect B3LYP results significantly. Analogous calculations using a suite of eight modern and (or) popular density functionals for the n = 1–10 [n]phenacenes revealed similar problems in estimating the IEs and EAs of these compounds, with the sole exception of the M062X functional for adiabatic IEs and potentially the APFD, B3LYP, and MN12SX functionals for adiabatic EAs. The poor IE/EA prediction performance for the parent [n]acenes and [n]phenacenes may extend to their substituted derivatives and heteroatom-substituted analogs. Consequently, caution should be exercised in the application of non-high-level calculations for estimating the IE/EA of these important classes of materials.

Theoretical design of tetra(arenediyl)bis(allyl) derivatives as model compounds for Cope rearrangement transition states

Delocated structures bearing 2.3–2.5 Å C⋯C bonds are preferred for some tetra(arenediyl)bis(allyl) systems.

The substituent effect on benzene dications

It was shown that the substituent effect in the dicationic benzene ring, which is a 4n π-electron system, can be numerically quantified and then further interpreted.

Spin-spin and spin-orbit interactions in nanographene fragments: a quantum chemistry approach

The relativistic behavior of graphene structures, starting from the fundamental building blocks--the poly-aromatic hydrocarbons (PAHs) along with other PAH nanographenes--is studied to quantify any associated intrinsic magnetism in the triplet (T) state and subsequently in the ground singlet (S) state with account of possible S-T mixture induced by spin-orbit coupling (SOC). We employ a first principle quantum chemical-based approach and density functional theory (DFT) for a systematic treatment of the spin-Hamiltonian by considering both the spin-orbit and spin-spin interactions as dependent on different numbers of benzene rings. We assess these relativistic spin-coupling phenomena in terms of splitting parameters which cause magnetic anisotropy in absence of external perturbations. Possible routes for changes in the couplings in terms of doping and defects are also simulated and discussed. Accounting for the artificial character of the broken-symmetry solutions for strong spin polarization of the so-called "singlet open-shell" ground state in zigzag graphene nanoribbons predicted by spin-unrestricted DFT approaches, we interpolate results from more sophisticated methods for the S-T gaps and spin-orbit coupling (SOC) integrals and find that these spin interactions become weak as function of size and increasing decoupling of electrons at the edges. This leads to reduced electron spin-spin interaction and hence almost negligible intrinsic magnetism in the carbon-based PAHs and carbon nanographene fragments. Our results are in agreement with the fact that direct experimental evidence of edge magnetism in pristine graphene has been reported so far. We support the notion that magnetism in graphene only can be ascribed to structural defects or impurities.

Rational design of high-spin biradicaloids in the isobenzofulvene and isobenzoheptafulvene series

The relative energies of singlet biradicaloid and of triplet and singlet biradical electronic states for a series of benzannelated isobenzofulvenes and isobenzoheptafulvenes were calculated at the (u-)B3LYP/6-31G(d), full π-space CASSCF-CASPT2 (≤14 π-e(-)s), and full π-space RASSCF-RASPT2 (≤24 π-e(-)s) levels of theory. Both absolute and relative CASPT2 energies were reproduced quite well by the RASPT2 approach, which can be extended to much larger active spaces. RASPT2 (and DFT) calculations find that increasing benzannelation leads to triplet ground states in both hydrocarbon series, in violation of the classical principle of maximum bonding. This confirmed the expectations that the combined effects of resonance energy and aromaticity could compensate for the extra formal π-bond of the biradicaloid singlet, and that the strong exchange coupling inherent to the embedded trimethylenemethane (TMM) would manifest itself in the biradicaloids. The relative energy of the biradicaloid singlet rises rapidly upon benzannelation, as π-bonding between the high-energy delocalized GVB orbitals decreases. The underlying π-orbital topology is revealed when this weak π-bonding is artificially eliminated by a 1:1 mixing of the nondegenerate HOMO and LUMO to produce an overcorrelated valence bond (OCVB) orbital pair. For members of both biradicaloid series, the OCVB pairs are nondisjoint, revealing a limiting triplet preference with increasing benzannelation. Within the two-electron, two-orbital approximation, the effects of π-bonding in the singlet biradicaloids and orbital localization away from the acene π-system in the triplet biradicals can be analyzed as perturbations of the singlet OCVB biradicals. The application of a VB-based spin coupling scheme is discussed, in which the unpaired electrons of these species can be considered both ferromagnetically and antiferromagnetically coupled, with the strength of the latter strongly dependent on the acene subunit.