Adiabatic Singlet-triplet Energy Gaps Research Articles

Correlation balance for describing carbenes: An NOF study

Carbenes are a remarkable type of molecules because of the two electrons that might be paired or unpaired, providing a singlet or a triplet state, respectively. The preference for one of these states can be measured by the singlet-triplet energy gap; however, theoretical prediction is challenging when static correlation arises, and an adequate balance with dynamic correlation is required to achieve correct predictions. Piris Natural Orbital Functionals (PNOFs) have been used before to deal with other static correlation problems, but they have suffered from lack of dynamic correlation, which has been solved by coupling PNOF7 with many-body perturbation theory. Recently, the development of a Global Natural Orbital Functional (GNOF) has been proposed with the aim of including dynamic correlation without the need to couple with perturbation theory, thus becoming a promising alternative to study challenging chemical problems. In this work, we applied the PNOF family of functionals to compute the adiabatic singlet-triplet energy gaps of a set of simple carbenes and compared them with those computed with coupled-cluster methods and experimental values when available. We have found that the GNOF achieves promising results due to an intrinsic balance of static and dynamic correlation. In this regard, the GNOF presents errors that are lower than those of PNOF7, comparable to those of NOF-c-MP2, and is capable of predicting the tendency of substituent effects, proving to be suitable for further application to predict general singlet-triplet energy gaps.

Effects of Secondary Acceptors on Excited-State Properties of Sky-Blue Thermally Activated Delayed Fluorescence Molecules: Luminescence Mechanism and Molecular Design

The development of efficient sky-blue thermally activated delayed fluorescence (TADF) emitters is highly desired. However, the types and amounts of sky-blue TADF are far from meeting the requirements, and effective molecular design strategies are expected. Herein, the photophysical properties and excited-state dynamics of 12 molecules are theoretically studied based on the thermal vibration correlation function method. Distributions of holes and electrons are analyzed by the heat maps. The frontier molecular orbital distribution, adiabatic singlet-triplet energy gap, and reorganization energy are analyzed in detail. Furthermore, the radiative and non-radiative as well as the intersystem crossing (ISC) and reverse intersystem crossing (RISC) processes are studied, and the up-conversion process is illustrated. Our results indicate that different substitution positions and numbers play an important role in the luminescence properties of TADF molecules. The meta-position substitutions restrict the geometry variations, hinder the non-radiative energy consumption process, and promote the radiative process of TADF molecules. Meanwhile, molecules with ortho-position substitutions possess the smallest energy gaps (ΔEst) and the largest RISC rates. Moreover, molecules with the substitutions of one tBCz group and two PO groups have the smallest ΔEst and the largest spin orbital coupling. Thus, a wise molecular design strategy, namely, ortho-position substitutions as well as substitutions with one tBCz group and two PO groups, is proposed to facilitate the RISC process. Based on this rule, new efficient TADF molecules are theoretically designed and proposed. Our work reasonably elucidates the experimental measurements, and the effects of different substitution numbers and positions of secondary acceptors on TADF properties are highlighted, which could provide a theoretical perspective for designing efficient sky-blue TADF molecules.

Intermolecular interaction on excited-state properties of fluoro-substituted thermally activated delayed fluorescence molecules with aggregation-induced emission: a theoretical perspective

ABSTRACT Thermally activated delayed fluorescence (TADF) molecules have shown promising applications in organic light- emitting diodes. Theoretical investigations to reveal the fluoro-substitution and intermolecular interaction on their photophysical properties especially for aggregation-induced emission (AIE) and TADF mechanisms are highly desired. In this work, two efficient TADF molecules SFDBQPXZ and DFDBQPXZ with fluoro-substitution are selected and studied. The solvent and solid environments are considered by polarisable continuum model and the combined quantum mechanics and molecular mechanics (QM/MM) method, respectively. The frontier molecular orbital properties, heat maps, adiabatic singlet–triplet energy gap (ΔEst ) and intermolecular interactions as well as excited-state dynamic process are analysed in both toluene and solid phase. Results show that the small ΔEst and large spin-orbital coupling constant facilitate the up-conversion process. Moreover, small reorganisation energies and large intermolecular interactions are determined in the solid phase, the non-radiative energy consumption processes of SFDBQPXZ and DFDBQPXZ are significantly suppressed in the aggregation state due to the restricted rotations in low-frequency region, the AIE feature is illustrated, and inner mechanisms for higher luminescence efficiency of SFDBQPXZ than that of DFDBQPXZ ae determined. The experimental measurements are reasonably elucidated and the effect of fluoro-substitution on excited-state dynamics is revealed.

Impact of secondary donor units on the excited-state properties and thermally activated delayed fluorescence (TADF) efficiency of pentacarbazole-benzonitrile emitters.

The performance of organic light-emitting diodes based on thermally activated delayed fluorescence emitters depends on the efficiency of reverse intersystem crossing (RISC) processes, which are promoted by a small energy gap between the lowest singlet (S1) and triplet (T1) excited states and large spin-orbit couplings. Recently, it was proposed that the introduction of secondary donor units into 2,3,4,5,6-penta(9H-carbazol-9-yl)benzonitrile (5CzBN) can significantly increase the mixing between triplet states with charge-transfer (CT) and local-excitation characteristics and consequently increase the spin-orbit couplings. Here, the results of long-range corrected density functional theory calculations show that the main impact on the RISC rates of substituting 5CzBN with secondary donors is due to a decrease in adiabatic singlet-triplet energy gaps and intramolecular reorganization energies rather than to a change in spin-orbit couplings. Our calculations underline that at least two singlet and three triplet excited states contribute to the ISC/RISC processes in 5CzBN and its derivatives. In addition, we find that in all emitters, the lowest singlet excited-state potential energy surface has a double-minimum shape.

On the radicalar properties of graphene fragments: double-hybrid DFT and perturbation theory approaches

The physical–chemical properties of polycyclic aromatic hydrocarbons (PAHs), molecules formed by fused carbon rings passivated by hydrogen atoms, make them attractive to several applications, including light-emitting diodes, photovoltaic cells, and transistors. They borrow some of the unique properties of graphene, nanotubes, and fullerenes. Additionally, radicals related to these structures may be involved in carcinogenic effects. In this work, electronic and energetic aspects of PAHs, including triangulenes, were analyzed using BLYP and B2PLYP density functionals as well as with unrestricted Hartree–Fock (UHF) and second-order Moller–Plesset perturbation (MP2) theories. The results show that DFT BLYP and B2PLYP functionals predict adiabatic singlet–triplet energy gap in better agreement to reference data when compared to MP2, with the double-hybrid B2PLYP producing better results than BLYP. On the other hand, for calculation of properties involving radical species, as homolytic bond dissociation energies, B2PLYP overestimates the binding energy, especially for larger PAHs. The erratic behavior of UHF and MP2 for open-shell species limits the B2PLYP performance regarding the stability analysis of triangulenes over different multiplicities.

Simplified Treatment of Electronic Structures of the Lowest Singlet and Triplet States of Didehydropyrazines.

Experiments on the lowest lying singlet and triplet states of didehydropyrazine isomers (that focus on energy gaps, geometries, and vibrational frequencies) have been carried out computationally by implementing the improved virtual orbital-based multireference (MR) ab initio methods. Pyrazines possess a reasonable MR nature making their description challenging with the conventional quantum chemical approaches. Although wave functions of the diradicals usually have two dominant configurations, a larger reference space is warranted to consistently and accurately describe pyrazine diradicals indicating the complex nature of the systems. Present calculations predict a singlet ground state for ortho- and para-pyrazines, while a triplet ground state is suggested for the meta isomer. The adiabatic singlet-triplet energy gap for the para form is found to be notably higher (by 28.4 kcal/mol) compared to ortho (2.0 kcal/mol) and meta isomers (-5.1 kcal/mol). Accurate and reliable computations are imperative for forecasting the state-ordering in such diradicals. The structural properties obtained from the present calculations lend strong support toward future experimental explorations on these systems.

RPM6 parameters for phosphorous and sulphur-containing open-shell molecules

ABSTRACTIn this article, we have introduced a reparameterisation of PM6 (rPM6) for phosphorus and sulphur to achieve a better description of open-shell species containing the two elements. Two sets of the parameters have been optimised separately using our training sets. The performance of the spin-unrestricted rPM6 (UrPM6) method with the optimised parameters is evaluated against 14 radical species, which contain either phosphorus or sulphur atom, comparing with the original UPM6 and the spin-unrestricted density functional theory (UDFT) methods. The standard UPM6 calculations fail to describe the adiabatic singlet-triplet energy gaps correctly, and may cause significant structural mismatches with UDFT-optimised geometries. Leaving aside three difficult cases, tests on 11 open-shell molecules strongly indicate the superior performance of UrPM6, which provides much better agreement with the results of UDFT methods for geometric and electronic properties.

Reparameterization of PM6 Applied to Organic Diradical Molecules.

We have performed a reparameterization of PM6 (called rPM6) to compute open-shell species, specifically organic diradical molecules, within a framework of the spin-unrestricted semiempirical molecular orbital (SE-UMO) method. The parameters for the basic elements (hydrogen, carbon, nitrogen, and oxygen) have been optimized simultaneously using the training set consisting of 740 reference data. On the basis of the GMTKN30 database, the mean absolute error of rPM6 is decreased from 16.1 to 14.1 kcal/mol, which reassures its accuracy for ground-state properties. Applications of the spin-unrestricted rPM6 (UrPM6) method to small diradicals and relatively large polycyclic aromatic hydrocarbons have provided substantial improvement over the standard SE-UMO methods like UAM1, UPM3, and the original UPM6. The UrPM6 calculation is much less susceptible to spin contamination and, therefore, reproduces geometric parameters and adiabatic singlet-triplet energy gaps obtained by UDFT (UB3LYP and/or UBHandHLYP) at much lower computational cost.

Singlet-triplet energy gaps for diradicals from particle-particle random phase approximation.

The particle-particle random phase approximation (pp-RPA) for calculating excitation energies has been applied to diradical systems. With pp-RPA, the two nonbonding electrons are treated in a subspace configuration interaction fashion while the remaining part is described by density functional theory (DFT). The vertical or adiabatic singlet-triplet energy gaps for a variety of categories of diradicals, including diatomic diradicals, carbene-like diradicals, disjoint diradicals, four-π-electron diradicals, and benzynes are calculated. Except for some excitations in four-π-electron diradicals, where four-electron correlation may play an important role, the singlet-triplet gaps are generally well predicted by pp-RPA. With a relatively low O(r(4)) scaling, the pp-RPA with DFT references outperforms spin-flip configuration interaction singles. It is similar to or better than the (variational) fractional-spin method. For small diradicals such as diatomic and carbene-like ones, the error of pp-RPA is slightly larger than noncollinear spin-flip time-dependent density functional theory (NC-SF-TDDFT) with LDA or PBE functional. However, for disjoint diradicals and benzynes, the pp-RPA performs much better and is comparable to NC-SF-TDDFT with long-range corrected ωPBEh functional and spin-flip configuration interaction singles with perturbative doubles (SF-CIS(D)). In particular, with a correct asymptotic behavior and being almost free from static correlation error, the pp-RPA with DFT references can well describe the challenging ground state and charge transfer excitations of disjoint diradicals in which almost all other DFT-based methods fail. Therefore, the pp-RPA could be a promising theoretical method for general diradical problems.

Benchmark theoretical study of the ionization energies, electron affinities and singlet–triplet energy gaps of azulene, phenanthrene, pyrene, chrysene and perylene

The vertical and adiabatic singlet–triplet energy gaps, electron affinities and ionization energies of azulene, phenanthrene, pyrene, chrysene, and perylene are computed by applying the principles of a focal point analysis onto a series of single-point calculations at the level of Hartree–Fock theory, second-, third-, and fourth-order Møller–Plesset perturbation theory, as well as coupled cluster theory including single, double and perturbative triple excitations, in conjunction with correlation consistent basis sets of improving quality. Results are supplemented with an extrapolation to the limit of an asymptotically complete basis set. According to our best estimates, azulene, phenanthrene, pyrene, chrysene, and perylene exhibit adiabatic singlet–triplet energy gaps of 1.79, 2.92, 2.22, 2.79 and 1.71eV, respectively. In the same order, the corresponding adiabatic electron affinities (EAs) amount to 0.71, −0.08, −0.40, 0.24, and 0.87eV, whereas benchmark values equal to 7.43, 8.01, 7.48, 7.66 and 7.15eV, are found for the adiabatic ionization energies.

Phenyloxenium Ions: More Like Phenylnitrenium Ions than Isoelectronic Phenylnitrenes?

The geometries and energies of the electronic states of phenyloxenium ion 1 (Ph-O(+)) were computed at the multireference CASPT2/pVTZ level of theory. Despite being isoelectronic to phenylnitrene 4, the phenyloxenium ion 1 has remarkably different energetic orderings of its electronic states. The closed-shell singlet configuration ((1)A(1)) is the ground state of the phenyloxenium ion 1, with a computed adiabatic energy gap of 22.1 kcal/mol to the lowest-energy triplet state ((3)A(2)). Open-shell singlet configurations ((1)A(2), (1)B(1), (1)B(2), 2(1)A(1)) are significantly higher in energy (>30 kcal/mol) than the closed-shell singlet configuration. These values suggest a revision to the current assignments of the ultraviolet photoelectron spectroscopy bands for the phenoxy radical to generate the phenyloxenium ion 1. For para-substituted phenyloxenium ions, the adiabatic singlet-triplet energy gap (ΔE(ST)) is found to have a positive linear free energy relationship with the Hammett-like σ(+)(R)/σ(+) substituent parameters; for meta substituents, the relationship is nonlinear and negatively correlated. CASPT2 analyses of the excited states of p-aminophenyloxenium ion 5 and p-cyanophenyloxenium ion 10 indicate that the relative orderings of the electronic states remain largely unperturbed for these para substitutions. In contrast, meta-donor-substituted phenyloxenium ions have low-energy open-shell states (open-shell singlet, triplet) due to stabilization of a π,π* diradical state by the donor substituent. However, all of the other phenyloxenium ions and larger aryloxenium ions (naphthyl, anthryl) included in this study have closed-shell singlet ground states. Consequently, ground-state reactions of phenyloxenium ions are anticipated to be more closely related to closed-shell singlet arylnitrenium ions (Ar-NH(+)) than their isoelectronic arylnitrene (Ar-N) counterparts.

Automerization reaction of cyclobutadiene and its barrier height: An ab initio benchmark multireference average-quadratic coupled cluster study

The problem of the double bond flipping interconversion of the two equivalent ground state structures of cyclobutadiene (CBD) is addressed at the multireference average-quadratic coupled cluster level of theory, which is capable of optimizing the structural parameters of the ground, transition, and excited states on an equal footing. The barrier height involving both the electronic and zero-point vibrational energy contributions is 6.3 kcal mol(-1), which is higher than the best earlier theoretical estimate of 4.0 kcal mol(-1). This result is confirmed by including into the reference space the orbitals of the CC sigma bonds beyond the standard pi orbital space. It places the present value into the middle of the range of the measured data (1.6-10 kcal mol(-1)). An adiabatic singlet-triplet energy gap of 7.4 kcal mol(-1) between the transition state (1)B(tg) and the first triplet (3)A(2g) state is obtained. A low barrier height for the CBD automerization and a small DeltaE((3)A(2g),(1)B(1g)) gap bear some relevance on the highly pronounced reactivity of CBD, which is briefly discussed.