Reliable TDDFT Protocol Based on a Local Hybrid Functional for the Prediction of Vibronic Phosphorescence Spectra Applied to Tris(2,2'-bipyridine)-Metal Complexes

Ab initio multireference calculation of electronic spectra of the osmium complexes, [Os(bpy) 3 $$ {}_3 $$ ] 2 + $$ {}^{2+} $$ and [Os(phen) 3 $$ {}_3 $$ ] 2 + $$ {}^{2+} $$

The spin-orbit coupling corrected absorption spectra of osmium complexes, [Os(bpy)3 $$ {}_3 $$ ]2 + $$ {}^{2+} $$ and [Os(phen)3 $$ {}_3 $$ ]2 + $$ {}^{2+} $$ , were calculated by using ab initio multireference perturbation method (NEVPT2) with relativistic effects taken into account throughout ZORA approximation and corresponding all-electron basis sets. For the same purpose, the time-dependent DFT techniques were used. A very good agreement between NEVPT2 and experimental spectra should be highlighted, especially for the MLCT transitions that occur in visible and near-UV regions (16 , 000 - 33 , 000 $$ 16,000-33,000 $$ cm- 1 $$ {}^{-1} $$ ). Moreover, the present study offers description of excited states of titled osmium complexes and their spectra interpretation using molecular orbitals.

Learning from the 4-(dimethylamino)benzonitrile twist: Two-parameter range-separated local hybrid functional with high accuracy for triplet and charge-transfer excitations

The recent ωLH22t range-separated local hybrid (RSLH) is shown to provide outstanding accuracy for the notorious benchmark problem of the two lowest excited-state potential energy curves for the amino group twist in 4-(dimethylamino)benzonitrile (DMABN). However, the design of ωLH22t as a general-purpose functional resulted in less convincing performance for triplet excitations, which is an important advantage of previous LHs. Furthermore, ωLH22t uses 8 empirical parameters to achieve broad accuracy. In this work, the RSLH ωLH23ct-sir is constructed with minimal empiricism by optimizing its local mixing function prefactor and range-separation parameter for only 8 excitation energies. ωLH23ct-sir maintains the excellent performance of ωLH22t for the DMABN twist and charge-transfer benchmarks but significantly improves the errors for triplet excitation energies (0.17 vs 0.24 eV). Additional test calculations for the AE6BH6 thermochemistry test set and large dipole moment and static polarizability test sets confirm that the focus on excitation energies in the optimization of ωLH23ct-sir has not caused any dramatic errors for ground-state properties. Although ωLH23ct-sir cannot replace ωLH22t as a general-purpose functional, it is preferable for problems requiring a universally good description of localized and charge-transfer excitations of both singlet and triplet multiplicity. Current limitations on the application of ωLH23ct-sir and other RSLHs to the study of singlet-triplet gaps of emitters for thermally activated delayed fluorescence are discussed. This work also includes the first systematic analysis of the influence of the local mixing function prefactor and the range-separation parameter in an RSLH on different types of excitations.

TURBOMOLE: Today and Tomorrow

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

Phosphorescent Properties of Heteroleptic Ir(III) Complexes: Uncovering Their Emissive Species

In this contribution, we assess the computational machinery to calculate the phosphorescence properties of a large pool of heteroleptic [Ir(C^N)2(N^N)]+ complexes (where N^N is an ancillary ligand and C^N is a cyclometalating ligand) including their phosphorescent rates and their emission spectra. Efficient computational protocols are next proposed. Specifically, different flavors of DFT functionals were benchmarked against DLPNO-CCSD(T) for the phosphorescence energies. The transition density matrix and decomposition analysis of the emitting triplet excited state enable us to categorize the studied complexes into different cases, from predominant triplet ligand-centered (3LC) character to predominant charge-transfer (3CT) character, either of metal-to-ligand charge transfer (3MLCT), ligand-to-ligand charge transfer (3LLCT), or a combination of the two. We have also calculated the vibronically resolved phosphorescent spectra and rates. Ir(III) complexes with predominant 3CT character are characterized by less vibronically resolved bands as compared to those with predominant 3LC character. Furthermore, some of the complexes are characterized by close-lying triplet excited states so that the calculation of their phosphorescence properties poses additional challenges. In these scenarios, it is necessary to perform geometry optimizations of higher-lying triplet excited states (i.e., Tn). We demonstrate that in the latter scenarios all of the close-lying triplet species must be considered to recover the shape of the experimental emission spectra. The global analysis of computed emission energies, shape of the computed emission spectra, computed rates, etc. enable us to unambiguously pinpoint for the first time the triplet states involved in the emission process and to provide a general classification of Ir(III) complexes with regard to their phosphorescence properties.

Benchmark Study on Phosphorescence Energies of Anthraquinone Compounds: Comparison between TDDFT and UDFT

Phosphorescent material is widely used in light-emitting devices and in the monitoring of cell phenomena. Anthraquinone compounds (AQs), as important phosphorescent materials, have potential applications as emitters for highly efficient organic light-emitting diodes (OLEDs). Therefore, the accurate calculation of the phosphorescence energy of anthraquinone compounds is particularly important. This study mainly analyzes the phosphorescence energy calculation method of anthraquinone compounds. The time-dependent density functional theory (TDDFT) and the unrestricted density functional theory (UDFT) with seven functionals are selected to calculate the phosphorescence of AQs, taking the high-precision coupled-cluster singles and doubles (CC2) method as a reference. The results showed that the mean unsigned error (MUE) of UDFT was 0.14 eV, which was much smaller than that of TDDFT at 0.29 eV. Therefore, UDFT was more suitable for calculating the phosphorescence energy of AQs. The results obtained by different functionals indicate that the minimum MUE obtained by M06-2X was 0.14 eV. More importantly, the diffuse function in the basis set played an important role in calculating the phosphorescence energy in the M06-HF functional. In the BDBT, FBDBT, and BrBDBT, when M06-HF selected the basis set containing a diffuse function, the differences with CC2 was 0.02 eV, which is much smaller than the one obtained without a diffuse function at 0.80 eV. These findings might be of great significance for the future study of the phosphorescence energy of organic molecules.

Full Implementation, Optimization, and Evaluation of a Range-Separated Local Hybrid Functional with Wide Accuracy for Ground and Excited States

We report the first full and efficient implementation of range-separated local hybrid functionals (RSLHs) into the TURBOMOLE program package. This enables the computation of ground-state energies and nuclear gradients as well as excitation energies. Regarding the computational effort, RSLHs scale like regular local hybrid functionals (LHs) with system or basis set size and increase timings by a factor of 2-3 in total. An advanced RSLH, ωLH22t, has been optimized for atomization energies and reaction barriers. It is an extension of the recent LH20t local hybrid and is based on short-range PBE and long-range HF exchange-energy densities, a pig2 calibration function to deal with the gauge ambiguity of exchange-energy densities, and reoptimized B95c correlation. ωLH22t has been evaluated for a wide range of ground-state and excited-state quantities. It further improves upon the already successful LH20t functional for the GMTKN55 main-group energetics test suite, and it outperforms any global hybrid while performing close to the top rung-4 functional, ωB97M-V, for these evaluations when augmented by D4 dispersion corrections. ωLH22t performs excellently for transition-metal reactivity and provides good balance between delocalization errors and left-right correlation for mixed-valence systems, with a somewhat larger bias toward localized states compared to LH20t. It approaches the accuracy of the best local hybrids to date for core, valence singlet and triplet, and Rydberg excitation energies while improving strikingly on intra- and intermolecular charge-transfer excitations, comparable to the most successful range-separated hybrids available.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Local Hybrid Functional Applicable to Weakly and Strongly Correlated Systems

The recent idea (Wodyński, A.; Arbuznikov, A. V.; Kaupp M. J. Chem. Phys. 2021, 155, 144101) to augment local hybrid functionals by a strong-correlation (sc) factor obtained from the adiabatic connection in the spirit of the KP16 model has been extended and applied to generate the accurate sc-corrected local hybrid functional scLH22t. By damping small values of the ratio between nondynamical and dynamical correlation entering the correction factor, it has become possible to avoid double counting of nondynamical correlation for weakly correlated situations and thereby preserve the excellent accuracy of the underlying LH20t local hybrid for such cases almost perfectly. On the other hand, scLH22t improves substantially over LH20t in reducing fractional-spin errors (FSEs), in providing improved spin-restricted bond dissociation curves, and in treating some typical systems with multireference character. The obtained FSEs are similar to those of the KP16/B13 model and slightly larger than for B13, but performance for weakly correlated systems is better than for these two related methods, which are also difficult to use self-consistently. The recent DM21 functional based on the training of a deep neural network still performs somewhat better than scLH22t but allows no physical insights into the origins of reduced FSEs. Examination of local mixing functions (LMFs) for the corrected scLH22t and uncorrected LH20t functionals provides further insights: in weakly correlated situations, the LMF remains essentially unchanged. Strong-correlation effects manifest in a reduction of the LMF values in certain regions of space, even to the extent of producing negative LMF values. It is suggested that this is the mechanism by which also DM21, which may be viewed as a range-separated local hybrid, is able to reduce FSEs.

Importance of imposing gauge invariance in time-dependent density functional theory calculations with meta-generalized gradient approximations

It has been known for more than a decade that the gauge variance of the kinetic energy density τ leads to additional terms in the magnetic orbital rotation Hessian used in linear-response time-dependent density functional theory (TDDFT), affecting excitation energies obtained with τ-dependent exchange-correlation functionals. While previous investigations found that a correction scheme based on the paramagnetic current density has a small effect on benchmark results, we report more pronounced effects here, in particular, for the popular M06-2X functional and for some other meta-generalized gradient approximations (mGGAs). In the first part of this communication, this is shown by a reassessment of a set of five Ni(II) complexes for which a previous benchmark study that did not impose gauge invariance has found surprisingly large errors for excitation energies obtained with M06-2X. These errors are more than halved by restoring gauge invariance. The variable importance of imposing gauge invariance for different mGGA-based functionals can be rationalized by the derivative of the mGGA exchange energy integrand with respect to τ. In the second part, a large set of valence excitations in small main-group molecules is analyzed. For M06-2X, several selected n → π* and π→π_⊥ ^* excitations are heavily gauge-dependent with average changes of -0.17 and -0.28 eV, respectively, while π→π_‖ ^* excitations are marginally affected (-0.04 eV). Similar patterns, but of the opposite signs, are found for SCAN0. The results suggest that reevaluation of previous gauge variant TDDFT results based on M06-2X and other mGGA functionals is warranted.

Vibration-Assisted Intersystem Crossing in the Ultrafast Excited-State Relaxation Dynamics of Halocoumarins

Due to its numerous applications, triplet formation and resulting phosphorescence remain a frontier area of research for over eight decades. Facile intersystem crossing (ISC) is the primary requirement for triplet formation and observation of phosphorescence. The incorporation of a heavy atom in molecules is one of the common approaches employed to facilitate ISC. A detailed study of the excited state dynamics that governs ISC is necessary to understand the mechanism of heavy atom effect (HAE). Incorporation of iodine at the 3 position of coumarin-1 reduces fluorescence quantum yield (ϕ_f) drastically as expected, whereas bromine substitution at the same position increased the ϕ_f. Such a contrasting effect of the two heavy atoms suggests that there are other features yet to be discovered to fully understand the HAE. Detailed steady state and femtosecond transient absorption studies along with theoretical calculations suggest that the C3-X (X = Br, I) bond vibration plays an important role in the ISC process. The study reveals that while in the case of the iodo-derivative there is no energy barrier in the singlet triplet crossing path, there is a barrier in the case of the bromo-derivative, which slows the ISC process. Such an unexpected phenomenon is not limited to halocoumarins as this rationalizes the photobehavior of 1-bromo-/iodo-substituted naphthalenes as well.

Structural characterization and luminescence properties of trigonal Cu(i) iodine/bromine complexes comprising cation–π interactions

Trigonal copper(i) complexes comprising cation–π interactions achieve satisfactory photoluminescence properties.

Assessment of hybrid functionals for singlet and triplet excitations: Why do some local hybrid functionals perform so well for triplet excitation energies?

The performance of various hybrid density functionals is assessed for 105 singlet and 105 corresponding triplet vertical excitation energies from the QUEST database. The overall lowest mean absolute error is obtained with the local hybrid (LH) functional LH12ct-SsirPW92 with individual errors of 0.11 eV (0.11 eV) for singlet (triplet) n → π* excitations and 0.29 eV (0.17 eV) for π → π* excitations. This is slightly better than with the overall best performing global hybrid M06-2X [n → π*: 0.13 eV (0.17 eV), π → π*: 0.30 eV (0.20 eV)], while most other global and range-separated hybrids and some LHs suffer from the "triplet problem" of time-dependent density functional theory. This is exemplified by correlating the errors for singlet and triplet excitations on a state-by-state basis. The excellent performance of LHs based on a common local mixing function, i.e., an LMF constructed from the spin-summed rather than the spin-resolved semilocal quantities, is systematically investigated by the introduction of a spin-channel interpolation scheme that allows us to continuously modulate the fraction of opposite-spin terms used in the LMF. The correlation of triplet and singlet errors is systematically improved for the n → π* excitations when larger fractions of the opposite-spin-channel are used in the LMF, whereas this effect is limited for the π → π* excitations. This strongly supports a previously made hypothesis that attributes the excellent performance of LHs based on a common LMF to cross-spin-channel nondynamical correlation terms.