On the performance of DFT/MRCI Hamiltonians for electronic excitations in transition metal complexes: The role of the damping function

A new parameterization of the DFT/CIS method with applications to core-level spectroscopy

Time-dependent density functional theory (TD-DFT) within a restricted excitation space is an efficient means to compute core-level excitation energies using only a small subset of the occupied orbitals. However, core-to-valence excitation energies are significantly underestimated when standard exchange-correlation functionals are used, which is partly traceable to systemic issues with TD-DFT's description of Rydberg and charge-transfer excited states. To mitigate this, we have implemented an empirically modified combination of configuration interaction with single substitutions (CIS) based on Kohn-Sham orbitals, which is known as "DFT/CIS." This semi-empirical approach is well-suited for simulating x-ray near-edge spectra, as it contains sufficient exact exchange to model charge-transfer excitations yet retains DFT's low-cost description of dynamical electron correlation. Empirical corrections to the matrix elements enable semi-quantitative simulation of near-edge x-ray spectra without the need for significant a posteriori shifts; this should be useful in complex molecules and materials with multiple overlapping x-ray edges. Parameter optimization for use with a specific range-separated hybrid functional makes this a black-box method intended for both core and valence spectroscopy. Results herein demonstrate that realistic K-edge absorption and emission spectra can be obtained for second- and third-row elements and 3d transition metals, with promising results for L-edge spectra as well. DFT/CIS calculations require absolute shifts that are considerably smaller than what is typical in TD-DFT.

Calculation of quasi-diabatic states within the DFT/MRCI(2) framework: The QD-DFT/MRCI(2) method

We describe a procedure for the calculation of quasi-diabatic states within the recently introduced DFT/MRCI(2) framework [S. P. Neville and M. S. Schuurman, J. Chem. Phys. 157, 164103 (2022)]. Based on an effective Hamiltonian formalism, the proposed procedure, which we term QD-DFT/MRCI(2), has the advantageous characteristics of being simultaneously highly efficient and effectively black box in nature while directly yielding both quasi-diabatic potentials and wave functions of high quality. The accuracy and efficiency of the QD-DFT/MRCI(2) formalism are demonstrated via the simulation of the vibronic absorption spectra of furan and chlorophyll a.

A DFT/MRCI Hamiltonian parameterized using only ab initio data: I. valence excited states

A new combined density functional theory and multi-reference configuration interaction (DFT/MRCI) Hamiltonian parameterized solely using the benchmark ab initio vertical excitation energies obtained from the QUEST databases is presented. This new formulation differs from all previous versions of the method in that the choice of the underlying exchange-correlation (XC) functional employed to construct the one-particle (orbital) basis is considered, and a new XC functional, QTP17, is chosen for its ability to generate a balanced description of core and valence vertical excitation energies. The ability of the new DFT/MRCI Hamiltonian, termed QE8, to furnish accurate excitation energies is confirmed using benchmark quantum chemistry computations, and a mean absolute error of 0.16 eV is determined for the wide range of electronic excitations included in the validation dataset. In particular, the QE8 Hamiltonian dramatically improves the performance of DFT/MRCI for doubly excited states. The performance of fast approximate DFT/MRCI methods, p-DFT/MRCI and DFT/MRCI(2), is also evaluated using the QE8 Hamiltonian, and they are found to yield excitation energies in quantitative agreement with the parent DFT/MRCI method, with the two methods exhibiting a mean difference of 0.01 eV with respect to DFT/MRCI over the entire benchmark set.

A Case-Study on the Photophysics of Chalcogen-Substituted Zinc(II) Phthalocyanines

Singlet dioxygen has been widely applied in different disciplines such as medicine (photodynamic therapy or blood sterilization), remediation (wastewater treatment) or industrial processes (fine chemicals synthesis). Particularly, it can be conveniently generated by energy transfer between a photosensitizer's triplet state and triplet dioxygen upon irradiation with visible light. Among the best photosensitizers, substituted zinc(II) phthalocyanines are prominent due to their excellent photophysical properties, which can be tuned by structural modifications, such as halogen- and chalcogen-atom substitution. These patterns allow for the enhancement of spin-orbit coupling, commonly attributed to the heavy atom effect, which correlates with the atomic number ( Z ${Z}$ ) and the spin-orbit coupling constant ( ζ ${\zeta }$ ) of the introduced heteroatom. Herein, a fully systematic analysis of the effect exerted by chalcogen atoms on the photophysical characteristics (absorption and fluorescence properties, lifetimes and singlet dioxygen photogeneration), involving 30 custom-made β-tetrasubstituted chalcogen-bearing zinc(II) phthalocyanines is described and evaluated regarding the heavy atom effect. Besides, the intersystem crossing rate constants are estimated by several independent methods and a quantitative profile of the heavy atom is provided by using linear correlations between relative intersystem crossing rates and relative atomic numbers. Good linear trends for both intersystem crossing rates (S1-T1 and T1-S0) were obtained, with a dependency on the atomic number and the spin-orbit coupling constant scaling asZ 0 . 4 ${{Z}^{0.4}}$ andζ 0 . 2 ${{\zeta }^{0.2}}$ , respectively The trend shows to be independent of the solvent and temperature.

Structural Control of Highly Efficient Thermally Activated Delayed Fluorescence in Carbene Zinc(II) Dithiolates

Luminescent metal complexes based on earth abundant elements are a valuable target to substitute 4d/5d transition metal complexes as triplet emitters in advanced photonic applications. Whereas CuI complexes have been thoroughly investigated in the last two decades for this purpose, no structure-property-relationships for efficient luminescence involving triplet excited states from ZnII complexes are established. Herein, we report on the design of monomeric carbene zinc(II) dithiolates (CZT) featuring a donor-acceptor-motif that leads to highly efficient thermally activated delayed fluorescence (TADF) with for ZnII compounds unprecedented radiative rate constants kTADF =1.2×106  s-1 at 297 K. Our high-level DFT/MRCI calculations revealed that the relative orientation of the ligands involved in the ligand-to-ligand charge transfer (1/3 LLCT) states is paramount to control the TADF process. Specifically, a dihedral angle of 36-40° leads to very efficient reverse intersystem-crossing (rISC) on the order of 109  s-1 due to spin-orbit coupling (SOC) mediated by the sulfur atoms in combination with a small ΔES1-T1 of ca. 56 meV.

Synthesis, Structural Characterization, and Phosphorescence Properties of Trigonal Zn(II) Carbene Complexes

The sterically demanding N-heterocyclic carbene ITr (N,N'-bis(triphenylmethyl)imidazolylidene) was employed for the preparation of novel trigonal zinc(II) complexes of the type [ZnX2(ITr)] [X = Cl (1), Br (2), and I (3)], for which the low coordination mode was confirmed in both solution and solid state. Because of the atypical coordination geometry, the reactivity of 1-3 was studied in detail using partial or exhaustive halide exchange and halide abstraction reactions to access [ZnLCl(ITr)] [L = carbazolate (4), 3,6-di-tert-butyl-carbazolate (5), phenoxazine (6), and phenothiazine (7)], [Zn(bdt)(ITr)] (bdt = benzene-1,2-dithiolate) (8), and cationic [Zn(μ2-X)(ITr)]2[B(C6F5)4]2 [X = Cl (9), Br (10), and I (11)], all of which were isolated and structurally characterized. Importantly, for all complexes 4-11, the trigonal coordination environment of the ZnII ion is maintained, demonstrating a highly stabilizing effect due to the steric demand of the ITr ligand, which protects the metal center from further ligand association. In addition, complexes 1-3 and 8-11 show long-lived luminescence from triplet excited states in the solid state at room temperature, according to our photophysical studies. Our quantum chemical density functional theory/multireference configuration interaction (DFT/MRCI) calculations reveal that the phosphorescence of 8 originates from a locally excited triplet state on the bdt ligand. They further suggest that the phenyl substituents of ITr are photochemically not innocent but can coordinate to the electron-deficient metal center of this trigonal complex in the excited state.

Benchmarks for transition metal spin-state energetics: why and how to employ experimental reference data?

Accurate prediction of energy differences between alternative spin states of transition metal complexes is essential in computational (bio)inorganic chemistry-for example, in characterization of spin crossover materials and in the theoretical modeling of open-shell reaction mechanisms-but it remains one of the most compelling problems for quantum chemistry methods. A part of this challenge is to obtain reliable reference data for benchmark studies, as even the highest-level applicable methods are known to give divergent results. This Perspective discusses two possible approaches to method benchmarking for spin-state energetics: using either theoretically computed or experiment-derived reference data. With the focus on the latter approach, an extensive general review is provided for the available experimental data of spin-state energetics and their interpretations in the context of benchmark studies, targeting the possibility of back-correcting the vibrational effects and the influence of solvents or crystalline environments. With a growing amount of experience, these effects can be now not only qualitatively understood, but also quantitatively modeled, providing the way to derive nearly chemically accurate estimates of the electronic spin-state gaps to be used as benchmarks and advancing our understanding of the phenomena related to spin states in condensed phases.

Polarity-Tunable Luminescence and Intersystem Crossing of a Zinc(II) Diimine Dithiolate Complex

Combined density functional theory and multireference configuration interaction methods including spin-orbit interactions have been employed to investigate the photophysical properties and deactivation pathways of a zinc diimine dithiolate complex involving the phenanthroline derivative bathocuproine and the dianionic dithiosquarate as chelating ligands. Zn(batho)(dtsq) is one of the few luminescent zinc complexes for which triplet emission had been reported in the solid state [Gronlund, P. Inorg. Chim. Acta 1995, 234, 13-18]. Because of the high dipole moment of the complex in the electronic ground state, ligand-to-ligand charge-transfer (LLCT) states experience strong hypsochromic shifts in polar media, while ligand-centered (LC) states are nearly unaffected. Rate constants for the thermally activated upconversion of the TLLCT population to the SLLCT state are promising due to a small singlet-triplet energy gap and the participation of the sulfur in the electronic excitation, but the TLLCT state is not the lowest-lying excited triplet state in ethanol solution. In addition to the TLLCT electronic structure, TLC(batho)' and TLC(dtsq) ππ* excitations form minima on the T1 potential energy surface. The SLLCT luminescence is expected to be quenched at the nanosecond time scale by the dark TLC(dtsq)ππ* state. Moreover, a TLC(dtsq)σπ* state has been identified, which leads to degradation of the compound. In mildly polar media, the dark triplet LC states are energetically inaccessible and the lowest excited singlet and triplet states clearly exhibit an LLCT character. However, their mutual spin-orbit coupling is reduced to the extent that reverse intersystem crossing is not very likely at room temperature. While Zn(diimine)(dithiolate) complexes continue to be perceived as an interesting substance class with potential application as emitters in electroluminescent devices, the particular Zn(batho)(dtsq) complex is not considered suitable for that purpose.

Thermal site energy fluctuations in photosystem I: new insights from MD/QM/MM calculations

Cyanobacterial photosystem I (PSI) is one of the most efficient photosynthetic machineries found in nature. Due to the large scale and complexity of the system, the energy transfer mechanism from the antenna complex to the reaction center is still not fully understood. A central element is the accurate evaluation of the individual chlorophyll excitation energies (site energies). Such an evaluation must include a detailed treatment of site specific environmental influences on structural and electrostatic properties, but also their evolution in the temporal domain, because of the dynamic nature of the energy transfer process. In this work, we calculate the site energies of all 96 chlorophylls in a membrane-embedded model of PSI. The employed hybrid QM/MM approach using the multireference DFT/MRCI method in the QM region allows to obtain accurate site energies under explicit consideration of the natural environment. We identify energy traps and barriers in the antenna complex and discuss their implications for energy transfer to the reaction center. Going beyond previous studies, our model also accounts for the molecular dynamics of the full trimeric PSI complex. Via statistical analysis we show that the thermal fluctuations of single chlorophylls prevent the formation of a single prominent energy funnel within the antenna complex. These findings are also supported by a dipole exciton model. We conclude that energy transfer pathways may form only transiently at physiological temperatures, as thermal fluctuations overcome energy barriers. The set of site energies provided in this work sets the stage for theoretical and experimental studies on the highly efficient energy transfer mechanisms in PSI.

R2022: A DFT/MRCI Ansatz with Improved Performance for Double Excitations

A reformulation of the combined density functional theory and multireference configuration interaction method (DFT/MRCI) is presented. Expressions for ab initio matrix elements are used to derive correction terms for a new effective Hamiltonian. On the example of diatomic carbon, the correction terms are derived, focusing on the doubly excited ¹Δ_g state, which was problematic in previous formulations of the method, as were double excitations in general. The derivation shows that a splitting of the parameters for intra- and interorbital interactions is necessary for a concise description of the underlying physics. Results for ¹L_a and ¹L_b states in polyacenes and ¹A_u and ¹A_g states in mini-β-carotenoids suggest that the presented formulation is superior to former effective Hamiltonians. Furthermore, statistical analysis reveals that all the benefits of the previous DFT/MRCI Hamiltonians are retained. Consequently, the here presented formulation should be considered as the new standard for DFT/MRCI calculations.

On the Cooperative Origin of Solvent-Enhanced Symmetry-Breaking Charge Transfer in a Covalently Bound Tetracene Dimer Leading to Singlet Fission

Singlet fission in covalently bound acene dimers in solution is driven by the interplay of excitonic and singlet correlated triplet ¹(TT) states with intermediate charge-transfer states, a process which depends sensitively on the solvent environment. We use high-level electronic structure methods to explore this singlet fission process in a linked tetracene dimer, with emphasis on the symmetry-breaking mechanism for the charge-transfer (CT) states induced by low-frequency antisymmetric vibrations and polar/polarizable solvents. A combination of the second-order algebraic diagrammatic construction (ADC(2)) and density functional theory/multireference configuration interaction (DFT/MRCI) methods are employed, along with a state-specific conductor-like screening model (COSMO) solvation model in the former case. This work quantifies, for the first time, an earlier mechanistic proposal [Alvertis et al., J. Am. Chem. Soc. 2019, 141, 17558] according to which solvent-induced symmetry breaking leads to a high-energy CT state which interacts with the correlated triplet state, resulting in singlet fission. An approximate assessment of the nonadiabatic interactions between the different electronic states underscores that the CT states are essential in facilitating the transition from the bright excitonic state to the ¹(TT) state leading to singlet fission. We show that several types of symmetry-breaking inter- and intra-fragment vibrations play a crucial role in a concerted mechanism with the solvent environment and with the symmetric inter-fragment torsion, which tunes the admixture of excitonic and CT states. This offers a new perspective on how solvent-induced symmetry-breaking CT can be understood and how it cooperates with intramolecular mechanisms in singlet fission.

Finding Design Principles of OLED Emitters through Theoretical Investigations of Zn(II) Carbene Complexes

In this work, Zn(II) carbene complexes carrying a dianionic 1,2-dithiolbenzene (dtb) or 1,2-diolbenzene (dob) ligand were investigated regarding their suitability as organic light-emitting diode (OLED) emitter. For the optimization of the complexes, density functional-based methods were used and frequency analyses verified the obtained structures as minima. All calculations were carried out including a polarizable continuum model to mimic solvent-solute interactions. Multireference configuration interaction methods were used to determine excitation energies, spin-orbit couplings, and luminescence properties. Rate constants of spin-allowed and spin-forbidden transitions were calculated according to a Fermi golden rule expression. Using carbene ligands with varying σ-donor and π-acceptor strengths, the luminescence is found to be tunable from yellow to orange/red to deep red/near-infrared. The calculated intersystem crossing (ISC) time constants indicate thermally activated delayed fluorescence (TADF) to be the main decay channel. In contrast to many d¹⁰ coinage metal complexes, a parallel orientation of dtb or dob and the carbene ligand is found to be highly favorable. For the complexes with a cyclic (alkyl)(amino) carbene (CAAC) or cyclic (amino)(aryl) carbene (CAArC) ligand, the S₁ and T₁ states have ligand-to-ligand charge-transfer (LLCT) character and are energetically close. The complex with a classical N-heterocyclic carbene (NHC) ligand has S₁ and T₁ states with mixed ligand-to-metal charge-transfer (LMCT)/LLCT character and is a very rare example in which the zinc ion contributes to the excitation.

Elucidation of LMCT Excited States for Lanthanoid Complexes: A Theoretical and Solid-State Experimental Framework

Photophysical and magnetic properties arising from both ground and excited states of lanthanoid ions are relevant for numerous applications. These properties can be substantially affected, both adversely and beneficially, by ligand-to-metal charge-transfer (LMCT) states. However, probing LMCT states remains a significant challenge in f-block chemistry, particularly in the solid state. Intriguingly, the europium compounds [Eu^III(18-c-6)(X₄Cat)(NO₃)]·MeCN (18-c-6 = 18-crown-6; X = Cl (tetrachlorocatecholate, 1-Eu) or Br (tetrabromocatecholate, 2-Eu) are distinctly darkly-colored, in marked contrast to the analogues with other lanthanoid ions in the 1-Ln and 2-Ln series (Ln = La, Ce, Nd, Gd, Tb, and Dy). Herein, we report a multi-technique investigation of these compounds that has allowed elucidation of the LMCT character of the relevant absorption bands using magnetometry, absorption and emission spectroscopies, and solid-state electrochemistry. To support experimental observations, we present a semi-quantitative multireference ab initio model that (i) captures the anomalously low-lying LMCT excited state observed in the visible spectrum of 1-Eu (and its absence in the other 1-Ln analogues); (ii) elucidates the contribution of the LMCT excitation to the crystal field split ⁷F_J ground-state wave functions; and (iii) identifies the crucial role played by radial dynamical correlation of the Eu^III 4f electrons in the description of the LMCT excited state, modeled by the inclusion of 4f → 5f excitations in the optimized wave function. By providing a set of experimental and theoretical tools, this work establishes a framework for the elucidation of LMCT excited states in lanthanoid compounds in the solid state.

Thermally Activated Delayed Fluorescence Mechanism of a Bicyclic "Carbene-Metal-Amide" Copper Compound: DFT/MRCI Studies and Roles of Excited-State Structure Relaxation

Herein we investigated the luminescence mechanism of one "carbene-metal-amide" copper compound with thermally activated delayed fluorescence (TADF) using density functional theory (DFT)/multireference configuration interaction, DFT, and time-dependent DFT methods with the polarizable continuum model. The experimentally observed low-energy absorption and emission peaks are assigned to the S₁ state, which exhibits clear interligand and partial ligand-to-metal charge-transfer character. Moreover, it was found that a three-state (S₀, S₁, and T₁) model is sufficient to describe the TADF mechanism, and the T₂ state should play a negligible role. The calculated S₁-T₁ energy gap of 0.10 eV and proper spin-orbit couplings facilitate the reverse intersystem crossing (rISC) from T₁ to S₁. At 298 K, the rISC rate of T₁ → S₁ (∼10⁶ s^-1) is more than 3 orders of magnitude larger than the T₁ phosphorescence rate (∼10³ s^-1), thereby enabling TADF. However, it disappears at 77 K because of a very slow rISC rate (∼10¹ s^-1). The calculated TADF rate, lifetime, and quantum yield agree very well with the experimental data. Methodologically, the present work shows that only considering excited-state information at the Franck-Condon point is insufficient for certain emitting systems and including excited-state structure relaxation is important.

Q-Band relaxation in chlorophyll: new insights from multireference quantum dynamics

The ultrafast relaxation within the Q-bands of chlorophyll plays a crucial role in photosynthetic light-harvesting. We investigate this process via nuclear and electronic quantum dynamics on multireference potential energy surfaces.

Theoretical studies on boron dimesityl-based thermally activated delayed fluorescence organic emitters: excited-state properties and mechanisms

At 300 K, S1 excitons could emit fluorescence or undergo ISC to T1, where rISC exceeds the phosphorescence emission enabling TADF.

Removing the Deadwood from DFT/MRCI Wave Functions: The p-DFT/MRCI Method

The combined density functional theory and multireference configuration interaction (DFT/MRCI) method is a powerful tool for the calculation of excited electronic states of large molecules. There exists, however, a large amount of superfluous configurations in a typical DFT/MRCI wave function. We show that this deadwood may be effectively removed using a simple configuration pruning algorithm based on second-order Epstein-Nesbet perturbation theory. The resulting method, which we denote p-DFT/MRCI, is shown to result in orders of magnitude saving in computational timings, while retaining the accuracy of the original DFT/MRCI method.

Linear Carbene Pyridine Copper Complexes with Sterically Demanding N,N'-Bis(trityl)imidazolylidene: Syntheses, Molecular Structures, and Photophysical Properties

The sterically demanding carbene ITr (N,N'-bis(triphenylmethyl)imidazolylidene) was used as a ligand for the preparation of luminescent copper(I) complexes of the type [(ITr)Cu(R-pyridine/R'-quinoline)]BF₄ (R = H, 4-CN, 4-CHO, 2,6-NH₂, and R' = 8-Cl, 6-Me). The selective formation of linear, bis(coordinated) complexes was observed for a series of pyridine and quinoline derivatives. Only in the case of 4-cyanopyridine a one-dimensional coordination polymer was formed, in which the cyano group of the cyanopyridine ligand additionally binds to another Cu atom in a bridging manner, thus leading to a trigonal planar coordination environment. In contrast, employing sterically less demanding monotrityl-substituted carbene 3, no (NHC)Cu-pyridine complexes could be prepared. Instead, a bis-carbene complex [(3)₂Cu]PF₆ was obtained which showed no luminescence. All linear pyridine/quinoline coordinated complexes show weak emission in solution but intense blue to orange luminescence doped with 10% in PMMA films and in the solid state either from triplet excited states with unusually long lifetimes of up to 4.8 ms or via TADF with high radiative rate constants of up to 1.7 × 10⁵ s^-1 at room temperature. Combined density functional theory and multireference configuration interaction calculations have been performed to rationalize the involved photophysics of these complexes. They reveal a high density of low-lying electronic states with mixed MLCT, LLCT, and LC character where the electronic structures of the absorbing and emitting state are not necessarily identical.

Hot exciplexes in U-shaped TADF molecules with emission from locally excited states

Fast emission and high color purity are essential characteristics of modern opto-electronic devices, such as organic light emitting diodes (OLEDs). These properties are currently not met by the latest generation of thermally activated delayed fluorescence (TADF) emitters. Here, we present an approach, called "hot exciplexes" that enables access to both attributes at the same time. Hot exciplexes are produced by coupling facing donor and acceptor moieties to an anthracene bridge, yielding an exciplex with large T1 to T2 spacing. The hot exciplex model is investigated using optical spectroscopy and quantum chemical simulations. Reverse intersystem crossing is found to occur preferentially from the T3 to the S1 state within only a few nanoseconds. Application and practicality of the model are shown by fabrication of organic light-emitting diodes with up to 32 % hot exciplex contribution and low efficiency roll-off.

H2 Evolution from Electrocatalysts with Redox-Active Ligands: Mechanistic Insights from Theory and Experiment vis-à-vis Co-Mabiq

Electrocatalytic hydrogen production via transition metal complexes offers a promising approach for chemical energy storage. Optimal platforms to effectively control the proton and electron transfer steps en route to H₂ evolution still need to be established, and redox-active ligands could play an important role in this context. In this study, we explore the role of the redox-active Mabiq (Mabiq = 2-4:6-8-bis(3,3,4,4-tetramethlyldihydropyrrolo)-10-15-(2,2-biquinazolino)-[15]-1,3,5,8,10,14-hexaene1,3,7,9,11,14-N₆) ligand in the hydrogen evolution reaction (HER). Using spectro-electrochemical studies in conjunction with quantum chemical calculations, we identified two precatalytic intermediates formed upon the addition of two electrons and one proton to [Co^II(Mabiq)(THF)](PF₆) (Co_Mbq). We further examined the acid strength effect on the generation of the intermediates. The generation of the first intermediate, Co_Mbq-H¹, involves proton addition to the bridging imine-nitrogen atom of the ligand and requires strong proton activity. The second intermediate, Co_Mbq-H², acquires a proton at the diketiminate carbon for which a weaker proton activity is sufficient. We propose two decoupled H₂ evolution pathways based on these two intermediates, which operate at different overpotentials. Our results show how the various protonation sites of the redox-active Mabiq ligand affect the energies and activities of HER intermediates.

Internal conversion of singlet and triplet states employing numerical DFT/MRCI derivative couplings: Implementation, tests, and application to xanthone

We present an efficient implementation of nonadiabatic coupling matrix elements (NACMEs) for density functional theory/multireference configuration interaction (DFT/MRCI) wave functions of singlet and triplet multiplicity and an extension of the Vibes program that allows us to determine rate constants for internal conversion (IC) in addition to intersystem crossing (ISC) nonradiative transitions. Following the suggestion of Plasser et al. [J. Chem. Theory Comput. 12, 1207 (2016)], the derivative couplings are computed as finite differences of wave function overlaps. Several measures have been taken to speed up the calculation of the NACMEs. Schur's determinant complement is employed to build up the determinant of the full matrix of spin-blocked orbital overlaps from precomputed spin factors with fixed orbital occupation. Test calculations on formaldehyde, pyrazine, and xanthone show that the mutual excitation level of the configurations at the reference and displaced geometries can be restricted to 1. In combination with a cutoff parameter of t_norm = 10^-8 for the DFT/MRCI wave function expansion, this approximation leads to substantial savings of cpu time without essential loss of precision. With regard to applications, the photoexcitation decay kinetics of xanthone in apolar media and in aqueous solution is in the focus of the present work. The results of our computational study substantiate the conjecture that S₁ T₂ reverse ISC outcompetes the T₂ ↝ T₁ IC in aqueous solution, thus explaining the occurrence of delayed fluorescence in addition to prompt fluorescence.

Excitonic and charge transfer interactions in tetracene stacked and T-shaped dimers

Extended quantum chemical calculations were performed for the tetracene dimer to provide benchmark results, analyze the excimer survival process, and explore the possibility of using long-range-corrected (LC) time-dependent second-order density functional tight-biding (DFTB2) for this system. Ground- and first-excited-state optimized geometries, vertical excitations at relevant minima, and intermonomer displacement potential energy curves (PECs) were calculated for these purposes. Ground-state geometries were optimized with the scaled-opposite-spin (SOS) second-order Møller-Plesset perturbation (MP2) theory and LC-DFT (density functional theory) and LC-DFTB2 levels. Excited-state geometries were optimized with SOS-ADC(2) (algebraic diagrammatic construction to second-order) and the time-dependent approaches for the latter two methods. Vertical excitations and PECs were compared to multireference configuration interaction DFT (DFT/MRCI). All methods predict the lowest-energy S₀ conformer to have monomers parallel and rotated relative to each other and the lowest S₁ conformer to be of a displaced-stacked type. LC-DFTB2, however, presents some relevant differences regarding other conformers for S₀. Despite some state-order inversions, overall good agreement between methods was observed in the spectral shape, state character, and PECs. Nevertheless, DFT/MRCI predicts that the S₁ state should acquire a doubly excited-state character relevant to the excimer survival process and, therefore, cannot be completely described by the single reference methods used in this work. PECs also revealed an interesting relation between dissociation energies and the intermonomer charge-transfer interactions for some states.

Ultrafast processes: coordination chemistry and quantum theory

Coordination compounds, characterized by fascinating and tunable electronic properties, are capable of binding easily to proteins, polymers, wires and DNA. Upon irradiation, these molecular systems develop functions finding applications in solar cells, photocatalysis, luminescent and conformational probes, electron transfer triggers and diagnostic or therapeutic tools. The control of these functions is activated by the light wavelength, the metal/ligand cooperation and the environment within the first picoseconds (ps). After a brief summary of the theoretical background, this perspective reviews case studies, from 1st row to 3rd row transition metal complexes, that illustrate how spin-orbit, vibronic coupling and quantum effects drive the photophysics of this class of molecules at the early stage of the photoinduced elementary processes within the fs-ps time scale range.

Spin-state energetics of metallocenes: How do best wave function and density functional theory results compare with the experimental data?

We benchmark the accuracy of quantum-chemical methods, including wave function theory methods [coupled cluster theory at the CCSD(T) level, multiconfigurational perturbation-theory (CASPT2, NEVPT2) and internally contracted multireference configuration interaction (MRCI)] and 30 density functional theory (DFT) approximations, in reproducing the spin-state splittings of metallocenes. The reference values of the electronic energy differences are derived from the experimental spin-crossover enthalpy for manganocene and the spectral data of singlet-triplet transitions for ruthenocene, ferrocene, and cobaltocenium. For ferrocene and cobaltocenium we revise the previous experimental interpretations regarding the lowest triplet energy; our argument is based on the comparison with the lowest singlet excitation energy and herein reported, carefully determined absorption spectrum of ferrocene. When deriving vertical energies from the experimental band maxima, we go beyond the routine vertical energy approximation by introducing vibronic corrections based on simulated vibrational envelopes. The benchmarking result confirms the high accuracy of the CCSD(T) method (in particular, for UCCSD(T) based on Hartree-Fock orbitals we find for our dataset: maximum error 0.12 eV, weighted mean absolute error 0.07 eV, weighted mean signed error 0.01 eV). The high accuracy of the single-reference method is corroborated by the analysis of a multiconfigurational character of the complete active space wave function for the triplet state of ferrocene. On the DFT side, our results confirm the non-universality problem with approximate functionals. The present study is an important step toward establishing an extensive and representative benchmark set of experiment-derived spin-state energetics for transition metal complexes.

Doping Capabilities of Fluorine on the UV Absorption and Emission Spectra of Pyrene-Based Graphene Quantum Dots

Functionalization of quantum carbon dots (QCDs) and graphene quantum dots (GQDs) is a popular way to tune their optical spectra increasing their potential applicability in material science and biorelated disciplines. Based on the experimental observation, functionalization by fluorine atoms induces substantial shifts in absorption and emission spectra and an intensity increase. Understanding of the effects due to fluorine functionalization at the atomic scale level is still challenging due to the complex structure of fluorinated QCDs. In this work, the effect of covalent edge-fluorination and fluorine anion doping on absorption and emission spectra of prototypical polycyclic aromatic hydrocarbons pyrene and circum-pyrene has been investigated. The ways to achieve efficient red-shifts in the UV spectra and obtaining reasonable intensities stood in the focus of the work. High-level quantum chemical methods based on density functional theory/multireference configuration interaction (DFT/MRCI) and single-reference second-order algebraic diagrammatic construction (ADC(2)) and density functional theory (DFT) using the CAM-B3LYP functional have been used for this purpose. The calculations show that doping with the fluoride anion can have significant effects on the electronic spectrum. However, the effect of the fluoride ion is strongly dependent on its position with respect to the QCD. The localization above the GQDs causes large red-shifts to both the absorption and emission of spectra of GQDs, while in-plane localization leads to only negligible shifts and a tendency to dissociation after electronic excitation. Thus, large red-shifts, observed in complexes with F^-, are obtained due to the introduction of new excited states with large CT character not yet been considered previously in this context, although they have the potential to significantly influence the photophysics of quantum dots. Doping by edge fluorination redshifts the spectra only slightly. This study provides insights on fluorine-doped GQDs, which is conducive to promoting its rational design and controllable synthesis.

Understanding the luminescence properties of Cu(i) complexes: a quantum chemical perusal

Electronic structures and excited-state properties of Cu(i) complexes with varying coordination numbers have been investigated by means of advanced quantum chemical methods. The computational protocol employs density functional-based methods for geometry optimizations and vibrational analyses including solvent effects through continuum models. Excitation energies, spin-orbit couplings and luminescence properties are evaluated using multireference configuration interaction methods. Rate constants of spin-allowed and spin-forbidden transitions have been determined according to the Fermi golden rule. The computational results for the 4-coordinate (DPEPhos)Cu(PyrTet), the 3-coordinate [IPr-Cu-Py₂]⁺, and the linear CAAC^Me₂-Cu-Cl complexes agree well with experimental absorption and emission wavelengths, intersystem crossing (ISC) time constants, and radiative lifetimes in liquid solution. Spectral shifts on the ligand-to-ligand charge transfer (LLCT) and metal-to-ligand charge transfer (MLCT) transitions caused by the polarity of the environment are well represented by the continuum models whereas the shifts caused by pseudo-Jahn-Teller distortions in the MLCT states are too pronounced in comparison to solid-state data. Systematic variation of the ligands in linear Cu(i) carbene complexes shows that only those complexes with S₁ and T₁ states of LLCT character possess sufficiently small singlet-triplet energy gaps ΔE_ST to enable thermally activated delayed fluorescence (TADF). Complexes whose S₁ and T₁ wavefunctions are dominated by MLCT excitations tend to emit phosphorescence instead. Unlike the situation in metal-free TADF emitters, the presence of low-lying locally excited triplet states does not promote ISC. These states rather hold the danger of trapping the excitation with nonradiative deactivation being the major deactivation channel.

Tuning the UV spectrum of PAHs by means of different N-doping types taking pyrene as paradigmatic example: categorization via valence bond theory and high-level computational approaches

Tuning of the electronic spectra of carbon dots by means of inserting heteroatoms into the π-conjugated polycyclic aromatic hydrocarbon (PAH) system is a popular tool to achieve a broad range of absorption and emission frequencies. Especially nitrogen atoms have been used successfully for that purpose. Despite the significant progress achieved with these procedures, the prediction of specific shifts in the UV-vis spectra and the understanding of the electronic transitions is still a challenging task. In this work, high-level quantum chemical methods based on multireference (MR) and single-reference (SR) methods have been used to predict the effect of different nitrogen doping patterns inserted into the prototypical PAH pyrene on its absorption spectrum. Furthermore, a simple classification scheme based on valence bond (VB) theory and the Clar sextet rule in combination with the harmonic oscillator measure of aromaticity (HOMA) index was applied to arrange the different doping structures into groups and rationalize their electronic properties. The results show a wide variety of mostly redshifts in the spectra as compared to the pristine pyrene case. The most interesting doping structures with the largest red shifts leading to absorption energies below one eV could be readily explained by the occurrence of diradical VB structures in combination with Clar sextets. Moreover, analysis of the electronic transitions computed with MR methods showed that several of the low-lying excited states possess double-excitation character, which cannot be realized by the popular SR methods and, thus, are simply absent in the calculated spectra.

Visible Light-Induced Homolytic Cleavage of Perfluoroalkyl Iodides Mediated by Phosphines

In an effort to explain the experimentally observed variation of the photocatalytic activity of t Bu 3 P, n Bu 3 P and (MeO) 3 P in the blue-light regime [Helmecke et al., Org. Lett. 21 (2019) 7823], we have explored the absorption characteristics of several phosphine- and phosphite-IC 4 F 9 adducts by means of relativistic density functional theory and multireference configuration interaction methods. Based on the results of these computational and complementary experimental studies, we offer an explanation for the broad tailing of the absorption of t Bu 3 P-IC 4 F 9 and (MeO) 3 P-IC 4 F 9 into the visible-light region. Larger coordinate displacements of the ground and excited singlet potential energy wells in n Bu 3 P-IC 4 F 9 , in particular with regard to the P-I-C bending angle, reduce the Franck-Condon factors and thus the absorption probability compared to t Bu 3 P-IC 4 F 9 . Spectroscopic and computational evaluation of conformationally flexible and locked phosphites suggests that the reactivity of (MeO) 3 P may be the result of oxygen lone-pair participation and concomitant broadening of absorption. The proposed mechanism for the phosphine-catalyzed homolytic C-I cleavage of perfluorobutane iodide involves S₁ ← S₀ absorption of the adduct followed by intersystem crossing to the photochemically active T 1 state.

On the photophysical properties of IrIII, PtII, and PdII (phenylpyrazole) (phenyldipyrrin) complexes

The absorption and emission characteristics of (ppz)2(dipy)IrIII, (ppz)(dipy)PtII and (ppz)(dipy)PdII, where ppz stands for phenylpyrazole and dipy for a phenyl meso-substituted dipyrrin ligand, have been investigated by means of combined density functional theory and multireference configuration interaction including scalar relativistic and spin-orbit coupling effects. These results were compared with experimental spectra. The complexes exhibit a high density of low-lying electronically excited states originating from ligand-centered (LC) and metal-to-ligand charge transfer (MLCT) states involving the dipyrrin ligand. In addition, metal-centered (MC) states are found to be low-lying in the Pd complex. In all three cases, the first strong absorption band and the phosphorescence emission band stem from LC excitations on the dipyrrin ligand with small MLCT contributions. The MLCT states show more pronounced relaxation effects than the LC states, with the consequence that the first excited state with predominant singlet multiplicity is of SMLCT/LC type in the heavier Ir and Pt complexes. Substantial spin-orbit coupling between SMLCT/LC and TLC enables fast and efficient intersystem crossing (ISC) and a high triplet quantum yield. Phosphorescence rate constants are rather small in accord with the dominant LC character of the transitions. Out-of-plane distortion promotes nonradiative decay of the excited state population via the MC states thus explaining the lower phosphorescence quantum yield of the Pt complex. The spectral properties of the Pd complex are different in many aspects. Optimization of the S1 state yields a dipyrrin intraligand charge transfer (ILCT) state with highly distorted nuclear arrangement in the butterfly conformers leading to nonradiative deactivation. In contrast, the primarily excited SLC state and the SMLCT/LC state of the twist conformer have nearly equal adiabatic excitation energies. The lack of a driving force toward the SMLCT/LC minimum, the high fluorescence rate constant of the bright SLC state and its moderately efficient ISC to the triplet manifold explain the experimentally observed dual emission of the Pd complex at room temperature.

DFT/MRCI assessment of the excited-state interplay in a coumarin-schiff Mg2+ fluorescent sensor

Fluorescent sensors with selectivity and sensitivity to metal ions are an active field in supramolecular chemistry for biochemical, analytical, and environmental problems. Mg²⁺ is one of the most abundant divalent ions in the cell, and it plays a critical role in many biological processes. Coumarin-based sensors are widely used as desirable fluorophore and binding moieties showing a remarkable sensitivity and fluorometric enhancement for Mg²⁺ . In this work, density functional theory/multireference configuration interaction (DFT/MRCI) calculations were performed in order to understand the sensing behavior of the organic fluorescent sensor 7-hydroxy-4-methyl-8-((2-(pyridin-2-yl)hydrazono)methyl)-2H-chromen-2-one (PyHC) in ethanol to solvated Mg²⁺ ions. The computed optical properties reproduce well-reported experimental data. Our results suggest that after photoexcitation of the free PyHC, a photo-induced electron transfer (PET) mechanism may compete with the fluorescence decay to the ground state. In contrast, this PET channel is no longer available in the complex with Mg²⁺ making the emissive decay more efficient. © 2019 Wiley Periodicals, Inc.

Emission Energies and Stokes Shifts for Single Polycyclic Aromatic Hydrocarbon Sheets in Comparison to the Effect of Excimer Formation

Emission spectra of paradigmatic single-sheet polycyclic aromatic hydrocarbons (PAHs), pyrene, circum-1-pyrene, coronene, circum-1-coronene, and circum-2-coronene and Stokes shifts were computed and compared with previously calculated comparable data for relaxed excimer structures using the SOS-ADC(2), TD-B3LYP, and TD-CAM-B3LYP methods with multireference DFT/MRCI data as the benchmark. Vertical emission transitions and Stokes shifts were extrapolated to infinite PAH size. Comparison of Stokes shifts computed from theoretical monomer and dimer data confirms assumptions that relaxed excimers are responsible for the unusually large Stokes shifts in carbon dots observed in experimental investigations.

Structure-Emission Property Relationships in Cyclometalated Pt(II) β-Diketonate Complexes

Extending the ligand π-system of phosphorescent (C^∧C*) or (C^∧N) cyclometalated platinum(II) β-diketonate complexes can lead to large and seemingly abrupt variations of the photophysical properties such as triplet quantum yields and phosphorescence lifetimes. Quantum chemical studies using methods including elements from density functional theory (DFT) and multireference configuration interaction (MRCI) as well as spin-orbit coupling (SOC) provide a rationale for these observations. In the Franck-Condon region, the first excited singlet states (S₁) of these complexes are characterized by mixed metal-to-ligand charge-transfer (MLCT) and ligand-centered (LC) excitations. With increasing extension of the effective π-system, the lowest-lying triplet state yields more and more LC character, thus leading to a decrease of the phosphorescence rate constant. The ability to undergo efficient intersystem crossing from S₁ to T₁ is not diminished as the S₁ state largely retains its character. In the N-heterocyclic carbene (NHC) complexes investigated here, at least two triplet states are found energetically below the S₁ state. Out-of-plane distortion enhances the probability for nonradiative decay of the triplet population. In the smaller compounds emitting in the violet or blue spectral region, the phosphorescent state is separated from the lowest-lying dark metal-centered (MC) triplet state by a small barrier only, explaining their experimentally observed low photoluminescence quantum yields in liquid solution. The semiempirical DFT/MRCI-R2018 Hamiltonian employed in our studies proves well-suited for investigating the absorption and emission properties of these platinum(II) complexes. Generally, good agreement is observed between our calculated data and the experimental findings.

Excited states and excitonic interactions in prototypic polycyclic aromatic hydrocarbon dimers as models for graphitic interactions in carbon dots

The HOMO–LUMO transition in a stacked circum-1-coronene dimer as a model for excimer interactions in carbon dots.

DFT/MRCI-R2018 study of the photophysics of the zinc(ii) tripyrrindione radical: non-Kasha emission?

The fluorescence of a radical-based emitter has been theoretically investigated after measurements had shown absorption bands to lie below the emission energy. The results of the all-multiplicity DFT/MRCI-R2018 study indicate D₃ emission.