Simulating the full spin manifold of triplet-pair states in a series of covalently linked TIPS-pentacenes.

Combined density functional theory and multireference configuration interaction methods have been used to elucidate singlet fission (SF) pathways and mechanisms in three regioisomers of side-on linked pentacene dimers. In addition to the optically bright singlets (S 1 $$ {}_1 $$ and S 2 $$ {}_2 $$ ) and singly excited triplets (T 1 $$ {}_1 $$ and T 2 $$ {}_2 $$ ), the full spin manifold of multiexcitonic triplet-pair states ( 1 $$ {}^1 $$ ME, 3 $$ {}^3 $$ ME, 5 $$ {}^5 $$ ME) has been considered. In the ortho- and para-regioisomers, the 1 $$ {}^1 $$ ME and S 1 $$ {}_1 $$ potentials intersect upon geometry relaxation of the S 1 $$ {}_1 $$ excitation. In the meta-regioisomer, the crossing occurs upon delocalization of the optically bright excitation. The energetic accessibility of these conical intersections and the absence of low-lying charge-transfer states suggests a direct SF mechanism, assisted by charge-resonance effects in the 1 $$ {}^1 $$ ME state. While the 5 $$ {}^5 $$ ME state does not appear to play a role in the SF mechanism of the ortho- and para-regioisomers, its participation in the disentanglement of the triplet pair is conceivable in the meta-regioisomer.

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 ß-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 as Z 0 . 4 ${{Z}^{0.4}}$ and ζ 0 . 2 ${{\zeta }^{0.2}}$ , respectively The trend shows to be independent of the solvent and temperature.

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.

Toward the improvement of vibronic spectra and non-radiative rate constants using the vertical Hessian method.

For the computation of vibrationally resolved electronic spectra, various approaches can be employed. Adiabatic approaches simulate vibronic transitions using harmonic potentials of the initial and final states, while vertical approaches extrapolate the final state potential from the gradients and Hessian at the Franck-Condon point, avoiding a full exploration of the potential energy surface of the final state. Our implementation of the vertical Hessian (VH) method has been validated with a benchmark set of four small molecules, each presenting unique challenges, such as complex topologies, problematic low-frequency vibrations, or significant geometrical changes upon electronic excitation. We assess the quality of both adiabatic and vertical approaches for simulating vibronic transitions. For two types of donor-acceptor compounds with promising thermally activated delayed fluorescence properties, our computations confirm that the vertical approaches outperform the adiabatic ones. The VH method significantly reduces computational costs and yields meaningful emission spectra, where adiabatic models fail. More importantly, we pioneer the use of the VH method for the computation of rate constants for non-radiative processes, such as intersystem crossing and reverse intersystem crossing along a relaxed interpolated pathway of a donor-acceptor compound. This study highlights the potential of the VH method to advance computational vibronic spectroscopy by providing meaningful simulations of intricate decay pathway mechanisms in complex molecular systems.

Multiexcitonic and optically bright states in subunits of pentacene crystals: A hybrid DFT/MRCI and molecular mechanics study.

A hybrid quantum mechanics/molecular mechanics setup was used to model electronically excited pentacene in the crystal phase. Particularly interesting in the context of singlet fission (SF) is the energetic location of the antiferromagnetically coupled multiexcitonic singlet state, 1(TT), and the ferromagnetically coupled analog in relation to the optically bright singlet state. To provide photophysical properties of the accessible spin manifold, combined density functional theory and multi-reference configuration interaction calculations were performed on pentacene dimers and a trimer, electrostatically embedded in the crystal. The likelihood of a quintet intermediate in the SF process was estimated by computing singlet-quintet electron spin-spin couplings employing the Breit-Pauli Hamiltonian. The performance of the applied methods was assessed on the pentacene monomer. The character of the optically bright state and the energetic location of the 1(TT) state depend strongly on the relative orientation of the pentacene units. In the V-shaped dimers and in the trimer, the optically bright state is dominated by local and charge transfer (CT) excitations, with admixtures of doubly excited configurations. The CT excitations gain weight upon geometry relaxation, thus supporting a CT-mediated SF mechanism as the primary step of the SF process. For the slip-stacked dimer, the energetic order of the bright and the 1(TT) states swaps upon geometry relaxation, indicating strong nonadiabatic coupling close to the Franck-Condon region-a prerequisite for a coherent SF process. The multiexcitonic singlet, triplet, and quintet states are energetically too far apart and their spin-spin couplings are too small to bring about a noteworthy multiplicity mixing.

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.

An Air- and Moisture-stable Zinc(II) Carbene Dithiolate Dimer Showing Fast Thermally Activated Delayed Fluorescence and Dexter Energy Transfer Catalysis.

A dimeric ZnII carbene complex featuring bridging and chelating benzene-1,2-dithiolate ligands is highly stable towards air and water. The donor-Zn-acceptor structure leads to visible light emission in the solid state, solution and polymer matrices with λmax between 577-657 nm and, for zinc(II) complexes, unusually high radiative rate constants for triplet exciton decay of up to kr =1.5×105  s-1 at room temperature. Variable temperature and DFT/MRCI studies show that a small energy gap between the 1/3 LL/LMCT states of only 79 meV is responsible for efficient thermally activated delayed fluorescence (TADF). Time-resolved luminescence and transient absorption studies confirm the occurrence of long-lived, dominantly ligand-to-ligand charge transfer excited states in solution, allowing for application in Dexter energy transfer photocatalysis.

A Thermally Activated Delayed Fluorescence Emitter Investigated by Time-Resolved Near-Infrared Spectroscopy.

Emitters for organic light-emitting diodes (OLEDs) based on thermally activated delayed fluorescence (TADF) require small singlet (S1 )-triplet (T1 ) energy gaps as well as fast intersystem crossing (ISC) transitions. These transitions can be mediated by vibronic mixing with higher excited states Sn and Tn (n=2, 3, 4, …). For a prototypical TADF emitter consisting of a triarylamine and a dicyanobenzene moiety (TAA-DCN) it is shown that these higher states can be located energetically by time-resolved near-infrared (NIR) spectroscopy.

Electron affinities and lowest triplet and singlet state properties of para-oligophenylenes (n = 3-5): theory and experiment.

We apply photodetachment-photoelectron spectroscopy to measure the electron affinities and the energetics of the lowest excited electronic states of the neutral molecules para-terphenyl (p3P), para-quaterphenyl (p4P) and para-quinquephenyl (p5P), including especially the triplet states below S1. The interpretation of the experimental data is based on the comparison to calculated 0-0 energies and Dyson norms, using density functional theory and multireference configuration interaction methods, as well as Franck-Condon patterns. The comparison between calculated and experimental vibrational fine-structures reveals a twisted benzoid-like molecular structure of the S0 ground state and nearly planar quinoid-like nuclear arrangements in the S1 and T1 excited states as well as in the D0 anion ground state. For all para-oligophenylenes (ppPs) in this series, at least two triplet states have been identified in the energy regime below the S1 state. The large optical S0-S1 cross sections of the ppPs are rationalised by the nodal structure of the molecular orbitals involved in the transition. The measured electron affinities range from 380 meV (p3P) over 620 meV (p4P) to 805 meV (p5P). A saturation of the electron binding energy with the increasing number of phenyl units is thus not yet in sight.

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.

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 1Δg 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 1La and 1Lb states in polyacenes and 1Au and 1Ag states in mini-ß-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.

Ultra-Long Lived Luminescent Triplet Excited States in Cyclic (Alkyl)(amino)carbene Complexes of Zn(II) Halides.

The high element abundance and d10 electron configuration make ZnII -based compounds attractive candidates for the development of novel photoactive molecules. Although a large library of purely fluorescent compounds exists, emission involving triplet excited states is a rare phenomenon for zinc complexes. We have investigated the photophysical and -chemical properties of a series of dimeric and monomeric ZnII halide complexes bearing a cyclic (alkyl)(amino)carbene (cAAC) as chromophore unit. Specifically, [(cAAC)XZn(µ-X)2 ZnX(cAAC)] (X=Cl (1), Br (2), I (3)) and [ZnX2 (cAAC)(NCMe)] (X=Br (4), I (5)) were isolated and fully characterized, showing intense visible light photoluminescence under UV irradiation at 297 K and fast photo-induced transformation. At 77 K, the compounds exhibit improved stability allowing to record ultra-long lifetimes in the millisecond regime. DFT/MRCI calculations confirm that the emission stems from 3 XCT/LEcAAC states and indicate the phototransformation to be related to asymmetric distortion of the complexes by cAAC ligand rotation. This study enhances our understanding of the excited state properties for future development and application of new classes of ZnII phosphorescent complexes.

Aggregation-Induced Dual Phosphorescence from (o-Bromophenyl)-Bis(2,6-Dimethylphenyl)Borane at Room Temperature.

Designing highly efficient purely organic phosphors at room temperature remains a challenge because of fast non-radiative processes and slow intersystem crossing (ISC) rates. The majority of them emit only single component phosphorescence. Herein, we have prepared 3 isomers (o, m, p-bromophenyl)-bis(2,6-dimethylphenyl)boranes. Among the 3 isomers (o-, m- and p-BrTAB) synthesized, the ortho-one is the only one which shows dual phosphorescence, with a short lifetime of 0.8 ms and a long lifetime of 234 ms in the crystalline state at room temperature. Based on theoretical calculations and crystal structure analysis of o-BrTAB, the short lifetime component is ascribed to the T1 M state of the monomer which emits the higher energy phosphorescence. The long-lived, lower energy phosphorescence emission is attributed to the T1 A state of an aggregate, with multiple intermolecular interactions existing in crystalline o-BrTAB inhibiting nonradiative decay and stabilizing the triplet states efficiently.

Understanding and Controlling Intersystem Crossing in Molecules.

This review article focuses on the understanding of intersystem crossing (ISC) in molecules. It addresses readers who are interested in the phenomenon of intercombination transitions between states of different electron spin multiplicities but are not familiar with relativistic quantum chemistry. Among the spin-dependent interaction terms that enable a crossover between states of different electron spin multiplicities, spin-orbit coupling (SOC) is by far the most important. If SOC is small or vanishes by symmetry, ISC can proceed by electronic spin-spin coupling (SSC) or hyperfine interaction (HFI). Although this review discusses SSC- and HFI-based ISC, the emphasis is on SOC-based ISC. In addition to laying the theoretical foundations for the understanding of ISC, the review elaborates on the qualitative rules for estimating transition probabilities. Research on the mechanisms of ISC has experienced a major revival in recent years owing to its importance in organic light-emitting diodes (OLEDs). Exemplified by challenging case studies, chemical substitution and solvent environment effects are discussed with the aim of helping the reader to understand and thereby get a handle on the factors that steer the efficiency of ISC.

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.

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.

Intersystem crossing processes in the 2CzPN emitter: a DFT/MRCI study including vibrational spin-orbit interactions.

Multireference quantum chemical calculations were performed in order to investigate the (reverse) intersystem crossing ((R)ISC) mechanisms of 4,5-di(9H-carbazol-9-yl)-phthalonitrile (2CzPN). A combination of density funcional theory (DFT) and multireference configuration interaction methods (MRCI) was used. The excellent agreement of the computed absorption spectrum with available experimental absorption spectra lends confidence to the chosen computational protocol. Vertically, two triplet excited states (T1 and T2) are found below the S1 state. At the excited state minima, the calculated adiabatic energies locate only the T1 state below the S1 state. The enhanced charge transfer (CT) character of the geometrically relaxed excited states causes their mutual (direct) spin-orbit coupling (SOC) interaction to be low. Contributions of vibronic SOC to the (R)ISC probability, evaluated by a Herzberg-Teller-like procedure for a temperature of 300 K, are small but not negligible. For ISC, the S1→ T1 channel is the fastest (8 × 106 s-1), while the S1→ T2 channel is found to be thermally activated (9 × 104 s-1) and less efficient when proceeding from the adiabatic S1 state. Our calculations also reveal, however, a barrierless S1→ T2 ISC pathway near the Franck-Condon region. RISC is found to essentially proceed via the T1→ S1 channel, with a rate constant of (3 × 104 s-1) if our adiabatic singlet-triplet energy gap in vacuum (ΔEST = 0.12 eV) is employed. Shifting the potentials to match two experimentally reported singlet-triplet energy gaps in toluene (ΔEST = 0.21 and 0.31 eV, respectively) leads to a drastic reduction of the computed rate constant by up to 4 orders of magnitude. The T2 state is not expected to play a major role in mediating triplet-singlet transitions in 2CzPN unless it is directly populated by hot excitons. No indication for a strong vibronic coupling of the T2 and T1 potentials is found, which could help overcome the negative exponential dependence of the RISC rate constant on the magnitude of the energy gap.

Large Inverted Singlet-Triplet Energy Gaps Are Not Always Favorable for Triplet Harvesting: Vibronic Coupling Drives the (Reverse) Intersystem Crossing in Heptazine Derivatives.

Heptazine derivatives are promising dopants for electroluminescent devices. Recent studies raised the question whether heptazines exhibit a small regular or an inverted singlet-triplet (IST) gap. It was argued that the S1 ← T1 reverse intersystem crossing (RISC) is a downhill process in IST emitters and therefore does not require thermal activation, thus enabling efficient harvesting of triplet excitons. Rate constants were not determined in these studies. Modeling the excited-state properties of heptazine proves challenging because fluorescence and intersystem crossing (ISC) are symmetry-forbidden in first order. In this work, we present a comprehensive theoretical study of the photophysics of heptazine and its derivative HAP-3MF. The calculations of electronic excitation energies and vibronic coupling matrix elements have been conducted at the density functional theory/multireference configuration interaction (DFT/MRCI) level of theory. We have employed a finite difference approach to determine nonadiabatic couplings and derivatives of spin-orbit coupling and electric dipole transition matrix elements with respect to normal coordinate displacements. Kinetic constants for fluorescence, phosphorescence, internal conversion (IC), ISC, and RISC have been computed in the framework of a static approach. Radiative S1 ↔ S0 transitions borrow intensity mainly from optically bright E' π → π* states, while S1 ↔ T1 (R)ISC is mediated by E″ states of n → π* character. Test calculations show that IST gaps as large as those reported in the literature are counterproductive and slow down the S1 ← T1 RISC process. Using the adiabatic DFT/MRCI singlet-triplet splitting of -0.02 eV, we find vibronically enhanced ISC and RISC to be fast in the heptazine core compound. Nevertheless, its photo- and electroluminescence quantum yields are predicted to be very low because S1 → S0 IC efficiently quenches the luminescence. In contrast, fluorescence, IC, ISC, and RISC proceed at similar time scales in HAP-3MF.

Lowest Triplet and Singlet States in N-Methylacridone and N,N'-Dimethylquinacridone: Theory and Experiment.

In this work, radical anion photodetachment photoelectron (PD-PE) spectra of N-methylacridone (NM-AC) and N,N'-dimethyl-trans-quinacridone (NNM-QAC) are presented, from which we derived electron affinities and transition energies from S0 to the lowest excited triplet and singlet states (T1, T2, and S1). Because in molecules with extended π systems and heteroatoms the state density even in the energy range of the lowest excited electronic states is already high, assignment of most of the spectral structures in the PD-PE spectra was possible only on the basis of theoretical calculations. To this end, adiabatic transition energies including zero-point vibrational energy corrections were determined using a combination of density functional theory, time-dependent density functional theory, and multireference configuration interaction methods. Calculated Franck-Condon spectra proved to be particularly valuable for the assignment of the spectra. Surprisingly, the density of electronically excited states in the low-energy regime is smaller for NNM-QAC than for NM-AC. This is due to the fact that the nπ* energies remain nearly the same in the two molecules whereas the lowest ππ* excited singlet and triplet transitions are strongly red-shifted in going from NM-AC to NNM-QAC.

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 tnorm = 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.