Excited States of Weak Interacting Complexes of Formaldehyde and Alkali Metal Ions

The electronically excited states of formaldehyde and its complexes with alkali metal ions are investigated with the time-dependent density functional theory (TD DFT) method. Vertical transition energies for several singlet and triplet excited states, adiabatic transition energies for the first singlet and triplet excited states S₁ and T₁, the adiabatic geometries and vibrational frequencies of the ground state S₀ and the first singlet and triplet excited states S₁ and T₁ for formaldehyde and its complexes are calculated. Better agreement with the experiment than that of the CIS method is obtained for CH₂O at the TD DFT level. The nonlinear C=O?M⁺ interaction in the excited states S₁ and T₁ is weaker than the linear interaction in the ground state. In the S₀ and S₁ states, the C=O bond is elongated by cation complexation and its stretching frequency is red-shifted, but in the T₁ state the C=O bond is shortened and its frequency is blue-shifted.     

Chromophore-radical excited state antiferromagnetic exchange controls the sign of photoinduced ground state spin polarization

A change in the sign of the ground-state electron spin polarization (ESP) is reported in complexes where an organic radical (nitronylnitroxide, NN) is covalently attached to a donor–acceptor chromophore via two different meta-phenylene bridges in (bpy)Pt(CAT-m-Ph-NN) (mPh-Pt) and (bpy)Pt(CAT-6-Me-m-Ph-NN) (6-Me-mPh-Pt) (bpy = 5,5′-di-tert-butyl-2,2′-bipyridine, CAT = 3-tert-butylcatecholate, m-Ph = meta-phenylene). These molecules represent a new class of chromophores that can be photoexcited with visible light to produce an initial exchange-coupled, 3-spin (bpy˙⁻, CAT⁺˙ = semiquinone (SQ), and NN), charge-separated doublet ²S₁ (S = chromophore excited spin singlet configuration) excited state. Following excitation, the ²S₁ state rapidly decays to the ground state by magnetic exchange-mediated enhanced internal conversion via the ²T₁ (T = chromophore excited spin triplet configuration) state. This process generates emissive ground state ESP in 6-Me-mPh-Pt while for mPh-Pt the ESP is absorptive. It is proposed that the emissive polarization in 6-Me-mPh-Pt results from zero-field splitting induced transitions between the chromophoric ²T₁ and ⁴T₁ states, whereas predominant spin–orbit induced transitions between ²T₁ and low-energy NN-based states give rise to the absorptive polarization observed for mPh-Pt. The difference in the sign of the ESP for these molecules is consistent with a smaller excited state ²T₁ – ⁴T₁ gap for 6-Me-mPh-Pt that derives from steric interactions with the 6-methyl group. These steric interactions reduce the excited state pairwise SQ-NN exchange coupling compared to that in mPh-Pt.

A change in the sign of the ground state electron spin polarization (ESP) is reported in complexes where an organic radical (nitronylnitroxide, NN) is covalently attached to a donor–acceptor chromophore via two different meta-phenylene bridges.     

Sub‐Picosecond Singlet Exciton Fission in Cyano‐Substituted Diaryltetracenes

Thin films of 5,11‐dicyano‐6,12‐diphenyltetracene ( TcCN ) have been studied for their ability to undergo singlet exciton fission (SF). Functionalization of tetracene with cyano substituents yields a more stable chromophore with favorable energetics for exoergic SF (2E(T₁)?E(S₁)=?0.17 eV), where S₁ and T₁ are singlet and triplet excitons, respectively. As a result of tuning the triplet‐state energy, SF is faster in TcCN relative to the corresponding endoergic process in tetracene. SF proceeds with two time constants in the film samples (τ=0.8±0.2 ps and τ=23±3 ps), which is attributed to structural disorder within the film giving rise to one population with a favorable interchromophore geometry, which undergoes rapid SF, and a second population in which the initially formed singlet exciton must diffuse to a site at which this favorable geometry exists. A triplet yield analysis using transient absorption spectra indicates the formation of 1.6±0.3 triplets per initial excited state.     

Singlet fission in a hexacene dimer: energetics dictate dynamics

Singlet fission (SF) is an exciton multiplication process with the potential to raise the efficiency limit of single junction solar cells from 33% to up to 45%. Most chromophores generally undergo SF as solid-state crystals. However, when such molecules are covalently coupled, the dimers can be used as model systems to study fundamental photophysical dynamics where a singlet exciton splits into two triplet excitons within individual molecules. Here we report the synthesis and photophysical characterization of singlet fission of a hexacene dimer. Comparing the hexacene dimer to analogous tetracene and pentacene dimers reveals that excess exoergicity slows down singlet fission, similar to what is observed in molecular crystals. Conversely, the lower triplet energy of hexacene results in an increase in the rate of triplet pair recombination, following the energy gap law for radiationless transitions. These results point to design rules for singlet fission chromophores: the energy gap between singlet and triplet pair should be minimal, and the gap between triplet pair and ground state should be large.

We report the synthesis and photophysical characterization of highly exoergic singlet fission in a hexacene dimer revealing exciton dynamics that follow the energy gap law.     

Insight into the drastically different triplet lifetimes of BODIPY obtained by optical/magnetic spectroscopy and theoretical computations

The triplet state lifetimes of organic chromophores are crucial for fundamental photochemistry studies as well as applications as photosensitizers in photocatalysis, photovoltaics, photodynamic therapy and photon upconversion. It is noteworthy that the triplet state lifetime of a chromophore can vary significantly for its analogues, while the exact reason was rarely studied. Herein with a few exemplars of typical BODIPY derivatives, which show triplet lifetimes varying up to 110-fold (1.4–160 μs), we found that for these derivatives with short triplet state lifetimes (ca. 1–3 μs), the electron spin polarization (ESP) pattern of the time-resolved electron paramagnetic resonance (TREPR) spectra of the triplet state is inverted at a longer delay time after laser pulse excitation, as a consequence of a strong anisotropy in the decay rates of the zero-field state sublevel of the triplet state. For the derivatives showing longer triplet state lifetimes (>50 μs), no such ESP inversion was observed. The observed fast decay of one sublevel is responsible for the short triplet state lifetime; theoretical computations indicate that it is due to a strong coupling between the T_z sublevel and the ground state mediated by the spin–orbit interaction. Another finding is that the heavy atom effect on the shortening of the triplet state lifetime is more significant for the T₁ states with lower energy. To the best of our knowledge, this is the first systematic study to rationalize the short triplet state lifetime of visible-light-harvesting organic chromophores. Our results are useful for fundamental photochemistry and the design of photosensitizers showing long-lived triplet states.

The electron spin polarization inversion and anisotropic decay of triplet substates explain the short triplet state lifetime of BODIPY derivatives.     

Exploiting the Aromatic Chameleon Character of Fulvenes for Computational Design of Baird‐Aromatic Triplet Ground State Compounds

Due to the reversal in electron counts for aromaticity and antiaromaticity in the closed‐shell singlet state (normally ground state, S₀) and lowest ππ* triplet state (T₁ or T₀), as given by Hückel's and Baird's rules, respectively, fulvenes are influenced by their substituents in the opposite manner in the T₁ and S₀ states. This effect is caused by a reversal in the dipole moment when going from S₀ to T₁ as fulvenes adapt to the difference in electron counts for aromaticity in various states; they are aromatic chameleons. Thus, a substituent pattern that enhances (reduces) fulvene aromaticity in S₀ reduces (enhances) aromaticity in T₁, allowing for rationalizations of the triplet state energies (E_T) of substituted fulvenes. Through quantum chemical calculations, we now assess which substituents and which positions on the pentafulvene core are the most powerful for designing compounds with low or inverted E_T. As a means to increase the π‐electron withdrawing capacity of cyano groups, we found that protonation at the cyano N atoms of 6,6‐dicyanopentafulvenes can be a route to on‐demand formation of a fulvenium dication with a triplet ground state (T₀). The five‐membered ring of this species is markedly Baird‐aromatic, although less than the cyclopentadienyl cation known to have a Baird‐aromatic T₀ state.     

Radical-Enhanced Intersystem Crossing in Perylene-Oxoverdazyl Radical Dyads

Attaching stable radicals to organic chromophores is an effective method to enhance the intersystem crossing (ISC) of the chromophores. Herein we prepared perylene-oxoverdazyl dyads either by directly connecting the two units or using an intervening phenyl spacer. We investigated the effect of the radical on the photophysical properties of perylene and observed strong fluorescence quenching due to radical enhanced ISC (REISC). Compared with a previously reported perylene-fused nitroxide radical compound (triplet lifetime, τ_T=0.1 μs), these new adducts show a longer-lived triplet excited state (τ_T=9.5 μs). Based on the singlet oxygen quantum yield (Φ_Δ=7 %) and study of the triplet state, we propose that the radical enhanced internal conversion also plays a role in the relaxation of the excited state. Femtosecond fluorescence up-conversion indicates a fast decay of the excited state (<1.0 ps), suggesting a strong spin-spin exchange interaction between the two units. Femtosecond transient absorption (fs-TA) spectra confirmed direct triplet state population (within 0.5 ps). Interestingly, by fs-TA spectra, we observed the interconversion of the two states (D₁↔Q₁) at ∼80 ps time scale. Time-resolved electron paramagnetic resonance (TREPR) spectral study confirmed the formation of the quartet sate. We observed triplet and quartet states simultaneously with weights of 0.7 and 0.3, respectively. This is attributed to two different conformations of the molecule at excited state. DFT computations showed that the interaction between the radical and the chromophore is ferromagnetic (J>0, 0.05∼0.10 eV).     

Singlet and Triplet Excited States and Intersystem Crossing in Free‐Base Porphyrin: TDDFT and DFT/MRCI Study

Extensive time-dependent DFT (TDDFT) and DFT/multireference configuration interaction (MRCI) calculations are performed on the singlet and triplet excited states of free-base porphyrin, with emphasis on intersystem crossing processes. The equilibrium geometries, as well as the vertical and adiabatic excitation energies of the lowest singlet and triplet excited states are determined. Single and double proton-transfer reactions in the first excited singlet state are explored. Harmonic vibrational frequencies are calculated at the equilibrium geometries of the ground state and of the lowest singlet and triplet excited states. Furthermore, spin–orbit coupling matrix elements of the lowest singlet and triplet states and their numerical derivatives with respect to nuclear displacements are computed. It is shown that opening of an unprotonated pyrrole ring as well as excited-state single and double proton transfer inside the porphyrin cavity lead to crossings of the potential energy curves of the lowest singlet and triplet excited states. It is also found that displacements along out-of-plane normal modes of the first excited singlet state cause a significant increase of the 2|H_so|S₁>, 1|H_so|S₁>, and 1|H_so|S₀> spin–orbit coupling matrix elements. These phenomena lead to efficient radiationless deactivation of the lowest excited states of free-base porphyrin via intercombination conversion. In particular, the S₁→T₁ population transfer is found to proceed at a rate of ≈10⁷ s⁻¹ in the isolated molecule.     

Long-lived triplet charge-separated state in naphthalenediimide based donor–acceptor systems

1,4,5,8-Naphthalenediimides (NDIs) are widely used motifs to design multichromophoric architectures due to their ease of functionalisation, their high oxidative power and the stability of their radical anion. The NDI building block can be incorporated in supramolecular systems by either core or imide functionalization. We report on the charge-transfer dynamics of a series of electron donor–acceptor dyads consisting of a NDI chromophore with one or two donors linked at the axial, imide position. Photo-population of the core-centred π–π* state is followed by ultrafast electron transfer from the electron donor to the NDI. Due to a solvent dependent singlet–triplet equilibrium inherent to the NDI core, both singlet and triplet charge-separated states are populated. We demonstrate that long-lived charge separation in the triplet state can be achieved by controlling the mutual orientation of the donor–acceptor sub-units. By extending this study to a supramolecular NDI-based cage, we also show that the triplet charge-separation yield can be increased by tuning the environment.

Ultrafast electron transfer from singlet and triplet excited states in equilibrium results in the population of both singlet and triplet charge-separated states.     

Excited state dynamics of Michler's ketone: a laser flash photolysis study

Steady state absorption and fluorescence as well as the time resolved absorption studies in the pico and subpicosecond time domain have been performed to characterize the excited singlet and triplet states of Michler's ketone (MK). The nature of the lowest excited singlet (S₁) and triplet (T₁) states depends on the polarity of the solvent - in nonpolar solvents they have either pure nπ * character or mixed character of nπ * and ππ * states but in more polar solvents the states have CT character. Concentration dependence of the shapes of the fluorescence as well the excited singlet and triplet absorption spectra provide the evidence for the association of the MK molecules in the ground state.     

Ab initio study of cyclobutadiene in excited states: optimized geometries,electronic transitions and aromaticities

An Ab initio SCF-CI study of planar cyclobutadiene (CB) in ground and excited states has been carried out. The equilibrium geometries of some valence and Rydberg states have been calculated, as well as the energies of the vertical (absorption and emission) and non-vertical transitions. Using the optimized geometries, it is discussed how the aromaticity changes upon excitation of CB to the lowest-lying singlet and triplet states. The following conclusion is made: upon excitation to the fluorescent (S₁) or phosphorscent (T₁), states, the aromaticity of the anti-Hückel system cyclobutadiene increases significantly, whereas that of the Hückel system benzene descreases.     

Electronic spectra and luminescence properties of 1,2-benzotetraphene in crystalline matrices at 77 K

Quasilinear absorption and luminescence spectra of 1,2-benzotetraphene were obtained in polycrystalline matrices at 77 K. Tne energies of successive excited singlet states as well as the energy of the lowest excited triplet state were found experimentally and compared with those calculated by the PPP CI method. The fluorescence lifetime and quantum yield were determined experimentally. Moreover, the radiationless transition probabilities, lifetime of triplet state and phosphorescence quantum yield were estimated employing the Siebrand-Williams model. The results obtained suggest that radiationless ISC processes are the main deactivation channel of the S₁ and T₁ states. The vibrational analysis of quasilinear absorption and luminescence spectra was performed and fundamental frequencies of ground and first excited singlet states were determined.     

Can Anti-Aufbau DFT Calculations Estimate Singlet Excited State Aromaticity? Correspondence on “Dibenzoarsepins: Planarization of 8π-Electron System in the Lowest Singlet Excited State”

The simple anti-aufbau DFT approach for estimating singlet excited state aromaticity suggested in a recent Communication published in this journal is shown to produce incorrect results because it targets a linear combination of the singlet and triplet configurations involving the HOMO and LUMO rather than the first singlet excited state. If the S₁ state of a molecule is dominated by the HOMO→LUMO excitation, a comparably simple but theoretically consistent and qualitatively correct approximation to the S₁ wavefunction can be achieved by performing a small “two electrons in two orbitals” CASSCF(2,2) calculation which can be followed by the evaluation of magnetic aromaticity criteria such as NICS.     

Can Anti‐Aufbau DFT Calculations Estimate Singlet Excited State Aromaticity? Correspondence on “Dibenzoarsepins: Planarization of 8π‐Electron System in the Lowest Singlet Excited State”

The simple anti‐aufbau DFT approach for estimating singlet excited state aromaticity suggested in a recent Communication published in this journal is shown to produce incorrect results because it targets a linear combination of the singlet and triplet configurations involving the HOMO and LUMO rather than the first singlet excited state. If the S₁ state of a molecule is dominated by the HOMO→LUMO excitation, a comparably simple but theoretically consistent and qualitatively correct approximation to the S₁ wavefunction can be achieved by performing a small “two electrons in two orbitals” CASSCF(2,2) calculation which can be followed by the evaluation of magnetic aromaticity criteria such as NICS.     

An AB initio SCF MO CI study of the n → π* transition of methylenimine

The electron correlation energies of both the ground and n → π* excited states of methylenimine (CH₂NH) are investigated by means of ab initio SCF MO CI calculations. Then n → π* singlet and triplet state energies of methylenimine are obtained through 3461-dimensional CI including the singly, doubly and triply excited configurations. the excitation energy from the ground state to the ¹(n → π*) state nearly coincides with that obtained in the framework of the singly excited configuration interaction (SECI) procedure. This result suggests that there is good cancellation of the correlation energy between the ground and the excited singlet sates, proving the usefulness of the SECI method for the excitation energies.     

In silico prediction of annihilators for triplet–triplet annihilation upconversion via auxiliary-field quantum Monte Carlo

The energy of the lowest-lying triplet state (T1) relative to the ground and first-excited singlet states (S0, S1) plays a critical role in optical multiexcitonic processes of organic chromophores. Focusing on triplet–triplet annihilation (TTA) upconversion, the S0 to T1 energy gap, known as the triplet energy, is difficult to measure experimentally for most molecules of interest. Ab initio predictions can provide a useful alternative, however low-scaling electronic structure methods such as the Kohn–Sham and time-dependent variants of Density Functional Theory (DFT) rely heavily on the fraction of exact exchange chosen for a given functional, and tend to be unreliable when strong electronic correlation is present. Here, we use auxiliary-field quantum Monte Carlo (AFQMC), a scalable electronic structure method capable of accurately describing even strongly correlated molecules, to predict the triplet energies for a series of candidate annihilators for TTA upconversion, including 9,10 substituted anthracenes and substituted benzothiadiazole (BTD) and benzoselenodiazole (BSeD) compounds. We compare our results to predictions from a number of commonly used DFT functionals, as well as DLPNO-CCSD(T₀), a localized approximation to coupled cluster with singles, doubles, and perturbative triples. Together with S1 estimates from absorption/emission spectra, which are well-reproduced by TD-DFT calculations employing the range-corrected hybrid functional CAM-B3LYP, we provide predictions regarding the thermodynamic feasibility of upconversion by requiring (a) the measured T1 of the sensitizer exceeds that of the calculated T1 of the candidate annihilator, and (b) twice the T1 of the annihilator exceeds its S1 energetic value. We demonstrate a successful example of in silico discovery of a novel annihilator, phenyl-substituted BTD, and present experimental validation via low temperature phosphorescence and the presence of upconverted blue light emission when coupled to a platinum octaethylporphyrin (PtOEP) sensitizer. The BTD framework thus represents a new class of annihilators for TTA upconversion. Its chemical functionalization, guided by the computational tools utilized herein, provides a promising route towards high energy (violet to near-UV) emission.

Electronic structure theories such as AFQMC can accurately predict the low-lying excited state energetics of organic chromophores involved in triplet–triplet annihilation upconversion. A novel class of benzothiadiazole annihilators is discovered.     

Tuning phenoxyl-substituted diketopyrrolopyrroles from quinoidal to biradical ground states through (hetero-)aromatic linkers

Strongly fluorescent halochromic 2,6-di-tert-butyl-phenol-functionalised phenyl-, thienyl- and furyl-substituted diketopyrrolopyrrole (DPP) dyes were deprotonated and oxidised to give either phenylene-linked DPP1˙˙ biradical (y₀ = 0.75) with a singlet open shell ground state and a thermally populated triplet state (ΔE_ST = 19 meV; 1.8 kJ mol⁻¹; 0.43 kcal mol⁻¹) or thienylene/furylene-linked DPP2q and DPP3q compounds with closed shell quinoidal ground states. Accordingly, we identified the aromaticity of the conjugated (hetero-)aromatic bridge to be key for modulating the electronic character of these biradicaloid compounds and achieved a spin crossover from closed shell quinones DPP2q and DPP3q to open shell biradical DPP1˙˙ as confirmed by optical and magnetic spectroscopic studies (UV/vis/NIR, NMR, EPR) as well as computational investigations (spin-flip TD-DFT calculations in combination with CASSCF(4,4) and harmonic oscillator model of aromaticity (HOMA) analysis). Spectroelectrochemical studies and comproportionation experiments further prove the reversible formation of mixed-valent radical anions for the DPP2q and DPP3q quinoidal compounds with absorption bands edging into the NIR spectral region.

By variation of spacer aromaticity, a spin crossover from thienylene/furylene-linked quinones DPP2q/DPP3q to phenylene-bridged biradical DPP1˙˙ (y₀ = 0.75) with a singlet open shell ground state (ΔE_ST = 19 meV) was achieved.     

The Low‐Lying Excited States of 2,2′‐Bithiophene: A Theoretical Analysis

The low‐energy regions of the singlet→singlet, singlet→triplet, and triplet→triplet electronic spectra of 2,2′‐bithiophene are studied using multiconfigurational second‐order perturbation theory (CASPT2) and extended atomic natural orbitals (ANO) basis sets. The computed vertical, adiabatic, and emission transition energies are in agreement with the available experimental data. The two lowest singlet excited states, 1¹B_u and 2¹B_u, are computed to be degenerate, a novel feature of the system to be borne in mind during the rationalization of its photophysics. As regards the observed high triplet quantum yield of the molecule, it is concluded that the triplet states 2³A_g and 2³B_u, separated about 0.4 eV from the two lowest singlet excited states, can be populated by intersystem crossing from nonplanar singlet states.     

Evidence for long-lived excited states of [CnH2]2+ carbodications

The energetics, structures, stabilities and reactivities of[C_nH₂]²⁺ ions have been investigated using computational methods and experimental mass spectrometric techniques. Spontaneous decompositions of [C_nH₂]²⁺ into [C_nH]⁺ + H⁺ products, observed for ions with odd-n values, have been explained by invoking the formation of excited triplet states. Even-n [C_nH]⁺ ions possess triplet ground states with low-lying excited states, whereas odd-n ions have triplet states with energies several eV above ground singlet states. Radiationless transitions of vibrationally excited long-lived triplet state ions into singlet state continua are suggested as possible mechanisms for spontaneous deprotonation processes of odd-n [C_nH₂]²⁺ ions. Evidence for these long-lived excited states has been obtained in bimolecular single electron transfer reactions.     

Photophysical Behavior of Angelicins and Thioangelicins: Semiempirical Calculations and Experimental Study

The decay processes of the lowest excited singlet and triplet states of five methylated angelicins (4,6,4′-trimethyl-angelicin, MA, and four methylated thioangelicins, MTA; see Scheme 1) were investigated in live solvents by stationary and pulsed fluorometric and flash photolytic techniques. In particular, the solvent effects on absorption, fluorescence, quantum yields of fluorescence (φ_F) and triplet formation (φ_T), lifetimes of fluorescence (τ_F) and the triplet state (τ_T) and the quantum yields of singlet oxygen production (φ_Δ) were investigated. Semiempirical (ZINDO/S-CI) calculations were carried out to obtain information (transition probabilities and nature) on the lowest excited singlet and triplet states. The quantum mechanical calculations and the solvent effect on the photophysical properties showed that the lowest excited singlet state (S¹) is a partially allowed π,π* state, while the close-lying S₂ state is n,π* in nature. The efficiencies of fluorescence, S₁→T₁ intersystem crossing (ISC) and S₁→ S₀ internal conversion (IC) strongly depend on the energy gap between S₁, and S₂ and are explained in terms of the so-called proximity effect. In fact, for MA in cyclohexane, only the S₁→ S₀ internal conversion is operative, while in acetonitrile and ethanol, where the n.π* state is shifted to higher energy, the efficiencies of fluorescence and ISC increase significantly. The energy gap between S₁ and S₂ increases in MTA, where the furanic oxygen is replaced by a sulfur atom. Consequently, the solvent effect on the photophysical parameters of MTA is less marked than for MA; e.g. fluorescence and triplet-triplet absorption are also detectable in the nonpolar cyclohexane. The lowest excited singlet state of molecular oxygen O₂(¹D_g) was produced efficiently in polar solvents by energy transfer from the T₁ state of MA and MTA.