Vertical Singlet Research Articles

Rapid Computational Approach Towards Designing Singlet-Fission Chromophores by Tuning the Diradical Character of Heteroatom-Doped Polycyclic Aromatic Hydrocarbons Using the Atom-Specific Fukui Function.

Singlet fission (SF) is proposed as a promising method to circumvent the Shockley-Queisser threshold of single junction photovoltaics. Progress towards realizing efficient SF-based devices has been impeded by the fact that only a handful of molecules and their derivatives practically exhibit efficient SF. In the present work, we demonstrate a TDDFT-based rapid and cost-effective computational approach for designing SF chromophores by doping various atomic sites (substituting carbon atoms) of polycyclic aromatic hydrocarbons with nitrogen, phosphorus, and silicon. We establish a hitherto unexplored, direct correlation between the atom-specific chemical reactivity parameter─Fukui function─of these molecules with their frontier molecular orbital energies, diradical characters, and vertical singlet and triplet excitation energies. These quantitative correlations show exactly opposite trends for nitrogen-doped molecules and phosphorus- or silicon-doped molecules. The doped derivatives that have the Fukui function falling in a range of 0.03-0.14 possess the required intermediate diradical character and suitable singlet-triplet energies to qualify for SF candidature. Our findings enable one, at reasonable computational times and cost, to easily assess the doping criteria and to develop design rules for SF molecules in particular and for diradicaloids in general.

Schiff Base Zinc(II) Complexes as Promising Emitters for Blue Organic Light-Emitting Diodes

Organometallic blue fluorescent Zn(II) Schiff base complexes are synthesized and explored computationally in order to use them in organic electroluminescent heterostructures. Characterization of these pyrazolone-based azomethine–zinc complexes was accomplished by various physicochemical techniques to get insight into their applicability as an active layer in light-emitting diodes. All the complexes demonstrate high thermal stability and remarkable photoluminescence both in solution and in the solid state with maximum in the blue region. Quantum chemical calculations of the first exited electronic state and vertical singlet–singlet electronic transitions by means of time-dependent density functional theory calculations and results show that the origin of the luminescence for the target complexes refers to the intraligand charge transfer within the Schiff bases. The constructed light-emitting diodes demonstrate low input voltage (3.2–4.0 V), brightness at a level of 4300–11,600 Cd m–2, and external quantum efficiency of up to 3.2%, which is a good value for purely fluorescent organic light-emitting diodes.

Prediction of Excited-State Properties of Oligoacene Crystals Using Fragment-Based Quantum Mechanical Method.

A fundamental understanding of the excited-state properties of molecular crystals is of central importance for their optoelectronics applications. In this study, we developed the electrostatically embedded generalized molecular fractionation (EE-GMF) method for the quantitative characterization of the excited-state properties of locally excited molecular clusters. The accuracy of the EE-GMF method is systematically assessed for oligoacene crystals. Our result demonstrates that the EE-GMF method is capable of providing the lowest vertical singlet (S1) and triplet excitation energies (T1), in excellent agreement with the full-system quantum mechanical calculations. Using this method, we also investigated the performance of different density functionals in predicting the excited-state properties of the oligoacene crystals. Among the 13 tested functionals, B3LYP and MN15 give the two lowest overall mean unsigned errors with reference to the experimental S1 and T1 excitation energies. The EE-GMF approach can be readily utilized for studying the excited-state properties of large-scale organic solids at diverse ab initio levels.

The extended explicitly-correlated second-order approximate coupled-cluster singles and doubles ansatz suitable for response theory.

We report the extended explicitly correlated approximate coupled-cluster singles and doubles CC2(F12*)-XSP method suitable for response properties. Equations are derived using an automated approach and have subsequently been hand-coded into the computer program KOALA, in which for all two-electron integrals, density fitting is employed. Numerical results are presented for the lowest two vertical singlet excitation energies of a set of selected molecules. The results show that the CC2(F12*)-XSP method provides the correct basis-set limit with no bias to the ground state, and an excellent agreement with reference CC2 values using large basis sets is found. Using Dunning's aug-cc-pVTZ basis, the CC2(F12*)-XSP method yields excitation energies which are converged within 1 mEh to the basis-set limit for valence excitations.

Spin-state energetics of iron(II) porphyrin from the particle-particle random phase approximation

The particle-particle random phase approximation (pp-RPA) has been deployed to study the spin-state energetics of transition metal (TM) complexes for the first time in this work. Namely, we designed and implemented a non-canonical reference pp-RPA protocol that is capable of capturing the singlet low-spin (LS) – triplet intermediate-spin (IS) excitation process of iron(II) complexes; herein we applied this method to iron-porphyrin related heme derivatives with clearly defined LS and IS electronic states. Coupled to the CAM-B3LYP functional and to Dunning-type basis sets, we utilized both the active-space and Davidson methods to solve the pp-RPA equation effectively to obtain vertical singlet–triplet excitation energies. Correcting these vertical metrics with a structural relaxation factor for each species, we evaluated the relative stability of LS and IS electronic states. Comparison of the pp-RPA results to established ab initio data revealed that pp-RPA describes well excitation energies and related relative spin state stabilities if the transition is based on non-bonding d-orbitals, such as complexes without an axial ligand in the investigated set of molecules. But it notably overestimates the stability of the singlet LS state to the triplet IS state in complexes, where the d-orbitals at which the excitation is centered have bonding or antibonding character.

Analytic gradient and derivative couplings for the spin-flip extended configuration interaction singles method: Theory, implementation, and application to proton transfer.

We present the formalism of analytic gradients and derivative couplings for the spin-flip extended configuration interaction with single excitations (SF-XCIS) method. We report an efficient implementation of the SF-XCIS method in the framework of semiempirical quantum chemistry that allows fast excited-state calculations for large systems. The performance of the SF-XCIS method in combination with semiempirical orthogonalization-corrected models (OMx) is statistically evaluated for vertical singlet excitation energies. The SF-XCIS method treats the ground state and excited states in a fully balanced manner and properly describes conical intersections involving the ground state. It can thus be used in fewest switches surface hopping (FSSH) simulations of nonadiabatic dynamics processes. This is demonstrated in an OM2/SF-XCIS FSSH pilot study of excited-state proton transfer in 7-(2-pyridyl)indole.

Computational Studies of Aromatic and Photophysical Properties of Expanded Porphyrins.

Magnetically induced current densities and ring-current pathways have been calculated at density functional theory (DFT) and second-order Møller-Plesset perturbation theory (MP2) levels of theory for a set of expanded porphyrins consisting of five or six pyrrolic rings. The studied molecules are sapphyrin, cyclo[6]pyrrole, rubyrin, orangarin, rosarin, and amethyrin. Different functionals have been employed to assess the functional dependence of the ring-current strength susceptibility. Vertical singlet and triplet excitation energies have been calculated at the second-order approximate coupled cluster (CC2), expanded multiconfigurational quasi-degenerate perturbation theory (XMC-DPT2), and time-dependent density functional theory levels. The lowest electronic transition of the antiaromatic molecules was found to be pure magnetic transitions providing an explanation for the large paratropic contribution to the total current density. Rate constants for different nonradiative deactivation channels of the lowest excited states have been calculated yielding lifetimes and quantum yields of the lowest excited singlet and triplet states. The calculations show that the spin-orbit interaction between the lowest singlet ( S0) and triplet ( T1) states of the antiaromatic molecules is strong, whereas for the aromatic molecule the spin-orbit coupling vanishes. The experimentally detected fluorescence from S2 to S0 of amethyrin has been explained. The study shows that there are correlations between the aromatic character and optical properties of the investigated expanded porphyrins.

Understanding the Difference in Photophysical Properties of Cyclometalated Iridium(III) and Rhodium(III) Complexes by Detailed Time-Dependent Density Functional Theory and Frontier Molecular Orbital Supports

Two sets of new mononuclear cyclometalated complexes of the types [MIII(ppy)2(L)] (Ir1 and Rh1) and [MIII(bzq)2(L)] (Ir2 and Rh2) [where M = Rh/Ir; L = N-(furan-2-ylmethyl)-2-pyridinecarboxamide; ppy = 2-phenylpyridine (1); bzq = benzo[h]quinoline (2)] are presented to understand the significant differences of emission behaviors between Ir(III) and Rh(III) complexes. The complexes were fully characterized by using physicochemical and spectroscopic tools along with the detailed structural studies of Ir1 and Rh2 by single-crystal X-ray diffraction. Structural analyses showed that in both complexes the metal exhibits a distorted octahedral geometry. The geometries, electronic structures, lowest-lying singlet–singlet absorptions, vertical singlet–triplet excitation, and triplet–singlet emission behaviors of all the complexes (Ir1–2 and Rh1–2) were examined by means of DFT and TDDFT approaches. In order to find out the considerable differences in experimentally observed emission properties of Ir(III) (5d6) and...

Prediction of excited-state properties of oligoacene crystals using polarizable continuum model-tuned range-separated hybrid functional approach.

A methodology combining the polarizable continuum model and optimally-tuned range-separated (RS) hybrid functional was proposed for the quantitative characterization of the excited-state properties in oligoacene (from anthracene to hexacene) crystals. We show that it provides lowest vertical singlet and triplet excitation energies, singlet-triplet gap, and exciton binding energies in very good agreement with the available experimental data. We further find that it significantly outperforms its non-tuned RS counterpart and the widely used B3LYP functional, and even many-body perturbation theory within the GW approximation (based on a PBE starting point). Hence, this approach provides an easily applicable and computationally efficient tool to study the excited-state properties of organic solids of complexity. © 2017 Wiley Periodicals, Inc.

Benchmarking singlet and triplet excitation energies of molecular semiconductors for singlet fission: Tuning the amount of HF exchange and adjusting local correlation to obtain accurate functionals for singlet–triplet gaps

Vertical and adiabatic singlet and triplet excitation energies of molecular p-type semiconductors calculated with various DFT functionals and wave-function based approaches are benchmarked against MS-CASPT2/cc-pVTZ reference values. A special focus lies on the singlet–triplet gaps that are very important in the process of singlet fission. Singlet fission has the potential to boost device efficiencies of organic solar cells, but the scope of existing singlet-fission compounds is still limited. A computational prescreening of candidate molecules could enlarge it; yet it requires efficient methods accurately predicting singlet and triplet excitation energies. Different DFT formulations (Tamm-Dancoff approximation, linear response time-dependent DFT, Δ-SCF) and spin scaling schemes along with several ab initio methods (CC2, ADC(2)/MP2, CIS(D), CIS) are evaluated. While wave-function based methods yield rather reliable singlet–triplet gaps, many DFT functionals are shown to systematically underestimate triplet excitation energies. To gain insight, the impact of exact exchange and correlation is in detail addressed.

Excitation spectra of aromatic molecules within a real-spaceGW-BSE formalism: Role of self-consistency and vertex corrections

We present first-principles calculations on the vertical ionization potentials (IPs), electron affinities (EAs), and singlet excitation energies on an aromatic-molecule test set (benzene, thiophene, 1,2,5-thiadiazole, naphthalene, benzothiazole, and tetrathiafulvalene) within the $GW$ and Bethe-Salpeter equation (BSE) formalisms. Our computational framework, which employs a real-space basis for ground-state and a transition-space basis for excited-state calculations, is well suited for high-accuracy calculations on molecules, as we show by comparing against ${G}_{0}{W}_{0}$ calculations within a plane-wave-basis formalism. We then generalize our framework to test variants of the $GW$ approximation that include a local density approximation (LDA)--derived vertex function (${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LDA}}$) and quasiparticle-self-consistent (QS) iterations. We find that ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LDA}}$ and quasiparticle self-consistency shift IPs and EAs by roughly the same magnitude, but with opposite sign for IPs and the same sign for EAs. ${G}_{0}{W}_{0}$ and $\mathrm{QS}GW{\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LDA}}$ are more accurate for IPs, while ${G}_{0}{W}_{0}{\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LDA}}$ and $\mathrm{QS}GW$ are best for EAs. For optical excitations, we find that perturbative $GW$-BSE underestimates the singlet excitation energy, while self-consistent $GW$-BSE results in good agreement with previous best-estimate values for both valence and Rydberg excitations. Finally, our work suggests that a hybrid approach, in which ${G}_{0}{W}_{0}$ energies are used for occupied orbitals and ${G}_{0}{W}_{0}{\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LDA}}$ for unoccupied orbitals, also yields optical excitation energies in good agreement with experiment but at a smaller computational cost.

Excited State Studies of Polyacenes Using the All-Order Constricted Variational Density Functional Theory with Orbital Relaxation.

For the polyacenes series from naphthalene to hexacene, we present the vertical singlet excitation energies 1 (1)La and 1 (1)Lb, as well as the first triplet excitation energies obtained by the all-order constricted variational density functional theory with orbital relaxation (R-CV(∞)-DFT). R-CV(∞)-DFT is a further development of variational density functional theory (CV(∞)-DFT), which has already been successfully applied for the calculation of the vertical singlet excitation energies (1)La and (1)Lb for polyacenes,15 and we show that one obtains consistent excitation energies using the local density approximation as a functional for singlet as well as for triplet excitations when going beyond the linear response theory. Furthermore, we apply self-consistent field density functional theory (ΔSCF-DFT) and compare the obtained excitation energies for the first triplet excitations T1, where, due to the character of the transition, ΔSCF-DFT and R-CV(∞)-DFT become numerically equivalent, and for the singlet excitations 1 (1)La and 1 (1)Lb, where the two methods differ.

Reliable Prediction with Tuned Range-Separated Functionals of the Singlet-Triplet Gap in Organic Emitters for Thermally Activated Delayed Fluorescence.

The thermally activated delayed fluorescence (TADF) mechanism has recently attracted significant interest in the field of organic light-emitting diodes (OLEDs). TADF relies on the presence of a very small energy gap between the lowest singlet and triplet excited states. Here, we demonstrate that time-dependent density functional theory in the Tamm-Dancoff approximation can be very successful in calculations of the lowest singlet and triplet excitation energies and the corresponding singlet-triplet gap when using nonempirically tuned range-separated functionals. Such functionals provide very good estimates in a series of 17 molecules used in TADF-based OLED devices with mean absolute deviations of 0.15 eV for the vertical singlet excitation energies and 0.09 eV [0.07 eV] for the adiabatic [vertical] singlet-triplet energy gaps as well as low relative errors and high correlation coefficients compared to the corresponding experimental values. They significantly outperform conventional functionals, a feature which is rationalized on the basis of the amount of exact-exchange included and the delocalization error. The present work provides a reliable theoretical tool for the prediction and development of novel TADF-based materials with low singlet-triplet energetic splittings.

The third-order algebraic diagrammatic construction method (ADC(3)) for the polarization propagator for closed-shell molecules: efficient implementation and benchmarking.

The implementation of an efficient program of the algebraic diagrammatic construction method for the polarisation propagator in third-order perturbation theory (ADC(3)) for the computation of excited states is reported. The accuracies of ADC(2) and ADC(3) schemes have been investigated with respect to Thiel's recently established benchmark set for excitation energies and oscillator strengths. The calculation of 141 vertical excited singlet and 71 triplet states of 28 small to medium-sized organic molecules has revealed that ADC(3) exhibits mean error and standard deviation of 0.12 ± 0.28 eV for singlet states and -0.18 ± 0.16 eV for triplet states when the provided theoretical best estimates are used as benchmark. Accordingly, the ADC(2)-s and ADC(2)-x calculations revealed accuracies of 0.22 ± 0.38 eV and -0.70 ± 0.37 eV for singlets and 0.12 ± 0.16 eV and -0.55 ± 0.20 eV for triplets, respectively. For a comparison of CC3 and ADC(3), only non-CC3 benchmark values were considered, which comprise 84 singlet states and 19 triplet states. For these singlet states CC3 exhibits an accuracy of 0.23 ± 0.21 eV and ADC(3) an accuracy of 0.08 ± 0.27 eV, and accordingly for the triplet states of 0.12 ± 0.10 eV and -0.10 ± 0.13 eV, respectively. Hence, based on the quality of the existing benchmark set it is practically not possible to judge whether ADC(3) or CC3 is more accurate, however, ADC(3) has a much larger range of applicability due to its more favourable scaling of O(N(6)) with system size.

Photophysical properties and photochemistry of substituted cinnamates and cinnamic acids for UVB blocking: effect of hydroxy, nitro, and fluoro substitutions at ortho, meta, and para positions

Photophysical properties and photochemistry of various substituted cinnamates and cinnamic acids for ultraviolet B blocking were investigated experimentally and theoretically. This series includes monohydroxy, -nitro, and -fluoro derivatives. The absorption spectra were satisfactorily reproduced by the direct SAC-CI method with respect to the peak position and intensity. The transition character of the low-lying two ππ* and σπ* states for these 18 derivatives was analyzed. The para derivatives have a different transition character of the ππ* transitions compared with those of the ortho and meta derivatives. To elucidate the relaxation mechanism, the emission spectra were observed with oxygen quenching and the photostability was examined experimentally. The calculated radiative lifetimes indicate that the ortho- and meta-substituted derivatives have longer lifetimes for emission than the para derivatives. The potential energy curves of the first and second singlet excited states of the hydroxy derivatives as well as the vertical singlet and triplet transitions were examined to investigate the relaxation qualitatively. The ortho and meta derivatives have an energy barrier or flat surface in S1 resulting in fluorescence, whereas the para derivatives show nonradiative decay without an energy barrier. The para-hydroxy derivative was found to be an excellent UV absorber based on its broad absorption in the UVB/UVA regions, less emission, and higher photostability.

Photochemical Mechanisms of Radiationless Deactivation Processes in Urocanic Acid

Urocanic acid is a UV filter found in human skin that protects the skin from UV damage but has also been linked to the onset of skin cancer and to photoimmunosuppression. We report on ab initio investigations of two rotameric forms of each of the two tautomers of neutral (E)- and (Z)-urocanic acid. We have computed the vertical singlet excitation energies of eight isomers and have explored the singlet excited-state reaction paths of several photochemical processes for radiationless excited-state deactivation: the E/Z photoisomerization, an electron-driven proton transfer for an intramolecularly hydrogen-bonded Z isomer, as well as the hydrogen-atom detachment process and the ring-puckering process involving the NH group inherent to the imidazole moiety. We have optimized the S1/S0 conical intersections for each of these processes and located additional ππ*/nπ* conical intersections. Because of the reversed energetic order of the nπ* and ππ* states in the N3H and N1H tautomers, an energy window exists where the N3H tautomers can be excited to the nπ* state, from which only the photoisomerization process is accessible, while the N1H tautomers can be excited to the ππ* state, from which several deexcitation processes compete from the onset of the absorption. These results explain the unusual dependence of the quantum yield for E→Z photoisomerization on the excitation wavelength. The present work provides novel insight into the complex photochemistry of this biomolecule and paves the way for future computational studies of the photoinduced excited-state dynamics of urocanic acid.

Theoretical Study on Cationic Iridium(III) Complexes with a Diphosphane Ligand – Geometry, Electronic Properties, and Application for Light‐Emitting Electrochemical Cells

AbstractA DFT/time‐dependent DFT (TD‐DFT) investigation was conducted on a series of cationic iridium(III) complexes with 2‐phenylpyridine (ppyn) derivatives and a diphosphane (PPn) ancillary ligand to shed light on the effects of stereoisomerism and ligand substituents on the photophysical properties. The geometries, electronic structures, lowest‐lying singlet–singlet absorptions, vertical singlet–triplet excitations, and triplet–singlet emissions of N,N‐cis‐[Ir(ppy0)2(PP)]+ (1), N,N‐trans‐[Ir(ppy0)2(PP)]+ (2) and their derivatives were investigated with DFT‐based approaches [ppy0 = 2‐phenylpyridine, PP = 1,2‐bis(diphenylphosphanyl)ethene]. The complex N,N‐trans‐[Ir(ppy2)2(PP2)]+ (3b) shows high quantum phosphorescence efficiency (ΦPL) of 91 %, whereas an extremely low ΦPL (<1 %) was observed for N,N‐trans‐[Ir(ppy4)2(PP1)]+ (2d). To clarify this behavior, the S1–Tn splitting energy (ΔE), the transition dipole moment (μ) upon the S0→S1 transition, and the energy gap between the triplet metal‐to‐ligand charge transfer (3MLCT) π–π* and triplet metal‐centered (3MC) d–d states (ΔEMC–MLCT) were calculated. A drastically small ΔE and large μ for 3b (<0.05 eV and 1.38 D, respectively), compared to those for 2d (>0.2 eV and 1.26 D, respectively), were found to be closely linked to the substituents on the ppyn ligands. The remarkably small ΔE and similar μ for N,N‐cis 1c (<0.05 eV and 1.41 D, respectively), compared to those for N,N‐trans 2c (>0.1 eV and 1.42 D, respectively), could be attributed to the effects of the trans–cis structural isomerism. On the basis of these parameters, the higher ΦPL of 3b with respect to that of 2d was explained, and 1c, 1d, 2b, and 2e were considered to have better physical properties than the experimentally synthesized complexes 2, 2d, and 3b. The newly designed 1c, 1d, 2b, and 2e are expected to be highly emissive in the blue‐green region for light‐emitting electrochemical cell (LEC) applications.

Accurate Theoretical Description of the (1)La and (1)Lb Excited States in Acenes Using the All Order Constricted Variational Density Functional Theory Method and the Local Density Approximation.

We present the results of calculations on the vertical singlet (1)La and (1)Lb excitation energies in acenes within time dependent density functional theory (TDDFT), second order constricted variational DFT (CV(2)-DFT), and all order constricted variational DFT (CV(∞)-DFT) using the local density approximation LDA(VWN). For the linear acenes it is shown that the application of the Tamm-Dancoff (TD) approximation to TDDFT (TDDFT-TD) substantially improves the agreement with experiment compared to pure TDDFT. This improvement leads to the correct ordering of the (1)La and (1)Lb excitation energies in naphthalene. As TDDFT-TD is equivalent to the second order CV(2)-TD method one might hope for further improvements by going to all orders in CV(∞)-TD. Indeed, for linear acenes the application of the CV(∞)-TD method brings the agreement with experiment to within 0.1 eV for both types of excitations using the simple LDA functional. The CV(∞)-TD method based on LDA is also shown to be accurate for 15 nonlinear acenes with root-mean-square deviations of 0.24 eV for (1)La and 0.17 eV for (1)Lb.

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

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

Effects of Ethynyl Substituents on the Electronic Structure of Cyclobutadiene

The effects of ethynyl substitution on the electronic structure of cyclobutadiene are investigated in this work. Ethynyl substituted cyclobutadienes may be involved in Bergman cyclization reactions and are possible intermediates in the formation of fullerenes and graphitic sheets. Prediction of the electronic structure of cyclobutadiene is challenging for single-reference ab initio methods because of Jahn-Teller distortions and the diradical character of the singlet state. The equation-of-motion spin-flip coupled-cluster with single and double excitations (EOM-SF-CCSD) method accurately describes diradical states and is used to determine vertical and adiabatic singlet-triplet energy splittings in the substituted cyclobutadienes. The adiabatic singlet-triplet gaps decrease upon substituent addition, but the singlet states remain lower in energy. However, the results are affected by spin-contamination of the reference state and deteriorate when an unrestricted HF reference is employed. Additional insights in the electronic structure of cyclobutadienes are obtained by analyzing natural charges and spin densities. The substituents pull the charge out of the cyclobutadiene ring; however, the natural charges and spin densities are found to be nearly independent of the geometry and spin state.