Singlet-triplet Gap Research Articles

Curious Case of Singlet Triplet Gaps in Nonlinear Polyaromatic Hydrocarbons

The singlet triplet (ST) gap of linear polyacenes decays exponentially with the system size as a result of extended conjugation and reducing highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gaps. These low ST gaps can ideally be leveraged toward energy applications but are hindered by the decreasing stability of the systems. Thus, there is the need to understand the ST gap of nonlinear polyacenes, which are markedly more stable than their linear counterparts. Here, we show that the ST gaps of the nonlinear polyacenes do not decrease with the system size and have no correlation with the HOMO-LUMO gaps or increased conjugation. The reason behind this is identified as the high multireference character of the triplet high-spin state. These unprecedented results are in stark contrast to the observations in linear polyacenes and are due to the combined effects of topology and geometrical factors.

Design and Synthesis of Kekulè and Non-Kekulè Diradicaloids via the Radical Periannulation Strategy: The Power of Seven Clar’s Sextets

This work introduces an approach to uncoupling electrons via maximum utilization of localized aromatic units, i.e., the Clar's π-sextets. To illustrate the utility of this concept to the design of Kekulé diradicaloids, we have synthesized a tridecacyclic polyaromatic system where a gain of five Clar's sextets in the open-shell form overcomes electron pairing and leads to the emergence of a high degree of diradical character. According to unrestricted symmetry-broken UCAM-B3LYP calculations, the singlet diradical character in this core system is characterized by the y0 value of 0.98 (y0 = 0 for a closed-shell molecule, y0 = 1 for pure diradical). The efficiency of the new design strategy was evaluated by comparing the Kekulé system with an isomeric non-Kekulé diradical of identical size, i.e., a system where the radical centers cannot couple via resonance. The calculated singlet-triplet gap, i.e., the ΔEST values, in both of these systems approaches zero: -0.3 kcal/mol for the Kekulé and +0.2 kcal/mol for the non-Kekulé diradicaloids. The target isomeric Kekulé and non-Kekulé systems were assembled using a sequence of radical periannulations, cross-coupling, and C-H activation. The diradicals are kinetically stabilized by six tert-butyl substituents and (triisopropylsilyl)acetylene groups. Both molecules are NMR-inactive but electron paramagnetic resonance (EPR)-active at room temperature. Cyclic voltammetry revealed quasi-reversible oxidation and reduction processes, consistent with the presence of two nearly degenerate partially occupied molecular orbitals. The experimentally measured ΔEST value of -0.14 kcal/mol confirms that K is, indeed, a nearly perfect singlet diradical.

Tailoring intersystem crossing of perylenediimide through chalcogen-substitution at bay-position: A theoretical perspective.

Molecular-scale design strategies for promoting intersystem crossing (ISC) in small organic molecules are ubiquitous in developing efficient metal-free triplet photosensitizers with high triplet quantum yield (ΦT). Air-stable and highly fluorescent perylenediimide (PDI) in its pristine form displays very small ISC compared to the fluorescence due to the large singlet-triplet gap (ΔES-T) and negligibly small spin-orbit coupling (SOC) between the lowest singlet (S1) and triplet state (T1). However, its ΦT can be tuned by different chemical and mechanical means that are capable of either directly lowering the ΔES-T and increasing SOC or introducing intermediate low-lying triplet states (Tn, n = 2, 3, …) between S1 and T1. To this end, herein, a few chalcogen (X = O, S, Se) bay-substituted PDIs (PDI-X2) are computationally modeled aiming at introducing geometrical-strain at the PDI core and also mixing nπ* orbital character to ππ* in the lowest singlet and triplet excited states, which altogether may reduce ΔES-T and also improve the SOC. Our quantum-chemical calculations based on optimally tuned range-separated hybrid reveal the presence of intermediate triplet states (Tn, n = 2, 3) in between S1 and T1 for all three PDI-X2 studied in dichloromethane. More importantly, PDI-X2 shows a significantly improved ISC rate than the pristine PDI due to the combined effects stemming from the smaller ΔES-T and the larger SOC. The calculated ISC rates follow the order as PDI-O2 < PDI-S2 < PDI-Se2. These research findings will be helpful in designing PDI based triplet photosensitizers for biomedical, sensing, and photonic applications.

Either Accurate Singlet-Triplet Gaps or Excited-State Structures: Testing and Understanding the Performance of TD-DFT for TADF Emitters.

The energy gap between the lowest singlet and triplet excited states (ΔEST) is a key property of thermally activated delayed fluorescence (TADF) emitters, where these states are dominated by charge-transfer (CT) character. Despite its well-known shortcomings concerning CT states, time-dependent density functional theory (TD-DFT) is widely used to predict this gap and study TADF. Moreover, polar CT states exhibit a strong interaction with their molecular environment, which further complicates their computational description. Addressing these two major challenges, this work studies the performance of Tamm-Dancoff-approximated TD-DFT (TDA-DFT) on the recent STGABS27 benchmark set,1 exploring different strategies to include orbital and structural relaxation, as well as dielectric embedding. The results show that the best-performing strategy is to calculate ΔEST at the ground-state structure using functionals with a surprisingly small amount of Fock exchange of ≈10% and without a (complete) solvent model. However, as this approach heavily relies on error cancellation to mimic dielectric relaxation, it is not robust and exhibits large systematic deviations in excited state energies, state characters, and structures. More rigorous approaches, including state-specific solvation, do not share these systematic deviations, but their predicted ΔEST values exhibit larger statistical errors. We thus conclude that for the description of CT states in dielectric environments, none of the tested TDA-DFT methods is competitive with the recently presented ROKS/PCM approach regarding robustness, accuracy, and computational efficiency.

Pivot invariance of multiconfiguration perturbation theory via frame vectors.

Multiconfiguration perturbation theory (MCPT) is a general framework for correcting the reference function of arbitrary structures. The variants of MCPT introduced so far differ in the specification of their zero-order Hamiltonian, i.e., the partitioning. A common characteristic of MCPT variants is that no numerical procedure is invoked when handling the overlap of the reference function and determinants spanning the configuration space. This comes at the price of pinpointing a principal term in the determinant expansion of the reference, rendering the PT results dependent on this choice. It is here shown that the pivot dependence of MCPT can be eliminated by using an overcomplete set of projected determinants in the space orthogonal and complementary to the reference. The projected determinants form a so-called frame, a generalization of the notion of basis, allowing for redundancy of the set. The simple structure of the frame overlap matrix facilitates overlap treatment in closed form, a feature shared by previous MCPT variants. In particular, the Moore-Penrose inverse of singular matrices appearing in frame-based MCPT can be constructed without the need for any pivoting algorithm or numerical zero threshold. Pilot numerical studies are performed for the singlet-triplet gap of biradicaloid systems, relying on geminal-based, incomplete model space reference function. Comparison with previous MCPT variants as well as illustration of pivot invariance is provided.

New HATNA(CN)6 ligand in the design of dianion magnetic assemblies with lanthanides {Cryptand(K+)}2{HATNA(CN)6·3LnIII(TMHD)3}2− (Ln = Gd, Tb and Dy)

Hexaazatrinaphthylenehexacarbonitrile ligand, HATNA(CN)6, when reduced to dianion state, forms crystalline {Cryptand[2.2.2](K+)}2{HATNA(CN)6}2−·2C6H4Cl2 (1) salt whose structure, optical and magnetic properties are studied. The HATNA(CN)6}2− dianions absorb light in the whole visible and a wide NIR range from 900 up to 2200 nm and have singlet EPR silent ground state. The dianions form trinuclear {Cryptand[2.2.2](K+)}2{HATNA(CN)6·3LnIII(TMHD)3}2−·3C6H5CH3 complexes where Ln is Gd (2), Tb (3) and Dy (4), and TMHD is 2,2,6,6-tetramethyl-3,5-heptanedionate. The {HATNA(CN)6}2− dianions are strongly distorted in coordination assemblies and have the length of the La-N{HATNA(CN)6} bonds of 2.58–2.66 Å. Dianions preserve low-energy absorption at the coordination of three metal complexes with maxima of the bands at 1440–1460 nm. DFT calculations support strong acceptor properties of HATNA(CN)6 and the non-degenerated LUMO for this ligand. As a result, dianions have singlet ground state whereas triplet state is positioned higher by 139 meV only (1620 K) and is thermally unattainable at 300 K. Coordination of the lanthanide complexes increases the singlet–triplet gap up to 210 meV (2440 K). Complexes 2–4 show weak antiferromagnetic coupling between high-spin lanthanide ions. J value estimated by PHI program for the gadolinium-complex is close to zero. Among 2–4 only gadolinium-containing complex 2 manifests an EPR signal with a complicated structure which can be approximated with D = 0.19 and E = 0.02 cm−1.

Porphyryne.

Density functional theory calculations with the B3LYP*-D3 method with large STO-QZ4P basis sets unambiguously predict a singlet ground state for Zn-porphyryne. However, the calculations also predict a low singlet-triplet gap of about 0.4 eV and a high adiabatic electron affinity of 2.4 eV. Accordingly, the reactivity of porphyryne species may be dominated by electron transfer, hydrogen abstraction, and proton-coupled electron transfer processes.

Benchmarking the semi-stochastic CC(P;Q) approach for singlet-triplet gaps in biradicals.

We recently proposed a semi-stochastic approach to converging high-level coupled-cluster (CC) energetics, such as those obtained in the CC calculations with singles, doubles, and triples (CCSDT), in which the deterministic CC(P;Q) framework is merged with the stochastic configuration interaction Quantum Monte Carlo propagations [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev. Lett. 119, 223003 (2017)]. In this work, we investigate the ability of the semi-stochastic CC(P;Q) methodology to recover the CCSDT energies of the lowest singlet and triplet states and the corresponding singlet-triplet gaps of biradical systems using methylene, (HFH)-, cyclobutadiene, cyclopentadienyl cation, and trimethylenemethane as examples.

Origins of Molecular-Twist-Triggered Intersystem Crossing in Functional Perylenediimides: Singlet-Triplet Gap versus Spin-Orbit Coupling.

Singlet-triplet gap (ΔES-T) and spin-orbit coupling (SOC) primarily govern intersystem crossing (ISC)-mediated photo- and electro-luminescence processes. Structural-twist in organic molecules is known to improve ISC efficiency. However, how and to what extent a twist affects the ΔES-T and SOC are not yet fully understood. In this work, the impact of molecular-twist on these energetics governing ISC is unveiled in a series of highly fluorescent prototype perylenediimides (PDIs) in dichloromethane implementing reliable quantum-chemical calculations. While S1 → T1 ISC remains suppressed with increasing twist, a relatively larger decrease in ΔES-T together with a modest increase in SOC results in enhanced S1 →T2 ISC. Significantly modulated ISC rates are predicted in a few experimentally relevant -CN- and -Br-substituted PDIs, where twist of varied extent arises naturally depending on substituent's chemical nature, numbers, and positions. This study uncovers the critical role of molecular-twist in tailoring ISC and thereby helps designing functional organic triplet-generating materials.

Multiconfiguration Pair-Density Functional Theory for Chromium(IV) Molecular Qubits.

Pseudotetrahedral organometallic complexes containing chromium(IV) and aryl ligands have been experimentally identified as promising molecular qubit candidates. Here we present a computational protocol based on multiconfiguration pair-density functional theory for computing singlet–triplet gaps and zero-field splitting (ZFS) parameters in Cr(IV) aryl complexes. We find that two multireference methods, multistate complete active space second-order perturbation theory (MS-CASPT2) and hybrid multistate pair-density functional theory (HMS-PDFT), perform better than Kohn–Sham density functional theory for singlet–triplet gaps. Despite the very small values of the ZFS parameters, both multireference methods performed qualitatively well. MS-CASPT2 and HMS-PDFT performed particularly well for predicting the trend in the ratio of the rhombic and axial ZFS parameters, |E/D|. We have also investigated the dependence and sensitivity of the calculated ZFS parameters on the active space and the molecular geometry. The methodologies outlined here can guide future prediction of ZFS parameters in molecular qubit candidates.

Near-exact nuclear gradients of complete active space self-consistent field wave functions.

In this paper, we study the nuclear gradients of heat bath configuration interaction self-consistent field (HCISCF) wave functions and use them to optimize molecular geometries for various molecules. We show that HCISCF nuclear gradients are fairly insensitive to the size of the "selected" variational space, which allows us to reduce the computational cost without introducing significant errors. The ability of the HCISCF to treat larger active spaces combined with the flexibility for users to control the computational cost makes the method very attractive for studying strongly correlated systems, which require a larger active space than possible with a complete active space self-consistent field. Finally, we study the realistic catalyst, Fe(PDI), and highlight some of the challenges this system poses for density functional theory (DFT). We demonstrate how HCISCF can clarify the energetic stability of geometries obtained from DFT when the results are strongly dependent on the functional. We also use the HCISCF gradients to optimize geometries for this species and study the adiabatic singlet-triplet gap. During geometry optimization, we find that multiple near-degenerate local minima exist on the triplet potential energy surface.

Multireference Study of Optically Addressable Vanadium-Based Molecular Qubit Candidates.

Molecular electron spin qubits with optical manipulation schemes are some of the most promising candidates for modern quantum technologies. Key values that determine a compound's viability for optical-spin initialization and readout include its singlet-triplet gap and zero-field splitting (ZFS) parameters. Generally, these values are very small in magnitude and are thus difficult to reproduce with theoretical methods. Here, we study a previously identified optically addressable molecular qubit, (C6F5)3trenVCNtBu (tren = tris(2-aminoethyl)amine), using the complete active space self-consistent field (CASSCF) and post-CASSCF methods: complete active space second-order perturbation theory (CASPT2), multiconfiguration pair-density functional theory (MC-PDFT), and hybrid MC-PDFT (HMC-PDFT). Of those methods, we successfully reproduce the singlet-triplet gap and ZFS parameters with reasonable accuracy using 0.5 HMC-PDFT and CASPT2. Four additional V3+ complexes with differing ligands were also investigated. We found that the ligands have minimal effect on the spin properties of the molecule and propose them to be optically addressable qubit candidates. These potential qubits are further analyzed in terms of ab initio ligand field theory (AILFT) to understand the influence of the ligands on the singlet-triplet gap and ZFS parameters.

Organic molecules with inverted singlet-triplet gaps.

According to Hund’s multiplicity rule, the energy of the lowest excited triplet state (T1) is always lower than that of the lowest excited singlet state (S1) in organic molecules, resulting in a positive singlet-triplet energy gap (ΔE ST). Therefore, the up-converted reverse intersystem crossing (RISC) from T1 to S1 is an endothermic process, which may lead to the quenching of long-lived triplet excitons in electroluminescence, and subsequently the reduction of device efficiency. Interestingly, organic molecules with inverted singlet-triplet (INVEST) gaps in violation of Hund’s multiplicity rule have recently come into the limelight. The unique feature has attracted extensive attention in the fields of organic optoelectronics and photocatalysis over the past few years. For an INVEST molecule possessing a higher T1 with respect to S1, namely a negative ΔE ST, the down-converted RISC from T1 to S1 does not require thermal activation, which is possibly conducive to solving the problems of fast efficiency roll-off and short lifetime of organic light-emitting devices. By virtue of this property, INVEST molecules are recently regarded as a new generation of organic light-emitting materials. In this review, we briefly summarized the significant progress of INVEST molecules in both theoretical calculations and experimental studies, and put forward suggestions and expectations for future research.

Understanding reaction mechanisms of metal-free dinitrogen activation by methyleneboranes

Dinitrogen activation under mild conditions is important but extremely challenging due to the inert nature of the NN triple bond evidenced by high bond dissociation energy (945 kJ/mol) and large HOMO-LUMO gap (10.8 eV). In comparison with largely developed transition metal systems, the reported main group species on dinitrogen activation are rare. Here, we carry out density functional theory calculations on methyleneboranes to understand the reaction mechanisms of their dinitrogen activation. It is found that the methyleneboranes without any substituent at the boron atom performs best on dinitrogen activation, which could be contributed to its small singlet-triplet gap. In addition, strong correlations are achieved on dinitrogen activation between the singlet-triplet energy gap and the reaction energies for the formation of the end-on products as well as the side-on ones. The principal interacting orbital analysis suggests that methyleneboranes can mimic transition metals to cleave the NN triple bond. Our findings could be helpful for experimental chemists aiming at dinitrogen activation by main group species.

Modular design for constructing narrowband deep-blue multiresonant thermally activated delayed fluorescent emitters for efficient organic light emitting diodes

The simultaneous achievement of high efficiency and deep blue narrowband emission in multi resonant thermally activated delayed fluorescence (MR-TADF) materials are crucial and challenging. Herein we report two deep blue MR-TADF emitters, namely, TPD4PA and tBu-TPD4PA, using double boron, three nitrogen and two oxygen atoms. The design is based on amalgamating the high charge transfer (CT) characteristic moiety into MR-type fragments towards efficient MR-TADF emitters with improved CT characteristics. Both the materials show deep blue photo luminescent emissions of ∼450 nm with a high photoluminescence quantum yield (PLQY) of ∼90 %. These materials showed very small singlet–triplet gap (≤0.06 eV) and a high rate of reverse intersystem crossing of ∼2.5 × 105 s−1. The TADF devices based on TPD4PA and tBu-TPD4PA showed maximum external quantum efficiencies of 30.7 and 32.5 %, respectively. Furthermore, both devices exhibited narrow band deep blue emissions and corresponding CIE y coordinates 0.06 and 0.07, which match near NTSC and BT2020 blue color requirements.

On Neutral Unsaturated Ouroboric Borylenes.

The search is on for stable isolated borylenes. Potential roles in modern synthetic chemistry for boron analogues of carbenes continue to motivate interest in locating them. Using density functional and ab initio methods, we posit and examine the thermochemistry, and chemical bonding, including aromaticity, of several classes of 5- and 6-membered borylenic rings. In these systems, cyclization relies on dative bonding (ouroboric coordination) and π donation to a monovalent boron center from an adjacent O center. Certain neutral five-membered rings (heterocyclic cyclopentadienyl analogues) in particular are found to exhibit exceptionally strong preferences for the singlet multiplicity, each with singlet-triplet (S-T) gaps in excess of 40 kcal·mol-1. The singlet five-membered rings with the largest S-T gaps and some of the six-membered rings show evidence of weak aromaticity. Relationships of the form N = A·r-b, in line with Gordy's and other functions linking bond order, N, and covalent bond length, are identified for dative B←O contacts, r, reinforced in rings by π-delocalization.

The numerical evaluation of Slater integrals on graphics processing units.

This article presents SlaterGPU, a graphics processing unit (GPU) accelerated library that uses OpenACC to numerically compute Slater-type orbital (STO) integrals. The electron repulsion integrals (ERI) are computed under the RI approximation using the Coulomb potential of the Slater basis function. To fully realize the performance capabilities of modern GPUs, the Slater integrals are evaluated in mixed-precision, resulting in speedups for the ERIs of over 80×. Parallelization on multiple GPUs allows for integral throughput of over 3 million integrals per second. This places STO integral throughput within reach of single-threaded, conventional Gaussian integration schemes. To test the quality of the integrals, the fluorine exchange reaction barrier in fluoromethane was computed using heat-bath configuration interaction (HBCI). In addition, the singlet-triplet gap of cyclobutadiene was examined using HBCI in a triple- , polarized basis set. These benchmarks demonstrate the library's ability to generate the full set of integrals necessary for configuration interaction with up to functions in the auxiliary basis.

Fast and Accurate Determination of the Singlet–Triplet Gap in Donor–Acceptor and Multiresonance TADF Molecules by Using Hole–Hole Tamm–Dancoff Approximated Density Functional Theory

AbstractOne of the requirements to design efficient emitters based on the multiresonance (MR)‐ or donor–acceptor (D‐A) thermally activated delayed fluorescence (TADF) materials is a relatively small energy gap between the lowest singlet and triplet excited states (ΔEST). High‐level ab initio calculations of their ΔEST provide benchmark results, but they are very time consuming and little practical for large‐size systems. Here, the performances of hole–hole Tamm–Dancoff approximated density functional theory (hh‐TDA‐DFT) and the functional dependent accuracy of hh‐TDA are examined on ΔEST of a large number of MR‐ and D‐A TADF molecules. The results indicate that hh‐TDA combined with the hybrid functional B3LYP can predict ΔEST values for a wide number of MR‐TADF molecules with mean absolute error (MAE) within 0.04 eV with correlation as high as 0.75. For D‐A TADF molecules, ΔEST is less sensitive to the nature of the functionals, with MAE as low as 0.07 eV. The larger discrepancy between ΔEST obtained from hh‐TDA‐DFT and experimental data in several oxygen‐containing MR‐TADF molecules is assumed to stem from the aggregation tendency of these compounds in solution. These findings provide important insights on the role of aggregation in reducing the ΔEST of MR‐TADF compounds.

Donor–Acceptor–Donor “Hot Exciton” Triads for High Reverse Intersystem Crossing in OLEDs

AbstractHot exciton materials have the potential to improve the quantum efficiency of organic light‐emitting diodes (OLEDs) by promoting high reversed intersystem crossing (hRISC) between a high‐lying triplet (Tn, n ≥ 2) and a radiative singlet (Sm). In recent years, donor–acceptor–donor (D–A–D) molecular systems have shown great promise in its ability to enhance the hRISC process under certain conditions. However, strategies to find appropriate D–A–D combinations beyond trial‐and‐error are still elusive. This work exposes the limited applicability of the current fragment‐based design rules and proposes high‐throughput screening as the optimal route to find candidates that fulfill the energy criteria for hRISC. The strategy consists of first establishing the thresholds for large triplet–triplet splitting and small singlet–triplet gap, then filtering combinations through rate comparison of competitive crossing pathways, and finally confirming hRISC with spin‐orbital coupling evaluation. Based on a dataset of 234 compounds, this protocol identifies 31 candidates with potential for hRISC, 4 of which are reported in the literature. Remarkably, while most of the promising systems show prominent hybridized local and charge transfer character, several candidates do not fulfill this condition, indicating that different routes are possible to design efficient OLED materials.

Excited-State Properties of Some Thermally Activated Delayed Fluorescence Emitters: Quest for an Accurate and Reliable Computational Method.

Thermally activated delayed fluorescence (TADF) finds application in organic light-emitting diodes. The molecules exhibiting TADF are characterized by small singlet-triplet energy gaps that help reverse intersystem crossing. Recently, ionization potential (IP)-tuned range-separated (RS) density functionals have been well accepted for studying excited-state properties. In the present work, two efficient descriptor-based tuning schemes [electron localization function (ELF) and Sol] of RS density functionals have been used to accurately reproduce the excited-state properties of TADF emitters by performing a single self-consistent field calculation. The lowest singlet vertical excitation energies (EVA(S1)) and the vertical singlet-triplet energy gaps (ΔEVST) are computed with ELF-, Sol-, and IP-tuned RS functionals (LC-BLYP, ωB97, ωB97X, and ωB97XD). Encouraging mean absolute deviations from the experimental values with ELF*-, Sol*-, and IP-tuned functionals are observed. Consistent performance of the non-empirical tuned functionals is noted in different solvent dielectrics. In addition to these, fractional occupation calculations have shown that our tuned functionals almost satisfy the energy linearity curve. Thus, ELF*- and Sol*-tuned functionals are promising and reliable alternatives in computing the excited-state properties. Considering the small experimental singlet-triplet gap, we recommend ELF* to calculate EVA(S1) and Sol* to calculate ΔEVST.