Triplet Instability Research Articles

On the Performance of Second-Order Polarization Propagator Methods in the Calculation of 1JFC and nJFH NMR Spin-Spin Coupling Constants.

This study evaluates the performance of doubles-corrected random phase approximation (RPA) and higher random phase approximation (HRPA) approaches in predicting nuclear magnetic resonance (NMR) coupling constants involving fluorine. Their performance is benchmarked against experimental data and compared with that of higher-level theoretical methods, specifically second-order polarization propagator (SOPPA) and SOPPA(CCSD). Additionally, we discuss their performance relative to density functional theory (DFT). We find that RPA(D) is severely constrained by (near) triplet instabilities, while HRPA(D) demonstrates markedly improved stability. Statistical analysis reveals stronger patterns for carbon-fluorine couplings across the methods and systems investigated compared with fluorine-hydrogen couplings. While SOPPA-based methodologies prove to be superior in accuracy, HRPA(D) shows promising performance in reducing the computational burden of these calculations, albeit with a tendency to underestimate the coupling strength. These findings highlight the potential of HRPA(D) as a practical alternative to SOPPA methods, even for such difficult properties as NMR spin-spin coupling constants involving fluorine, emphasizing its role in improving predictive accuracy and efficiency across diverse chemical environments.

Neuroinflammation and the role of epigenetic-based therapies for Huntington's disease management: the new paradigm.

Huntington's disease (HD) is an inherited, autosomal, neurodegenerative ailment that affects the striatum of the brain. Despite its debilitating effect on its patients, there is no proven cure for HD management as of yet. Neuroinflammation, excitotoxicity, and environmental factors have been reported to influence the regulation of gene expression by modifying epigenetic mechanisms. Aside focusing on the etiology, changes in epigenetic mechanisms have become a crucial factor influencing the interaction between HTT protein and epigenetically transcribed genes involved in neuroinflammation and HD. This review presents relevant literature on epigenetics with special emphasis on neuroinflammation and HD. It summarizes pertinent research on the role of neuroinflammation and post-translational modifications of chromatin, including DNA methylation, histone modification, and miRNAs. To achieve this about 1500 articles were reviewed via databases like PubMed, ScienceDirect, Google Scholar, and Web of Science. They were reduced to 534 using MeSH words like 'epigenetics, neuroinflammation, and HD' coupled with Boolean operators. Results indicated that major contributing factors to the development of HD such as mitochondrial dysfunction, excitotoxicity, neuroinflammation, and apoptosis are affected by epigenetic alterations. However, the association between neuroinflammation-altered epigenetics and the reported transcriptional changes in HD is unknown. Also, the link between epigenetically dysregulated genomic regions and specific DNA sequences suggests the likelihood that transcription factors, chromatin-remodeling proteins, and enzymes that affect gene expression are all disrupted simultaneously. Hence, therapies that target pathogenic pathways in HD, including neuroinflammation, transcriptional dysregulation, triplet instability, vesicle trafficking dysfunction, and protein degradation, need to be developed.

Wind Effects on Wave Overtopping at a Vertical Sea Defense

The wind effect on the efficiency of a coastal defense structure is studied in this paper. It is normally assumed that the strength of the wind impact is characterized by the impulse parameter. If it is lower than a certain value, the wind is expected to have a dominant effect on the wave overtopping rate. In contrast to the regular observation, this study reports a new regime of wave overshoot when a low value of the impulse parameter does not lead to increased importance of wind. It is argued that the new regime appears due to the triplet instability previously studied by others. The variation of the standing wave height and the overshooting jet between the sequential cycles results in independence of the overtopping rates of the wind speed.

TDDFT versus GW/BSE Methods for Prediction of Light Absorption and Emission in a TADF Emitter.

Design concepts for organic light emitting diode (OLED) emitters, which exhibit thermally activated delayed fluorescence (TADF) and thereby achieve quantum yields exceeding 25%, depend on singlet-triplet splitting energies of order kT to allow reverse intersystem crossing at ambient temperatures. Simulation methods for these systems must be able to treat relatively large organic molecules, as well as predict their excited state energies, transition energies, singlet-triplet splittings, and absorption and emission cross sections with reasonable accuracy, in order to prove useful in the design process. Here we compare predictions of TDDFT with M06-2X and ωB97X-D exchange-correlation functionals and a GoWo@HF/BSE method for these quantities in the well-studied DPTZ-DBTO2 TADF emitter molecule. Geometry optimization is performed for ground state (GS) and lowest donor-acceptor charge transfer (CT) state for each functional. Optical absorption and emission cross sections and energies are calculated at these geometries. Relaxation energies are on the order of 0.5 eV, and the importance of obtaining excited state equilibrium geometries in predicting delayed fluorescence is demonstrated. There are clear trends in predictions of GoWo@HF/BSE, and TDDFT/ωB97X-D and M06-2X methods in which the former method favors local exciton (LE) states while the latter favors DA CT states and ωB97X-D makes intermediate predictions. GoWo@HF/BSE suffers from triplet instability for LE states but not CT states relevant for TADF. Shifts in HOMO and LUMO levels on adding a conductor-like polarizable continuum model dielectric background are used to estimate changes in excitation energies on going from the gas phase to a solvated molecule.

Systematic Evaluation of Modern Density Functional Methods for the Computation of NMR Shifts of 3d Transition-Metal Nuclei.

A wide range of density functionals from all rungs of Jacob's ladder have been evaluated systematically for a set of experimental 3d transition-metal NMR shifts of 70 complexes encompassing 12 × 49Ti, 10 × 51V, 10 × 53Cr, 11 × 55Mn, 9 × 57Fe, 9 × 59Co, and 9 × 61Ni shift values, as well as a diverse range of electronic structure characteristics. The overall 39 functionals evaluated include one LDA, eight GGAs, seven meta-GGAs (including their current-density-functional─CDFT─versions), nine global hybrids, four range-separated hybrids, eight local hybrids, and two double hybrids, and we also include Hartree-Fock and MP2 calculations. While recent evaluations of the same functionals for a very large coupled-cluster-based benchmark of main-group shieldings and shifts achieved in some cases aggregate percentage mean absolute errors clearly below 2%, the best results for the present 3d-nuclei set are in the range between 4 and 5%. Strikingly, the overall best-performing functionals are the recently implemented CDFT versions of two meta-GGAs, namely cM06-L (4.0%) and cVSXC (4.3%), followed by cLH14t-calPBE (4.9%), B3LYP (5.0%), and cLH07t-SVWN (5.1%), i.e., the previously best-performing global hybrid and two local hybrids. A number of further functionals achieve aggregate deviations in the range 5-6%. Range-separated hybrids offer no particular advantage over global hybrids. Due to the overall poor performance of Hartree-Fock theory for all systems except the titanium complexes, MP2 and double-hybrid functionals are unsuitable for these 3d-nucleus shifts and provide large errors. Global hybrid functionals with larger EXX admixtures, such as BHLYP or M06-2X, also perform poorly, and some other highly parametrized global hybrids also are unsuitable. For many functionals depending on local kinetic energy τ, their CDFT variants perform much better than their "non-CDFT" versions. This holds notably also for the above-mentioned M06-L and VSXC, while the effect is small for τ-dependent local hybrids and can even be somewhat detrimental to the agreement with experiment for a few other cases. The separation between well-performing and more poorly performing functionals is mainly determined by their results for the most critical nuclei 55Mn, 57Fe, and 59Co. Here either moderate exact-exchange admixtures or CDFT versions of meta-GGAs are beneficial for the accuracy. The overall deviations of the better-performing global or local hybrids are then typically dominated by the 53Cr shifts, where triplet instabilities appear to disfavor exact-exchange admixture. Further detailed analyses help to pinpoint specific nuclei and specific types of complexes that are challenges for a given functional.

TD-DFT and Experimental Methods for Unraveling the Energy Distribution of Charge-Transfer Triplet/Singlet States of a TADF Molecule in a Frozen Matrix.

Reverse intersystem crossing (RISC) rate of a thermally activated delayed fluorescence (TADF) molecule is sensitive to the energy alignment of the singlet charge-transfer state (1CT), triplet charge-transfer state (3CT), and locally excited triplet state (3LE). However, the energy distribution of the charge-transfer states originating from the conformational distribution of TADF molecules in a solid matrix inevitably generated during the preparation of a solid sample due to the rotatable donor-acceptor linkage is rarely considered. Moreover, the investigation of the energy distribution of the 3CT state is both theoretically and experimentally difficult due to the triplet instabilities of time-dependent density functional (TD-DFT) calculations and difficulties in phosphorescence measurements, respectively. As a result, the relationships between conformational distribution, configurations of excited state transition orbitals, and excited state energies/dynamics have not been clearly explained. In this work, we determined the energy distribution of CT states of the TADF emitter TPSA in frozen toluene at 77 K by the measurement of time-resolved spectra in the full time range (1 ns to 30 s) of emission including prompt fluorescence, TADF, 3CT phosphorescence, and 3LE phosphorescence. We obtained the energy band of CT states where 1CT and 3CT states are distributed in the range of 2.85-3.00 and 2.64-2.96 eV, respectively. We tested various global hybrid and long-range corrected functionals for the TD-DFT calculation of 3CT energy of TPSA and found that only the M11 functional shows consistent results without triplet instability. We performed TD-DFT with the M11* functional optimized for a robust dihedral angle scan of 3CT states without triplet instability and reproduced the energy band structure obtained from the experiment. Through TD-DFT and experimental investigations, it is estimated that the dihedral angles of donor-acceptor (θD-A) and acceptor-linker (θA) of TPSA in frozen toluene lie within the range 70° ≤ θD-A ≤ 90° and 0° ≤ θA ≤ 30° respectively. Our results show that the dihedral angle distribution must be considered for further investigation of the photophysics of TADF molecules and the development of stable and efficient TADF emitters.

Electronic Structure Correspondence of Singlet-Triplet Scale Separation in Strained Sr2RuO4

At a temperature of roughly 1 K, Sr2RuO4 undergoes a transition from a normal Fermi liquid to a superconducting phase. Even while the former is relatively simple and well understood, the superconducting state has not even been understood after 25 years of study. More recently, it has been found that critical temperatures can be enhanced by the application of uniaxial strain, up to a critical strain, after which it falls off. In this work, we take an “instability” approach and seek divergences in susceptibilities. This provides an unbiased way to distinguish tendencies to competing ground states. We show that in the unstrained compound, the singlet and triplet instabilities of the normal Fermi liquid phase are closely spaced. Under uniaxial strain, electrons residing on all orbitals contributing to the Fermiology become more coherent, while the electrons of the Ru-dxy character become heavier, and the electrons of the Ru-dxz,yz characters become lighter. In the process, Im χ(q,ω) increases rapidly around q = (0.3,0.3,0)2π/a and q = (0.5,0.25,0)2π/a, while it gets suppressed at all other commensurate vectors, in particular at q = 0, which is essential for spin-triplet superconductivity. We observe that the magnetic anisotropy under strain drops smoothly, which is concomitant with the increment in singlet instability. Thus, the triplet superconducting instability remains the lagging instability of the system, and the singlet instability enhances under strain, leading to a large energy-scale separation between these competing instabilities. However, since this happens even without spin-orbit coupling, we believe it is primarily the enhancement in the spin fluctuation glue around quasi-anti-ferromagnetic vectors that drives the Cooper pairing instead of the magnetic anisotropy. At large strain, an instability to a spin density wave overtakes the superconducting one. The analysis relies on a high-fidelity, ab initio description of the one-particle properties and two-particle susceptibilities, based on the quasiparticle self-consistent GW approximation augmented by dynamical mean field theory. This approach is described and its high fidelity confirmed by comparing to observed one- and two-particle properties.

Addressing an instability in unrestricted density functional theory direct dynamics simulations.

In Density Functional Theory (DFT) direct dynamics simulations with Unrestricted Hartree Fock (UHF) theory, triplet instability often emerges when numerically integrating a classical trajectory. A broken symmetry initial guess for the wave function is often used to obtain the unrestricted DFT potential energy surface (PES), but this is found to be often insufficient for direct dynamics simulations. An algorithm is described for obtaining smooth transitions between the open-shell and the closed-shell regions of the unrestricted PES, and thus stable trajectories, for direct dynamics simulations of dioxetane and its •OCH2 -CH2 O• singlet diradical. © 2018 Wiley Periodicals, Inc.

Molecular excited states from the SCAN functional

ABSTRACTThe performance of the strongly constrained and appropriately normed (SCAN) meta-generalised gradient approximation exchange–correlation functional is investigated for the calculation of time-dependent density-functional theory molecular excitation energies of local, charge-transfer and Rydberg character, together with the excited potential energy curve in H2. The SCAN results frequently resemble those obtained using a global hybrid functional, with either a standard or increased fraction of exact orbital exchange. For local excitations, SCAN can exhibit significant triplet instability problems, resulting in imaginary triplet excitation energies for a number of cases. The Tamm–Dancoff approximation offers a simple approach to improve the situation, but the excitation energies are still significantly underestimated. Understanding the origin of these (near)-triplet instabilities may provide useful insight into future functional development.

An assessment of low-lying excitation energies and triplet instabilities of organic molecules with an ab initio Bethe-Salpeter equation approach and the Tamm-Dancoff approximation.

The accurate prediction of singlet and triplet excitation energies is an area of intense research of significant fundamental interest and critical for many applications. Most calculations of singlet and triplet energies use time-dependent density functional theory (TDDFT) in conjunction with an approximate exchange-correlation functional. In this work, we examine and critically assess an alternative method for predicting low-lying neutral excitations with similar computational cost, the ab initio Bethe-Salpeter equation (BSE) approach, and compare results against high-accuracy wavefunction-based methods. We consider singlet and triplet excitations of 27 prototypical organic molecules, including members of Thiel's set, the acene series, and several aromatic hydrocarbons exhibiting charge-transfer-like excitations. Analogous to its impact in TDDFT, we find that the Tamm-Dancoff approximation (TDA) overcomes triplet instabilities in the BSE approach, improving both triplet and singlet energetics relative to higher level theories. Finally, we find that BSE-TDA calculations built on effective DFT starting points, such as those utilizing optimally tuned range-separated hybrid functionals, can yield accurate singlet and triplet excitation energies for gas-phase organic molecules.

Spectroscopic, Structural, and Kinetic Investigation of the Ultrafast Spin Crossover in an Unusual Cobalt(II) Semiquinonate Radical Complex.

A comprehensive spectroscopic and structural investigation of [CoII (l-N4 tBu2 )(dbsq)][B(p-C6 H4 Cl)4 ] (1, l-N4 tBu2 =N,N'-di-tert-butyl-2,11-diaza[3.3](2,6)pyridinophane, dbsq1- =3,5-di-tert-butylsemiquinonate), the first known octahedral complex with a low-spin (ls) CoII semiquinonate ground state, is reported. Above 200 K, solids as well as solutions of 1 exhibit thermally induced spin-crossover (SCO) from the ls to the high-spin (hs) CoII semiquinonate state instead of the frequently observed valence tautomerism from ls CoIII catecholate to hs CoII semiquinonate. DFT calculations demonstrate that the (closed shell) CoIII catecholate suffers from a triplet instability leading to the ls CoII semiquinonate ground state. The thorough temperature-dependent spectroscopic study of the SCO enables a photophysical investigation. Thus, by selective photoexcitation of the ls fraction of 1 in solution at room temperature, ultrafast conversion to the hs state is observed using femtosecond electronic and IR-vibrational (infrared) transient absorption spectroscopy. The kinetics of the photocycle is described by a stretched exponential with τ=3.3-3.6 ps and β=0.52-0.54, representing an upper limit for the hs-ls relaxation time. This is, to our knowledge, the fastest interconversion ever determined for a SCO complex, and is attributed to the special situation that in 1 a CoII complex is coordinated to a π-radical ligand allowing very efficient coupling between the ls and hs spin states.

Finding symmetry breaking Hartree-Fock solutions: The case of triplet instability.

Determining the lowest unrestricted Hartree-Fock (UHF) solution is often difficult in even-electron systems. We have developed a deterministic method for locating approximately the UHF minimum using the restricted Hartree-Fock triplet instability matrix. The current method is truncated to fourth order. The minimum energy solution for this model can be determined by solving a small linear system of equations. This solution gives a suitable starting point to determine the exact UHF solution. This should be useful for the black-box determination of active spaces spanned by the fractionally occupied charge natural orbitals of the ground-state UHF wavefunction. The results can be generalized to higher (6th and 8th) degree expansions (odd expansion orders vanish by symmetry), and to other types of instability, including complex instability. The results are illustrated by calculations on ozone, benzene, nitrobenzene, butadiene, hexatriene, octatetraene, dichromium, and nickel porphine. Further examples are given in the supplementary material.

Singlet and triplet instability theorems.

A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree-Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree-Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree-Fock-theory-based explanations of Hund's rule, a singlet instability in Jahn-Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.

Molecular properties in the Tamm–Dancoff approximation: indirect nuclear spin–spin coupling constants

The Tamm–Dancoff approximation (TDA) can be applied to the computation of excitation energies using time-dependent Hartree–Fock (TD-HF) and time-dependent density-functional theory (TD-DFT). In addition to simplifying the resulting response equations, the TDA has been shown to significantly improve the calculation of triplet excitation energies in these theories, largely overcoming issues associated with triplet instabilities of the underlying reference wave functions. Here, we examine the application of the TDA to the calculation of another response property involving triplet perturbations, namely the indirect nuclear spin–spin coupling constant. Particular attention is paid to the accuracy of the triplet spin–dipole and Fermi-contact components. The application of the TDA in HF calculations leads to vastly improved results. For DFT calculations, the TDA delivers improved stability with respect to geometrical variations but does not deliver higher accuracy close to equilibrium geometries. These observations are rationalised in terms of the ground- and excited-state potential energy surfaces and, in particular, the severity of the triplet instabilities associated with each method. A notable feature of the DFT results within the TDA is their similarity across a wide range of different functionals. The uniformity of the TDA results suggests that some conventional evaluations may exploit error cancellations between approximations in the functional forms and those arising from triplet instabilities. The importance of an accurate treatment of correlation for evaluating spin–spin coupling constants is highlighted by this comparison.

Theory of chemical bonds in metalloenzymes XVI. Oxygen activation by high-valent transition metal ions in native and artificial systems

Activation mechanisms of oxygen dianion and hydroxide by high-valent transition metal ions for the oxygen–oxygen (O–O) bond formation of water splitting reaction have been investigated on the theoretical grounds, together with experimental results. First of all, broken-symmetry MO formulations are revisited to elucidate the instability of the dπ–pπ bond in high-valent metal–oxo M(X)O (M=Mn, Fe, Ru, etc.; X=IV, V) systems that react with hydroxide anion (or radical) or water to afford hydroperoxide anion (or peroxide). The triplet instability of these bonds entails strong or intermediate diradical characters: •M(X−1)O• and ••M(X−2)O••; the broken-symmetry (BS) molecular orbitals (MO) resulted from strong electron correlation, leading to the concept of electron localizations and local spins. As a continuation of these theoretical results, the BS MO interaction diagrams, namely orbital and spin correlation diagrams, for one-electron and electron-pair transfer mechanisms for the O–O bond formation have been depicted to reveal scope and applicability of local singlet diradical (LSD) and local triplet diradical (LTD) mechanisms that have been successfully utilized for theoretical understanding of mechanisms of oxygenation reactions by p450, methane mono- oxygenase (MMO) and homolytic radical coupling mechanisms by oxygen evolving complex (OEC) of PSII. The spin alignments in high-valent M(X)O systems are found directly corresponding to possible mechanisms of the O–O bond formation between Mn(X)O and hydroxide (OH) anion via one-electron, electron-pair transfer and their superposed (chameleon) processes. The broken-symmetry (BS) UB3LYP calculations of the model systems have been performed to confirm these mechanisms for oxygen evolution; charge and spin densities by BS UB3LYP are utilized for elucidation and confirmation of the LSD and LTD mechanisms and orbital and spin correlation diagrams. Implications of the theoretical results are discussed in relation to three scenarios of the O–O bond formation for water oxidation: (a) HO–OH, (b) OOH and (c) O–O, and water oxidation of OEC of PSII.

On the triplet instability in TDDFT

The utility of a Hartree–Fock triplet stability threshold, for identifying time-dependent density functional theory triplet excitations for which the inclusion of exact orbital exchange is detrimental, is illustrated for a benchmark set of 63 excitations in 20 organic molecules. Following earlier spin–spin coupling observations that suggest a relatively small triplet instability problem, the accuracy of triplet excitation energies from the B97-2 hybrid functional is also quantified. As anticipated, the results are relatively accurate and this is readily understood in terms of the stabilities. Application of the Tamm–Dancoff approximation dramatically improves all the triplet excitation energies corresponding to low stabilities, whilst also providing a modest improvement in the corresponding singlet states.

Overcoming Low Orbital Overlap and Triplet Instability Problems in TDDFT

Low orbital overlap and triplet instability problems in time-dependent density functional theory (TDDFT) are investigated for a new benchmark set, encompassing challenging singlet and triplet excitation energies of local, charge-transfer, and Rydberg character. The low orbital overlap problem is largely overcome for both singlet and triplet states by the use of a Coulomb-attenuated functional. For all the categories of functional considered, however, errors associated with triplet instability problems plague high overlap excitations, as exemplified by the excited states of acenes and polyacetylene oligomers. Application of the Tamm-Dancoff approximation reduces these errors for both singlet and triplet states, while leaving low-overlap excitations unaffected. The study illustrates the synergy between overlap and stability and highlights the success of a combined, Coulomb-attenuated Tamm-Dancoff approach.

Decrease in topoisomerase I is responsible for activation-induced cytidine deaminase (AID)-dependent somatic hypermutation

Somatic hypermutation (SHM) and class-switch recombination (CSR) of the Ig gene require both the transcription of the locus and the expression of activation-induced cytidine deaminase (AID). During CSR, AID decreases the amount of topoisomerase I (Top1); this decrease alters the DNA structure and induces cleavage in the S region. Similarly, Top1 is involved in transcription-associated mutation at dinucleotide repeats in yeast and in triplet-repeat contraction in mammals. Here, we report that the AID-induced decrease in Top1 is critical for SHM. Top1 knockdown or haploinsufficiency enhanced SHM, whereas Top1 overexpression down-regulated it. A specific Top1 inhibitor, camptothecin, suppressed SHM, indicating that Top1's activity is required for DNA cleavage. Nonetheless, suppression of transcription abolished SHM, even in cells with Top1 knockdown, suggesting that transcription is critical. These results are consistent with a model proposed for CSR and triplet instability, in which transcription-induced non-B structure formation is enhanced by Top1 reduction and provides the target for irreversible cleavage by Top1. We speculate that the mechanism for transcription-coupled genome instability was adopted to generate immune diversity when AID evolved.

Communication: Orbital instabilities and triplet states from time-dependent density functional theory and long-range corrected functionals

Long-range corrected hybrids represent an increasingly popular class of functionals for density functional theory (DFT) that have proven to be very successful for a wide range of chemical applications. In this Communication, we examine the performance of these functionals for time-dependent (TD)DFT descriptions of triplet excited states. Our results reveal that the triplet energies are particularly sensitive to the range-separation parameter; this sensitivity can be traced back to triplet instabilities in the ground state coming from the large effective amounts of Hartree-Fock exchange included in these functionals. As such, the use of standard long-range corrected functionals for the description of triplet states at the TDDFT level is not recommended.

Influence of Triplet Instabilities in TDDFT.

Singlet and triplet vertical excitation energies from time-dependent density functional theory (TDDFT) can be affected in different ways by the inclusion of exact exchange in hybrid or Coulomb-attenuated/range-separated exchange-correlation functionals; in particular, triplet excitation energies can become significantly too low. To investigate these issues, the explicit dependence of excitation energies on exact exchange is quantified for four representative molecules, paying attention to the effect of constant, short-range, and long-range contributions. A stability analysis is used to verify that the problematic TDDFT triplet excitations can be understood in terms of the ground state triplet instability problem, and it is proposed that a Hartree-Fock stability analysis should be used to identify triplet excitations for which the presence of exact exchange in the TDDFT functional is undesirable. The use of the Tamm-Dancoff approximation (TDA) significantly improves the problematic triplet excitation energies, recovering the correct state ordering in benzoquinone; it also affects the corresponding singlet states, recovering the correct state ordering in naphthalene. The impressive performance of the TDA is maintained for a wide range of molecules across representative functionals.