Excited Quartet States Research Articles

Dual-quartet phosphorescent emission in the open-shell M1Ag13 (M = Pt, Pd) nanoclusters

Dual emission (DE) in nanoclusters (NCs) is considerably significant in the research and application of ratiometric sensing, bioimaging, and novel optoelectronic devices. Exploring the DE mechanism in open-shell NCs with doublet or quartet emissions remains challenging because synthesizing open-shell NCs is difficult due to their inherent instability. Here, we synthesize two dual-emissive M1Ag13(PFBT)6(TPP)7 (M = Pt, Pd; PFBT = pentafluorobenzenethiol; TPP = triphenylphosphine) NCs with a 7-electron open-shell configuration to reveal the DE mechanism. Both NCs comprise a crown-like M1Ag11 kernel with Pt or Pd in the center surrounded by five PPh3 ligands and two Ag(SR)3(PPh3) motifs. The combined experimental and theoretical studies revealed the origin of DE in Pt1Ag13 and Pd1Ag13. Specifically, the high-energy visible emission and the low-energy near-infrared emission arise from two distinct quartet excited states: the core-shell charge transfer and core-based states, respectively. Moreover, PFBT ligands are found to play an important role in the existence of DE, as its low-lying π* levels result in energetically accessible core-shell transitions. This novel report on the dual-quartet phosphorescent emission in NCs with an open-shell electronic configuration advances insights into the origin of dual-emissive NCs and promotes their potential application in magnetoluminescence and novel optoelectronic devices.

Oxidative two-state photoreactivity of a manganese(IV) complex using near-infrared light.

Highly reducing or oxidizing photocatalysts are a fundamental challenge in photochemistry. Only a few transition metal complexes with Earth-abundant metal ions have so far advanced to excited state oxidants. All these photocatalysts require high-energy light for excitation, and their oxidizing power has not been fully exploited due to energy dissipation before reaching the photoactive state. Here we demonstrate that the complex [Mn(dgpy)2]4+, based on Earth-abundant manganese and the tridentate 2,6-diguanidylpyridine ligand (dgpy), evolves to a luminescent doublet ligand-to-metal charge transfer (2LMCT) excited state (1,435 nm, 0.86 eV) with a lifetime of 1.6 ns after excitation with low-energy near-infrared light. This 2LMCT state oxidizes naphthalene to its radical cation. Substrates with extremely high oxidation potentials up to 2.4 V enable the [Mn(dgpy)2]4+ photoreduction via a high-energy quartet 4LMCT excited state with a lifetime of 0.78 ps, proceeding via static quenching by the solvent. This process minimizes free energy losses and harnesses the full photooxidizing power, and thus allows oxidation of nitriles and benzene using Earth-abundant elements and low-energy light.

Enhancing Coherence Times of Chromophore-Radical Molecular Qubits and Qudits by Rational Design.

An important criterion for quantum operations is long qubit coherence times. To elucidate the influence of molecular structure on the coherence times of molecular spin qubits and qudits, a series of molecules featuring perylenediimide (PDI) chromophores covalently linked to stable nitroxide radicals were synthesized and investigated by pulse electron paramagnetic resonance spectroscopy. Photoexcitation of PDI in these systems creates an excited quartet state (Q) followed by a spin-polarized doublet ground state (D0), which hold promise as spin qudits and qubits, respectively. By tailoring the molecular structure of these spin qudit/qubit candidates by selective deuteration and eliminating intramolecular motion, coherence times of Tm = 9.1 ± 0.3 and 4.2 ± 0.3 μs at 85 K for D0 and Q, respectively, are achieved. These coherence times represent a nearly 3-fold enhancement compared to those of the initial molecular design. This approach offers a rational structural design protocol for effectively extending coherence times in molecular spin qudits/qubits.

Electronically Excited States of Free Radicals

Formation of the excited doublet (D) and quartet (Q) states of free radicals under their photoexcitation is discussed. The relative positions of the D and Q states are compared to the positions of the photoexcited states of organic molecules (Jablonsky diagram). A number of representative cases of the excited states of free radicals detected by their transient absorption or emission are presented. A special case of the population having the lowest Q state in some radicals is discussed. A spin–statistical factor in the reactions of Q and D is debated.

Electronic origin of ferroic quadrupole moment under antiferroic quadrupole order and finite magnetic moment in Jeff=32 systems

We study the electronic origin of parasitic ferroic quadrupole moments in antiferroic quadrupole orders by extending a model studied in G. Chen et al., Phys. Rev. B 82, 174440 (2010) with the effective angular momentum ${J}_{\mathrm{eff}}=3/2$ quartet ground states. Taking into account the first crystalline-electric-field (CEF) excited doublet, cubic anisotropy in the quadrupole moments emerges, which leads to the induced ferroic quadrupole moments in the antiferroic quadrupolar phases. The hybridization with the CEF excited quartet states also causes finite magnetic moments compatible to the observed size of the effective moment in typical ${J}_{\mathrm{eff}}=3/2$ systems, as opposed to the naive expectation of vanishing moments in the ${J}_{\mathrm{eff}}=3/2$ systems. These results suggest the importance of the corrections arising from the high-energy CEF excited states in the ${J}_{\mathrm{eff}}=3/2$ systems.

Direct Determination of the Rate of Intersystem Crossing in a Near-IR Luminescent Cr(III) Triazolyl Complex.

A detailed understanding of the dynamics of photoinduced processes occurring in the electronic excited state is essential in informing the rational design of photoactive transition-metal complexes. Here, the rate of intersystem crossing in a Cr(III)-centered spin-flip emitter is directly determined through the use of ultrafast broadband fluorescence upconversion spectroscopy (FLUPS). In this contribution, we combine 1,2,3-triazole-based ligands with a Cr(III) center and report the solution-stable complex [Cr(btmp)2]3+ (btmp = 2,6-bis(4-phenyl-1,2,3-triazol-1-yl-methyl)pyridine) (13+), which displays near-infrared (NIR) luminescence at 760 nm (τ = 13.7 μs, ϕ = 0.1%) in fluid solution. The excited-state properties of 13+ are probed in detail through a combination of ultrafast transient absorption (TA) and femtosecond-to-picosecond FLUPS. Although TA spectroscopy allows us to observe the evolution of phosphorescent excited states within the doublet manifold, more significantly and for the first time for a complex of Cr(III), we utilize FLUPS to capture the short-lived fluorescence from initially populated quartet excited states immediately prior to the intersystem crossing process. The decay of fluorescence from the low-lying 4MC state therefore allows us to assign a value of (823 fs)-1 to the rate of intersystem crossing. Importantly, the sensitivity of FLUPS to only luminescent states allows us to disentangle the rate of intersystem crossing from other closely associated excited-state events, something which has not been possible in the spectroscopic studies previously reported for luminescent Cr(III) systems.

A cationic sulfur-hydrocarbon triradical with an excited quartet state.

The triptycene-bridged tris(thianthrene) compound 1 was designed and synthesized. Three-electron oxidation of 1 by NO[Al(OC(CF3)3)4], followed by crystallization at two different temperatures resulted in the triradical trication salts 2a and 2b respectively, which feature different crystal packing patterns. The triradical trications in 2a and 2b both feature a doublet ground state which can be thermally populated to a quartet state, representing the first examples of cationic main-group triradicals.

Dianionic States of Trithiadodecaazahexaphyrin Complexes with Homotrinuclear MII3O Clusters (M = Ni and Cu): Crystal Structures, Metal- Or Macrocycle-Centered Reduction, and Doublet-Quartet Transitions in the Dianions.

Metal complexes of trithiadodecaazahexaphyrin (Hhp) that contain MII3O clusters inside a π-extended trianionic (Hhp3-) macrocycle have been prepared. Studies of the magnetic properties of NiII3O(Hhp) and CuII3O(Hhp) reveal a diamagnetic and EPR-silent trianionic (Hhp3-) macrocycle and diamagnetic NiII3(O2-) or paramagnetic CuII3(O2-) tetracations. The positive charge of MII3O(Hhp) is compensated by one acetate anion {MII3O(Hhp)}+(CH3CO2-). The three-electron reduction of {MII3O(Hhp)}+ yields {cryptand(Cs+)}2{NiII2NiIO(Hhp5-)}2-·2C7H8 (1) and {cryptand(Cs+)}2{CuII3O(Hhp•6-)}2-·C7H8 (2) crystalline salts. The magnetic properties of 1 reveal the formation of Hhp5- and the reduction of nickel(II) to the paramagnetic NiI ion (S = 1/2), which is accompanied by the formation of the {NiII2NiIO(Hhp5-)}2- dianion. As a result, the magnetic moment of 1 is 1.68 μB in the 20-220 K range, and a broad EPR signal of NiI was observed. The Hhp5- macrocycle has a singlet ground state, but the increase in the magnitude of the magnetic moment of 1 above 220 K is attributed to the population of the triplet excited state in Hhp5-. The {NiII2NiIO(Hhp5-)}2- dianion is transferred from the doublet excited state to the quartet excited state with an energy gap of 1420 ± 50 K. Salt 1 also shows an unusually strong low-energy NIR absorption, which was observed at 1000-2200 nm. In 2, a highly reduced Hhp•6- radical hexaanion (S = 1/2) coexists with a CuII3(O2-) cluster (S = 1/2) in the {CuII3O(Hhp•6-)}2- dianions. The dianions have a triplet ground state with antiferromagnetic exchange between two S = 1/2 spins with J = -6.4 cm-1. The reduction of Hhp in both salts equalizes the initially alternated C-N bonds, supporting the increase in the Hhp macrocycle electron delocalization.

The triplet mechanism of electron spin polarization in moderately coupled triplet-doublet rigid complexes as a source of the enhanced +1/2 ↔ -1/2 transitions.

The light-induced electron spin polarization generated in the excited quartet and doublet states of a system consisting of a chromophore with an attached radical is investigated theoretically. Excitation of the chromophore and subsequent relaxation leads to a coupled triplet-doublet spin system. In many such systems, the electronic coupling between the triplet and doublet spins is expected to be strong enough to split the spin system into so-called trip-doublet and trip-quartet states but sufficiently weak that it does not promote significant mixing between the sing-doublet and trip-doublet states. In such moderately coupled systems, the sing-doublet can relax to the trip-doublet and trip-quartet states by spin-orbit coupling mediated intersystem crossing within the chromophore. An analytical expression is derived for the intensity of the polarization generated by this mechanism for the ms = +1/2 ↔ -1/2 electron paramagnetic resonance transitions of the trip-doublet and trip-quartet states. The expression shows that the intensity and sign of the polarization depend strongly on ratio jω = 3J/ω0 between the triplet-doublet exchange interaction J and the Zeeman energy ω0. The polarization becomes undefined when jω = 1 and when jω = 2 because level-anticrossings between the trip-doublet and trip-quartet sublevels occur. The sign of the polarization is also found to change above and below these values. Thus, for such moderately coupled systems, the sign of the polarization and its Zeeman energy dependence can be used to estimate the magnitude of the exchange coupling.

Hyperfine tensors for a model system for the oxygen evolving complex of photosystem II: calculation of the anisotropy shift that occurs beyond the strong exchange limit.

Broken-symmetry density functional calculations have been used to calculate effective 55Mn hyperfine (A) tensors for a mixed-valence tetranuclear manganese complex, a model system for the S2 state of the oxygen-evolving complex of photosystem II. Recent investigations carried out in our laboratory showed that for calculations within the strong exchange limit, density functional calculations cannot reproduce the relative magnitude of the anisotropy of the hyperfine tensors of the MnIII center compared to the MnIV centers. In this work we therefore go beyond the strong exchange limit and investigate the effect of multiplet mixing, induced by zero-field splitting, on the effective hyperfine tensors through a perturbational treatment within the numerical spin projection procedure. Results show that the inclusion of zero-field splitting leads to a shift of the anisotropy from the MnIII ion towards the three MnIV ions, thus reconciling the calculated and experimentally observed anisotropy pattern. However, the final results are quite sensitive to the energy gap between the ground (doublet) and the first excited (quartet) state and therefore critically depend on the appropriate choice of the isotropic exchange coupling constants.

Direct emission from quartet excited states triggered by upconversion phenomena in solid-phase synthesized fluorescent lead-free organic–inorganic hybrid compounds

We report, for the first time, the solid-phase gram-scale synthesis of two lead-free, zero-dimensional (0D) fluorescent organic–inorganic hybrid compounds, [Bu4N]2[MnBr4] (1) and [Ph4P]2[MnBr4] (2).

DFT/MRCI Hamiltonian for odd and even numbers of electrons

DFT/MRCI is a well-established method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] combining density functional theory and multireference configuration interaction. It was later redesigned by Lyskov, Kleinschmidt, and Marian [J. Chem. Phys. 144, 034104 (2016)] to provide a better treatment of bi-chromophores while treating all other systems as well as Grimme's version did by computing individual energy shifts for each state function of a configuration. But all previous operators lack the ability to compute states with an odd number of electrons (doublet and quartet states). Here we present a general Hamiltonian based on Lyskov's redesign which calculates excited singlet, doublet, triplet, and quartet states of systems that have up to one open shell in the parent determinant. The multiplicity-independent correction parameters provide an extra correction for the open shell in the parent determinant. The Hamiltonian in combination with two parameter sets for different selection thresholds has been tested and compared to experimental vertical excitation and ionization energies yielding similar statistics for all multiplicities with a root mean square deviation smaller than 0.2 eV while maintaining the good computational performance of the Hamiltonians of Grimme and Lyskov.

Low Curie temperature ferromagnetic phase in SmPt2Cd20 possibly accompanied by strong quantum fluctuations

Electrical resistivity, magnetization and specific heat have been measured for single crystals of SmPt$_{2}$Cd$_{20}$. It has been found that SmPt$_{2}$Cd$_{20}$ exhibits a ferromagnetic (FM) transition at $T_{\rm C} = 0.64$ K, the lowest among cubic compounds. Specific heat divided by temperature increases with decreasing temperature even below $T_{\rm C}$ and attains 4.5 J/mol K$^{2}$ at 0.26 K, implying substantial magnetic quantum fluctuations. An analysis of the magnetic entropy suggests the crystalline-electric-field splitting of the Sm $J = 5/2$ multiplet with a $\Gamma_{7}$ doublet ground state and a $\Gamma_8$ quartet excited state (the excitation energy of $\sim30$ K). The electrical resistivity shows a power-law behavior with $T^{0.74}$ below 2 K without showing any noticeable anomaly at $T_{\rm C}$. SmPt$_{2}$Cd$_{20}$ is regarded as a rare cubic system that is located in the vicinity of a FM quantum critical point.

Comparison of nitrogen-vacancy complexes in diamond and cubic SiC: dose dependencies and spin-Hamiltonian parameters

At present the nitrogen-vacancy (NV) complex in diamond is the most promising defect for application in the area of quantum computing. This provides a stimulus for an extensive search of other defects in semiconductors with similar properties. Recently it was shown that the NCVSi defect complex in SiC is perspectively appropriate for this goal as well. In the present work we perform comparative ab initio studies of NV complexes in diamond and 3C-SiC. We focus both on radiospectroscopic characterization of these defects and on the calculation of the equilibrium concentration of complexes in irradiated crystals. In particular a full set of spin-Hamiltonian parameters including g-tensors, hyperfine tensors and the spin–spin part of zero-field splitting constant Dss were calculated for both negative and neutral charge states as well as for excited quartet states of neutral complexes. Comparison of calculated values with the available experimental data and results of other calculations show good agreement, especially in the case when hybrid and meta-hybrid functionals were used. This makes the unambiguous identification of negative NV complexes in both materials possible. Our calculations reveal that the ground states of neutral complexes are a difficult case for both DFT calculations and experimental observations. This is caused by multi-determinantal behavior of wave function for such complexes, which leads to a large amount of spin contamination and to the broken symmetry solution which appeared for single Slater determinant DFT calculations. Based on the calculated minimum of free energy of neutral and negative complexes in SiC and diamond we obtained the equilibrium concentrations of these complexes depending on the vacancy concentration produced by irradiation. We show that in some dose regions both negative and neutral complexes coexist, while in other regions only one charge state prevails. Comparison of the calculated and experimental dose dependencies for diamond shows good qualitative agreement.

Critical Assessment of Time-Dependent Density Functional Theory for Excited States of Open-Shell Systems: II. Doublet-Quartet Transitions

Compared with closed-shell systems, open-shell systems place three additional challenges to time-dependent density functional theory (TD-DFT) for electronically excited states: (a) the spin-contamination problem is a serious issue; (b) the exchange-correlation (XC) kernel may be numerically instable; and (c) the single-determinant description of open-shell ground states readily becomes energetically instable. Confined to flip-up single excitations, the spin-contamination problem can largely be avoided by using the spin-flip TD-DFT (SF-TD-DFT) formalism, provided that a noncollinear XC kernel is employed. As for the numerical instabilities associated with such a kernel, only an ad hoc scheme has been proposed so far, viz., the ALDA0 kernel, which amounts to setting the divergent components (arising from density gradients and kinetic energy density) simply to zero. The ground-state instability problem can effectively be avoided by introducing the Tamm-Dancoff approximation (TDA) to TD-DFT. Therefore, on a general basis, the SF-TDA/ALDA0 Ansatz is so far the only promising means within the TD-DFT framework for flip-up single excitations of open-shell systems. To assess systematically the performance of SF-TDA/ALDA0, in total 61 low-lying quartet excited states of the benchmark set of 11 small radicals [J. Chem. Theory Comput. 2016, 12, 238] are investigated with various XC functionals. Taking the MRCISD+Q (multireference configuration interaction with singles and doubles plus the Davidson correction) results as benchmark, it is found that the mean absolute errors of SF-TDA/ALDA0 with the SAOP (statistical averaging of model orbital potentials), global hybrid, and range-separated hybrid functionals are in the range of 0.2-0.4 eV. This is in line not only with the typical accuracy of TD-DFT for singlet and triplet excited states of closed-shell systems but also with the gross accuracy of spin-adapted TD-DFT for spin-conserving excited states of open-shell systems.

Correlating the structures and activities of the resting oxidized and native intermediate states of a small laccase by paramagnetic NMR

Multicopper oxidases (MCO) are the fastest and most efficient known catalysts of the oxygen-reduction reaction. When all four copper ions are oxidized during catalysis, the native intermediate state (NI) decays in seconds to the resting oxidized state (RO), which returns to the catalytic cycle via reduction, but at a much slower rate than NI. We report the long-lived (months at 4°C) NI state of the small laccase (SLAC) MCO and the subsequent characterization of both its RO and NI states by paramagnetic 1H NMR. We find that the RO state of the trinuclear cluster (TNC) is best described as an isolated Type-3 dicopper site, antiferromagnetically coupled by a hydroxo group with −2J=500cm−1. The NI state is more complicated; we develop a theoretical treatment for the case in which all three copper ions in the TNC are coupled, and find that the results are consistent with three coupling constants of −2J=300, 240, and 160cm−1. These couplings result in a ground doublet state, a low-lying excited doublet state at 121cm−1, and a quartet excited state at 411cm−1, in good agreement with DFT models in which the Type-2 copper has a terminal hydroxo ligand.

Energy, fine structure, hyperfine structure, and radiative transition rates of the high-lying multi-excited states for B-like neon

The Rayleigh-Ritz variational method with multiconfiguration interaction wave functions is used to obtain the energies of high-lying multi-excited quartet states 1s 22s2pnl and 1s 22p 2 nl 4Pe,o (n ≥ 2) in B-like neon, including the mass polarization and relativistic corrections. The fine structure and hyperfine structure of the excited quartet states for this system are investigated. Configuration structures of the high-lying multi-excited series are further identified by relativistic corrections and fine structure splittings. The transition rates and wavelengths are also calculated. Calculated wavelengths include the quantum electrodynamic effects. The results are compared with other theoretical and experimental data in the literature.

Ab initio calculations of the electronic structure of the low-lying states for the ultracold LiYb molecule.

Ab initio techniques have been applied to investigate the electronic structure of the LiYb molecule. The potential energy curves have been computed in the Born-Oppenheimer approximation for the ground and 29 low-lying doublet and quartet excited electronic states. Complete active space self-consistent field, multi-reference configuration interaction, and Rayleigh Schrödinger perturbation theory to second order calculations have been utilized to investigate these states. The spectroscopic constants, ωe, Re, Be, …, and the static dipole moment, μ, have been investigated by using the two different techniques of calculation with five different types of basis. The eigenvalues, Ev, the rotational constant, Bv, the centrifugal distortion constant, Dv, and the abscissas of the turning points, Rmin and Rmax, have been calculated by using the canonical functions approach. The comparison between the values of the present work, calculated by different techniques, and those available in the literature for several electronic states shows a very good agreement. Twenty-one new electronic states have been studied here for the first time.

Multi-reference Ab initio calculations of 3d transition-metal dimers: Sc2

The problem of calculation of the electronic structure of transition-metal clusters (even dimers) still presents a challenge for computational chemistry. The reason is that the expansion of the ground state wave function on electronic configurations does not contain a principal configuration and a large number of reference configurations must be treated equally. Thus, the multi-reference (MR) approaches are, in general, mandatory. A short description of the MRCI methods is presented. The calculation of Sc2 at the MRCISD(+Q)/cc-pV5Z level, showed that the its ground state corresponds to a quintet, 5Σu−, in agreement with experiment and previous precise calculations. The triplet 3Σu− state is located about 1.1 kcal/mol above. We calculated the ground state, X5Σu−, of the Sc2 dimer by the MRCISD(+Q) method at the complete basis set (CBS) limit. This is the first MRCISD(+Q) calculation of 3d transition-metal clusters at the CBS limit. From the Mulliken population analysis and comparison with atomic energies follows that in the ground state Sc2 dissociates on one Sc in the ground state and the other in the second excited quartet state, 4Fu. The spectroscopic parameters of the ground potential curve, obtained by the Dunham analysis at the valence MRCISD(+Q)/CBS level, are: Re = 5.20 bohr, De = 50.37 kcal/mol, and e = 234.5 cm−1. The obtained value for the harmonic frequency agrees very well with the experimental one, e = 239.9 cm−1. From the indistinguishability of identical atoms in quantum mechanics follows that in spite of an asymmetric dissociation limit for Sc2, both Sc atoms have the same electron population and it is incorrect to consider them as different. Therefore, the accepted classification of the dimer states should be revised, since some of them are forbidden by the Pauli Exclusion Principle.

Orientation Information from the Dipolar Interaction Between a Complex in the Excited Quartet State and a Doublet Spin Label

An algorithm is proposed for deriving the position of a stable radical relative to a photoexcited quartet state from the electron spin–spin interactions measured by double resonance methods. Intersystem crossing generates multiplet polarization in the quartet state and microwave excitation of the ±3/2 ↔ ±1/2 transitions converts the multiplet polarization into net polarization of the ±1/2 levels. The dependence of the electron spin echo envelope modulation (ESEEM) of the +1/2 ↔ −1/2 transition on the field/frequency of the stimulation pulse is demonstrated. The algorithm is tested by comparing the predicted ESEEM patterns to those from explicit numerical calculations of the spin evolution (so-called numerical experiments), which act as a model for experiment results. The comparison demonstrates that within the point-dipole approximation it is feasible to obtain not only the distance between the two paramagnetic centers but also the orientation of the distance vector relative to the principal axes of the quartet state.