Theoretical study of dynamic electron-spin-polarization via the doublet-quartet quantum-mixed state (II). Population transfer and magnetic field dependence of the spin polarization

The population transfer to the spin-sublevels of the unique quartet (S = 3/2) high-spin state of the strongly exchange-coupled (SC) radical-triplet pair (for example, an Acceptor-Donor-Radical triad (A-D-R)) via a doublet-quartet quantum-mixed (QM) state is theoretically investigated by a stochastic Liouville equation. In this work, we have treated the loss of the quantum coherence (de-coherence) due to the de-phasing during the population transfer and neglected the effect of other de-coherence mechanisms. The dependences on the magnitude of the exchange coupling or the fine-structure parameter of the QM state are investigated. The dependence on the velocity of the population transfer (by the electron transfer or the energy-transfer) from the QM state to the SC quartet state is also clarified. It is revealed that the de-coherence during the population transfer mainly originates from the fine-structure term of the QM state in the doublet-triplet exchange coupled systems. This de-coherence leads to the unique dynamic electron polarization (DEP) on the high-field spin sublevels of the SC state, which is similar to the unique DEP pattern of the photo-excited triplet states of the reaction centers of photosystems I and II. The magnetic field dependence of the population transfer leading to the populations of the spin-sublevels of the SC states is also calculated. The possibility of the control of energy transport, spin transport and information technology by using the QM state is discussed based on these results. The knowledge obtained in this work is useful in the spin dynamics of any doublet-triplet exchange coupled systems.     

pi-topology and spin alignment utilizing the excited molecular field: observation of the excited high-spin quartet (S = 3/2) and quintet (S = 2) states on purely organic pi-conjugated spin systems.

As a model system for the photoinduced/photoswitched spin alignment in a purely organic pi-conjugated spin system, 9-[4-(4,4,5,5-tetramethyl-1-yloxyimidazolin-2-yl)phenyl]anthracene (1a), 9-[3-(4,4,5,5-tetramethyl-1-yloxyimidazolin-2-yl)phenyl]anthracene (1b), 9,10-bis[4-(4,4,5,5-tetramethyl-1-yloxyimidazolin-2-yl)phenyl]anthracene (2a), and 9,10-bis[3-(4,4,5,5-tetramethyl-1-yloxyimidazolin-2-yl)phenyl]anthracene (2b) were designed and synthesized. In these spin systems, 9-phenylanthracene and 9,10-diphenylanthracene were chosen as photo spin couplers and iminonitroxide was chosen as a dangling stable radical. Time-resolved electron spin resonance (TRESR) spectra of the first excited states with resolved fine-structure splittings were observed for 1a and 2a in an EPA or a 2-MTHF rigid glass matrix. Using the spectral simulation based on the eigenfield method, the observed TRESR spectra for 1a and 2a were unambiguously assigned as an excited quartet (S = 3/2) spin state (Q) and an excited quintet (S = 2) spin state (Qu), respectively. The g value and fine-structure splitting for the quartet state of 1a were determined to be g(Q) = 2.0043, D(Q) = 0.0235 cm(-1), and E(Q) = 0.0 cm(-1). The relative populations (polarization) of each M(S)() sublevel in Q were determined to be P(+1/2') = P(-1/2') = 0.5 and P(+3/2') = P(-3/2') = 0.0 with an increasing order of energy in zero magnetic field. The spin Hamiltonian parameters for Qu are g = 2.0043, D = 0.0130 cm(-1), and E = 0.0 cm(-1), and the relative populations in Qu were determined to be P(0') = 0.30, P(-1') = P(+1') = 0.35 and P(-2') = P(+2') = 0.0. These are the first observations of a photoexcited quartet and a quintet high-spin state in pi-conjugated triplet-radical pair systems. In contrast high-spin excited states were not observed for 1b and 2b, the pi-topological isomers of 1a and 2a, showing the role of pi-topology in the spin alignment of the excited states. Since a weak antiferromagnetic exchange interaction was observed in the ground state of 2a, the clear detection of the excited quintet high-spin state shows that the effective exchange coupling between the two dangling radicals through the diphenylanthracene spin coupler has been changed from antiferromagnetic to ferromagnetic upon photoexcitation. Thus, a photoinduced spin alignment utilizing the excited triplet molecular field was realized for the first time in the purely organic pi-conjugated spin system. Furthermore, the mechanism for the generation of dynamic electron spin polarization was investigated for the observed quartet and quintet states, and a plausible mechanism of the enhanced selective intersystem crossing was proposed. Ab initio molecular orbital calculations based on density functional theory were carried out to determine the electronic structures of the excited high-spin states and to understand the mechanism of the spin alignment utilizing the excited molecular field. The role of the spin delocalization and the spin polarization mechanisms were revealed on the photoexcited state.     

Design,synthesis and electronic states of an iminonitroxide radical with excited quartet high-spin state and photo-induced electron transfer in its CT complex

In this paper, we report the design, synthesis and electronic state of a π-conjugated stable iminonitroxide radical, 1, the electron donor property of which is improved by an attachment of dimethylamino group. The photo-excited quartet high-spin state was observed by a time-resolved ESR experiment. CV measurement has clarified that the π-HOMO of the ground state is located higher ca. 0.35 eV in energy than 2 reported previously. These results show that the electron donor property is improved and the nature of the photo-excited spin alignment is conserved. Two CT complexes (1-TCNQ and 1-BQF₄) were synthesized using 1 as an electron donor. Their complexes have shown strong CT bands. The time-resolved ESR signal without the fine-structure splitting was observed for 1-TCNQ CT complex. The signal may arise from the photo-induced electron transfer from the quartet excited state of 1 to the TCNQ acceptor.     

Quantized Hamilton Dynamics

The paper describes the quantized Hamilton dynamics (QHD) approach that extends classical Hamiltonian dynamics and captures quantum effects, such as zero point energy, tunneling, decoherence, branching, and state-specific dynamics. The approximations are made by closures of the hierarchy of Heisenberg equations for quantum observables with the higher order observables decomposed into products of the lower order ones. The technique is applied to the vibrational energy exchange in a water molecule, the tunneling escape from a metastable state, the double-slit interference, the population transfer, dephasing and vibrational coherence transfer in a two-level system coupled to a phonon, and the scattering of a light particle off a surface phonon, where QHD is coupled to quantum mechanics in the Schrödinger representation. Generation of thermal ensembles in the extended space of QHD variables is discussed. QHD reduces to classical mechanics at the first order, closely resembles classical mechanics at the higher orders, and requires little computational effort, providing an efficient tool for treatment of the quantum effects in large systems.     

Organic polyanionic high-spin molecular clusters: topological-symmetry controlled models for organic ferromagnetic metals

Trianionic spin-quartet and tetraanionic spin-quintet molecular clusters derived from m-dibenzoylbenzene in solution were identified by CW-ESR/pulse-ESR based two-dimensional electron spin transient nutation spectroscopy, and their spin and clustering structures in the ground state were determined in terms of a D-tensor based phenomenological approach and DFT calculations. The molecular structures obtained semiempirically are supported by DFT-based quantum chemical calculations. The DFT calculations have been tested for a sodium ion bridged fluorenone-based cluster, [fluorenone(-)˙ {Na(+)(dme)(2)}](2), whose crystal structure was reported in the literature [H. Bock, H.-F. Herrmann, D. Fenske and H. Goesmann, Angew. Chem., Int. Ed. Engl., 1988, 27, 1067], reproducing the experimentally determined moelcular structure of the dimer cluster. It is suggested that both the quartet and quintet clusters in the 2-MTHF glass and solution form the cross-typed structures with the two m-dibenzoylbenzene moieties in cis-configuration. A dianionic spin-triplet m-dibenzoylbenzene derivative was detected for the first time and its charge and spin densities were studied by the quantum chemical calculations. The high-spin states of the open-shell entities under study were confirmed by X-band pulse-ESR based electron spin nutation spectroscopy in organic frozen glasses. The D values and other spin Hamiltonian parameters of all the polyanionic high-spin species were determined by the hybrid eigenfield spectral simulation for fine-structure ESR spectra. m-Dibenzoylbenzene provides pseudo-degenerate π-LUMOs arising from its topological symmetry of the π-electron network and its dianion in the triplet ground state is a prototypical model for topologically-controlled genuinely organic ferromagnetic metals.     

Three-pulse photon echo of an excitonic dimer modeled via Redfield theory

In this article the third-order response of an excitonically coupled dimer is studied. The three-pulse photon echo signals were calculated by extracting polarization components from the total polarization in the corresponding phase-matched directions. The total nonlinear response was obtained by numeric propagation of the density matrix, with the exciton-vibrational coupling modeled via Redfield relaxation theory. The full two-dimensional three-pulse photon echo signals and the peak shift were analyzed in terms of the density-matrix dynamics of coherence dephasing and population relaxation. The location of the two-exciton state was found to be essential for proper modeling of the three-pulse photon echo. In particular, an oscillation in the three-pulse photon echo peak shift is found if the two-exciton state is displaced. The oscillations can be related to the dynamics of the one-exciton coherences.     

Electronic structure of 1,3,5-triaminobenzene trication and related triradicals: doublet versus quartet ground state

Quantum chemical calculations have been carried out to determine the electronic ground state of the parent 1,3,5-triaminobenzene trication triradical (TAB3+,C6H9N3 3+) containing a six-membered benzene ring coupled with three exocyclic amino NH(*+)2 groups, each containing an unpaired electron, as the simplest model for high-spin polyarylamine polycations. Related triradicals, including the 1,3,5-trimethylenebenzene (TMB, C9H9) and its nitrogen derivatives such as the monocation C8H9N+, the dication C7H9N2 2+, and the neutral C8H8N, C7H7N2, and C6H6N3 systems containing NH groups, have also been considered. Results obtained using the CASSCF [multiconfigurational complete active space (SCF--self-consistent field)] method, with active spaces ranging from (9e/9o) to (15e/12o), followed by second-order perturbation theory [CASPT2 and MS-CASPT2 (MS--multistate)] with polarized 6-311G(d,p) and natural orbital (ANO-L) basis sets reveal the following: (i) both TAB3+ and TMB (D3h) have a quartet 4A"1 ground state with doublet-quartet 2B1-4A"1 energy gaps of 8.0+/-2.0 and 12.4+/-2.0 kcal/mol, respectively; (ii) in the neutral N series, the quartet state remains the electronic ground state, irrespective of the number of N atoms, but each with slightly reduced gap, 11 kcal/mol for C8H8N (4A"), 10 kcal/mol for C7H7N2 (4A2), and 9 kcal/mol for C6H6N3 (4A2); and (iii) the ground state of monoamino cation and diamino dication is a low-spin doublet state (2B1 for C8H9N+ and 2A2 for C7H9N2 2+) and lying well below the corresponding quartet state by 10 and 12 kcal/mol, respectively. In the monocationic and dicationic amino systems, a slight preference is found for the low-spin state, apparently violating Hund's rule. This effect is due to the splitting of the orbital energies and the presence of the positive charge whose delocalization strongly modifies the electronic distribution and some structural features. In the latter cations, the positive charge basically pushes unpaired electrons onto the ring forming a kind of distonic radical cations and thus gives a preference for a low-spin state.     

Adiabatic population transfer in a liquid: taking advantage of a decaying target state

The feasibility of efficient population transfer between an initial state and a decaying target state of the same parity without populating an intermediate state, in the presence of large-amplitude stochastic energy level fluctuations that mimic the dephasing in a solute molecule due to the influence of a solvent, is demonstrated theoretically. In particular, it is shown that a decaying target state, whose decay rate constant is large compared with the band width of picosecond laser pulses but small compared with the associated peak Rabi frequencies, can dramatically suppress the dephasing-induced nonadiabaticity associated with the dynamics of population transfer, resulting in, irrespective of the correlation time of stochastic energy level fluctuations, negligible population in the intermediate state and complete population transfer to the decaying target state. These results should further motivate experimental studies of optical control of molecular dynamics in a liquid. An interesting connection between our results and the quantum Zeno and anti-Zeno effects is also discussed.     

Light-induced electron spin polarization in vanadyl octaethylporphyrin: I. Characterization of the excited quartet state

Laser flash induced spin-polarized transient electron paramagnetic resonance (TREPR) spectra for vanadyl octaethylporphyrin in isotropic and partially ordered frozen solutions are presented and compared with corresponding luminescence data. The TREPR spectra show well-resolved hyperfine couplings to the vanadium nucleus and a multiplet polarization pattern with features typical of zero-field splitting (ZFS). The principal values of the vanadium hyperfine coupling tensor evaluated from the spectra are 1/3 of the corresponding values found from steady-state EPR spectra of the ground state. On the basis of these characteristics and numerical simulations, the polarization patterns are assigned to the excited quartet state. The values of the ZFS parameters of the trip-quartet obtained from simulation of the spectra (D = 17.5 mT and E = 1.5 mT) are comparable to those of the triplet state of the zinc and free base octaethyl porphyrin. The lifetime of the spin polarization is found to be temperature dependent and is essentially the same as that of the optical emission. The temperature dependence is rationalized using a model in which the decay to the ground state occurs from both the trip-quartet and trip-doublet, which are in thermal equilibrium even at 15 K. A fit of the model to the observed spin polarization lifetimes yields an energy gap of 47 cm(-1) between the trip-quartet and trip-doublet. It is shown that the spin polarization evolves from a multiplet pattern at early times to a net absorptive pattern at late times following the laser flash. It is proposed that the establishment of thermal equilibrium leads to the evolution of the spin from multiplet to net polarization.     

Electron spin polarization of functionalized fullerenes. Reversed quartet mechanism

Time-resolved electron paramagnetic resonance (TREPR) spectroscopy was used to study two functionalized fullerenes consisting of a C60 moiety covalently linked to TEMPO radical via spacers of different length. Photoinduced electron spin polarization (ESP) reflecting a non-Boltzmann population within the energy levels of the spin system was observed in the electronic ground and excited states. Both fullerenes are characterized by a sign inversion of their TREPR spectra. A new mechanism of ESP generation was suggested to explain the experimental results. This mechanism, termed as the reversed quartet mechanism (RQM), includes the intersystem crossing process, which generates ESP in the excited trip-doublet and trip-quartet (2T1 and 4T1) states. This ISC is accompanied by ESP transfer to the ground state (2S0) by either electron-transfer reaction (in our case via charge transfer state, 2CT, i.e., 2T1--> 2CT --> 2S0 or internal conversion, 2T1--> 2S0.     

Observation of a photoexcited state of a paramagnetic transition metal complex by time-resolved electron paramagnetic resonance spectroscopy

The first observation of a spin polarized excited state of a paramagnetic metal-complex using time-resolved electron paramagnetic resonance (TREPR) spectroscopy is reported for octaethylporphinatooxovanadium(iv). The TREPR spectra show well resolved orientation dependent hyperfine splitting to the I = 7/2 vanadium nucleus. The reduction of the hyperfine splitting by a factor of 3 compared to the ground state and the observation of a multiplet pattern of spin polarization allow the TREPR spectra to be assigned to the excited quartet state of the complex. The spin polarization patterns evolve with time and it is postulated that this is a result of the equilibration between the lowest excited quartet and doublet states.     

Solid-state NMR of a paramagnetic DIAD-FeII catalyst: sensitivity, resolution enhancement, and structure-based assignments

A general protocol for the structural characterization of paramagnetic molecular solids using solid-state NMR is provided and illustrated by the characterization of a high-spin Fe(II) catalyst precursor. We show how good NMR performance can be obtained on a molecular powder sample at natural abundance by using very fast (>30 kHz) magic angle spinning (MAS), even though the individual NMR resonances have highly anisotropic shifts and very short relaxation times. The results include the optimization of broadband heteronuclear (proton-carbon) recoupling sequences for polarization transfer; the observation of single or multiple quantum correlation spectra between coupled spins as a tool for removing the inhomogeneous bulk magnetic susceptibility (BMS) broadening; and the combination of NMR experiments and density functional theory calculations, to yield assignments.     

Resonance enhanced tunneling in an asymmetric double well potential: The 2B1Σ+ state of HCl

We investigate the exact quantum tunneling dynamics using a density matrix approach in the 2B¹Σ⁺ state of HCl which has recently been calculated to be an asymmetric double well potential. With the exact dynamics and a simple model of the collisional interaction process the transfer rate shows strong resonance enhancement for particular rotational states. The transmission coefficient approach, commonly used in tunneling calculations, shows no such features. This system suggests the possibility of the experimental observation of such rotationally induced tunneling resonances (perhaps in HCl in the gas phase). Although not strongly coupled to the environment itself the large resonance effects, caused by near degeneracies, in this system suggest that in treating systems which are strongly coupled to their environment (such as in the solid state) the exact quantum dynamics should be used rather than the transmission coefficient model.     

2,3,5,6-Tetrafluorophenylnitren-4-yl: electron paramagnetic resonance spectroscopic characterization of a quartet-ground-state nitreno radical

2,3,5,6-Tetrafluorophenylnitren-4-yl (5) was synthesized in argon at 4 K via the photolysis of 2,3,5,6-tetrafluoro-4-iodo-phenyl azide (6). Electron paramagnetic resonance (EPR) spectroscopy allows us to observe triradical 5 in its quartet state with the zero-field splitting (ZFS) parameters |D/hc| = 0.285 and |E/hc| = 0.043 cm-1. The quartet ground state of 5 is in accordance with our previous infrared (IR) spectroscopic investigation, in which the high-spin quartet state, but no low-spin doublet state, of 5 was observed in solid argon at 4 K [Wenk, H. H.; Sander, W. Angew. Chem., Int. Ed. 2002, 41, 2742-2745]. Because annealing of the matrix at temperatures of >10 K results in the rapid recombination of the highly reactive species 5 with I atoms produced during the photolysis of 6, the Curie-Weiss behavior could not be investigated. However, the absence of low-spin states in the IR investigations, as well as the results of ab initio and density functional theory (DFT) calculations, strongly suggest that 5 has a robust quartet ground state that is best-described as an unprecedented sigma,sigma,pi-triradical. The ZFS of 5 has been successfully reproduced by DFT calculations, which furthermore provide qualitative insight into the origin of the observed EPR parameters.     

Spin ground state and magnetic properties of cobalt(II): relativistic DFT calculations guided by EPR measurements of bis(2,4-acetylacetonate)cobalt(II)-based complexes

The spin ground state of the core ion and structure of the bis(2,4-acetylacetonate)cobalt(II) model complex and its synthetic aqua and ethanol derivatives, Co(acac)(2)L(n), (L = EtOH, H(2)O), were examined by means of density functional theory (DFT) calculations supported by electron paramagnetic resonance (EPR) measurements. Geometry optimizations were carried out for low-spin (doublet) and high-spin (quartet) states. For the Co(acac)(2) complex two possible conformations, a square-planar and a tetrahedral one, were taken into account. For all structures relative energies were calculated with both "pure" and hybrid functionals. The calculated data were complemented with the results of the EPR investigations carried out at liquid helium temperature, allowing for definite assignment of the high-spin state for the Co(acac)(2)(EtOH)(2) complex. However, because of the unresolved spectral features, only effective g-values could be assessed, whereas the zero-field splitting parameters (ZFS) were calculated by means of the spin-orbit mean field (SOMF) relativistic DFT method for which direct spin-spin (SS) and spin-orbit coupling (SOC) contributions were quantified.     

Driving force and electronic coupling effects on photoinduced electron transfer in a fullerene-based molecular triad

Tuning thermodynamic driving force and electronic coupling through structural modifications of a carotene (C) porphyrin (P) fullerene (C60) molecular triad has permitted control of five electron and energy transfer rate constants and two excited state lifetimes in order to prepare a high-energy charge-separated state by photoinduced electron transfer with a quantum yield of essentially unity (> or = 96%). Excitation of the porphyrin moiety of C-P-C60 is followed by a combination of photoinduced electron transfer to give C-P(.+)-C60.- and singlet-singlet energy transfer to yield C-P-1C60. The fullerene excited state accepts an electron from the porphyrin to also generate C-P(.+)-C60.-. Overall, this initial state is formed with a quantum yield of 0.97. Charge shift from the carotenoid to yield C(.+)-P-C60.- is at least 60 times faster than recombination of C-P(.+)-C60.-, leading to the overall quantum yield near unity for the final state. Formation of a similar charge-separate species from the zinc analog of the triad with a yield of 40% is also observed. Charge recombination of C(.+)-P-C60.- in 2-methyltetrahydrofuran yields the carotenoid triplet state, rather than the ground state. Comparison of the results for this triad with those for related triads with different structural features provides information concerning the effects of driving force and electronic coupling on each of the electron transfer steps.     

Design,synthesis and physical property of a π-conjugated photo-excited organic high-spin systems toward the functional material

In this paper, we report a design, synthesis and electronic state of a π-conjugated stable verdazyl radical, 1, which electron donor property is improved by an attachment of dimethylamino group. The photo-excited quartet high-spin state was observed by a time-resolved ESR experiment and CV measurement has clarified that the π-HOMO of the ground state is located higher ca. 0.1 eV in energy than 2 reported previously. These results show that the electron donor property is improved and the nature of the photo-excited high-spin state is conserved. In addition, A CT complex 1-BQF₄ was synthesized using 1 as an electron donor.     

The Kinetic Isotope Effect as a Probe of Spin Crossover in the CH Activation of Methane by the FeO+ Cation

Two‐state reactivity (TSR) is often used to explain the reaction of transition‐metal–oxo reagents in the bare form or in the complex form. The evidence of the TSR model typically comes from quantum‐mechanical calculations for energy profiles with a spin crossover in the rate‐limiting step. To prove the TSR concept, kinetic profiles for C? H activation by the FeO⁺ cation were explored. A direct dynamics approach was used to generate potential energy surfaces of the sextet and quartet H‐transfers and rate constants and kinetic isotope effects (KIEs) were calculated using variational transition‐state theory including multidimensional tunneling. The minimum energy crossing point with very large spin–orbit coupling matrix element was very close to the intrinsic reaction paths of both sextet and quartet H‐transfers. Excellent agreement with experiments were obtained when the sextet reactant and quartet transition state were used with a spin crossover, which strongly support the TSR model.     

Radical-Enhanced Intersystem Crossing in a Bay-Substituted Perylene Bisimide−TEMPO Dyad and the Electron Spin Polarization Dynamics upon Photoexcitation**

A 4-amino-2,2,6,6-tetramethyl-1-piperidinyloxyl (TEMPO) radical was attached to the bay position of perylene-3,4 : 9,10-bis(dicarboximide) (perylenebisimide, PBI) to study the radical-enhanced intersystem crossing (REISC) and electron spin dynamics of the photo-induced high-spin states. The dyads give strong visible light absorption (ϵ=27000 M⁻¹ cm⁻¹at 607 nm). Attaching a TEMPO radical to the PBI unit transforms the otherwise non-radiative decay of S₁ state (fluorescence quantum yield: Φ_F=2.9 %) of PBI unit to ISC (singlet oxygen quantum yield: Φ_Δ=31.8 %, Φ_F=1.6 %). Moreover, the REISC is more efficient as compared to the heavy atom effect-induced ISC (Φ_Δ=17.8 % for 1,8-dibromoPBI). For the dyad, ISC takes 245 ps and triplet state lifetime is 1.5 μs, much shorter than the native PBI (τ_T=126.6 μs). X- and Q-band time-resolved electron paramagnetic resonance spectroscopy shows that the exchange interaction in the photoexcited radical-chromophore dyad is larger than the triplet zero-field splitting (ZFS) and the difference of Zeeman energies of the radical and chromophore. The inversion of electron spin polarization from emissive to absorptive was observed and attributed to the initial completion of the quartet state population and the subsequent depopulation processes induced by the zero-field splitting.