Time-Resolved Electron Paramagnetic Resonance Study of Rhodium(III)

J. Phys. Chem. A 2010, 114, 2059–2072

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Time-Resolved Electron Paramagnetic Resonance Study of Rhodium(III) Corrole Excited States Linn Wagnert,† Alexander Berg,† Irena Saltsman,‡ Zeev Gross,‡ and Vladimir Rozenshtein*,† Department of Physical Chemistry, The Hebrew UniVersity of Jerusalem, Jerusalem 91904, Israel, and Schulich Faculty of Chemistry, Technion - Israel Institute of Technology, Haifa 32000, Israel ReceiVed: October 18, 2009; ReVised Manuscript ReceiVed: December 8, 2009

Photoexcited states of three Rh(III) 5,10,15-tris(pentafluorophenyl)corroles coordinated by different axial ligands; namely, triphenylphosphine P(C6H5)3 group (1), pyridine C6H5N group (2), and two pyridine groups (3) were studied by X- and Q-band time-resolved electron paramagnetic resonance (TREPR) in frozen toluene and liquid crystal E-7. Transient mutations were utilized to identify multiplicity of the detected paramagnetic species. The spectra of 1 and 2 were assigned to triplet (3ππ*) states, while contributions of triplet (3dd and charge transfer 3CT) and quintet (5dd) states were revealed in the spectrum of 3. The results are interpreted in terms of a peculiar nature of transition metal complexes with the unfilled d-shell, where close lying electronic states of different multiplicities may be mixed through configurational, spin-orbit, and vibronic coupling. From the EPR spectra, the spin-orbit coupling constant was estimated to be about 25 cm-1. It is shown that different axial ligation of complexes shifts the relative energy of the excited states and, consequently, leads to population of different states. Plausible explanations of the effects governing unusual spectral and dynamic parameters of the photoexcited Rh corrole complexes are presented. Introduction

Experimental Section

A general characteristic feature and a distinguishing mark of the transition metal complexes is the existence of a substantial number of electronic states of a relatively low energy. The configurational mixing between them, together with the spin-orbit (SO) and vibronic couplings, results in a distortion of the electronic potentials in terms of the energy difference and the electronic coupling matrix elements. In turn, this results in a complicated overall spectral picture, and in a nontrivial dynamic behavior.1–4 The lowest electronic excited states of the transitionmetal complexes with the unfilled d-shell (especially with a d6 configuration) can have various origins (ππ*, dπ*, πd, or dd). Furthermore, by a proper choice of metal ion, chelating macrocycle, and axial ligands, a nature of the excited states can be stipulated.2

Three Rh(tpfc) (1, 2, and 3) coordinated by different axial ligands (AL) were synthesized as described elsewhere (cf. Chart 1).6,7 The X-ray structures of 1 and 3 can be found in literature.6,7 The Rh complexes were dissolved in toluene and liquid crystal E-7. In both cases, concentration of Rh(tpfc) was 5 × 10-4-10-3 M. Toluene (Merck Ltd.) was dried over molecular sieves and kept under vacuum during sample preparation. LC was used without further purification.8–11 In this report, we will reason that the LC solid solvent between 30 and 211 K represents a glassy phase, as it is generally accepted.12,13 E-7 has a positive magnetic anisotropy ∆χ and in the nematic phase forms the monodomain uniaxial anisotropic medium under exposure to a strong magnetic field. Such orientation is conserved upon freezing to solid phase. In the case of LC, the corroles were first dissolved in toluene, then toluene was evaporated, and LC was introduced into the sample tube. The samples were degassed by several freeze-pump-thaw cycles on vacuum line and sealed under vacuum. The LC molecules were aligned at room temperature along the magnetic field in the electron paramagnetic resonance (EPR) cavity by applying a strong field of 1.5 T, and then the sample was cooled down to the required temperature. This orientation was used to record the timeresolved EPR (TREPR) spectra when the LC director (L) was parallel to the magnetic field B (the L|B orientation). The spectra with the director being perpendicular to the magnetic field were taken after rotating the cooled sample by 90° about the axis perpendicular to B inside the cavity (the L⊥B orientation). The TREPR measurements were performed by using the Q-band (∼34.1 GHz) microwave bridge (Bruker ER 050 QGT) with the integrated broadband amplifier (0-200 MHz) in combination with the Bruker ESP 300E console. The quartz sample tube (inside diameter of 0.2 cm) was placed in the cylindrical EPR cavity (the effective volume VC ≈ 0.55 cm3) with the Q-factor of the loaded resonator, Q, approximately

Recently, the photoexcited triplet states of two 5,10,15tris(pentafluorophenyl)corroles (tpfc), hosting Rh(III) in their core, namely, Rh(pyr)(PPh3)(tpfc) (1) and Rh(PPh3)(tpfc) (2), where pyr and PPh3 (tpp) denote the pyridine C6H5N and the triphenylphosphine P(C6H5)3 ligands, respectively, have been detected and studied in the liquid crystal (LC) matrix.5 In this work, we present new results on 1 and 2 and also report on the detection of the quintet excited state upon photoexcitation of Rh(pyr)2(tpfc) (3). The complexes were dissolved in either toluene or LC. The corrole complexes 1-3 are shown in Chart 1. With the intention of seeking a unified explanation of the processes occurring within the excited states of the transition metal-corrole complexes, we analyze both the experimental data obtained in this work and those presented in part recently.5 * To whom correspondence should be addressed. E-mail: roz@ chem.ch.huji.ac.il. † The Hebrew University of Jerusalem. ‡ Technion - Israel Institute of Technology.

10.1021/jp909967b  2010 American Chemical Society Published on Web 01/13/2010

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CHART 1: Molecular Structures of Rh(tpfc) (1, 2, and 3) Coordinated by Different Axial Ligands: by One Triphenylphosphine (tpp) P(C6H5)3 group (1), by One P(C6H5)3 and One Pyridine (pyr) C6H5N Ligand (2), and by Two Pyridine Ligands (3)

equal to 700 (the bandwidth of 50 MHz). EPR spectrometer was combined with the OPO system (OPTA GmbH), pumped by the Nd:YAG laser (Spectra Physics Quanta Ray GCR 190-10). Laser light pulses were of 2.5 ns duration, 3 mJ energy, and 10 Hz repetition rate. The spot of the laser beam was reduced to 0.2 × 0.3 cm2 by means of cylindrical long focal lens. To avoid photoselection, the laser beam was passed through the quartz depolarizer. The TREPR signal was acquired by the transient recorder LeCroy 9354A. The overall response time of the setup was measured to be 20 ns. Most TREPR experiments were carried out at 30-100 K. Some measurements were performed at higher temperatures (up to 300 K). Sample temperature was controlled by the helium flow cryostat (Oxford CF-935) within ( 0.2 K. Detailed descriptions of the TREPR method and the apparatus were done elsewhere.14,15 Results 1. TREPR Spectra. TREPR measurements were carried out within a temperature range of 30-300 K. For an exception of experiments performed at room temperature when LC was in the nematic phase, all other studies were carried out at temperatures when samples were solid. For LC at high temperature, weak spectra were observed for 2 and 3 only. Between 30 and 170 K, for toluene we observed the TREPR spectra of 2 and 3 and did not detect the TREPR signal of 1, whereas for LC the TREPR spectra of all three complexes were obtained. Even though we succeeded to establish an overdamping regime of the detection for higher temperatures of 100-170 K only and could not obtain this linear regime at low temperature of 30 K, the TREPR spectra were found to be very similar for every complex under study within the whole temperature region (30-170 K). On the other hand, the spectra of the different complexes obtained for the identical conditions (the same temperature, concentration of Rh(tpfc), solvent, delay time

between the laser pulse and the detection gate, orientation of L with respect to the external magnetic field B) were found to be qualitatively different. The representative TREPR spectra (100 K) detected at 150-160 ns after the photoexcitation are shown in parts a-c of Figure 1. It is obvious that both the spectral and the polarization (the emission mode vs the absorption mode) patterns strongly depend on the axial ligation. It is worth noting that the spectra of 1 and 2 do not strongly differ from one another. For LC, between 1100 and 1300 mT, they have the same emission/absorption (e/a) pattern if L|B (the parallel orientation of the sample, the PAR spectra) and the reversed a/e polarization if L⊥B (the perpendicular orientation of the sample, the PER spectra). In addition, the PAR spectrum of 1 shows a narrower (the peak-to-peak width ∆Bpp ≈ 40 mT) weak e/a signal, which is overlapped with a wider (∆Bpp ≈ 100 mT) and stronger main spectrum. 2. Transient Nutations. The transient nutation experiments were carried out to identify species responsible for the observed strongly overlapped TREPR spectra (cf. parts a-c of Figures 2).14–20 In distinction to the classical Torrey’s nutation experiments,21 where a spin magnetization is rapidly affected by the microwave (MW) radiation, in our case, the same initial situation is achieved under a permanent MW field when the laser pulse and the following fast processes steeply creates the metastable species with spin S > 0 within the EPR cavity.16 The underdamping regime, where an oscillatory TREPR signal can be observed, manifests itself when 4ω12 > (T1-1 - T2-1)2, where T1 and T2 are the longitudinal (the population) and the transverse (the phase) relaxation times, respectively, ω1 ) (gβB/p)B1 is the Rabi frequency, g is the g-factor, and B1 is the amplitude of the magnetic component of the circularly polarized MW field directed perpendicular to the static magnetic field B. In our case where the inhomogeneous broadening is large compared to the Rabi frequency, the time-dependent EPR signal, S(t), is pro-

EPR Study of Rhodium(III) Corrole Excited States

J. Phys. Chem. A, Vol. 114, No. 5, 2010 2061

Figure 1. TREPR spectra (χ′′(B) presentation) of Rh(tpfc) complexes embedded in the liquid crystal E-7 and toluene: (a) Rh(PPh3)(tpfc) (1), (b) Rh(PPh3)(pyr)(tpfc) (2), and (c) Rh(pyr)2(tpfc) (3) all taken 150-160 ns after the laser pulse (596 nm) at 100 K by Q-band EPR and (d) Ga(pyr)(tpfc) (4) recorded 1 µs after the laser pulse (590 nm) at 175 K by X-band EPR. Blue color relates to spectra obtained at long delay time of 7 µs.

portional to J0(ωNt)exp[-(t/2T1)] (J0(ωNt) ∝ (1/ωNt)1/2 sin(ωNt), if as in our experiments ωNt . 1),22 where ωN is the nutation frequency and J0(ωNt) is the zero-order Bessel function.17 Thus, decay of the nutations in the inhomogeneously broadened spin systems occurs both due to a relaxation to the other electronic states (like in the homogeneously broadened systems, and the term exp[-(t/2T1)] is responsible for this channel) and due to a redistribution between the spin packets formed the line shape (the Bessel function describes this process). For our case of the sudden excitation, neglecting the slow decay term (ωNt)-1/2, we can describe transients as S(t) ∝ exp[-(t/2T1)] sin(ωNt)u(t), where u(t) is the step function. In our case of a weak MW field (where the zero field splitting (ZFS) interaction, HZFS, is much larger than the interaction with the MW field, HMW (2gβBB1S)), only transitions |S,mS〉 T |S,mS - 1〉 are allowed, and thus, the nutation frequencies are defined by the following expression19 1

ω ) [S(S + 1) - mS(mS - 1)] /2ω1

The nutation experiments were carried out with B1 ) 0.025 mT. As examples, three oscillatory TREPR transients together with their Fourier transforms (in the insets) are presented in Figure 2. The curves in the insets represent the energy spectral density Φ(ω/2π) of the time-dependent signal S(t). Here Φ(ω) 2 ) (2π)-1F(ω)F*(ω) ) |(2π)-1∫+∞ -∞S(t)exp(-iωt)dt| , where F(ω) and F*(ω) are the continuous Fourier transform of S(t) and its complex conjugate, respectively. For the independent calibration, we recorded the nutation pattern for the photoinduced triplet state of H2TPP and obtained that ωNH2TPP/2π ≈ 1 MHz. This means that ω1/2π ≈ 0.707 MHz. 3. Kinetic Dependences. We endeavored to get the kinetic dependences under an overdamping regime (ω12T1T2 , 1), i.e., when nutations are absent, and thus, the TREPR signal can be expressed as follows

S(t) ∝ MZ(0)ω1f(ωMW)exp(- t/T1)

(2)

(1)

In the strict sense, eq 1 holds good for the homogeneous broadening. However, it was established that, though different spin packets of the inhomogeneous broadened system have different magnitudes of a detuning from the resonance (δ) and, thus, their nutation frequencies differ from one another ([δ2 + ωN2]1/2), upon summation the resulting nutation frequency remains virtually the same (ωN) and eq 1 can be used as it is used for the resonance conditions.20

where MZ(0) is the initial magnetization, f(ωMW) is the line shape function, and ωMW is the frequency of the MW field.17 In such a case, the population relaxation time T1 determines dynamic behavior, contrary to the case of nutation where decay is determined by T2. To find an overdamping regime, we varied the MW power in the range 1-100 mW. At 100 K and higher, saturation effects were absent up to 100 mW and the TREPR spectra obtained for different MW powers exactly match each other, while at the low temperature of 30 K the feeble wiggles were observed even for low MW power. Thus, the most reliable

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Figure 3. The absorption spectrum of Rh(PPh3)(pyr)(tpfc) (2).

Figure 2. Oscillatory TREPR transients together with their Fourier transforms (in insets) of complex 3, taken at 30 K: (a) L⊥B, 1190 mT; (b) L|B, 1242 mT; (c) L⊥B, 1202 mT.

information was extracted from spectral and kinetic data obtained at 100 K. Discussion 1. General. Molecular properties of metallocomplexes, such as energies and lifetimes of the excited states, are dependent upon their electronic structure, which modification brought about by a lot of factors such as the nature of the central ion, the symmetry of the chelating macrocycle, a π-π interaction (back bonding), aggregation, a Jahn-Teller effect, axial ligation, etc. Two immediate general conclusions can be made even from a cursory comparing the presented experimental results (parts a-c of Figures 1) with the results obtained for the free-base corroles (H3(tpfc)) and the non-transition-metal corroles, like Ga(tpfc) and Sn(tpfc).23,24 The TREPR spectrum of Ga(pyr)(tpfc) (4) is shown in Figure 1d.23 First, the asymmetric TREPR spectra of Rh(III)(tpfc) are qualitatively different of the symmetric spectra obtained for Ga(tpfc), H3(tpfc), and Sn(tpfc) (the spectra of H3(tpfc) and Sn(tpfc) are not shown). Second, for the three Rh(III)(tpfc) complexes under study the spectral lineshapes, the spin polarization patterns, and the dynamic parameters depend crucially on axial ligands. Thus, mechanistic models, which we develop in this work to explain our observations, should be based on approaches where effects of the axial ligands and the

d-electrons of Rh(III) on the electronic properties of the complexes are essential. A major question is the relation between the metal d, the corrole π, and the axial ligand πa and na electrons. In particular, what are the relative energetic positions of the excited states of different nature, namely, the dd states (also known as the ligand field, LF, or the metal centered, MC, states), the dπ* states (the metal-to-ligand charge transfer, MLCT, states), the πd states (the ligand-to-metal charge transfer, LMCT, states), the ππ* states (the corrole centered, CC, states), the πaπa* and naπa* states (the axial ligand centered, ALC, states), the naπ* and πaπ* states (the axial-ligand-to-ligand charge transfer, ALLCT, states), the nad and πad states (the axialligand-to-metal charge transfer, ALMCT, states), etc. The spin-orbit coupling (SOC) constant of Rh(III) ion is large, namely, λRh ≈ 1200 cm-1.25 This fact leads to several general conclusions about the TREPR spectral patterns and the rates of relaxation processes. First, anisotropy of g values is expected to be large, thus, resulting in asymmetry of the EPR spectra. Second, the intersystem crossing (ISC) and the energy transfer (EnT) radiationless processes occurring with a change of multiplicity must be fast. Third, radiation transitions between states of different multiplicity may be rather intensive. Both axial ligands used in this work, pyr and tpp, are the Lewis bases. They incorporate the aromatic rings, but the lone pairs of electrons of the N or P atom are not a part of these aromatic systems and extend out of the ring. According to the simplified ligand field model, such ligands donate a pair of their lone electrons to the central Rh(III) ion resulting in the coordinate covalent bond, which once formed is no different from a regular covalent bond. As to the corrole ring, it represents the aromatic polypyrrolic macrocycle. Every one of its pyrrole groups themselves are the nonbasic rings where the lone pairs of electrons of the imine nitrogen atoms are delocalized over the pyrrole ring and thus also over the whole macrocycle π-system. In metal complexes, pyrrole loses a hydrogen atom, and this deprotonation is responsible for the negative charge of the corrole macrocycle. A corresponding electrostatic attraction of the negatively charged ring with the metal cation makes main contribution to the metal-corrole bonding. The different nature of the macrocycle-metal and the axial ligand-metal interactions should receive primary emphasis, while considering strong ligation effects in the Rh(III)(tpfc) complexes. It is mportant to outline again that the many characteristics of the transition metal complexes are related to the fact that a lot of electronic states cover a relatively narrow energy range. 2. Photoexcitation. 2.1. Single Color Excitation. The UV-visible spectrum of 2 is shown in Figure 3. The spectral

EPR Study of Rhodium(III) Corrole Excited States patterns of 1 and 3 (not shown) were the same as those of 2. The spectral locations of the band peaks were found to be very close for all three complexes: their difference is within several nanometers. The relative intensities and the widths of the bands are also very similar for the different rhodium corroles under study. In the 300-1000 nm range, we observed bands with the following maxima ((3 nm): 315, 380, 410, 445, 515, 555, and 595 nm. In the 400-600 nm spectral range, very similar spectra have been observed earlier both for the free-base corroles and for the Cu, Ni, Mn, Fe, Mo, and Co corroles.26–30 This fact points out that the above-mentioned visible and UV spectra result mainly from the electronic transitions within the corrole macrocycle. The LF and the CT transitions may contribute, if any, only to the background absorption in this spectral range. It is noteworthy that the metallocorrole spectra are not perceptibly different from those of the metalloporphyrins.31 By analogy with metalloporphyrin complexes, we will refer the absorption bands of corroles lying in the visible 500-nm region to the Q bands and those lying in the near-UV 400-nm region to the Soret bands (B bands). Spectral features located in the 300-nm region can be assigned to both the N bands and the LMCT and MLCT bands.32 The main distinction from the porphyrin spectra is that the corrole spectral lines split as compare to the porphyrin ones. The reason is that the electronic transitions for corroles, possessing C2V symmetry, are no longer degenerate, by contrast with porphyrins, possessing D4h symmetry. In case of the metallocorroles like for the metalloporphyrins, the Q and Soret transitions are the ππ* transitions, i.e., they mostly correspond to the electrons of the aromatic pyrrolic ring. The Hartree-Fock self-consistent field (HFSCF) molecular orbital (MO) calculations taking into account configuration interactions between 20 singly excited configurations of the corrole ring showed that, in corroles similarly to porphyrins, both the Q and Soret bands stem from transitions between four MOs only (cf. Figure 4): two highest-occupied molecular orbitals (HOMOs), 6a2 and 7b1, and two lowest-unoccupied molecular orbitals (LUMOs), 7a2 and 8b1 (which replace 3a2u and 1a1u and the pair of degenerate 4eg orbitals, respectively, for porphyrins).26,33 As a result of lifting degeneracy, the Q band splits into two Q bands, which are consistent with the S1 r S0 and S2 r S0 electronic transitions shown in the energy scheme of Figure 5 (Supporting Information). According to the above-mentioned HFSCF calculations, the Q bands are associated mainly with the following transitions between the MOs: the first Q band is due to 8b1 r 6a2 and 7a2 r 7b1 (the former transition prevails with a contribution of 90%), and the second Q band is due to 7a2 r 6a2 and 8b1 r 7b1 (the contribution of the first transition is 70%).26 In frameworks of the above model, two low-energy lines (595 and 555 nm in our case of Rh(III)(tpfc)) can be assigned to the 0-0 and 0-1 vibrational components of the first Q-band, i.e., to the S1 r S0 electronic transition. Further, the 515-nm line is considered to be due to the 0-0 component of the second Q band (the 0-1 component, likely, is buried into the Soret band). The lines lying near 400 nm, apparently, belong to the first and second Soret bands, and spectra at 300 nm relate to the N bands and may be to the transitions with a participation of the central ion. The lack of pronounced absorption peaks in the 300-nm region for the free-base corroles, with different peripheral meso substituents, argues for the CT character of the analogous bands of Rh(III)(tpfc).27,34 The density functional theory (DFT) calculations, carried out for a prototype non-transition-metal corrole (Ga(tpfc)), confirmed that the four-orbital model holds well for corroles.35 However, the lowest excited singlet states, S1 and S2, were found in this study to be very close to each


Figure 4. Orbital correlation diagram of Rh(tpfc) complexes.

other with an energy difference of only 0.02 eV, which is consistent with ca.10 nm between lines and that, in turn, results in unresolved bands. In addition, it was shown that both transitions between the MOs proceed with the almost equal probabilities. In such a case, three low-energy lines (595, 555, and 515 nm) can be assigned to the 0-0, 0-1, and 0-2 vibronic components of both first and second Q-bands.36 We consider this latter representation as the most reliable one. In our experiments, the Rh(III)(tpfc) complexes were excited by light of the wavelengths corresponding to their Q band (590 nm for 1, 596 nm for 2, and 580 nm for 3). As was discussed above, it means that one generates S1(ππ*) alone or both S1(ππ*) and S2(ππ*) excited states, each of which represents a mixture of two MOs of a2 and b1 symmetry (cf. Figures 4 and 5). The extinction coefficient (ε) of the different metallocorrole complexes in the region of the 590 nm band was found to be, on the average, 2 × 104 M-1 cm-1 and, thus, the corresponding cross section (σ) to be 3 × 10-17 cm2.7,30,35,37 In fact, the absorption ability of the Rh(III) corrole complexes strongly depends on the axial ligands. We found, particularly, that at room temperature for complexes dissolved in dichloromethane the extinction coefficient ε ) 0.7 × 104 M-1 cm-1 (590 nm) for 1, ε ) 3.4 × 104 M-1 cm-1 (596 nm) for 2, and ε ) 5.0 × 104 M-1 cm-1 (580 nm) for 3. Earlier, it was found that ε ) 5.3 × 104 M-1 cm-1 (at 589 nm) for 1 and ε ) 1.7 × 104 M-1 cm-1 (at 593 nm) for the five-coordinated complex with the single chiral amine as a ligand. Similar results concerning the effect of axial ligands were reported for the Soret bands.7 Such observations indicate that axial ligation results in the radical alterations in distribution of electrons throughout the Rh corrole system.

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Figure 5. Energy state scheme of Rh(tpfc) complexes.

For the energy density of the laser radiation of 40 mJ/cm2 coming to the EPR sample and the duration of the laser pulse (τP) of 2.5 ns, the photon flow (I) in our experiments may be as much as 4 × 1025 cm-2 s-1. As a result, the rate of the light absorption, kA (σI), is estimated to be 109 s-1 for the absorption cross section σ ) 3 × 10-17 cm2. On the reasonable assumption that the rate of ISC to the triplet state within the corrole π system is comparable with, or larger than, the rate of the light absorption and that a decay of the triplet state is slower than the above ISC process, we obtain that an initial population of the excited triplet state (or states) comprises as high as 95% of the initial concentration of the complexes, i.e., ∼10-3 M. The photoinduced metal-centered d-d transitions can be excluded due to a high ligand field strength of the Rh complexes and because they are orbitally forbidden by the Laporte parity selection rule (which is somewhat violated since a center of symmetry is vanished for corroles). 2.2. Double-Color Excitation. The fact that a large excitedstate population is induced by the single photon absorption of the laser radiation (which we term as a “single-color” excitation) offers a further development. Namely, in our case, the energy of a photoexited state may considerably exceed that of the single photon. This may occur as a result of the successive absorption of two (or even more) photons during the laser pulse. Since the population of first excited triplet state, formed during the initial phase of the laser pulse via the fast ISC processes, appears to be comparable with the initial ground-state concentration, the secondary photoexcitation of lower triplet states to higher ones (3Tn) are made possible within the same laser pulse. This resembles a ‘two-color” excitation by the simultaneous sample irradiation with two laser pulses of different wavelengths and, thus, can be called the “double-color” excitation.38–42 In this manner, the excited states of the energy, as high as 30000 cm-1, become attainable with a population measuring tens of percents of the initial concentration (Supporting Information). Regarding the above model, we have to assume that the electronic terms of higher triplet states are shifted relatively to that of 3T1, and

as a result, a number of the vibronic states of 3Tn can be excited in accordance with the Franck-Condon principle, thus forming broad triplet-triplet absorption bands. This assures the absorption of the second photon of the same energy as first one. Apparently, this energy is larger than the energy gap between the vibrationally unexcited 3T1 and 3Tn states. We also emphasize that only if the reciprocal rates of the radiationless energy transfer from 3Tn to some metastable states Tf (which can represent the CT, LF, or ALC states of the triplet or quintet origin; see below) are shorter than or comparable with the laser pulse, one can expect observing (e.g., by EPR) such extraenergetic species after the laser pulse. In the opposite case, upon terminating the laser pulse the 3Tn states will promptly relax via fast internal conversion (IC) to 3T1. The “final” states, i.e., those surviving through the laser pulse, lose a bit of their energy in a picoseconds time scale via the vibrational relaxation. It is important to outline that the above analysis was carried out for the averaged value of the extinction coefficient. In fact, as it was shown above, the absorption ability of the Rh(III)(tpfc) complexes strongly depends on their axial ligands. Thus, on the basis of the above quantitative data, we can expect that if the double color excitation actually occurs in the systems under study its efficiency has to be very different for the different cases of a ligation. Namely, a large effect is expected for 3 and a minor one, if any, for 1. This is true, however, only if the axial ligands affect the rates of the light absorption from the ground and triplet states in a similar way. The double-color absorption may also result in a direct photoexcitation of the CT states. In such a case, initially, as before, the 3T1(ππ*) state is populated, and then the photoinduced ET from the 3T1(ππ*) state results in a formation of the 3 LMCT state. 3. Transient Nutations: Multiplicity of Excited States. A qualitative answer about the nature of the detected excited states and their spectroscopic transitions can be obtained from the nutation experiments that are sensitive to the spin of the detected state and the spin projections characterized the Zeeman sublevels



participated in the transition (eq 1). In this paragraph, we present a qualitative explanation of the transient nutation experiments (cf. Figure 2). By utilization of eq 1, one obtains that for the doublet species the nutation frequency corresponding to the only |1/2, -1/2〉 T |1/2, 1/2〉 transition is ωND ) ω1. Both |1, 0〉 T |1, 1〉 and |1, -1〉 T |1, 0〉 transitions of the triplet species display the same nutation frequency, namely, ωNT ) 2ω1. For the quintet species, the nutation frequency of the |2, 1〉 T |2, 2〉 and |2, -2〉 T |2, -1〉 transitions is ωNQ1 ) 2ω1, and for the |2, 0〉 T |2, 1〉 and |2, -1〉 T |2, 0〉 transitions it is ωNQ2 ) 6ω1. Actually, the above values are valid for a strongly underdamping regime, where ω12 . (2T1)-2, i.e., provided T1 is in the microsecond region. Inspection of Figure 2 shows that such a condition is satisfied for cases (a) and (b) with characteristic decay times of 2 µs but not for case (c), where the signal decays by an order of magnitude faster. For the latter case, the transient kinetic curve can be presented as (see above)

S(t) ∝ exp[-(t/2T1)] sin(ωNt)u(t)

(3)

Its Fourier transform (FT) is

F(ω) )

ωN

/[(a

2] + iω)2+ωN

(4)

where a ) (2T1)-1 is the parameter defining a shift of the resonance frequency from the underdamping value ωN. Such shifted frequency corresponds to the maximum of the power spectrum Φ(ω) ) (2π)-1F(ω)F*(ω) and is expressed as 1

ωNS ) [ωN2 - a2] /2

(5)

For all three corroles (1, 2, and 3) at 30 K, we succeeded in obtaining the nutation transients recorded for the magnetic fields related to the different peaks in the TREPR spectra. In cases of 1 and 2, both for the PAR and PER spectra and for various magnetic fields (1154, 1270, 1200, 1230, and 1293 mT), FT was found to have only one maximum corresponding to ωNS/ 2π ) ωNH2TPP/2π ) 1 MHz (see also ref 5). In the case of 3, for the PAR spectrum (1190 and 1242 mT) and for the outmost lines of the PER spectrum (1190 and 1250 mT), FTs are also characterized by the single frequency, approximately equal to 1 MHz. For the other two lines of the PER spectrum (1202-1210 and 1220 mT), Φ(ω) possesses several maxima. Figure 2c (the PER spectrum, 1202 mT) shows two prominent (ωNS(1)/2π ) 0.8 and ωNS(2)/2π ) 1.2 MHz) and one feeble (ωNS(3)/2π ) 1.65 MHz) maxima. We assume that the single-peak FTs (parts a and b of Figure 2), characterized by ωNS/2π ) 1 MHz, evolve, essentially, due to the 3ππ* state,5 while the three-peak FTs (Figure 2c) arise mainly due to both the 3dd (or the charge transfer 3πd and/or 3 dπ* state) and 5dd states or due to the 5dd state only. A feasibility of the excited dd and CT states appearance will be justified below in this paper. We also expect that the relaxation times of the ππ* states are much longer than those of the dd states, T1(ππ*) . T1(dd). Inspection of the transient kinetics in Figure 2 confirms such an assumption: the decay times are of 2 µs (a and b) and 0.2 µs (c). T1(ππ*) ≈ 2 µs corresponds to a magnitude of a (1/2T1 ) 2.5 × 105 rad/s) , ωNS (6 × 106 rad/s), and thus, according to eq 5 the resonance frequency remains practically unaltered, ωNS ≈ ωN (cf. parts a and b of Figure 2).

In case of the relatively strong damping regime (Figure 2c), to obtain agreement with the experimentally observed shifted frequencies ωNS(1)/2π ) 0.8, ωNS(2)/2π ) 1.2, and ωNS(3)/2π ) 1.65 MHz) one needs to substitute the underdamping frequency (ωNT/2π ) 2ω1/2π ) 1 MHz, ωNQ1 ) 2ω1/2π ) 1.41 MHz and ωNQ2 ) 6ω1) 1.73 MHz) and the value of a/2π equal (0.6 ( 0.15) MHz into eq 5. The latter corresponds to a value of T1 equal to 0.1-0.2 µs, which is in line with the observed kinetics (Figure 2c). In summary of this section, we managed to develop a self-consistent description of the EPR transient nutations related to the triplet and the quintet states of the Rh(tpfc) complexes. 4. Energy of Excited States and Intramolecular Energy Transfer. For justification of the above identification of the detected excited states, we need to estimate the energies of these states and to find the reasonable routes of the energy transfer between them. It was highlighted above that the absorption visible-range spectra of the all corrole complexes, studied both in this work and earlier, are characterized by the same features and can be assigned to the ππ* transitions, i.e., to the transitions within corrole macrocycle, regardless of the central ion and the axial ligands. This fact indicates that, from the point of view of energy, a transition-metal corrole complex may be considered, to the first approximation, as one involving several quasiindependent subsystems, namely, the CC π-system of the corrole ring, the MC d-system of the metal ion, and the ALC p(π)system(s) and the lone pair system(s) of the axial ligand(s). As it follows from the inspection of the X-ray structures,6,7 the corresponding constituents of the complex are separated in space by an estimated 2 Å. Figures 4 and 5 show qualitative energetic diagrams of Rh(tpfc) systems: (a) the orbital correlation diagram and (b) the energy state scheme plotted vs an effective coordinate Q.43 In our analysis, we have to keep in mind that, although both diagrams described the same system, the orbitals represent the one-electron wave functions (their eigenvalues shown in Figure 4), and thus, for the many-electron systems we study, the electron repulsion is not allowed, while the energy terms shown in Figure 5 relate to the many-electron wave functions and take into account the interelectron interactions (the configuration interaction, CI) as well. Generation of a CT state corresponds to a transition between orbitals that are centered on the different moieties. Among the organometallic complexes, the complexes with the d6 configuration demonstrate their ability to form the low-lying CT states. However, since we cannot estimate the energies of the CT states, they are not shown in Figure 5. For the noncrystalline and semicrystalline media, the distribution of the energy states does not differ considerably from the corresponding distribution in crystal.44 With this concept, the conduction band is shown in Figure 5. An electron may be promoted to the conduction band or to the “localized” states, located below the conduction band, due to autoionization from both the π and the d orbitals immersed into these bonds. Such high π orbitals are populated due to the double (or triple) color excitation, while the high d orbitals are formed as a result of the energy transfer from the high π orbitals. The energies of orbitals and states shown in Figures 4 and 5 were calculated by the methods presented in Supporting Information. The primary photoexcited singlet states relax via a series of charge transfer and energy transfer processes. The intramolecular CT and EnT can occur between the different quasi-independent moieties: the corrole macrocycle, the Rh ion, and the axial ligands. These processes take place in parallel to the IC and

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ISC deactivation processes occurring within every moiety. Hereby, the corrole ring is shown to be a chromophore absorbing the 590-nm light. We consider both the triplet-triplet and the singlet-triplet EnT to be operative. It is important to realize that, in case of the Rh complexes, the heavy atom effect enhances, by a large SO coupling, a formally spin-forbidden S-T process, such as ISC within the corrole macrocycle and EnT from the excited singlet state of the corrole to the triplet MC and ALC states.45,46 Actually, these channels become practically allowed. Out of two major mechanisms of EnT, namely, the dipole-dipole (Forster) and the electron exchange (Dexter) mechanism, we dwell on the latter since it predominates at shorter distances typical for our complexes.47–49 Moreover, in the triplet excited systems, the Dexter mechanism is the only possible one.50 For ET and for EnT of the Dexter type, it is the orbital overlap together with the energy and the symmetry matching of the initial and final vibronic levels that determines the ET or EnT rate. If the electron of the corrole macrocycle is promoted to the conduction band due to the double-color mechanism, the overlap of LUMOs of the corrole ring and the metal ion is no longer necessary as well as not necessary to overcome potential barrier, thus increasing the rate of the transfer or the exchange of electrons. In case of ET, electron of the photoexcited triplet residing onto the higher CC orbital is transferred via the conduction band’s states or the Anderson’s states to the MC unoccupied orbital, thus, forming the triplet LMCT (πd*) state, which can be also considered as the triplet radical pair (Rh2+, C2-) with constituents separated by approximately 2 Å. However, since the MC and CC HOMOs possess the same symmetry (cf. Figure 4) one expects that, with large probability, the electron of the MC HOMO would move to the CC HOMO simultaneously with a transfer of electron from the higher CC orbital to the MC unoccupied orbital, thus forming the triplet MC state. The above-described EnT mechanism actually represents a variant of the Dexter mechanism with the transient electronic states. The T-T EnT from the lowest-energy photoexcited ππ* triplet state (3T1) to the low 3dd* state can occur also without participation of the conduction band, i.e., via a regular Dexter mechanism. Such a process might proceed with a considerable reorganization activation energy or be activationless in the case of tunneling.51 EnT from the same photoexcited triplet state could occur to the triplet MLCT state as well. Such EnT is accompanied by the metal-to-ring ET. As it was outlined earlier, the fast S-T EnT may compete with ISC and, thus, can be also taken into account for populating the low-lying dd and CT states. In addition to the heavy atom effect, a small energy gap can favor EnT. In such a case, the activation energy for the S-T EnT may be very small and, thus, despite the fact that the process is spin-forbidden (the electronic coupling matrix element decreased by the order of magnitude as compared to that of the T-T EnT) a rate of the process can still be large.51 It is unlikely that the 5dd state is formed via a Dexter-type mechanism. We expect that the 3dd state is generated initially, and then the 5dd state could be formed via ISC within the MC states. The σ-donor and π-acceptor properties of the aromatic ligands may result in the low-lying states, which genesis is connected with the central metal ion.52 For the mixed-ligand complexes of the 4d6 and 5d6 metal ions (Rh(III) and Ir(III), respectively) with pyridines, it was found that the LC ππ* states, the MLCT dπ* states, and the MC dd states in many cases may lie close to each other. The energy of the MLCT state was found to be strongly dependent on the surroundings. As a result, in some

Wagnert et al. cases, the lowest triplet state can represent the MLCT state (3MLCT ≡ 3dπ*), which is shifted below the CC state (3CC ≡ 3 ππ*).52 In addition, these triplet states are substantially mixed. It is noteworthy that, generally, the 3ππ* excited state can be localized on one type of ligands (e.g., on the pyrrole ring), whereas the 3dπ* excited state can correspond to another ligand type (e.g., to the axial ligands). Since energy of the 3MLCT depends more on the molecular environment than that of the 3 CC, we can expect that there might exist a sufficiently broad distribution of the energy gaps between these two triplets stemming from the existence of the corresponding inhomogeneous distribution of the complex sites in the glassy phase.53,54 In turn, this means that the order of 3MLCT and 3CC can be reversed for different sites and, thus, statistically it makes possible the observation both triplet states simultaneously. The same result, i.e., a simultaneous observation of two or more triplets of various origins, could be obtained also in the absence of the complex site distribution, namely, in cases where the energy gaps between triplets are small enough to have a noticeable populations of the several triplet states (consistent with thermal equilibration of the close-lying states). As a case in point, such energy difference was reported to be of only 300 cm-1 for the Ir(III)-bipyridine complexes.55 Another reason, and likely the most probable, for the simultaneous observation of several metastable excited states is the existence of barriers between them (cf. Figure 5). The laser photolysis (at 532 nm) of Rh(III) and Co(III) porphyrins with similar electronic configurations is an example of T-T EnT. It was shown that the ejection of the axial ligand (pyr) occurs from the 3dπdz2 state of the central ion with a high quantum yield of 0.9.56,57 Such a dissociative state was found to be formed via a chain of excited states: 3ππ* f 3πdz2 f 3 dπdz2. In summary, excited states of the different origins and multiplicities are expected to be the objects of this study. 5. Mechanistic Model. We present a qualitative model, which is based on a gross simplification of the real processes but, nonetheless, provides a simple picture that seems to be consistent with all main results of this work. For the Rh(III) corrole complexes under study, due to the possible close proximity between the 3MLCT and 3CC states and the large SOC constant of Rh(III), one may expect a strong mixing of the charge transfer character into the 3CC state, resulting in a short lifetime and a large ZFS parameter, much larger than that in the case of nonheavy ions. This ZFS can differ from that typical for the 3LC cases of the Rh(III) complexes, where the ZFS parameters were found to be in the range of 0.1 cm-1.58,59 The dd excited states are generally characterized by the strong SOC interactions, and thus, their ZFS parameters often become larger than the MW quanta used in the EPR experiments.60 In such cases, the EPR spectra exhibit severe distortions from the symmetrical ones, typical for free-base and nontransition metal complexes. As the ZFS constant increases, some transitions are lost, resulting in a disappearance of the low-field lines.61 5.1. TREPR Spectra. As it was already outlined above, the spectra of the different Rh(tpfc) complexes, each with its distinctive axial ligands, obtained for the identical conditions were found to be different from one another and distinctive from other corrole complexes. The TREPR spectra of the Rh(tpfc) complexes (100 K) detected at 150-160 ns after the photoexcitation are shown in parts a-c of Figure 1. For the purpose of comparison, the X-band TREPR spectra of the Ga(tpfc) complex (4) embedded in E-7 (175 K, 1 µs time delay) is also shown



(Figure 1d).23 The latter represents a corrole complex similar to those shown in Chart 1 but has a non-transition-metal Ga(III) ion instead of a transition-metal Rh(III) ion. Several observations need the appropriate explanations. (1) The parallel spectra (L|B) of 1, 2, and 3 are antisymmetric about the center of the spectra. They are similar to each other and resemble the spectrum of 4. However, the polarization patterns are different: e/a for Rh(tpfc) compared to a/e for Ga(tpfc) (in addition, the spectrum of 1 exhibits in its center a weak e/a feature, 350 G in width, superimposed on the strong main pattern). The characteristic peak-to-peak distances show a wide variety of values: 1150 G for 1 and 2, 600 G for 3, and 500 G for 4. (2) The perpendicular spectra (L⊥B) are qualitatively different for the different complexes. The Ga(tpfc) spectrum retains the a/e polarization (i.e., a, a/e, e) and the antisymmetric pattern with the same central magnetic field as before for the parallel orientation. For Rh(tpfc) complexes, the perpendicular spectra are shifted as compare to the parallel ones, and their polarization patterns exhibit no clear symmetry and no order in the spectral widths (e/a/e/a for 1, e/a/e for 2, and e/a/e/a/e/a for 3). We suggest that the above-outlined spectral features (Figure 1) result mainly from the effects of SOC. The scales of such effects are determined both by the magnitude of the SOC constant and by availability of the proper electronic states, which can be mixed with the states detected by EPR (see Supporting Information). The Rh(III) ion is rather heavy and has the large SOC constant (see Supporting Information).62 This fact leads us to several general conclusions about the TREPR spectra patterns and the rates of relaxation processes. First, the anisotropy of the g values is expected to be large, thus, resulting in the asymmetry of the EPR spectra, which should be most pronounced for the high-field EPR where the interval of magnetic field related to the interval of the g values is considerably increased compare to that of the X-band EPR while the anisotropy associated with the dipolar interaction is conserved. Second, the ISC and the energy-transfer processes, occurring with a change of multiplicity, are expected to be very fast. Let us treat the observed TREPR spectra as the spectra of the triplet excited states. In such a case, the spin-Hamiltonian involves just the dipolar and the Zeeman interactions (see Supporting Information)

HS ) HZFS + HZ ) SDS + βBBgS

(6)

The line shape of the triplet EPR spectra is determined mainly by an anisotropy stemming from the large ZFS parameters (which are typically of the order of 0.1 cm-1 for the macrocycle localized states but can exceed several dozens of cm-1 for the MC states) and from the large SOC which affects the g tensor (the heavy atom effect). The approach of taking into account the mutual orientations of the ZFS and g value tensors requires the specific computer simulations of the experimental spectra. In the context of an approximate approach, we consider here the ZFS and the Zeeman terms of eq 6 separately, within a concept of the orientation of their principal frames about the laboratory frame. Distances between the canonical positions are associated with the SDS term of the Hamiltonian, which, in the principal frame of the dipolar tensor D is expressed as

SDS ) DxxS2x + DyyS2y + DzzSz2 ) DZFS[Sz2 - (1/3)S(S + 1)] + EZFS(S2x - S2y )

(7)

where the axial ZFS parameter DZFS ) (3/2)Dzz and the rhombic ZFS parameter EZFS ) (1/2)(Dxx - Dyy). The width of the triplet spectra is determined mainly by the DZFS value. Thus, we expect very different DZFS values for different complexes under study. As outlined in Supporting Information, ZFS contains two contributions: (1) the direct dipolar spin-spin contribution, DSS, which is due to the interaction of the classical magnetic dipole moments of two electrons, and (2) a contribution arisen from SOC, DSOC

D ) DSS + DSOC

(8)

The parameter DZFS is then expressed as

DZFS ) (DSS)ZFS + (DSOC)ZFS

(9)

For Ga(tpfc), it was assumed that DZFS(Ga(tpfc)) ≈ DSS (Ga(tpfc)) ) -0.03 cm-1.23 Taking the overall width of the perpendicular spectra to be approximately equal to 2DZFS, we obtain that DZFS(1) ≈ 0.1, DZFS(2) ≈ 0.06, and DZFS(3) ≈ 0.05 cm-1. In turn, taking DSS(Rh(tpfc)) ≈ DSS(Ga(tpfc)) we can estimate from eq 9 that (DSOC)ZFS(1) ≈ 0.13, (DSOC)ZFS(2) ≈ 0.09, and (DSOC)ZFS(3) ≈ 0.08 cm-1. Various contributions of SOC to the ZFS splitting of the different Rh(tpfc) complexes under study appear to be associated with effect of the axial ligands, which modify the energies of the transition-metalcomplex excited states admixed to the detected triplet state. It is known that such effect “tunes” the photochemical and magnetic properties of the nitrogen aromatic heterocycle transition-metal complexes.63 Thus, we suggest that DZFS changes its sign upon the replacement of Ga for Rh. In turn, this results in the change of a sign of polarization, as it was observed, on retention of the population differences between the zero-field triplet sublevels.64,65 According to Supporting Information

(DSOC)ZFS ) (3/2)DZZ ) (3/2)λ2ΛZZ

(10)

where

ΛZZ ) -

∑ {〈n|LZ|n*〉〈n*|LZ|n〉/(E*n - En)}

(11)

n**n

with the notation n* related to the states that are admixed in the second order, by SOC, to the reference state of interest n and the notation Lz, which represents the z projection of the operator of the orbital angular momentum. For further estimations, we assume, in compliance with the discussions in previous paragraphs, that the detected state is the 3ππ* (3T1 in Figure 5), formed via the promotion of an electron from a bonding to an antibonding corrole ring orbital. Inspection of Figure 5 shows that a number of excited states (n* in eq 11) lie near the detected 3 T1 state, within the energy range of 10000 cm-1. The magnitudes of the nonvanishing matrix elements in eq 11 are expected to be of a several units of p.31,55 By substitution of the expected values in eqs 10 and 11 we obtain a rough estimate

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Wagnert et al.

of λ ≈ 25 cm-1. This value is apparent to be reasonable if one takes into account the points discussed in Supporting Information. We cannot consider the Zeeman splitting tensor to be isotropic, as is usually assumed for aromatic hydrocarbons with a weak SOC. For the metal complexes under study which possess a strong SOC, such approach is no longer a good approximation. Normally, the βBSgB term is presented as

βBSgB ) βB(gxxSxBx + gyySyBy + gzzSzBz)

(12)

where Bx,y,z is the projection of B on the corresponding axis of the principal frame of the g tensor. If we consider the orientational distribution of the complexes about the director to be rather narrow (i.e., the direction of one of the axes of g almost coincides with L) then, for the L|B case, one of three magnetic field projections would be much larger than the others. This means that expression in the right side of eq 12 degenerates to one term. As a result, the spectrum would be effectively described by single g value. This can be a reason why the parallel spectra possess a similar spectral pattern and look like the spectra with the isotropic g-value. For the L⊥B case, two other magnetic field projections should be larger than the first one. Thus, the g values become smeared over considerable interval, and as a result, the different canonical lines may be overlapped. In the case where these lines have polarizations of the different signs, the overall pattern might be complicated, with peaks shifted from the canonical positions. The g-value anisotropy can be expressed as (Supporting Information)

∆g ) (gzz - ge) ) 2λΛzz

(13)

By substitution of reasonable values of λ (10-25 cm-1) and Λzz (10-4-10-3) in eq 13 we obtain that ∆g ≈ 0.005-0.2. For the Q band, such magnitudes of ∆g are consistent with 30 and 120 G, respectively, that is comparable with the peak-to-peak distances of 100 G (cf. Figure 1). The SOC constant of Ga(III) (λGa ≈ 800 cm-1)62 is comparable with that of Rh(III). However, since Ga(III) does not hold the unfilled d shell, no excited states lie near the detected 3T1 state, which is contrary to the case of Rh. This fact is a major reason for a negligible effect of SOC on the D- and g-values of the Ga corroles. 5.2. Electron Spin Polarization. It is well-known that the ∆m ) 1 EPR spectra (the oscillating magnetic component of the MW field is perpendicular to the external steady magnetic field and a host medium is isotropic) of the randomly oriented triplet molecules exhibit discontinuities at six magnetic field positions.66,67 Generally, the resonance magnetic field positions (Br) depend on two Euler angles between the laboratory frame and the molecular dipolar interaction frame. As a result, they continuously cover a wide interval of the magnetic field, thus, specifying the anisotropic pattern of the spectrum. The abovementioned six resonance fields apply to the canonical orientations, where the magnetic field is parallel to every of three principal axes of the ZFS tensor. In such cases, Br is stationary with respect to changes in the Euler angles (i.e., the derivatives of Br with the respect to both angles are simultaneously equal to zero). For the ∆m ) 1 transitions between three triplet sublevels, there are two values of the resonance magnetic field for every canonical orientation, related to either the (0 T +1) or the (-1 T 0) transition (in the high-field notations). They are conventionally labeled as X1 and X2, Y1 and Y2, and Z1

and Z2. Their interlocation depends on the signs of the ZFS constants. For partially oriented triplets, the EPR signals at the canonical orientations are changed as compared to those for the isotropic distribution. In LC with a uniaxial alignment of the guest molecules (such as the “discoid” porphyrin molecules), some canonical lines can almost disappear.68–70 Such an effect is associated with a fact that, for particular orientations, the angle between the magnetic dipole moment of the molecule and the magnetic component of the MW radiation can be equal or close to π/2 (for discoid triplet molecules, magnetic moment is directed perpendicular to the discus plane). Namely, for the L|B orientation of nematic sample, the Z lines nearly vanish while the X components are increased. In contrast, for the L⊥B orientation, the X lines are greatly decreased while the Z components are increased. For both cases, the Y lines are less dependent on the L-B mutual orientation. In the case where one can neglect an anisotropy of the g value, the features in the EPR spectrum are evident in the canonical resonance magnetic fields at Br ) B0 ( (D - 3E)/2, Br ) B0 ( (D + 3E)/2, and Br ) -D, where B0 relates to the center of the spectrum.61 Such a triplet spectrum, in fact, represents the superposition of the spectra of two “doublet species” corresponding to the (0 T +1) and (-1 T 0) transitions, every of which in turn are characterized by the overall width (3/2)(D + E) and by three peaks (for the randomly oriented molecules) labeled X1, Y1, Z1 and X2, Y2, Z2, respectively. In most reported studies of the triplet EPR spectra taken in LCs, the polarization of the same canonical lines was observed to be the same both for the “parallel” and for the “perpendicular’ spectra. This is not true in our experiments (cf. Figure 1) and, thus, needs special consideration. One can suggest several mechanisms that could be used, separately or together, for an explanation of the polarization patterns. Below in this paragraph, we will be focused on the spectra of 3 (Figure 1c). First, a considerable effect on the line positions and the line polarizations is expected if we take into account the reason behind the g-value anisotropy (see previous paragraph). In the case where the different canonical lines are overlapped and have polarizations of different signs, the overall patterns can look like having different polarization for different director orientations. Second, we can separate peaks 3, 4, and 5 in Figure 1c from the remaining spectrum (various field positions are marked from 1 to 7). As it was shown above, the quintet state is detected for 3 by the nutation experiments. We assume here that peak 3 is due to the sole quintet state transition while peaks 4 and 5 are due the radical pair described and justified below. One may expect the ZFS of such quintet state to be larger than the MW quantum, and thus, other quintet transitions are not observed by the Q-band EPR.71 Optionally, the 3dd, 3ππ*, 3dπ*, and 3πd states can be also responsible for the peak 3. We will treat the rest of the spectrum considering D to be positive (as it was shown above) and E to be positive as well (an arbitrary assignment, which is chosen for the sake of definiteness). In such a case, we can consider lines 1 and 7 to be the Z lines, lines 2 and 6 to be the Y lines, and the two lines in the PAR spectrum to be the X lines (generally, the X and Y lines can trade their positions). Summarizing, we assume that the main spectral pattern is due to the e/a/e/a/e/a polarization of the TREPR spectrum of the 3T1(ππ*) state (cf. Figure 5). The third approach is associated to the possibility of generating two close-lying 3ππ* states, 3T1(ππ*), and 3T2(ππ*) in Figure 5. These states are formed via the promotion of electron from the b1 HOMO to the a2 LUMO, 3T1 ) 3[π(b1)π*(a2)], or from the a2 HOMO to the b1 LUMO, 3T2 ) 3[π(a2)π*(b1)]. One


Figure 6. X-band TREPR spectra (χ′′(B) presentation) of the Rh(pyr)2(tpfc) (3) taken 840 ns after laser pulse (591 nm) at 170 K.

can imagine that the rest of the spectrum (without the central peaks) represents a superposition of two spectra, associated with the above-mentioned triplets and possessed the ZFS parameters closely related to each other. On the other hand, since the symmetries of these two configurations are different, as well as the symmetries of the two primary excited singlet configurations, 1 S1(ππ*) and 1S2(ππ*), the different ISC rates are expected for the same sublevels of the 3T1(ππ*) and 3T2(ππ*) states. If the E parameter is rather small for both triplets, so that the X and Y lines coalesce, then the polarization signs of the two PAR lines and the lines 2 and 6 of the PER spectrum can be a result of a competition between the polarizations of the two triplets: for the PAR lines the polarization of one of the triplet prevails, while for the PER lines 2 and 6 the opposite-sign polarization of the second triplet is surpassed. 5.3. Comparison of the Q-Band and X-Band TREPR Spectra. The indication that the excited states, which are associated with the d orbitals, are responsible for the TREPR spectra of the complex 3 can be found by comparing the Q-band spectra (cf. Figure 1c) to the X-band spectra (cf. Figure 6). One can see that both PAR spectra are very similar with the same e/a polarization pattern and the peak-to-peak distances of 500-550 G, while the PER spectra appear at first glance differently. However, if we drop the peak 3, associated with the quintet state (see above), then we can see that both PER spectra consist of six lines each and have the same e/a/a/e/e/a polarization pattern (the outermost lines 1 and 6 of the X-band spectrum shown in Figure 6 are considerably weaker than the other lines). The lines 2 and 6 (Q band) and the lines 2 and 5 (X band) are separated by approximately 620 G while the lines 4 and 5 (Q band) and the lines 3 and 4 (X-band) are divided by about 180 G. On the basis of the discussion given in previous section we ascribe, in the case of the X band, both lines of the PAR spectrum and the lines 1, 2, 5, and 6 of the PER spectrum to the Z, X, and Y lines of the ππ* triplet. These peaks correspond, in the Q-band case, to both peaks of the PAR spectrum and the peaks 1, 2, 6, and 7 of the PER spectrum (cf. Figure 1c). A similar situation is found for the Q-band spectra of 1 (Figure 1a). In this case, we observe eight lines in the PAR and the PER spectra. Six of the lines appear to relate to the X, Y, and Z lines of the ππ* triplet. For 1, contrary to the case of 3, the central relatively narrow doublet of lines (270 G)

J. Phys. Chem. A, Vol. 114, No. 5, 2010 2069 possesses an e/a pattern. For 2, such central extra lines are not observed (cf. Figure 1b). The presence of these lines for 1 and 3 and their absence for 2 apparently indicate that their origin is different as compared to that of the above ππ* triplet. An additional confirmation of the above contention is the different decay rates of the central doublet lines and the remaining lines ascribed to the triplet. The characteristic decay time of the EPR signal of the spectral doublet (both for 1 and for 3) were found to be significantly longer than those related to the other lines of the same spectra. We associate the central a/e pair of lines (4 and 5 for the Q-band and 3 and 4 for the X-band for 3) or the e/a pair (for 1) with the charge separated intramolecular structure corresponding to the CT states discussed above. Such structure represents in certain respects the radical pair (RP) since it comprises two doublet species separated by a sizable distance (see also Supporting Information). It is noteworthy that the Rh(III) corrole itself represents also charge separated species. The RP spectra which show antiphase doublets were observed in a number of studies, both for the triplet and correlated RPs (TRP and CRP, respectively) formed via the photoinduced intramolecular charge transfer within the covalently linked electron donor-acceptor (D-A) systems with the D-A distances, rDA, of 10-30 Å.72–77 For RPs, the separation distances between the field positions of the doublet components were found to be 5-40 G, which is in agreement with rDA (Supporting Information). The overall width of both RPs (where the exchange interaction is typically less than the dipolar one), and the triplet spectra is determined mainly by the magnitude of the dipolar parameter D. For the linear dipole, the only component of the dipolar tensor, DZZ, makes a major contribution (Supporting Information). In systems under study, the DZZ values were found to be between 90 and 130 G (considering the peak-to-peak distance to be equal 2DZZ). In the point dipole approximation (Supporting Information), we estimate that rDA ) 5.9-6.7 Å. In turn, this makes possible the estimation of the constant of the exchange interaction (J) acting between spins of the charge separated structure. Generally, J is presented in the exponential form J ) J0 exp(-κ(rDA - r0)), where the constant κ ≈ 1 Å-1, r0 is the distance of the closest approach, and J0 is the interaction corresponding to r0. For a rough estimation, the above formula can be rewritten in form J ≈ 101010- rDA, where J and rDA come in G and Å, respectively.78 Utilizing this expression we obtain J ) 2000-10000 G (0.2-1 cm-1). Thus, in our cases the values of J are expected to be comparable to the available magnetic interactions such as the dipolar and the Zeeman interactions, so that the state mixing (mainly the ST (1 mixing since for the S-T0 mixing such J values are too large) is plausible. In other words, formation of the correlated RP is expected.79 However, since the above estimates are very approximate the expected J values may be actually larger than the magnetic interactions and, in such a case, the observed pattern can be associated with the triplet RP.80,81 The energy states related the charge separated RP will be termed, as before, the CT states. We suggest the following mechanism of the RP formation (cf. Figures 4 and 5). Initial photoexcitation of the {Rh3+ Cor3-} complex promotes the electron to LUMO of the Cor3- moiety. This electron is transferred either to the dσ orbital of Rh(III) or to LUMO of an axial ligand (L) forming the CT configuration, {Rh2+ (dσ)Cor2-(π)} or {Rh3+ Cor2-(π)L-(π*)}, respectively. Promotion of the electron to the axial orbital of Rh(III) or to the orbital of the axial ligand is in line with the estimated interspin distance of 6-7 Å, which considerably exceeds the formal “geometrical” distance between the central metal ion and

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the macrocycle ring (∼4 Å).6,7 As it was already outlined the resulting CT state may refer to the singlet RP (1CT) or the triplet RP (3CT) or the correlated RP (mixed multiplicity). Apparently, the photoexcited 1S1,2 state is relaxed via two competitive routes forming on the first stage either the 3T1,2 state via ISC or the 1 CT state via the intramolecular electron transfer. In case of CRP, the singlet precursor state experiences mixing with the triplet substates generating specific polarization pattern, which particularly depends on the sign of J. In case of triplet RP, the 3 CT state can be formed either by ET within the 3T1,2 state or by ISC from the 1CT state. In both these occasions, a spin polarization builds up via ISC.73 For the PAR and PER spectra, the sign and the intensity of TREPR signal are varied in accordance with the different molecular alignment. According to Supporting Information, the RP dipolar parameter is dependent on the angle θRP between the dipolar axis and the magnetic field direction and, as a result, its magnitude falls in the range between -DZZ (θRP ) π/2) and 2DZZ (θRP ) 0).72 The angle θRP for the PAR and PER orientations differs by π/2, and this fact is the reason of the sign inversion of the polarization (cf. Figure 1). The above-discussed CT states convert into the 1S0 ground state or transform into the 3T state via the back ET (the charge recombination). In the latter case, the triplet state acquires the polarization of the corresponding RP. If the triplet and CT states are close in energy and the transition between them is activationless then such states can be in equilibrium and decay with the same rate. In such a case, their polarization should decrease with the same relaxation time. However, if there is an activation barrier between these states then they should decay with different rates. The latter appears to be our case. 5.4. TREPR Spectra Obtained for Isotropic Toluene Matrix. The TREPR spectra of 2 and 3 dissolved in the isotropic toluene matrix are shown in parts b and c of Figure 1. To the first approximation, such spectra may be visualized as a superposition of the PAR and PER spectra obtained in experiments with LC (cf. Figure 1) and taken with corresponding weight coefficients. Typically, a summation of the “parallel” and the “perpendicular” spectra obtained in LC results in a pattern very similar to the spectrum taken in the isotropic matrix. Likely, this is our case since, for rather “broad” distribution about the director, two “interperpendicular” distributions complement each other, and, as a result, give an overall distribution reminiscent of the isotropic distribution. Conclusion We have demonstrated that the photoinduced population of electronic states in the three Rh(III) corroles strongly depends on the kind and the number of ligands coordinated to the metal. Transient species with both triplet and quintet multiplicities were experimentally detected. This phenomenon is explained by the specifics of transition metal complexes, wherein a substantial number of electronic states lie in a relatively narrow interval of low energies. A mixing between them causes a distortion of the electronic potentials in terms of the energy difference and the electronic coupling matrix elements. The axial ligation of the Rh(tpfc) complexes affects the relative energetic positions of the excited states, which in turn leads to the population of different energy levels for the different complexes. The fact that we do detect the quintet state for 3 points out that in this case the ZFS interaction is comparable with the Zeeman splitting. This conclusion is in line with results of the recent high-field/high-frequency EPR studies of the quintet ground state in Mn(III) corrole complexes (3d4) dissolved in

Wagnert et al. the frozen pyridine matrix.82 It was found that D ) -2.6 cm-1 and |E|) 0.015 cm-1 and that the pyr axial coordination results in the increase of both ZFS parameters. A significant mixing of the quintet ground and excited triplet states was proposed, which is also in line with our model. Such mixing results in a larger D magnitude for the metal corrole complexes as compared to that of similar metal porphyrin complexes. Analysis of the results shows that the 3ππ* states make major contribution to the TREPR spectra of 1 and 2 while the 3dd, 5dd, and 3CT states contribute to the spectrum of 3 as well. In the latter case, the ZFS parameters are expected to be comparable with, or larger than, the energy of the MW quantum, and thus, a number of observed transitions are limited as compared to the 3ππ* case where the ZFS interactions are considered to be permutation to the Zeeman energy. The SOC is one of the leading spin-dependent interactions resulting in the admixture of the triplet and quintet dd states to the triplet ππ* state (cf. Supporting Information). In the EPR spectroscopy of the “atomlike” systems with a single unfilled electron shell and with a spherical Coulomb potential, a common practice is to express the spin-orbit coupling term as HSOC ) ξ∑iouter lisi ) λLS, where the index i refers to the outer electrons, li and si are the orbital and spin angular momenta of the ith electron, respectively, (ZA/rA3) ≡ ξ is the one-electron strength of SOC for an outer electron (the effective spin-orbit coupling constant), ZA is the effective atomic number of the “atom”, rA is the distance between the electron and the “atom”. The righthand part of the above equation represents the SO interaction si and term in the Russel-Sounders coupling scheme (S ) ∑outer i li) with the average many-electron SOC constant λ. L ) ∑outer i The constant ξ includes a part of the two-electron contribution. The constants are related by the simple equation |λ| ) ξ/2S. However, our case is different from the above one. The Rh corrole complexes represent a multicenter system with the molecular orbitals spread out over the entire molecules. They are noncentrosymmetric and are comprised of many (and various) atoms (Ai) with quite different individual ξAi values. In addition, atoms are connected to each other by different kinds (ionic, covalent, coordinate, etc.) of chemical bonding. The effective form λLS may nevertheless be applied as before, but one should take into account several aspects. First, the constant λ, related mainly to the interactions of spins of the two outer unpaired electrons (of the 3ππ* state of the corrole macrocycle) with their orbital momenta about the nuclei of atoms comprising the complex skeleton, cannot be presented as a more-or-less simple function of the SOC constants of isolated atoms (ξAi ) 1200 (Rh(III)), 76 (N), 28 (C), 266 (F), 231 (P), and 0.24 (H) cm-1). Second, the SOC constants, assigned to the interaction of electron with the atomic nucleus or other electron, are diminished as a function of the distance between them, r, according to the r-3 law. This means, particularly, that the effective value of ξRh for the π electrons of the macrocycle should be noticeably less than that in case of the d electrons since the π electrons are spaced farther from the Rh nucleus. Last, in transition metal complexes, the ξ value of the metal ion as obtained from the EPR spectra can be significantly smaller than that of the free ion due to the effect of covalent bonding. It means that n and n* of eq 11 cannot be fully assigned to the orbitals localized near the ion since a fraction of time the d electrons reside on the symmetry-adapted ligand orbitals. In turn, it means that both n and n* should be multiplied by the coefficients less than one. Formally, these factors are effectively ascribed to the SOC coefficient resulting in a reduction of its value. A similar effect is active in case of the electrons of the

EPR Study of Rhodium(III) Corrole Excited States 3

ππ* excited state of the corrole macrocycle. However, since the π-electrons spend definite time near the central ion on the orbital with the ξRh value, much larger than that of the corrole (ξCor), the bonding results in an increase of the effective SOC constant. The above consideration shows that, for the complexes under study, the SOC constant λ is essentially a phenomenological parameter whose value may be far away from that of the core transition-metal ion. In fact, the SOC constant in the case of the many-center molecule, unlike the case of the centrosymmetric atom, is not a physical constant and it cannot be measured directly. Its value can be obtained from experimental data based on a sort of approximation. Moreover, λ relates herewith to a particular state, i.e., λ ) λ(L,S). The off-diagonal SOC matrix elements mix into state of interest one or more excited states of a suitable symmetry. The one-electron part of HSOC can couple only states that differ by one orbital (like the ππ* and πd or the πd and dd states). But, the two-electron contribution, which for heavy-atom systems amounts to an average of several percents of the one-electron contribution, can mix states differed by two orbitals (like the ππ* and dd orbital). We found that λ is in the order of 10-25 cm-1 for the ππ* states and about 50 cm-1 for the dd states. The latter estimate is obtained by using eqs 10 and 13 and taking into account expectation that (DSOC)ZFS of the quintet state is comparable with the energy of the MW quantum of the Q band EPR. The complex 3 is the most symmetrical among three complexes under study, and its metal ion is within the plane defined by the four N atoms. This means that for 3 the distance between the Rh ion and the atoms of corrole ring is the smallest as compared to the other corroles (e.g., see the X-ray structures6,7). Since the SOC drops according to the r-3 law, the strongest state mixing and consequently population of the πd and dd states is expected with highest probability for 3. Population of these states can be also explained in framework of the double color mechanism if take into account that the absorption cross section of 3 is larger than those of 1 and 2. Since the high-field approximation is no longer valid, for a rigorous simulation of the spectra of 3 a diagonalization of the full Hamiltonian should be fulfilled numerically to obtain the energy levels of the system. Then, to fit calculated and experimental spectra, one should match a lot of parameters, namely, the principal values of the ZFS and g tensors, two sets of Euler angles, the populations of the zero-field levels, the intrinsic Gaussian line width, and the values of parameters of an orientational potential. Hence, normally one should fit 16 (triplet) or 18 (quintet) parameters for each considered excited state. Taking into account also a simultaneous participation of several excited states, computer simulations may not be expected to be capable of providing the accurate magnitudes of the spectroscopic, structural, and dynamic parameters. Acknowledgment. We would like to thank Prof. Haim Levanon of the Hebrew University of Jerusalem and Prof. Gerd Kothe of the University of Freiburg for the opportunity to exploit the facilities of their laboratories and for their support and helpful discussions. We are grateful to Mr. T. Berthold (University of Freiburg) for his contribution in carrying out Q-band measurements and Dr. E. Stavitski for his help in running of some experiments. Work at the Hebrew University of Jerusalem was supported by the Israel Science Foundation (Grant No. 740/06), Deutsche Forschungsgemeinschaft, and the KAMEA Foundation (V.R. and A.B.). Work at the Technion was supported by the Israel Science Foundation (Grant No. 740/ 06) and a Technion VPR fund (Z.G.). The center for absorption in Science, Ministry of Immigration is also acknowledged (I.S.).

J. Phys. Chem. A, Vol. 114, No. 5, 2010 2071 This work is in partial fulfillment of the requirements for a Ph.D. degree (L.W.) at the Hebrew University of Jerusalem. Supporting Information Available: Mathematical explanations for double-color excitation, energy of excited states, Hamiltonian equations, mixing of states, spin-orbit coupling, and radical pairs. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) El-Sayed, M. A. J. Chem. Phys. 1965, 43, 2864. (2) Crosby, G. A. Acc. Chem. Res. 1975, 8, 231. (3) Endicott, J. F.; Chen, Y. J.; Xie, P. Coord. Chem. ReV. 2005, 249, 343. (4) Solovyov, K. N.; Borisevich, E. A. Phys.-Usp. 2005, 48, 231. (5) Rozenshtein, V.; Wagnert, L.; Berg, A.; Stavitski, E.; Berthold, T.; Kothe, G.; Saltsman, I.; Gross, Z.; Levanon, H. J. Phys. Chem. A 2008, 112, 5338. (6) Simkhovich, L.; Galili, N.; Saltsman, I.; Goldberg, I.; Gross, Z. Inorg. Chem. 2000, 39, 2704. (7) Saltsman, I.; Simkhovich, L.; Balazs, Y.; Goldberg, I.; Gross, Z. Inorg. Chim. Acta 2004, 357, 3038. (8) Thermodynamically, between the crystalline-to-nematic melting point (263 K) and the clearing temperature of the mesogenic (liquid cristalline)-to-isotropic transition (331 K), the LC samples represent an anisotropic nematic phase. However, normally E-7 avoids crystallization and, thus, exhibits a nematic LC phase between 331 K and the glass transition temperature of 211 K being supercooled LC phase below 263 K. Upon further cooling below 211 K, E-7 forms a “glassy nematic” phase, which was found to be stable up to very low temperatures and not to crystallize even upon rewarming.9–11 (9) Roussel, F.; Buisine, J. M.; Maschke, U.; Coqueret, X. Liq. Cryst. 1998, 24, 555. (10) Viciosa, M. T.; Nunes, A. M.; Fernandes, A.; Almeida, P. L.; Godinho, M. H.; Dionisio, M. D. Liq. Cryst. 2002, 29, 429. (11) Bra´s, A. R. E.; Henriques, S.; Casimiro, T.; Aguilar-Ricardo, A.; Sotomayor, J.; Caldeira, J.; Santos, C.; Dionisio, M. Electronic - Liquid Crystal Communications, www.e-lc.org/docs/2005_03_21_07_41_31. (12) We cannot entirely discard a possibility of forming crystalline domains within the mostly glassy phase. The crystalline phase of a nematic LC is established to conserve a parallel order of the long narrow molecules. The solid-to-nematic transition is characterized by breakdown of the molecular positional order but not of the orientational order.13 (13) Chandrasekhar, S. Liquid Crystals; Cambridge University Press: Cambridge, 1977. (14) Stehlik, D.; Bock, C. H.; Turnauer, M. C. AdVanced EPR; Hoff, A. J., Ed.; Elsevier: Amsterdam, 1989; Chapter 11, p 371. (15) Heinen, U.; Berthold, T.; Kothe, G.; Stavitski, E.; Galili, T.; Levanon, H.; Wiederrecht, G.; Wasielewski, M. R. J. Phys. Chem. A 2002, 106, 1933. (16) Kim, S. S.; Weissman, S. I. ReV. Chem. Intermed. 1979, 3, 107. (17) Furrer, R.; Fujara, F.; Lange, C.; Stehlik, D.; Vieth, H. M.; Vollmann, W. Chem. Phys. Lett. 1980, 75, 332. (18) Weissman, S. I. Annu. ReV. Phys. Chem. 1982, 33, 301. (19) Astashkin, A. V.; Schweiger, A. Chem. Phys. Lett. 1990, 174, 595. (20) Fedoruk, G. G. J. Appl. Spectrosc. 2002, 69, 161. (21) Torrey, H. Phys. ReV. 1949, 76, 1059. (22) Janke, E.; Emde, F.; Losch, F. Tafeln hoherer funktionen; Teubner, B. G.; Stuttgart, 1960. (23) Stavitski, E.; Berg, A.; Ganguly, T.; Mahammed, A.; Gross, Z.; Levanon, H. J. Am. Chem. Soc. 2004, 126, 6886. (24) Wagnert, L.; Berg, A.; Stavitski, E.; Berthold, T.; Kothe, G.; Goldberg, I.; Mahammed, A.; Simkhovich, L.; Gross, Z.; Levanon, H. Appl. Magn. Reson. 2006, 30, 591. (25) Khudyakov, I. V.; Serebrennikov, Y. A.; Turro, N. J. Chem. ReV. 1993, 93, 537. (26) Hush, N. S.; Dyke, J. M.; Williams, M. L.; Woolsey, I. S. J. Chem. Soc., Dalton Trans. 1974, 4, 395. (27) Paolesse, R.; Sagone, F.; Macagnano, A.; Boschi, T.; Prodi, L.; Montalti, M.; Zaccheroni, N.; Bolletta, F.; Smith, K. M. J. Porphyrins Phthalocyanines 1999, 3, 364. (28) Grodkowski, J.; Neta, P.; Fujita, E.; Mahammed, A.; Simkhovich, L.; Gross, Z. J. Phys. Chem. A 2002, 106, 4772. (29) Sashuk, V.; Koszarna, B.; Winiarek, P.; Gryko, D. T.; Grela, K. Inorg. Chem. Commun. 2004, 7, 871. (30) Kadish, K. M.; Shao, J.; Ou, Z.; Zhan, R.; Burdet, F.; Barbe, J. M.; Gros, C. P.; Guilard, R. Inorg. Chem. 2005, 44, 9023. (31) Gouterman, M. Optical Spectra and Electronic Structure of Porphyrins and Related Rings. In The Pophyrins; Dolphin, D., Ed.; Academic Press: New York, 1978; Vol. 3; p 1.

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(32) Endicott, J. F.; Uddin, M. J. Coord. Chem. ReV. 2001, 219, 687. (33) The energy diagram in Figure 4 was obtained as described in Supporting Information. In Figure 4 the orbital prefix numbers are eliminated from the orbital notations since we consider the LUMO/HOMO region only. (34) Ventura, B.; Degli Esposti, A.; Koszarna, B.; Gryko, D. T.; Flamigni, L. New J. Chem. 2005, 29, 1559. (35) Ghosh, A.; Wondimagegn, T.; Parusel, A. B. J. J. Am. Chem. Soc. 2000, 122, 5100. (36) The 515-nm band can be also assigned to the πd LMCT band by analogy with the similar band observed for the hypso porphyrins. (37) Weaver, J. J. Corroles, Ph.D. Thesis, California Institute of Technology, 2005. (38) The double-color absorption is also termed as the excited state absorption and as the reverse saturable absorption, since the effective absorption coefficient increased upon a light intensity increase. This is reverse to a regular saturable absorption, where the absorption coefficient decreases with increasing the light intensity.39,40,42 (39) Chen, P.; Tomov, I. V.; Dvornikov, A. S.; Nakashima, M.; Roach, J. F.; Alabran, D. M.; Rentzepis, P. M. J. Phys. Chem. 1996, 100, 17507. (40) Perry, J. W. Organic and Metal-Containing Reverse Saturable Absorbers for Optical Limiters. In Nonlinear optics of organic molecules and polymers; Nalwa, H. S., Miyata, S., Eds.; CRC Press: New York, 1996; Ch.13, p 813. (41) Cai, X.; Hara, M.; Kawai, K.; Tojo, S.; Majima, T. Chem. Phys. Lett. 2003, 368, 365. (42) Scuppa, S.; Orian, L.; Dini, D.; Santi, S.; Meneghetti, M. J. Phys. Chem. A 2009, 113, 9286. (43) The effective coordinate has nothing more than a pictorial sense. It may include several actual physical parameters, like distances and angles, and these parameters can be various for the states of different origin shown in Figure 5. (44) Mott, N. F. Conduction in Non-Crystalline Materials; Clarendon Press: London, 1993. (45) The singlet-to-triplet EnT from the pyridylporphyrin chromophore to the ruthenium center was found to be an efficient quenching channel.46 (46) Prodi, A.; Kleverlaan, J.; Indelli, M. T.; Scandola, F.; Alessio, E.; Iengo, E. Inorg. Chem. 2001, 40, 3498. (47) Dexter, D. L. J. Chem. Phys. 1953, 21, 1953. (48) It was shown that, at a close separation, it is not normally correct to consider only the Forster or Dexter mechanism. Actually, the electronic donor-acceptor coupling represents a sum of Coulombic and short-range interactions and occurs via intermediate excitons.49 (49) Harcourt, R. D.; Scholes, G. D.; Ghiggino, K. P. J. Chem. Phys. 1994, 101, 10521. (50) Valeur, B. Molecular Fluorescence. Principle and Applications; Wiley-VCH: Weinheim, 2002. (51) Benniston, A. C.; Chapman, G. M.; Harriman, A.; Mehrabi, M. J. Phys. Chem. A 2004, 108, 9026. (52) Colombo, M. G.; Brunold, T. C.; Riedener, T.; Gudel, H. U.; Fortsch, M.; Burgi, H. B. Inorg. Chem. 1994, 33, 545. (53) Zilian, A.; Gudel, H. U. Inorg. Chem. 1992, 31, 830. (54) Colombo, M. G.; Gudel, H. U. Inorg. Chem. 1993, 32, 3081. (55) Colombo, M. G.; Hauser, A.; Gudel, H. U. Inorg. Chem. 1993, 32, 3088. (56) Tait, C. D.; Holten, D.; Gouterman, M. J. Am. Chem. Soc. 1984, 106, 6653.

Wagnert et al. (57) Hoshino, M.; Saki, H.; Yasufuku, K.; Shizuka, H. J. Phys. Chem. 1986, 90, 5149. (58) Komada, Y.; Yamauchi, S.; Hirota, N. J. Phys. Chem. 1986, 90, 6425. (59) Giesbergen, C. P. M.; Sitters, R.; Frei, G.; Zilian, A.; Gudel, H. U.; Glasbeek, M. Chem. Phys. Lett. 1992, 197, 451. (60) Boca, R. Coord. Chem. ReV. 2004, 248, 757. (61) Wasserman, E.; Snyder, L. C.; Yager, W. A. J. Chem. Phys. 1964, 41, 1763. (62) www.chem.tamu.edu/rgroup/dunbar/Chem634/. (63) Ford, P. C.; Wink, D.; Dibenedetto, J. Prog. Inorg. Chem. 1983, 30, 213. (64) In a realistic “finite field” case (where the Zeeman splitting is not much larger than the ZFS, and the spin eigenfunctions I, O, and -I correspond to the 1, 0, and -1 eigenfunctions in the high field approximation) the populations were found to be p(I ) pO ( (2/5)(DZFS)/B)(pz + py 2pz) and pO ) (1/3)(pz + py + pz), where pz, py, and pz are the zero field populations. Upon changing the sign of D, the population differences (p(I - pO) change their signs as well. (65) Wong, S. K.; Hutchinson, D. A.; Wan, J. K. S. J. Chem. Phys. 1973, 58, 985. (66) Kottis, P.; Lefebvre, R. J. Chem. Phys. 1963, 39, 393. (67) Kottis, P.; Lefebvre, R. J. Chem. Phys. 1964, 41, 379. (68) Krebs, P.; Sackmann, E. Mol. Phys. 1972, 23, 437. (69) Krebs, P.; Sackmann, E. J. Magn. Reson. 1976, 22, 359. (70) Grebel, V.; Levanon, H. Chem. Phys. Lett. 1980, 72, 218. (71) If the 5dd state is populated in course of the double color excitation, a noticeable signal of the quintet state is expected for 3 only. This is true since the absorption rate of 3 is much larger than that of 1 or 2. (72) Hasharoni, K.; Levanon, H.; Greenfield, S. R.; Gosztola, D. J.; Svec, W. A.; Wasielewski, M. R. J. Am. Chem. Soc. 1996, 118, 10228. (73) Levanon, H.; Galili, T.; Regev, A.; Wiederrecht, G. P.; Svec, W.; Wasielewski, M. R. J. Am. Chem. Soc. 1998, 120, 6366. (74) Asano-Someda, M.; Levanon, H.; Sessler, J. L.; Wang, R. Mol. Phys. 1998, 95, 935. (75) Kiefer, A. M.; Kast, S. M.; Wasielewski, M. R.; Laukermann, K.; Kothe, G. J. Am. Chem. Soc. 1999, 121, 188. (76) Shaakov, S.; Galili, T.; Stavitski, E.; Levanon, H.; Lukas, A.; Wasielewski, M. R. J. Am. Chem. Soc. 2003, 125, 6563. (77) Di Valentin, M.; Bisol, A.; Agostini, G.; Fuhs, M.; Liddell, P. A.; Moore, A. L.; Moore, T. A.; Gust, D.; Carbonera, D. J. Am. Chem. Soc. 2004, 126, 17074. (78) Turro, N. J. Modern Molecular Photochemistry; Benjamin/Cummings Publishing Co., Inc.: Mento Park, 1978. (79) It is noteworthy that actually in CRP two electrons are quasiindependent (weakly correlated), and they are less correlated than in the case of TRP where the pair of electrons behave as a spin 1 system and, thus, the electrons are strongly correlated. (80) Recently, it has been found that J value of RP can strongly depend on temperature.81 (81) Dance, Z. E.; Mi, Q.; McCamant, D. W.; Ahrens, M. J.; Ratner, M.; Wasielewski, M. R. J. Phys. Chem. B 2006, 110, 25163. (82) Krzystek, J.; Pardi, L. A.; Brunel, L.-C.; Goldberg, D. P.; Hoffman, B. M.; Licoccia, S.; Telser, J. Spectochim. Acta A: Molecular and Biomolecular Spectroscopy 2002, 58, 1113.

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Time-Resolved Electron Paramagnetic Resonance Study of Rhodium(III)

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