Electronic properties of charged fullerenes characterized by EPR and Vis-NIR spectroscopy

EPR and Vis-NIR absorption spectra have both been measured for clarification of contradictory statements about the para-and diamagnetic states of fullerenes. Thereby identification of one sharp EPR signal in solution at room temperature to C ₆₀ ^? (g=2.000±4.0001; ΔB=0.07±0.01 mT) could be made upon using different fullerene sources (TechnoCarbo, Hoechst) and methods of anion generation (chemically, electrochemically, and photochemically). This fact is also supported by the similar observation for a monosubstituted derivative (g=1.9999; ΔB=0.10 mT), in which a small broadening of this sharp signal is found originating from additional¹H hyperfine interactions. Furthermore theg-values of the radical anions of C₆₀ increase with charge (g(C ₆₀ ^? <g(C ₆₀ ^2? ) < <g(C ₆₀ ^3? ) <g(C ₆₀ ^5? )) indicating largest contributions from spin-orbit coupling for the monoanion. No diamagnetic states for the dianions of [60]- and [70]- fullerenes could be found so far but biradical species with largest zero field splittingsD=2.7 mT (C ₆₀ ^2? ), andD=3.1 mT (C ₇₀ ^2? ), respectively. The cation formation of C₆₀ (g=2.0023-2.0029; ΔB=0.15-0.20 mT) with antimony pentachloride was controlled by mass spectrometry. Stable cations were found only in methylenechloride. In other solvents like toluene addition reactions seem to occur.     

Simultaneous electrochemical and electron paramagnetic resonance studies of fullerene anion radicals C 60 1− and C 60 3−

Simultaneous electrochemical and electron paramagnetic resonance experiments have been carried out on the reduced C₆₀ fullerene to examine theg-factor assignment of the radical species. C ₆₀ ^1? and C ₆₀ ^3? show the following EPR characteristics at room temperature: C ₆₀ ^1? :g _1?=2.0002±0.0001, 2ΔB _1s=0.17 mT, and C ₆₀ ^3? :g _{3?=2.0008±0.0002}, 2ΔB _1s=0.07 mT. EPR linewidths are apparently narrower compared to those in most of the spectra previously reported. Variable temperature EPR study on solution containing C ₆₀ ^1? has shown thatg _1? value is not while the linewidth is only slightly temperature dependent.     

Stoichiometric synthesis of fullerene compounds with lithium and sodium and analysis of their IR and EPR spectra

A modified method is proposed for preparing fullerene compounds with alkali metals in a solution. The compounds synthesized have the general formula Me _n C₆₀(THF)_x, where Me = Li or Na; n=1–4, 6, 8, or 12; and THF = tetrahydrofuran. The use of preliminarily synthesized additives MeC₁₀H₈ makes it possible to prepare fullerene compounds with an exact stoichiometric ratio between C ₆₀ ^n? and Me ⁺. The IR and EPR spectra of the compounds prepared are analyzed and compared with the spectra of their analogs available in the literature. The intramolecular modes T _u (1)-T _u (4) for the C ₆₀ ^n? anion are assigned. The splitting of the T _u (1) mode into a doublet at room temperature for Me _n C₆₀(THF)_x (n=1, 2, 4) compounds indicates that the fullerene anion has a distorted structure. An increase in the intensity of the T _u (2) mode, a noticeable shift of the T _u (4) mode toward the long-wavelength range, and an anomalous increase in the intensity of the latter mode for the Li₃C₆₀(THF)_x complex suggest that, in the fullerene anion, the coupling of vibrational modes occurs through the charge-phonon mechanism. The measured EPR spectra of lithium-and sodium-containing fullerene compounds are characteristic of C ₆₀ ^? anions. The g factors for these compounds are almost identical and do not depend on temperature. The g factor for the C ₆₀ ^n? anion depends on the nature of the metal and differs from the g factor for the C ₆₀ ^? anion.     

Investigation of the two quasiparticle rotational band at 1172 keV in172Yb and determination of theg R -factor of the 3+ 3 band head

Investigations of the rotational band based on the 3⁺ 3 two quasiparticle state in¹⁷²Yb have shown that some of its properties can be well described by the collective model of Bohr and Mottelson. As a result of these investigations we have derived the ratio (g _k – g _R )/Q _o =? (0.0136 ± 0.0007). The magneticg-factor of the band head has also been determined by an integral angular correlation measurement perturbed by an external magnetic field. As a result we foundg=0.201 ± 0.030. Using this value and our result of (g _k – g _R )/Q _o we have calculated theg _R -factor of the two quasiparticle state asg _R =0.283 ± 0.018 which is out of the errors smaller than theg _R -factor of the ground state rotational band. An analysis of our angular correlation experiments gave for the mixing parameter δ of theK-forbidden 1094 keV intraband transition: δ=? (3.63 _?0.06 ^+0.14 ) in agreement with the results of other authors.     

Investigation of N 2 + (C 2Σ u + → X 2Σ g + fluorescence excited through auger decay of the 1s −1π* resonance

A theoretical investigation of N ₂ ⁺ (C ²Σ _u ⁺ → X ²Σ _g ⁺ molecular fluorescence excited through the Auger decay of the 1s ^?1π* resonance is carried out. The fluorescence cross sections are calculated with due regard for the dependence of the matrix element of the C → X dipole transition on the internuclear distance, the interference between channels of excitation via different vibrational levels v _r of the 1s ^?1π* resonance, the rotational structure of the fluorescence band, and the predissociation of the N ₂ ⁺ C ²Σ _u ⁺ v′ ≥3) states. The calculated cross sections are in good agreement with the experimental results of recent measurements. The results of the calculations have demonstrated that the observed dependence of the cross section of the (C ²Σ _u ⁺ (v′) → X ²Σ _g ⁺ (v″) fluorescence on the excitation energy and the fluorescence wavelength for a group of bands with equal values of the difference Δv = v′ ? v″ is associated with transitions between the vibrational levels of the electronic states involved in the excitation and subsequent cascade decay of the 1s ^?1π* resonance: N₂ (v ₀ = 0) → N*₂(1s ^?1π*(v _r)) ? N ₂ ⁺ : (C ²Σ _u ⁺ (v′) → X ²Σ _g ⁺ (v″).     

A computational study of entropy rules for charged fullerenes

Thermochemical data on fullerenes are relatively scarce. However, some thermochemical information can be derived from gas-phase experiments using the Knudsen cell mass spectrometry method. The third-law treatment can be carried out on the observed data, though one has to make the crucial presumption that the change in the thermodynamic potential ΔΦ _T ^o in the course of the reactions considered is negligible: ΔΦ _T ^o =0. It would be difficult to check the presumption directly in the experiment, but it can be checked computationally. Model reactions like C₆₀+ ₇₀ ^? = ₆₀ ^? +₇₀ are selected. The change in the thermodynamic potential ΔΦ _T ^o and the change in the standard entropy ΔS _T ^o are computed. For example, at a temperature of T=1000 K, the standard changes for the reaction evaluated using the SAM1 method are ΔΦ _T ^o =1.513 cal/(mol K) and ΔS _T ^o =?0.054 cal/(mol K). Overall, the computations support the critical thermodynamic presumption.     

Measurements of lifetime andg-factor of the 32S(4 1 + ) state at 4.459 MeV

Precessions of the very short-lived 2 ₁ ⁺ - and 4 ₁ ⁺ -states in³²S have been measured using the transient field technique. The deducedg-factor of the 4 ₁ ⁺ -state g=+0.40(15) agrees with the known value of the 2 ₁ ⁺ -state and with theoretical predictions. In addition, the lifetimes of both states were redetermined and are consistent with previous results.     

Measurement of theg-factor of the 4 1 + -state of202Pb

Theg-factor of the 4 ₁ ⁺ -state of²⁰²Pb was investigated by the IPAC-technique. Inspite of the long half-life, which was measured as:T _1/2(4 ₁ ⁺ -state)=1.97(2)ns and the strong applied external magnetic field of 95.0 kG no rotation of the 787 keV-(422keV)-961 keVγ-γ angular correlation could be observed. Theg-factor must therefore be very small. A computer fit gave the limits:g(4 ₁ ⁺ -state)=+0.002(4). This smallg-factor can be understood by the assumption of an accidental cancellation of a positive contribution by the main [f _5/2 ² ]₄-configuration and several negative contributions by admixtures of all other possible two neutron configurations.     

g-factors of the lowest 2+ and 4+ states in198, 200, 202Hg

Theg-factors of the 2 ₁ ⁺ and 4 ₁ ⁺ states in^198,200,202Hg were simultaneously measured by means of the transient-field perturbed angular correlation method in Coulomb excitation using multi-isotopic targets and thin polarized Gd foils as ferromagnetic host. Theg(2 ₁ ⁺ ) andg(4 ₁ ⁺ ) were found identical within errors in^{198, 200}Hg, while in²⁰⁰Hg lowerg-factor values have been determined. The experimentalg-factors were compared with the predictions of the pairing-plus-quadrupole, dynamical deformation and interacting boson models.     

Observation of perturbations in the rovibronic transition probabilities for the (4d)r 3Π g − , (4d) s 3 Δ g − → (2p) c 3Π u ± band systems of the H2 molecule

The ratios of the radiative transition probabilities for the lines of the P, Q, and R branches of the (4d)r ³Π _g ^? , (4d)s ³Δ _g ^? → (2p) c ³Π _u ^± band systems of the H₂ molecule have been measured for the first time. Significant (to two orders of magnitudes) differences are found between the experimental values and the adiabatic theory predictions. It is established that the results of the nonadiabatic calculation performed by us in the pure-precession approximation taking into account the electronic-rotational interaction of the 4d ³Π_g and 4d ³Δ_g states are in agreement with the experimental data. The optimal energies of rovibronic levels of the r ³Π _g ^? , s ³Δ _g ^? , c ³Π _u ^? , and c ³Π _u ⁺ states have been found and reidentification of 11 from 54 spectral lines, assigned previously to the (0-0) and (1-1) bands, was performed.     

g-factor of the second 4+ state in24Mg

The transient field technique has been used to determine theg-factor of the 4 ₂ ⁺ state at 6.010MeV excitation in²⁴Mg. The deduced value ofg=+0.5(4) is consistent with collective model expectations. Further, the equality within experimental accuracies, of the g-factors of the 2 ₁ ⁺ , 2 ₂ ⁺ , 4 ₁ ⁺ and 4 ₂ ⁺ states agrees with theoretical predictions for thisT=0 self-conjugate nucleus, in contrast to the results for²⁰Ne.     

A new many-body solution of the Friedel resonance problem

It is numerically shown that the groundstate of the Friedel problem (consisting of a conduction band and a dresonance), occupied with (n+ 1) electrons, can be written as Ψ = (A a ₀ ^* +Bd*) Π _v=1 ⁿ a _v ^* Φ₀, where a ₀ ^* represents a localized conduction electron state, d* is the Friedel resonance state and Π _v=1 ⁿ a _v ⁸ Φ₀ is a Slater determinant of n single electron states a _t ^* , (Φ₀ is the vacuum state). The a _i ^* together with a ₀ ^* are part of a full ortho-normalized basis of the conductions band.     

Remeasurement of the lifetime of the 4 1 + -state of156Gd and recalculation of itsg-factor

The half-life of the 4 ₁ ⁺ -state of¹⁵⁶Gd has been remeasured by the delayed coincidence technique. The excellent time resolution which can now be achieved by use of small BaF₂ detectors allows a more reliable determination than with previously applied methods. The resultT _1/2(¹⁵⁶Gd,4 ₁ ⁺ )=108(2) ps is smaller than previously published data, but it fits well into the systematics of theB(E2) values of the rotational transitions of this nucleus. A recalculation of the previously measuredg-factor of the same state givesg(¹⁵⁶Gd,4 ₁ ⁺ ) =0.327(19). This value is still smaller than theg-factor of the 2 ₁ ⁺ state, but the magnitude of the reduction can now easier be interpreted by nuclear structure calculations.     

g-factors of rotational states in 176Hf, 177Hf,and 180Hf

g-factors of rotational states in ¹⁷⁶Hf and ¹⁸⁰Hf were measured with the twelve detector IPAC-apparatus of our laboratory [1]. The natural radioactivity 3.78 · 10¹⁰y ¹⁷⁶Lu and the 5.5 h isomer ^180mHf were used which populate the ground-state rotational bands of ¹⁷⁶Hf and ¹⁸⁰Hf. The integral rotations of γ-γ directional correlations in strong external magnetic fields and in static hyperfine fields of (Lu → Hf)Fe₂ and HfFe₂ were observed. The following results were obtained: The hyperfine field in (Lu → Hf)Fe₂ was calibrated by observing the integral rotation of the 9/2^? first excited state of ¹⁷⁷Hf populated in the decay of 6.7d ¹⁷⁷Lu. The g-factor of this state was redetermined in an external magnetic field as Finally the g-factor of the 2 ₁ ⁺ state of ¹⁷⁶Hf was derived from the measured g(2 ₁ ⁺ ) of ¹⁸⁰Hf by use of the precisely known ratio g(2 ₁ ⁺ , ¹⁷⁶Hf)/g(2₁ ⁺, ¹⁸⁰Hf) [2] as      

Pulse ENDOR studies on the radical pair P 700 +· A 1 ·− and the photoaccumulated quinone acceptor A 1 ·− of photosystem I

The secondary acceptor A₁ of the electron transport chain(s) of photosystem (PS) I is a phylloquinone (vitamin K₁, VK₁). Pulse electron paramagnetic resonance and electron nuclear double resonance (ENDOR) experiments at X-band frequencies were performed on the photoaccumulated acceptor radical A ₁ ^·? and the radical pair state P ₇₀₀ ^·+ A ₁ ^·? in PS I ofThermosynechococcus elongatus. The data obtained were compared with data from the respective radical anion of VK₁ in organic solvents. The unusualg tensor magnitude of A ₁ ^·? is explained by the hydrophobic binding pocket of this radical. The hyperfine couplings and the spin (and charge) density distribution is very different for A ₁ ^.? in PS I and VK ₁ ^·? in frozen alcoholic solution. This is attributed to a rather strong one-sided hydrogen bond to A ₁ ^·? . The presence of a hydrogen bond to A ₁ ^·? has only a minor effect ong. The hyperfine coupling constants of A ₁ ^·? determined from the radical pair spectra deviate only slightly from those derived from photoaccumulated A ₁ ^·? in PS I treated with dithionite at high pH. ENDOR resonances of the proton in a H bond were detected and an estimate of the strength and geometry of this bond to A ₁ ^·? was obtained. The significance of the hydrogen bond and other (hydrophobic) interactions of A₁ with the surrounding are briefly discussed.     

(T1u+T1g)⊗(hg+τ1u)vibronic interaction and superconductivity in C 60 n− fullerides

The closeness of low-lying T_1u and T_1g levels of C ₆₀ ^? could enable their mixing under an odd parity vibration of (T_{1 u} + T_{1 g} ? (h_g + τ_{1 u})type. In addition, the two levels are susceptible to Jahn-Teller interaction due to five-fold degenerate h_g vibrations. This complex problem of (T_1u+T_1g)?(h_g+τ_1u) vibronic interaction is transformed to a form similar to T_2g ? (ε_g + τ_2g) vibronic problem of octahedral symmetry. The problem is analysed in an infinite coupling model and compared with the experimental spectroscopic results for the C ₆₀ ^? radical. The resulting parameters are used to calculate the pair-binding energy and superconducting transition temperature in C ₆₀ ^n? fullerides. Vibronic mixing with the T_1g level is found to be responsible for maximising the pair-binding energy at the doping level n=3. It is also found to be an important source of T_c enhancement.     

Vacuum energy ingϕ d /4 -theory forg→∞

In the nonlocalg? _d ^/4 (d≧1) and localg? ₂ ⁴ theory theS-matrix is obtained in a form of the functional integral which is proved to exist. The density of vacuum energy $$E(g) = - \mathop {\lim }\limits_{V \to \infty } \frac{1}{V}\ln \left\langle {0\left| {S_V (g)} \right|0} \right\rangle $$ is investigated. It is proved to be analytic through the whole complexg-plane except for the negative real axis and pointg=0. Its asymptotic behaviour forg→∞ is found.     

EPR of carbonate derived radicals: Applications in dosimetry, dating and detection of irradiated food

After exposure of biological (tooth enamel, bone, …) and synthetic apatites to ionizing radiation, the so-called “asymmetric EPR signal nearg = 2” is formed. Although this signal is being used in EPR dosimetry, dating and detection of irradiated food for many years already, its composite character and the precise nature of the radicals contributing to the spectrum are still insufficiently known and/or recognized. For some fifteen years already, the EPR group in Ghent is gaining extensive experience on the radicals present in calcified tissues and model systems like synthetic apatites, calcites and single crystals doped with carbonate. It will be shown that the majority of radicals in calcified tissues are carbonate derived, e.g., CO ₂ ^? , CO ₃ ^? , CO ₃ ^3? while also phosphate derived radicals like PO ₄ ^2? and oxygen species (O^?, O ₃ ^? ) have been identified with EPR and/or ENDOR. For the EPR applications mentioned above, the most important type of radicals is CO ₂ ^t- (g values ranging from 2.0035 to 1.9970). A second type of radicals which is very intriguing but still badly known, exhibits a spectrum atg values around 2.0045. It is very apparent in tooth enamel below doses of 1 Gy, it has been observed in certain fossil teeth in a very prominent way and also in irradiated food containing bone (e.g., frog legs). It will be shown that the organic origin of this signal can be questioned. The importance of other radicals like CO ₃ ^3t- and CO ₃ ^t- for EPR applications will also be discussed.     

Comparative study of the semiempirical three-parameter potential energy functions for diatomic molecules

A comparative study is made of four three-parameter semiempirical potential energy functions for 32 electronic states of diatomic molecules and their ions:n ₂:X¹gS _g ⁺ ,B ³π_g,A ³ gS_u,C ³ _u,B′ ³ gS_u.a ¹ π_g, a′gS _u ^? ,Ω ¹δ_u N ₂ ⁺ :X ² gS _g ^gS +A ² π,C ² gS _u ⁺ ,B ² gS _u ⁺ CO:X¹gS⁺,a ³ π, a′³ gS_u,e ³ gS^?,d ³gD₁,A ¹π CO⁺:X²gS⁺,A ² π,B ²gS⁺ O₂:X³gS _g ^? ,B ³ gS_u,c ¹ gS _u ^? ,b ¹gS _g ^s ,a ¹ δ_g,c ³ δ_u O ₂ ⁺ :X ²π_g,A ² π_g, a¹ π_g,b ⁴ gS _g ^? A program for numerically integrating the radial Schrödinger equation by the Cooley method is worked out. Certain additional units are introduced to conserve computer time. The resulting vibrational levels are compared with the experimental levels for all the electronic states studied. It is concluded on the basis of this analysis that it is not possible to describe equally well all the electronic states of various molecules on the basis of any single three-parameter potential function. A method for choosing a potential function for describing some particular electronic state of a diatomic molecule is proposed.