Calculation of the geometry of the complex of spatially hindered quinones and phenols from E.S.R. spectra of radical pairs

Geometry of the binary complex of 3,6-di-t-butyl-o-quinone and 2,4,6-tri-t-butyl phenol is investigated. Photolysis of this system produces two types of radical pairs with unequal zero-field splitting tensors. The values of the components, D and E, for each type of radical pair were calculated by diagonalizing the dipole-dipole interaction matrix; the elements of this matrix were calculated by using spin density distributions, either known from the experiment or obtained theoretically. The four parameters (three coordinates of the centre of the benzene ring in the phenoxy radical, and one Euler angle) were found by variational search techniques, through comparing the experimental and calculated values of the zero-field splittings. It is shown that benzene rings of the two radicals are displaced with respect to one another by approximately 1·6 Å and rotated relative to one another by 86·5°. This configuration is interpreted in terms of interaction between the t-butyl groups, hydroxyl and carbonyl groups.     

The phosphorescent triplet state of p-xylene in an isotopically mixed crystal at 1·2K: an investigation by E.S.R. and MIDP

The phosphorescence spectrum of p-xylene-h ₁₀ in a p-xylene-d ₁₀ host is first presented. Secondly we report E.S.R. experiments performed on p-xylene-α,α′-d ₆ in p-xylene-d ₁₀; from an analysis of the orientations of the principal axes in combination with the crystal structure and of the hyperfine splittings it is concluded that the in-plane principal axes of the zfs tensor make an angle of 68° with the molecular axes. Thirdly we discuss Microwave-Induced Delayed Phosphorescence (MIDP) experiments on p-xylene-h ₁₀ in p-xylene-d ₁₀ in which the relative radiative rate constants for decay from the zero-field spin components of the triplet state to single vibronic bands of the ground state have been obtained.

The results of the MIDP and E.S.R. measurements are shown to be mutually consistent in terms of a model in which the effect of the crystal field and the methyl substituents on the pseudo-Jahn-Teller unstable electronic structure of the triplet state of benzene is described.     

Symmetry enforced gauge invariance of nuclear magnetic shielding constants

E.S.R. experiments performed at 1·3 K by optical detection are reported for the photo-excited triplet state of palladiumporphin in a single crystal of n-octane, and the observation of a level anticrossing signal is described.

In the crystal the orbital degeneracy of the ³ E _u state of the free molecule is lifted by the crystal field and in n-octane the energy difference between the two orbital components |x> and |y> is found to be 58 ± 2 cm^-1. The spinorbit coupling (SOC) and the orbital Zeeman interaction couple the triplet manifolds of |x> and |y>, and for a proper understanding of the magnetic properties of these states it is necessary to work in the basis of the six spin-orbit functions deriving from the ³ E _u state of the free molecule. It is shown that either of the two triplet states can be described by an effective spin hamiltonian of the common form and expressions for the zero-field parameters D and E and the principal values of the g tensor are given. The experimental values of the parameters in the lowest triplet state are D = -24·38 ± 0·03 GHz, |E| = 320 ± 60 MHz, g _‖ = 1·677 ± 0·001 and g _⊥ = 1·989 ± 0·002. The matrix element of the SOC connecting the |x> and |y> triplet manifolds amounts to qZ = 15 ± 3 cm^-1 and the vibronic orbital angular momentum (in units of ?) in the ³ E _u state of the free molecule to qΛ = 1·5 ± 0·3. A tentative value of 0·63 for the orbital reduction factor q is obtained by comparison with a theoretical estimate of Λ. The value of q is indicative of weak Jahn-Teller coupling.     

Optical and Zeeman studies of the first excited singlet state of zinc porphin in a single crystal of n-octane: Evidence for Jahn-Teller instability

The absorption and fluorescence spectra of Zn porphin in an n-octane single crystal at 4·2 K are reported in the region between 17 400 and 18 500 cm^-1. A strong peak appears in both spectra at 17 961 cm^-1 and is assigned to the origin of one component (|x, 0>) of the nearly degenerate Q-band. In absorption a second strong line occurs at a frequency δ = 109 cm^-1 above the first; a corresponding line is almost totally absent in the emission spectrum at 4·2 K, but it appears as a hot band of appreciable intensity when the temperature is raised to 80 K. This feature is assigned to the origin of the other component (|y, 0>) of the Q-band. The lifting of the degeneracy of the Q-band is interpreted as a crystal field splitting of the Jahn-Teller unstable ¹ E_u state.

The Zeeman effect is investigated for the 0–0 transition of the phosphorescence spectrum and the |x, 0> and |y, 0> components of the Q-band absorption spectrum. From the phosphorescence experiment it is concluded that the great majority of the ZnP guests are oriented in the host with an angle of about 25° between the out-of-plane molecular axes and the crystal a-axis. The analysis of the Zeeman effect in absorption (H//crystal a-axis) is complicated by the Jahn-Teller instability which causes two additional unknowns to appear in the problem: the frequency ν and the nuclear displacement parameter α of the active mode. When not making an assumption about these parameters one can only derive a lower limit for the matrix element of the orbital angular momentum between the two electronic components: Λ > 4·6. If is identified with the low-frequency mode of 180 cm^-1 appearing in the absorption spectrum, then it follows that Λ = 6·1 ± 0·6 with α = 1·4 ± 0·1.     

Isobaric Analogue State of the 0.211 MeV Level of Mn56 in Fe56

Gamma-ray spectrum from the reaction Mn⁵⁵(p, γ) Fe⁵⁶ at the isobaric analogue resonance at E_p = 1537 ± 4keV has been measured with a 15 cm³ Ge(Li) detector. Double and triple angular correlations at this resonance state have been measured. Proton elastic scattering was studied also at this resonance at the angles 135° and 150°. Analysis of these data yields a spin and parity assignment 2+, proton radiative width 2 ± 0.2 keV and total width 9 keV to this resonance state which is the isobaric analogue of the third excited state of Mn⁵⁶ at excitation energy 0.211 MeV.     

Electron spin resonance in the photo-excited triplet state of free base porphin in a single crystal of n-octane

E.S.R. experiments have been performed on the lowest triplet state of free base porphin (H₂P) in a n-octane single crystal at 1·3 K. The results demonstrate that the large majority of guest molecules occur in two orientations. While the molecules in these two orientations are coplanar, they have their N-H H-N axes at right angles. The fine structure results show that the two molecular orientations have zero-field splittings that differ by a few per cent in magnitude. Further, the 65 cm^-1 doublet separation which appears in the fluorescence spectrum of H₂P is related to the occurrence of these two orientations.

Resolved hyperfine structure is obtained for the two in-plane canonical orientations of the magnetic field and also when the field bisects the angle between these two directions. From an analysis of the fine structure and hyperfine structure results it is established that the zero-field splitting pattern is described by the parameters (average over the two orientations) the x axis is taken along the N-H H-N direction and z is the out-of-plane axis. From a computer simulation of the hyperfine structure it further follows that this structure is dominated by a high spin density at the methine carbons; with the coupling constants of the C-H fragment proposed by Hirota et al. the methine density is found to be ρ_m = 0·163.

In order to interpret the experimental results the zero-field splitting parameters and spin density distribution have been calculated for the lower triplet states of H₂P on the basis of a set of PPP-SCF-MO-CI calculations. From these calculations it follows that the lowest triplet state must correspond to the excitation e_g ←a _2u in Gouterman's four-orbital model. In terms of the D _2h symmetry of the H₂P molecule the assignment is ³ B _2u (b _3g ←b _1u ). For this assignment the calculations yield .     

Probable location of a 1E2g state of the benzene molecule

Photoexcitation spectra of benzene in rare gas matrices show a previously unreported transition near 46000 cm^?1. The observed bands are not explicable in terms of site splittings, impurity states, aggregation effects, intermediate radius states of the matrix, triplet states, excimer states, exciplex states or $\text{σ-π}{}^1$ transitions. The vibronic spacings in these spectra could be those expected for a ¹E_2g ← ¹A_1g transition and on this and other evidence we argue that the ordering of origins of the first four spin allowed intravalence states of benzene is ¹B_2u (38086 cm^?1), ¹E_2g (near 46400 cm^?1), ¹B_1u (48450 cm^?1) and ¹E_1u (55430 cm^?1). Our data also show that the transition ¹B_1u ← ¹A_1g accounts for most of the intensity of the 210 nm absorption band system. Our ordering of the spin allowed states permits interpretation of experimental data of others, confirms certain semi-empirical and ab initio SCF MO CI calculations in which account is taken of higher excitations and illustrates the necessity of including such higher excitations. The intensity of the ¹E_2g ← ¹A_1g transition is at least an order of magnitude less than previously calculated indicative of the difficulty of choosing suitable wavefunctions for the ¹E_2g state and of calculating “forbidden” transition probabilities.     

π* ←π electronic transition in hydroxy-benzonitriles. I. Orthohydroxybenzonitrile

The longest wavelengthπ* ←π electronic band system of ortho-hydroxybenzonitrile vapour through the absorption technique has been reported for the first time. Assuming a planar molecular geometry in both the electronic states, the molecule is classified into aC _s point group, and the present spectrum is attributed to¹ A′ ←¹ A′ type corresponding to electric dipole forbidden transition¹ B _2u ←¹ A _1g (260 nm band system) of benzene. The most intense band at 33914 cm⁻¹ has been assigned as the 0, 0 band, and the other vibronic bands have been interpreted in terms of the excited state and a few ground state fundamentals.     

Radiative decay of the metastable quartet state of copperporphin

In CuP the low temperature luminescence originates from eight transitions between a quartet (M = ±3/2, ±1/2) and a doublet (M′ = ±1/2) with M and M′ denoting the (approximate) eigenvalues of the spin angular momentum S_z along the fourfold axis. Here we report (1) the selection rules governing the polarizations of the transitions; (2) the zero-field splitting ξ between the ±3/2 and ±1/2 components of the quartet for CuP in an n-octane crystal (ξ = 1·1 ± 0·2 cm^-1); (3) a photo-selection experiment on CuP in an isopentane glass from which it is concluded that the ratio of in-plane to out-of-plane polarization in the 0-0 band at 2·1 K amounts to an intensity ratio I _‖/I _⊥ ≈ 2. The implications of these results for the different SOC pathways are analysed.     

EPR of photo-excited triplet states: A personal account

A sketch is presented of the path that has led from Zavoisky’s pioneering experiments to modern investigations by electron paramagnetic resonance (EPR) of the phosphorescent (S = 1) triplet state of polyatomic molecules or ions. The group-theoretical method first introduced by Wigner in his analysis of the multiplets of atomic spectroscopy, likewise provides a key for understanding the zero-field splitting and selection rules for radiative decay of the phosphorescent triplet state. Examples to illustrate the progress made through EPR experiments are selected from three fields. (i) Conformational instability on excitation. Both the zero-field splitting and the electron spin density distribution provide unique fingerprints of a triplet state’s geometry — structural information of a kind that is nonexistent for singlet states! Illustrations are provided by benzene C₆H₆ and fullerene C₆₀. (ii) The optical pumping cycle. The spin selectivity of singlet-to-triplet intersystem crossing and radiative decay of the individual spin components of the triplet state is discussed. In practice this selectivity is put to advantage by performing EPR on triplet states in zero-field by means of optical detection. In turn, such experiments have led to a detailed insight into the spin-orbit coupling mechanisms responsible for the spin selectivity of the above processes. The high sensitivity attainable with optical detection has recently culminated in EPR experiments on single molecules. (iii) Quantum interference. In a triplet state of low symmetry two of the spin sublevels may decay to the ground state by the emission of photons of a common polarization (i.e., out of plane for an aromatic hydrocarbon). In such a situation quantum interference between the two decay channels can be induced by an appropriate preparation of the excited state. An example is shown where flash-excitation in the singlet manifold followed by rapid intersystem crossing causes theS = 1 spin angular momentum to be created in a spin state which is not an eigenstate of the zero-field splitting tensor. This nonstationary character of the initial triplet state, which reflects the spin-orbit coupling pathway, is observed through the detection of a spontaneous microwave signal following the 25 ps laser flash.     

Theoretical studies of the defect structures and spin Hamiltonian parameters for manganese(II) and nickel(II) doped Zn(en)3(NO3)2 single crystals

The spin Hamiltonian parameters (g factors, hyperfine structure constants and zero-field splittings D and E) and local structures for Mn²⁺ and Ni²⁺ in [Zn(en)₃](NO₃)₂ single crystal are theoretically investigated from the perturbation calculations for trigonally distorted 3d⁵ and trigonally (or orthorhombically) distorted 3d⁸ cluster. The trigonal Mn²⁺ and Ni²⁺ centres are found to undergo the moderate angular variations Δβ of 4.5° and 5.2°, respectively, related to host Zn²⁺ site due to size mismatch. The orthorhombic Ni²⁺ centre shows the relative axial elongation ratio ρ (≈ 2.5%) and the relative perpendicular bond length variation ratio τ (≈0.2%). For Mn²⁺ centre, the contributions to g-shifts Δg_CT (or hyperfine structure constants A_CT and zero-field splitting D_CT) from charge-transfer (CT) mechanism are opposite in sign and five times (or 5% and 8%) in magnitude compared with those from crystal-field (CF) mechanism. For the trigonal Ni²⁺ centre, Δg_CT (or D_CT) are the same (or opposite) in sign and 17% (or 2%) in magnitude related to those from CF mechanism. For the orthorhombic Ni²⁺ centre, Δg_CT and E_CT (or D_CT) are same (or opposite) in sign and 16% and 48% (or 442%) in magnitude with respect to those from the CF mechanism. The signs and magnitudes of the trigonal distortion angles δβ (≈ ?0.3 and 0.4°) related to an ideal octahedron and the local angular variations Δβ related to the host bond angle are suitably illustrated by those of the axial distortion degree (ADD) and the angular variation degree (AVD) of the systems, respectively.     

Optical pumping in an organic crystal: quinoxaline in durene

Experiments have been performed to determine the path of entry into and exit from the phosphorescent triplet state T₀ of quinoxaline in a durene host. First of all the decay of phosphorescence after flash excitation was followed at 4.2 and 1.34 °K. It was found that for both perdeutero- and perhydroquinoxaline the lifetime is shortened by a factor of about three when the temperature is lowered from 4.2 to 1.34 °K. At 1.34 °K relaxation between the spin components (i.e. re-orientation of the triplet spin angular momentum) is slow relative to the decay, and the observed reduction in lifetime indicates that entry into and exit from T₀, are through the same spin component. Similar decay experiments were then carried out at 1.34 °K in a 10 kG magnetic field or in a somewhat weaker field so chosen that the effect of microwave saturation of one of the E.S.R. transitions between the components could be observed. From the results it follows that on intersystem crossing the molecules enter the manifold T₀ through the top zero-field component and thus initially have their spins aligned. Decay departs almost exclusively from the same component, even in the case of perhydroquinoxaline, where at least 45 per cent of it must be radiationless. The decay route agrees with out-of-plane polarization of phosphorescence for the free molecule. Finally, spin alignment on intersystem crossing is discussed from the theoretical point of view. It appears that the phenomenon is clear-cut only in molecules such as those of the aza-aromatics, where strong spin-orbit coupling of the atomic type occurs betwen ππ? and nπ? states.     

Investigation of the role of the projectile-target orientation angles on the evaporation residue production

The measured yield of evaporation residues in reactions with massive nuclei have been well reproduced by using the partial fusion and quasifission cross sections obtained in the dinuclear-system model. The influence of the orientation angles of the projectile- and target-nucleus symmetry axes relative to the beam direction on the production of the evaporation residues is investigated for the ⁴⁸Ca + ¹⁵⁴Sm reaction as a function of the beam energy. At the low beam energies only the orientation angles close to αP = 30° (projectile) and αP = 0°–15° (target) can contribute to the formation of evaporation residues. At large beam energies (about E _c.m. = 140–180 MeV) the collisions at all values of orientation angles αP and α _T of reactants can contribute to the evaporation residue cross section which ranges between 10–100 mb, while at E _c.m. > 185 MeV the evaporation residue cross section ranges between 0.1–1 mb because the fission barrier for the compound nucleus decreases by increasing its excitation energy and angular momentum.     

Pair exchange interaction in a crystalline nitroxide radical ESR study of dimers in the triplet state

The dimerization of the 9-aza-bicyclo (3,3,1) nonan-3-one-9-oxyl in the solid state is investigated by use of ESR spectroscopy. The ESR spectrum of a single crystal is characteristic of symmetric pairs of exchange-coupled radicals in a thermally accessible triplet state. The presence of well-resolved hyperfine structure is evidence for strongly localized excitations with a jumping rate lower than 10⁷ Hz.

The ESR spectrum is well described by the spin hamiltonian

At 35 GHz the observed splitting of the m _s=+ 1?0 transition has been found to be slightly different from that of the m _s=0?-1 one; this anomaly is explained by the mixing of the m _s electronic states.

The parameters and the principal directions of the zero-field splitting, spectroscopic and hyperfine tensors are determined and discussed. The principal directions of the dipolar tensor indicate a nearly equal spin density on the nitrogen and oxygen atoms; from the fine structure parameters D and E, determined to be (-0·0723 ± 0·0005) cm^-1 and (-0·0044±0·0003) cm^-1 at T=293 K respectively, it is suggested that the unpaired electron is partly delocalized on the molecule.

The singlet-triplet energy gap (J) and the zero-field splitting parameters are shown to be linearly temperature-dependent. These variations with temperature are attributed to the thermal expansion of the crystal lattice.     

The 2000 Å absorption system of the benzene single crystal in polarized light

The 2000 Å absorption system in the benzene single crystal is investigated at liquid nitrogen temperature. The analysis of the polarized spectra recorded along b and c in (100) plates appears to be not in favour of the assignment of the π* └π system to an upper state of B _1u symmetry, and it is not in contrast with the hypothesis of a ¹ E _2g upper state.

The first band in the system, located at 46 565 cm^-1, and totally polarized along c, is discussed in terms either of an out-of-plane false origin of the ¹ E _2g └¹ A _1g system, or of a new transition lying between the first two well known π-systems of benzene, possibly of π* └σ type.     

The Zeeman effect in spin-allowed and forbidden doublet-doublet transitions in orthorhombic rotating molecules

Theoretical predictions of the Zeeman effect on spin-allowed and forbidden doublet-doublet transitions in near-symmetric top molecules are reported, with the assistance of computer simulations of band profiles. Bandwidths in the high-field limit have been determined. Marked differences have been found between the behavior of spin-allowed and forbidden transitions. The intermediate-field effect on spin-allowed transitions is sensitive to the relative energy order of the zero-field spin components of the rotational sublevels in the combining vibronic states. In the high-field limit the rotational components of spin-allowed transitions give rise to a single band, corresponding to ΔM_S = 0, whereas the bands with ΔM_S = ±1 are also expected in spin-forbidden transitions. The applicability to actual cases is finally discussed.     

Optically detected E.P.R. and low-field ENDOR of triplet benzophenone

The ENDOR spectrum of ¹³C substituted (carbonyl carbon) triplet excited benzophenone was studied at ca. 100 G applied magnetic field by means of optical detection. The benzophenone was substitutionally dissolved in dibromodiphenylether (DDE). The ENDOR transitions and the E.P.R. transitions were studied as a function of applied field direction in the ab and bc crystal planes. The angle ? between the line joining the phenyl group centres and a principal axis of the fine structure tensor was found to be 23·6° ± 0·02° (standard deviation limited to one set of measurements). The principal axes of the ¹³C hyperfine tensor were within experimental error (±10°) coincident with the fine structure axes. The principal values of the hyperfine tensor were found to be : |A_xx /h| = 43·16 ± 1·84, |A_yy /th| = 22·66 ± 2·50, |A_zz /h| = 10·25 ± 1·30 MHz. The low-field ENDOR does not provide an indication of the signs of these tensor elements, so the value of the isotropic coupling constant cannot be measured. Two values of the anisotropic (dipole) hyperfine tensor elements were deduced on the assumption that the transitions frequencies are mainly determined by interactions between the nuclear spin and electron density on the carbonyl carbon atom. These values were (i) A _xx / ^d /h = 17·82, A_yy /h = -22·68, A_zz /h = -15·14 MHz and (ii) A_xx /h = 39·73, A_yy /h = -26·09, A_zz /h = -13·63 MHz. Set (ii) is consistent with recent calculations of the spin density distribution in triplet benzophenone in which the orbital spin densities are 0·64 for the carbonyl carbon π-orbital, 0·17 for the oxygen π-orbital, and 0·88 for the non-bonding orbital on oxygen (all expressed as fractions of one electron).

Isotope effects on the fine structure constants of triplet benzophenone were measured and found to be consistent with the changes occurring in the spin-orbit coupling with the ground state.

The kinetic parameters for the excitation and de-excitation of the triplet substates were deduced from transient ODMR studies of benzophenone in DDE. The T_z spin state is mainly populated (85–88 per cent) and this is also the most strongly radiative state (k_z ^r = 0·88). The steady-state populations of the three triplet levels are similar.     

Fine and hyperfine structure in three low-lying 3Σ+ states of molecular hydrogen

The fine structure constant (electron spin-spin coupling) and the hyperfine structure parameters (electron-nuclear spin coupling, including spin-rotation and electron-nuclear quadrupole coupling) in the low-lying triplet states b³Σ⁺ _u, a³Σ⁺ _g and e³Σ⁺ _u of molecular hydrogen and deuterium are calculated using a recently developed technique with full configuration interaction and multiconfiguration self-consistent field wave functions. The second-order spin-orbit coupling contribution to the ³Σ⁺ states splitting is negligible, and the calculations therefore provide a good estimate of the zero-field splitting based only on the electron spin-spin coupling values. For the bound a³Σ⁺ _g state a negligible zero-field splitting is found, in qualitative agreement with the e-a spectrum. The zero-field splitting parameter is considerable for the repulsive b³Σ⁺ _u state (?1 cm^?1) and of intermediate size for the bound e³Σ⁺ _u state. The isotropic hyperfine coupling constant is very large not only for the valence b³Σ⁺ _u state (1580 MHz) but also for the Rydberg a and e triplet states (?1400 MHz). The quadrupole coupling constants for the deuterium isotopes are negligible (0.04–0.07 MHz) for all studied triplet states. The electric dipole activity of the spin sublevels in the triplet-singlet transitions to the ground state is estimated by means of the quadratic response technique.     

N.M.R. solid echoes in systems of dipolar-coupled inequivalent spins-1 or dipolar-coupled inequivalent pairs of spins-1/2

Proton solid-echo transverse relaxation functions for many thermotropic and lyotropic mesophases, mapped by measurement of the echo amplitude S_yx (t′ = τ) as a function of τ using a P_y (90°)-τ-P_x (90°)-t′ sequence, yield gaussian behaviour of the form exp [-½M ^E ₂τ²] for decays up to 20–30 per cent of the value at τ = 0. M ^E ₂, the second moment for the dipolar interactions between the spin-½ pairs, is related to the van Vleck second moment M ^VV ₂ through a factor f. Whilst experiments suggested a value of 0·70–0·72 for f = M ^E ₂/M ^VV ₂, simple models that ignored the non-equivalence of the dipolar-coupled spin-pairs had predicted f = 0·65. In this paper we derive an exact analytic expression for the spin response of a model of two dipolar-coupled inequivalent spins-1 to the pulse sequence P_y (90°)-τ-P _α(β)-t′, and show that the present model, with the quenching of the spin-flip terms of the dipolar hamiltonian, resolves the afore-mentioned discrepancy. We also reconcile the differences between the experimental and the earlier predicted values of f for deuteron N.M.R. spin echoes in perdeuterated solids.     

Calculation of the fine structure of the triplet state $$\tilde a^3 A_2 $$ of the ozone molecule by the method of multiconfiguration self-consistent field

The zero-field splitting of the \(\tilde a^3 A_2 \) state of the O₃ molecule is interpreted on the basis of ab initio quantum-chemical calculations. The spin—orbit coupling with the ground X¹A₁ state is shown to make the main contribution to the zero-field splitting of the \(\tilde a^3 A_2 \) term (the state of the ³σπ type). The calculated parameters D and E agree well with experiment.