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 .     

Methyl group tunnelling and torsion in 2,4-hexadiyne

The tunnelling splitting of the ground torsional level of solid 2,4-hexadiyne and transitions to excited torsional states have been measured at low temperatures using neutron inelastic scattering. At 4 K the tunnelling splitting is 1·060 μeV (0·0086 cm^-1). It decreases as the temperature is raised, to 0·834 μeV (0·0067 cm^-1) at 35 K, and to less than 0·6 μeV at 50 K. A V-2←V=0 transition in the torsional vibration has been observed at 222 cm^-1 which shifts to 160 cm^-1 in the fully deuterated compound.

The values of the torsional frequencies, tunnelling frequency, and the change of tunnelling splitting with temperature have been fitted exactly to a potential energy for rotation of a methyl group given by

with a barrier to rotation of 432 cm^-1.

Changes in the tunnelling transitions as the temperature increases are compared with existing theories of the mechanism.     

Resonance absorption and fluorescence in argon

Absorption cross sections of argon for argon resonance radiation have been measured by several techniques. The apparent cross sections are small (0·1 to 1·6 × 10^-18 cm²) for resonance absorption and the values depend on the technique used for measurement. These observations are interpreted in terms of extensive reversal and broadening in the source. The excitation and quenching of resonance fluorescence was studied to provide information about the rates of the processes

The rate constants were estimated relative to k _r, the rate constant for radiation. Radiation imprisonment leads to a reduction of k _r from its natural value and observations of the decay of resonance fluorescence suggest that k _r ～ 1·5 × 10⁵ s^-1 in our system at [Ar] = 2 × 10¹⁷ atom cm^-3. Combining this value with the relative values for the quenching rate constants gives k ₁ < 1·5 × 10^-13, k ₁′(M = N₂) ～ 6 × 10^-12, k ₁′(M = NO) ～ 4 × 10^-10, in units of cm³ s^-1 molecule^-1.     

Rotational band contour analysis in the 2760 Å system of p-chlorofluorobenzene

The origin band of the 2760 å system of p-chlorofluorobenzene has been shown to be a type B band of a prolate asymmetric top. The electronic assignment of the system is therefore ¹ B ₂-¹ A ₁.

The excited state rotational constants are:

compared with the estimated ground state constants:

The rotational origin of the band is at 36275·1 ± 0·2 cm^-1.     

Electron spin resonance study of radiation-produced radical pairs in single crystals of 1-methyluracil

Five different types of radical pairs produced in single crystals of 1-methyl-uracil by irradiation with X-rays were identified. Partial differentiation between pairs was achieved by utilizing different stabilities versus ultraviolet illumination or annealing, and variation of relative yields with temperature. The composition of pairs was derived from hyperfine couplings, the orientation from the maxima of dipolar couplings. These were found to agree with the directional cosines obtained from the crystal structure. Further evidence was provided by half-field spectra (Δm _S=2). The zero-field splitting constant D was determined for five pairs, the value of E for one pair. Second-order effects observed at 9·5 GHz and at 35 GHz have been fully analysed for two pairs by application of the appropriate theory which permitted to determine the absolute sign of D. Two pairs are homogeneously composed of hydrogen abstraction radicals 1-methyleneuracil. These are located two layers apart for one pair with the link normal to the molecular planes (D/gβ = -107·5 G), and within one plane for the other (-224·0 G). The three remaining pairs consist heterogeneously of an abstraction radical and a hydrogen addition radical 1-methyl-5,6-dihydrouracil-6-yl. Two of these are intraplanar (-180·0 G; -129·0 G), and the other one located in neighbouring layers (-183·0 G).     

The excitonic and zero-field splittings of the first triplet state of toluquinone single crystals

The pure electronic S ₀ → T ₁ transition of toluquinone has been studied in absorption using single crystals at 6 K and polarized light. The theory of the Zeeman effect on the crystal exciton levels is developed and compared with the experimental results. High-field measurements show that the factor group splitting is 0·32 cm^-1 and that the orbital plus state lies at higher energy. The ordering and energy separation of the magnetic substates of the factor group levels is also obtained. The latter results are confirmed by low field measurements and the following molecular zero-field splitting parameters are obtained: Y = +0·12, X = -0·02 and Z = -0·09 cm^-1.     

Ecriture de l'énergie cinétique à l'aide d'opérateurs quasi-moments

Cet article concerne l'utilisation des quasi-moments ?π _m , définis par

,

pour exprimer l'opérateur correspondant à l'énergie cinétique de N particules en Mécanique Quantique. La condition de Wilson-Howard portant sur les coefficients s^ml est interprétée comme la condition pour que les opérateurs ?π _m soient hermitiques quand on utilise l'élément de volume s dq ₁ … dq ₃ N (s=[dét {s^ml }]^-1). La condition générale pour qu'il soit possible de trouver un élément de volume avec lequel les opérateurs ?π _m sont hermitiques est donnée et différentes expressions de l'opérateur énergie cinétique sont établies quand cette condition est remplie et quand elle ne l'est pas.     

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.     

Hyperfine anomaly arising from the nuclear spin-forbidden transition,and absolute sign determination of the zero-field splitting constant

It has been found in the triplet E.S.R. spectra of radical pairs in irradiated potassium deuterium fumarate that the hyperfine structure of the two transitions, M _s = 1?0 and M _s = 0?+1, are entirely different. This anomaly has been interpreted in terms of the forbidden transition arising from the mixing of the nuclear spin states by the anisotropic hyperfine interaction. The theory has been developed for multiplet electron spin systems and includes the nuclear Zeeman interaction which is often neglected. The theoretical predictions are in good agreement with the observed separations and intensities of the anomalous hyperfine lines. In addition, it has been found that since the forbidden lines of the electron spin multiplet system with S ≥ 1 appear strongly only in transitions which include some specific electronic spin states, the anomalous features of the spectra make it possible to determine the absolute sign of the zero-field or hyperfine splitting constant, if the sign for one of them is known. Using this principle, attempts have been made to determine the absolute sign of the zero-field splitting constant for a number of triplet E.S.R. spectra which exhibit a hyperfine anomaly arising from the proposed mechanism.     

Molecular orientation correlations and reorientational motions in liquids carbon monoxide,nitrogen and oxygen at 77 K; A Raman and Rayleigh light-scattering study

Reorientational autocorrelation functions have been determined from measurements of depolarized vibrational Raman scattering for liquid carbon monoxide, nitrogen and oxygen at 77 K and atmospheric pressure. The autocorrelation functions, which for these liquids are not significantly affected by vibration-rotation interaction, reveal that free rotation is an important feature of the molecular motion in liquid nitrogen but is less important for carbon monoxide and oxygen. The differences in behaviour are discussed in terms of intermolecular forces.

New values for the depolarized Rayleigh scattering cross section have been determined from intensity measurements made relative to the 992 cm^-1 Raman line of benzene. These values are compared to those reported previously by the authors using a different intensity standard (Chem. Phys. Lett., 31, 355 (1975)). The scattering cross sections yield the following values , where ?_ij is the angle between the major axes of molecules i and j (i≠j) and P ₂ indicates the second Legendre polynomial: -0·15 ± 0·2 for CO, +0·30 ± 0·2 for N₂ and +0·40 ± 0·2 for O₂. The large errors result from uncertainties in the local field correction factor. The negative value for CO can be explained as a result of strong quadrupole interactions which tend to align neighbouring molecules perpendicular to one another. The forms of the reorientational cross-correlation functions determined from the current Raman data and previous Rayleigh data are briefly discussed.     

Rotational band contours in the 5000 Å 1 B 1g -1 Ag electronic system of p-benzoquinone

Using the technique of computer simulation of rotational band contours the 1–0 band in v ₇, band E, in the 5000 Å ¹ B _1g -¹ A_g system of p-benzoquinone has been rotationally analysed. It is a type A band and the excited state rotational constants are:

The excited state inertial defect determined from these constants is -0·8 ± 0·2 uÅ ². This value is almost certainly due not to non-planarity of the excited state but to a Coriolis interaction between v ₇ and perhaps the b _1u vibration v ₁₃. Such an interaction, if it were weak, would affect only the A′ rotational constant.

Previous assignments [2] of other type A bands and type B bands in the spectrum are reviewed where possible with the new evidence of the computed contours and the assignments remain largely unaltered.     

Thermodynamic parameters for gaseous sulphate ion

Electrostatic energies and Madelung parameters for M ₂SO₄ (M = Li, Na, K, Rb and Cs) and for MSO₄ (M = Ca) are reported. An assessment of the charge distribution within the sulphate ion (q ₀ = -0·80) is made and values:

and

are assigned to the enthalpies of formation and solvation of the gaseous sulphate ion. The total lattice potential energies are found to be

A value of -1267 kJ mol^-1 is assigned for the oxide ion affinity of sulphur trioxide.     

Ab initio potential surfaces for the à and states of HCN+

Ab initio configuration interaction calculations for the à ²Σ⁺ and states of HCN⁺ are presented. Minima occur at r _CH = 2·03 a ₀, r _CN = 2·25 a ₀ (à ²Σ⁺) and r _CH = 2·75 a₀, r _CN = 2·26 a ₀ (). The potential surface for the state has a local maximum as the hydrogen atom is pulled away from CN. The barrier height is calculated to be 0·27 eV.     

An electron paramagnetic resonance study of a manganese(IV) ion in a trigonal environment

An electron paramagnetic resonance (E.P.R.) study on ammonium 9-molybdomanganate (NH₄)₆MnMo₉O₃₂.8H₂O, has been carried out. The system has a Mn(IV) central ion and can be considered as a d ³ ion in a D ₃ environment. The results are fitted to a spin hamiltonian with S = 3/2 and I = 5/2 which is due to ⁵⁵Mn. The values of the spin hamiltonian parameters determined were

A ligand field theory approach has been taken in an attempt to interpret the observed zero-field splitting parameter.     

The properties of some derivative autocorrelation functions computed with the atom-atom potential

High-resolution quasi-elastic neutron-scattering measurements have been made on two nematogens: DMBCA with a nematic range 108 to 119°C, and 5CB and a tail-deuteriated sample (D5CB), having a nematic range 22·6 to 35·1°C.

Results on 5CB in the crystal phase at ～18°C showed no significant quasielastic broadening, which means that any random motions of the alkyl chain are slower than about 5 × 10⁹ rad s^-1. Measurements were made at a single temperature in the nematic phases on specimens aligned in a magnetic field of 0·25T; for DMBCA with scattering vector Q⊥n (n is the nematic director) and for 5CB and D5CB with Q⊥n and Q∥n and also on the isotropic liquid phase of D5CB at 45°C. Analysis of the coherent scattering from nematic D5CB at Q = 1·2 Å^-1 and 25°C gave an order parameter <P ₂>=0·55, close to the simple mean field value for this temperature. The coherent scattering from DMBCA is too weak to allow this experiment to be performed.

The most remarkable qualitative feature of the results is the close similarity of the scattering law S(Q, ω) for D5CB (and 5CB) with Q⊥n and Q∥n. Analysis of the results in all cases was made using values for the translational diffusion constants measured previously. Corrections for multiple scattering are shown to be important and a single simple model has been devised which fits the line shapes of all the results for D5CB in nematic (Q⊥n and Q∥n) and isotropic liquid phases and DMBCA. The model involves uniaxial rotational diffusion about the long molecular axis m coupled to a displacement along the rotation axis giving a net rotation in a plane whose normal makes an angle ∝ relative to the direction m. Values for the rotational diffusion constant D _rd ns^-1 are as follows: D5CB, 25°C, 6 (∝ ～ 50°); 45°C, 10. DMBCA, 112°C, 16, (all ±10–15 per cent).

The results for D5CB and 5CB are so similar that no additional detailed model fitting was attempted for the fully hydrogenous sample and it is concluded that while the motion of the alkyl tails is freer, the time scale of the motions is not more than about a factor of 2 faster than that of the molecular cores.     

Magnetic circular dichroism of the first spin-forbidden transition in 2[Cr(en)3Cl3] . KCl . 6H2O

The longitudinal Zeeman effect of the ² E ←⁴ A ₂ transition of the Cr⁺³ ion in single crystals of 2[Cr(en)₃Cl₃] . KCl . 6H₂O has been measured using circularly polarized light as a function of magnetic field strength between 0 and 160 kgauss at ～80 K. The g factor for the ground state was determined to be g _‖(⁴ A ₂) = 2·01±0·05, in agreement with the E.S.R.-determined value. The ratio between the excited state g values and that of the ground state was determined; using the value g _‖(⁴ A ₂) = 1·99, the g factors g _‖(2) = 2·61±0·04 and g _‖() = 1·47±0·04 were obtained.     

Proton shielding function for hydrogen chloride

For a diatomic molecule the nuclear shielding constant σ(ξ) of either nucleus can be expanded as a power series in the relative displacement from equilibrium ξ. Thus the nuclear shielding function is

where ξ=(r-r _e)/r _e with r the actual bond length and r _e the equilibrium bond length. The σ_e ⁽ⁱ⁾ are molecular parameters. By experimental observation of the temperature dependence of the proton magnetic shielding of hydrogen chloride gas it is possible, after allowing for intermolecular effects, to obtain the values σ_e ⁽⁰⁾=32·48 (±0·33) p.p.m. and σ_e ⁽¹⁾=-100 (±24) p.p.m. for the coefficients of the proton shielding function. Using this data it is possible to show that the isotope shift between H³⁷Cl and H³⁵Cl is about 0·001 p.p.m. By a comparison with earlier results for molecular hydrogen it would appear that in some instances differences in vibrational and rotational averaging may alter chemical shifts between different compounds by amounts considerably larger than the experimental error in chemical shift measurement.     

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.     

Proton N.M.R. study of the dynamics of the ammonium ion in ferroelectric langbeinite, (NH4)2Cd2(SO4)3

The proton N.M.R. lineshape of polycrystalline Langbeinite, (NH₄)₂Cd₂(SO₄)₃, has been studied in the temperature range 300 K to 1·8 K. The resonance line is motionally narrowed over the entire temperature range, and the low temperature proton line shows clear evidence for tunnelling motion of the ammonium ion between spin-symmetry states. From a computer simulation of the lineshape, we obtain an estimate for the tunnelling splitting parameter, J, of the torsional ground state of the ammonium ion, as 375 ± 125 gauss. For an undistorted tetrahedral crystal field this corresponds to a tunnelling splitting Δ = 4J = 6·3 ± 2·1 MHz.

Pulsed proton N.M.R. studies have also been carried out on the above compound at 30·8 MHz and 48·2 MHz and the spin-lattice relaxation time (T ₁) has been measured by the π - t - π/2 pulse sequence as a function of temperature down to 77 K. At 30·8 MHz, a T ₁ minimum of 13 ms occurs at 105·8 K, and is ascribed to random reorientations of the NH₄ ⁺ ion. An activational energy barrier of 0·74 ± 0·1 kcal/mole and an associated pre-exponential factor of 8·0 × 10^-13 s are calculated for the above motional process, and the value of the activation energy is correlated with the tunnelling splitting of the torsional ground state.

An anomaly in T ₁ has been observed at the ferroelectric Curie point (95 K), indicating the order-disorder nature of the transition. This is the first experimental evidence relating to the nature of the transition in Langbeinite.     

On the Taylor expansion of the expression for the transition probability for normal absorption processes

Molecular reorientation of 2-chloropyrimidine dissolved in CS₂ (0·1 M) has been investigated by means of ¹³C and proton relaxation. Although weakly coupled, the proton system subjected to non-selective 180-τ-90 pulse sequences allows the determination of one autocorrelation and one cross-correlation dipolar spectral density. The proton and carbon-13 relaxation data allow the complete determination of the rotational diffusional tensor:

and

It is shown that scalar relaxation due to nitrogen-14, has no effect on proton longitudinal relaxation time, because of a cross term due to the symmetry of the molecule, although this mechanism could, a priori, have been thought to be important. Finally, the nitrogen relaxation time recalculated with D_xx , D_yy , D_zz and the quadrupolar coupling tensor is in agreement with the observed linewidth.