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The charge and current densities for variational molecular wavefunctions in finite basis spaces are examined, and the consequences of their failure to satisfy a continuity equation, and the local charge generation and annihilation, are discussed. The current can be used to compute observables even though it might not satisfy the continuity equation. When approximate wave-functions are used charge is not conserved locally, but is conserved globally, and the details of the structure of the charge sources and sinks are discussed in the case of benzene. A valence bond technique for the calculation of current density is described and applied to benzene. Valence bond and molecular orbital methods are compared.

The decay of a classical hindered rotor over the whole domain of motion from almost free overall rotation to harmonic vibration in a well is examined. The decay is described by a modification of a projection operator formalism involving the separation of dynamical and lattice time scales, and depends on a canonical transformation into a hindered rotating frame that rotates and oscillates in accord with the unperturbed equation of motion of two coaxial dipoles.

Chemically induced electron polarization (CIDEP) has been observed for the durosemiquinone radical anion generated in the flash photolysis of solutions of duroquinone in the presence of various amines. The initial polarization has been measured directly by using a fast response time-resolved E.S.R. spectrometer. The magnitude of polarization is shown to depend on amine concentration and identity, and the solvent medium. Conventional nanosecond flash photolysis has been used to measure duroquinone triplet lifetimes under various conditions. The results are discussed in terms of the triplet mechanism and the radical pair mechanism.

The density matrix equations of motion arising in the triplet mechanism of chemically induced electron spin polarization are solved exactly without the imposition of the Redfield approximation. It is shown that the triplet spin relaxation time occurring in the final expression is not the true relaxation time because the spectral density involved depends both on the rotational correlation time and on the quenching rate. The effective spin relaxation time differs only slightly from the true time. The equations are extended to the case where the initial triplet passes on its polarization to the secondary triplet and exact solutions for the polarizations of the latter's doublets are obtained in the form ΠB = cΠA; an explicit expression for c is presented. The consequences of the secondary triplet being able to pass back its polarization to the initial triplet are explored and a ‘coherence effect’ on the polarization on the first triplet's doublets is analysed.

The two-dimensional Coulomb problem is examined from the point of view of a mapping onto a harmonic oscillator basis which is suitable for the introduction of a species of coherent state. These multispace coherent states are especially suitable for the discussion of the time-evolution of the system under the influence of a stochastic perturbation, and the method permits the deduction of explicit forms for the matrix elements of a general evolution operator in terms of parameters describing the perturbation.

Schwinger's theory of sources is examined in connection with the electromagnetic interactions of molecules. Using his constructive principles of causality and space-time uniformity it is shown how to arrive at the starting-points of conventional calculations of photon-molecule scattering and of molecule-molecule interactions through the electromagnetic field.

The effect of a magnetic field on the intensity of fluorescence from chemiluminescent reactions occurring in fluid solutions is calculated. The calculation first considers pairs of triplet molecules rotating in each other's vicinity and calculates the effect of a magnetic field on the rate at which the overall singlet state is populated. The field diminishes this rate, as in the solid-state situation. The triplets are then allowed to diffuse apart, and the process of populating the overall singlet state of the pair is treated as a relaxation process occurring during the diffusive trajectory. In this case too at high fields the intensity diminishes. The calculations are repeated for triplet-doublet quenching, and, in accord with the solid-state results, the intensity is enhanced at high fields because the quenching rate for doublet-triplet collisions is diminished, and the resultant fluorescence arises via triplets which escape abortive D-T encounters. Explicit expressions involving the dynamical parameter...

The triplet model of electron spin polarization in fluid media is evaluated. The model consists of an initial singlet molecule rotating in a static, externally applied magnetic field. Intersystem crossing into different zero-field states is represented by a rate matrix diagonal in the molecular frame, and this matrix is expressed as an effective spin operator. The triplet rotates, and the motion affects the polarization in the laboratory frame, and also causes spin relaxation in the triplet manifold. The triplet is chemically quenched, and the polarization appears in the doublet fragments. The model is treated in a density matrix formalism and on the basis of anisotropic rotational diffusion of the triplet molecule. Explicit expressions are obtained in terms of the molecular parameters, the various rate constants, and the rotational correlation time.

The proportion of singlets generated during a recombination of atoms or ions in a radiolytic spur reaction is examined from the viewpoint of a combinatorial analysis. The results obtained differ from other, already conflicting, published work. The problem is formulated in a way that enables spin relaxation effects to be incorporated.

The electron spin resonance line-shape of a tumbling radical is treated by a projection operator formalism that enables analytical expressions to be obtained. These are valid from the fast-motion limit to well into the slowmotion region so long as non-secular terms may be ignored.

A quantum-mechanical approach based on a projection-operator formalism is presented for the ion motion and the instantaneous power absorption in ion cyclotron resonance. The role of non-linearities in the power absorption is investigated by incorporating the formalism in a non-linear response theory, and their effect on the line-shape is discussed.

The rate of interconversion of ortho and para hydrogen in a solution of paramagnetic ions is calculated. The rate depends on the correlation of the magnetic fields at the two protons, and this is calculated on the basis of a dipolar interaction modulated by rotational and translational motion of the molecule and the ion. The theory is applied to experimental data on conversion caused by lanthanon and transition metal ions, and is used to estimate the radii of first hydration spheres.

Analytical expressions for population transfer and spin polarization are deduced for a two-level system in which the levels converge linearly or exponentially from a finite separation. The asymptotic populations and polarizations are discussed for rapid and slow approach trajectories and, in the exponential case, a simple closed form exact to second order in the perturbation for all rates of approach is discussed.

A general description of linear optical birefringence effects is presented in terms of the effect of forward scattering on the photon polarization density matrix. The approach enables explicit statements to be given for the polarization changes involved in any linear birefringence phenomenon in terms of R matrix elements between plane-polarized base states. Expressions in terms of molecular quantities are listed for the R matrix elements involved in some typical natural and induced birefringence effects. This description of birefringence is related to the infinitestimal unitary transformations of the density matrix and rotations in Poincare space.

The extension of the polarization density matrix description of optical birefringence phenomena involving multiple interactions between molecules and the electromagnetic field is described. This extension of the previous theory [1, 2] enables non-linear phenomena to be incorporated consistently into the description of birefringence.

Rules for constructing operator equivalents off-diagonal in the angular momentum quantum number are described. Hyperbolic angular momentum operators are used in conjunction with the usual (spherical) angular momentum operators to obtain equivalents for all values of Δj and Δm. Tables of operator equivalents for harmonics of rank 0–6 are given.

The theoretical dependence of optical birefringence phenomena on the statistical nature of the light is investigated. Photon S-matrix calculations lead to expressions relating the change induced in the statistical nature of the beam to the molecular properties of the target sample. A hypothetical generalized optical birefringence experiment is analysed: in the experiment the coincidences of photons arriving at spatially separated detectors sensitive to different polarizations are observed with and without the sample in the beam, and the difference in the photon correlations depend on the initial statistical composition and polarization of the beam and the molecular properties of the sample. When the beam is generated by a thermal source the difference of the signals (with and without the sample) depends on the product of the polarizability and optical rotation tensors. When the light is generated by a single-mode coherent source the statistical properties of the light are such as to eliminate the second-o...

The scattering of polarized light by molecules is discussed in terms of a polarization density matrix. Particular attention is paid to scattering out of the direction of the incident beam, and the formalism enables the polarization characteristics of the non-forward scattered beam to be predicted for any polarization condition of the incident beam. Both Rayleigh and Raman scattering processes are contained in the formalism, although most attention is given to the former. Explicit expressions for the polarization of the scattered beams are obtained in terms of the polarizability and gyration tensors of the molecules by the application of diagrammatic perturbation theory, and it is demonstrated that a determination of the precise polarization state of the scattered beam can provide useful molecular information which is additional to that obtained from depolarization ratios alone. This is because the depolarization ratio depends on only the diagonal elements of the polarization density matrix and so does not...

The Dirac equation for the electron is solved to terms that are second order in the applied field by the application of the Foldy-Wouthuysen transformation. In the process this generates all the terms that are necessary to ensure that the g tensor is gauge-invariant to the third order. An explicit expression is given for the third-order g tensor and the result is compared with the formula given by Tippins [1]. A term that reflects the velocity dependence by the Bohr magneton gives a significant contribution especially for atoms of high atomic number. This same term is additional to the extra term obtained by Stone [2] and is of the same magnitude: it must be invoked to account for the g factor of atomic hydrogen.

The inverse Faraday effect, in which a magnetization is induced in a solution through which is passed a polarized light beam of arbitrary ellipticity, is discussed on the basis of the S-matrix formulation of optical birefringence. It is shown that the Faraday effect and the inverse Faraday effect are topologically identical problems of diagrammatic perturbation theory and so it follows automatically that the magnetization should be proportional to the Verdet constant. The optical Faraday effect is the circular birefringence induced by an intense circularly polarized beam of light propagated colinearly with the weak measuring beam: the electric vector of the circularly polarized beam interacts with the molecule in a way that resembles the interaction of a static magnetic field. The interrelations of these two effects and the normal Faraday effect the self-rotation of the polarization ellipse of an intense beam are discussed.

A theory of nuclear magnetic relaxation in solution is developed for situations in which the molecules of interest can tumble in a way that resembles their rotation in the gas phase. The equations are constructed heuristically from the exact correlation function for the free axially symmetric top and the classical limit of the quantum-mechanical equation is obtained. In the limit when the symmetric top becomes a spherical top the equations are identical to these obtained on a classical model by Steele.

It is demonstrated that the Kubo and Tomita formalism of the line shape of magnetic resonance spectra can, contrary to previous statements, account for alternating line widths. In the course of the...

Chemically induced electron polarization provides a new method for the direct determination of electron spin-lattice relaxation times of radicals in liquids. A rapid-response time-resolved E.S.R. spectrometer has been used to observe the decay of an emission spectrum into the corresponding absorption, and the effective relaxation time extracted by fitting an exponential curve to the early part of the decay, and then obtaining the true T 1 at any point of the spectrum by extrapolation to zero microwave power. The decay is monitored on resonance in the dispersion mode and at the points of maximum slope in the absorption mode : both results converge to T 1 at zero power with a gradient determined by T 2. Results for T 1 and T 2 on the benzophenone ketyl radical in liquid paraffin over a viscosity range 0·3 poise to 30 poise are reported. In this preliminary investigation the deuterated radical was used, and no attempt was made to resolve the hyperfine lines. The values of T 1 and T 2 for the modulation broad...

A theory of nuclear magnetic relaxation induced by inertial rotation in polar liquids is described. It is proposed that such rotation occurs only when the neighbourhood of a molecule attains an expanded lattice configuration. The non-markovian processes involved in the relaxation are expressed in terms of rate constants that occur in a formulation due to Anderson, and these are interpreted in terms of the unconditioned inertial rotation theory described in the preceding paper. The theory is used to interpret the values of T 1 obtained for 14N and D in liquid ammonia. The paper concludes with an outline of a general theory of anisotropic diffusion in liquids.