A. D. Buckingham

The Polarization of Laser Light Scattered by Gases

Measurements of the polarization of light scattered from the beam of a helium-neon gas laser at low pressures are described. The intensity, polarization and parallelism of the beam permit high accuracy, and new values for the depolarization ratios of twenty-four simple species are reported. The general quantum theory of scattering is discussed and applied in detail to the evaluation of a formula for the depolarization ratio of the scattered light. It is found that quantum corrections to the classical formula arise from (i) the effects of frequency changes due to rotational Raman scattering, (ii) changes in the molecular polarizability with rotational state due to centrifugal distortion, (iii) approximations inherent in the polarizability scattering formula, and (iv) vibrational Raman scattering. Effect (i) reduces the depolarization of hydrogen to 91% of its classical value; (iii) is unimportant unless the frequency of the light is near an absorption frequency of the molecule. The depolarization measurements have been combined with refractivity data to yield the anisotropies in molecular polarizabilities of the molecules studied.

Solvent Effects in Nuclear Magnetic Resonance Spectra

Contributions to nuclear screening (chemical shifts) arising from molecular interactions with solvent molecules (excluding hydrogen bonding) are discussed in terms of appropriate theoretical models. These include contributions from van der Waals interactions σw, from the magnetic anisotropy of the solvent molecule σa, and from polar effects σE. By a suitable choice of solute‐solvent systems it has been possible to demonstrate each of these effects experimentally for proton resonances. For CH4 as a solute, σw was in all cases negative, its magnitude varying with the nature of the solvent and amounting to as much as 0.6 ppm for high molecular weight solvents. In agreement with the theoretical models, σa was found to be positive for disk‐shaped solvent molecules and negative for cylindrically symmetrical rod‐shaped molecules, its magnitude in extreme cases reaching 0.75 ppm. For CH3CN as a solute, σE was negative and showed the expected dependence on the dielectric constant of the solvent.

Rayleigh and Raman scattering from optically active molecules

The intensity of Rayleigh and Raman scattering from optically active molecules is shown to be slightly different in right and left circularly polarized incident light. The circular intensity differential of the Rayleigh line is dependent on components of the optical activity tensor, and that of the Raman lines is a function of the variation of the optical activity with the vibrational coordinates. This circular intensity differential might be of the order of 10-3 times that of the Rayleigh or Raman intensity.

Medium Effects in Proton Magnetic Resonance. I. Gases

The position of the proton resonance signal of a molecule in a gas is found to depend upon the gas pressure. Four distinct phenomena are considered to contribute to the displacement which the signal undergoes as the density is changed: (a) bulk susceptibility, (b) van der Waals interactions, (c) electric fields, and (d) neighbor‐molecule magnetic anisotropy. Theoretical expressions are presented for each of these effects. Experiments were performed on CH4, C2H6, and HCl as pure gases and as mixtures with a variety of foreign gases. For HCl at 30°C, the chemical shift changes by —0.41 ppm as the pressure is raised to 55 atm. Good correlation between theory and experiments is obtained in all cases. Parameters describing the influence of an electric field on the proton screening constant are deduced for C–H bonds and for HCl. The bulk susceptibility contribution is large, van der Waals and neighbor‐molecule anisotropy effects are small, and the electric fields from permanent dipoles and quadrupoles and from ...

Direct Method of Measuring Molecular Quadrupole Moments

An experiment whose object is the determination of permanent molecular quadrupole moments is suggested. It is analogous to those used in measurements of electro‐optical Kerr constants, but the uniform electric field proportional to the applied voltage V is replaced by the field gradient of a square four‐wire condenser. If the wires at x=±a are at a potential V relative to those at y=±a, then the field gradient on the z axis will tend to orient quadrupolar molecules so that a fluid in the condenser will become doubly refracting. The induced anisotropy in the refractive index of a gas is shown to be first order in the applied voltage and of the form nx—ny=[B+(A/T)]V, while in the Kerr effect it is second order in V, and is given by nx—ny=[C+(D/T)+(E/T 2)]V2. The constant A is proportional to the molecular quadrupole moment and to the anisotropy in the polarizability, while B is proportional to the quadrupole moment induced in a molecule by a uniform field. In spherical molecules A, D, and E are zero. Calcul...

The quadrupole moment of the carbon dioxide molecule

A direct measurement of the magnitude and sign of the quadrupole moment of the carbon dioxide molecule has been made by determining the birefringence induced in gaseous C02 by an inhomogeneous electric field. The method of measurement and the experimental details are described. The observable is the product of the molecular quadrupole moment 0 and the difference between parallel and perpendicular components of the optical polarizability tensor. F o r CO2, this quantity was found to have the value — (9.1±0.5)x 10-50 e.s.u. can be determined by other methods, but unfortunately the present uncertainty in this quantity is greater than that of the product. The most satisfactory value of a a8-a1 is taken to be 2.2 x 10-24cm3, giving for the molecular quadrupole moment of CO2— 4.1 x 10 -26 e.s.u., the sign indicating that the oxygen atoms are negative with respect to the carbon atom. The role of the ‘ quadrupole polarizability ’ of the molecule in complicating the interpretation of the experimental results is discussed, and experiments on argon and sulphur hexafluoride used to provide an estimate of its effect in the case of CO2.

Angular Distribution and Intensity in Molecular Photoelectron Spectroscopy I. General Theory for Diatomic Molecules

A theory of the angular distribution of photoelectrons ejected with a given energy from diatomic molecules is presented. The differential cross-section OO is of the form a = ^ [l+ /JP ,(co»® )] where O Total is the total cross-section, B an anisotropy parameter and O the angle between the polarization vector of the incident light and the direction of the photoelectron. Expressions for O total and B in terms of internal transition dipole moments are obtained for transitions between individual rotational states of the molecule and ion, for either of Hund’s cases (a) or (b) . The formulae have been developed for central-field bases for the eigenstates of the electron before and after ionization. When rotational structure in the photoelectron spectrum is unresolved the angular distribution is independent of the choice of Hund’s case

SOLVENT EFFECTS IN VIBRATIONAL SPECTROSCOPY

The effects of solute-solvent interactions on the frequencies, intensities and shapes of the infra-red absorption bands of dissolved molecules are discussed. The interaction potential energy U between a single solute molecule and its environment is treated as a variable depending upon the solvent configuration and on the normal co-ordinates of the isolated vibrating solute. Formulae relating the mean solvent shifts Δω to the derivatives of U with respect to the normal co-ordinates and to the anharmonic constants of the free solute are deduced for diatomic and polyatomic molecules. Invariants on isotopic substitution, such as Δω/ω, are discussed and it is shown that the effects of isotopic changes on the solvent shift, and hence on the probability of a particular solvent configuration occurring, are normally small. The different solvent environments around ground-state and excited-state solute molecules are found to lead to a small difference between the displacements of the Stokes and anti-Stokes lines in the Raman spectra of dissolved substances; the difference has not yet been established experimentally, and it may prove hard to measure, as it is proportional to the square of the half-width of the band, and is therefore only appreciable when the band is broad.

A theory of the dielectric polarization of polar substances

With the aid of classical statistical mechanics, a general expression for the static dielectric constant is derived. It is found, as in earlier work, that the dielectric constant is dependent upon the mean-square dipole moment of a macroscopic spherical sample of the substance. This mean-square moment is expanded as a series in powers of the mean molecular polarizability, and the terms proportional to the zero and first powers are evaluated in detail and in such a way that the long- and the short-range effects are separated. The former are determined with the aid of macroscopic arguments, so that a purely molecular theory remains. In the limit when short-range directional forces are zero, the formula reduces to the well-known Onsager equation. It is found that it is not in general legitimate to replace the surroundings of a macroscopic sample by a continuum having the bulk properties of the substance, and for this reason the approximate equation of Harris & Alder is found to lead to doubtful conclusions. The general equations are applied to the experimental data for water and other liquids, and the results are not unsatisfactory.

Simple two-group model for Rayleigh and Raman optical activity

Rayleigh and Raman circular intensity differentials are calculated for a dissymmetric molecule comprised of two neutral optically inactive groups. The dominant mechanism has no counterpart in optical rotation, being of longer range than Kirkwoods dynamic-coupling interaction that leads to optical rotation. Differential scattering increases with increasing separation of the two groups, whereas optical rotation decreases. Predicted magnitudes are of the order of those observed. The signs of the effects give the absolute configuration of the molecule.