T. Thirunamachandran

On three‐dimensional rotational averages

In theories which describe the response of freely rotating molecules to externally imposed stimuli it is frequently necessary to average rotationally a product of direction cosines relating space‐fixed and molecular coordinate frames. In this paper a systematic method for deriving the required tensor averages is presented, and results up to the seventh rank are explicitly shown. Where appropriate both reducible and irreducible expressions are given and their equivalence is demonstrated. Finally, some useful identities relating rotational averages of different ranks are noted.

The hyper‐Raman effect: A new approach to vibrational mode classification and assignment of spectral lines

The theory of vibrational hyper‐Raman scattering (inelastic second harmonic light scattering) is developed within the framework of quantum electrodynamics. The dynamical system comprises the molecule and the radiation field, coupled by multipolar interactions. In the present work, the electric dipole approximation is employed and the results involve the hyperpolarizability tensor. In contrast to previous work, full index symmetry of this tensor is not assumed. The tensor is decomposed into irreducible weights forming the basis for a new vibrational mode classification scheme. A set of five experiments is specified which allows unambiguous assignment of an active mode to one of six classes. The scheme has been applied to several molecules and compared with some experimental results. Explicit expressions for scattering intensities for a wide variety of experimental configurations are given; results for depolarization ratios are also presented.

Circular dichroism: A general theory based on quantum electrodynamics

A theory of circular dichroism is developed through a direct calculation of the absorption rates for circularly polarized light on molecules. From this a differential rate as between left and right circularly polarized light is calculated. This is immediately related to the experimental data on circular dichroism. When the calculations are restricted to the dipole approximation we reproduce the rotatory strength in the form of a differential Einstein B coefficient. Higher moments are considered in detail and their effects analyzed for both the locked‐in situation and the case of randomly oriented molecular absorbers. A general expression is obtained for the differential absorption rate.

The crystal spectrum of naphthalene in the region 3200 Å to 2200 Å

The absolute intensity of absorption in the naphthalene crystal spectrum has been measured at room temperature. Measurements on the intense system at 2200 A and on the system at 2850 A of medium intensity are recorded for the first time along both the a and b crystal axes and indicate that the transitions are polarized along the long and short molecular axis respectively. The assignment of the weak system at 3200 A as arising from a long axis transition is confirmed.

The Interaction of Optically Active Molecules

The difference in interaction energies between two laevo molecules, and one dextro and one laevo, are analysed. Formulae are given for the discriminating terms in the dispersion and induction energies for molecules in fixed orientations, between freely rotating molecules, and molecules rotating about the intermolecular axis. Discrimination in the resonance interaction between optical isomers appears in the retarded interaction (in dipole approximation) as a term with an inverse square dependence on distance in the near zone. Its significance is discussed for pairwise interactions and in crystalline systems.

A theory of vibrational circular dichroism in terms of vibronic interactions

A theory of vibrational circular dichroism is developed along the lines of the theory of intensity borrowing by forbidden electronic transitions. The vibrational transition exhibiting circular dichroism is a one-quantum jump in a mode capable of mixing different electronic states. The degree of mixing is different for the initial and final states of the vibrational transition; this is shown to be a source of circular dichroism. The theory is developed on the basis of the adiabatic and crude adiabatic approximations; expressions for rotatory strengths are given. Within the crude adiabatic picture, effects due to any change in the equilibrium configuration on electronic excitation are examined. Vibrational effects in electronic circular dichroism are also analysed.

Elementary derivation of long-range moments of two coupled centrosymmetric systems

Abstract The expression for the long-range dipole moment of a pair of non-identical centrosymmetric systems (varying as R −7 ) in terms of frequency-dependent polarizabilities and hyperpolarizabilities is recovered more simply than hitherto. An expression in terms of frequency-dependent quantities for the quadrupole moment of an identical pair (∞ R −6 ) is given for the first time.

A NEW GENERALIZATION OF THE CASIMIR-POLDER POTENTIAL TO HIGHER ELECTRIC MULTIPOLE POLARIZABILITIES

An elementary method for calculating retarded interaction energies for a pair of molecules with electric multipole polarizabilities of arbitrary order is presented. In the multipolar framework of quantum electrodynamics, the interaction energy is viewed as arising from two‐photon exchange and calculated using fourth order perturbation theory. It is shown how the energy may be expressed in terms of derivatives of the Casimir–Polder formula written in a special form as an integral over imaginary frequency. Explicit formulas are presented for (a) an electric dipole polarizable molecule interacting with an electric quadrupole polarizable molecule, (b) an electric dipole polarizable molecule interacting with an electric octupole polarizable molecule, and (c) an electric quadrupole polarizable molecule interacting with another electric quadrupole polarizable molecule. The results are expressed in terms of reducible and irreducible components of multipole moments. For case (b) it is shown that in addition to the...

The non-additive dispersion energies for N molecules: a quantum electrodynamical theory

With the aid of the Heisenberg operators for the electromagnetic field in the neighbourhood of several molecules, the many-body interaction potentials are calculated by finding the energy of a test molecule in this field. In the first instance the calculation is made for the case where the intermolecular separations are very large. In this far-zone range, the energies depend on the molecules through their static polarizabilities. The three-body non-additive dispersion energy is calculated for an arbitrary configuration and the dependence on the geometry is investigated. The four-body non-additive potential is found for the regular tetrahedral configuration. The theory is extended to cover all separations outside regions of overlap. It is shown that the interaction energy in this case depends on the dynamic polarizabilities. The full Casimir-Polder potential follows directly from the general expression. The near-zone limit of the complete formula tends to the form obtained by using electrostatic couplings only: as with, for example, the Axilrod-Teller potential for N = 3. The work described here presents an alternative viewpoint to the conventional perturbation theory and lends further insight into the nature of intermolecular forces.

The multipolar Hamiltonian in radiation theory

The multipolar Hamiltonian is widely used in applications of quantum electrodynamics to quantum optics and theoretical chemistry. In this paper, it is shown how this form of the Hamiltonian, normally derived within the Coulomb gauge, may be obtained from a Lagrangian in an arbitrary gauge. The method involves the construction of the Routhian functional to eliminate ignorable coordinates from which the Hamiltonian is obtained. Further, the electrostatic interactions arise from a constraint and are independent of the initial choice of the scalar potential. The contributions from Röntgen currents, arising from dielectric motion, are allowed for by including nuclear motions in the theory.