D.P. Craig

Third-body mediation of resonance coupling between identical molecules

Abstract A calculation is given of the contribution to the rate of energy transfer, and to the energy shift, for two identical molecules A and B due to mediation by a non-identical molecule C. In a solution C may be a solvent molecule; in a gas it could be any molecule present adventitiously. In the near zone the main term in the energy shift is proportional to the polarizability of C, and to the inverse cube of the product of the A–C and B–C distances. With realistic assumptions the shift and the transfer rate due to indirect coupling can be as much as several percent of the direct.

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.

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.

Dispersion and resonance terms in exciton—phonon coupling: absorption band profiles in molecular crystals

Abstract Absorption band profiles in the exciton spectra of molecular crystals depend on exciton—phonon coupling. The combined influence of dispersion and resonance terms in the coupling is analysed by the Green function method and the profiles discussed as a function of temperature. The profiles depend on the broadening of individual transitions by phonon damping, and on the spread of intensity over various phonon sidebands forming spectral progressions. The nature of the profiles is shown by representative calculations and applications indicated.

An analysis of models for resonant transer of excitation using quantum electrodynamics

Abstract The resonance coupling of identical molecules A and B is further explored over all separation distances R . Three models are analyzed. In the first, applicable for short separations, stationary states of the coupled pair are employed. In the second the process is viewed as a time development of |A*B〉 and the probability of finding the system in |AB*〉 is calculated. In the third energy transfer is treated as emission followed by absorption. At distances beyond the stationary state regime, where the process is energy transfer from A* to B, we show that the rate calculation must be based on spontaneous emission by A* and absorption by B. Also we note that when some conventional approximations are replaced by a more exact treatment the result appears superficially to be non-causal. However over short times, arguments from time—energy uncertainty indicate that conclusions drawn from attempts to establish causality are difficult to sustain.

Structural disturbance and lattice relaxation in molecular crystal packing calculations

Abstract Lattice calculations on impurity-containing crystals are reported, made with the help of standard intermolecular potentials. A lattice containing a substitutional impurity, or a vacancy, relaxes in its vicinity, the equilibrium structure being little changed in either orientation or translation. The small changes do however enable the strain energy to be greatly reduced. The energies are sensitive to the assumed intermolecular potentials but the optimised structures are rather insensitive. An impurity larger than the host (tetracene in anthracene) adopts closely the host orientation. This applies also to a smaller impurity (e.g. napthalene in anthracene) but in this case the impurity may move away from the lattice site to one of two inversion related displaced positions. The cage surrounding a vacant site relaxes little, leaving the “hole” more or less intact. Lattice relaxations found in this way seem too small to accommodate guest—host photochemical reactions in those lattices which, in the pure crystal, are photochemically stable.

Dynamic instabilities in excited molecular crystals. Packing calculations in anthracenic systems

Abstract Lattice energy calculations on excited molecules in crystals, carried out using a simple centre-of-mass attractive excitation potential, are reported for two phases of anthracene, 9-cyanoanthracene and 9-methylanthracene. Calculations with a fixed environment can show whether or not short-term instability is expected, predisposing the structure to excimer formation or photochemical change, whereas calculations including relaxation show what the topochemical possibilities are for a lattice equilibrium structure in the vicinity of the excited molecule. In neither P2 1 /a nor P 1 anthracene crystal is there a significant change in position or orientation of the excited molecule or its neighbours. For 9-cyanoanthracene there is instability within the fixed environment, in which a movement of the excited molecule over distances around 0.1 nm occurs, preforming an excimer for short periods followmg excitation. With inclusion of lattice relaxation, simulating events at longer times, there is lattice contraction about the excited site and disappearance of the asymmetric displacement. For 9-methylanthracene, however, there is a local lattice instability for an excited molecule both in a fixed environment and one allowing full relaxation.

Exciton trapping and self-trapping in molecular crystals

Abstract Exciton traps in molecular crystals at low temperature are discussed for three types: chemical traps formed by foreign molecules, physical traps formed by structural disturbance of the host or pure crystal and self-traps. Self-traps are redefined in terms of intra- and intermolecular processes which slow the rate of exciton transfer below the rate for rigid molecules in a rigid lattice. Trapping rates from initially delocalized exciton states into trap states on exciton—photon coupling. Expressions are given for these rates.

A simple model of photoinduced lattice instability

Abstract A simple model is developed to describe lattice distortions following photon absorption by a molecular crystal. For excitation localised on the vibrational time scale, the classical motion of a one-dimensional lattice with realistic nearest neighbour interactions is examined. The lattice structure is initially unstable and relaxes via two competing mechanisms: one leads directly to a new symmetric equilibrium, the other produces an intermediate metastable asymmetric lattice structure. This second structure is a possible precursor to excimer formation and photochemical reaction. We present algebraic and numerical analyses to demonstrate that the phonon distribution before excitation determines the dominant relaxation mechanism. In this model, acoustic phonon modes near the zone boundary promote the excimer-like distortion.

Electrostatic terms in the interaction of chiral molecules

In a model in which molecular interactions are analysed in three components (i) short-range ‘contact’ interactions, (ii) dispersion interactions and (iii) ectrostatic interactions between permanent moments, attention is drawn in this paper to the electrostatic terms. Discrimination (energy difference between laevo-laevo and laevo-dextro interactions) occurs both in the limit of nearly free rotation of the coupled molecules, and in that of locked molecules in a fixed average relative orientation. Electrostatic discrimination in the freely rotating systems has a leading term in the inverse seventeenth power of the separation and can be disregarded. In locked situations values of tens to hundreds of joules per mole are possible with realistic moment values. Where the interacting systems owe their chirality to the helicity of sources on a lattice, or to helical polymers, there may be much larger discriminations. Reference is also made to hypothetical systems in which chirality depends on permanent magnetic and electric dipoles.