The calculation of frequency-dependent hyperpolarizabilities including electron correlation effects

The theory for the calculation of the frequency-dependent hyperpolarizabilities β(?2ω; 0, ω), β(?ω; 0, ω), and β(0; ω, ?ω) is discussed. New relations between these tensors are derived for those wave functions that obey the time-dependent Hellmann–Feynman theorem (e.g., the self-consistent field [SCF] or the exact wave function). Using second-order Møller–Plesset perturbation theory (MP2), expressions are obtained for the hyperpolarizabilities in terms of derivatives of appropriately defined linear polarizability tensors with respect to a static electric field. Results are presented for ammonia and formaldehyde for the optical Kerr effect and for secondharmonic generation. These results indicate that it is desirable to determine the frequency-dependent contribution to the hyperopolarizability at the MP2 rather than the SCF level of theory, in cases where the static hyperpolarizability has a large contribution from electron correlation and/or where the frequency-dependent contribution may be more significant, such as for secondharmonic generation.     

Dynamical properties of the Peierls-Fröhlich state on the many-phonon-coupling model

The amplitude and phase phonons and the frequency dependent conductivity below the mean-field Peierls-Fröhlich transition temperature T_c, and the Kohn anomaly and fluctuation induced charge-density-wave conductivity above T_c, are discussed on the basis of the many-phonon-coupling model recently introduced by Rice, Duke and Lipari. For dominant intramolecular phonon coupling an isotope effect in T_c is related to the isotopic shift in the small polaron binding energy.     

Cavity QED with quantized center of mass motion

We investigate the quantum fluctuations of a single atom in a weakly driven cavity, where the center of mass motion of the atom is quantized in one dimension. We present analytic results for the second order intensity correlation function g((2))(tau) and the intensity-field correlation function h(theta)(tau), for transmitted light in the weak driving field limit. We find that the coupling of the center of mass motion to the intracavity field mode can be deleterious to nonclassical effects in photon statistics and field-intensity correlations, and compare the use of trapped atoms in a cavity to atomic beams.     

Anion control of the formation of geometric isomers in a triple helical array

The amide-substituted unsymmetrical ligand L(1) upon coordination to Co(2+) forms the dinuclear triple helicate [Co(2)(L(1))(3)](4+) which exists as both possible C(1) and C(3) symmetric geometric isomers in solution, however, upon addition of nitrate ions, the formation of an anion binding cavity is favoured and hence the sole product is the C(3) symmetric isomer in which all three amide substituents are hydrogen bonded to the nitrate anion.     

Cooperative dynamics in two dimensions

We report results from molecular dynamics simulations of cooperative motion in a quasi-two-dimensional system of colloid particles. We find that the onset of the deviation of the single-particle displacement distribution from Gaussian form starts in the liquid phase and extends, with increasing magnitude, through the hexatic phase into the crystalline phase. The time for which the deviation is maximum increases exponentially with the density. As the density increases toward the hexatic phase a third dynamical relaxation mode emerges. We argue that the collective motion is generated by superpositions of instantaneous normal mode vibrations, with lifetimes that increase with the density, along paths with strong bond-orientation correlation.     

Hexagonal to square lattice conversion in bilayer systems

We report the results of extensive molecular dynamics simulations of the reconstructive hexagonal to square lattice conversion in bilayer colloid systems. Two types of interparticle potential were used to represent the colloid-colloid interactions in the suspension. One potential, due to Marcus and Rice, is designed to describe the interaction of sterically stabilized colloid particles. This potential has a term that represents the attraction between colloid particles when there is incipient overlap between the stabilizing brushes on their surfaces, a (soft repulsion) term that represents the entropy cost associated with interpenetration of the stabilizing brushes, and a term that represents core-core repulsion. The other potential we used is an almost hard core repulsion with continuous derivatives. Our results clearly show that the character of the reconstructive hexagonal to square lattice conversion in bilayer colloid systems is potential dependent. For a system with colloid-colloid interactions of the Marcus-Rice type, the packing of particles in the square array exhibits a large interlayer lattice spacing, with the particles located at the minima of the attractive well. In this case the hexagonal to square lattice transition is first order. For a system with hard core colloid-colloid interactions there are two degenerate stable intermediate phases, linear and zigzag rhombic, that are separated from the square lattice by strong first order transitions, and from the hexagonal lattice by either weak first or second order transitions.