Dimerization of C60: Symmetry Considerations

Orbital‐symmetry analysis (OCAMS) of the dimerization of C₆₀ via [2+2] cycloaddition indicates that the reactant monomers should approach one another along a pathway in which C_2h symmetry is conserved. Point‐by‐point computations (AM1/UHF) confirm this prediction: a low‐energy pathway leads to a single‐bonded dimer 2 with C_2h symmetry. Closure to the stable D_2h dimer 1 is effected by relatively facile rotation about the single bond. A similar symmetry analysis was performed on a second isomer 3 with D_2h symmetry, the moieties of which are linked by two two‐atom chains. It raises the possibility that 3 , the so‐called `window' isomer, may be interconvertible with 1 along a pathway that retains C_i (S₂) symmetry. Although the computational results indicate that C₆₀ is in thermal equilibrium with its stable dimer 1 at moderate temperatures, the latter is not observed in the gas phase for thermodynamic reasons. According to THERMO computations (AM1/RHF), the equilibrium is shifted strongly towards the monomer pair at temperatures where vaporization of the solid C₆₀ is observed (>400°).     

A simple perturbational approach for the determination of favourable reaction pathways

A simple perturbational approach has been used to establish the symmetry conditions for energetically favourable nuclear motions on a potential energy surface. In particular, the operational rules of Orbital Correspondence Analysis in Maximum Symmetry (OCAMS) for specifying the symmetry species of the nuclear displacements, which make a symmetry forbidden pathway symmetry-allowed, have been derived. A general, symmetry-independent, procedure is then proposed for finding the energetically most favourable pathway by referring to the form of the overlap density function of non-correlating orbitals. The method is demonstrated by selecting from among the several symmetry-allowed nuclear motions on the potential energy surface for the H₂ + D₂ exchange reaction, that which is energetically most favourable.     

The complete infinite series solution of systems governed by the wave equation with boundary damping

A common method of solving initial boundary value problems is separation of variables, denoted as modal analysis in the field of flexible structures. For systems with undamped boundary conditions the method is well-established, but for systems with boundary damping it does not provide closed form solutions. In this paper the exact modal series solution for second order systems with damped boundaries is derived with explicit expressions for the series coefficients. Knowledge of these coefficients enables practical applications of the solution, such as finite dimension approximation. The key element of the derivation is a new orthogonality condition for the damped eigenfunctions. The modal series is also transformed into a traveling wave form. The solution, which is the extension of the classical D’Alembert formula, is represented by a single equivalent propagating wave. A component of the solution, denoted by “end waves”, is identified to provide the continuity of the systems displacement response.     

Tunable photonic crystals with semiconducting constituents

We propose that the photonic band structure (PBS) of semiconductor-based photonic crystals (PCs) can be made tunable if the free-carrier density is sufficiently high. In this case, the dielectric constant of the semiconductor, modeled as varepsilon(omega) = varepsilon(0)(1-omega(2)(p)/omega(2)), depends on the temperature T and on the impurity concentration N through the plasma frequency omega(p). Then the PBS is strongly T and N dependent; it is even possible to obliterate a photonic band gap. This is shown by calculating the 2D PBS for PCs that incorporate either intrinsic InSb or extrinsic Ge.     

Polariton modes at the interface between two conducting or dielectric media

A review of polariton modes at interfaces composed of two semiinfinite, homogeneous, and isotropic media is given. Both media are characterized by frequency-dependent dielectric functions ?_i(ω), i = 1, 2, and may become “interface-wave-active” in different frequency regions. The conditions for the existance of propagation windows are analyzed and applied to two particular cases: an interface composed of (a) two dielectrics with dielectric functions $\text{?}{}_{\mathrm{i}}\text{= ?}{}_{\mathrm{?\infty i}}\text{(}\text{ω}{}^2\text{ω}{}_{\mathrm{<mtext>Li</mtext>}}{}^2\text{ω}{}^2\text{ω}{}_{\mathrm{<mtext>T</mtext><mtext>i</mtext>}}{}^2$, where ?_t8i are the dielectric constants for very large frequencies and ωTi and ωLi are the transverse and longitudinal phonon frequencies; (b) two conductors with dielectric functions $\text{?}{}_{\mathrm{i}}\text{= ?}{}_{\mathrm{\infty i}}\text{(}\text{1 ?ω}{}_{\mathrm{i}}{}^2\text{ω}{}^2\text{)}$, where ω_iare the plasma frequencies. In the first case there exist two propagation windows in the infrared region, while in the second case there is one propagation window in the ultraviolet, visible, or infrared region. The dispersion relations of the modes and their decay distances into the two media are presented, and various damping effects are discussed. The review is concluded with theoretical results on the optical excitation and detection (ATR) of the interface modes.