Shinji Yamada
Review: Nanotribology of Symmetric and Asymmetric Liquid Lubricants
Symmetry 2010, 2(1), 320-345; doi:10.3390/sym2010320 - published online 15 March 2010
Show/Hide AbstractAbstract: When liquid molecules are confined in a narrow gap between smooth surfaces, their dynamic properties are completely different from those of the bulk. The molecular motions are highly restricted and the system exhibits solid-like responses when sheared slowly. This solidification behavior is very dependent on the molecular geometry (shape) of liquids because the solidification is induced by the packing of molecules into ordered structures in confinement. This paper reviews the measurements of confined structures and friction of symmetric and asymmetric liquid lubricants using the surface forces apparatus. The results show subtle and complex friction mechanisms at the molecular scale.

Athanassios C. Tsipis, Ioannis G. Depastas and Constantinos A. Tsipis
Article: Diagnosis of the σ-, π- and (σ+π)-Aromaticity by the Shape of the NICS_zz-Scan Curves and Symmetry-Based Selection Rules
Symmetry 2010, 2(1), 284-319; doi:10.3390/sym2010284 - published online 15 March 2010
Show/Hide AbstractAbstract: The NICS_zz-scan curves of aromatic organic, inorganic and “all-metal” molecules in conjunction with symmetry-based selection rules provide efficient diagnostic tools of the σ-, π- and/or double (σ + π)-aromaticity. The NICS_zz-scan curves of σ-aromatic molecules are symmetric around the z-axis, having half-band widths approximately less than 3 Å with the induced diatropic ring current arising from T_x,y-allowed transitions involving exclusively σ-type molecular orbitals. Broad NICS_zz-scan curves (half-band width approximately higher than 3 Å) characterize double (σ + π)-aromaticity, the chief contribution to the induced diatropic ring current arising from T_x,y-allowed transitions involving both σ- and π-type molecular orbitals. NICS_zz-scan curves exhibiting two maxima at a certain distance above and below the molecular plane are typical for (σ + π)-aromatics where the π-diatropic ring current overwhelms the σ-type one. In the absence of any contribution from the σ-diatropic ring current, the NICS_zz(0) value is close to zero and the molecule exhibits pure π-aromaticity.

Ken Wharton
Article: Time-Symmetric Boundary Conditions and Quantum Foundations
Symmetry 2010, 2(1), 272-283; doi:10.3390/sym2010272 - published online 8 March 2010
Show/Hide AbstractAbstract: Despite the widely-held premise that initial boundary conditions (BCs) corresponding to measurements/interactions can fully specify a physical subsystem, a literal reading of Hamilton’s principle would imply that both initial and final BCs are required (or more generally, a BC on a closed hypersurface in spacetime). Such a time-symmetric perspective of BCs, as applied to classical fields, leads to interesting parallels with quantum theory. This paper will map out some of the consequences of this counter-intuitive premise, as applied to covariant classical fields. The most notable result is the contextuality of fields constrained in this manner, naturally bypassing the usual arguments against so-called “realistic” interpretations of quantum phenomena.

Giovanni Amelino-Camelia
Article: Doubly-Special Relativity: Facts, Myths and Some Key Open Issues
Symmetry 2010, 2(1), 230-271; doi:10.3390/sym2010230 - published online 8 March 2010
Show/Hide AbstractAbstract: I report, emphasizing some key open issues and some aspects that are particularly relevant for phenomenology, on the status of the development of “doubly-special” relativistic (“DSR”) theories with both an observer-independent high-velocity scale and an observer-independent small-length/large-momentum scale, possibly relevant for the Planck-scale/quantum-gravity realm. I also give a true/false characterization of the structure of these theories. In particular, I discuss a DSR scenario without modification of the energy-momentum dispersion relation and without the қ-Poincaré Hopf algebra, a scenario with deformed Poincaré symmetries which is not a DSR scenario, some scenarios with both an invariant length scale and an invariant velocity scale which are not DSR scenarios, and a DSR scenario in which it is easy to verify that some observable relativistic (but non-special-relativistic) features are insensitive to possible nonlinear redefinitions of symmetry generators.

Franca Lattanzi and Carlo di Lauro
Article: On the Physical Reasons for the Extension of Symmetry Groups in Molecular Spectroscopy
Symmetry 2010, 2(1), 213-229; doi:10.3390/sym2010213 - published online 25 February 2010
Show/Hide AbstractAbstract: Several situations of general interest, in which the symmetry groups usually applied to spectroscopy problems need to be extended, are reviewed. It is emphasized that any symmetry group of geometrical operations to be used in Molecular Spectroscopy should be extended for completeness by considering the time reversal operator, as far as the Hamiltonian is invariant with respect to the inversion of the direction of motion. This can explain the degeneracy of pairs of vibrational and rotational states spanning the so-called separably degenerate irreducible representations, in symmetric tops of low symmetry, and Kramers degeneracy in odd electron molecules in the absence of magnetic fields. An extension with account of time reversal is also useful to determine relative phase conventions on vibration-rotation wavefunctions, which render all vibration-rotation matrix elements real. An extension of a molecular symmetry group may be required for molecules which can attain different geometries by large amplitude periodical motions, if such motions are hindered and are not completely free. Special cases involving the internal rotation are discussed in detail. It is observed that the symmetry classification of vibrational modes involving displacements normal to the internal rotation axis is not univocal, but can be done in several ways, which actually correspond to different conventions on the separation of vibration and internal rotation in the adopted basis functions. The symmetry species of the separate vibrational and torsional factors of these functions depend on the adopted convention.

Xiaoping Sun
Article: Symmetry Analysis in Mechanistic Studies of Nucleophilic Substitution and β-Elimination Reactions
Symmetry 2010, 2(1), 201-212; doi:10.3390/sym2010201 - published online 25 February 2010
Show/Hide AbstractAbstract: A mechanistic study of the bimolecular nucleophilic substitution (S_N2) reaction for halomethane CH₃X (X = Cl, Br, or I) is approached by using symmetry principles and molecular orbital theory. The electrophilicity of the functionalized sp³–carbon is attributable to a 2p-orbital-based antibonding MO along the C–X bond. This antibonding MO, upon accepting an electron pair from a nucleophile, gives rise to dissociation of the C–X bond and formation of a new Nuc–C bond. Correlations are made between the molecular orbitals of reactants (Nuc^_- and CH₃X) and products (NucCH₃ and X^_-). Similar symmetry analysis has been applied to mechanistic study of the bimolecular b-elimination (E2) reactions of haloalkanes. It well explains the necessity of an anti-coplanar arrangement of the C_α–X and C_β–H bonds for an E2 reaction (anti-elimination). Having this structural arrangement, the bonding C_α–X (σ_C-X) and antibonding C_β–H (σ_C-H*) orbitals become symmetry–match. They can partially overlap resulting in increase in electron density in σ_C-H*, which weakens and polarizes the C_β–H bond making the β-H acidic. An E2 reaction can readily take place in the presence of a base. The applications of symmetry analysis to the S_N2 and E2 reactions represent a new approach to studying organic mechanisms.