Evidence for a high-pressure isostructural transition in nitrogen

Understanding the high-pressure behaviors of diatomic molecules (H2, O2, N2, etc) is one of the most basic as well as important objective in high-pressure physics. Under high pressure diatomic molecule solids often exhibit rich crystal polymorphs. High-pressure isostructural transitions (HPIT) in solid hydrogen and oxygen, involving considerable technical challenges, have been experimentally documented, suggesting a possible prevailing pressure-driven molecular-symmetry breaking pathway. In spite of extensive efforts, however, HPIT in nitrogen has not been observed so far. Here we present a monoclinic-to-monoclinic isostructural phase transition (λ→λ’) in solid nitrogen at approximately 50 GPa accompanied with anomalies in lattice parameter, atomic volume and Raman vibron modes. Further ab initio calculations strongly confirmed the HPIT in nitrogen, showing the weak distortion of orientation and slight rotation in nitrogen molecules possibly drive the low-pressure phase, λ-N2, to an isostructural high-pressure phase, λ’-N2 without changing crystal symmetry. In addition, we probed in detail the phase stability and revisited the pressure-temperature (P-T) phase diagram of nitrogen, discovering a new high-pressure amorphous phase, η’-N2.

Molecular Vibrations Are Not Asymmetric

There is considerable confusion when naming vibrations in infrared and Raman spectra. One of the most common errors is the identification of some stretching and bending vibrations as “asymmetric”. There are no asymmetric vibrations as such vibrations incur rotations and translations. The correct term is antisymmetric and it is demonstrated, through molecular symmetry operations, why this is the correct term.

Properties and interactions – melting point of tribromobenzene isomers

Single crystals of isomeric 1,2,3-tribromobenzene (123TBB), 1,2,4-tribromobenzene (124TBB) and 1,3,5-tribromobenzene (135TBB) have been grown from different solvents and their structures determined by X-ray diffraction at 100, 200 and 270 K. The melting-point differences of ca 40 K between 135TBB, 123TBB and 124TBB have been correlated with the molecular symmetry and packing preferences in the crystal, as well as with the main types of intermolecular halogen interactions, i.e. Br...Br, Br...C (Br...π) and Br...H. The relationship between symmetry and melting point in Carnelley's rule has been extended to the accessibility of terminal atoms for the formation of intermolecular interactions, their occurrences and distribution, and the close packing. The electrostatic potential mapped on molecular surfaces demonstrates that in more symmetric molecules the more evenly distributed substituents are more accessible and form more optimum intermolecular interactions.

Artificial Symmetries for Calculating Vibrational Energies of Linear Molecules

Linear molecules usually represent a special case in rotational-vibrational calculations due to a singularity of the kinetic energy operator that arises from the rotation about the a (the principal axis of least moment of inertia, becoming the molecular axis at the linear equilibrium geometry) being undefined. Assuming the standard ro-vibrational basis functions, in the 3N−6 approach, of the form ∣ν1,ν2,ν3ℓ3;J,k,m⟩, tackling the unique difficulties of linear molecules involves constraining the vibrational and rotational functions with k=ℓ3, which are the projections, in units of ℏ, of the corresponding angular momenta onto the molecular axis. These basis functions are assigned to irreducible representations (irreps) of the C2v(M) molecular symmetry group. This, in turn, necessitates purpose-built codes that specifically deal with linear molecules. In the present work, we describe an alternative scheme and introduce an (artificial) group that ensures that the condition ℓ3=k is automatically applied solely through symmetry group algebra. The advantage of such an approach is that the application of symmetry group algebra in ro-vibrational calculations is ubiquitous, and so this method can be used to enable ro-vibrational calculations of linear molecules in polyatomic codes with fairly minimal modifications. To this end, we construct a—formally infinite—artificial molecular symmetry group D∞h(AEM), which consists of one-dimensional (non-degenerate) irreducible representations and use it to classify vibrational and rotational basis functions according to ℓ and k. This extension to non-rigorous, artificial symmetry groups is based on cyclic groups of prime-order. Opposite to the usual scenario, where the form of symmetry adapted basis sets is dictated by the symmetry group the molecule belongs to, here the symmetry group D∞h(AEM) is built to satisfy properties for the convenience of the basis set construction and matrix elements calculations. We believe that the idea of purpose-built artificial symmetry groups can be useful in other applications.

[38]Octaphyrin bis-Sn(IV) complexes with unique coordination geometries

Metal complexation of octaphyrin(1.1.1.1.1.1.1.1) triggers unique ring-fixation aptitudes or unexpected rearrangement (cleavage) reactions. In this paper, a unique complexation behavior of [38]octaphyrin upon tin(IV) metalation is showcased. Two new [38]octaphyrin bis-Sn(IV) complexes 2Sn and 3Sn were isolated and characterized as weakly aromatic molecules. While 2Sn with the [Formula: see text] molecular symmetry displayed a similar characteristic to octaphyrin bis-Si(IV) and bis-Ge(IV) complexes reported previously, 3Sn showed a different coordination mode that is fixed by intramolecular hydrogen bondings between pyrrolic NH and axially ligated OH on the tin ion as revealed by X-ray diffraction analysis. An unexpected dimeric structure was also observed during an attempt to grow crystals of 2Sn. These characteristic behaviors indicate that the ring-fixation aptitude of octaphyrin is quite sensitive to the nature of metal ions even for the same group 14 elements.