Mirco Ragni

Roto-torsional Levels for Symmetric and Asymmetric Systems: Application to HOOH and HOOD Systems

Two pictures of separation of torsional mode in intramolecular dynamics are given for the treatment of hindered rotations of molecular systems like ABCD, which present a large amplitude motion associated with the torsional mode. The energy profile (torsional potential) is described by a dihedral angle and the chosen coordinates are based on orthogonal local vectors. Our model consists of two linear rigid rotors AB and CD that rotate around the Jacobi vector connecting the centers of mass of the diatoms AB and CD. We have used two procedures to calculate the roto-torsional energy levels. The first, referred to bi-rotor, uses the Hamiltonian as function of the azimuth angles of the AB and CD rotors. In the second one, referred to roto-torsion, we separate the internal rotation (torsional mode) from the overall rotation around the Jacobi vector. For the cases where the two moments of inertia are equal, e.g. HOOH, conservation of both energy and angular momentum for a system viewed as involving either torsion plus external rotation or interaction of two rotors requires correlation of levels with symmetries τ = 1 and 4 with zero or even values of the external rotation angular momentum quantum number k in units of \(\hbar\). Conversely, torsional energy levels that belong to the τ = 2 and 3 symmetries, correlate with odd values of k. In HOOD the two rotors have different moments of inertia, and this causes further level splitting for τ = 2 and 3 only. Here we apply the two procedures to understanding the roto-torsional levels for HOOH and HOOD molecules.

Structural Properties and Torsional Dynamics of Peroxides and Persulfides

For the study of molecules containing O—O and S—S bonds, an analysis on the effect of level of theory and basis sets on electronic properties and geometrical parameters for H2O2 and H2S2 was done. Substitutions of one or both hydrogens in these molecules either by halogen atoms or alkyl groups were investigated for properties like geometries, dipole moments, cis and trans barriers. Attention has also been dedicated to the study of energy levels in the very anharmonic torsional potentials, obtaining their distributions as a function of temperature and partition functions for the torsional motion, of relevance for the isomerization rate leading to exchange between chiral enantiomers. Estimated rates both for underbarrier tunnelling and overbarrier transitions are consistently smaller for the S—S cases with respect to the corresponding O—O ones, due to the generally higher barriers. Regarding intermolecular interactions, of specific importance for collisional chirality exchange, an exploration was done for both H2O2– and H2S2–rare gases systems, extending the joint experimental and theoretical approach already tackled in this laboratory for interactions of H2O and H2S with the rare gases.

Spin networks and sturmian orbitals: Orthogonal complete polynomial sets in molecular quantum mechanics

An outline is given of current advances on some basic ingredients of applied quantum mechanics, that were previously developed along different lines and are now being compacted within a unifying framework. Specifically, (i) complete orthogonal expansion basis sets for the atomic and molecular orbitals of quantum chemistry are classified within angular momentum theory, presently incorporated in and generalized as spin network theory; (ii) spin-networks and the underlying theory of hypergeometrical polynomials are presented within a graphical approach; (iii) the combinatorial significance of the graphical approach is given a projective geometry foundation; (iv) emergence and role of hidden (Regge’s) symmetries are revealed and discussed in a variety of contexts.