Vincenzo Aquilanti

Angular momentum coupling schemes in the quantum mechanical treatment of P‐state atom collisions

For the multichannel Schrodinger equations which arise in the quantum mechanical close coupling treatment of atomic collisions involving fine structure effects, alternative representations are developed by angular momentum algebra. The various representations are closely related to Hund’s coupling schemes for rotating diatomic molecules. Matrix elements for the electrostatic interaction and for the orthogonal transformations which connect the various representations, are given explicitly for the case when only one atom has internal angular momenta and follows LS coupling. The limit of large angular momenta, of interest under semiclassical conditions, is also considered. Some examples of applications to P atom collisions are discussed.

Hyperquantization algorithm. I. Theory for triatomic systems

In this paper we present the theoretical concepts and methodology of the hyperquantization algorithm for the three body quantum mechanical problem. Within the framework of the hyperspherical approach to reaction dynamics, we use angular momentum algebra (or its generalization, e.g., including Hahn coefficients which are orthonormal polynomials on a set of grid points which span the interaction region) to compute matrix elements of the Hamiltonian operator parametrically in the hyperradius. The particularly advantageous aspects of the method proposed here is that no integrals are required and the construction of the kinetic energy matrix is simple and universal: salient features are the block tridiagonal structure of the Hamiltonian matrix and a number of symmetry properties. The extremely sparse structure is a further advantage for the diagonalization required to evaluate the adiabatic hyperspherical states as a function of the hyperradius. Numerical implementation is illustrated in the following paper by...

Hyperspherical coordinates for molecular dynamics by the method of trees and the mapping of potential energy surfaces for triatomic systems

Some results on hyperspherical coordinates and harmonics for the representation of the many‐body problem are presented, extensive use being made of the method of trees. Properties of these trees are examined: a lemma on the simplification of trees possessing a particular symmetry is proven, and used to discuss the internal coordinates for a system of three particles and the mapping of potential energy surfaces. A framework is provided for relating different couplings of particles by rotations on hyperspheres and alternative hyperangular parametrizations by orthogonal basis transformations. Extensions to nonzero angular momentum or to more than three particles are shown not to be trivial, and the possible role of developments of the tree method, leading to more general hyperspherical coordinates, is briefly considered.

Molecular beam studies of weak interactions for open‐shell systems: The ground and lowest excited states of ArF, KrF, and XeF

Absolute integral cross sections for scattering of ground state fluorine atoms by argon, krypton, and xenon have been measured in the thermal velocity range. Information has been obtained on the long range interaction and using a technique for magnetic analysis of substates of F atoms, a characterization is given for the bonding in the ground and the two lowest excited states of these rare gas fluorides. The potentials are represented as a spherical part and an anisotropic component, which have been obtained in an adiabatic decoupling treatment, including also information from other scattering data. Nonadiabatic coupling matrix elements and other general features of these interactions are also presented.

Experimental benchmarks and phenomenology of interatomic forces: open-shell and electronic anisotropy effects

This article gives a perspective view of some representative experimental information available on interatomic forces. They play a role in gaseous properties, but modern quantitative information comes from spectroscopy and molecular beam scattering. This latter technique is emphasized here: recent experimental results and consideration of physical properties of interacting species is complementary to progress of modelling based on ab initio or other quantum chemical calculations. Interactions involved in closed-shell–closed-shell species are considered to be typical of the so-called ‘non-covalent’ forces, although additional effects of a ‘chemical’ nature are demonstrated to be non-negligible in some cases. The partition of the interaction into van der Waals (repulsion + dispersion) and possibly electrostatic and/or induction components is analysed. Interactions involving open-shell species offer a most interesting phenomenology, because electronic anisotropy often provides further strength to the bonds, which are usually weaker than ordinary chemical bonds. Again, the focus is on experimental information (especially on scattering of magnetically analysed open-shell atoms) and on the understanding that comes from the analysis of the ample phenomenology accumulated. Additional terms such as those of specific ‘covalent’ nature appear in the partition of the interaction, besides those already mentioned. The extension of this approach for describing molecular anisotropies is also outlined. Contents PAGE 1.  Introduction  1.1. Motivation and dedication 166  1.2. Scope and outline of the paper 167 2.  Isotropic interactions and van der Waals forces 168  2.1. 2 S +1S atom– 168  2.2. Combination rules and correlation formulas 170  2.3. 2 S +1S Ion– 172 3.  Anisotropic interactions and open-shell effects 175  3.1. General 175  3.2. 2 S +1P atom– 176  3.3. Charge transfer and bond stabilization 178  3.4. 2 S +1P ion – 180  3.5. Dications 181 4.  Final remarks 182  4.1.  Towards atom–molecule and molecule–molecule interactions 182  4.2.  Prospects for future work 184  4.3.  From van der Waals interactions to chemical bonds 185 Acknowledgements 185 Appendix A– Interatomic forces by molecular beam scattering 185 Appendix B–Basic contributions to the interatomic interactions and their dependence on physical properties f involved species 188 Appendix C–Electronic anisotropy and orbital alignment 192 References

Decoupling approximations in the quantum mechanical treatment of P‐state atom collisions

Several decoupling schemes are considered, for the effective simplifications of the close coupling equations which arise in the treatment of atomic collisions involving fine structure. Calculations were performed for two models of 2P atoms colliding at thermal energy with a 1S species. From the comparison of exact and approximate results, the relative merits and limits of full or partial decoupling schemes were assessed. Possible improvements and extensions are suggested.

Scattering of magnetically analyzed F (2P) atoms and their interactions with He, Ne, H2 and CH4

Abstract An improved source of a beam of fluorine atoms has been characterized by magnetic analysis of sublevels for F( 2 P). Ground state and lower lying excited state potential energy curves for the interaction of fluorine atoms with He, Ne, H 2 and CH 4 have been obtained from measurements of integral scattering cross sections at thermal energies. The results for the rare gas systems are discussed in connection with previous work on Ar, Kr, and Xe fluorides; those for the H 2 and CH 4 systems provide information of fine structure effects on the long range pan of entrance channels for reactive potential energy surfaces.

Coordinates for molecular dynamics: Orthogonal local systems

Systems of orthogonal coordinates for the problem of the motion of three or more particles in classical or in quantum mechanics are considered from the viewpoint of applications to intramolecular dynamics and chemical kinetics. These systems, for which the kinetic energy of relative motion is diagonal, are generated by making extensive use of the concept of kinematic rotations, which act on coordinates of different particles and describe their rearrangements. An explicit representation of these rotations by mass dependent matrices allows to relate different particle couplings in the Jacobi scheme, and to build up alternative systems (such as those based on the Radau–Smith vectors or variants thereof): this makes it possible to obtain coordinates which, while being rigorously orthogonal, may approximate closely the local ones, which are based on actual interparticle distances and are in general nonorthogonal. It is also briefly shown that by defining as variables the parameters describing the kinematic rot...

Molecular beam studies of weak interactions for open‐shell systems: The ground and lowest excited states of rare gas oxides

Integral cross sections as a function of velocity for scattering of ground state oxygen atoms by the rare gases have been measured at thermal energy. Analysis of atomic sublevels by a Stern–Gerlach magnet allows a control of the relative contribution from different fine structure scattering channels. The results are analyzed using an adiabatic decoupling scheme to derive the interaction as a spherical part and an anisotropic component, from which information is obtained on the six lowest states of the rare gas oxides and on nonadiabatic coupling terms.

The d-dimensional hydrogen atom: hyperspherical harmonics as momentum space orbitals and alternative Sturmian basis sets

Abstract Hydrogenoid orbitals, i.e. the solutions to the Schrodinger equation for a central Coulomb field, are considered in mathematical dimensions d = 2 and d > 3 different from the physical case, d = 3. Extending known results for d = 3, Sturmian basis sets in configuration (or direct) space — corresponding to variable separation in parabolic coordinates — are introduced as alternatives to the ordinary ones in spherical coordinates: extensions of Fock stereographic projections allow us to establish the relationships between the corresponding momentum (or reciprocal) space orbitals and the alternative forms of hyperspherical harmonics. Properties of the latter and multi-dimensional Fourier integral transforms are exploited to obtain the matrix elements connecting the alternative basis sets explicitly in terms of Wigners rotation matrix elements for d = 2 and generalized vector coupling (or Hahn) coefficients for d > 3. The use of these orbitals as complete and orthonormal expansion basis sets for atomic and molecular problems is briefly commented.