The available data on the van der Waals radii of atoms in molecules and crystals are summarized. The nature of the continuous variation in interatomic distances from van der Waals to covalent values and the mechanisms of transformations between these types of chemical bonding are discussed.

Van der Waals Radii of Elements

This paper presents a review of the current state of the art in the research field of cold and ultracold molecules. It serves as an introduction to the focus issue of New Journal of Physics on Cold and Ultracold Molecules and describes new prospects for fundamental research and technological development. Cold and ultracold molecules may revolutionize physical chemistry and few-body physics, provide techniques for probing new states of quantum matter, allow for precision measurements of both fundamental and applied interest, and enable quantum simulations of condensed-matter phenomena. Ultracold molecules offer promising applications such as new platforms for quantum computing, precise control of molecular dynamics, nanolithography and Bose-enhanced chemistry. The discussion is based on recent experimental and theoretical work and concludes with a summary of anticipated future directions and open questions in this rapidly expanding research field.

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Cold and ultracold molecules: science, technology and applications

The three-body problem with short-range interactions

This review discusses recent quantum scattering calculations on bimolecular chemical reactions in the gas phase. This theory provides detailed and accurate predictions on the dynamics and kinetics of reactions containing three atoms. In addition, the method can now be applied to reactions involving polyatomic molecules. Results obtained with both time-independent and time-dependent quantum dynamical methods are described. The review emphasises the recent development in time-dependent wave packet theories and the applications of reduced dimensionality approaches for treating polyatomic reactions. Calculations on over 40 different reactions are described.

Quantum scattering calculations on chemical reactions.

It is essential to evaluate the role of Coriolis coupling effect in molecular reaction dynamics. Here we consider Coriolis coupling effect in quantum reactive scattering calculations in the context of both adiabaticity and nonadiabaticity, with particular emphasis on examining the role of Coriolis coupling effect in reaction dynamics of triatomic molecular systems. We present the results of our own calculations by the time-dependent quantum wave packet approach for H + D2 and F(2P3/2,2P1/2) + H2 as well as for the ion–molecule collisions of He + H2+, D− + H2, H− + D2, and D+ + H2, after reviewing in detail other related research efforts on this issue.

Effect of Coriolis coupling in chemical reaction dynamics

Molecular beam experiments are reported for collisions between oxygen molecules. Total integral cross sections have been measured as a function of the collision energy with the control of molecular alignment. The low collision energy (in the thermal and subthermal range) and the high angular resolution permit observation of the “glory” effect, manifestation of quantum-mechanical interference, which allows an accurate probe of intermolecular interactions. This first complete experimental characterization of the interaction yields a ground (singlet) state bond energy of 17.0 ± 0.8 meV for the most stable dimer geometry (the two oxygen molecules lying parallel at a distance of 3.56 ± 0.07 A). Also the splittings among the singlet, the triplet, and the quintet surfaces are obtained, and a full representation of their angular dependence is reported via a novel harmonic expansion functional form for diatom−diatom interactions. These results indicate that most of the bonding in the dimer comes from van der Waals...

Molecular Beam Scattering of Aligned Oxygen Molecules. The Nature of the Bond in the O2−O2 Dimer

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.

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

Hyperquantization algorithm. I. Theory for triatomic systems

This work was supported by the Italian CNR and MURST, and the European Union (Contract No. ERG-FMRX-CT96-0088)

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Simonetta Cavalli

Papers

Molecular Beam Scattering of Aligned Oxygen Molecules. The Nature of the Bond in the O2−O2 Dimer

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

Hyperquantization algorithm. I. Theory for triatomic systems

Quantum interference scattering of aligned molecules: Bonding in O-4 and role of spin coupling

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