Scaling laws for atomic compressibility

Abstract

We consider the concept of atomic pressure for atoms subjected to quantum confinement. New scaling rules are introduced which allow the compressibility to be expressed as the product of two factors. The first is a term independent of compression, which varies widely from atom to atom, but can be computed in the free atom limit. The second is a term expressed in dimensionless variables, whose dependence on compression is in general nonlinear and may exhibit discontinuities. However, it is shown not to vary much from one atom to another and to follow general rules which are easily understood. We have performed fully relativistic ab initio calculations to illustrate these general rules of atomic compressibility, and we characterize the variation of atomic compressibility for both soft and hard atoms.

Hydrogen molecular ion inside penetrable prolate spheroidal boxes: Electronic and vibrational properties

“…In spite of their relative simplicity as compared with the more sophiticated methods, the quantum confinement models have gained increasing attention in recent years due to their ability to model local pressure effects on atomic and molecular properties as well as properties of other electronic systems under spatial confinement, as reviewed by Fröman et al in 8 and Jaskolski in 9. More recent contributions reflect this growing interest, as, for example, in the case of properties of atoms under pressure 10–18, H 2 molecular dissociation induced by pressure 19, confinement effects on atomic and molecular ionization energies 20–22, reversible insertion of atoms into solids 23, hydrogenic systems under different confining geometries 24, 25, chemical confinement effects 26 etc.…”

Quasi-Atoms and Super-Atoms

“…Provided one stays within the jellium scheme [47], a metallic cluster can be modelled by solving a single Schro¨dinger equation, and one obtains, at convergence, an effective average potential of the Woods-Saxon type [48]. Obviously, this is a simplified model, which does not allow the structure or excitations of the ionic core to be represented.…”

Contact model of the probe in form measurement

“…In the other hand, the problem may be studied form the point ofview of Cuantics. From [15], those forces compress or expand the atoms, mainly on the external layer. If the force variations are smooth, that is, the distance between the atoms changes slowly, that compressibility or expansion follows an exponential law [16], as it may be directly obtained from the Schrodinger formula [17]:…”