We developed a theoretical model to investigate the compressibility of atoms. Atoms are confined inside a spherical cavity, simulated numerically by a finite repulsive potential barrier. The energy levels and wavefunctions of confined atoms are determined by solving, for different cavity radii, the relativistic Dirac-Fock equations, including formally the repulsive barrier. The changes in the atomic size and in the ground-state energy level allow one to define a positive isotropic pressure exerted on the confined atom. The model is applied to atomic caesium and it is demonstrated quantitatively that the remarkable compressibility of caesium originates from a purely atomic mechanism, namely the pressure-induced collapse of the 5d orbital. We propose that this mechanism can also drive, at an atomic level, a reversible insertion of atoms into solids. Applications to lithium-ion batteries are briefly discussed at the end of this paper.

We present a new theoretical method for the calculation of the electronic structure of the hydrogen atom confined inside a prolate-shaped C60 fullerene cage. The method is based on solving the one-electron Schrödinger equation written in the prolate-spheroidal-coordinate system and using the quasi-atom concept for modelling the effects of the deformed endohedral environment. The energy levels of H@C60 are qualitatively studied as a function of the deformation parameter δ. Avoided crossing points between levels of the same symmetry are revealed.

We determine the electronic structure of the metallofullerene La@C 60 for different configurations of La, namely 5d6s 2 , 5d 2 6s and 4f5d6s. The fullerene environment is modelled by a confining potential V c (r), equivalent to an attractive spherical square well of depth −8.22 eV and width 1.89 au. The atomic orbitals of La are obtained by solving numerically the Dirac-Fock equations including V c (r). For both configurations 5d6s 2 and 4f5d6s, La donates two electrons to the fullerene molecule, while in 5d 2 6s, it is demonstrated that only a partial transfer of the 5d electron to the molecule occurs. For specific values of the well depth, we observe a collapse of the 5d orbital inside the hollow cage region. This phenomenon is interpreted by means of double-valley potentials.

We present a brief review of the subject of confined atoms, in which we emphasise the origins of the subject and its most recent applications. Emphasis is placed on the wide variety of situations to which the idealised quantum mechanical treatment is relevant. Both the nonrelativistic and relativistic methods are contrasted; an example of confinement in the Dirac‐Fock scheme is given and some special problems connected with relativistic confinement are mentioned. Finally, we present a discussion of the quantum pressure, and a novel, dimensionless choice of variables which allows universal atomic behaviour for confined atoms to be visualised.

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.