Atoms and molecules in cavities: A method for study of spatial confinement effects

Abstract

mA general method for solving the problems of spatially confined quantum mechanical systems is proposed. The method works within the framework of the model space approximation. In the case of atoms and molecules trapped into any-shape microscopic cavity (like molecular sieves or fullerenes), the method reduces to a simple modification of the commonly used basis-set quantum chemical calculations. The modification consists of a particular rotation and projection in the model space, leading to solutions better adapted to the boundary conditions of the spatial confinement than the functions that describe the free systems. To illustrate how this method works, it has been applied to the hydrogen atom confined in a spherical well, near a hard wall and confined in a cubic box. The results are also compared to the exact solutions. 0 1995

WKB and MAF quantization rules for spatially confined quantum mechanical systems

“…studying thermodynamic properties of non-ideal gases, investigation of anharmonic effects in solids, in atoms and in molecules under high pressure, impurity binding energies in quantum wells and nearsurface donor states, and even in the context of partially ionised plasmas. When an atom or a molecule is trapped inside any kind of microscopic cavity, it suffers a spatial confinement that affects its physical and chemical properties [1,2,4]. The same situation occurs for mesoscopic scale semiconductor artificial structures like 2-dim.…”

“…quantum wells [5][6][7], quantum-well wires [8,9] and quantum dots [10][11][12][13][14], where impurity or excitonic states are influenced by the small sizes of these structures. Spatial confinement, also called the boxing effect, significantly influences the bond formation and chemical reactivity inside the cavities [1,2,4]. There are many natural or artificial cavities that could produce sensitive effects -zeolite molecular sieves, fullerenes, or even mono-or 2-dimensional cavities formed by large organic molecules [1,2].…”

SWKB formalism for confined quantum systems

“…As the chemical as well as the physical properties of the system are radically altered by the change in boundary conditions, Contract grant sponsor: Council of Scientific and Industrial Research, India. such systems are of tremendous importance in present-day molecular and solid-state physics [4,5].…”

SWKB quantization rules for bound states in quantum wells

“…The study of confined quantum systems is of considerable importance in modern times as spatial confinement significantly alters the physical and chemical properties of the system [1][2][3][4]. It influences the bond formation and chemical reactivity inside the cavities to a great extent.…”