Electric properties of molecules confined by the spherical harmonic potential

Abstract

The harmonic oscillator potential is very often used in quantum chemical studies of electric properties to model the effect of spatial confinement. In the vast majority of works, the harmonic potential of cylindrical symmetry was applied. Thus far, its spherical counterpart was used mainly to describe properties of spatially restricted atomic systems. Therefore, our main goal was to study the molecular electric properties in the presence of the spherically symmetric harmonic oscillator potential and to characterize the impact of the relative position of the considered molecules and spherical confinement on these properties. Moreover, we analyzed how the topology of confining environment affects the dipole moment and (hyper)polarizability, by comparing the results obtained in the spherical and cylindrical harmonic potential.Based on the conducted research, it was found that the position of the molecules relative to the spherical confinement strongly influences their electric properties. The observed trends of changes in the electric properties, caused by increasing the confinement strength, vary significantly. Moreover, it was shown that in the vast majority of cases, significant differences in the values of electric properties, obtained in the cylindrical and spherical confinement of a given strength, occur. K E Y W O R D S dipole moment, (hyper)polarizability, spatial confinement, spherical harmonic oscillator potential 1 | INTRODUCTION In 1937 Michels et al proposed a model in which the hydrogen atom was placed inside the spherically symmetric, nonpenetrable potential of a givenradius. [1] The authors used this model to analyze the influence of pressure on the structure of energy levels and the polarizability of hydrogen atom.This was one of the first works, which initiated the development of quantum-chemical studies on the spatial confinement phenomenon. The current state of knowledge on this subject is summarized in many excellent reviews. [2][3][4][5][6][7][8] Atoms and molecules subjected to high pressure are just one of many examples of spatially confined systems. Another interesting one is the semiconductor structure such as quantum well, wire and dot. Their construction is based on the limitation of the movement of charge carriers (holes or electrons) in one or more directions in space. The properties of such systems are controlled, inter alia, by changing their size (quantum size effect). [2,4] Together with the development of nanotechnology, chemical objects, having in their structure empty spaces, gained much attention. Among them, one can mention: zeolites, crystalline mesoporous silica, metal-organic frameworks, as well as nanotubes and fullerenes. Inclusion compounds (also called guest-host system), resulting from trapping atoms, ions or molecules inside such chemical cages, are another important example of the spatial confinement phenomenon. [2,9,10]

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