Isotope effects for molecules in a cavity

Abstract

A model problem of the motion of a particle in an impenetrable cavity is considered in order to establish how the energy levels and transition energies between them depend on the linear size, R, of the cavity and on the particle mass. In the case of one particle problem with a uniform potential inside the cavity there exists a simple qualitative solution that describes the effect of the cavity size and shows that a decrease in R can cause the isotopic frequency shift to increase as compared to the free system. The estimates obtained were used to interpret the results of numerical calculations of low lying energy states of hydrogen molecule and its isotopomers confined within impenetrable spherical cavity. The effect of the cavity radius on the structure of the low lying part of the energy spectra of H 2 , D 2 , and HD molecules and on the reliability of adiabatic separation of nuclear variables are considered. The approach pro vides a qualitatively correct description of the changes in the energy level positions but the behavior of the isotopic frequency ratio is too smooth compared with results of more accurate calculations.Key words: hydrogen molecule, molecule in cavity, isotopic frequency shift, rovibrational energy levels, separation of variables.Analysis of the influence of isotopic substitution on the spectral characteristics of molecules is an important and efficient tool of investigation of the structure of mo lecular systems. In the framework of a simple harmonic model the frequency ratio of two isotopomers can be esti mated as the square root of the inverse ratio of their masses. However, experiments also give abnormally large isotopic shifts. For instance, considerations of vibrational motions of entire hydrogen molecule confined in an octahedral cavity between fullerene molecules in solid C 60 shows that H-D substitution leads to a frequency ratio of about , 1 which means that the model mentioned above is inapplicable in this case.When studying motions of molecular systems in cavi ties of solids or cage structures (e.g., a fullerene or zeolite) or in a crystal or matrix defect, one must take into ac count a variety of different type factors among which constraints on the region of free motion of particles de serves particular attention. The model of a system placed in a cavity with impenetrable walls is often used in studies of complex physicochemical systems (see, e.g., Refs 2-12 and references cited therein). In this work we considered the influence of the cavity size on the magnitude of isoto pic frequency shift. First, we performed a qualitative study of a model problem of the motion of a particle in a uni form potential; some of the results obtained were found to be valid for any potential. The estimates obtained make it possible to interpret the results of numerical calculations of the lowest part of rovibrational spectra of hydrogen molecule isotopomers in a spherical cavity, which corre sponds to the motions of the system as a whole. The model systemConsider a model problem of the motion of a...

Spectroscopic characteristics of simple systems in a spherical cavity

“…(5) Similar relations were used in [28] for analyzing iso tope shifts of diatomic molecules in a cavity.…”

Isotopic Effects on Covalent Bond Confined in a Penetrable Sphere

“…A great effort has been devoted to elucidate the changes in molecules when the bonding electrons are confined by impenetrable surfaces, not necessarily closed, with different symmetries; see, for example, ref and references therein. Less studies have been devoted to situations where the surrounding boundary surfaces are penetrable. − To the best of our knowledge, the study of the role of isotopic substitution in confined diatomic molecules has been addressed by only one paper considering isotope effects in molecules located inside a cavity with impenetrable surfaces …”

“…11−13 To the best of our knowledge, the study of the role of isotopic substitution in confined diatomic molecules has been addressed by only one paper considering isotope effects in molecules located inside a cavity with impenetrable surfaces. 14 Electronic properties of a trapped hydrogen molecule are studied. The molecule is confined at the center of a spherical box with penetrable walls.…”