Quantum dynamics of a hydrogen molecule confined in a cylindrical potential

Abstract

We study the coupled rotation-vibration levels of a hydrogen molecule in a confining potential with cylindrical symmetry. We include the coupling between rotations and translations and show how this interaction is essential to obtain the correct degeneracies of the energy level scheme. We applied our formalism to study the dynamics of H 2 molecules inside a "smooth" carbon nanotube as a function of tube radius. The results are obtained both by numerical solution of the (2J+1)-component radial Schrödinger equation and by developing an effective Hamiltonian to describe the splitting of a manifold of states of fixed angular momentum J and number of phonons N. For nanotube radius smaller than ≈3.5Å, the confining potential has a parabolic shape and the results can be understood in terms of a simple toy model. For larger radius, the potential has the "Mexican hat" shape and therefore the H 2 molecule is off centered, yielding radial and tangential translational dynamics in addition to rotational dynamics of H 2 molecule which we also describe by a simple model. Finally, we make several predictions for the the neutron scattering observation of various transitions between these levels. Disciplines Physics | Quantum Physics CommentsAt the time of publication, author Taner Yildirim was affiliated with the National Institute of Standards and Technology, Gaithersburg, Maryland. Currently, he is a faculty member in the Materials Science and Engineering Department at the University of Pennsylvania.This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/336 We study the coupled rotation-vibration levels of a hydrogen molecule in a confining potential with cylindrical symmetry. We include the coupling between rotations and translations and show how this interaction is essential to obtain the correct degeneracies of the energy level scheme. We applied our formalism to study the dynamics of H 2 molecules inside a ''smooth'' carbon nanotube as a function of tube radius. The results are obtained both by numerical solution of the (2Jϩ1)-component radial Schrödinger equation and by developing an effective Hamiltonian to describe the splitting of a manifold of states of fixed angular momentum J and number of phonons N. For nanotube radius smaller than Ϸ3.5 Å, the confining potential has a parabolic shape and the results can be understood in terms of a simple toy model. For larger radius, the potential has the ''Mexican hat'' shape and therefore the H 2 molecule is off centered, yielding radial and tangential translational dynamics in addition to rotational dynamics of H 2 molecule which we also describe by a simple model. Finally, we make several predictions for the the neutron scattering observation of various transitions between these levels. Quantum dynamics of a hydrogen molecule confined in a cylindrical potential

Titanium-Decorated Carbon Nanotubes as a Potential High-Capacity Hydrogen Storage Medium

“…3b), both yielded a binding energy of 0.13 eV/H 2 . This is the weakest bond in the system and yet it is 4-5 times stronger than the van der Walls interactions between hydrogen and SWNT [27].…”

5D quantum dynamics of the H2@SWNT system: Quantitative study of the rotational-translational coupling

“…Among these effects, we find distortions of the electronic structure and geometry of the species, 4 as well as changes in their dynamic behavior due to a strong translation-rotation coupling. [5][6][7][8] These effects lead to potential applications in chemistry and physics: they allow a tight control of certain reactions, 9 or the separation of isotopes of gaseous species at the molecular level, known as quantum sieving. 3,10 In particular, the hydrogen molecule (H 2 ) has been a popular target for these studies due to the interest of nanostructures as hydrogen storage devices for technological applications.…”

“…For this kind of system, Yildirim et al made an extensive formal study of the energetic levels of hydrogen using a cylindricalsymmetry potential energy surface model. 6,12 Later on, Gray and coworkers improved the potential model and were able to give deeper insight into the system with a four dimensional Hamiltonian which did not take into account the vibrational degree of freedom (DoF). 5 The first five-dimensional study of hydrogen confined in carbon nanotubes, considering hydrogen's vibration, was later carried out by some of us.…”

Quantum dynamics of H2 in a carbon nanotube: Separation of time scales and resonance enhanced tunneling

“…7,[23][24][25][26][27][28] One particular feature present in single-walled carbon nanotubes (SWCNTs) that makes them especially interesting materials is their cylindrical shape, which gives rise to the coexistence of a 2D confinement in the space perpendicular to the nanotube's axis and unbound motion along this latter coordinate. Even though 2D confinement has been relatively studied and reviewed in the literature, 12,16,29,30 only few studies have treated both the confined and the quasi-free coordinates in a fully quantum formalism. To the best of our knowledge, only Skouteris and Laganá, 31 treating the motion of an OH radical along a (10,0) SWCNT, and some of the present authors, 32,33 dealing with the H 2 molecule in a (8,0) SWCNT, have performed such studies.…”

“…Hydrogen adsorbed in carbon-based nanostructured materials, such as fullerenes and carbon nanotubes, was among the first systems to be studied and still remain the most relevant in the literature. 3,[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] More recently, studies have appeared focusing on different adsorbates, such as CO, CH 4 , CO 2 , SO 2 , or H 2 O, and different substrates such as zeolites and metal-organic frameworks. 7,[23][24][25][26][27][28] One particular feature present in single-walled carbon nanotubes (SWCNTs) that makes them especially interesting materials is their cylindrical shape, which gives rise to the coexistence of a 2D confinement in the space perpendicular to the nanotube's axis and unbound motion along this latter coordinate.…”