Quantum states of a hydrogen atom adsorbed onCu(100)and (110) surfaces

Abstract

Quantum states of a hydrogen atom adsorbed on Cu͑100͒ and Cu͑110͒ are studied theoretically. In calculating eigenenergies and wave functions of hydrogen atom motion, three-dimensional adiabatic potential energy surfaces ͑PESs͒ are constructed within density functional theory and the Schrödinger equation for hydrogen atom motion on the PESs is solved by the variation method. The wave function on Cu͑100͒ indicates a localized mode on the hollow ͑HL͒ site at the ground state. Wave functions of the first few excited states indicate vibrational modes on the HL site and suggest migration from an HL site to a neighboring HL site over the bridge ͑BR͒ site. In the case of Cu͑110͒, the ground state wave function is spread from the short bridge ͑SB͒ site and to the pseudothreefold ͑PT͒ site. The first few excited states are vibrational modes centered at the SB and long bridge ͑LB͒ sites. The excited state wave function of the hydrogen atom motion on Cu͑110͒ show isotope effects as follows. The fourth excited state wave function for the H atom motion shows a localized character on the LB site, and those for D and T atom motion show vibrational modes parallel to the surface. On the other hand, the fifth excited state wave functions for D and T atom motion show localized characters on the LB site and that for H atom motion shows a vibrational mode parallel to the surface. Our calculated eigenenergies of the hydrogen atom motion in excited states on Cu͑100͒ and Cu͑110͒ are fairly in agreement with their corresponding experimental findings.

Potential energy of hydrogen atom motion on Pd(111) surface and in subsurface: A first principles calculation

“…[5][6][7][8][9][10][11][12][13][14][15] Although it is necessary to consider quantum effects in investigating the behavior of the hydrogen atom on solid surfaces due to the small mass of the hydrogen, these depend consid-erably on the breadth ͑or curvature͒ of the adiabatic potential energy surface for the hydrogen atom motion. [16][17][18][19][20][21][22][23][24][25][26][27] In this article, we calculate the potential energy for the interaction of the hydrogen atom with Pd͑111͒ up to the third subsurface atom layer based on the density functional theory. Although there are no calculations made on the quantum states for the hydrogen atom motion, improvements on the typical features of the behaviors of the hydrogen atom can be obtained from the characters of the potential energy surface ͑PES͒ that we calculated.…”

Development of Novel Materials through Computational Materials Design (CMD®)

“…b. Naniwa Statics: The quantum states of an atomic motion (i.e. H, D, and Li atoms) on the constructed PES can be obtained by solving the three-dimensional Schrӧdinger equation via the variational method (32)(33)(34)(35).…”

First Principles Study of Positive Muon and Hydrogen Nucleus (H+, D+) on Graphene

“…In recent years, the quantum mechanical behaviors for H atom motions on transition metal surfaces were studied by solving Schrödinger equations using the variation method [4][5][6][7][8][9][10][11][12][13]. The wave functions and eigenvalues for H atom motion elucidated the properties of their localized ground state and vibrational excited states and predicted the various quantum effects.…”

“…Although many first principles theoretical studies have been performed on hydrogen storage of metalized graphene [14,15], quantum states of nucleus are not taken into account. In order to predict the quantum states of particles, µ + , H + and D + on graphene, we have performed the quantum ab-initio based dynamics calculation by using the computer code NANIWA [16] which has been developed for quantum behavior of light nucleus in materials [4][5][6][7][8][9][10][11][12][13]17].…”