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

Abstract

Quantum states of a hydrogen atom adsorbed on $\mathrm{Cu}(100)$ and $\mathrm{Cu}(110)$ are studied theoretically. In calculating eigenenergies and wave functions of hydrogen atom motion, three-dimensional adiabatic potential energy surfaces (PESs) are constructed within density functional theory and the Schr\odinger equation for hydrogen atom motion on the PESs is solved by the variation method. The wave function on $\mathrm{Cu}(100)$ indicates a localized mode on the hollow (HL) 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 (BR) site. In the case of $\mathrm{Cu}(110)$, the ground state wave function is spread from the short bridge (SB) site and to the pseudothreefold (PT) site. The first few excited states are vibrational modes centered at the SB and long bridge (LB) sites. The excited state wave function of the hydrogen atom motion on $\mathrm{Cu}(110)$ 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 $\mathrm{Cu}(100)$ and $\mathrm{Cu}(110)$ are fairly in agreement with their corresponding experimental findings.