Quantum states of a hydrogen atom adsorbed on $\mathrm{Cu}\left(100\right)$ and (110) surfaces

Quantum states of a hydrogen atom adsorbed on $\mathrm{Cu}\left(100\right)$ and $\mathrm{Cu}\left(110\right)$ 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 Schrödinger equation for hydrogen atom motion on the PESs is solved by the variation method. The wave function on $\mathrm{Cu}\left(100\right)$ 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 $\mathrm{Cu}\left(110\right)$, 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 $\mathrm{Cu}\left(110\right)$ 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 $\mathrm{Cu}\left(100\right)$ and $\mathrm{Cu}\left(110\right)$ are fairly in agreement with their corresponding experimental findings.

Figure 1

Representations of the three dimensional potential energy surface for adiabatic hydrogen atom motion on $\mathrm{Cu}\left(100\right)$, from a diagonal view, top view (along the $\left[100\right]$ axis) and side view (along the $\left[01\overline{1}\right]$ axis). In increasing shading depth, the PES is represented by isosurfaces with values of $-2.0$, $-2.20$, $-2.30$, $-2.40$, $-2.45$, and $-2.48\mathrm{eV}$. Cu atoms are located at $(0.00,0.00,0.00)$, $(2.55,0.00,0.00)$, $(0.00,2.55,0.00)$, and $(2.55,2.55,0.00)$. (b) Same as (a), but for the top view (along the $\left[011\right]$ axis) and side view (along the $\left[01\overline{1}\right]$ axis) on $\mathrm{Cu}\left(110\right)$. In increasing shading depth, the PES is represented by isosurfaces with values of $-2.0$, $-2.10$, $-2.16$, $-2.26$, $-2.30$, and $-2.34\mathrm{eV}$. Cu atoms are located at $(0.00,0.00,0.00)$, $(3.64,0.00,0.00)$, $(0.00,2.55,0.00)$, and $(3.64,2.55,0.00)$.

Figure 2

Supercell geometries (only two layers shown) of (a) $\mathrm{Cu}\left(100\right)$ and (b) $\mathrm{Cu}\left(110\right)$ surfaces, with their high symmetry sites indicated by the small black circles: TP, top; BR, bridge; LB, long bridge; SB, short bridge; HL, hollow; and PT, pseudothreefold. The white and gray-colored circles correspond to the substrate atoms in the first and second layers, respectively. The origin of of the PES for hydrogen atom motion is taken as the position of the first layer atoms.

Figure 3

Wave function at the (a) ground state, (b) first excited state, and (c) second excited state for H atom motion on $\mathrm{Cu}\left(100\right)$, taken from a diagonal view, top view (along the $\left[100\right]$ axis) and side view of (along the $\left[01\overline{1}\right]$ axis). The labels “$+$” and “$-$” indicate the positive and negative valued regions of wave functions, respectively. The absolute value of the wave function increases with increasing isosurface shading depth.

Figure 4

(a) Same as Fig. 3a, but for the third, (b) fourth, and (c) fifth excited states.

Figure 5

Wave function at the (a) ground state, (b) first excited state, (c) second excited state, and (d) third excited state for H atom motion on $\mathrm{Cu}\left(110\right)$, taken from a diagonal view, top view, top view (along the $\left[110\right]$ axis) and side view (along the $\left[1\overline{1}0\right]$ axis), respectively. The labels “$+$” and “$-$” indicate the positive and negative valued regions of the wave functions, respectively. The absolute value of the wave function increases with increasing isosurface shading depth.

Figure 6

(a) Same as Fig. 5a, but for the fourth, taken from side view along the $\left[001\right]$ axis, (b) fifth, (c) sixth, and (d) seventh excited states.

Figure 7

(a) Same as Fig. 5a, but for the eighth, taken from side view along the $\left[001\right]$ axis, (b) ninth, and (c) tenth excited states.