Quantum delocalization of hydrogen on metal surfaces

Surface Science Reports 57 (2005) 113–156 www.elsevier.com/locate/surfrep

Quantum delocalization of hydrogen on metal surfaces Mitsuaki Nishijima a, Hiroshi Okuyama a,
, Noriaki Takagi a,1, Tetsuya Aruga a, Wilhelm Brenig b a

Department of Chemistry, Graduate School of Science, Kyoto University, Sakyo-ku, Kitashirakawa, Kyoto 606-8502, Japan b Physik-Department, Technische Universita¨t Mu¨nchen, D-85747 Garching, Germany Received 4 March 2005 Available online 7 April 2005

Abstract Experimental and theoretical studies on the quantum delocalization of hydrogen atoms, in particular in vibrationally excited states, on transition-metal surfaces are reviewed. The present status and remaining problems are discussed. The quantum delocalization of hydrogen atoms in the ground state is briefly reviewed. # 2005 Elsevier B.V. All rights reserved. Keywords: Metal surfaces; Hydrogen; Quantum delocalization

Abbreviations: cm1, wave number (1 meV ¼ 8:0657 cm1); DFT, density-functional theory; EELS, electron energy loss spectroscopy; EMT, effective medium theory; Ep , primary electron energy; fcc, face-centered-cubic; FWHM, full-width at halfmaximum; GGA, generalized gradient approximation; hcp, hexagonal-close-packed; IETS, inelastic electron tunnelling spectroscopy; IRAS, infrared reflection-absorption spectroscopy; LAPW, linear augmented plane wave; LDA, local-density approximation; LEED, low-energy electron diffraction; NNCFC, near-neighbor central force-constant; PRBS, pseudo-random binary sequence; rms, root-mean-square; STM, scanning tunnelling microscopy; u, fractional hydrogen coverage (number of adsorbed hydrogen atoms per bulk-like-surface metal atom); ue , emission angle; ui , incidence angle; TOF, time-of-flight; UPS, ultraviolet photoelectron spectroscopy
Corresponding author. Tel.: +81 75 753 3977; fax: +81 75 753 4000. E-mail addresses: [email protected] (M. Nishijima), [email protected] (H. Okuyama), [email protected] (W. Brenig). 1 Present address: Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8651, Japan. 0167-5729/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.surfrep.2005.03.001

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Contents 1.

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2. Theoretical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1. Single-particle band structure at low coverage . . . . . . . . . . . . . . . 1.2.2. Effects of short-range H–H repulsion at high coverage . . . . . . . . . 1.2.3. Effects of indirect interactions at high coverage . . . . . . . . . . . . . . Experimental work and comparison with theoretical calculations . . . . . . . . . . . . . 2.1. Experimental method — high resolution electron energy loss spectroscopy . 2.1.1. EELS spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2. The probability for the vibrational excitation and selection rules . . 2.1.3. Origins of the EELS peak broadening. . . . . . . . . . . . . . . . . . . . . 2.2. Hydrogen on Ni surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1. Hydrogen on Ni(1 0 0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2. Hydrogen on Ni(1 1 0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3. Hydrogen on Ni(1 1 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Hydrogen on Pd surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1. Hydrogen on Pd(1 1 0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2. Hydrogen on Pd(1 1 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Hydrogen on Cu surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1. Hydrogen on Cu(1 1 0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2. Hydrogen on Cu(1 1 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5. Hydrogen on Rh surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1. Hydrogen on Rh(1 0 0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2. Hydrogen on Rh(1 1 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6. Hydrogen on Pt surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1. Hydrogen on Pt(1 1 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7. Hydrogen on W surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8. Hydrogen on other transition-metal surfaces . . . . . . . . . . . . . . . . . . . . . . 2.9. Quantum delocalization of hydrogen in the ground state . . . . . . . . . . . . . . 2.9.1. Hydrogen on Ni(1 0 0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9.2. Hydrogen on Ni(1 1 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9.3. Hydrogen on Pd(1 1 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9.4. Hydrogen on Cu(1 0 0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9.5. Hydrogen on Pt(1 1 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prospective for the future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Theoretical prospectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Reliability of the experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Further study on various transition-metal surfaces . . . . . . . . . . . . . . . . . . 3.4. Experimental techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. Further interesting studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction 1.1. General A study of the adsorbed states of hydrogen on transition-metal surfaces is important not only from the scientific viewpoint of understanding the gas–surface interactions, but also from the technological applications related with, e.g., heterogeneous catalysis, surface electronics and energy storage. Many studies have been made in the past to understand the adsorbed states of hydrogen both theoretically and experimentally, and great progress has been made, especially in the last two decades, in our understanding of the various aspects of the surface-hydrogen interactions [1]. Nevertheless, there still remain many problems which have yet to be solved. One reason for the difficulty is that hydrogen is a light atom. This gives rise to the high mobility of hydrogen atom on the surface, quantum effects, etc. The hydrogen atom has the simplest structure of all the elements in the periodic table. It consists of a nucleus containing one proton and one electron. It has a rest mass of 1:67  1027 kg. Although the hydrogen mass is larger than the electron mass by a factor of 1836, one may expect that hydrogen atoms on transition-metal surfaces behave similar to electrons in the free-electron metals, if the energy barrier for hydrogen atoms to move around on the surface (activation energy for the surface diffusion) is very small. Indeed, typical vibrational energies of H-atoms on the transition-metal surfaces are in the range of  60–160 meV, and comparable with the typical activation energy for surface diffusion of  200 meV. Table 1 includes a summary of the vibrational energies hn (in meV) observed for H on various transition metals. See Fig. 1 for a schematic of the vibrational modes of ‘‘localized’’ hydrogen atoms in highsymmetry sites. Table 2 includes a summary of the activation energies for diffusion DE (in meV) and diffusivities D0 (in cm2 s1) of H on various surfaces [2,3]. Note that the data in Table 2 have been obtained by the use of various techniques, e.g., field electron microscopy, laser induced desorption and linear optical diffraction, and that scattering of the data is partly attributed to the difference of diffusion distances depending on the techniques employed [2]. Thus, although hydrogen atoms in the ground state may be adsorbed in localized sites, there are good reasons to expect that hydrogen atoms in the vibrationally excited states are quantum-mechanically delocalized, and that they behave as Bloch waves [4]. Fig. 2 shows a schematic diagram showing the vibrational states fn expected for a hydrogen atom on a hypothetic one-dimensional metal surface. V represents the potential energy surface for hydrogen, and Ed is the activation energy for diffusion of hydrogen. n ¼ 0 indicates the vibrational state of hydrogen in the ground state, and n ¼ 1; 2 and 3 indicate those in the excited states. In Fig. 2, it is assumed that the n ¼ 0 state is almost localized, whereas the n ¼ 1; 2 and 3 states are delocalized. The idea of the quantum delocalization was initially proposed by Christmann et al. [5] in 1979 in order to elegantly interpret the disordered phase of hydrogen atoms adsorbed on the Ni(1 1 1) surface at room temperature. They assumed that the majority of the hydrogen atoms is in localized states, while the rest is delocalized. The first theoretical study on the quantum motion of chemisorbed hydrogen was reported by Puska et al. [6] in 1983, which was followed by the work of Puska and Nieminen [7] published in 1985. Puska et al. solved the Schro¨ dinger equation for a single hydrogen atom on Ni(1 0 0), Ni(1 1 0) and Ni(1 1 1) surfaces. The results show considerable quantum effects for the hydrogen atom in both the ground and excited states. The basic formalism of these studies is described in Section 1.2.1. Theoretical studies were also made concerning the effects on the delocalization of the interactions between the adsorbed hydrogen atoms, and are described in Sections 1.2.2 and 1.2.3. Mate and Somorjai [8] claimed

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Table 1 Vibrational (loss-peak) energies hn (in meV), isotopic ratios hnH / hnD and the intrinsic peak widths DðhnÞ (in meV) for H(D) on various metals Surface

Fractional coverage

hnH (hnD )

hnH / hnD

DðhnH Þ[ DðhnD Þ]

Reference

(s)80(57) 1.40  4(4) [67] (as)  84(56)  1.5  19(12) Ni(1 1 0) 1.0 (s)79(63) 1.25 9(5) [21] (as)108(80) 1.35 12(–) (s)132(92) 1.44 19(–) Ni(1 1 1)  0:5 (as)90(–)  7(–) [76] (s)130(–)  9(–) 0.5 (as)91,96(69,72) 1.32,1.33 [78] (s)131,136(–,99) –,1.37 a Pd(1 1 0) 0.04(0.06) 87(66) 1.32 [83] 100(–) 121(88) 1.38 Pd(1 1 1) 1 (as)96(72) 1.33 [84,100] (s)124(89) 1.39 b Cu(1 1 0) 0.01 62(58) 1.07 [20] 90(58) 1.55 Cu(1 1 1)  0.1 (as)92(–) 12 [93] (s)124(–) 8 Rh(1 1 1) 0–1 (as)79(60)-90(67) 1.32–1.34 15–24(10–14) [98] (s)  135(98)  1.38 W(1 1 0) 0.5 96(71) 1.35 8(5) [125] 156(112) 1.39 6(3) Ru(0 0 0 1) > 0.3 (s)85(–) [131] Ir(1 1 1) low u (as)67(65) 1.03 [128] Pt(1 1 1)  0.7 (s)68(50) 1.36 [99] (as)153(112) 1.37 1 (s)156 11 [101] 1 (as)67(51) 1.31 16(–) [100] (s)112(84) 1.33 4(–) 153(108) 1.42 26(–) DðhnÞ was mainly estimated by DðhnÞ ¼ ½ðDEloss Þ2  ðDEelastic Þ2 1=2, where DEloss and DEelastic are the full-widths at half maxima of the loss and elastic peaks, respectively. In some cases, DðhnÞ was estimated from the peak separation. s(as) means the symmetric (asymmetric) stretch mode. a Separation of the 87 and 100 meV losses: 13 meV. b Separation of the 62 and 90 meV losses: 28 meV. Ni(1 0 0)

1.0

in 1986 that they obtained experimental evidence of the quantum delocalization in the study of hydrogen on Rh(1 1 1) by the use of high resolution electron energy loss spectroscopy (EELS). EELS is an experimental technique to measure the vibrational excitations of gas atoms and molecules adsorbed on solid surfaces [9]. One irradiates the surface with monochromatic electrons, and measures energy loss spectra of the reflected electrons. This technique will be discussed in more detail in Section 2.1. The above pioneering studies were followed by the work of many other research groups. Experimental evidence was obtained which was considered to support the quantum delocalization in the studies of hydrogen on single-crystal surfaces of Ni, Pd, Cu, Rh, Pt, W. More recent experimental work indicates, however, that some results of the earlier workers were disturbed by the coadsorbing surface contaminants

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Fig. 1. Schematic representation of the vibrational modes of ‘‘localized’’ hydrogen atoms in high-symmetry sites: s, symmetric stretch; as, asymmetric stretch. For fcc(1 1 0), the ‘‘perpendicular’’ mode is tilted from the surface normal, and one of the ‘‘parallel’’ modes is tilted from the surface plane. The vibrational modes for the 2-coordinated bridge sites are also included.

such as water molecules from the background. The possibility of quantum delocalization was also examined theoretically on various surfaces. Details of the experimental and theoretical studies for various systems which have been reported up to now are discussed in Sections 2.2–2.8. The studies on the quantum delocalization of hydrogen in the ground state are briefly described in Section 2.9. The prospective for the future is discussed in Section 3. A chronological list of the published papers associated with the quantum delocalization of hydrogen atoms is shown in Table 3. It is well known that the diffusion of hydrogen on transition metals, e.g., W, does not depend on temperature in the very low temperature region [2]. This is attributed to the tunnelling of hydrogen through an isolated diffusion barrier, which is another quantum behavior of hydrogen atoms on transition metals. This tunnelling may be called incoherent tunnelling. The quantum delocalization discussed in this paper can be called coherent tunnelling of hydrogen atoms in which the hydrogen wave functions located at each adsorbed site are added coherently to form extended states, in ordered systems, as Bloch

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Table 2 Activation energies for diffusion DE (in meV) and diffusivities D0 (in cm2 s1) of H(D) on various systems Surface Ni(1 0 0)

DEH (DED )

D DH 0 (D0 )

139(156) 152 176 152(191) 152(217) 148(165) 196(218) 197(194) 135–161 (161–187) 260 304(304) –(301) 68(76) 174(174) 161(178)

8  106 ð2  105 Þ

Remark and reference

100–140 K, low u [153] 156–161 K, u  0:9 [134]  8  106 223–283 K, low u 4:5  103 211–263 K 2:5  103 ð8:5  103 Þ 160–200 K, u ¼ 0:7 [178] 1:1  106 ð5  105 Þ 125–154 K, u ¼ 0:3 [179] Ni(1 1 1) 1:7  105 ð1:6  105 Þ 110–240 K, u ¼ 0:3 [136] 2:8  103 ð3:4  103 Þ Cu(1 0 0) – 60–80(50–80) K, u  0:01 [144] Rh(1 1 1) – 0:02  u  0:33 (8  102 ) Pt(1 1 1) 1 u ¼ 0:3 – 210–240 K, u ¼ 0:24 [180] 200–250 K, u ¼ 0:33 –(5  101 ) 140–250 K, u ¼ 0:1 [106] 1:1  103 ð1:4  103 Þ u ¼ 0:1 W(1 1 0) 1  107 ð3  105 Þ Ru(0 0 0 1) 230–270 K 8  104 ð4:6  104 Þ Except for the cases in which references are included, the data are obtained from the review papers of Gomer [2] and Bonzel [3]. The readers are referred to these papers and references therein.

waves. The quantum delocalization is entirely different from a (classical) disordered distribution of hydrogen atoms in various adsorption sites. Disorder, on the other hand, can lead to localization of delocalized particles in particular in 2D and 1D systems. This localization, often called weak localization, however, occurs on length scales large

Fig. 2. Schematic representation of a simple one-dimensional model illustrating the quantum delocalization of a hydrogen atom on the transition-metal surface.

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Table 3 A chronological list of the published papers associated with the quantum delocalization of hydrogen atoms on various transitionmetal surfaces Surface Ni(1 0 0)

First author

Puska Karlsson Mattsson Okuyama Ni(1 1 0) Puska Jo Voigtla¨ nder Brenig Ni(1 1 1) Christmann Puska Yanagita Okuyama Pd(1 1 0) Takagi Pd(1 1 1) Hsu Cu(1 0 0) Lauhon Cu(1 1 0) Astaldi Cu(1 1 1) Lee Ag(1 1 0) Sprunger Rh(1 1 1) Mate Yanagita Pt(1 1 1) Baro´ Richter Reutt Ka¨ lle´ n Ba˘ descu W(1 0 0) Lou W(1 1 0) Balden Ir(1 1 1) Hagedorn Theoretical/Experimental paper is denoted by T/E.

T/E

Published year

Reference

T E T E T E E T E T E E E E E E E E E E E E E T E,T T E E

1983, 1985 1986 1997 2002 1983, 1985 1985 1989 1993 1979 1983, 1985 1997 2001 1996 1991 2000 1992 2002 1993 1986 1999 1979 1987 1987 2001 2002 1990 1996 1999

[6,7] [60] [65] [67] [6,7] [70] [21] [24] [5] [6,7] [76] [78] [83] [140] [144] [20] [93] [129] [8] [98] [99] [100] [101] [105] [107] [108] [125] [128]

compared to the lattice constant and has little effect on the density of states (number of single-particle levels per unit energy). The weak localization will not be considered here. 1.2. Theoretical From the theoretical point of view there are at least three problems: (a) the single-particle band structure at low coverage; (b) the effects of hydrogen–hydrogen interactions on the band structure at high coverage; (c) the occurrence of collective excitations – such as optical phonons – at high coverage. 1.2.1. Single-particle band structure at low coverage Stimulated by the experimental results on large structural disorder of hydrogen adsorbed on Ni(1 1 1) as described above [5], in EELS [10] and in line with the observed tunnelling effects in diffusion of hydrogen [11], a number of theoreticians [6,7] started to calculate the atomic band structure of hydrogen

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on Ni. After these pioneering calculations they were improved and extended to different situations. We are going to describe the corresponding results in the context of these situations below. In the limit of zero coverage only a single hydrogen atom has to be taken into account. Because of the large masses of transition-metal atoms, one considers only rigid substrate lattices. Similarly, the proton mass is large compared to the electron mass. Hence the adiabatic approximation is used. The single-particle potential VðrÞ to be used in the Schro¨ dinger equation for the hydrogen motion then is equal to the total interaction energy EðrÞ of a hydrogen atom at the position r. In order to simplify the calculation of this energy the effective medium theory is used [12,13]. This approximation is known to yield good chemisorption energies and bond lengths when compared to both other theoretical approaches and experiments. On transition metals, the energy E in this approximation takes the form EðrÞ ¼ VðrÞ ¼ Ehom ½n0 ðrÞ þ Ehybr ðrÞ þ Ec ðrÞ:

(1)

The first term, which is called the effective medium term, Ehom ½n0 ðrÞ represents the interaction between hydrogen and the valence electrons of the substrate–metal surface. This term depends only on the local substrate valence-electron density n0 ðrÞ at the position of hydrogen. The second term Ehybr ðrÞ describes the hybridization term between hydrogen and the substrate–metal d electrons. The last term Ec ðrÞ describes the core repulsion between hydrogen and the metal-atom cores. The Schro¨ dinger equation for the hydrogen atom then reads ½T þ VðrÞ f pi ðrÞ ¼ e pi f pi ðrÞ;

(2)

where T ¼ ½ h2 =2mH r2 is the kinetic energy, mH the hydrogen mass, e pi the energy eigenvalue, and f pi the wave function of the propagating Bloch state corresponding to a momentum p parallel to the surface and a band label i. Eq. (2) is solved fully three-dimensionally. The point-group symmetry of the adsorption sites (potential minima) classifies the eigenstates in accordance with its different representations. Puska et al. [6] calculated the band structures for hydrogen on the Ni(1 0 0) surface. The top left of Fig. 3 shows the potential used for hydrogen on Ni(1 0 0) in a vertical plane along the [0 1 1] azimuth through the four-fold center position where the potential has its minimum. The lengths of the cuts are the Ni nearest-neighbor distances both in the parallel and perpendicular directions. The lowest energy contour shown corresponds to 2.70 eV and the spacing between contours is 0.15 eV. The potential is quite anharmonic, and shows a strong coupling between motions parallel and perpendicular to the surface. Hence the harmonic approximation is not accurate enough. The Schro¨ dinger equation was solved numerically by a discrete mesh relaxation technique. The energy band structure for hydrogen on Ni(1 0 0) in the A1 representation of the C4v point group was calculated at p ¼ 0 and two nonzero p-points in the surface Brillouin zone, i.e., the high-symmetry ¯ shown in the inset of Fig. 4[6]. The calculated bands, after the results for high-symmetry points X¯ and M points are connected by straight lines, are shown in Fig. 4. The zero of energy is the ground-state energy (2.6 eV) at the G¯ point. This includes a zero-point energy of 0.1 eV. One may note that, in particular, the hydrogen bands of the excited states have considerable widths. Similar calculations were made for states in the E representation. Note that p ¼ 0 corresponds to the bottom of the A1 bands but to the top of the E bands. This follows from the opposite bonding–antibonding characters of the states belonging to the A1 and E representations.

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Fig. 3. Potential, A1 wave functions, and densities for hydrogen chemisorbed on the Ni(1 0 0) surface. The left panel shows the potential and wave functions in a vertical plane along the [0 1 1] direction through the four-fold center position where the potential has its minimum. The lengths of the cuts are the Ni nearest-neighbor distance (4.7 a0 ) both in the parallel and the perpendicular directions. At the top of the right panel, the potential is shown in a cut parallel to the surface through the absolute minimum. Underneath are shown the hydrogen densities, integrated perpendicular to the surface in the same parallel cut. In the right panel, the cuts are one Ni lattice constant (6.65 a0 ) in each direction. The lowest energy contour shown is 2.70 eVand the spacing between contours is 0.15 and 0.22 eV for (a) and (b), respectively. The wave function contours are shown with a constant spacing, and with the same minimum contour value in all cuts. The same is true for the density contours. Dashed lines denote negative contours. All wave functions are evaluated at G¯ (reprinted with permission from Ref. [6]).

1.2.2. Effects of short-range H–H repulsion at high coverage With increasing coverage the interaction between adsorbed hydrogen atoms has to be taken into account. By now the basic mechanisms of the adsorbate–adsorbate interaction are essentially understood. It is the sum of direct interactions (electrostatic interactions such as dipole–dipole interaction, Van der Waals interaction, etc. and electronic interactions such as Pauli repulsion, covalent-bond formation, etc.) and indirect interactions (substrate-mediated electronic interaction, substrate-mediated elastic interaction, etc.) [14–19].

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Fig. 4. The band structure for hydrogen chemisorbed on the Ni(1 0 0) surface shown along the high-symmetry directions indicated in the inset. Only the states belonging to the A1 representation of the C4v point group are shown. The zero of energy is the ground-state energy (2.6 eV) at the G¯ point. This includes a zero-point energy of 0.1 eV. In the inset, the Brillouin zone has been rotated 45  relative to the convention used in Fig. 3 (reprinted with permission from Ref. [6]).

We start with the discussion of short-range repulsion, which was considered first in the context of vibrational spectra of H and D on Cu(1 1 0) in a simple one-dimensional model [20], applicable to hydrogen on fcc(1 1 0) surfaces. One assumes that (a) the quantum hopping for a hydrogen atom in the ground state is negligible relative to that in the excited states, (b) the repulsion of two hydrogen atoms in the ground state is such that only one hydrogen can occupy a certain site, and that (c) a hydrogen atom in the excited state can hop to the neighboring sites thermally occupied by the ground-state atoms. All these effects can be treated in a one-dimensional Hubbard-like model Hamiltonian given by, X y1 X X X n1i þ T c j c1i þ U n1i n0i þ V n1i n0j : (3) H¼E i

i; j

i

i; j

Here the indices 1, 0, i and j refer to the excited state, the ground state, the sites in the linear chain, and the nearest neighbors of site i, respectively. E is the on-site excitation energy, T the nearest-neighbor (N-N) hopping energy in the excited state, U is the repulsive energy when the excited hydrogen atom shares a site with another hydrogen atom in the ground state, and V the repulsive energy between the excited

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y1

hydrogen atom and the ground-state hydrogen atom in the N-N sites. ci (c1i ) is the creation (annihilation) y1 operator for the site i and ni = ci c1i is the occupation number of the site i. The energy eigenvalues of the Hamiltonian (Eq. (3)) have been calculated numerically for a finite chain with 20 sites [20]. The density-of-states curves were averaged over the various spatial distributions of hydrogen atoms in the ground state, and convoluted with a Gaussian to fit them to the EELS spectra. Fig. 5 shows the dependence of bandwidth of delocalized D-atom states on Cu(1 1 0) as a function of coverage resulting from these calculations [20]. Further details are discussed in Sections 2.3.1 and 2.4.1 in relation to hydrogen on Pd(1 1 0) and Cu(1 1 0), respectively. 1.2.3. Effects of indirect interactions at high coverage Indirect electron mediated interactions. Besides the direct interaction there is an indirect one mediated by electrons. This interaction has been considered by many authors [14–16,19]. It is usually also repulsive at short distances but oscillates with increasing distance r having substantial attractive contributions. In general, the interaction energy can be approximated by 2kf r  2h : (4) vðrÞ ¼ v0 cos rn Here kf is the Fermi wave number of the electrons, h a phase shift related to the screening charge and n an integer between 1 and 5, depending on the (effective) dimensionality of the metal band states mediating the interaction. Fig. 6 shows results for H/Ni(1 1 0) assuming that not only the H-atoms but also the electrons move along one-dimensional troughs on the surface [19]. The n in Eq. (4) is then unity. At larger distances r of course also electron hopping between troughs (and into the bulk) becomes relevant and the effective n correspondingly larger. Phonon-like excitations at higher coverages. An important phenomenon at higher coverages which is strongly influenced by such interactions is the occurrence of phonon-like collective excitations. They show up as a dispersion (dependence of peak position on momentum transfer) superimposed on the single particle broadening observed at low coverage. A situation like this has been observed [21] for hydrogen adsorbed on Ni(1 1 0). Typically in this case the single-particle width of the vibrational levels is a factor

Fig. 5. Bandwidth of delocalized D-atom states on Cu(1 1 0) as a function of coverage. Solid line: results of numerical calculations using Eq. (3) (reprinted with permission from Ref. [20]); dashed line: approximation of the result by a straight line extrapolating to zero at half coverage.

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Fig. 6. Theoretical indirect interaction energy vðrÞ between two hydrogen atoms on Ni(1 1 0) assumed to be in contact with ˚ (reprinted quasi-one-dimensional electronic states localized in the troughs of the surface. The H–H distance r is measured in A with permission from Ref. [19]). See Ref. [19] for parameters of the interaction.

2–3 bigger than the maximum dispersion shifts at higher coverages. The shifts are small compared to the single-particle excitation energies but comparable to the substrate phonon dispersions. For coverages up to about u ’ 1 hydrogen appears to reside on three-fold coordinated sites of the Ni(1 1 0) surface. At monolayer coverage a ð2  1Þ-structure appears to form with hydrogen occupying zig-zag shaped chains within the dense Ni rows as shown in Fig. 7[22]. Fig. 8 shows the dispersion curves of Ni(1 1 0)(2  1)-H along G¯ X¯ and G¯ Y¯ directions [21]. The hydrogen–substrate interaction is strongly anisotropic: the three vibrational levels are well separated. Table 4 shows several parameters of the three low lying excited states [23,24]: their polarization and excitation energies vi ¼ ei  e0 ; i ¼ 1; 2; 3, their width De which is a measure of the bandwidth of the delocalized vibrational levels and the dispersion Dv ¼ vzb  v0 at full coverage of the ð2  1Þ-structure (vzb the zone boundary frequency). In [21] for waves propagating along the X-axis in the (2  1)-structure an extended zone has been used. In a reduced difference of the two k ¼ 0 zone scheme there would be two branches, say, v , and Dv would be the p ffiffiffi modes. The vibrational frequencies vi show an isotope effect close to 2 somewhat modified by anharmonicity. The isotope effect inpDe ffiffiffiffi is bigger. It can be expected to be of the order of a tunnelling matrix element which is / exp ða mÞ. For Ni(1 1 0) the hydrogen overlayer at full coverage forms a quasi-hexagonal lattice with two atoms in the unit cell of the (2  1)-superstructure. The nearest neighbors in this lattice belong to different pffiffiffi ˚ (a ¼ 3:52 A ˚ the lattice constant of Ni). The next sublattices and have a distance of 3 a=2 ¼ 3:05 A nearest (second nearest) neighbors belong to the same sublattice and have a distance of a. The third

Fig. 7. View of hydrogen atoms (white circles) on Ni(1 1 0)(2  1)-H. The Ni atoms are shown by dark(er) circles (courtesy of A. Gross).

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Fig. 8. Dispersion curves of the (2  1) unreconstructed surface along G¯ X¯ and G¯ Y¯ directions. The modes below 300 cm1 are nickel substrate phonons. The mode at 870 cm1 was observed at low primary energies (  3 eV) only, where it was experimentally impossible to measure modes in the second half of the Brillouin zone because of the restricted range of scattering angle (reproduced with permission from Ref. [21]); 1 meV ¼ 8:0657 cm1.

pffiffiffi ˚ . We take nearest neighbors belong again to the original sublattice and have a distance of 2a ¼ 4:98 A all couplings up to third nearest neighbors into account and neglect higher neighbor couplings. We also assume the Ni-substrate lattice to be frozen because of its large mass. Phonon dispersion is an effect well known from lattice dynamics. The canonical variables of lattice dynamics (the displacement coordinates and momenta of the lattice particles), however, can not be used straightforwardly in a situation where the delocalization width exceeds the dispersion shifts. In our case the velocity of particles is somewhat bigger than the phonon (group) velocity. This corresponds to phonons in a gas or liquid rather than in a solid, or to zero sound in liquid He or else to electronic excitons in solids. The appropriate framework for such effects is the random phase approximation (RPA or Landau Fermi liquid theory) [25,26]. It allows treating the single-particle broadening and phonon dispersion on the same footing. A convenient tool to introduce the random phase approximation [25,26] is the generalized susceptibility the imaginary part of which is proportional to the EELS intensity. In the absence of delocalization and H–H interactions it takes the simple form x0i ðvÞ ¼

2v0i ðv0i Þ2  v2  i0  v

:

(5)

Table 4 Energy parameters for the vibrational bands of Ni(1 1 0)(2  1)-H(D) [21,23,24] Polarization

vH

vD

DeH

DeD

DvG¯ X¯

DvG¯ Y¯

? Ni-rows 640 510 75 40 80 20 k Ni-rows 870 644 100 –   40 – ? Ni surface 1065 745 150 –   20  40 1 vHðDÞ is the vibrational energy (in cm ) and DeHðDÞ is the experimental intrinsic peak width (full width at half maximum) in ¯ G¯ Y) ¯ is parallel (perpendicular) to the Ni-rows. cm1 for H(D). Dv is the vibrational dispersion shift (in cm1) for H. G¯ X(

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v0i is the vibrational energy of a single adsorbate, and i0 a width parameter which has to be taken infinitesimal here but will become nonzero in general. If delocalization is taken into account — but possible effects of disorder are disregarded — transitions do not occur at a given site with frequency v0i but at a given momentum transfer k starting at momentum p. The susceptibility then becomes k-dependent: x0i ¼ x0i ðk; vÞ. This general form, however, becomes simplified if the ground-state band has negligible width [ e0 ð pÞ ’ e0 )]. This is usually the case and is supported by the results of corresponding band structure calculations [6,7]. The single-particle susceptibility then will be a function of v only, but more general than (5), depending on the density of excited states. In principle the density of 1D states of the excited bands would show singularities at the band edges and a corresponding structure in the susceptibility. Such a structure has been observed, e.g., for H/Pd(1 1 0) (Section 2.3.1). But often due to experimental broadening and possible disorder such a structure does not show up experimentally. The observed broadening of the susceptibility then can most simply be described by introducing a width parameter ig i as a measure of the excited state bandwidth instead of the i0 in (5). Furthermore there will be a shift in the frequency v0i to a renormalized vi . If we consider the simple case of energetically well separated bands which remain uncoupled at higher coverages the RPA equation for the susceptibility takes the simple (diagonal) form xi ðk; vÞ ¼

x0i ðk; vÞ : 1 þ vi ðkÞx0i ðk; vÞ

(6)

In the case of electronic collective excitation (such as plasmons or excitons) the interaction matrix elements would be / 1=k2 for small k and would lead to discrete ‘split off’ states outside the singleparticle bands. For H-atoms the matrix elements are generally smaller and nonsingular for small k. In this case the phonons appear as resonances inside the single-particle bands. In [24] an approximate calculation of the matrix elements was proposed connecting them to standard lattice dynamics. One first of all expresses the Bloch type solutions of the Schro¨ dinger equation (2) in terms of Wannier states f0 ðr  Rm Þ: f pi ðrÞ ¼

X

ei pRm

m

fi ðr  Rm Þ pffiffiffiffi : N

(7)

Here Rm is the position of lattice sites and N the total number of these sites. Since the bandwidth of the Bloch states is small compared to excitation energies one can assume that the Wannier states are well localized. Furthermore we use for the excited states the ansatz  fi ðrÞ ¼

2 mvi

1=2

@f0 ðrÞ ; @xi

i ¼ 1; 2; 3;

(8)

where f0 ðrÞ is the localized vibrational wave function for the ground state. Eq. 8 would be exact for the harmonic oscillator and can be used as a variational ansatz in the anharmonic case. If (7) and (8) is inserted into the matrix element vi ðkÞ ¼ h p0; q0 ijvj p0 i; q0i (with p0 ¼ p þ k, 0 q ¼ q þ k) one obtains a four-fold sum over Wannier states which can be ordered according to their overlap: the leading term would come from the single sum with all Wannier states at the same site. This term, however, will be strongly suppressed by the correlations introduced by the short-range repulsions

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discussed above. The corresponding suppression of double occupancies is not contained in (plain) RPA but can be taken into account approximately by just omitting the single sum completely. The next leading term is a double sum with two ground-state holes at two different sites, say m and n, and the two excited Wannier states at the same two sites. In the language of excitons this corresponds to the so-called Frenkel excitons. All other terms in the four-fold sum contain more than two sites. Hence they are of higher order in the overlap and will be neglected. For a central force with potential vðrÞ the result can be written as [24] 1 ½vi ðkÞ2  v02 (9) vi ðkÞ ¼ i

2vi with vi ðkÞ2 ¼

1 X @2 vðRm Þ  ½1  cos ðk  Rm Þ

2 m m @Xmi

an expression well known from lattice dynamics and X @2 vðRm Þ mv02 : i ¼ 2 @Xmi m 6¼ 0 The susceptibility then takes the form 2vi : xi ðk; vÞ ¼ 2 02 vi  vi þ vi ðkÞ2  v2  ig i v

(10)

(11)

(12)

In general the three bands with i ¼ 1; 2; 3 mix. One then has to consider off diagonal matrix elements of the susceptibility and the interaction v. In the case of Ni(1 1 0) the bands are well separated and do not mix but one has a quasi hexagonal structure with two atoms per unit cell. Then one has also to consider 2  2 susceptibility matrices and the corresponding secular equations for the phonons. We refer to [24] for the details. So the main result is: For sufficiently weak delocalization the inelastic electron spectrum near full coverage can be calculated in two independent steps. First one determines the band structure ei ð pÞ of the excited vibrational states and the corresponding width g i of the i th band. Then one determines the vibrational frequencies vi ðkÞ according to standard lattice dynamics and inserts both results into (12). As mentioned already in the context of (2) the vibrational frequency vi will become renormalized by the Hartree–Fock potential of the H–H interaction. Rather than calculating this explicitly one may infer it from translation invariance. For a two particle interaction which conserves total momentum of the Hoverlayer the k ¼ 0 mode should not show any effect of the interaction. Since vi ðk ¼ 0Þ ¼ 0 the v02 i just has to cancel the Hartree–Fock contribution to v2i : 02 v2i ¼ v02 i þ vi ;

where v0i

(13)

is the vibrational frequency of a single adsorbate. In more general terms this equation expresses a Ward identity (a relation between the vertex part and the self-energy) as a consequence of total momentum conservation [29]. The independence of the frequency of k ¼ 0 mode on concentration hence is a test of the translation invariance of the H–H interaction which may be broken by strong substratemediated indirect interactions. This is probably a small effect but it may be interesting to check it experimentally. If there is no substrate (and hence v0i ¼ 0) the acoustic mode frequencies vanish for

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k ¼ 0. This case has been treated earlier [31]. We refer to [24] for the details and quote only some of the results: the description of the in-surface-plane modes is possible in terms of two body central forces with potential vðrÞ which differ strongly from the bare H–H interaction (see Fig. 9). Since from fitting the data only the first and second derivatives of vðrÞ at first, second and third nearest neighbors can be inferred the determination of the potential is not unique. But certain basic facts make it rather unambiguous. For instance the fact that the transverse modes show much stronger dispersion than the longitudinal ones is closely related to the oscillatory behavior of vðrÞ as characteristic for indirect interactions mediated by the metal electrons. On the other hand if the modes polarized perpendicular to the surface are taken into account the central force model leads to problems. These modes show little dispersion and some fluctuations in particular at k ¼ 0. If nevertheless the two values of Dv in the last line of Table 4 would be taken seriously, they could not be fit with central forces. This may be an indication that there are strong noncentral forces (or many body forces). The importance of such forces is known from other experiments as well [30]. Effect of long-range interactions on single-particle bandwidth. The long-range indirect interaction does not only lead to phonon-like excitations but also to renormalizations of the single particle energies via Hartree–Fock terms in the self consistent single-particle potentials. Here we present an estimate of such effects and point out an important property, namely their dependence on the quantum statistics of the

Fig. 9. Indirect interaction energy vðrÞ between two hydrogen atoms on Ni(1 1 0) as determined from a fit of the phonon excitation energies (reprinted with permission from Ref. [24]). Good agreement with the height (and the sign and approximate values of the first and second derivatives) at the second and third nearest-neighbor (N-N) distances of Fig. 6 is seen. The slope of vðrÞ at the first nearest neighbor and the curvature at the second nearest neighbor, however, are about a factor of 5 bigger than in ˚ , second N-N: 3.52 A ˚ , third N-N: 4.98 A ˚. Fig. 6. First N-N: 3.05 A

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adsorbates: the Fock terms change sign under a change of this statistics. This is an important isotope effect which may be observable. Protons and deuterons adsorbed on metals are in close contact with an infinite reservoir of electrons. As a consequence they will be neutralized to a large extent. The neutralization can occur, however, in two different ways: either the metal electrons pile up as a (spinless) screening cloud near the adsorbates or a single electron (with its spin) is bound to the adsorbates in a state localized at the adsorbates with a discrete energy in the band gap. The two alternatives will show a profound difference in their quantum statistical behavior. In the first case the adsorbates will show the statistics of bare protons (deuterons) in the second case the statistics of hydrogen (deuterium) atoms. Unfortunately, besides the long-range interactions there are short range repulsions. Normally these short-range interactions do not contribute much to the phonon dispersion but they can, of course, contribute to the bandwidth of the Bloch states at higher coverages by blocking occupied sites. Indeed, the blocking effect can be shown to lead to a strong reduction of protonic bandwidths with increasing coverage as discussed above, see [20] and Fig. 5. Fortunately this blocking effect depends little on statistics. The contribution of long-range interactions to the bandwidth has not been considered in the literature so far, except [32]. A systematic treatment of it is not possible at present, since the interaction is not known in sufficient detail yet. One can, however, use the information from phonon data to learn something about these interactions as indicated above. The situation concerning the dependence of bandwidth and phonon dispersion on coverage may be described in terms of three statements: (a) At low coverage the bandwidth is determined by some near neighbor hopping matrix elements. The single-particle interaction responsible for these terms has been discussed above. The resulting bandwidths can be determined rather directly from experiment. (b) Short-range repulsive interactions. In the limit of strong repulsion (large U limit of the Hubbard model) these interactions do not introduce new parameters but just lead to the blocking of occupied sites. In the strong tight binding limit they do not contribute to the dispersion of phonons and to exchange terms and hence do not lead to a dependence of bandwidths on the statistics of particles: the bandwidth for H and D d ecreases linearly with coverage extrapolating to zero at half coverage [20]. For H/Cu(1 1 0) this behavior should, however, only be used for coverages below 0.3 because of reconstruction occurring at higher coverages. (c) Long-range forces. They are responsible for the dispersion of phonons and for the occurrence of exchange forces depending on the statistics of particles. The long-range forces introduce new parameters into the model which are not known very well. Usually they have an oscillatory dependence on distance. At nearest neighbor distances they are attractive as we have described above. For H/Ni(1 1 0) the corresponding parameters could be determined from the known phonon dispersion. The exchange forces will lead to an isotope effect having the opposite sign for H and D. Which sign is relevant will not only depend on the statistics of the particles but also the sign of the long-range two body forces relative to the short-range repulsive and the single-particle forces. In our case where the repulsive forces lead to a reduction of bandwidth with increasing coverage we expect that the predominantly attractive long-range forces will produce exchange effects which work in the same (opposite) direction as the blocking effect for fermions (bosons).

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In order to determine the order of magnitude of the effects we evaluate the exchange matrix elements h p0; qijvjqi; p0i in the Hartree–Fock approximation for the single-particle energies in the same way as in (9) — neglecting double occupancies and keeping only terms of maximum overlap in the Wannier functions. One then obtains for the exchange energy contributions to the single particle energies X vi ð p  qÞnðqÞns ; (14) ei;ex ð pÞ ¼  q

where the negative (positive) sign holds for fermions (bosons). Here nðqÞ is the occupation probability of momentum (normalized to unity) q, ns a spin dependent factor which is 1/2 in the case of bare protons, 1/3 in the case of bare deuterons, 1/4 for hydrogen atoms and 1/6 for deuterium atoms. This expression is most easily evaluated for low temperatures and coverages, where only low q-values are occupied. Then X nðqÞ: (15) ei;ex ð pÞ ’  vi ð pÞ ns In this case the exchange contribution to the single-particle dispersion would be proportional to the phonon dispersion and the corresponding contribution to the single-particle bandwidth would be equal to the phonon bandwidth. At higher temperatures larger portions of the Brillouin zone will become occupied and the exchange part of the bandwidth will become smaller. It may be interesting to look for these effects experimentally. Furthermore at lower coverages fewer nearest-neighbor sites will be occupied leading to a reduction of the exchange effects. Unfortunately an analysis of the phonon dispersion has only been considered for H and D on Ni(1 1 0) where there exists no systematic experimental investigation of the dependence of single-particle bandwidth on coverage [23]. In order to estimate the sign and the order of magnitude of possible effects let us consider the example of bare protons for H and bare deuterons for D on Ni(1 1 0). Using the value of Dvt ’ 10 meV from above and the spin factors for bare protons (deuterons) of 1/2 (1/3) one finds the exchange contributions to the single-particle bandwidth of the order of ’ 5 meV ( ’ þ3 meV) respectively. Preliminary unpublished experimental data on the bandwidth for H on Cu(1 1 0) appear to fall below the line for the pure blocking effect but to lie above for D [27]. Hence these data are compatible with the assumptions of our example indicating that, indeed, protons (deuterons) adsorbed on Cu behave as fermions (bosons).

2. Experimental work and comparison with theoretical calculations 2.1. Experimental method — high resolution electron energy loss spectroscopy The main source of experimental information is high resolution electron energy loss spectroscopy (EELS). Thus, the EELS spectrometer, the probability for excitation corresponding to the transition between the band states, selection rules associated with EELS, and origins of the EELS peak broadening are discussed. 2.1.1. EELS spectrometer The spectrometer incorporates, basically, an electron gun, a monochromator, an accelerator (sample), a decelerator, an analyzer, and a collector. The construction of a (single-pass) EELS spectrometer is

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shown schematically in Fig. 10[33]. The electron gun produces electrons which impinge on the entrance slit of the monochromator. A portion of these electrons, in a small energy band, passes through the monochromator (127  cylindrical-deflector-type energy analyzer), accelerated, and strikes a sample. The secondary electrons produced at the sample are decelerated and strike the entrance slit of the analyzer. A portion of these electrons, in a small energy band, passes through the analyzer (127  analyzer) and is collected. An electron energy loss spectrum is measured by varying the voltage applied to the decelerator, while keeping the voltages applied to the other components of the spectrometer fixed. High resolution can be obtained by lowering the pass energies of electrons in the monochromator and analyzer. An angle-dependent measurement is made by the rotation of the analyzer. During a study of the ejection of electrons from the W surface by low energy ions (He+, etc.), Propst and Lu¨ scher [34] found that the yields and energy distributions of the ejected electrons were strongly dependent on the nature and coverages of gases adsorbed on the surface. This led Propst to consider that more information could be obtained simply by studying the energy loss of monochromatic electrons. In 1967, Propst and Piper [35] succeeded in the measurement of the vibrational spectra of hydrogen on W(1 0 0) by the use of the EELS spectrometer for the first time. However, the energy resolution was rather poor (50 meV). Ibach and coworkers [9,36,37] improved the resolution to the 3–10 meV range by the modifications of various parts of the spectrometer, and by addition of the pre-monochromator and post-analyzer (double-pass spectrometer). In 1991, a drastic progress was reported in which the method of numerical simulations of electron trajectories was employed for the spectrometer designing [38]. The spectrometer uses lens systems and dispersive elements which are optimized not only in the classical sense of electron optics, but also in taking into account the space charge effect in the electron beam of high current density. In 1993, a new spectrometer with controlled aberrations was reported [39]. The EELS spectrometer built with such

Fig. 10. Basic construction of an EELS spectrometer (reprinted with permission from Ref. [33]).

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dispersive elements has a theoretical resolution limit of 0.3 meV, and an experimentally achieved resolution of 0.5 meV. The corresponding electron current detected by the collector in the direct mode (primary beam entering directly into the analyzer without reflection from the sample) is 3:5  1013 A. It is noted that, in the reflection mode, the signal intensity is reduced by a factor of  100 owing, in general, to the low reflection coefficient of the sample. 2.1.2. The probability for the vibrational excitation and selection rules In EELS, the energy losses of electrons scattered following the excitation of vibrational modes of the adsorbates are monitored. The probability Pnn0, for exciting an adsorbed hydrogen atom from the vibrational state cn ðrH Þ to the state cn0 ðrH Þ is proportional to the matrix element, Pnn0 / jhff ðre Þcn0 ðrH ÞjVðre  rH Þjfi ðre Þcn ðrH Þij2 ;

(16)

where fi ðre Þ and ff ðre Þ are the wave functions of the incident and reflected electrons, respectively. In Eq. (16), the hydrogen and electron coordinates are separated considering the large hydrogen/electron mass ratio (Born–Oppenheimer approximation). The electron–hydrogen interaction potential Vðre  rH Þ is related to its Fourier component VðqÞ by, Z (17) Vðre  rH Þ ¼ VðqÞexp ½iq  ðre  rH Þ dq: Inserting Eq. (17) into Eq. (16), and after some manipulations, the excitation probability Pnn0 can be expressed more explicitly, and therefore, the selection rules can be derived [7]. If Vðre  rH Þ reflects the interaction between an electron and the dipole moment induced by the adsorbed hydrogen (long-range dipole scattering), VðqÞ is peaked near q ¼ 0 and Dkk ¼ kik  kfk ¼ 0 (specular mode), where kk is the component parallel to the surface of the electron wave vector. In this case, the wave vector K of the hydrogen atom in the Bloch state parallel to the surface is conserved, i.e., the transitions are vertical. In addition, due to the screening of the parallel component of the dipole moment by the substrate–metal electrons, only the totally symmetric A1 state is excited (surface-normal dipole selection rule). If Vðre  rH Þ reflects the short-range interaction between an electron and the adsorbed hydrogen (short-range impact scattering), VðqÞ is broad and Dkk 6¼ 0 (off-specular mode). In this case, nonvertical transitions are allowed, and transitions from the ground state to excited states other than the A1 states are allowed. In addition, if the scattering plane coincides with some high-symmetry direction of the surface, several selection rules are derived which are determined by the geometrical symmetry of the impact scattering [9]. 2.1.3. Origins of the EELS peak broadening The EELS peak may be broadened by vibrational band formation. However, there are other possible origins which induce peak broadening, and these are briefly discussed below [40–49]. Possible origins which have been considered are (1) the homogeneous broadening, (2) inhomogeneous broadening, (3) quantum delocalization, in addition to (4) the instrumental broadening. The origins (1)– (3) can be called the intrinsic broadening. Homogeneous broadening is divided into the lifetime broadening (energy relaxation) and dephasing (phase relaxation). The energy relaxation occurs by: (a) the electron–hole pair excitation [40,45], (b) phonon excitation of the substrate [40], (c) excitation of other vibrational modes of the adsorbed species (accompanied by the emission or absorption of one or

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more substrate phonons) [42], and (d) the photon emission [42]. The energy width attributed to the electron–hole pair excitation of the frustrated translation mode (parallel to the surface) at 96 meV for H of Cu(1 1 1)(3  3)-H is 0.9 meV [50]. It is 0.7 meV for hydrogen on Ni(1 1 1) [50]. This process is almost temperature independent. The energy width associated with phonon excitation of the hydrogen vibration on metal has not been estimated to our knowledge. For CO on transition metals, the phonon excitation is considered to be important if the localized excitation can decay by emission of two or three phonons [40]. This process is strongly temperature dependent. No estimate has been made for the energy width associated with the excitation of other vibrational modes of adsorbed hydrogen to our knowledge. Ariyasu et al. [51] attributed the linewidth of 5 meV, observed for the Ni O stretch of Ni(1 0 0)p(2  2)-O [52], to both (1) emission of two substrate phonons and (2) excitation of the parallel adsorbate mode with the absorption of one substrate phonon, of comparable magnitudes. The width associated with photon emission seems entirely negligible [42]. The phase incoherence of the higher-energy vibrational mode by the anharmonic coupling (which does not exist for a perfect harmonic oscillator) with the thermally-excited lower-energy mode causes the phase relaxation [40]. For the C O stretch of CO in the 2-coordinated site of Ni(1 1 1)c(4  2)-CO, the energy width associated with the phase relaxation (anharmonic coupling p toffiffiffia hindered rotation) is estimated to be 2.1 meV [53,54]. In the pffiffiffi case of the C O stretch for Ru(0 0 1)( 3  3) R30  -CO, the energy width associated with the phase relaxation by the anharmonic coupling to the hindered translational CO mode (parallel to the surface) is estimated to be 0.3–1.4 meV [55]. Dephasing is strongly temperature dependent. The inhomogeneous broadening associated with the C O stretch peak is estimated to be less than 1 meV for incomplete monolayers of CO on Cu(1 0 0) [56]. It is noted that the inhomogeneous broadening of  2.8 meV has been reported for CO on Pt(1 1 1) [42,57,58]. Thus, from the studies cited above, if a single mechanism is predominant, neither the homogeneous broadening nor inhomogeneous broadening can account for the intrinsic broadening of more than  5 meV. Even if several mechanisms are involved, it is difficult to understand the intrinsic broadening of more than  10 meV. Therefore, we have to consider seriously the contribution from quantum delocalization if the intrinsic broadening is more than  5 meV. 2.2. Hydrogen on Ni surfaces 2.2.1. Hydrogen on Ni(1 0 0) For H (D) on Ni(1 0 0), the vibrational excitation was observed at 78 (55) meV, which was attributed to the perpendicular excitation of H (D) in the 4-coordinated site [59–61]. See Fig. 1 for the schematic of the vibrational mode. The perpendicular vibrational energy was measured at u ¼ 1. Little broadening of the loss peaks was observed, which indicates negligible contribution of the quantum delocalization of hydrogen. On the other hand, the theoretical calculations [6,7,62] discussed in Section 1.2.1 predicted the quantum delocalization of hydrogen on Ni(1 0 0). The starting point for the theoretical description of hydrogen on transition metal is a calculation of the full adiabatic potential energy surface for hydrogen outside the surface in question. Thus, the calculations of the hydrogen-surface interaction energies have to be made for all possible hydrogen positions. For the first calculations, the effective-medium theory [12] was used, which gives potential energy surfaces good enough for the qualitative explanations of the experimental results, but not very quantitative. Umrigar and Wilkins [63] calculated the adsorption site, adsorption energy, and the perpendicular vibrational energy of H on Ni(1 0 0) by the density-functional total energy calculations using the linear

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augmented plane wave (LAPW) method. The equilibrium H position was found to be the 4-coordinated site. The 2-coordinated site binding-energy minimum lies only 0.1 eV higher than the 4-coordinated site minimum, whereas the top-site minimum lies about 0.3 eV higher, which is consistent with a high hydrogen surface mobility (Table 2). It is noted that the diffusion constant for H on Ni(1 0 0) has been calculated by Mattsson et al. [64] using the path-centroid formula for the transition rate, the embedded atom method for the potential, and the numerical quantum Monte Carlo technique. Umrigar and Wilkins calculated the vibrational energy of the perpendicular mode to be 90 meV. Mattsson et al. [65,66] performed the first-principles density-functional calculations of hydrogen on Ni(1 0 0) (u ¼ 1), and calculated the total energies for some important configurations. Two different approximations for the exchange and correlation potential were used, i.e., the local-density approximation (LDA) and the generalized gradient approximation (GGA). A model potential was fitted to the firstprinciples data-points and the hydrogen band structure was derived by solving the Schro¨ dinger equation. The calculated vibrational excitation energies were 86 (62) and 68 (48) meV for the perpendicular and parallel modes, respectively, but the hydrogen bands were very narrow. Recently, Okuyama et al. [67] investigated the vibrational states of Ni(1 0 0)(1  1)-H by means of an advanced EELS. Fig. 11 shows a series of EELS spectra of Ni(1 0 0)(1  1)-H as a function of the normalized momentum transfer z along the G¯ X¯ direction of the surface Brillouin zone. z ¼ 1 corresponds to the X¯ point. The primary energy Ep is 20 eV, and the incidence angle ui ¼ 80 for the upper two spectra and ui ¼ 70 for the others. The elastic peak is shown for z ¼ 0. The two main features are due to H vibrations. In addition to the perpendicular mode at 79 meV, they detected a parallel mode at  84 meV near the G¯ point for the first time. This mode is a longitudinal mode, and is collective and exhibits a dispersion up to 105 meV at the X¯ point. It is noted that the results of first-principles density-functional calculations mentioned above are deviated from the experimental results in particular for the parallel mode. The parallel mode is characterized by an anomalously large width (  19 meV) in contrast to relatively small width observed for the perpendicular mode (  4 meV). As a possible mechanism, Okuyama et al. proposed the vibrational-damping via two-phonon emission where the parallel mode decays with the excitation of a substrate phonon and the perpendicular mode extending the work of Ariyasu et al. [51] on Ni(1 0 0)p(2  2)-O. It is noted that the effect of the quantum delocalization cannot be eliminated. Also, Okuyama et al. investigated the parallel mode at low coverage and determined the energy to be  99 meV. The parallel mode showed a large width similar to that at high coverage. Unfortunately, they could not quantify the linewidth due to the complexity of the spectra caused by the coexistence of two adsorbed states, i.e., isolated species and the (1  1)-H island species. To determine the contribution of quantum delocalization to the observed width, it is necessary to measure the peak width as a function of the coverage. 2.2.2. Hydrogen on Ni(1 1 0) The Ni(1 1 0)-H (D) system was studied by several groups [21,68–71]. For low coverages, two losses were observed at 71 and 131 meV which were attributed to vibrations of H, in the 3-coordinated site (formed by the two nearest-neighbor surface-layer Ni atoms and one second-layer Ni atom), ‘‘perpendicular’’ to the Ni rows [‘‘parallel’’ to the Ni(1 1 0) surface] and ‘‘perpendicular’’ to the Ni(1 1 0) surface, respectively (Fig. 1), in reasonable agreement with the calculations based on the effective medium theory [12]. In particular, the linewidth of the 130 meV peak was broad. But it was difficult to conclude that hydrogen is delocalized due to the limited energy resolution of the EELS spectrometer. No peaks were observed which were associated with H in the long-bridge sites discussed below.

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Fig. 11. A series of EELS spectra of Ni(1 0 0)(1  1)-H as a function of the normalized momentum transfer z along the G¯ X¯ direction of the surface Brillouin zone (shown in the inset). z ¼ 1 corresponds to the X¯ point. The primary energy Ep is 20 eV, and the incidence angle ui ¼ 80 for the upper two spectra and ui ¼ 70 for the others. The elastic peak is shown for z ¼ 0 (intensity: 105 cps). The two main features are due to H vibrations (reprinted with permission from [67]); 1 meV = 8.0657 cm1.

Puska and Nieminen [7] calculated the wave functions and quantum mechanical energy levels for hydrogen on the Ni(1 1 0) surface. The potential formed minimum valley over the 2-coordinated longbridge site and over the 3-coordinated site. Assigning the long-bridge site as the adsorption site, the relevant point-group symmetry is C2v which has only the one-dimensional representations A1, A2, B1 and B2. The hydrogen density corresponding to K = 0 (G¯ point) of the A1 representation in the ground state (A01 ) is shown in Fig. 12[7]. In Fig. 12, the Ni atoms are denoted by open circles. The contour spacing is a constant fraction of the maximum density. The hydrogen in the ground state is delocalized along the close-packed [1 1¯ 0] azimuth, whereas its wave function overlap parallel to the [1 0 0] azimuth essentially vanishes. The hydrogen density is the largest at the 2-coordinated long-bridge site, whereas it is repelled from the 4-coordinated site due to the second-layer Ni atom underneath. The 3-coordinated site is not favored by hydrogen, because localization at this site leads to an increase in the kinetic energy. It is noted that the lowest B1 state at K = 0 shows localization at the 3-coordinated site. The energy diagram for hydrogen on Ni(1 1 0) is shown in Fig. 13[7]. The lowest A01 band is narrow, because, in the ground state, hydrogen is localized in the 2-coordinated long-bridge site. The first excited-state A11 band has a 15 meV width. The second excited-state A21 band is much broader (45 meV) as hydrogen is very much delocalized along the Ni[1 1¯ 0] rows. Voigtla¨ nder et al. [21] obtained, by using an advanced EELS spectrometer [38], the phonon dispersion for the Ni(1 1 0)(2  1)-H surface (Fig. 8). They observed three losses at 79, 108 and 132 meV which are attributed to vibrations predominantly ‘‘perpendicular’’ to the Ni rows, parallel to the Ni rows and

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Fig. 12. The density of hydrogen on Ni(1 1 0) in the A1 representation which corresponds to the ground state (A01 ). The Ni atoms are denoted by open circles (reprinted with permission from Ref. [7]).

‘‘perpendicular’’ to the Ni(1 1 0) surface, respectively, as discussed in Section 1.2.3. The single-particle widths of the vibrationally excited levels (bands) were broader than the maximum dispersion shifts. The extraordinary broadening of the hydrogen vibrational losses was attributed to the delocalized nature of the adsorbed hydrogen [72].

Fig. 13. The energy diagram for hydrogen on Ni(1 1 0). The zero of energy is the ground state A01 energy at K ¼ 0 (reprinted with permission from Ref. [7]).

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At high coverages, the phonon dispersion may be superimposed on the single-particle broadening as discussed in Section 1.2.3. Brenig [24] applied the random phase approximation (RPA; Landau–Fermi liquid theory) to the case of Ni(1 1 0)(2  1)-H. As long as the vibrational ground state has negligible bandwidth, the single particle broadening and phonon dispersion turn out to be independent. Experimental dispersion curves for hydrogen on Ni(1 1 0) were fitted using a model with first-, second- and thirdnearest-neighbor forces. Due to the delocalization, the dependence of force constants on distance were found to be unusual, indicating strong indirect interactions and even noncentral forces (many-body forces). In the case of electrons in bulk metal, the Hamiltonian of the system can be divided into the collective part and individual part [73]. Thus, one can observe plasmon peaks and interband excitation peaks at different loss energies in an electron energy loss spectrum. Similarly, one may argue that, in the case of atomic vibrations on metal, the Hamiltonian of the vibrating system can be divided into the collective and individual parts. Thus, one might observe phonon peaks and peaks associated with the individual excitations (i.e., the vibrational excitations associated with isolated atoms whose peaks are broadened by the quantum delocalization) at different loss energies. However, in reality, we observe, as in the case of Ni(1 1 0)(2  1)-H, only broadening of the phonon peaks. This is understood as follows: the electron– plasmons are qualitatively similar to the H-phonons. However, there is a quantitative difference. The long-range Coulomb interaction for electrons produces very large matrix element ( / 1=jkj2 ; k: electron wave vector) and hence very large plasmon shifts away from the unperturbed interband transitions at least for small k. For the H phonons, the matrix element is comparable to the single-particle bandwidth of the excited band, and thus the phonon shift is of the order of the bandwidth. 2.2.3. Hydrogen on Ni(1 1 1) Christmann et al. [5] studied the adsorbed states of hydrogen in the temperature range of 150 to 500 K by the use of low-energy electron diffraction (LEED), thermal desorption spectroscopy and work function change measurements. In the ordered region where a (2  2)-2H structure is formed (u ¼ 0:5), it was found that the hydrogen atoms are arranged in an overlayer of graphitic structure with a (2  2) unit cell with respect to the substrate unit cell. Hydrogen adatoms were found to occupy both types of 3coordinated sites (fcc and hcp sites, Fig. 1) without a detectable difference in the Ni H bond lengths ˚ corresponding to an overlayer-substrate between the two sites. The Ni H bond length was 1.84 A ˚ . Christmann et al. studied the relation between this structure and its (continuous) orderspacing of 1.15 A disorder phase transition as a function of temperature and hydrogen coverage. The measured phase diagram is shown in Fig. 14[5]. The disordered phase was studied in detail, and a novel atomic bandstructure model was proposed for the first time which was thought to be consistent with a substantial amount of disorder and a large hydrogen mobility. It is noted, according to a detailed LEED intensity analysis of the (2  2)-2H structure, that hydrogen-induced reconstruction occurs and that hydrogencoordinated Ni atoms are pulled out of the surface [74]. Ho et al. [10] observed two losses at 88 and 139 meV. Both were nondipole excitations. On the basis of the calculations performed using the effective medium theory, Nordlander et al. [12] attributed these losses to the parallel and perpendicular modes, respectively, although substantial mixing was predicted due to the anharmonicity of the adiabatic potential. Mortensen et al. [75] studied D on Ni(1 1 1) by transmission channeling. The rms displacement of D ˚ for the (2  2)-2D and (1  1)-D phases, parallel to the surface was fairly large, 0.25 and 0.23 A respectively, which was considered to be consistent with the theoretical prediction that chemisorbed hydrogen is delocalized on Ni(1 1 1) [6,7].

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Fig. 14. Phase diagram of hydrogen on Ni(1 1 1) (reprinted with permission from [5]).

According to a recent experimental study, the quantum delocalization was not observed in the fundamental-mode excitation of hydrogen on Ni(1 1 1), which is at variance with the expectation of Christmann et al. [5]. Yanagita et al. [76] studied H on Ni(1 1 1) at 100 K. Losses were observed at 90 and 130 meV associated with the parallel and perpendicular modes, respectively, for u < 0:5. For u ¼ 1, two losses were observed at 115 and 140 meV. In the region where 0:5 < u < 1, vibrational spectra were the weighted superposition of those for u ¼ 0:5 and 1. Yanagita et al. proposed that, for low coverage, the (2  2)-2H islands are formed, the surface is fully covered with the (2  2)-2H structure at u ¼ 0:5, the (2  2)-2H and (1  1)-H structures coexist in the intermediate region where 0:5 < u < 1, and that the surface is covered with the (1  1)-H structure at u ¼ 1. The widths of the losses for u ¼ 0:05 are narrow and are comparable to that of the elastic peak. The EELS spectra for the low u region show no peak broadening. It was interpreted that this is closely connected with the formation of the (2  2)-2H islands, and that the attractive interaction makes H localized even for u ¼ 0:05. Yanagita et al. [76] measured the temperature dependence of the EELS spectra of H on Ni(1 1 1) for u ¼ 0:5 in the range of 100–320 K. A broadening of the 90 meV loss attributed to the parallel mode was observed with increasing temperature. The intrinsic width becomes  16 meV at the largest. This seems abnormally large if the origin is predominantly attributed to the inhomogeneous broadening caused by the existence of H in various local configurations as argued in Ref. [76]. A quantum effect may be involved, and more detailed study is required. Vibrational line shapes for a hydrogen atom on an embedded atom model of the Ni(1 1 1) surface were extracted from path integral Monte Carlo data [77]. The results indicate that the anharmonic effect is significant, particularly for the vibrational motion parallel to the surface. The calculated vibrational excitation energies for the parallel and perpendicular modes were 87 and 114 meV, respectively, in fair agreement with the experimental results. Recently, vibrational states of H on Ni(1 1 1) were investigated by means of an advanced EELS [78]. In addition to the perpendicular and parallel modes, the corresponding overtone structures were detected. The overtone of the parallel mode exhibits a doublet structure, which was interpreted to result from the delocalization of the excited vibrational states. The doublet was attributed to the ‘‘bonding’’ and ‘‘antibonding’’ H-atom orbitals, analogous to the linear combination of atomic orbitals (LCAO) for simple molecule.

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Fig. 15a and b shows the EELS spectra for (2  2)-2H and (2  2)-2D on Ni(1 1 1) [78]. The peaks at 91 (69) and 136 (99) meV were assigned to the parallel and perpendicular stretching vibrational modes of H (D) adsorbed in the 3-coordinated sites, respectively. Due to the high sensitivity of the advanced EELS spectrometer [39], Okuyama et al. could further resolve the fundamental modes. New peaks appear for H species at 96 and 131 meV in the higher- and lower-energy sides of the dominant losses (91 and 136 meV), respectively. The assignments were straightforward: there exist two kinds of adsorption sites for H in the (2  2)-2H phase, i.e., fcc and hcp sites. Although Okuyama et al. could not determine which loss pair was associated with the fcc or hcp sites, they tentatively denoted the dominant losses at 91 and 136 meVas parallel and perpendicular modes for H in fcc sites, respectively, while the less intense losses at 96 and 131 meVas parallel and perpendicular modes for H in hcp sites, respectively. For D species, the corresponding parallel modes appear at 69 and 72 meV, whereas the perpendicular modes were hardly resolved and only a single loss was observed at 99 meV. In addition to these fundamental losses, peaks were observed at 155 (125), 172 (134) and 270 (198) meV for H (D) species. The 270 (198) meV peak was readily attributed to the overtone of the perpendicular mode judging from the energy. The activation energy of surface diffusion has been investigated on Ni(1 1 1) and determined to be  150–200 meV at uH ¼ 0:3 (Table 2). The secondexcited state of the parallel mode lies in the range of 143–186 meV and is comparable with the potential barrier, giving rise, possibly, to the delocalized vibrational states. The delocalization of vibrational states

Fig. 15. EELS spectra for (a) (2  2)-2H and (b) (2  2)-2D phases on Ni(1 1 1). Ep ¼ 9:5 eV, ui ¼ 60 and emission angle ue ¼ 50 were used. The high-energy-loss regions are also shown for Ep ¼ 17:5 eV. The inset shows the emission-angle dependencies of several loss intensities for (2  2)-2H (reprinted with permission from [78]). 1 meV ¼ 8:0657 cm1.

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would result in the formation of the bonding and antibonding states with the doublet structure. Hence, the doublet observed for the overtone of the parallel mode is attributable to the transition of H from the localized ground state to the delocalized excited states. The vibrational properties of H in the (1  1)-H phase strongly support this proposal, where only a single peak is observed for the overtone of the parallel mode. In this case, the nearest-neighbor site exhibits a steep barrier due to the repulsive H–H interactions, which promotes the localization of the excited state. Recently, an ab initio analysis based on the density-functional theory was performed to clarify the nature of the vibration of hydrogen on Ni(1 1 1) [79]. The adiabatic potential energy surface for H of Ni(1 1 1)(2  2)-2H perpendicular and parallel to the surface, and the vibrational states were numerically calculated. The calculations are consistent with the above experimental results. 2.3. Hydrogen on Pd surfaces 2.3.1. Hydrogen on Pd(1 1 0) Early work for H on Pd(1 1 0) were reported by Jo et al. [80] and Ellis and Morin [81]. Two vibrational peaks were observed at  100 and 120 meV. Similar to the case of Ni(1 1 0) (Section 2.2.2), these peaks were attributed to vibrations of H, in the 3-coordinated site, ‘‘perpendicular’’ to the Pd-rows and ‘‘perpendicular’’ to the Pd(1 1 0) surface, respectively. Toma´ nek et al. [82] performed an ab initio density-functional calculation and found the vibrational energies of the adsorbate at 57 meV (longbridge), 100 meV (short-bridge), 189 meV (hollow) and 263 meV (on-top). Takagi et al. [83] studied hydrogen on the Pd(1 1 0) surface at 90 K. Fig. 16 shows EELS spectra in the specular mode for various hydrogen coverages (primary electron energy Ep ¼ 4 eV). Loss peaks were observed at 87–89, 96–100, and 121–122 meV. The 87–89 meV peak was observed in the region where uH is below 0.3. The 96–100 meV peak was observed at 100 meV for uH ¼ 0:04. The 100 meV peak monotonically shifts towards lower energy with increasing coverage, and was observed at 96 meV for uH ¼ 0:23. The 96 meV peak shifts towards higher energy for higher hydrogen coverages. For uH ¼ 0:63, the peak was observed at 100 meV. For uH ¼ 1, the loss peaks were observed at 100 and 122 meV. Angle-dependent measurements showed that all the observed loss peaks are decreased in intensity as the off-specular angle is increased, similarly to the elastic peak intensity, which indicated that all the observed loss peaks are excited mainly by the dipole mechanism (Section 2.1.2). EELS measurements for D on Pd(1 1 0) were also performed. Only two peaks were observed at 66 and 88 meV for uD below 0.34. For higher coverages, the loss at 66 meV shifts gradually towards higher energy and was observed at 74 meV for uD ¼ 0:8. These results were similar to those observed for H (D)/ Cu(1 1 0) [20], which will be discussed in Section 2.4.1. According to the calculations of H on Ni(1 1 0) by Puska and Nieminen [7], hydrogen is delocalized especially along the close-packed Ni[1 1¯ 0] rows, and the energy bandwidth of the ground state is a few meV, whereas those of the excited states of the order of several tens of meV (Section 2.2.2). By the use of EELS in the specular mode, the direct transitions (DK ¼ 0, where K is the wave vector parallel to the surface) at any K within the surface Brillouin zone are predominantly observable (Section 2.1.2). Thus, for hydrogen on Pd(1 1 0) at 90 K in which all states within the ground-state band are considered to be populated, the loss intensity measured in the specular mode is proportional to the density of states (DOS) of hydrogen in the excited-state energy bands on the basis of the assumptions that the energy band of the ground state is nearly flat and that the excitation cross section is independent of K. Moreover, as hydrogen on Pd(1 1 0) is a quasi-one-dimensional system (apparently) two peaks are expected to be observed,

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Fig. 16. EELS spectra in the specular mode for hydrogen on Pd(1 1 0) (Ep ¼ 4 eV) (reprinted with permission from [83]).

which are associated with the excitation from the ground state to an excited-state band, because the density of states are generally large near the band edges [4]. Also, similarly to Astaldi et al. [20], it was considered that the interactions between the adsorbed hydrogen lead to the decrease of the bandwidth with increasing coverage. Thus, the uH -dependent variation of the shape of the peaks observed in the 87–100 meV range was interpreted as follows: for high coverages, hydrogen atoms in both the ground and excited states are localized in the well-defined adsorption sites, i.e., the 3-coordinated sites, due to the hydrogen–hydrogen interaction, and a sharp loss peak is observed at 100 meV. With decreasing hydrogen coverage, the hydrogen–hydrogen interaction decreases, and the bandwidth increases. A broadened bandwidth of the excited state results in two loss peaks at 87–89 and 96–100 meV corresponding to the band edges for low coverages. The separation of the two peaks reaches 13 meV for uH ¼ 0:04. The model discussed in Section 1.2.2 was applied to hydrogen on Pd(1 1 0). Reasonable agreements between the calculations and experimental results were made when E ¼ 94, T ¼ 5, U ¼ 80, and V ¼ 1 meV were used. In this study, the effect of the indirect interactions was not considered. To evaluate the effect, the coverage dependence of the EELS spectra for both H and D should be investigated as described in Section 1.2.3. For the 66 meV peak of D on Pd(1 1 0), Takagi et al. did not observe two peaks which are associated with the band edges of the excited-state band. This was understood as follows: as the mass of D is twice that of H, the bands are shifted towards lower energies for D on Pd(1 1 0), and thus the bandwidth for D is smaller than that for H. The bandwidth in the tight-binding approximation is determined by the quantum

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hopping energy, which is related to the tunnelling current between nearest-neighbor sites. It can be shown that, similarly to the tunnelling current across a one-dimensional rectangular barrier, the bandwidth is pffiffiffiffi proportional to exp ða mÞ (m is the particle mass). All the observed loss peaks were excited mainly by the dipole mechanism. Thus, considering the surface-normal dipole selection rule (Section 2.1.2), the losses correspond to the excitations from the ground-state band A01 to the excited-state A1 bands. According to the calculation of Puska and Nieminen [7] for H on Ni(1 1 0), the excited-state A1 bands are in the ranges between 15 and 30 meV (A11 band), 45 and 90 meV (A21 ), and 75 and 140 meV (A31 ) as shown in Fig. 13. It is considered that the losses in the 87–100 meV range correspond to the A01 ! A21 band excitations and the 120–121 meV peak to the A01 ! A31 band excitation. The A01 ! A11 band excitation may be hidden in the tail of elastic peak. 2.3.2. Hydrogen on Pd(1 1 1) Conrad et al. [84,85] observed the parallel and perpendicular modes at 96 and 124 meV at high H coverages, respectively. Rick et al. [86,87] calculated the ground and excited vibrational states for the three hydrogen isotopes on Pd(1 1 1) by the use of the embedded atom method potential. Notable features of these states are the high degree of anharmonicity, which is most prominently seen in the weak isotopic dependence of the parallel vibration transition and the narrow bandwidths of these states ( < 2:2 meV for the A11 state). Rick et al. predicted the parallel and perpendicular modes at 120 and 110 meV, respectively. It is noted that the ordering of the parallel and perpendicular modes was opposite to the experimental work of Conrad et al. Løvvik and Olsen [88] calculated them to be 85–88 and 131 meV, respectively, in reasonable agreement with the experimental results by the use of periodic density-functional calculations within the GGA. 2.4. Hydrogen on Cu surfaces 2.4.1. Hydrogen on Cu(1 1 0) One of the early theoretical work for H on Cu(1 1 0) was done (using the effective medium theory) by Jacobsen and Nørskov [13], who predicted that hydrogen would be delocalized on the surface. Early experimental work was reported by Hayden et al. [89]. They observed EELS peaks at 63 and 77 meV in the coverage range of u ¼ 0:151. Astaldi et al. [20] studied the vibrational spectra of hydrogen on the Cu(1 1 0) surface. Hydrogen was dissociatively adsorbed by vibrationally exciting hydrogen molecules with a W filament (1550 K) placed in front of the sample surface. For uH ¼ 0:33, the 79 and 118 meV peaks were observed which were attributed to the vibrations of H, in the 3-coordinated site, ‘‘perpendicular’’ to the Cu-rows and ‘‘perpendicular’’ to the Cu(1 1 0) surface, respectively. With decreasing coverage, the 79 meV peak broadened, while a shoulder developed on the low-energy side, and finally it split into two components of comparable intensity, whose separation reached 28 meV at uH ¼ 0:01. The 118 meV peak also broadened, but could not be resolved for coverages lower than uH ¼ 0:05. Astaldi et al. proposed that the EELS spectra at very low coverages strongly support the hydrogen quantum delocalization. They considered that the localization is observed with increasing hydrogen coverage due to the repulsive interactions between the adsorbed hydrogen, and proposed the theoretical model in Section 1.2.2, which qualitatively describes the coverage dependence of the spectra. However, Modesti [27,28] questioned the conclusions by Astaldi et al. [20] on hydrogen on Cu(1 1 0) because the line shape of the hydrogen vibrational peak at low coverage was appreciably affected by very

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small contamination from the residual gases, mainly perhaps, water. Modesti has some evidence that water molecules, with coverage below the detection limit of Auger electron spectroscopy, are adsorbed near the hydrogen atoms, which causes broadening and splitting of the hydrogen peak. Recently, Bae et al. [90] investigated the energetics of the H on Cu(1 1 0) at u ¼ 0:125 by the firstprinciples density-functional calculations. Very unexpectedly, they found that the potential energy surface is very different from previous models. The potential energy surface is marked by a relatively flat region between adjacent 3-coordinated sites along the [0 0 1] direction (which is directed perpendicular to the Cu rows) and a relatively large potential energy maximum at the hollow site. If true, such a potential energy surface geometry suggests that the picture of the dynamics in this system as being essentially quasi-onedimensional in nature is incorrect. The calculated vibrational energies for H in 3-coordinated site were 56 meV (‘‘perpendicular’’ to the Cu surface), 128 meV (parallel to the Cu-rows) and 134 meV (‘‘perpendicular’’ to the Cu-rows). They found that the vibrational energy of the ‘‘perpendicular’’ stretch mode at the 3-coordinated site to be lower than that of the ‘‘parallel’’ mode opposite to the assignments of Astaldi et al. [20]. The theoretical calculations have to be confirmed by other groups. Mijiritskii et al. [91] performed a low-energy ion scattering study of the Cu(1 1 0)(1  2)-H surface (u ¼ 0:5) with the H-induced 1  2 reconstruction of Cu(1 1 0). The H-atoms were found to be situated in the 3-coordinated sites of the missing-row reconstructed surface. Large thermal vibration amplitudes ˚ ) of the H-atoms had to be assumed to obtain good fits to the experimental data. These large (0.34–0.43 A amplitudes were attributed to a nonharmonic potential giving rise to the quantum delocalization. 2.4.2. Hydrogen on Cu(1 1 1) Early study on H on Cu(1 1 1) was performed by McCash et al. [92] using a single-stage EELS spectrometer, however, the energy resolution was not good. Lamont et al. [50] studied the dynamics of H and D adsorbed in the 3-coordinated hollow sites on Cu(1 1 1) by infrared reflection-absorption spectroscopy (IRAS). The strongest feature in the infrared spectra of the Cu(1 1 1)(3  3)-H surface was the dipole-forbidden parallel vibrational mode at 96 meV which gives rise to an anti-absorption peak with an intensity about 10 times higher than that of the dipole-allowed perpendicular mode at 129 meV. A theoretical analysis shows that the parallel mode has an electron–hole pair damping corresponding to a lifetime (linewidth) of about 1 ps (0.7 meV). The observed vibrational linewidth for H (8 meV) is about 10 times larger than indicated by this energy relaxation time, and is suggested to be caused by lateral tunnelling of the protons and dephasing processes. Lee and Plummer [93] studied hydrogen on Cu(1 1 1) at 100 K by using an advanced EELS [39]. At a very low H coverage (u  0:1), two losses were observed at 92 and 124 meV, which are attributed to the parallel and perpendicular modes of H at a 3-coordinated site on Cu(1 1 1), respectively. These results are in reasonable agreement with the calculations reported by Gundersen et al. (ab initio pseudo-potential and effective medium calculations) [94] and Stro¨ mquist et al. (DFT and GGA) [95]. The intrinsic linewidths were 12 and 11 meV, respectively. The low-coverage widths were greater than the highcoverage ones. However, the delocalization of the excited vibrational state was not clearly supported. 2.5. Hydrogen on Rh surfaces 2.5.1. Hydrogen on Rh(1 0 0) The vibrational properties of H (D) in the 4-coordinated site of Rh(1 0 0) were studied by Richter et al. [96]. At u ¼ 1, the parallel and perpendicular modes were found at 65.5 (47) and 82.0 (59.2) meV,

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respectively. In addition, several overtones were observed. Hamann and Feibelman [97] calculated the potential for H-atoms in the vicinity of the 4-coordinated site of Rh(1 0 0) at u ¼ 1 using the localdensity-functional theory and LAPW method. The potential was found to contain important anharmonic components, one that couples parallel and perpendicular motion, and another producing azimuthal anisotropy. The parallel and perpendicular H vibrational excitations were found to have energies of 67 and 92 meV, respectively, in good agreement with the experimental results of Richter et al. 2.5.2. Hydrogen on Rh(1 1 1) Mate and Somorjai [8] studied the adsorbed states of hydrogen on the Rh(1 1 1) surface by the use of EELS. They used a single-pass EELS spectrometer with the energy resolution of 8 meV. At u ¼ 0:4, a broad loss peak was observed at 56 and 53 meV for H and D, respectively. They considered that the small isotope effect (  1.05) of the peak, the observation of broad energy-loss peaks, and reasonable agreement of the loss energies with the theoretical calculations for hydrogen on Ni(1 1 1) [6,7] provide strong support for the delocalized quantum nature of hydrogen. The small isotope effect was interpreted to result from the high degree of anharmonicity of the interaction potential associated with the quantum motion parallel to the surface. Yanagita et al. [98] measured EELS spectra, by using a home-made double-pass EELS spectrometer, of H (D) on Rh(1 1 1) at 90 K in detail. Losses were observed at 79–90 (60–67) and 135 (98) meV for u ¼ 01, which were attributed to the parallel and perpendicular modes of H (D) in the 3-coordinated sites, respectively. The 79–90 (60–67) meV loss was anomalously broad and the intrinsic width was 15– 24 (10–14) meV. The broadening was observed throughout the whole coverage range studied. Yanagita et al. interpreted the results by the localized model, although contribution of the inhomogeneous broadening, etc. (Section 2.1.3), could not be well estimated. Yanagita et al. could not exclude the possibility that the quantum delocalization contributes to the loss peak width at a low coverage where the adsorbed H–H interaction is small. It is noted that no loss was observed at around 56 meV, though the rest of the losses reported by Mate and Somorjai [8] were observed. Yanagita et al. observed occasionally the 48 meV loss, which was assigned to the hindered translation normal to the surface of water from the background. The origin of the 56 meV loss could be the same as that of the 48 meV loss. 2.6. Hydrogen on Pt surfaces 2.6.1. Hydrogen on Pt(1 1 1) For H on Pt(1 1 1) (u ¼ 1), Baro´ et al. [99] observed two peaks at 68 and 152 meV by EELS which were assigned to the perpendicular and parallel modes of H in the 3-coordinated site, respectively. Richter and Ho [100] observed three peaks at 67, 112 and 153 meV, which were assigned to the parallel mode, perpendicular mode, and unresolved overtone of the of the parallel mode and combination band of the parallel and perpendicular modes, respectively. It is noted that the parallel mode was softer than predicted by the near-neighbor central force-constant (NNCFC) model. Although broadening of the peaks were observed (Table 1), Richter and Ho interpreted their data by the localized model. In addition, for u  0:2, Richter and Ho found that the 67 meV peak shifted by about 10 meV and broadened. On the other hand, Reutt et al. [101] found only one peak at 156 meV by IRAS. An early theoretical work of H on Pt(1 1 1) was reported by Feibelman and Hamann [102,103]. They performed LAPW calculations and predicted the perpendicular vibrational energy of 166 meV and the parallel vibrational energy of 114 meV.

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By performing extensive calculations on H interacting with Pt(1 1 1), Olsen et al. [104] predicted, using a DFT/GGA approach which includes scalar relativistic and spin–orbit effects, that the perpendicular mode of H in 3-coordinated site be observed at 148–149 meV. Recently, a static potential energy surface for hydrogen on Pt(1 1 1) (u ¼ 0:25) was calculated by Ka¨ lle´ n and Wahnstro¨ m [105] using first-principles DFT calculations with the exchangecorrelation treated at the GGA level. The Scro¨ dinger equation was solved for the hydrogen atoms in this potential. They found agreement with experiment for the stable site, binding distance and adsorption energy. The hydrogen vibrational motion was found to be strongly anharmonic with several modes close in energy. They claimed that their calculations gave a consistent account for both EELS and IRAS data. The measured peak at 67 meV was attributed to two unresolved excitations at 44 meV (A01 ! E1 ) and 65 meV (A01 ! A11 ), which would give a broad peak around ð44 þ 65Þ=2 ¼ 55 meV in agreement with the measured result for this coverage [100]. According to the calculations, this combined peak should have a small dipole moment, which was not observed by Richter and Ho [100], but indicated in the measurements by Baro´ et al. [99]. The second peak at 112 meV was attributed to two unresolved peaks, computed at 111 meV (A01 ! A21 ) and 113 meV (A01 ! E2 ). This was interpreted as a perpendicular mode in Ref. [100] and for low coverages also detected by Baro´ et al. [99]. The third measured peak at 153 meV agreed well with the computed value at 141 meV (A01 ! A31 ). Based on the calculated matrix elements, this was the most intense dipole-active excitation in agreement with the results of Reutt et al. [101]. It is noted that several excited states have been found theoretically in this energy range. The corresponding calculated values for D were 44, 74 and 96 meV in reasonable agreement with the measured results (Table 1). The prefactor (1:1  103 cm2 s1) and activation energy (68 meV) for microscopic diffusion of extremely mobile hydrogen measured by quasielastic helium atom scattering (Table 2) [106] were described by the transition state theory with the vibrational degrees of freedom treated as quantum oscillators. On the other hand, Ba˘ descu et al. [107] presented a combination of experiments and theoretical calculations on the energetics and vibrational properties of H (D) on Pt(1 1 1). The experimental data taken using an advanced EELS spectrometer for the loss peaks at low coverages (u  0:75) differ significantly from previous studies at u ¼ 1. For u  0:75, the EELS peaks were observed at 31 and 68 meV. At u ¼ 1, the 31 meV peak disappeared from the observation and two additional peaks appeared at 110 and 153 meV, which agree nicely with the earlier results of Richter and Ho [100]. The firstprinciples calculations at u ¼ 0:25 for 3D adiabatic potential energy surface were done self-consistently by the use of the DFT with GGA. The results are close to those of Ka¨ lle´ n and Wahnstro¨ m [105]. However, there are quantitative differences particularly concerning the curvature and anharmonicity of the fcc sites, which leads to substantial differences in the vibrational-band excitations. The vibrational modes of the H and D adatoms were calculated for the single-particle Hamiltonian with the first-principles 3D adiabatic potential energy surface obtained. The first excitation was calculated to occur at 29.1 meV. This mode had mixed in-plane and vertical character with sizable dipole element in the normal direction. This is in agreement with the mode experimentally observed at 31 meV. The next excitations occur at 42 and 60 meV, both of which have mainly an in-plane character, and the observed peak at 68 meV could be a composite of these unresolved transitions. These results demonstrate the need to go beyond local harmonic-oscillator picture to understand the dynamics of hydrogen on Pt(1 1 1). A more detailed coverage-dependent study of hydrogen on Pt(1 1 1) by the use of an advanced EELS technique is greatly expected.

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2.7. Hydrogen on W surfaces Lou et al. [108] calculated the three-dimensional adiabatic potential energy surfaces for a single hydrogen atom chemisorbed on unreconstructed W(1 0 0) [and Mo(1 0 0)] using effective medium theory. The Schro¨ dinger equation for hydrogen and deuterium motion on the surface was solved numerically. The equilibrium geometry as well as the wave functions of the vibrationally excited states were obtained. It was shown, due to the large anharmonicity of surface potential, that the parallel and perpendicular motion of the adsorbate mixes. For W(1 0 0) saturated with H, a number of experiments have established that the surface is unreconstructed and H is located in the bridge site (Fig. 1) with u ¼ 2[109–115]. Three EELS peaks are observed at 80 meV (wagging), 130 meV (symmetric stretch) and 160 meV (asymmetric stretch). In addition, IRAS has shown a peak, with a characteristic Fano line shape [116], at 158 meV which is ascribed to the overtone of the wagging mode coupled with the electron–hole pair excitation due to the strong breakdown of adiabaticity [117–123]. Also IRAS has shown clearly that the 130 meV peak is exceptionally broad with its intrinsic linewidth of 11 meV [117,118,120]. Similar results have been obtained on Mo(1 0 0) [101,124]. This broadening may be associated with the quantum delocalization. If this is indeed correct, the analysis of the line shape of the 158 meV peak may have to be modified. The quantum delocalization has been experimentally supported on W(1 1 0) at 110 K [125]. At very low coverage, the H modes were extremely broad ( > 15 meV). With increasing coverage, the linewidth decreases and reaches a relative minimum at the coverage belonging to the maximum intensities of the extra spots of the p(2  1)-H phase (u ¼ 0:5). For the (2  2)-3H phase (u ¼ 0:75), the linewidth is constant over a wide exposure range and the modes above 124 meV are narrower than the corresponding p(2  1)-H mode. For both phases, the modes below 124 meV are broader than the modes above and the deuterium modes are narrower than the hydrogen modes. The modes above 124 meV were assigned mainly to be perpendicularly polarized. It is noted that hydrogen is adsorbed in the 3-coordinated site of unreconstructed W(1 1 0) [126]. Grizzi et al. [127] studied hydrogen on W(211) by time-of-flight scattering and recoiling spectroscopy ˚ above the first-layer W using Ne+ and Ar+ ions. The hydrogen position was determined to be 0.58 A ¯ ¯ plane and confined within a band that was centered above the [1 1 1] troughs. The results are interpreted to indicate that hydrogen in the excited states are delocalized by using the effective-medium-theory calculations. 2.8. Hydrogen on other transition-metal surfaces Hagedorn et al. [128] studied hydrogen on Ir(1 1 1) at 90 K by EELS. Absence of a significant isotopic energy shift for the parallel mode was found in the vibrational spectra for low coverages of H and D, and was interpreted to be indicative of the quantum delocalized motion of hydrogen. They proposed that the vibrational coupling between this delocalized motion and Ir phonon modes was suggested by the broad linewidths of these low energy loss features. As the surface coverage was increased, the hydrogen atoms were localized in the on-top sites. The quantum delocalization has not been experimentally supported on Ag(1 1 0) [129], Ru(0 0 0 1) [130,131] and Ru(1121) [132]. But it has to be pointed out that, by looking at the data reported, it appears that broadening, if not very much, is observed. Sprunger and Plummer [129] observed the 59–64 meV peak associated with the vibration of H ‘‘perpendicular’’ to the Ag rows [and ‘‘parallel’’ to the Ag(1 1 0)

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surface] at 100 K. The intrinsic peak width at low coverage was  10 meV, which increased to  26 meV at u  1. The increase made these authors to conclude that the delocalization does not occur on Ag(1 1 0). Nevertheless, this has to be reexamined because the peak width is abnormally broad ( > 10 meV) independent of the coverages. The metal dependence has to be studied further to find whether the quantum delocalization is observed on certain metals, but not on other metals. 2.9. Quantum delocalization of hydrogen in the ground state The experimental and theoretical studies of quantum delocalization of hydrogen in the ground state are briefly reviewed. The surfaces discussed are Ni(1 0 0), Ni(1 1 1), Pd(1 1 1), Cu(1 0 0) and Pt(1 1 1). 2.9.1. Hydrogen on Ni(1 0 0) There is a question whether H in the ground state is delocalized or not. Stensgaard and Jakobsen [133] studied the adsorption-site location of deuterium on Ni(1 0 0) by transmission channeling of 3 Heþ ions. ˚ above the first It was concluded that the D-atoms are adsorbed in 4-coordinated hollow sites at 0.5 A ˚ layer, and obtained a value of the rms displacement (  0.21 A) parallel to the surface in qualitative agreement with the delocalized model. On the other hand, Zhu et al. [134] estimated, from the surface diffusion study of hydrogen by linearly diffracting a probe laser beam from a monolayer grating of adsorbed hydrogen, the bandwidth of the ground state for H on Ni(1 0 0) to be  8  104 meV, which indicates that hydrogen is essentially localized. 2.9.2. Hydrogen on Ni(1 1 1) Mortensen et al. [135] determined the adsorption position of D on Ni(1 1 1) by transmission channeling at 140 K. They found that, for the (2  2)-2D surface, the two-dimensional D displacement ˚ ), which was interpreted to indicate that chemisorbed parallel to the surface is fairly large (  0.25 A hydrogen is delocalized. The diffusion coefficient of H on Ni(1 1 1) (u ¼ 0:3) in the ground state by the quantum-mechanical tunnelling is experimentally found to be less than 1011 cm2/s in the temperature range from 65 to 110 K [136]. The diffusion coefficient D is related to the hopping process of each hydrogen by D  l2 =t, where l is the hopping distance and t the residence time (Einstein–Smoluchowski relation). Thus, the residence time of hydrogen in a certain adsorption site is estimated to be more than 105 s, which is much longer than the ‘‘classical’’ interaction time of electrons with hydrogen on the surface (1016  1014 s) [137,138]. This raises the question that, for the incoming electrons, hydrogen is located in a certain site during the interaction time. Therefore, it requires additional investigations if delocalization of hydrogen in the ground state can be determined by the experimental techniques which utilize electrons, e.g., LEED and EELS. Note that the residence time for hydrogen on Pd(1 1 0) in the excited state is very roughly estimated to be 1013 s, which is comparable with the interaction time of electrons, from the quantum hopping energy (T  5 meV) discussed in Section 2.3.1. A similar argument can be made for He scattering where the interaction time is less than 1013 s [139,140]. 2.9.3. Hydrogen on Pd(1 1 1) Hsu et al. [139,140] claimed that hydrogen on Pd(1 1 1) is delocalized by using the He diffraction measurements. They found the hydrogen phase at u  0:5 with six-fold symmetry and the anomalous

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attenuation of the specular peak in the temperature range of 140–270 K. It is noted that, for the (1  1)-H surface (u ¼ 1), the C3v symmetry was observed and the specular intensity was large. A close examination of these results led them to consider that the scattered He atoms had to sample the occupation of neighboring 3-coordinated sites by the same H-atom; the results were explained in terms of hydrogen being quantum mechanically delocalized over two adjacent 3-coordinated fcc and hcp sites on the time scale of the He scattering event ( < 1013 s). The intensity analysis was made within the framework of the sudden approximation, instead of the eikonal approximation which is incapable of incorporating a quantum motion of H. Examining the data in the coverage range u ¼ 01 and the temperature range 140–350 K, they concluded that the H system is a correlated quantum liquid where particle delocalization occurs at medium and low whereas, at high coverages, strong repulsive pffiffiffi coverages, pffiffiffi H–H correlations at short distances lead to ( 3  3)-H or (1  1)-H phases. Hsu et al. [140] interpreted that the localization–delocalization phenomenon was seen in the UPS spectra of H on Pd(1 1 1) measured by Eberhardt et al. [141,142]. The H-induced UPS peaks observed at full coverage and low temperatures disappeared completely and irreversibly upon warming the sample to 270 K where thermal desorption and work function change measurements indicated u  0:5. This effect coincides with that observed by Hsu et al. The UPS results were ascribed to H delocalization which leads to sampling of different bonding configurations on the metal surface and consequently to the smearing out of discernible peaks. 2.9.4. Hydrogen on Cu(1 0 0) Recently, single hydrogen atoms on Cu(1 0 0) were imaged by STM, and the perpendicular vibrations of individual H- and D-atoms located in the 4-coordinated sites were excited and detected by STMinelastic electron tunnelling spectroscopy (STM-IETS) [143–145]. Variable temperature measurements of H-atom diffusion showed a transition from thermally activated diffusion, in which H-atoms readily acquire enough energies to surmount the classical barrier to diffusion, to quantum tunnelling at 60 K. The diffusion from 9 to 60 K was described as incoherent tunnelling in the presence of lattice and electronic excitations by Lauhon and Ho [144]; the H-atom is assumed to be delocalized at zero temperature. At finite temperatures (9–25 K), electron and phonon scattering lead to decoherence of the H-atom wave function and particle localization. Successive hops become uncorrelated when the phase-correlation damping rate becomes comparable to the tunnelling rate between potential minima [146,147]. The Hatom then hops between the adjacent lattice sites at a reduced rate. (An additional reduction in the tunnelling rate arises from the static distortion of the lattice in response to hydrogen adsorption; the distortion takes the ground states of neighboring potential minima out of resonance.) As the temperature increases (25–60 K), lattice vibrations assist the H in overcoming the barrier induced by the static lattice distortion as the ground state levels of the occupied and nearest-neighbor unoccupied sites are brought into resonance by the lattice fluctuations (phonon assisted tunnelling). It is noted that, as an H-atom moves, it is accompanied by a co-moving cloud of phonons, and the resultant quasi-particle is called a polaron. 2.9.5. Hydrogen on Pt(1 1 1) Di et al. [148] made a high-resolution angle-resolved UPS study of H on Pt(1 1 1) at room temperature. Essentially all clean surface bands were quenched upon hydrogen exposure similarly (but with some difference) to the case of Pd(1 1 1). Thus, the correlated quantum-liquid model was suggested to be a possibility.

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Recently, the quantum mechanical behaviors of an H-atom on Pt(1 1 1) [and on Cu(1 1 1)] were calculated [149,150]. The potential energy curves for the H adsorption were calculated within the density-functional theory, and the model potential energy surface was constructed based on the potential energy curves. The wave function for an H-atom on the potential energy surface was thus calculated: in the case of Pt(1 1 1), the wave function extends from the fcc hollow site to the bridge site and to the hcp hollow site, i.e., the wave function is delocalized on the surface. [In the case of Cu(1 1 1), the wave function is localized around the fcc hollow site.] An attempt has recently been made to study the potential energy surface of hydrogen in the ground state by the resonance nuclear reaction of 1 H( 15 N, ag) 12 C. The resonance spectrum [the g-ray yield (which is proportional to the amount of hydrogen) versus incident 15 N2þ ion energy] is broadened by the Doppler effect reflecting the zero-point motion of hydrogen [151]. Fukutani et al. [152] obtained the zero-point energies for H on Pt(1 1 1) at 80.0 and 62.1 meV, and attributed them to the perpendicular and parallel modes, respectively. The 80.8 meVenergy was associated with the 153–155 meV peak observed by EELS [99,100] and IRAS [101], and the perpendicular mode is considered to be harmonic. The 62.1 meV peak is, surprisingly, associated with the 68 meV peak observed by EELS [99,100], but not with the 112 meV peak [100]. Fukutani et al. concluded that the parallel mode is strongly anharmonic, with the deviation from the harmonic potential even in the vibrational ground state. It is noted that their assignment was based on comparison with the He atom scattering study which indicates that the lateral diffusion barrier is 68 meV [106]. To summarize, the studies made up to now on the quantum delocalization of hydrogen in the ground state were briefly reviewed. At the present stage, it is concluded that hydrogen in the ground state is not much delocalized, and that more detailed work are needed. Experimental studies by various techniques are needed, especially for systems in which the delocalization has been suggested. A particularly interesting perspective is in the progress of STM-IETS whose capability has been demonstrated for hydrogen on Cu(1 0 0) [144].

3. Prospective for the future 3.1. Theoretical prospectives Development of the recent surface electronic-structure calculations is very rapid, and it has now become feasible to obtain high accuracy for a variety of systems including hydrogen interacting with metal surfaces. This has opened the possibility of calculations from first-principles properties of the potential energy surface. The total energies of hydrogen for some important configurations on a transition-metal surface can be calculated by the DFT. The LDA or GGA can be used for the exchange and correlation potential. A model potential can be fitted to the first-principles data-points thus calculated. However, even within the LDA to the DFT, calculations of the potential energy surface is time consuming and difficult without further approximations. Nevertheless, advances in the computer technology (shorter computational time, bigger memory capacity, parallel processing, etc.) and development of a new theoretical formalism which drastically shortens the computational time are expected to give better potential energy surfaces in the near future. In the calculations, a rigid surface has been assumed, and lowering of the potential energy of hydrogen due to the relaxation of the substrate atoms around it, i.e., coupling of hydrogen to the substrate-atom

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displacements (surface polaron effect), are not considered. However, the picture of hydrogen as a quantum-mechanical surface polaron would be more adequate [7,87,144,153]. Furthermore, excitation of the electronic states which may be induced by coupling to the hydrogen vibration has been neglected (adiabatic approximation). However, on the metal surface, electronic excitations with very low energy can always be expected as electronic states are occupied by electrons up to the Fermi level, and thus, the adiabatic approximation does not necessarily hold. These problems are expected to give topics full of variety, and would be of special interest to the theorists. In order to interpret experiments at higher coverages the effects of H–H interactions have to be considered in more detail. So far the effects of short ranged and long-ranged interactions have been treated only separately and the long-range interactions only approximately (in Hartree– Fock or random phase approximation). It would be highly desirable to consider the combined effect of long and short range interactions on the excitation spectrum as a function of coverage. Two separate calculations would be required assuming the hydrogen (or deuterium) atoms to be bosons or fermions. 3.2. Reliability of the experimental results For comparison with theoretical calculations, reliability of the experimental results is of great importance. The experiments have to be performed avoiding the effects of the surface contaminants such as CO and water from the background, hydrogen inlet system, etc. Effects of the surface contamination can be avoided or minimized even at the present stage, considering the current level of the ultrahigh vacuum technology (vacuum: 1010  1011 Torr), by the through bakeout of the vacuum chamber and the vacuum pumping system, careful examination of the quality of the vacuum by the mass spectrometer, etc. In addition, it is noted that a remarkable progress has been made in the extreme-high vacuum technology (1012 Torr) [154]. Thus, further confirmation of the data obtained in the early work by utilizing the advanced technology is quite meaningful and of great importance. 3.3. Further study on various transition-metal surfaces Experiments associated with quantum delocalization have been made for the single crystal surfaces of Ni, Pd, Cu, Rh, Pt, W, etc., as discussed in this review. But there are still many other transition metals and their alloys [155] which have to be studied. It is noted that quantum delocalization of hydrogen on semiconductor surfaces has not been reported yet. For the interpretation of the unusual first-order desorption kinetics of molecular hydrogen from the monohydride phase of Si(1 0 0), an irreversible excitation of a hydrogen adatom into a delocalized two-dimensional band state on the surface with an activation energy of 2 eV was assumed [156]. However there are more plausible interpretations using the ‘‘pre-pairing’’ assumption (see [157] and references therein). In addition, the crystal-face specificity has to be studied in detail. For example, the first calculations for the Ni(1 1 1), Ni(1 1 0) and Ni(1 0 0) surfaces indicate that the bandwidth for Ni(1 1 1) is larger than that for Ni(1 1 0), and is much larger than that for Ni(1 0 0) [6,7]. It has been predicted that this is not because the potential energy barriers are lower on the Ni(1 1 1) surface but because the distance between the potential minima of the Ni(1 1 1) surface is smaller, which increases the overlap between the hydrogen wave functions centered at each minimum.

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3.4. Experimental techniques For comparison with theoretical calculations and simplicity of the interpretation, the experiments have necessarily to be carried out in the low hydrogen-coverage region where the hydrogen– hydrogen interaction can be neglected. However, for the experimentalists, this gives a serious problem because the signal intensity is low and the noise level high. Up to now, mainly the conventionaltype single- or double-pass EELS spectrometer has mostly been used. Application of advanced EELS spectrometers described in Section 2.1.1 with higher output current intensity would be desirable. The EELS technique has matured to a level where further rapid improvements are difficult to be made. Nevertheless, one may consider, for example, addition of the multichannel detection to the advanced EELS spectrometer in which the electron optics is optimized and the space charge effect is taken into account [158–160]. The parallel processing of the signal with a multichannel detector located at the exit focal plane of the analyzer increases the signal intensity accumulated per measurement time. One may also consider the application of the concept of the dispersion compensation which gives a different possibility for increasing the signal intensity [161–164]. In the simple spectrometer which consists of two 90  spherical sectors, the exit and entrance slits of the monochromator and analyzer are removed, respectively. Electrons passing through the monochromator are dispersed at the exit focal plane depending on their energy relative to the mean pass energy of the monochromator. By following the time reversal trajectory, these spatially dispersed electrons can be focused again at the exit plane of the analyzer, which is placed symmetrically with respect to the monochromator. Thus, the parallel processing of electrons fed into the monochromator with a broad range of energies can, in principle, be achieved. Another possibility would be a time-of-flight (TOF) method with pseudo-random binary sequence (PRBS) modulation of the electron beam [165–168]. Application of an ‘‘interleaved comb’’ chopper is proposed for a fast electron-beam chopping device to provide a nanosecond timebase for TOF measurements [168]. LeGore et al. [167] analyzed the advantage of maximum likelihood methods for PRBS modulated TOF electron spectrometry. Their results indicate that meV resolution can be achieved with a dramatic performance advantage (throughput advantage of 500–1000) over conventional, serial detection analyzers with long data acquisition times. It is noted that the measurements should preferably be carried out at a low temperature, if possible, at the liquid He temperature, in order to minimize the thermal effects, e.g., localization of the delocalized hydrogen by its interaction with the surface phonons. Kadono et al. [169] have found that a light interstitial atom such as muonium (effectively a light isotope of atomic hydrogen whose proton is substituted by a positive muon having 1/9 of the proton mass) is in a Bloch state in an ordinary crystalline host of potassium chloride (KCl) at very low temperatures ( < 10 mK). In general, an atom placed in a crystalline solid strongly interacts with its host atoms to form the so-called ‘‘polaron state’’, i.e., a complex state associated with the deformation of the lattice and also with the perturbation of the conduction electrons in metals. However, such a polaron state can have a finite tunnelling matrix element to the nearest-neighbor sites. The study of Kadono et al. demonstrates that one can potentially study the energy band structure of the ‘‘polaron band’’ for a hydrogen isotope in any crystalline solid where one finds stable muonium upon muon implantation. An extension of this kind of study to surfaces may open up a path to the experimental study of a completely novel type of atomic state on crystalline surfaces.

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3.5. Further interesting studies The existence of subsurface hydrogen is well recognized on some transition metal surfaces [141,142,170–173]. It would be interesting to examine the relationship and interaction between the delocalized hydrogen, subsurface hydrogen and bulk hydrogen [174,175]. The existence of nonthermalized (‘‘hot’’) hydrogen atoms which move rapidly on the surface is known to be essential in some surface reactions involving hydrogen atoms and molecules [176,177]. The delocalized hydrogen can be considered to be an ‘‘ideal’’ hot hydrogen. It would be very interesting to ask if the delocalized hydrogen is really involved in some surface reactions. If this is indeed the case, the quantum delocalization would be directly related to the heterogeneous catalysis, and, considering the low temperature where the delocalization occurs, its study will be indispensable for the chemical industry. From the viewpoint of physics, it would be exceptionally interesting to know whether the delocalized H (D) is a boson (fermion) or not. As discussed in Section 1.2.3, the exchange force, which depends on the statistics of the hydrogen atoms, works between the H (D) adatoms; it is predicted that there exists an isotope effect between H and D in the coverage dependence (a change in sign of the attractive-part contribution to the coverage dependence) of the bandwidth, which should be observed by experiments. Finally, it may be interesting to extend the present study and examine the quantum delocalization of heavier atoms beyond deuterium.

4. Conclusion In this paper quantum-delocalization studies of hydrogen on transition-metal surfaces are reviewed. A summary of the experimental work and theoretical calculations for various systems, which have been considered up to now, is given. Increasing experimental evidence shows that hydrogen in the excited states is quantum-mechanically delocalized, and these experimental results are increasingly theoretically supported. It is probably fair, at the present stage, to conclude that quantum delocalization of hydrogen in the excited states is a rule, not an exception, the differences among various surfaces studied being the degree of the delocalization. On the other hand, hydrogen atoms in the ground state are not much delocalized. Clearly, there still remain many outstanding and unsolved fundamental problems more than those which have been solved up to now. These problems are closely connected with theories essential in surface science, experimental surface-science techniques and computer technology. Considering the rapid and unexpected developments of these fields in the last two decades, we expect that the problems associated with the quantum delocalization would be solved in the first two decades of the 21st century.

Acknowledgement The authors would like to thank all authors of cited references whose work was indispensable for writing this review. MN thanks Prof. A. Yoshimori for useful discussions and Prof. E. Ilisca for critical reading of the manuscript in its early stage. WB is grateful to Profs. H. Ibach, B. Voigtla¨ nder, D. Menzel and A. Gross for stimulating discussions and Profs. J. Nørskov, B. Voigtla¨ nder and S. Modesti for allowing us to use some of their figures. This work was supported in part by the Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology (Japan).

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