Unoccupied states

Figure A3.10.23 Schematic diagram of molecular CO chemisorption on a metal surface. The model is based on a donor-acceptor scheme where the CO 5 a FIOMO donates charge to surface unoccupied states and the surface back-donates charge to the CO 2 71 LUMO [58].

It is now possible to "see" the spatial nature of molecular orbitals (10). This information has always been available in the voluminous output from quantum mechanics programs, but it can be discerned much more rapidly when presented in visual form. Chemical reactivity is often governed by the nature of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Spectroscopic phenomena usually depend on the HOMO and higher energy unoccupied states, all of which can be displayed and examined in detail. 

Figure 5.2 The modification of the electron energy distribution curve by the presence of diffraction limits in a crystal. The lower filled band is separated from upper unoccupied states in a semiconductor by a small energy difference, so that some electrons can be promoted to conduction by an increase in temperature...

Consider Figure la, which shows the electronic energy states of a solid having broadened valence and conduction bands as well as sharp core-level states X, Y, and Z. An incoming electron with energy Eq may excite an electron ftom any occupied state to any unoccupied state, where the Fermi energy Ap separates the two... 

In SXAPS the X-ray photons emitted by the sample are detected, normally by letting them strike a photosensitive surface from which photoelectrons are collected, but also - with the advent of X-ray detectors of increased sensitivity - by direct detection. Above the X-ray emission threshold from a particular core level the excitation probability is a function of the densities of unoccupied electronic states. Because two electrons are involved, incident and the excited, the shape of the spectral structure is proportional to the self convolution of the unoccupied state densities. 

Because IPES maps the densities of unoccupied states, it is related to other techniques that do the same (e.g. STS and SXAPS). When used in conjunction with a technique that maps the densities of occupied surface states, e.g. UPS or ELS, a continuous spectrum of state density from occupied to unoccupied can be obtained. Just as in UPS, in which angular resolution enables elucidation of the three-dimensional occupied band structure, so in IPES angular resolution enables mapping of the three-dimensional unoccupied band structure. This version is called KRIPES (i. e. K-re-solved IPES). 

HOMO = highest occupied molecular orbital) is the Fermi limit. Whenever the Fermi limit is inside a band, metallic electric conduction is observed. Only a very minor energy supply is needed to promote an electron from an occupied state under the Fermi limit to an unoccupied state above it the easy switchover from one state to another is equivalent to a high electron mobility. Because of excitation by thermal energy a certain fraction of the electrons is always found above the Fermi limit. 

Fig. 3.8. Left schematic illustration of TRPE. The IR pump pulse (hi/1) perturbs the electronic states of the sample. The photon energy of the UV probe pulse (h.1/2) exceeds the work function and monitors changes in occupied and unoccupied states simultaneously. Right experimental setup for TRPE. Pairs of IR and UV pulses are time delayed with respect to each other and are focused onto the sample surface in the UHV chamber. The kinetic energy of photoelectrons is analyzed by an electron time-of-flight spectrometer (e-TOF). From [23]...

However, UPS and XPS do not both image the density of states in entirely the same way. In XPS, the photoelectrons originating from the valence band leave the sample with kinetic energies over 1 keV. In UPS, the exciting energy is on the order of 21 eV, and the kinetic energy of the electrons is low, say between 5 and 16 eV. This means that the final state of the photoelectron is within the unoccupied part of the density of states of the metal. As a result, the UPS spectrum represents a convolution of the densities of occupied and unoccupied states, which is sometimes called the "Joint Density of States."... 

The unoccupied part of the density of states can also be measured, by a technique called Inverse UPS (Sometimes also referred to as BIS, Bremsstrahlung Isochromat Spectroscopie). Here a beam of low energy electrons falls on the surface, where they go into the unoccupied states and fall back to the Fermi level, under emission of a quantum hv. Measurement of this radiation as a function of the incident electron energy gives the density of unoccupied states. This technique falls outside the scope of this book. The reader is referred to the literature [5, 44],... 

Figure 7.19 Principle of tunneling between two metals with a potential difference V, separated by a gap s. Electrons tunnel horizontally in energy from occupied states of the metal to unoccupied states of the tip.

Fein, A.P. J. Vac. Sci. Technol. A. in press)(3). Electronic structure measurements of occupied states are typically made with UPS, while unoccupied states are probed by IPS (49). EELS probes both filled and unfilled states simultaneously, and is therefore used in conjunction with either UPS or IPS to complete a band structure determination (44,49). A new electronic spectroscopy technique, Field Emission Scanning Auger Microscopy (50), utilizes STM-like technology to effect highly localized (c.a. 1 /im) Auger electron spectroscopy. The local electronic information afforded by STM is a valuable complement to these other techniques, and STM is the only one of these methods that may be applied to in situ investigations in condensed media. 

The bonding situation of the tetrahedral clusters may be described by the qualitative MO scheme that is depicted in Figure 2.3-5 and in which the orbitals involved in the bonding of the terminal ligands are ignored [33, 35, 53], The monomeric fragments M-X have a lone electron pair in a cr-orbital as the HOMO and a degenerate set of two orbitals of re-symmetry as the lowest unoccupied state. Linear... 

Models of CO adsorption show that top site binding is governed by the CO HOMO (5cr orbital) donating electrons into the metal unoccupied states, with simultaneous back-donation of electrons from the metal s occupied dxz and dyz states into the CO LUMO 2tt orbital). Therefore, it follows that the standard chemisorption model, which considers shifts in the total d-band center, can be inaccurate for systems in which individual molecular orbitals, involved in bonding with the adsorbate, shift differently due to external interactions. In particular, we have shown that the formation of hybrid orbitals with the support material can lead both to downward shifts in the metal d-band center, which do not affect the adsorption of molecules to the metal surface, and to upward shifts that are vitally important. 

Figure 9.4 The frontier orbital distribution in bulk FeS2 1 -lowest unoccupied state 2-highest occupied state...

In solid state physics, the sensitivity of the EELS spectrum to the density of unoccupied states, reflected in the near-edge fine structure, makes it possible to study bonding, local coordination and local electronic properties of materials. One recent trend in ATEM is to compare ELNES data quantitatively with the results of band structure calculations. Furthermore, the ELNES data can directly be compared to X-ray absorption near edge structures (XANES) or to data obtained with other spectroscopic techniques. However, TEM offers by far the highest spatial resolution in the study of the densities of states (DOS). 

Figure 2. Schematic representation of two models for the origin of electron energy-loss nearedge structures (ELNES) for the core-ionization edges, (a) Transition of strongly bound core electrons into unoccupied states (b) multiple scattering description of ELNES.

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