Down atom

The partially occupied 17eag orbital is of greatest interest in the interpretation of magnetic resonance parameters. As Table I shows, this orbital is split off from the other copper 3d levels, and is almost pure a spin, with only 0.14% population in the spin-down atomic orbital. As written, the orbital is nearly pure imaginary for example, the coefficients of Y22 and Y2-2 are nearly... 

Figure 5.3. Models of the Si(100) and Ge(100) surface (Left) (2 x 1) dimer reconstruction involving symmetric dimers (Middle) c(4 x 2) dimer reconstruction with buckled dimers These two structures are observed for silicon at room temperature and lower temperature, respectively. For germanium, the structure at (Right), the p(2 x 2) dimer reconstruction with buckled dimers, is also observed at lower temperatures. In the top view model, the open circles represent the top layer atoms, with the larger and smaller circles designating the up and down atoms of the dimer, respectively. The filled circles represent the next layer of atoms.

Figure 5.4. The highest occupied molecular orbital of a Si911,2 dimer cluster. The top two silicon atoms comprise the surface dimer, and the remaining seven Si atoms contain three subsurface layers which are hydrogen terminated to preserve the sp3 hybridization of the bulk diamond cubic lattice. The up atom is nucleophilic and the down atom is electrophilic.

A recent theoretical study has nicely addressed the question of mechanism on the silicon surface. Minary and Tuckerman carried out an ab initio molecular dynamics (MD) study of the [4 + 2] cycloaddition reaction on Si(100)-2 x 1 [251]. Because the previously reported ab initio DFT models were static , these were not able to address in detail the mechanisms by which the [4 + 2] product was formed. The results of the MD study indicate that rather than being concerted, the dominant mechanism is a stepwise zwitterionic process in which an initial nucleophilic attack of one of the C=C bonds by the down atom of the dimer leads to a carbocation. This carbocation exists for up to 1-2 ps, stabilized by resonance, and depending on which positively charged carbon atom reacts with which Si surface atom, can form... 

In addition to forming dimers with double-bond-like character that can participate in cycloaddition-type reactions, the reconstruction of the (100) semiconductor surface is also responsible for the presence of electrophilic and nucleophilic sites. The bond of a tilted dimer deviates from the plane of the surface, and the resulting structure of each dimer consists of an up dimer atom protruding from the surface and a down dimer atom recessed on the surface. The electron density at the up atom of the dimer is higher than that at the down atom, leading to nucleophilic and electrophilic behavior, respectively [49]. 

The participation of the germanium dimers in nucleophilic/electrophilic or Lewis acid/base reactions has been the subject of several investigations on the Ge(100)-2x1 surface [16,49,255,288,294,313-318]. As for the case of silicon, adsorption of amines has provided an excellent system for probing such reactions. Amines contain nitrogen lone pair electrons that can interact with the electrophilic down atom of a tilted Ge dimer to form a dative bond via a Lewis acid/base interaction (illustrated for trimethylamine at the Si(100)-2 x 1 surface in Ligure 5.17). In the dative bond, the lone pair electrons on nitrogen donate charge to the Ge down atom [49]. 

Pyridine, a six-membered cyclic aromatic amine, has also been studied on Ge(100)-2 x 1 both theoretically [315,316] and experimentally by STM [314]. It adsorbs selectively through a Ge—N dative bond on the surface. Theoretical calculations showed that the dative-bonded adduct is more stable than other possible reaction products (e.g., cycloaddition products) on Ge [315,316]. Furthermore, STM images show formation of a highly ordered monolayer at the surface with a coverage of 0.25 ML. The pyridine overlayer forms a c(4 x 2) structure in which the molecules bind to the down atoms of every other dimer to minimize repulsive interactions between pyridine molecules. 

An additional complication affecting silicon surface chemistry is the well-established fact that dimers tilt away from the symmetric position (c.f. Fig. 1(b)). Associated with dimer tilting is a charge transfer from the down atom to the up atom. Hence, the dimers exhibit somewhat zwit-terionic character, with one electron-poor atom and one electron-rich atom. Such a property of the Si(100)-(2 x 1) surface makes it possible to use nucleophilic and electrophilic attachment reactions. At temperatures less than 120 K, dimer tilting on Si(100)-(2 x 1) can be observed in STM experiments [3,9], while at higher temperatures the direction of the tilt oscillates on a time scale faster than the order milliseconds sampling times of the STM. 

Demonstration of levitation of micron-sized latex particles by radiation pressure dates back to 1970 in the experiments reported by Ashkin [Ashkin 1970]. The average force accelerating (or slowing down) atoms in a laser field was derived by A.Kazantsev in 1972 [Kazantsev 1974]. Later in 1972-1974 he classified the optical forces as spontaneous, induced and mixed. In particular, it was he who first presented the dipole potentials for velocity broadened lines of resonance atoms in the logarithmic form... 

A schematic diagram of an apparatus for optical cooling of atoms, deflection of the slowed-down atoms, and focusing is depicted in Fig. 9.13. 

Why is it interesting from a spectroscopic point of view to be able to cool down atoms to very low translation energies (temperatures) ... 

Figure 8(b) shows the results of a typical dimer flipping experiment. The tip is positioned above a down atom of a dimer at the Si(100)-c(4 x 2) surface and a A/(z) spectrum is acquired. (Although we can t see the down atom of the dimer in the NC-AFM image, we know where it is by symmetry). At a certain critical tip-sample separation - in this case, about 1.6 A closer to the surface than the tip position used for imaging - there is a sharp discontinuity in the frequency shift vj. z curve due to the sudden jump of the lower dimer atom towards the tip. On retraction of the tip, the dimer remains in its flipped conformation, as is clear from Fig. 8(b). 

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