Diatomics on a Surface

There certainly are parallels that can be drawn between the way molecules react in the gas or liquid phases and at metal surfaces [16]. Our emphasis in this chapter is to compare and contrast the bonding on surfaces compared to the situation for discrete molecules in several illustrative examples. For example, how does the bonding between a CO and an Ni surface compare to that for a d ML5 fragment We shall see that there are many similarities however, there are some important additional facets that surfaces bring to the table. 

We shall start the theoretical exploration for a c(2 x 2)CO coverage on Ni(IOO) in very qualitative terms using the Blyholder model [20]. The 3 r highest occupied molecular orbitals (HOMO) of CO will form a bonding interaction with zYs/z hybrids on surface Ni atoms, 23.14. The Itt lowest unoccupied molecular orbitals (LUMOs) of CO form bonding combinations with xz/yz Ni surface orbitals, 23.15. 

6 eV is C—O antibonding. This is consistent with the existence of CO hi states 

An alternative way to investigate the electronic structure is to carry out a so-called cluster calculation on a piece of the surface. 23.16 illustrates one approach 

Contour diagrams in the yz plane for the three it (a) and a (b) MOS that have the largest coefficients on the central Ni atom and/or CO. This is a B3LYP calculation on the 13 metal atom cluster shown in 23.16. 

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Figure B3.2.12. Schematic illustration of geometries used in the simulation of the chemisorption of a diatomic molecule on a surface (the third dimension is suppressed). The molecule is shown on a surface simulated by (A) a semi-infinite crystal, (B) a slab and an embedding region, (C) a slab with two-dimensional periodicity, (D) a slab in a siipercell geometry and (E) a cluster.

If we wish to understand the conditions under which a diatomic molecule such as H2, N2, or CO dissociates on a surface, we need to take two orbitals of the molecule into account - the highest occupied and the lowest unoccupied molecular orbital (the HOMO and LUMO of the so-called frontier orbital concept). Let us take a simple case to start with the molecule A2 with occupied bonding level a and unoccupied antibonding level a. We use jellium as the substrate metal and discuss the chemisorption of A2 in the resonant level model. What happens is that the two levels broaden due to the rather weak interaction with the free electron cloud of the metal. 

Figure 1 The ubiquitous elbow potential energy surface showing for the dissociation of a diatomic molecule on a surface. This is a function of die molecular bond length and the molecule-surface distance. The reactants are intact molecules, while die products are the atoms chemisorbed separately on the surface. The two extreme cases are shown, an early barrier for which the initial vibration of the molecule is ineffective in overcoming the barrier, and a late barrier for which vibration assists in the dissociation process.

For an adsorbate to be at equilibrium with a gas phase molecule, the detailed rates of adsorption and desorption must be equal [66], leading to a simple relationship between the detailed product final state distributions, P, for desorption and the sticking probability, S. Taking the explicit example of a diatomic molecule A2 dissociating on a surface at a temperature T and surface coverage 0A,... 

The high relative velocities following impact of a cluster on a surface suggests that such dissociation processes can readily take place when a diatomic molecule embedded inside the cluster is activated by a collision. Molecular dynamics simulations show that beyond a threshold, the yield of dissociation of halogen molecules solvated in a rare gas cluster is a rapidly increasing function of the collision velocity and can reach 100%, see Fig. 6. This, unlike the surface impact induced dissociation of unclustered, cold, halogen molecules where the yield reaches a plateau of below 40%. ° ... 

Figure 9 Separating single (unpaired) atoms from diatoms (compare to Fig. 5) an external repulsive potential causes both the single atoms and the diatoms to move on a surface of constant energy. The diatoms hit the top of the energy band after being displaced by a much shorter length than the unpaired atoms.

A chemical reaction in which a diatomic molecule A-B collides end-on with an atom C, to form a diatomic molecule B-C and an atom A, can be depicted as occurring on a surface within a theoretical three-dimensional space in which the vertical axis is potential energy and the other two axes are the A-B and the B-C bond distances. In 1931 Henry Eyring and Michael Polanyi took reaction rate studies to the individual molecule level by calculating a potential energy surfece for the colinear gas phase reaction... 

Finally, suppose a diatomic gas is adsorbed on a surface and the first step is for the molecule to dissociate and occupy two sites, one by each atom ... 

Now that we have a way to model the adsorption of gas species on a surface, we should consider how adsorbed species interact with a surface. There are two descriptions of molecule-surface interaction, differing mainly in terms of degree of interaction. In physisorption, molecules interact with surfaces in a weak and general way. It could be as simple as a van der Waals or dispersion interaction that keeps a molecule on a surface, like molecules of methane (CH4) or diatomic nitrogen (N2) on metal surfaces, or organic residues all over the place. Or, it could be a dipole interaction with a surface atom, which is how water molecules adsorb so easily on most surfaces. 

Molecular rotation has two competing influences on the dissociation of diatomics [, and ]. A molecule will only be able to dissociate if its bond is oriented correctly with respect to the plane of the surface. If the bond is parallel to the plane, then dissociation will take place, whereas if the molecule is end-on to the surface, dissociation requires one atom to be ejected into the gas phase. In most cases, this reverse Eley-RideaF process is energetically very... 

These electronic energies dependence on the positions of the atomic centres cause them to be referred to as electronic energy surfaces such as that depicted below in figure B3.T1 for a diatomic molecule. For nonlinear polyatomic molecules having atoms, the energy surfaces depend on 3N - 6 internal coordinates and thus can be very difficult to visualize. In figure B3.T2, a slice tln-oiigh such a surface is shown as a fimction of two of the 3N - 6 internal coordinates. 

Figure B3.4.7. Schematic example of potential energy curves for photo-absorption for a ID problem (i.e. for diatomics). On the lower surface the nuclear wavepacket is in the ground state. Once this wavepacket has been excited to the upper surface, which has a different shape, it will propagate. The photoabsorption cross section is obtained by the Fourier transfonn of the correlation function of the initial wavefimction on tlie excited surface with the propagated wavepacket.

The simplest condensed phase VER system is a dilute solution of a diatomic in an atomic (e.g. Ar or Xe) liquid or crystal. Other simple systems include neat diatomic liquids or crystals, or a diatomic molecule bound to a surface. A major step up in complexity occurs with poly atomics, with several vibrations on the same molecule. This feature guarantees enonnous qualitative differences between diatomic and polyatomic VER, and casts doubt on the likelihood of understanding poly atomics by studying diatomics alone. 

Suppose that W(r,Q) describes the radial (r) and angular (0) motion of a diatomic molecule constrained to move on a planar surface. If an experiment were performed to measure the component of the rotational angular momentum of the diatomic molecule perpendicular to the surface (Lz= -ih d/dQ), only values equal to mh (m=0,1,-1,2,-2,3,-3,...) could be observed, because these are the eigenvalues of ... 

A diatomic molecule constrained to rotate on a flat surface can be modeled as a planar... 

Filter aids should have low bulk density to minimize settling and aid good distribution on a filter-medium surface that may not be horizontal. They should also be porous and capable of forming a porous cake to minimize flow resistance, and they must be chemically inert to the filtrate. These characteristics are all found in the two most popular commercial filter aids diatomaceous silica (also called diatomite, or diatomaceous earth), which is an almost pure silica prepared from deposits of diatom skeletons and expanded perhte, particles of puffed lava that are principally aluminum alkali siheate. Cellulosic fibers (ground wood pulp) are sometimes used when siliceous materials cannot be used but are much more compressible. The use of other less effective aids (e.g., carbon and gypsum) may be justified in special cases. Sometimes a combination or carbon and diatomaceous silica permits adsorption in addition to filter-aid performance. Various other materials, such as salt, fine sand, starch, and precipitated calcium carbonate, are employed in specific industries where they represent either waste material or inexpensive alternatives to conventional filter aids. 

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