Atomic structure orbital shapes

For two and three dimensions, it provides a crude but useful picture for electronic states on surfaces or in crystals, respectively. Free motion within a spherical volume gives rise to eigenfunctions that are used in nuclear physics to describe the motions of neutrons and protons in nuclei. In the so-called shell model of nuclei, the neutrons and protons fill separate s, p, d, etc orbitals with each type of nucleon forced to obey the Pauli principle. These orbitals are not the same in their radial shapes as the s, p, d, etc orbitals of atoms because, in atoms, there is an additional radial potential V(r) = -Ze2/r present. However, their angular shapes are the same as in atomic structure because, in both cases, the potential is independent of 0 and (f>. This same spherical box model has been used to describe the orbitals of valence electrons in clusters of mono-valent metal atoms such as Csn, Cu , Na and their positive and negative ions. Because of the metallic nature of these species, their valence electrons are sufficiently delocalized to render this simple model rather effective (see T. P. Martin, T. Bergmann, H. Gohlich, and T. Lange, J. Phys. Chem. 95, 6421 (1991)). 

Photon-induced emission of electrons is an obvious tool for structural analysis in two ways. Firstly, it is sensitive to the initial density of states of the emitted electrons (originating from the first few atomic layers of a surface), and so to the surface geometry. Secondly, if the angular distribution of the emitted electrons is considered, additional information about the initial electron states (in particular orbital shape and bonding... 

The other aspect of fullerene electronic structure which relates to their ability to accept electron density is the rehybridization of the carbon n atomic orbitals as a result of the curvature which is imposed on the conjugated carbon atoms by the shape of the molecules (Haddon et al. 1986a, b). The discussion of rehybridization effects is deferred to 6, and we begin with a treatment of the topological contribution to fullerene electronegativity within simple hmo theory. The presence of 12 conjugated 5MR in the fullerenes suggests that they will be biased towards reduction in their redox chemistry. 

The quantum mechanical model of atomic structure is far too difficult to be explained in detail in an AP Chemistry course. However, some aspects of the theory are appropriate, and you should know them. These include the predicted number and shapes of orbitals in each energy level the number of electrons found in each orbital, sublevel, and energy level and the meaning of the four quantum numbers. 

The electrons are negatively charged particles. The mass of an electron is about 2000 times smaller than that of an proton or neutron at 0.00055 amu. Electrons circle so fast that it cannot be determined where electrons are at any point in time, rather, we talk about the probability of finding an electron at a point in space relative to a nucleus at any point in time. The image depicts the old Bohr model of the atom, in which the electrons inhabit discrete "orbitals" around the nucleus much like planets orbit the sun. This model is outdated. Current models of the atomic structure hold that electrons occupy fuzzy clouds around the nucleus of specific shapes, some spherical, some dumbbell shaped, some with even more complex shapes. Even though the simpler Bohr model of atomic structure has been superseded, we still refer to these electron clouds as "orbitals". The number of electrons and the nature of the orbitals they occupy basically determines the chemical properties and reactivity of all atoms and molecules. 

The angular overlap model, which has been of use in understanding the electronic structure and spectra of transition metal complexes is used to look at the factors which influence the shapes and relative bond strengths in main group systems AB ( = 2-7). Whilst the method is of some interest in itself, the main value of this paper is to show how several molecular orbital effects (Ugand-central atom p orbital bond energy, central atom s orbital involvement, and non-bonded interactions) contribute to determine the overall geometry. 

Ans. Three new quantum numbers appear, which characterize atomic structure in finer detail. These are /, the subshell number, a quantum number which specifies orbital shape, m, which specifies the orbitals orientation in space, and s, the spin quantum number, which describes the fact that electrons appear to rotate or spin on their axes. 

To begin with, we recall that atomic orbitals are mathematical functions that come from the quantum mechanical model for atomic structure. (Section 6.5) To explain molecular geometries, we can assume that the atomic orbitals on an atom (usually the central atom) mix to form new orbitals called hybrid orbitals. The shape of any hybrid orbital is different from the shapes of the original atomic orbitals. The process of mixing atomic orbitals is a mathematical operation called hybridization. The total number of atomic orbitals on an atom remains constant, so the number of hybrid orbitals on an atom equals the number of atomic orbitals that are mixed. 

Explain the role of the three quantum numbers, rt, / and in determining the overall structure and shape of the hydro n atomic orbitals... 

Fig. 4.22. Summary schematic representation of Is, 2s, 2p, 3s, 3p, 3d oibitals of the hydrogen atom. Is, 2s, 3s oibitals are spherically symmetric and increase in size Is has no node, 2s has one nodal Sphere (not shown), 3s has two nodal spheres (not shown). The shadowed area corresponds to the minus sign of the orbital. The 2p orbitals have a single nodal plane (perpendicular to the orbital shape). 3p orbitals are larger than 2p, and have a more complex nodal structure. Note that among 3d oibitals all except 3d 2, 2 have identical shape, but differ by orientation in space. A peculiar form of 3d 2 2 becomes more familiar when one realizes that it simply represents a sum of two usual 3d oibitals. Indeed, 3d 2, .2 [2 — +, v J]exp(—Zr/3) oc — x ) + — y2)]exp(—Zr/3)...

The Toulouse quantum-chemistry group created quasirelativistic pseudopotentials based on the atomic structure method developed by Barthelat et al. (1980) and the general procedure of adjustment devised by Durand and Barthelat (1974, 1975). The pseudopotential is constructed in such a way that the pseudo-orbitals coincide best with the all-electron valence orbitals and are smooth in the core region, i.e. an approach which has later been termed norm-conserving (Hamaim et al. 1979) or shape-consistent (Christiansen et al. 1979, Rappe et al. 1981). No parameter sets for the lanthanides and actinides have been published up to now. 

Different ECP approaches can be classified according to various criteria. If the original radial-node structure of the atomic valence orbitals is preserved, a model potential is produced [808-813]. If the nodal structure is not conserved, the ECP is called pseudo potential [814-817], While shape-consistent pseudo potentials [818-821] are optimized to obtain a maximum resemblance in the shape of pseudo-valence orbitals and original valence orbitals, energy-consistent pseudo potentials [822-829] reproduce the experimental atomic spectrum very accurately. 

The level structure of the T-shaped AH3 is readily derived from that for the square pyramid by removal of a tram pair of ligands. This is shown in Figure 14.6. Indeed the orbitals of AH5 and AHj are very similar. The nonbonding ligand-located bt orbital of the square pyramid is replaced by a nonbonding, central-atom-located orbital (hi). Notice that going from AHs to AH3 two valence orbitals are removed (corresponding to Og and o from the Hj unit which is lost). One of these is h] in AHs, which correlates with Og. The other is derived from one component from each of le and 2e. The nonbondir hi orbital in AH, is created (as shovm by the dashed Hnes), and the orbital of H, (not shown), on loss of the two hy-... 

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