Atomic orbitals fully occupied

This description is supported by the fact that the (degenerate) states of lowest energy for an isolated O atom involve one 2p orbital fully occupied and two half-filled 2p orbitals. 

Figure 20.11 shows the energy band dispersion diagram and DOS for Srln204 [20]. The lowest band consisted of the Sr 4s atomic orbital (AO). The second, third, and fourth bands from the bottom were formed by the O 2s, Sr 4p, and In 4d AOs, respectively. The valence band consisted of 48 orbitals, which was the number that all the O 2p AOs for 16 0 atoms were fully occupied ( 73 through 120 in this numbering as shown in Figure 20.11). 

The nature of the electronic states for fullerene molecules depends sensitively on the number of 7r-electrons in the fullerene. The number of 7r-electrons on the Cgo molecule is 60 (i.e., one w electron per carbon atom), which is exactly the correct number to fully occupy the highest occupied molecular orbital (HOMO) level with hu icosahedral symmetry. In relating the levels of an icosahedral molecule to those of a free electron on a thin spherical shell (full rotational symmetry), 50 electrons fully occupy the angular momentum states of the shell through l = 4, and the remaining 10 electrons are available... 

A second mechanism (the polarization mechanism) arises due to the polarization of the fully occupied (bonding) crystal orbitals formed by the eg. oxygen 2p. and Li 2s atomic orbitals in the presence of a magnetic field. A fully occupied crystal (or molecular) orbital in reality comprises one one-electron orbital occupied by a spin-up electron and a second one-... 

The formation of a Si crystal is shown in Fig. 1.10. Aside from the core, each Si atom has four valence electrons two 3s electrons and two 3p electrons. To form a Si crystal, one of the 3s electrons is excited to the 3p orbital. The four valence electrons form four sp hybrid orbitals, each points to a vertex of a tetrahedron, as shown in Fig. 1.10. Thpse four sp orbitals are unpaired, that is, each orbital is occupied by one electron. Since the electron has spin, each orbital can be occupied by two electrons with opposite spins. To satisfy this, each of the directional sp orbitals is bonded with an sp orbital of a neighboring Si atom to form electron pairs, or a valence bond. Such a valence bonding of all Si atoms in a crystal form a structure shown in (b) of Fig. 1.10, the so-called diamond structure. As seen, it is a cubic crystal. Because all those tetrahedral orbitals are fully occupied, there is no free electron. Thus, similar to diamond, silicon is not a metal. 

By analyzing the density matrix composition of planar and 3D structures of seven atom clusters (II and IV of Fig 1), calculated using scalar relativistic pseudo-potential at the GGA theory level, Fernandez and coworkers conclude that the planarity of An clusters is driven by the hybridization of the half-filled 6s orbital with the fully occupied 5d 2 orbital, which is favored by relativistic effects. Thus, the three valence electrons in the orbitals 6s and 5d 2, form a sticky-waist cylinder , where the cylinder is due to the almost filled s + d 2 hybrid, and the sticky-waist is due to the nearly half-filled s — d 2 hybrid orbital. 

The band of molecular orbitals formed by the 2s orbitals of the lithium atoms, described above, is half filled by the available electrons. Metallic beryllium, with twice the number of electrons, might be expected to have a full 2s band . If that were so the material would not exist, since the anti-bonding half of the band would be fully occupied. Metallic beryllium exists because the band of MOs produced from the 2p atomic orbitals overlaps (in terms of energy) the 2s band. This makes possible the partial filling of both the 2s and the 2p bands, giving metallic beryllium a greater cohesiveness and a higher electrical conductivity than lithium. 

The lowest available orbital for the outer electron is 3s, not Is. As discussed in Section 5.3, this is a consequence of the exclusion principle, and the fact that the Is, 2s, and 2p orbitals are fully occupied by the other 10 electrons in a sodium atom. 

Figure 17.1. Atom in the Bohr model. The electrons surround the nucleus. An incoming photon can lift an electron to a not fully occupied, higher orbital or remove it entirely from the atom.

Circular orbits are defined by n = 0. The principal quantum number specifies energy shells. For n = 1 the only solution is n = 0, k = 1, which specifies two orbits with angular momentum vectors in opposite directions. The solutions n = 0, k = 2 and n = 1, k = 1 define 8 possible orbits, 4 circular and 4 elliptic. The angular momentum vectors of each set are directed in four tetrahedral directions to define zero angular momentum when fully occupied. Taken together, these tetrahedra define a cubic arrangement, closely related to the Lewis model for the Ne atom. 

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