Orbitals overlap of atomic

In many crystals there is sufficient overlap of atomic orbitals of adjacent atoms so that each group of a given quantum state can be treated as a crystal orbital or band. Such crystals will be electrically conducting if they have a partly filled band but if the bands are all either full or empty, the conductivity will be small. Metal oxides constitute an example of this type of crystal if exactly stoichiometric, all bands are either full or empty, and there is little electrical conductivity. If, however, some excess metal is present in an oxide, it will furnish electrons to an empty band formed of the 3s or 3p orbitals of the oxygen ions, thus giving electrical conductivity. An example is ZnO, which ordinarily has excess zinc in it. 

We said in Section 1.5 that chemists use two models for describing covalent bonds valence bond theory and molecular orbital theory. Having now seen the valence bond approach, which uses hybrid atomic orbitals to account for geometry and assumes the overlap of atomic orbitals to account for electron sharing, let s look briefly at the molecular orbital approach to bonding. We ll return to the topic in Chapters 14 and 15 for a more in-depth discussion. 

Pi (77 ) bond (Section 1.8) The covalent bond formed by sideways overlap of atomic orbitals. For example, carbon-carbon double bonds contain a 7r bond formed by sideways overlap of two / orbitals. 

Sigma (covalent bond formed by head-on overlap of atomic orbitals. 

In Chapter 7, we used valence bond theory to explain bonding in molecules. It accounts, at least qualitatively, for the stability of the covalent bond in terms of the overlap of atomic orbitals. By invoking hybridization, valence bond theory can account for the molecular geometries predicted by electron-pair repulsion. Where Lewis structures are inadequate, as in S02, the concept of resonance allows us to explain the observed properties. 

We cannot generate a tetrahedron by simple overlap of atomic orbitals, because atomic orbitals do not point toward the comers of a tetrahedron. In this section, we present a modification of the localized bond model that accounts for tetrahedral geometry and several other common molecular shapes. 

The valence bond theory describes covalent bonding as the overlap of atomic orbitals to form a new kind of orbital, a hybrid orbital. 

In the valence bond theory, sigma bonds overlap on a line drawn between the two nuclei, while pi bonds result from the overlap of atomic orbitals above and below a line connecting the two atomic nuclei. 

The formation of bonding molecular orbitals by an overlap of atomic orbitals applies not only to the Is orbitals of hydrogen, but also to other atomic orbitals. When the atomic orbitals overlap along the axis of the bond, a covalent bond, called a sigma (a) bond, results. This is normally referred to as end-on overlap. Some examples of the formation of a bonds from overlapping atomic orbitals are shown in the diagrams. 

As we have already seen, two molecular orbitals form when two atomic orbitals overlap - a bonding molecular orbital and an antibonding molecular orbital. End-on overlap of atomic orbitals along the axis of the bond results In cr and cr molecular orbitals forming. Slde-on overlap of atomic orbitals at an angle perpendicular to the axis of the bond results In the formation of n and molecular orbitals. 

These various relationships between force and particle separation imply that the attractive force between particles will become infinite when they touch. In reality, other short-range forces will modify this relationship when r is very small, in particular the repulsion from overlap of atomic orbitals. The van der Waals attraction will then be balanced by this overlap repulsion. At these short distances (a few tenths of a nanometer), the van der Waals attraction will be strong enough to hold the particles fairly strongly together. This balance between van der Waals forces of attraction and overlap repulsion forces is shown schematically in Fig. 1.4, where the very steep repulsive interaction at atomic distances is due to the overlap repulsion. Hydration forces (see section 1.3.3) may also result in repulsion between surfaces at somewhat greater separations. 

Electrons occupy distinct orbitals within atoms (see Chapter 4 for details). When atoms covalently bond to form molecules, the shcired electrons cire no longer constrained to those atomic orbitals instead, they occupy molecular orbitals, larger regions that form from the overlap of atomic orbitals. Just as different atomic orbitals are associated with different levels of energy, so cire molecular orbitals. A stable covalent bond forms between two atoms because the energy of the moleculcir orbital associated with the bond is lower than the combined energies associated with the atomic orbitals of the sepcirated atoms. 

The localized-electron model or the ligand-field approach is essentially the same as the Heitler-London theory for the hydrogen molecule. The model assumes that a crystal is composed of an assembly of independent ions fixed at their lattice sites and that overlap of atomic orbitals is small. When interatomic interactions are weak, intraatomic exchange (Hund s rule splitting) and electron-phonon interactions favour the localized behaviour of electrons. This increases the relaxation time of a charge carrier from about 10 s in an ordinary metal to 10 s, which is the order of time required for a lattice vibration in a polar crystal. 

Here, Sy is the overlap of atomic orbitals i and j i runs over atomic orbitals (AOs) associated with the selected fragment / while j runs over all AOs. The fragment charges of the second adiabatic state are calculated analogously using the coefficients c homo-i of orbital HOMO-1 in place of c homo in Eq. 20. By the same token, the quantity qmnif) can be defined as... 

Covalent bonds are formed when atomic orbitals overlap. The overlap of atomic orbitals is called hybridization, and the resulting atomic orbitals are called hybrid orbitals. There are two types of orbital overlap, which form sigma (cr) and pi (tt) bonds. Pi bonds never occur alone without the bonded atoms also being joined by a ct bond. Therefore, a double bond consists of a O bond and a tt bond, whereas a triple bond consists of a ct bond and two tt bonds. A sigma overlap occurs when there is one bonding interaction that results from the overlap of two s orbitals or an s orbital overlaps a p orbital or two p orbitals overlap head to head. A tt overlap occurs only when two bonding interactions result from the sideways overlap of two parallel p... 

It is of interest to enquire how the electrons are redistributed during an interaction and how a bond is affected. We use a simplified Mulliken population analysis [see Appendix A, equations (A.77)-(A.79)]. The simplification consists of dropping all terms involving the overlap of atomic orbitals and assuming that, in any given MO, there is only one atomic orbital on any given center). Thus, we may assume that the following relations hold ... 

Electron-dot structures 1 describe a bond as a sharing of a pair of electrons. Valence bond theory explains how electrons become shared by the overlap of atomic orbitals. 

Covalent bonds are formed by overlap of atomic orbitals, each of which contains one electron of opposite spin. 

Overlap of atomic orbitals (AO s) or hybrids allows electrons to pair up, forming a chemical bond hybrid orbitals valence AO s mix to accommodate "equivalent" bonded neighbors. Non-hybridized orbitals form lone pairs or n bonds. 

Sn-Sn bonding model in [Sn CH(SiMe3)2h]2 (a) overlap of atomic orbitals, (b) representation of the donor-acceptor bonding. 

Bonding Molecular Orbital A molecular orbital which is formed by addition overlap of atomic orbitals is known as bonding molecular orbitals. 

---