Molecular orbital form

The atomic orbitals of atoms are combined to give a new set of molecular orbitals characteristic of the molecule as a whole. The number of molecular orbitals formed is equal to the number of atomic orbitals combined. When two H atoms combine to form H two s orbitals, one from each atom, yield two molecular orbitals. In another case, six p orbitals, three from each atom, give a total of six molecular orbitals. 

Relative energies, so far as filling order is concerned, for the molecular orbitals formed by combining 2s and 2p atomic orbitals. 

In Chapter 9, we considered a simple picture of metallic bonding, the electron-sea model The molecular orbital approach leads to a refinement of this model known as band theory. Here, a crystal of a metal is considered to be one huge molecule. Valence electrons of the metal are fed into delocalized molecular orbitals, formed in the usual way from atomic... 

Figures 6.14c and 6.14d show the energy and density of states of the resonances (adsorbed molecular orbitals) formed upon CO adsorption due to the interaction of the 2% orbitals (Fig. 6.14c) and 5a orbitals (Fig. 6.14d) with the metal surface. As Koper and van Santen, who have performed these intriguing calculations,98 point out, these resonances are rather broad due to the influence of the broad sp-band.

Figure 1.5. Localized molecular orbitals formed from the atomic basis orbitals and electronic transitions for the carbonyl group.

FIGURE 11.1 Interaction of atomic orbitals to produce four bonding and four antibonding molecular orbitals. As the number of atoms gets very large, the molecular orbitals form a continuum. In this case (described in the text) the atoms are assumed to be sodium. 

The orbitals of lower energy fill first. This means that the antibonding orbitals remain empty in the ground state. Molecular orbitals formed by the overlap of two atomic orbitals when the centers of electron density are on the axis common to the two nuclei are called o (sigma) orbitals and the bonds are o bonds. The corresponding anti orbitals are designated o or antibonding orbitals. 

In this case, it can be proved that the canonical SCF orbitals, being solutions of Eq. (26), are symmetry orbitals, i.e. that they belong to irreducible representations of the symmetry group. 12) If the number of molecular orbitals is larger than the dimension of the largest irreducible representation of the symmetry group, it must then be concluded that the set of all N molecular orbitals form a reducible representation of the group which is the direct sum of all the irreducible representations spanned by the CMO s. 

The electronic properties of solids can be described by various theories which complement each other. For example band theory is suited for the analysis of the effect of a crystal lattice on the energy of the electrons. When the isolated atoms, which are characterized by filled or vacant orbitals, are assembled into a lattice containing ca. 5 x 1022 atoms cm 3, new molecular orbitals form (Bard, 1980). These orbitals are so closely spaced that they form essentially continuous bands the filled bonding orbitals form the valence band (vb) and the vacant antibonding orbitals form the conduction band (cb) (Fig. 10.5). These bands are separated by a forbidden region or band gap of energy Eg (eV). 

Molecular orbitals formed by mixing two parallel p-orbitals are called n (pi) if bonding and it (pi star) if antibonding (Figure 1.6). 

Molecular orbitals are generated by combining atomic orbitals. The number of molecular orbitals formed is always equal to the number of atomic orbitals that combine. So, if two atomic orbitals combine, then two molecular orbitals will be formed. This is the case when two hydrogen Is atomic orbitals combine to produce two molecular orbitals in a hydrogen molecule (H ). 

When two atomic orbitals overlap end-on along the axis of the bond, a tr molecular orbital forms. Atomic orbitals that overlap side-on form x molecular orbitals. 

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. 

Just as in the non-linear polyatomic-molecule case, the atomic orbitals which constitute a given molecular orbital must have the same symmetry as that of the molecular orbital. This means that o,%, and 8 molecular orbitals are formed, via LCAO-MO, from m=0, m= 1, and m= 2 atomic orbitals, respectively. In the diatomic N2 molecule, for example, the core orbitals are of o symmetry as are the molecular orbitals formed from the 2s and 2pz atomic orbitals (or their hybrids) on each Nitrogen atom. The molecular orbitals fonned from the atomic 2p i =(2px- i 2py) and the 2p+j =(2px + i 2py ) orbitals are of Jt symmetry and have m = -1 and +1. 

Figure 1.5 The shape of selected molecular orbitals formed from the overlap of two atomic orbitals. From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

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. 

Review Section 2.2. The MO theory focuses attention on the interacting p AO s of the delocalized tr systems, such as conjugated polyenes. The theory states that the number of interacting p AO s is the same as the number of rr molecular orbitals formed. The molecular orbitals are considered to be stationary waves and their relative energies increase as the numbers of nodal points in the corresponding waves increase. Nodes may appear at a C atom, as indicated with a 0 rather than a +... 

Molecules containing two atoms of the same element are the simplest molecules to discuss. We have already seen the results for the hydrogen molecule (page 157 Fig. 5.7) and for the linear combination of s and p orbitals (Fig. 5.8). We shall now investigate the general case for molecular orbitals formed from two atoms having atomic orbitals Is. 2s, 2p, 3s, etc. 

Diamond, the hardest of natural materials, consists of a lattice of carbon atoms arranged in a tetrahedral slruclure at equal distances apait (1.544 A) and bonded by electron pairs in localized molecular orbitals formed by overlapping of Ihe. /> hybrids. See aiticle on Diamond. 

Molecular orbitals are formed by combining atomic orbitals on different atoms. The number of molecular orbitals formed is the same as the number of atomic orbitals combined. 

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