Molecular-orbital model

To obtain a more accurate picture of the bonding in metals, we must turn to molecular-orbital theory. In Sections 9.7 and 9.8 we learned how molecular orbitals are created from the overlap of atomic orbitals. Let s briefly review some of the rules of molecular-orbital theory  

Which element in each period has tne nighest melting point In eacn case, is the element you named at the beginning, middle, or end of its period  

A FIGURE 12.22 The melting points of metals from periods 4, 5, and 6. 

How does the energy spacing between molecular orbitals change as the number of atoms in the chain increases  

A FIGURE 12.23 Discrete energy levels in individual molecules become continuous energy bands In a solid. Occupied orbitals are shaded blue, and empty orbitals red. 

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The Most Elementary Molecular Orbital Models Contain Symmetry, Nodal Pattern, and Approximate Energy Information... 

We 11 expand our picture of bonding by introducing two approaches that grew out of the idea that electrons can be described as waves—the valence bond and molecular orbital models In particular one aspect of the valence bond model called orbital hybridization, will be emphasized... 

We 11 begin our discussion of hydrocarbons by introducing two additional theories of covalent bonding the valence bond model and the molecular orbital model... 

Valence bond and molecular orbital theory both incorporate the wave description of an atom s electrons into this picture of H2 but m somewhat different ways Both assume that electron waves behave like more familiar waves such as sound and light waves One important property of waves is called interference m physics Constructive interference occurs when two waves combine so as to reinforce each other (m phase) destructive interference occurs when they oppose each other (out of phase) (Figure 2 2) Recall from Section 1 1 that electron waves m atoms are characterized by their wave function which is the same as an orbital For an electron m the most stable state of a hydrogen atom for example this state is defined by the Is wave function and is often called the Is orbital The valence bond model bases the connection between two atoms on the overlap between half filled orbifals of fhe fwo afoms The molecular orbital model assembles a sef of molecular orbifals by combining fhe afomic orbifals of all of fhe atoms m fhe molecule... 

Generally speaking the three models offer complementary information Organic chemists use all three emphasizing whichever one best suits a particular feature of struc ture or reactivity Until recently the Lewis and orbital hybridization models were used far more than the molecular orbital model But that is changing... 

Theoretical Studies. Theoretical models for the Si(OR)4 hydrolysis, polycondensation, and dehydration reactions involved in sol—gel processes have been developed using semiempirical molecular orbital models. These have been reviewed (3,5). 

Dannenberg J. J. The Molecular Orbital Modeling of Free Radical and Diels-Alder Reactions Adv. Mol. Model. 1990 2 1-63... 

The molecular orbital model developed in this section is more elaborate than the localized bonds described earlier in this chapter. Is this more complicated model necessary to give a thorough picture of chemical bonding Experimental evidence for molecular oxygen suggests that the answer is yes. 

Our treatment of O2 shows that the extra complexity of the molecular orbital approach explains features that a simpler description of bonding cannot explain. The Lewis structure of O2 does not reveal its two unpaired electrons, but an MO approach does. The simple (t-tt description of the double bond in O2 does not predict that the bond in 2 is stronger than that in O2, but an MO approach does. As we show in the following sections, the molecular orbital model has even greater advantages in explaining bonding when Lewis structures show the presence of resonance. 

Thus there are five bonding electrons giving a bond order of 2.5, consistent with the bond length of 115 pm, versus 121 pm for the four-electron bond in O2 and 110 pm for the six-electron bond in N2. For these and other related molecules, the double-quartet model is a convenient and useful alternative to the conventional molecular orbital model. Moreover, it shows that for a singly bonded terminal atom such as F or Cl there is a ring of six nonbonding electrons rather than three separate lone pairs. As we will see in Chapters 7 and 8, this conclusion is confirmed by the analysis of electron density distributions. 

Theories of solvated electrons may be divided as follows (Jortner, 1970 Webster and Howat, 1972 Kevan, 1974 Kestner, 1976) (1) molecular orbital models, (2) structural models, (3) continuum models, and (4) semicontinuum models. We will consider these models a little in detail. 

A molecular orbital model (MO) treats all electrons belonging to a fixed number of solvent molecules plus an excess electron in the resultant field of the nuclei of the molecules as being in a fixed configuration. The nuclei belonging to a particular molecule normally keep the ground state structure of that molecule. The relative distances and orientations of these molecules are varied until energetic, and if possible configurational, stability is obtained. In some cases, molecular distortions have been considered. 

Scheme la shows the approximate molecular orbital model for the hypervalent X-E-X 3c-4e in EX4, such as SC14. Characters of the three molecular orbitals are bonding (v /i), nonbonding (v /2), and anti-bonding (v /3). Two electrons are in and two in v 2. Electrons in v 2 localize on X of X-E-X and the hypervalent bonds are mainly characterized by v 2. Consequently,... 

The hypervalent chalcogen chemistry has been developed to higher coordinated species with various ligands,7 10 where TBP changes to square pyramidal (SP) or octahedral (Oh), etc. Additional atomic orbitals of E, such as an 5-orbital, may operate to stabilize the structures.10b The concept is also extended over linear a-bonds constructed by m ( > 4) atoms with n electrons (extended hypervalent bonds mc-ne (in > 4)).11 14 The approximate molecular orbital model for mc-ne (m > 4) is also exhibited in Scheme la, exemplified by 4c-6e. 

The muon and 29Si hyperfine parameters provide compelling evidence in support of the BC model. In the simple molecular-orbital model proposed by Cox and Symons (1986) the muon is located at the center of a Si—Si bond near a node in the unpaired electron spin density, which is... 

The molecular orbital model can also be applied to complexes of the d-block elements. In octahedral complexes the d-orbitals of the metal are not degenerate, as they are in the free metal, because of the interaction between the ligand and metal orbitals. The five d-orbitals are split into three t2g (nonbonding) and two e (antibonding) MOs that is ... 

Chemical bonding can be described in terms of a molecular orbital model. The molecular orbital approach is based on the idea that, as electrons in atoms occupy atomic orbitals, electrons in molecules occupy molecular orbitals. Molecular orbitals have many of the same properties as atomic orbitals. They are populated by electrons, beginning with the orbital with the lowest energy and a molecular orbital is full when it contains two electrons of opposite spin. 

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