Shapes of Molecular Orbitals

Bonding orbital, electrons of highly polar covalent bond 

In Section 7-9 we described resonance formulas for molecules and polj tomic ions. Resonance is said to exist when two or more equivalent Lewis formulas can be written for the same species and a single such formula does not account for the properties of a substance. In molecular orbital terminology, a more appropriate description involves delocalization of electrons. The shapes of molecular orbitals for species in which electron delocalization occurs can be predicted by combining all the contributing atomic orbitals. 

O Lewis formulas of the three valence bond resonance structures 

0 Representation of the /i-orbital overlap in the valence bond resonance structures, In each resonance form, the p orbitals on two atoms would overlap to form then components of the hypothetical double bonds. Each 0 atom has two additional sp2 orbitals (not shown) in the plane of the nuclei. Each of these additional sp orbitals contains an oxygen unshared pair. 

Q In the MO description, the electrons in the n-bonded region are spread out, or delocalized, over all four atoms of the C03 ion. This MO description is more consistent with the experimental observation of equal bond lengths and energies than are the valence bond pictures in (a) and (b). 

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Figure 13.2 Combination of three atomic p orbitals to form three n molecular orbitals in the allyl radical. The bonding n molecular orbital is formed by the combination of the three p orbitals with lobes of the same sign overlapping above and below the plane of the atoms. The nonbonding n molecular orbital has a node at C2. The antibonding n molecular orbital has two nodes between Cl and C2, and between C2 and C3. The shapes of molecular orbitals for the allyl radical calculated using quantum mechanical principles are shown alongside the schematic orbitals.

Figure 13.3 The n molecular orbitals of the allyl cation. The allyl cation, like the allyl radical, is a conjugated unsaturated system. The shapes of molecular orbitals for the allyl cation calculated using quantum mechanical principles are shown alongside the schematic orbitals. 

Important point Ethene is not actually formed by bringing together two carbon atoms and four hydrogen atoms individual carbon atoms do not hybridize their atomic orbitals and then combine, We are simply trying to rationalize the shapes of molecular orbitals. Hybridization and LCAO are tools to help us accomplish this. 

This book is an introduction to quantum mechanics and mathematics that leads to the solution of the Schrodinger equation. It can be read and understood by undergraduates without sacrificing the mathematical details necessary for a complete solution giving the shapes of molecular orbitals seen in every chemistry text. Readers are introduced to many mathematical topics new to the undergraduate curriculum, such as basic representation theory, Schur s lemma, and the Legendre polynomials. 

Energy and Shape of Molecular Orbitals The bonding MO is lower in energy and the antibonding MO higher in energy than the AOs that combined to form them. Let s examine Figure 11.14 to see why this is so. 

Assume at the beginning (zeroth iteration) a certain shape of molecular orbitals. ... 

The shape of molecular orbitals can be seen in terms of hybrid orbitals, when the electrons forming a bond are in different types of... 

Bond Order and Bond Stability 9-4 Homonuclear Diatomic Molecules 9-5 Heteronuclear Diatomic Molecules 9-6 Delocalization and the Shapes of Molecular Orbitals... 

Molecular orbital (MO) theory begins with the hypothesis that electrons in atoms exist in atomic orbitals and assumes that electrons in molecules exist in molecular orbitals. Just as the Schrbdinger equation can be used to calculate the energies and shapes of atomic orbitals, molecular orbital theory assumes that the Schrodinger equation can also be used to calculate the energies and shapes of molecular orbitals. Following is a summary of the rules used in applying molecular orbital theory to the formation of covalent bonds. 

Moreover, many studies use the nature and shape of molecular orbitals for interpreting electronic effects. However, it should be kept in mind that the total energy of a molecule is invariant with respect to the occupied molecular orbitals. In other words, occupied molecular orbitals may strongly mix with each other without changing the energy of the system. Therefore, the interpretation of orbital shapes usually is not a unique source of information. 

The soft nucleophiles preferably attack the C4 atom, which can be well accounted for by greater localization of the 7r -orbital at this center in comparison with C2. The shapes of molecular orbitals of the species XVI obtained by means of STO-3G ab initio calculations [26] help clarify the reason for which the complexation with metal cations and the protonation results in the change of... 

A self-consistent field configuration interaction method in which simultaneous optimization of both the shapes of molecular orbitals and the contributions from different electronic configurations is carried out variational ly. 

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