Chemistry - A Molecular Science

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Chapter 6 Molecular Structure & Bonding


(b) out-of-phase combination = * MO

s

(a) in-phase combination =

MOs
= =

Figure 6.19

σ bonds from end-on combinations of p orbitals
+
b) out-of-phase
= * orbitalp

=
+
a) in-phase= orbital
p

=

Nodal plane perpendicular to bondingaxis makes the orbital antibondingNodal planes containing the bondingaxis makes the orbital a orbital

p

Figure 6.20

π bonds from side-on combinations of p orbitals

DE

DE*

ss

s* s

Energy

= =

Figure 6.21 MO diagram for combining two s orbitals

While the color of each AO in diagrams su


ch as Figure 6.18 represents its phase in the


combination, the


size of the sphere represents its relative contribution to the MO


. The fact


that the two AOs are the same size in Figure 6.18 means that the two AOs contribute equally to the MO, which means that the electr


on density in the MO is distributed equally


over both atoms. MOs can be represented by e


ither the resulting combination as shown on


the right of Figure 6.18 or as the combining orbitals as shown on the left of Figure 6.18. We will use the latter method, where spheres


showing the sign and relative magnitude of


the contributing AOs will be shown rather than the resulting MO.


As shown in Figure 6.18,


and σ



  • MOs are formed from the combination of two s σ


orbitals on different atoms. However,


σ
interactions are also pr

oduced by the head-on


combination of p orbitals. The combination of


orbitals that mixes lobes of the same phase


(Figure 6.19a) increases electron density


on the bonding axis, so it is a


bonding orbital. σ


The combination in which lobes of opposite phase interact (Figure 6.19b) annihilates electron density between the two atoms to produce a nodal plane perpendicular to the bonding axis, so it is a



  • antibonding orbital. σ


The side-on combination of two p orbitals (Figure 6.20) results in no electron density
on the bonding axis, so both co

mbinations are classified as


. The combination of orbitals π


of the same phase increases electron density


between the bound atoms, so it is the


π


bonding orbital. The combination in which


lobes of opposite phase interact produces a


nodal plane perpendicular to the bonding axis, so it is an antibonding



  • orbital. π


DIATOMIC MOLECULES The two nuclei in a


homonuclear diatomic molecule


are nuclei of the


same


element, so


the interacting atomic orbitals (AOs) are id


entical and contribute equally to the MO.


Consequently, the electron density in each MO


is symmetric and the bonds are nonpolar.


Each MO is characterized by an energy level, and electrons occupy the molecular orbitals in the same manner that they do atomic orbitals;


i.e.


, they fill the molecular orbitals at


lowest energy while obeying both Hund’s ru


le and the Pauli Exclusion Principle.


The energies of the


and σ



  • orbitals relative to the s orbσ


itals used to construct them


are shown in an MO diagram. Three important characteristics of MO diagrams like those in Figure 6.21 are:



  1. The energy of bonding interactions is


lower than that of the atomic orbitals (

E). Δ


  1. The energy of antibonding orbitals is


higher than that of the atomic orbitals (

E*). Δ

3.

E* > Δ

E. Δ

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