Copyright © Houghton Mifflin Company. All rights reserved. 14a–1 The Central Themes of VB Theory Basic Principle A covalent bond forms when the orbitals

Copyright © Houghton Mifflin Company. All rights reserved. 14a–1

The Central Themes of VB Theory

Basic Principle

•A covalent bond forms when the orbitals of two atoms overlap and are occupied by a pair of electrons that have the highest probability of being located between the nuclei.

Themes

•These overlapping orbitals can have up to two electrons that must have opposite spins (Pauli principle).

•The valence orbitals in a molecule are different from those in isolated atoms.


Figure 12.18: Three representations of the hydrogen 1s


Figure 13.1: (a) The interaction of two hydrogen atoms (b) Energy profile as a function of the distance

between the nuclei of the hydrogen atoms.





Figure 12.19b: Representation of the 2p orbitals.


Hydrogen, H2

Hydrogen fluoride, HF

Fluorine, F2


Figure 14.1: (a) Lewis structure of the methane molecule (b) the tetrahedral molecular geometry

of the methane molecule.


Figure 14.2: valence orbitals on a free carbon atom


Figure 14.1: (a) Lewis structure of the methane molecule (b) the tetrahedral molecular geometry

of the methane molecule.


Figure 14.3: native 2s and three 2p atomic orbitals characteristic of a free carbon atome are combined to

form a new set of four sp3 orbitals.


s

px py pz

Carbon 1s22s22p2

Carbon could only make two bondsif no hybridization occurs. However,carbon can make four equivalent bonds.

sp3

hybrid orbitals

Ene

rgy

sp3

C atom of CH4 orbital diagram

B

A

BB

B

Brown, LeMay, Bursten, Chemistry The Central Science, 2000, page 321


Figure 14.4: Cross section of an sp3 orbital


The four sp3 hybrid orbitals in CH4

Promotion


Figure 11.9 The bonds in ethane.

both C are sp3 hybridizeds-sp3 overlaps to bonds

sp3-sp3 overlap to form a bondrelatively even

distribution of electron density over all bonds (Greek sigma) bonds

have axial symmetry andgood overlap

Rotation about C-Cbond allowed.


Figure 14.6: Tetrahedral set of four sp3 orbitals on the carbon atom


Figure 14.7: The nitrogen atom in ammonia is sp3 hybridized.



Promotion



Promotion


The four sp3 hybrid orbitals in NH3

Promotion

N



Promotion

N


Figure 11.5 The sp3 hybrid orbitals in H2O

Lone pairs


Diamond - sp3 hybridized C


Figure 14.8: The hybridization of the s, px, and py atomic orbitals results in the formation of three

sp2 orbitals centered in the xy plane.

NB: The remaining p orbital can be empty or serve another function


The three sp2 hybrid orbitals in BF3

Promotion

Region of overlap

Note the single left overUnhybridized p orbital on B


Hybrid Orbitals

2s 2p

Ground-state B atom

s

px py pzEne

rgy

sp2 2p

B atom of BH3 orbital diagram

hybridize

s orbital

2s 2p

B atom with one electron “promoted”

sp2

hybrid orbitals

p orbitals sp2 hybrid orbitals shown together

(large lobes only)three sps hybrid orbitals

H

H

HB


Figure 14.10: When one s and two p oribitals are mixed to form a set of three sp2 orbitals, one p orbital remains unchanged and

is perpendicular to the plane of the hybrid orbitals.


Figure 14.13: (a) The orbitals used to form the bonds in ethylene. (b) The Lewis structure for ethylene.


The plastics shown here were manufactured with ethylene.

Source: Comstock - Mountainside, NJ


Figure 14.11: The s bonds in ethylene.


Figure 14.12: A carbon-carbon double bond consists of a s bond and a p bond.


Figure 14.48: The benzene molecule consists of a ring of six carbon atoms with one hydrogen atom bound to

each carbon; all atoms are in the same plane.

• Sp2 hybridized


Graphite – sp2 hybridized C


Fullerene-C60 and Fullerene-C70

What hybridization of C describes the structures?


Figure 14.14: When one s orbital and one p orbital are hybridized, a set of two sp orbitals oriented at 180 degrees results.


The sp hybrid orbitals in gaseous BeCl2

Why are sp hybrids invoked? Because if Be made one bond with its2s and one bond with a 2p orbital, then the two Be-Cl bonds would have different strengths & lengths. But both bonds are identical.

Promotion

Promote to create two half filled orbitals that participate in bond formation

Filled 2s orbital can’t bond to Cl


The two sp hybrid orbitals in gaseous BeCl2

Note the two “leftover” p orbitals of BeRegion of overlap


Figure 14.15: The hybrid orbitals in the CO2 molecule


Figure 14.16: orbital energy level diagram for the formation of sp hybrid orbitals of carbon.


Figure 14.17: Orbitals of an sp hybridized carbon atom


Figure 14.18: Orbital arrangement for an sp2 hybridized oxygen atom


Figure 14.19: (a) Orbitals predicted by the LE model to describe (b) The Lewis structure for carbon dioxide


Hybrid Orbitals

sp sp2 sp3 sp3d sp3d2

Types of Hybrid Orbitals

Shapes: linear triangular tetrahedral trig. bipyram. Octahedral# orbitals: 2 3 4 5 6


Figure 14.20: (a) An sp hybridized nitrogen atom (b) The s bond in the N2 molecule (c) the two p bonds

in N2 are formed



Promotion

N



Promotion

2p

sp

2p

sp


The conceptual steps from molecular formula to the hybrid orbitals used in bonding.

Molecular formula

Lewis structure

Molecular shape and e- group arrangement

Hybrid orbitals

Step 1 Step 2 Step 3


sp3 hybridization of a carbon atom

4 atomicorbitals

s p

4 hybridizedorbitals

sp3

4 tetrahedralbonds

sp3




sp3 hybridization of a nitrogen atom

4 atomicorbitals

s p

3 tetrahedralbonds with1 lone pair sp3


sp3


sp3 hybridization of a nitrogen atom

N


sp3 hybridization of a oxygen atom

4 atomicorbitals

s p

2 tetrahedralbonds with2 lone pairs sp3


sp3


sp3 hybridization of a oxygen atom



4 atomicorbitals

s p

3 trigonalBonds+ 1 for a pi bond sp2 px


sp2 px






sp2 hybridization of an oxygen atom

4 atomicorbitals

s p

1 trigonalBond with2 lone pairs+ 1 for a pi bond

sp2 px


sp2 px


Figure 14.19: (a) Orbitals predicted by the LE model to describe (b) The Lewis structure for carbon dioxide


sp hybridization of a carbon atom

4 atomicorbitals

s p


sp

2 linearbonds+ 2 for pi bonds sp py

py

px

px



sp hybridization of an nitrogen atom

4 atomicorbitals

s p


sp

1 linearBonds with1 lone pair+ 2 for pi bonds

sp py

py

px

px


Figure 14.20: (a) An sp hybridized nitrogen atom (b) The s bond in the N2 molecule (c) the two p bonds

in N2 are formed


Figure 14.21: A set of dsp3 hybrid orbitals on a phosphorous atom


Hybridization Involving d Orbitals

3s 3p 3d 3s 3p 3d

promote

five sp3d orbitals 3dF

F

FP

F

F

A Be

Be

Be

Ba

Ba

Trigonal bipyramidal

hybridize

degenerateorbitals

(all EQUAL)

unhybridized P atomP = [Ne]3s23p3

vacant d orbitals


Figure 11.6 The five sp3d hybrid orbitals in PCl5


Figure 14.22: The orbitals used to form the bonds in the PCL5 molecule


Figure 14.23: An octahedral set of d2sp3 orbitals on a sulfur atom


Figure 11.7

The six sp3d2 hybrid orbitals in SF6


Figure 14.24: The relationship among the number of effective pairs, their spatial arrangement,

and the hybrid orbital set required


Figure 14.24: The relationship among the number of effective pairs, their spatial arrangement,

and the hybrid orbital set required (cont’d)


Figure 11.8

The conceptual steps from molecular formula to the hybrid orbitals used in bonding.

Molecular formula

Lewis structure

Molecular shape and e- group arrangement

Hybrid orbitals

Figure 10.1

Step 1

Figure 10.12

Step 2 Step 3

Table 11.1








Figure 14.25: The combination of hydrogen 1s atomic orbitals to form MOs


Figure 14.25: The combination of hydrogen 1s atomic orbitals to form MOs

Copyright © Houghton Mifflin Company. All rights reserved. 14a–7710.6


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Amplitudes of wave functions added

An analogy between light waves and atomic wave functions.

Amplitudes of wave functions subtracted.

NOTE: +/- signs show PHASES of waves, NOTCHARGES!


Figure 14.26: (a) The MO energy-level diagram for the H2 molecule (b) The shapes of the Mos are obtained

by squaring the wave functions for MO1 and MO2.


Figure 14.27: Bonding and anitbonding MOs


Figure 14.30: The MO energy-level diagram for the He2

+ ion.

# BONDING e’s = 2

# ANTIBONDING e’s = 1

Bond order = ½(2-1) = ½


Figure 14.31: The MO energy-level diagram for the H2

+ ion


Figure 14.28: MO energy-level diagram for the H2 molecule


Figure 14.29: The MO energy-level diagram for the He2 molecule


Figure 14.30: The MO energy-level diagram for the He2

+ ion.



+ ion



- ion



Figure 14.33: The relative sizes of the lithium 1s and 2s atomic orbitals


Figure 14.34: The MO energy-level diagram for the Li2 molecule


Figure 14.35: The three mutually perpendicular 2p orbitals on tow adjacent boron atoms.


Figure 14.36: The two p oribitals on the boron atom that overlap head-on combine to form

bonding and antibonding orbitals.


Figure 14.37: The expected MO energy-level diagram for the combustion of the 2P orbitals

on two boron atoms.


Figure 14.37: The expected MO energy-level diagram for the combustion of the 2P orbitals

on two boron atoms.


Figure 14.38: The expected MO energy-level diagram for the B2 molecule


Figure 14.39: An apparatus used to measure the paramagnetism of a sample


Figure 14.40: The correct MO energy-level diagram for the B2 molecule.


Figure 14.41: The MO energy-level diagrams, bond orders, bond energies, and bond lengths for the

diatomic molecules, B2 through F2.


Figure 14.42: When liquid oxygen is poured into the space between the poles of a strong magnet, it remains

there until it boils away.

Source: Donald Clegg


Figure 14.43: The MO energy-level diagram for the NO molecule


Figure 14.44: The MO energy-level diagram for both the NO+ and CN- ions


Figure 14.45: A partial MO energy-level diagram for the HF molecule


Figure 14.46: The electron probability distribution in the bonding MO of the HF molecule


Figure 14.47: The resonance structures for O3 and NO3

-


Figure 14.48: The benzene molecule consists of a ring of six carbon atoms with one hydrogen atom bound to

each carbon; all atoms are in the same plane.


Figure 14.49: The s bonding system in the benzene molecule


Figure 14.50: The MO system in benzene is formed by combining the six p orbitals


Figure 14.51: The p orbitals used to form the bonding system in the NO3

- ion



Electromagnetic spectrum

λν





λν=c








Figure 14.52: Schematic representation of two electronic energy levels in a molecule


Figure 14.53: The various types of transitions are shown by vertical arrows.


Figure 14.54: Spectrum corresponding to the changes indicated in Fig. 14.53.


Figure 14.55: The molecular orbital diagram for the ground state of NO+


The molecular structure of beta-carotene


Figure 14.57: The electronic absorption spectrum of beta-carotene.

VIBRATIONS

VIBRATIONS


Figure 14.58: The potential curve for a diatomic molecule


Figure 14.59: Morse energy curve for a diatomic molecule.


Figure 14.60: The three fundamental vibrations for sulfur dioxide


Figure 14.61: The infrared spectrum of CH2Cl2.




Figure 14.62: Representations of the two spin states of the proton interacting


Figure 14.63: The molecular structure of bromoethane


Figure 14.64: The expected NMR spectrum for bromoethane


Figure 14.65: The spin of proton Hy can by "up" or "down"


Figure 14.66: The spins for protons Hy can be "up", can be opposed (in 2 ways) or can both be "down"


Figure 14.67: The spins for the protons Hy can by arranged as shown in (a) leading to four different magnetic environments


Figure 14.68: The NMR spectrum of CH3CH2Br (bromoethane) with TMS reference


Figure 14.69: The molecule (2-butanone)






Figure 14.70: A technician speaks to a patient before heis moved intot eh cavity of a magnetic

resonance imaging (MRI) machine.


Figure 14.71: A colored Magnetic Resonance Imaging (MRI) scan through a human head,

showing a healthy brain in side view.

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Copyright © Houghton Mifflin Company. All rights reserved. 14a–1 The Central Themes of VB Theory Basic Principle A covalent bond forms when the orbitals