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Topic 2

Structure and Bonding Models of CovalentCompounds of p-Block Elements

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Bonding

• Many different approaches to describe bonding:

• Ionic Bonding:Elements with large electronegativity differences; bonding isdue to electrostatic interaction between ions (formed by thetransfer of electrons between the two bonded atoms)

• Covalent Bonding:Electronegativity difference smaller; covalent interactionthrough sharing of electrons between bonded atoms)

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Bond Distance and Atom Radius

• The length of a covalent bond is given by the internucleardistance–> determined by microwave spectroscopy or diffractionmethods (X-ray, neutron or electron diffraction)

• Covalent radius of an atom X = half of the bond length of ahomonuclear single bond X–X

• Note: The van der Waals radius of an atom X is half of thedistance of closest approach of two non-bonded atoms(larger than the covalent radius)

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Covalent Bonding

• Modern models describe chemical bond based on quantummechanical methods using molecular orbitals

• Earlier models and concepts are much simpler, but can stillbe very useful for qualitative description of moleculestructures and geometries:

– Lewis theory– Resonance structures and formal charges– Valence Shell Electron Pair Repulsion Theory (VSEPR)

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Lewis Theory: The Octet Rule

• Lewis’ theory of bonding (1916) was one of the earliestmodels to have success

• Basic concept: OCTET RULE:Main group elements are surrounded by 8 electrons whenforming covalent compounds

• Note: works well with second period elements, but runs intoproblems with all others

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Bond Order

• Often, Lewis structures can be used to estimate bond ordersthat correlate well with experimentally measured bondstrengths and lengths:

N N

O O

F F Single bond: bond order =

Double bond: bond order =

Triple bond: bond order =

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Formal Charges

• Formal charges are calculated by dividing shared electronsequally between the bonded atom pair

Formal charge = number of electrons in valence shell –number of assigned electrons

• Note: A molecule may have more than one plausible Lewisstructure–> The best Lewis structure is the one that has the leastcharge separation and puts the negative charge on the mostelectronegative elements

N N O N N O N N O

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Oxidation Numbers

• Oxidation numbers are calculated by assigning sharedelectrons to the more electronegative atom

Oxidation number = number of electrons in valence shell – number of assigned electrons

• General rules for assigning oxidation numbers in molecules:– Group 1 metals:

– Group 2 metals:– Al is only Al3+

– F is always F–

– O is always O2–

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Resonance Structures

• Some molecules have more than one distinct Lewisstructures:Acetic acid:

• Note: The ‘real’ structure is an average of the two drawnstructures = resonance hybrid

–> the bond order of the the C–O bonds is therefore

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Failures of the Lewis Model

• Molecules with odd numbers of electrons exist than 8electrons in the valence shell of their atoms exist:

NOBCl3

–> both are stable molecules

• A central atom may have more than 8 electrons (for n > 3 =third period and higher period main group elements)

SF6

• O2

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VSEPR Theory

• Valence Shell Electron Pair Repulsion Theory is useful forpredicting the geometry of main group compounds

• Theory is based on idea, that molecules adopt the geometryfor which the repulsion between electron pairs (bonding ornon-bonding) are as small as possible

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Geometries with Minimum Repulsion

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Rules

1) Count all single bond electron pairs (BP)2) Count all non bonding electron pairs = lone pairs (LP)3) Calculate sum of BP + LP4) Determine geometry according to previous rules

Note: Four double and triple bonds only ONE BP is counted,since the second (or third) does not require much morespace

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Linear Geometry

Cl Be Cl O C O

180° 180°

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Trigonal Geometry

Note:• Lone pair require more space than bonding pairs

• One non-bonding electron requires less space than abonding pair

B

F

F F

120°

NO O

134°

NO O

115°

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Tetrahedral Geometry

The arrangement of LP and BP is tetrahedral, but the molecular shape isnamed after the arrangements of the ATOMS!

C

H

H H

109.5°

H

107° 104°

NH H

H OHH

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Trigonal Bipyramidal Geometry (TBP)

Note: Lone pair are placed equatorial to minimize repulsion

l P

Cl

Cl Cl

Cl

86°

Br

F

F

F Xe

F

F

S

F

F F

F S

F F

FF

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Octahedral Geometry

Note: Lone pair are placed such to minimize repulsion

S

F

F F

FF

FI

F

F

FF

FXe

F

FF

F

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Exceptions to VSEPR

• Transition metal compounds do not follow VSEPR rules• Species that are sterically crowded often do not obey

VSEPR

XeF6

TeCl62–

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Molecular Orbital Theory

• In principle, the electronic structure of molecules can beworked out in the same way as for atoms:–> solve the Schrödinger equation

• This gives molecular orbitals rather than atomic orbitals

• But: It is difficult to solve the Schrödinger equation formolecular species (only through approximation!)

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LCAO approximation

• LCAO = “Linear Combination of Atomic Orbitals”• The wavefunctions of molecular orbitals can be approximated by taking linear

combinations of atomic orbitals

Ψ Ψ Ψσ = +[ ]12 1 1s a s bH H( ) ( )

linear combination (addition) of the wavefunction from two 1s orbitals

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LCAO approximation

• A second MO (molecular orbital) can be obtained via subtraction of twoAOs

Ψ Ψ Ψσ * ( ) ( )= −[ ]12 1 1s a s bH H

linear combination (subtraction) of the wavefunction from two 1s orbitals

nodal plane

–> the resulting wavefunction has a nodal plane perpendicular tothe H–H bond axis (electron density = zero); the energy of anelectron in this orbital is higher compared to the additive linearcombination = “antibonding orbital”

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First Period Diatomic Molecules

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Linear Combinations of pz Orbitals

• Addition of two pz AOs results a bonding σp MO, subtractionwill give an antibonding σp* MO with a nodal planeperpendicular to the bond axis

Ψ Ψ Ψσ * ( ) ( )= −[ ]12 2 2p a p bz z

H H

Ψ Ψ Ψσ = +[ ]12 2 2p a p bz z

H H( ) ( )

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Linear Combinations of px and py Orbitals

• Addition of two px (or py) AOs results a bonding πp MO containing anodal plane along the bond axis:

• Subtraction results an antibonding πp* MO with two nodalplanes: one plane perpendicular and one parallel to the bondaxis

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Energy Level Diagram

energy

• Electrons are filled according to the same guidelines as formultielectron elements (Aufbau principle)

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Energy Level D

iagram

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Rules for the Use of MOs

• When two AOs to give MOs, two MOs will be produced• For mixing AOs must have similar energies• Each orbital can have a total of two electrons (Pauli

principle)• Lowest energy orbitals are filled first (Aufbau principle)• Unpaired electrons have parallel spin (Hund’s rule)

Bond order = 1/2 (bonding electrons – antibonding electrons)

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Molecular Oxygen

energy

AOs AOs

Bond order = unpaired electrons

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Molecular Fluorine

energy

AOs AOs

Bond order =

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Neon

energy

AOs AOs

Bond order =

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Orbital Mixing

• Orbitals with similar energy interact, if they have theappropriate symmetries

• The σ2p and σ2s orbitals are symmetry related and give riseto two new orbitals, one with higher and one with lowerenergy

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energy

Note: With mixing the σg orbital is higher in energy than the π2p orbitals

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Energy Levels

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Boron Molecule

energy

Bond order = unpaired electrons

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Carbon Molecule

energy

Bond order = unpaired electrons

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Photoelectron Spectroscopy

• UV-photoelectron spectroscopy can be used to verify the MOenergy level diagram:Molecules are ionized with monochromatic light:

N2(g) + hν N2(g)+ + e–

the kinetic energy of the resulting photoelectrons ismeasured

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Photoelectron Spectrum of Nitrogen

π2p

σ2p

σ2s

Note: the orbital energies may shiftwhen an electron is removed

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Molecular Nitrogen

• According to calculations the σg orbital is higher in energy than thetwo π2p orbitals:

energy

Bond order = unpaired electrons

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Beryllium Molecule

energy

Bond order =

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Lithium Molecule

energy

Bond order = unpaired electrons

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Bond Order vs. Bond Length & Energy