Chapter 9 Molecular Geometries and Bonding Theories

Chapter 9Chapter 9Molecular Molecular

GeometriesGeometriesand Bonding and Bonding

TheoriesTheories

Molecular ShapesMolecular Shapes

The shape of a The shape of a molecule plays an molecule plays an important role in important role in its reactivity.its reactivity.

By noting the By noting the number of bonding number of bonding and nonbonding and nonbonding electron pairs we electron pairs we can easily predict can easily predict the shape of the the shape of the molecule.molecule.

What Determines the What Determines the Shape of a Molecule?Shape of a Molecule?

Simply put, electron Simply put, electron pairs, whether they be pairs, whether they be bonding or bonding or nonbonding, repel nonbonding, repel each other.each other.

By assuming the By assuming the electron pairs are electron pairs are placed as far as placed as far as possible from each possible from each other, we can predict other, we can predict the shape of the the shape of the molecule.molecule.

Electron DomainsElectron Domains

We can refer to the We can refer to the electron pairs as electron pairs as electron domains.electron domains.

In a double or triple In a double or triple bond, all electrons bond, all electrons shared between those shared between those two atoms are on the two atoms are on the same side of the same side of the central atom; central atom; therefore, they count therefore, they count as one electron as one electron domain.domain.

• This molecule’s central atom has four electron domains.

Valence Shell Electron Valence Shell Electron Pair Repulsion Theory Pair Repulsion Theory

(VSEPR)(VSEPR)““The best The best arrangement of arrangement of a given number a given number of electron of electron domains is the domains is the one that one that minimizes the minimizes the repulsions repulsions among them.”among them.”

Electron-Electron-Domain Domain

GeometriesGeometries

These are the These are the electron-domain electron-domain geometries for geometries for two through six two through six electron electron domains around domains around a central atom. a central atom.

Electron-Domain Electron-Domain GeometriesGeometries

All one must do is All one must do is count the number count the number of electron of electron domains in the domains in the Lewis structure.Lewis structure.

The geometry will The geometry will be that which be that which corresponds to corresponds to that number of that number of electron domains.electron domains.

Molecular GeometriesMolecular Geometries

The electron-domain geometry is often The electron-domain geometry is often notnot the shape of the molecule, however. the shape of the molecule, however.

The molecular geometry is that defined The molecular geometry is that defined by the positions of by the positions of onlyonly the atoms in the the atoms in the molecules, not the nonbonding pairsmolecules, not the nonbonding pairs..

Molecular GeometriesMolecular Geometries

Within each Within each electron domain, electron domain, then, there then, there might be more might be more than one than one molecular molecular geometry.geometry.

Linear Electron DomainLinear Electron Domain

In this domain, there is only one In this domain, there is only one molecular geometry: molecular geometry: linearlinear..

NOTE: If there are only two atoms in NOTE: If there are only two atoms in the molecule, the molecule will be the molecule, the molecule will be linear no matter what the electron linear no matter what the electron domain is.domain is.

Trigonal Planar Electron Trigonal Planar Electron DomainDomain

There are two molecular geometries:There are two molecular geometries: Trigonal planarTrigonal planar, if all the electron domains , if all the electron domains

are bondingare bonding BentBent, if one of the domains is a , if one of the domains is a

nonbonding pair.nonbonding pair.

Nonbonding Pairs and Nonbonding Pairs and Bond AngleBond Angle

Nonbonding pairs are Nonbonding pairs are physically larger than bonding physically larger than bonding pairs.pairs.

Therefore, their repulsions are Therefore, their repulsions are greater; this tends to decrease greater; this tends to decrease bond angles in a molecule.bond angles in a molecule.

Multiple Bonds and Bond Multiple Bonds and Bond AnglesAngles

Double and triple Double and triple bonds place bonds place greater electron greater electron density on one density on one side of the central side of the central atom than do atom than do single bonds.single bonds.

Therefore, they Therefore, they also affect bond also affect bond angles.angles.

Tetrahedral Electron Tetrahedral Electron DomainDomain

There are three molecular geometries:There are three molecular geometries: TetrahedralTetrahedral, if all are bonding pairs, if all are bonding pairs Trigonal pyramidalTrigonal pyramidal if one is a nonbonding pair if one is a nonbonding pair BentBent if there are two nonbonding pairs if there are two nonbonding pairs

Trigonal Bipyramidal Trigonal Bipyramidal Electron DomainElectron Domain

There are two There are two distinct distinct positions in positions in this geometry:this geometry: AxialAxial EquatorialEquatorial


Lower-energy conformations result Lower-energy conformations result from having nonbonding electron from having nonbonding electron pairs in equatorial, rather than axial, pairs in equatorial, rather than axial, positions in this geometry.positions in this geometry.


There are four There are four distinct distinct molecular molecular geometries in geometries in this domain:this domain: Trigonal Trigonal

bipyramidalbipyramidal SeesawSeesaw T-shapedT-shaped LinearLinear

Octahedral Electron Octahedral Electron DomainDomain

All positions are All positions are equivalent in the equivalent in the octahedral octahedral domain.domain.

There are three There are three molecular molecular geometries:geometries: OctahedralOctahedral Square Square

pyramidalpyramidal Square planarSquare planar

Larger MoleculesLarger Molecules

In larger In larger molecules, it molecules, it makes more sense makes more sense to talk about the to talk about the geometry about a geometry about a particular atom particular atom rather than the rather than the geometry of the geometry of the molecule as a molecule as a whole.whole.

Larger MoleculesLarger Molecules

This approach This approach makes sense, makes sense, especially especially because larger because larger molecules tend molecules tend to react at a to react at a particular site in particular site in the molecule.the molecule.

Next TimeNext Time

We continue Chapter 9We continue Chapter 9 For the Lab Exam next Wednesday, For the Lab Exam next Wednesday,

you have access to your lab manual you have access to your lab manual and your lab notebook and a and your lab notebook and a calculator.calculator.

PolarityPolarity

In Chapter 8 we In Chapter 8 we discussed bond discussed bond dipoles.dipoles.

But just because a But just because a molecule possesses molecule possesses polar bonds does polar bonds does not mean the not mean the molecule molecule as a wholeas a whole will be polar.will be polar.

PolarityPolarity

By adding the By adding the individual bond individual bond dipoles, one can dipoles, one can determine the determine the overall dipole overall dipole moment for the moment for the molecule.molecule.

PolarityPolarity

Overlap and BondingOverlap and Bonding

We think of covalent bonds forming We think of covalent bonds forming through the sharing of electrons by through the sharing of electrons by adjacent atoms.adjacent atoms.

In such an approach this can only occur In such an approach this can only occur when orbitals on the two atoms overlap.when orbitals on the two atoms overlap.

Overlap and BondingOverlap and Bonding Increased overlap Increased overlap

brings the electrons brings the electrons and nuclei closer and nuclei closer together while together while simultaneously simultaneously decreasing electron-decreasing electron-electron repulsion.electron repulsion.

However, if atoms get However, if atoms get too close, the too close, the internuclear repulsion internuclear repulsion greatly raises the greatly raises the energy.energy.

Hybrid OrbitalsHybrid Orbitals

But it’s hard to imagine tetrahedral, But it’s hard to imagine tetrahedral, trigonal bipyramidal, and other trigonal bipyramidal, and other geometries arising from the atomic geometries arising from the atomic orbitals we recognize.orbitals we recognize.


Consider Consider beryllium:beryllium: In its ground In its ground

electronic state, electronic state, it would not be it would not be able to form able to form bonds because it bonds because it has no singly-has no singly-occupied orbitals.occupied orbitals.


But if it absorbs But if it absorbs the small amount the small amount of energy needed of energy needed to promote an to promote an electron from the electron from the 22ss to the 2 to the 2pp orbital, it can orbital, it can form two bonds.form two bonds.

Hybrid OrbitalsHybrid Orbitals Mixing the Mixing the ss and and pp orbitals yields two orbitals yields two

degenerate orbitals that are hybrids of degenerate orbitals that are hybrids of the two orbitals.the two orbitals. These These spsp hybrid orbitals have two lobes like hybrid orbitals have two lobes like

a a pp orbital. orbital. One of the lobes is larger and more rounded One of the lobes is larger and more rounded

as is the as is the ss orbital. orbital.


These two degenerate orbitals would These two degenerate orbitals would align themselves 180align themselves 180 from each other. from each other.

This is consistent with the observed This is consistent with the observed geometry of beryllium compounds: geometry of beryllium compounds: linear.linear.


With hybrid orbitals the orbital diagram With hybrid orbitals the orbital diagram for beryllium would look like this.for beryllium would look like this.

The The spsp orbitals are higher in energy than orbitals are higher in energy than the 1the 1ss orbital but lower than the 2 orbital but lower than the 2pp..


Using a similar model for boron Using a similar model for boron leads to… leads to…

Hybrid OrbitalsHybrid Orbitals……three degenerate three degenerate spsp22

orbitals.orbitals.


With carbon we get…With carbon we get…


……four degeneratefour degenerate

spsp33 orbitals. orbitals.


For geometries involving expanded For geometries involving expanded octets on the central atom, we octets on the central atom, we must use must use dd orbitals in our orbitals in our hybrids.hybrids.


This leads to five This leads to five degenerate degenerate spsp33dd orbitals…orbitals…

……or six degenerate or six degenerate spsp33dd22 orbitals. orbitals.

Hybrid Hybrid OrbitalsOrbitals

Once you know Once you know the electron-the electron-domain domain geometry, you geometry, you know the know the hybridization hybridization state of the state of the atom.atom.

Valence Bond TheoryValence Bond Theory

Hybridization is a major player in Hybridization is a major player in this approach to bonding.this approach to bonding.

There are two ways orbitals can There are two ways orbitals can overlap to form bonds between overlap to form bonds between atoms.atoms.

Sigma (Sigma () Bonds) Bonds

Sigma bonds are characterized bySigma bonds are characterized by Head-to-head overlap.Head-to-head overlap. Cylindrical symmetry of electron Cylindrical symmetry of electron

density about the internuclear axis.density about the internuclear axis.

Pi (Pi () Bonds) Bonds

Pi bonds are Pi bonds are characterized characterized byby Side-to-side Side-to-side

overlap.overlap. Electron Electron

density above density above and below the and below the internuclear internuclear axis.axis.

Single BondsSingle Bonds

Single bonds are always Single bonds are always bonds, bonds, because because overlap is greater, overlap is greater, resulting in a stronger bond and resulting in a stronger bond and more energy lowering.more energy lowering.

Multiple BondsMultiple Bonds

In a multiple bond one of the In a multiple bond one of the bonds is a bonds is a bond and the rest are bond and the rest are bonds. bonds.


In a molecule like In a molecule like formaldehyde formaldehyde (shown at left) an (shown at left) an spsp22 orbital on orbital on carbon overlaps in carbon overlaps in fashion with the fashion with the corresponding corresponding orbital on the orbital on the oxygen.oxygen.

The unhybridized The unhybridized pp orbitals overlap in orbitals overlap in fashion.fashion.


In triple bonds, In triple bonds, as in acetylene, as in acetylene, two two spsp orbitals orbitals form a form a bond bond between the between the carbons, and two carbons, and two pairs of pairs of pp orbitals orbitals overlap in overlap in fashion to form fashion to form the two the two bonds. bonds.

Next TimeNext Time

We finish Chapter 9We finish Chapter 9 For the Lab Exam Wednesday, you For the Lab Exam Wednesday, you

have access to your lab manual and have access to your lab manual and your lab notebook and a calculator.your lab notebook and a calculator.

Delocalized Electrons: Delocalized Electrons: ResonanceResonance

When writing Lewis structures for When writing Lewis structures for species like the nitrate ion, we draw species like the nitrate ion, we draw resonance structures to more resonance structures to more accurately reflect the structure of the accurately reflect the structure of the molecule or ion.molecule or ion.


In reality, each of the In reality, each of the four atoms in the four atoms in the nitrate ion has a nitrate ion has a pp orbital.orbital.

The The pp orbitals on all orbitals on all three oxygens overlap three oxygens overlap with the with the pp orbital on orbital on the central nitrogen.the central nitrogen.


This means the This means the electrons are electrons are not not localizedlocalized between the between the nitrogen and one of the nitrogen and one of the oxygens, but rather are oxygens, but rather are delocalized delocalized throughout throughout the ion.the ion.

ResonanceResonance

The organic The organic molecule benzene molecule benzene has six has six bonds bonds and a and a pp orbital on orbital on each carbon atom.each carbon atom.

ResonanceResonance

In reality the In reality the electrons in benzene are electrons in benzene are not not localizedlocalized, but , but delocalizeddelocalized..

The even distribution of the The even distribution of the electrons in electrons in benzene makes the molecule unusually benzene makes the molecule unusually stable.stable.

Molecular Orbital (MO) Molecular Orbital (MO) TheoryTheory

Though valence bond Though valence bond theory effectively theory effectively conveys most conveys most observed properties observed properties of ions and of ions and molecules, there are molecules, there are some concepts better some concepts better represented by represented by molecular orbitals. molecular orbitals.


In MO theory, we In MO theory, we invoke the wave invoke the wave nature of electrons.nature of electrons.

If waves interact If waves interact constructively, the constructively, the resulting orbital is resulting orbital is lower in energy: a lower in energy: a bondingbonding molecular molecular orbital.orbital.


If waves interact If waves interact destructively, the destructively, the resulting orbital is resulting orbital is higher in energy: higher in energy: an an antibondingantibonding molecular orbital.molecular orbital.

MO TheoryMO Theory

In HIn H22 the two the two electrons go into the electrons go into the bonding molecular bonding molecular orbital.orbital.

The bond order is one The bond order is one half the difference half the difference between the number between the number of bonding and of bonding and antibonding antibonding electrons.electrons.

MO TheoryMO Theory

For hydrogen, with For hydrogen, with two electrons in the two electrons in the bonding MO and none bonding MO and none in the antibonding in the antibonding MO, the bond order is MO, the bond order is

12

(2 - 0) = 1

MO TheoryMO Theory

In the case of In the case of HeHe22, the bond , the bond order would beorder would be

12

(2 - 2) = 0

• Therefore, He2 does not exist.

MO TheoryMO Theory For atoms with both For atoms with both

ss and and pp orbitals, orbitals, there are two types of there are two types of interactions:interactions: The The ss and the and the pp

orbitals that face orbitals that face each other overlap each other overlap in in fashion. fashion.

The other two sets The other two sets of of pp orbitals orbitals overlap in overlap in fashion.fashion.

MO TheoryMO Theory

The resulting MO The resulting MO diagram looks like diagram looks like this.this.

There are both There are both and and bonding bonding molecular orbitals molecular orbitals and and * and * and * * antibonding antibonding molecular molecular orbitals.orbitals.

MO TheoryMO Theory

The smaller The smaller pp-block -block elements in the second elements in the second period have a sizeable period have a sizeable interaction between the interaction between the ss and and pp orbitals. orbitals.

This flips the order of the s This flips the order of the s and p molecular orbitals in and p molecular orbitals in these elements.these elements.

Second-Row MO Second-Row MO DiagramsDiagrams

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Chapter 9 Molecular Geometries and Bonding Theories