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Formation of Covalent Bonds

Two different theories which attempt to explain covalent molecular/ionic structure/shape

Localized Electron (LE) Model-electron pairs are still localized around specific atoms, but orbitals around central atom are modified

Molecular Orbital (MO) Model-all electrons in molecule are combined into set of molecular orbitals which describe bonding in entire molecule

Why hybrid orbitals?Why hybrid orbitals?

VSEPR model does good job at predicting molecular shape, despite fact that it has no obvious relationship to filling and shapes of atomic orbitals

Based on shapes and orientations of 2s/2p orbitals on carbon atom, not obvious why CH4 molecule should have tetrahedral geometry

Used to reconcile covalent bonds formed from overlap of atomic orbitals with molecular geometries from VSEPR model

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Hybridization/Hybrid orbitalsHybridization/Hybrid orbitals

Hybridization (orbitals in covalently bonded atoms) Mixing of 2/more atomic orbitals of similar energies on same atom

to produce new orbitals of equal energies Hybrid orbitals

Valence bond theory creates hybrid orbitals that are linear combinations of s/p orbitals in valence shell (d if necessary) # atomic orbits = # hybrid orbitals Each hybrid orbital equivalent to others but large lobes point in

different directions Atomic orbitals not used to make hybrids unaffected Mixtures of atomic orbitals with intermediate energy

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One 2s electron promoted to empty (2p) orbital

2 occupied orbitals blend to form 2 sp hybrid orbitals/2 remaining p orbitals

unchanged

No unpaired electrons

sp has 50% s/50% p character 2 sp hybrids point in opposite directions at 180o to each

other Require energy to promote 2s 2p orbital Large lobe of hybrid orbital can be directed at other atoms better than

unhybridized atomic orbital Overlap more strongly/stronger bonds result Energy released by bond formation offsets energy expended to

promote electrons

Each sp hybrid involved in s bond/remaining p orbitals forms 2p bonds (All contain single unpaired electron)

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+

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2s electron promoted to 2p orbital Have 3 unpaired electrons that form 3 sp2 orbitals

Creates 3 identical orbitals of intermediate energy/lengthLeaves one unhybridized p orbital

http://college.hmco.com/chemistry/shared/media/animations/sp2hybridization.html

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+

Large lobes of orbitals lie in plane at angles of 120o and point toward corners of triangle

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Promotion of 2s electron to 2p orbital results in valence shell with 4 unpaired electrons in four sp3 hybrid orbitals.

4 orbitals form one 2s/three 2p orbitals (s1p3)

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Four sp3 orbitals identical in shape

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http://college.hmco.com/chemistry/shared/media/animations/sp3_hybridization.html

D-orbital hybridization

Central atoms located in Period 3 and above can use empty d orbitals to receive promoted s electron

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dspdsp33 HybridizationHybridization

5 effective pairs around central atom

Trigonal bipyramidal shape

Lobes have bond angles of 90o & 120O

PCl5 example

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•Each dsp3 orbital also has small lobe not shown in diagram

•Phosphorus uses set of 5 dsp3 orbitals to share electron pairs with sp3 orbitals on 5 chlorine

atoms •Other sp3 orbitals on each

chlorine atom hold lone pairs

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dd22spsp33 HybridizationHybridization

Six effective pairs around central atom Octahedral structure Lobes have angles of 90o

SF6 example

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Atomic Hybridorbital set orbital set_

s/p 2 sp

s/p/p 3 sp2

s/p/p/p 4 sp3

s/p/p/p/d 5 sp3d

s/p/p/p/d/d 6 sp3d2

Examples

BeF2, HgCl2

BF3, SO3

CH4, NH3, H O, NH4+

PF5, SF4, BrF3, SbCl52-

SF6, ClF5, XeF4, PF4-

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•Basic Derived Hybrid Bonding NonbondingStructure structure e- pairs e- pairs•Linear sp 2 0•Trigonal planar sp2 3 0•Trigonal planar Bent sp2 2 1•Tetrahedron sp3 4 0•Tetrahedron Triangular pyramid sp3 3 1•Tetrahedron Bent sp3 2 2•Trigonal bipyramid sp3d 5 0•Trigonal bipyramid Distorted tetrahedron sp3d 4 1•Trigonal bipyramid T-shape sp3d 3 2•Trigonal bipyramid Linear sp3d 2 3•Octahedron sp3d2 6 0•Octahedron Square pyramid sp3d2 5 1•Octahedron Square planar sp3d2 4 2

Strength of sigma bonds p-p > p-s > s-s p-orbitals allow overlap to greater

extent as compared to p-s which is larger as compared to s-s overlap

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(s/single /δ)

(Head-to-head overlap)

Lobes of bonding orbital point toward each other.

Overlap of two S orbitals to form sigma

bond (green)

Overlap of two P orbitals to form sigma

bond (green)

Maximum electron density lies along bond (electron pair shared in area centered on line connecting nuclei)

Line joining 2 nuclei passes through middle of overlap region (between nuclei)

Maximum overlap forms strongest-possible sigma bond

Atoms arrange themselves to give greatest-possible orbital overlap

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(p/)

• Axes parallel to each other but perpendicular to internuclear axis

• Occupies space above/below internuclear axis (imaginary line connecting nuclei of two atoms)

• Electron density zero along bond• Atomic orbitals interact above and below

nuclei

(perpendicular)

• Formed only in addition to sigma bond• Always present in molecules with

double/triple bonds• Occur only w/sp or sp2 hybridization

present on central atom, but not sp3

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•Pi bonds are superimposed on sigma bonds so they simply modify dimensions of molecule.

• Significantly less overlap between component p-orbitals due to parallel orientation

• Weaker than sigma bonds-electrons farther from nucleus, so more reactive

Multiple BondsMultiple Bonds

Double Bonds Consist of 1 s bond

(overlap of 2 sp orbitals) and 1 p bond (overlap of 2 p orbitals)

s bond where electron pair located directly between atoms

p bond where shared pair occupies space above and below s bond

Triple Bonds Consist of 1 s / 2 p bonds Side-to-side overlap

makes p bond electrons more reactive

Electron density no longer located on internuclear axis (one electron cloud above and one below)

Bond is weaker-p orbitals do not overlap as much in p bond as s bond

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Double bondsDouble bonds Triple bondsTriple bonds

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Consists of sigma (green)/2 pi bonds (red)

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(a) sp hybridized nitrogen atom

(b) s bond in N2 molecule

(c) 2 p bonds in N2 are formed when electron pairs are shared between two sets of parallel p orbitals

(d) Total bonding picture for N2

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Carbon is uniqueCarbon is unique

sp3 hybrid orbitals = single bonds

sp2 hybrid orbitals = double bonds

sp hybrid orbitals = triple bonds

Carbon atom of methane (CHCarbon atom of methane (CH44) )

Made up of 4 C-H sigma (σ) bondsEach hybrid sp3 orbitals of carbon undergoes

end-on overlap with s-orbitals of H atomsTetrahedral geometry

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Carbon atoms of ethyne Carbon atoms of ethyne (acetylene - C(acetylene - C22HH22) )

2 C-H σ bonds, 1 C-C σ bond, 2 C-C π bonds Δ bonds (gray) are linear in arrangement Unhybridized p-orbitals (green/purple) interact with

each other laterally, resulting in bond formation

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Carbon atoms of ethene Carbon atoms of ethene (ethylene - C(ethylene - C22HH44))

4 C-H σ bonds, 1 C-C σ bond, 1 C-C π bond Hybrid orbital overlap end-on with s-orbitals of H

atoms (δ bond in gray) Unhybridized p-orbitals (purple) at right angles to

plane of hybrids, overlap laterally (π bond-double)

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Formaldehyde has following Formaldehyde has following Lewis structure: Lewis structure:

Describe it bonding in terms of appropriate hybridized/unhybridized orbitals

VSEPR predicts trigonal planar geometry which suggests sp2 hybrid orbitals on C

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Acetonitrile moleculeAcetonitrile molecule

Predict bond angles around each C Approximately 109° around left C and 180° on

right C

Give hybridization of each C sp3, sp

Determine total number of δ/π bonds 5 δ bonds and 2 π bonds

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orbitals of sp hybridized carbon atom

orbital arrangement for sp2 hybridized oxygen atom

hybrid orbitals in the CO2 molecule

(a) orbitals in carbon dioxide-carbon-oxygen double bonds each consist of one s bond and one p bond. (b) Lewis structure for carbon dioxide

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Determine the total number of sigma and pi bonds in each of the following:Using the simple Lewis structure, also determine

the hybridization for each: CH3Cl 4 δ, 0 Π, sp3

PH3

2 δ, 2 Π, sp H2S 3 δ, 0 Π, sp3

CO32-

4 δ, 0 Π, sp3

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SO32-

2 δ, 0 Π, sp3

CS2

3 δ, 1 Π, sp2

SiF4

3 δ, 1 Π, sp2

NO3-

4 δ, 0 Π, sp3

PO43-

3 δ, 0 Π, sp2

ClO4-

4 δ, 0 Π, sp3

VSEPR did not explain why VSEPR did not explain why bonds exist between atomsbonds exist between atoms

Pair of electrons attracted to both atomic nuclei Bond is formed As extent of overlap increases, strength of bond

increases Electronic energy drops as atoms approach each

other Begin to increase again when they become too close Optimum distance (observed bond distance) at which

total energy is at minimum

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Basic s, px, py, and pz orbitals unsatisfactory for two reasons Orbitals not directed in particular direction-tend to

spread out in all directions Geometry of orbitals rarely consistent with

molecular geometry Could not adequately explain fact that some

molecules contain two equivalent bonds with bond order between that of single and double bonds

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Atomic orbitalsAtomic orbitals explain bonding/ explain bonding/ account for molecular geometriesaccount for molecular geometries

Mathematical descriptions of where electrons most likely found Obtained by solving Schrödinger equation

As angular momentum (ml) and energy of electron increases, it tends to reside in differently shaped orbitals

Orbitals corresponding to three lowest energy states (s, p, and d, respectively)

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Localized Electron ModelLocalized Electron Model(Valence Bond Theory)(Valence Bond Theory)

Describes structure of covalent bonds (how bonding occurs)

Atoms in molecule bond together w/shared electrons Lewis structure shows valence electron arrangement Use VSEPR model to predict molecular geometry Atoms use atomic orbitals to share electrons/hold lone

pairs (new set of hybridized orbitals can form) Lone pairsLone pairs: electron pairs localized on atom Bonding pairsBonding pairs: electron pairs in space between atoms

Combine Lewis’s notion of electron-pair bonds with atomic orbitals Lewis theoryLewis theory: covalent bonding occurs when atoms share

electrons (concentrates electron density between nuclei) Valence-bond theoryValence-bond theory: buildup of electron density between two

nuclei occurs when valence atomic orbital of one atom shares space (overlaps) with that of another atom

Shortcomings of LE Model Electrons not actually localized Does not deal effectively w/molecules containing unpaired electrons Gives no direct information about bond energies

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Direct overlap (electron sharing) of two atomic orbitals Local view of bonding (how adjacent atoms share electrons) How 2 electrons of opposite spin share space between

nuclei/form bond Paired electrons localized in specific internuclear spaces between

bonded atoms or remain unshared (lone pairs) As bond is formed, paired electrons spread out over molecule to

form final electron cloud surrounding nuclei Description confirmed by many chemistry/physics experiments,

including actual Scanning Tunneling Microscope picture of p-orbital

Electronic structure/geometry is best compromise between maximum overlap (electron-nucleus attraction) and repulsion (electron-electron/nucleus-nucleus)

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Bonds (δ-head on/π-sideways) made by overlap of atomic (s,p) or hybridized (sp2) orbitals Formation of bonding

orbital accompanied by formation of antibonding antibonding orbitals (orbitals (δδ*/*/ππ*) *) which remain unoccupied and does not contribute to structure of molecule

δ bonds have cylindrical symmetry Formed between pair of

atoms within molecule Increased electron

density on internuclear axis

Rotation around bond does not change overlap of contributing atomic orbitals

Lower energy than π bonds

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π bonds are not cylindrically symmetric May cover more than 2 nuclei (resonance) Increased electron density above/below internuclear

axis (not on axis itself) Rotation breaks bond

Electrons not always shared equally (EN) Skeletal structures (Lewis structures) correspond

to valence-bond model

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Resonance structures represent molecules not adequately described by single structure, because electrons shared by more than 2 nuclei

Rules for drawing reasonable resonance structures All resonance structures must be valid Lewis structures In all possible resonance structures atomic nuclei must not

change their positions All atoms must not change their hybridization Only electron distribution may be changed All resonance structures must have same # unpaired

electrons All atoms involved in resonance (electron sharing)/atoms

directly bonded to them must lie in (or nearly in) same plane

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Homework:

Read 9.1, pp. 413-426

Q pp. 441-443, #12, 14, 16, 21, 22, 27, 28

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Molecular Orbital (MO) Theory (Model)

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Molecular Orbital TheoryMolecular Orbital Theory

Explains distributions (organization of valence electrons) and energy of electrons in molecules Molecule is similar to atom (have distinct energy levels that

electrons can populate) Takes global view of bonding (all electrons in molecule are needed

to describe how bonding occurs) Useful for describing properties of compounds

Bond energies, electron cloud distribution, and magnetic properties

Solution to VB problems by creating new set of orbitals w/intermediate between those of basic orbitals used to construct them

Basic principles of MO Theory 2 atomic orbitals w/similar energies overlap to form 2 molecular orbitals Electrons from each element participating in bond occupy new molecular

orbitals MOs delocalized over many atoms (don’t directly correspond to specific

bond as in VB theory) No hybridization (all available atomic orbitals mixed into multiple

combination Molecular orbitals have different energies depending on type of

overlap Bonding orbitals (lower energy than corresponding AO) Nonbonding orbitals (same energy as corresponding AO) Antibonding orbitals (higher energy than corresponding AO)

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Molecular orbitals (MOs) made of fractions of atomic orbitals All atoms in molecule provide atomic orbitals to

make MOs, but not all atomic orbitals must participate in all MOs

MO filled by all available electrons (2 per orbital), starting with lowest energy MO orbital

π bonds perpendicular to δ bonds, so can’t mix Reflects orbital geometry of molecule

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Principles for formation of MOsPrinciples for formation of MOs

1. # MOs formed = # atomic orbitals combined

2. Atomic orbitals combine best with other atomic orbitals of similar energy

3. How effectively 2 atomic orbitals combine proportional to their overlap As overlap increases, energy of bonding MO lowered, energy of

antibonding MO raised Lower energy molecular orbitals fill first

4. Each MO accommodates 2 electrons w/opposite spins (Pauli exclusion principle)

5. When MOs of same energy populated, Hund’s rule is followed (equal energy orbitals ½ filled before pairing up)

6. Electron in antibonding orbital “cancels” its corresponding electron in bonding orbital

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In atoms, electrons occupy atomic orbitals,

In molecules they occupy molecular orbitals which surround molecule

Two atomic orbitals combine to form two molecular orbitals, one bonding () and one antibonding (*)

Each line in diagram represents orbital

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Bonding OrbitalBonding Orbital

MOs w/lower energy than its corresponding original atomic orbitals

Promotes formation of stable bond High electron density along internuclear axis

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Antibonding Orbital

MOs w/higher energy than its corresponding atomic orbitals

Destabilizes (negative impact) formation of bond Much lower electron density along internuclear

axis

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When two atomic orbitals overlap in side-by-side fashion, molecular orbitals called π molecular orbitals

Antibonding molecular orbital is designated as π* molecular orbital

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Bond Order (BO)Bond Order (BO)

Describes nature of bond formed by molecular orbitals

Refers to average number of bonds that atom makes in all of its bonds to other atoms

Bond order above 0 considered stable because it has excess of bonding electrons If bond order = 0 (BE = ABE), species does not

exist Larger bond order = Greater bond strength =

Greater bond energy = Shorter bond lengthBO =

# bonding electrons # antibonding electons2

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Pg. 434-444, Sample 9.6

For the species O2, O2+, and O2

-, give the electron configuration and the bond order for each. Which has the strongest bond?

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Magnetism can be induced in some Magnetism can be induced in some nonmagnetic materials when in nonmagnetic materials when in presence of magnetic fieldpresence of magnetic field

Paramagnetism: (oxygen-2 unpaired e’s) Unpaired electrons Attracted to induced magnetic field Much stronger than diamagnetism

Diamagnetism Paired electrons Repelled from induced magnetic field Much weaker than paramagnetism

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NONO++ ion has total of 7 + 8 -1 = 14 ion has total of 7 + 8 -1 = 14 electrons to place in molecular electrons to place in molecular orbitals as followsorbitals as follows

Calculate bond order of NO+ ion ½(10 - 4) = 3 

Is the NO+ ion diamagnetic or paramagnetic?   0 unpaired electrons

so ion is diamagnetic 

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Hydrogen Atom (H)Hydrogen Atom (H)

1 bonding electron/0 antibonding electrons

Stable (lower energy, greater stability)

Bond order of ½ One unpaired electron-

paramagnetic

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2 bonding electrons in δ1s

molecular orbital /0 antibonding electrons

Stable Bond order of 1 Electrons in line w/2 nuclei,

so are s molecular orbitals No unpaired electrons-

diamagnetic

Hydrogen Molecule (HHydrogen Molecule (H22))

Does HeDoes He22 exist? exist?

He2 has four

electrons, two in s1s orbital and two

in s*1s orbital

Bond order of 0, so He2 does not

exist

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Bonding in Homonuclear Diatomic Bonding in Homonuclear Diatomic Molecules (composed of two identical Molecules (composed of two identical atoms)atoms)

In order to participate in molecular orbitals, atomic orbitals must overlap in space

Larger bond order is favored When molecular orbitals are formed from p orbitals, s

orbitals are favored over p orbitals (stronger) Electrons are closer to nucleus = lower energy

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Molecular orbital energy-level diagrams, bond orders, bond energies, and bond lengths for diatomic molecules

Note that for O2 and F2, 2p orbital lower in energy than the π2p orbitals

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Bonding in Heteronuclear Diatomic Bonding in Heteronuclear Diatomic Molecules (different atoms)Molecules (different atoms)

For atoms adjacent to each other in periodic table Use molecular orbital diagrams for homonuclear

molecules

Significantly different atoms Each molecule must be examined individually Use only electrons that are going to be involved in

bonding

No universally accepted molecular orbital energy order

N2 NO bond order = 3 bond order = 2.5

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Outcomes of MO ModelOutcomes of MO Model

Strengths Correctly predicts relative bond strength and

magnetism of simple diatomic molecules Accounts for bond polarity Correctly portrays electrons as being delocalized

in polyatomic molecules Disadvantages

Difficult to apply quantitatively to polyatomic molecules

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Combining Localized Electron Combining Localized Electron and Molecular Orbital Modeland Molecular Orbital Model

Resonance Attempt to draw localized electrons in structure in

which electrons not localized s (δ) bonds can be described using localized electron

model p (π) bonds (delocalized) must be described using

molecular orbital model

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BenzeneBenzene

s bonds (C - H and C - C) are sp2 hybridized

Localized model p bonds result of

remaining p orbitals above/ below plane of benzene ring

Delocalizing gives stability

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Homework:

Read 9.2-9.5, pp. 426-441Q pp. 443-444, #32, 33, 38, 40, 46Do 1 additional exercise and 1 challenge problemSubmit quizzes by email to me:http://www.cengage.com/chemistry/book_content/

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