Why do they make chemical bonds ? Molecular Orbitalsbh.knu.ac.kr/~leehi/index.files/Molecular_Orbitals.pdf · 2018-10-24 · Types of Chemical Bonds . Covalent Bond • A molecule

Molecular Orbitals 5

N2 NH3 H2O

Why do they make chemical bonds ?

Stabilization

Bond energy

Why do they make chemical bonds?

Metallic Bond Ionic Bond Covalent Bond

Types of Chemical Bonds

Covalent Bond

• A molecule is composed of atoms that are bound together by sharing pairs of electrons using the atomic orbitals of the bound atoms.

•Description of valence electron arrangement

•Description of atomic orbital types used to share electrons or hold lone pairs.

•Prediction of geometry

•Analogous to atomic orbitals for atoms, MOs are the quantum mechanical solutions to the organization of valence electrons in molecules.

•Electron pairs in the molecule are assumed to be localized on a particular atom or in the space between two atoms

•Electron pairs localized on an atom : lone pairs

•Electron pairs found in the space between the atoms : bonding pairs

Covalent Bond

Fact: O2 is paramagnetic!

O OLewis structure VSEPR Valence bond theory

•sp2 hybridized •lone pairs in sp2 hybrid orbitals •bonding pairs in σ and π bonds

All show all electrons paired.

LE is great to predict bondings and structures and geometries of molecules.

BUT, there are some short points. •No concept of resonance. No paramagnetic properties. No information of bond energy.

In contrast to LE, molecular orbitals describe how electrons spread over all the atoms in a molecule and bind them together, which can give correct views of

• concept of resonance. paramagnetic properties. bond energy.

Formation of Molecular Orbitals from Atomic Orbitals

H2 – 2 protons and 2 electrons Schroedinger Eq => Molecular orbitals

But, no way to solve => LCAO (linear combination of atomic orbitals)

=> Approximate solutions of Schroedinger Eq

H – 1 proton and 1 electron Schröedinger Eq => Atomic orbitals

f+

f+2

Constructive overlap ⇒ enhance e- density between the nuclei

⇒ attract the nuclei ⇒ bonding orbital

fA fB A B

fA

fB

A B f- f-2

destructive overlap ⇒ node(s) between the nuclei

⇒ repel each other ⇒ antibonding orbital

+

– –

–

–

–

++

+

Overlap of wavefunctions (constructive Overlap)

(destructive Overlap)

φ+

φ+2

φΑ φΒ Α Β

φΑ

φΒ

Α Β φ− φ−2

Higher energy state

Lower energy state

Constructive overlap ⇒ enhance e- density between the nuclei

⇒ attract the nuclei ⇒ bonding orbital

destructive overlap ⇒ node(s) between the nuclei

⇒ repel each other ⇒ antibonding orbital

Ψ = caψa + cbψb

Formation of Molecular Orbitals from Atomic Orbitals

)]1()1([2

1)]1()1([)( babbaa ssscscN ψψψψσ +=+=Ψ

)]1()1([2

1)]1()1([*)( babbaa ssscscN ψψψψσ −=−=Ψ

Formation of Molecular Orbitals from Atomic Orbitals Molecular Orbitals from s Orbitals

H2

σ*1s antibonding m.o. (higher energy than separate atoms)

σ1s bonding m.o. (lower energy than separate atoms)

σ (C2 symmetric about the line connecting the nuclei)

Formation of Molecular Orbitals from Atomic Orbitals Molecular Orbitals from p Orbitals

π (C2 antisymmetric about the line connecting the nuclei)

Formation of Molecular Orbitals from Atomic Orbitals Molecular Orbitals from d Orbitals

No interaction

Classification of Covalent Bonds (by symmetry)

σ bond (C2 symmetric about z- axis)

π bond (C2 antisymmetric about z- axis)

δ bond (C4 antisymmetric about z- axis)

φ bond (C6 antisymmetric about z- axis)

U2, HTa2+ (in calculation)

0 node

1 node

2 node

3 node

Node(s) at z-axis

3 Things to Consider to Form Molecular Orbitals

N atomic orbitals => N molecular orbitals Symmetry match of atomic orbitals Relative energy of atomic orbitals

Forming nonbonding orbitals

Remember ! The more nodes, the higher energy.

Homonuclear Diatomic Molecules

bond order = (no. of e– in bonding m.o.s) - (no. of e– in antibonding m.o.s)

2

b.o. = 1

H2

1st Row Diatomic Molecules

σg2(1s)

b.o. > 0 (i.e., lower energy than separate atoms)

b.l = 74.1 pm BE = 436 kJ/mol

b.o. = 0.5

H2+

σg1(1s)

b.l = 105.2 pm BE = 258 kJ/mol

b.o. = 0

He2

σg2σu*2 (1s)

*detected at very low T and P *BE = 0.01 J/mol

b.o. = 0.5

He2+

σg2σu*1 (1s)

b.l. =108 pm BE = 233 kJ/mol

)]1()1([)( bbaa scscN ψψσ +=Ψ

)]1()1([*)( bbaa scscN ψψσ −=Ψ

Homonuclear Diatomic Molecules 2st Row Diatomic Molecules

Not big

No mixing (O2, F2, Ne2)

Mixing (Li2 - N2)

)]2()2()2()2([ bcacbbaa pcpcscscN ψψψψ +++=Ψ


b.o. = 1

Li2

σg2(2s)

* found in gas phase

b.o. = 0

Be2

σg2σu*2 (2s)

b.o. = 1

B2

σg2σu*2 (2s)πu1πu1(2p)

* B12 (solid phase) * Paramagnetic (gas phase)

b.o. = 2 (π)

C2

σg2σu*2 (2s)πu2πu2(2p)

* Found in gas phase * rare * C22- is more common C2 d(C-C) 124.2 pm (b.o. = 2) CaC2 d(C-C) 119.1 pm (b.o. = 3) C2H2 d(C-C) 120.5 pm (b.o. = 3)

b.o. = 3 (2π+σ)

N2

σg2σu*2(2s) πu2πu2σg2 (2p)

b.l. = 109.8 pm BE = 942 kJ/mol


b.o. = 2

O2

σg2σu*2(2s)σg2πu2πu2πg*1πg*1(2p)

b.l. = 120.8 pm * Paramagnetic

Other forms of O2n O2+ b.o = 2.5, b.l = 111.6 pm O2- b.o = 1.5, b.l = 135 pm O22- b.o = 1, b.l = 149 pm

b.o. = 1

F2

σg2σu*2(2s)σg2πu2πu2πg*2πg*2(2p)

b.o. = 0

Ne2

σg2σu*2(2s)σg2πu2πu2πg*2πg*2σu*2 (2p)


Big triumph of MO theory

HOMO (highest occupied molecular orbital)

LUMO (lowest unoccupied molecular orbital)

SOMO (singly occupied molecular orbital)

Frontier orbitals

Homonuclear Diatomic Molecules Bond Lengths

Bond length Covalent radius

H-X H-B H-C H-N H-O H-F

Length (pm) 120 109 101.2 96 91.8

1

1. Any trend found? OK with electronegativity difference

2

2. Any trend found? Don’t be fooled by the text book. Covalent radii are defined in X-X single bond (Table 2-8).

Homonuclear Diatomic Molecules How to measure the energy levels of MOs ? (Photoelectron spectroscopy)

photoelectron v

A + hν A+ + e- Ionization energy = hν - ½ mv2

IE

hν = UV UPS : outer electrons hν = X-ray XPS : inner electrons


N2 O2

Ionization energy = hν - ½ mv2

N2 O2

Why fine structure?


Ionization energy = hν - ½ mv2

Franck-Condon Principle: Classically, the Franck–Condon principle is the approximation that an electronic transition is most likely to occur without changes in the positions of the nuclei in the molecular entity and its environment. The resulting state is called a Franck–Condon state, and the transition involved, a vertical transition.

Mnucleus >> Melectron e-: faster motion

Ionization energy = hν - ½ mv2 – Evib+


Ionization energy = hν - ½ mv2 – Evib+

N2 O2

stronger bonding involved less bonding involved

Heteronuclear Diatomic Molecules

N atomic orbitals => N molecular orbitals Symmetry match of atomic orbitals Relative energy of atomic orbitals

3 things to consider to form MOs

|cA| = |cΒ|

|cA| > |cΒ| |cA| >> |cΒ| |cA| = |cΒ|

|cA| < |cΒ| |cA|

Heteronuclear Diatomic Molecules Polar Bonds

Average potential energy of all terms

Ex) E(C2p) = [E(1D) x 5 + E(3P) x 9 + E(1S) x 1]/15

Heteronuclear Diatomic Molecules CO

Significant mixing between O2pz and C2s


Significant mixing with C2s

C∞v


Significant mixing with C2s

C∞v

M – C≡O M – O≡C ?

Heteronuclear Diatomic Molecules Ionic Compounds and MOs

LiF

Li: 1s22s1 Li+: 1s2 F: 1s22s2sp5 F-: 1s22s22p6 Electrostatic interaction

View of ionic interaction

View of MO

F2p character Transfer of Li2s e- to F2p orbital which is lowered

Don’t forget that ionic interaction is omnidirectional and more accurate MO description requires bands.

Heteronuclear Diatomic Molecules Ionic Compounds and MOs

LiF

Li: 1s22s1 Li+: 1s2 F: 1s22s2sp5 F-: 1s22s22p6

View of ionic interaction

Is this process really helpful?

Thermodynamically unfavorable!!

Lattice enthalpy is the deriving force.

MOs for Larger Molecules

1. Determine the point group of molecules. (D∞h D2h, C∞v C2v) 2. Assign x, y, z coordinates. 3. Find reducible representations for ns orbitals on the outer atoms. Repeat for np

orbitals in the same symmetry. (valence orbitals) 4. Reduce the reducible representations of step 3 to derive group orbitals or

symmetry adapted linear combinations (SALCs) 5. Find the atomic orbitals of the central atoms with the same symmetries as those

found in step 4. 6. Combine the atomic orbitals of the central atom and the SALCs of the outer atoms

with the same symmetry and similar energy to form MOs.

MOs for Larger Molecules FHF-

F(2px)+F(2px) 2 -2 0 0 0 0 2 -2

F(2py)+F(2py) 2 -2 0 0 0 0 -2 2

F(2pz)+F(2pz) 2 2 0 0 0 0 2 2

F(2s) + F(2s) 2 2 0 0 0 0 2 2

B3u + B2g

B2u + B3g Ag + B1u Ag + B1u

D∞h D2h

Very strong H-bonding


H: 1s orbital

Ag

F---F: SALCs

D∞h D2h

can combine to form MOs


D∞h D2h

(-18.65 eV)

(-40.17 eV)

(-13.61 eV) H 1s

H 1s will strongly interact with F2Pzs (Ag). Don't forget if F2s contributes, 3 MOs are formed.


D∞h D2h

bonding

antibonding

non-bonding * there are slight long-range interactions.

MO 3-center 2-electron bond

Lewis structure

F H F

MOs for Larger Molecules CO2

D∞h D2h

2 -2 0 0 0 0 2 -2

2 -2 0 0 0 0 -2 2

2 2 0 0 0 0 2 2

O(2px)+O(2px) O(2py)+O(2py) O(2pz)+O(2pz) O(2s) + O(2s) 2 2 0 0 0 0 2 2

B3u + B2g

B2u + B3g Ag + B1u Ag + B1u


D∞h D2h

O---O: SALCs C: valence orbitals

combine to form MOs


D∞h D2h

Effective to form MOs


D∞h D2h


non-bonding σ

bonding σ

bonding π

non-bonding π

16 valence e-'s

O=C=O

Lewis structure

3-center 2 electron bond

2-center 2 electron bond

MOs for Larger Molecules H2O

H(1s)+H(1s) 2 0 2 0 A1 + B1

H------H: SALCs

H H H H

Ψa1= (1/√2){φa(H1s)+φb(H1s)}

Ψb1= (1/√2){φa(H1s)-φb(H1s)}

Α1 Β1

O: valence orbitals

2s A1 2px B1

2pz A1 2py B2


H------H: SALCs

H H

H H

Α1

Β1

O: valence orbitals

2s A1

2px B1

2pz A1

2py B2

1b1 bonding 2b1 antibonding

3a1 nearly non-bonding

4a1 antibonding 2a1 bonding

O

H 1b2 non-bonding

H2O MOs


Ψ1 Ψ3 Ψ5 Ψ2 Ψ6 Ψ4

Very weak contribution of H group orbital (1s) weak contribution of O(2pz)


Lewis structure

•Two lone pairs are equivalent (2 x sp3). •Two O-H bonds are equvalent [2 x (sp3 + H(1s))].

MO

lone pairs O-H bonds


O A1

2s 2pz sp sp

H----H SALCs

A1 B1

B2 B1

Other approach

b1

b2

b1


104.5°

Why 104.5o in MO theory?

Walsh Diagram - a diagram showing the variation of orbital energy with molecular geometry


Walsh Diagram - a diagram showing the variation of orbital energy with molecular geometry

* When x-, y- axes are defined differently, B1 and B2 symmetries are exchanged.

MOs for Larger Molecules NH3

3H(1s) 3 0 1 A1 + E

A1

E

)]()()([3

1cba HHH ψψψ ++=Ψ

)]()()(2[6

1cba HHH ψψψ −−=Ψ )]()([2

1cb HH ψψ −=Ψ

3H SALCs

A1 A1

E

s pz

px py

N


3H(1s) 3 0 1 A1 + E

Projection Operator Method : Group orbitals are constructed by summing the resulting orbitals of symmetry operations of an orbital A1

E

)]()()([3

1cba HHH ψψψ ++=Ψ

)]()()(2[6

1cba HHH ψψψ −−=Ψ )]()([2

1cb HH ψψ −=Ψ

3H SALCs

Ha

E px py

By inspecting N px, py orbitals, 2nd E (SALC) orbital is obtained.


A1

E

3H SALCs

A1

E

s

pz

px

py

N

A1

mostly pz character

MOs for Larger Molecules BF3

B F

F

F

3F(2s) 3 0 1 3 0 1 A1' + E'

3F(2px) 3 0 -1 3 0 -1 A2' + E'

3F(2py) 3 0 1 3 0 1 A1' + E'

3F(2pz) 3 0 -1 -3 0 1 A2'' + E''


B F

F

F

3F(2s) A1' + E'

A2' E'

3F(2pz) A2'' + E'' 3F(2px) A2' + E' A1' E'

3F(2py) A1' + E'

A2'' E''

A1' E'

3F SALCs

2s

2px, 2py

A2''

A1'

E'

2pz

B orbitals

MOs for Larger Molecules

A2' E'

A1' E'

A1' E'

A2'' E''

3F(2px)

3F(2py)

3F(2pz)

3F(2s) 3F SALCs

BF3

B orbitals

2pz A2''

2s A1'

E'

2py

2px


bonding (a2”:slightly bonding)

non-bonding almost non-bonding

antibonding

same for SO3, NO3-, CO32-

Lewis ? VBT? ? σ and ? π

MOs for Larger Molecules SALCs

MOs for Larger Molecules Hybrid Orbitals

One of the ways to predict the hybrid orbitals is..

(Which atomic orbitals form hybrides?)

MOs for Larger Molecules Hybrid Orbitals

Ex) CH4

4 C-H bonds 4 1 0 0 2 A1+ T2 s, (px, py, pz) sp3

why not d ? Ex) BF3

B

F

F

F

3B-F bonds = 3F(2s) 3 0 1 3 0 1 A1' + E'

s, (px, py) sp2

슬라이드 번호 1Why do they make chemical bonds?Types of Chemical BondsCovalent BondCovalent BondFormation of Molecular Orbitals from Atomic Orbitals슬라이드 번호 7슬라이드 번호 8슬라이드 번호 9슬라이드 번호 10슬라이드 번호 11슬라이드 번호 12슬라이드 번호 13슬라이드 번호 14슬라이드 번호 15슬라이드 번호 16슬라이드 번호 17슬라이드 번호 18슬라이드 번호 19슬라이드 번호 20슬라이드 번호 21슬라이드 번호 22슬라이드 번호 23슬라이드 번호 24슬라이드 번호 25슬라이드 번호 26슬라이드 번호 27슬라이드 번호 28슬라이드 번호 29슬라이드 번호 30슬라이드 번호 31슬라이드 번호 32슬라이드 번호 33슬라이드 번호 34슬라이드 번호 35슬라이드 번호 36슬라이드 번호 37슬라이드 번호 38슬라이드 번호 39슬라이드 번호 40슬라이드 번호 41슬라이드 번호 42슬라이드 번호 43슬라이드 번호 44슬라이드 번호 45슬라이드 번호 46슬라이드 번호 47슬라이드 번호 48슬라이드 번호 49슬라이드 번호 50슬라이드 번호 51슬라이드 번호 52슬라이드 번호 53슬라이드 번호 54슬라이드 번호 55슬라이드 번호 56슬라이드 번호 57슬라이드 번호 58

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Why do they make chemical bonds ? Molecular Orbitalsbh.knu.ac.kr/~leehi/index.files/Molecular_Orbitals.pdf · 2018-10-24 · Types of Chemical Bonds . Covalent Bond • A molecule