Lewis StructureLewis Structure Chemistry

A molecule is composed of atoms that are bound together by sharing electron pairs.

A bonding pair is of which two electrons are localized between two adjacent nuclei.

A lone pair is that the electron pair is localized in an atom.

Localized Electron Bonding Model

Octet Rule

1 electron dot (bar) formula

2 valence eletrons & net charge

3 multiple bond

4 dative bond (arrow to the acceptor)

5 formal charge What is the difference between f. c. & ox. no

6 generally good thru the 3rd period

What is the difference between f. c. & ox. no

Formal charge is for the comparison of the elctron change between the bonded and the non-bonded atomic molds.

Oxidation number is for the comparison of the electron change between the oxidized and the reduced molds.

Formal charge and oxidation numbers are the same for the ionic compounds.

Disadvantage of Lewis Structure

1 Octet rule is no good for d orbital or d electrons involved species – use 18 electron rule

2 no good for electron delocalization – use resonance

3 Octet rule is no good for odd electron species

4 no information for geometry- use VSEPR

5 It does not explain the bonding character – use VBT or MOT

Valence Bond Theory (VBT)

Atomic orbitals that involve in chemical bonding are the major concern.

ψiψj ≠ 0, wherein ψi and ψj represent the orbital wave functions of different atoms.

VBT for H2

Consideration of simple orbital coulomb overlap:ΨI = ψ1sa(1)ψ1sb (2) ― curve a

ΨI = ψ1sa(1) ψ1sb (2)

experimental

Consideration of indistinguishability of the electrons:

Heitler –London functions:Attractive ΨII

+ = ψ1sa(1)ψ1sb (2) + ψ1sa(2)ψ1sb (1) ― curve b

Repulsive ΨII

− = ψ1sa(1)ψ1sb (2) − ψ1sa(2)ψ1sb (1) ― curve g

ΨI = ψ1sa(1) ψ1sb (2)

experimental

ΨII+ = ψ1sa(1) ψ1sb(2) + ψψ1sa(2) ψ1sb(1)

ΨII– = ψ1sa(1) ψ1sb(2) – ψ1sa(2) ψ1sb(1)

Consideration of effective nulear charge:

Ψ1s = N(z/a0)3/2exp(-zr/a0), z = 1.17 ― curve c

The z-modification gives good bond length, but energy is still substantially off.

ΨI = ψ1sa(1) ψ1sb (2)

experimental

ΨII+ = ψ1sa(1) ψ1sb(2) + ψ1sa(2) ψ1sb(1)

ΨII– = ψ1sa(1) ψ1sb(2) – ψ1sa(2) ψ1sb(1)

z = 1.17

Consideration of polarizability or hybridization:

ψa = N (1sa + 2pza)ψb = N (1sb + 2pzb), assuming z is the nuclear axis.

Normalization condition gives N = 1/(1 + 2)1/2

Contribution of 1sa to ψa (or 1sb to ψb ) is 1/(1 + 2)Contribution of 2pza to ψa (or 2pzb to ψb ) is 2/(1 + 2)

If is set as 0.1, which gives 99% (1/1.01) of 1s and 1% (0.01/1.01) of 2pz. Note that 1% of contribution of pz accounts for about 5% energy stabilization, mainly due to the enhancement of orbital overlap efficiency.

ΨI =ψ1sa(1) ψ1sb (2)

experimental

ΨII+ = ψ1sa(1) ψ1sb(2) + ψ1sa(2) ψ1sb(1)

ΨII– =ψ1sa(1) ψ1sb(2) – ψ1sa(2) ψ1sb(1)

z = 1.17ψa = N (1sa + 2pza)ψb = N (1sb + 2pzb) = 0.1

Combine indistinguishability and hybridization:

Attractive Heitler –London functions:ΨIII = ψa(1)ψb (2) + ψa(2)ψb (1)

Consideration of other overlaps 1sa–2pb/2pa–1sb and 2pa–2pb

H―H ↔ Ha−―Hb

+ ↔ Ha+―Hb

−

ΨIV = ψa(1)ψb (2) + ψa(2)ψb (1)

+ ψa(1)ψa (2) +ψb(1)ψb (2)

= 0.25 would minimize the total energy. The value of 2 ~ 0.06, indicating that about 6% ionic contribution will only improve the energy to 2~3%.

Consideration of ionization:

ΨI = ψ1sa(1) ψ1sb (2)

experimental

ΨII+ = ψ1sa(1) ψ1sb(2) + ψ1sa(2) ψ1sb(1)

ΨII– = ψ1sa(1) ψ1sb(2) – ψ1sa(2) ψ1sb(1)

z = 1.17ψa = N (1sa + 2pza)ψb = N (1sb + 2pzb) = 0.1

ΨIV = ψa(1) ψb(2) + ψa(2) ψb(1)

+ ψa(1) ψa(2) +ψb(1) ψb(2)

Valence Bond of HF

Consideration of indistinguishable orbital overlapΨI = 1s(H)(1)2pz(F)(2) + 1s(H)(2)2pz(F)(1)

Consideration of hybridization:

Hybridization for A.O. of F would give the configuration of 2s12p6 which allows the use of 2s for bonding.ψF = N (2pz(F) + 2s(F)), < 0.5 and 2 < 0.25, the contribution of 2s (i.e. 2 /(1+2) in F is less than 20%.

Consideration of ionic model:

Ψ = ψ1s(H)(1)ψF (2) + ψ1s(H)(2)ψF (1)+ ψF(1)ψF(2)Pauling estimated that 2 ~ 50%.

1 It helps to have the electron density concentrated between the nuclei, thus leading to the enhancement of localized bonding character.

Advantages from hybridization :

2 It helps to decrease the electron-electron repulsion. ψlp(F) = N (2s(F) − 2pz(F))