Chapter 2Molecular Structure and Bonding

Lecture 609/17/2009

Dr. Andrei Jitianu

Outline• Lewis structures

– The octet rule;– The structure and bond properties;– The VSEPR model;

• Valence-bond theory– The hydrogen molecule;– Homonuclear diatomic molecules;– Polyatomic molecules;

• Molecular orbital theory– An introduction in theory – Homonuclear diatomic molecules;– Heteronuclear diatomic molecules;

Molecular orbital theory

This theory generalizes the atomic orbital description of atoms to a molecular orbital (MO) description of molecules

– the electrons spread over all the atoms in a molecule and bind them all together.

An introduction to the theorya. The approximation of the

theoryKey points:• Molecular orbitals are constructed as linear combinations of atomic orbitals;

•There is a high probability of finding electrons in atomic orbitals that have large coefficients in the linear combination;

•Each molecular orbital can be occupied by up to two electrons.

• First approximation - Orbital approximationThe wavefunction ψ of the N electrons can be written:

ψ=ψ(1)ψ(2)… ψ(N)Electron (1) is described by ψ(1)…

These one-electron wavefunctions are the molecular orbitals of the theory.ψ2-probability distribution for that electron in the

molecule;The electron in the molecular orbital is likely to be

found where the orbital has a large amplitude, and will be not found at all at any of its nodes.

• Second approximation – When an electron is close to the nucleus of one atom, its wavefunction closely resembles an atomic orbital of that atom.

– When an e- is close to the nucleus of an H atom in a molecule, its wavefunction is like a 1s orbital of that atom.

• The molecular orbital can be constructed by superimposing atomic orbitals contributed by each atom – Linear Combination of Atomic Orbitals (LCAO) approximation.

Elementary form for MO theory: Only the valence-shell atomic orbitals are used to form molecular orbitals.

The MO of H2 are approximated by using two hydrogen 1s orbitals

ψ = cAφA+cBφBAtomic orbitals:

- φ from which the molecular orbital is built, consists of two H 1s orbitals.

Coefficients c – show the extent to which each atomic orbital contributes to the MO: the greater the value of c2, the greater the contribution of that orbital to the molecular orbital;

H2- homonuclear diatomic molecule – electrons are equally likely to be found near each

nucleus • the linear combination that gives the lowest energy will

have equal contributions from each 1s orbital (cA2= cB

2).

- The coefficients in the unnormalized molecular orbital are cA= cB=1

ψ+=φA+φB

The combination that corresponds to the next higher energy orbital also has equal contributions from each 1s orbital (cA

2= cB2), but

the coefficients CA=+1, CB=-1ψ-=φA-φB

• The relative signs of coefficients in LCAO play an important role in determining the energies of the orbitals.

N molecular orbitals can be constructed from Natomic orbitals– Ex: H2 2 atomic orbitals – 2 MO

O2 8 atomic orbitals – 8 MO

Pauli exclusion principle is appliedEach molecular orbital may be occupied by up two electrons; if two electrons are present, their spins must be paired.

The general pattern of the energies of the molecular orbitals formed from N atomic orbitals is

– one MO lies below that of the parent atomic energy levels,

– one lies higher in energy than they do, – the remainder are distributed between these

two extremes.

Principles of molecular orbital theory1. The total number of MOs is always equal with the

total number of AO contributed by the atoms that have combined.

2. The bonding MO is lower in energy than the parent orbitals, and the antibonding orbital is higher in energy.

3. The electrons of the molecule are assigned to orbitals of successively higher energy.

4. Atomic orbitals combine to form MO most effectively when the atomic orbitals are of the similar energy.

b. Bonding and antibonding orbitals

Key points:• A bonding orbital arises from the constructive

interference of neighbouring atomic orbitals;

• An antibonding orbital arises from their destructiveinterference, as indicated by a node between atoms.

ψ+ - bonding orbital – with energy lower than for the separated atoms.

For an e- placed in ψ+ - enhanced probability of being found between internuclear region.

The enhancement of electron density in the internuclear region arising from the constructiveinterference between the atomic orbitals on neighbouring atoms.

ψ- - antibonding orbital –with higher energy than for the separated atoms.

e- placed in ψ- is largely excluded from the internuclear region -forced to occupy energetically less favorable positions.

The destructive interference that arises if the overlapping orbitals have opposite signs. This interference leads to a nodal surface in an antibondingmolecular orbital.

The molecular orbital energy level diagram for H2 and analogous molecules

Molecular orbital energy level diagram – a diagram depicting the relatives energies of molecular orbitals.

For H2 - the energy gap between the two molecular orbitals –spectroscopic absorption at 11.4 eV – transition of an electron from the bonding orbital to the antibonding orbital.

He2 –is not stable

The molecular orbital energy diagram for H2 and analogous molecules

It is possible to generate a molecular orbital that has the same energy as the initial atomic orbitals –nonbonding orbital.

Nonbonding Orbital - is a molecular orbital that consists of a single orbital on one atom

Homonuclear diatomic molecules

Key points:• Molecular orbitals are classified as σ, π, or δ according

to their rotational symmetry about the internuclear axis;• g or u according with their symmetry with respect to

inversion;

a. The orbitals

Building a molecular diagram for diatomic molecules from the period 2.

- eight atomic orbitals – one s and three 3p for each atom

The molecular orbital energy level diagram for the later Period 2 homonuclear diatomic molecules. This diagram should be used for O2 and F2.

A σ orbital can be formed in several ways, including s,s overlap, s,p overlap, and p,p overlap with the p orbitals directed along the internuclear axis

σ orbitals - Orbitals with cylindrical symmetry around the internuclear axis z –2s and 2pz

labeled 1σg, 1σu, 2σg and 2σu

π orbitals – 2p orbitals on each atom – 2px and 2py.

labeled 1πu and 1πg

Two p orbitals can overlap to form a π orbital. The orbital has a nodal plane passing through the internuclear axis, shown here from the side.

For orbitals

g – gerade, even- identical under inversion

u – ungerade, odd- it changes the sign under inversion

Inversion consists of starting at an arbitrary point in the molecule , traveling in a straight line to the center of the molecule and then continuing an equal distance out of the other site of the center.

Procedure of building the orbital diagrams

1. From a basis set of N atomic orbitals, N molecular orbitals are constructed.

In Period 2, N=8.

2. The eight orbitals can be classified by symmetry into two sets:

• Four σ orbitals;• Four π orbitals;

3. The four π orbitals form – one doubly degenerate pair of bonding orbitals and – one doubly degenerate pair of antibonding orbitals.

Procedure of building the orbital diagrams

4. The four σ orbitals span a range of energies, – one being strongly bonding– another strongly antibonding, with the remaining two σ orbitals lying

between these extremes.

5. To establish the actual location of the energy levels, it is necessary to use

• electronic absorption spectroscopy,• photoelectron spectroscopy • or computation.

The variation of orbital energies for Period 2 homonuclear diatomic molecules from Li2 to F2

The molecular orbital energy level diagram for Period 2 homonuclear diatomic molecules from Li2 to N2

• The reversal of order can be traced to the increasing separation of the 2s and 2porbitals that occurs on going to the right across Period 2.

• Mixing of wavefunctions is strongest if their energies are similar.– s and p energy separation

increases, the molecular orbitals become more purely s-like and p-like

• For a small separation, each molecular orbital is a more extensive mixture of s and pcharacter on each atom.

• dxy and overlap with matching orbitals on the other atom to give rise to doubly degenerate pairs of bonding and antibondingδ orbitals.

The formation of δ orbitals by d orbital overlap. The orbital has two mutually perpendicular nodal planes that intersect along the internuclear plane.

22 yxd

−

b. The building-up principle

Key points:• The building-up principle is used to predict

the ground-state electron configurations

• For N2 the electron configuration is:1σ2

g 1σ2u 1π4

u 2σ2g

• The Highest Occupied Molecular Orbital(HOMO) is the molecular orbital that according to the building-up principle, is occupied last.

• The Lowest Unoccupied Molecular Orbital(LUMO) is the next higher molecular orbital.

• SOMO – Single Occupied Molecular Orbital – crucial for the properties of radical species

Heteronuclear diatomic molecules

• For the atoms A and B:ψ = cAφA+cBφB+...

the atoms have unequal contribution.

A molecular orbital energy level diagram arising from interaction of two atomic orbitals with different energies.

The molecular orbital energy level diagram for HF. The relative positions of the atomic orbitals reflect the ionization energies of the atoms.

In HF the bonding orbital is more concentrated on the F atom and the antibonding orbital is concentrated on the H atom.

Shriver & AtkinsInorganic Chemistry

Fourth Edition

Shriver & AtkinsInorganic Chemistry

Fourth Edition

Chapter 4Acids and Bases

Copyright © 2006 by D. F. Shriver, P. W. Atkins, T. L. Overton, J. P. Rourke, M. T. Weller, and F. A. Armstrong

Atkins • Overton • Rourke • Weller • ArmstrongAtkins • Overton • Rourke • Weller • Armstrong

Outline• Brønsted acidity

– Proton transfer equilibria in water ;– Solvent leveling;

• Characteristics of Brønsted acids– Periodic trends in aqua acid strength;– Simple oxoacids;– Anhydrous oxides;– Polyoxo compound formation;

• Lewis acidity– Example of Lewis acids and bases; – Group characteristics of Lewis acids;

• Reactions and properties of Lewis acids and bases;

Outline• Brønsted acidity

– Proton transfer equilibria in water;– Solvent leveling;

• Characteristics of Brønsted acids– Periodic trends in aqua acid strength;– Simple oxoacids;– Anhydrous oxides;– Polyoxo compound formation;

• Lewis acidity– Example of Lewis acids and bases; – Group characteristics of Lewis acids;

• Reactions and properties of Lewis acids and bases;

Brønsted acidity

Key points:• A Brønsted acid is a proton donor and a

Brønsted base is a proton acceptor;

• A simple representation of a hydrogen ion in water is as the hydronium ion H3O+.

Brønsted acidity

• Brønsted acid – proton donor• Brønsted base – proton acceptor

Ex: HF(g)+H2O(l) →H3O+(aq) + F-

(aq)

H2O(l)+ NH3(aq) → NH4+

(aq)+ OH-(aq)

H2O - is an amphiprotic substance