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Qualitative introduction to quantum theory

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Principal Quantum Number, n, (1,2,3, ... Wave-particle duality. The uncertainty principle. The Schroedinger equation. Quantum numbers ... – PowerPoint PPT presentation

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Title: Qualitative introduction to quantum theory


1
Qualitative introduction to quantum theory
BS1030, Chemistry for Life Scientists November
25, 2008
  • Prof. Judith Klein-Seetharaman
  • School of Biological Sciences
  • j.klein-seetharaman_at_rhul.ac.uk

2
From last lecture
3
Schroedinger Equation
  • Born interpretation gives spatial distribution of
    electron
  • Quantum numbers
  • Principal Quantum Number, n, (1,2,3,)
  • Orbital Angular Momentum Quantum Number, l,
    (0,1,n-1), (s,p,d,f,g..)
  • Magnetic Quantum Number, ml , (l,l-1,-l)
  • Spin Magnetic Quantum Number, ms , (-1/2,1/2)

H? E?
Atkins Jones, Chapter 1
4
Atomic Orbitals
  • Electron configuration
  • Building up principle (Aufbauprinzip)

Atkins Jones, Chapter 1
5
Overview
  • Last 2 weeks From classical mechanics to quantum
    theory description of atomic structure
  • Energy is quantized
  • Wave-particle duality
  • The uncertainty principle
  • The Schroedinger equation
  • Quantum numbers
  • Atomic orbitals
  • This week Bonding and shapes of molecules
  • Types of bonds
  • MO theory
  • Next week (Dr. Cloarec) Delocalized electrons
  • Resonance structures
  • Aromaticity

Atkins Jones Chapter 1
Atkins Jones Chapter 23
6
What is a Chemical Bond?
7
What will decide if two atoms form a bond?
8
Example NaCl
  • Na(g) ? Na(g) e-(g)
  • energy required 494 kJ/mol (ionization energy)
  • Cl(g) e-(g) ? Cl-(g)
  • energy released 349 kJ/mol (electron affinity)
  • Net change in energy
  • energy required-energy released 494-349145
  • Gas of Na and Cl is more energetically favourable
    than gas of Na and Cl-
  • ???

9
What happens when Na and Cl- come together?
  • Na(g) Cl-(g) ? NaCl(s)
  • Their mutual attraction releases energy 787
    kJ/mol
  • Na(g) Cl(g) ? NaCl(s)
  • Energy required energy released 145-787-642
  • ? The attraction between the two opposite charges
    provides the driving force for bond formation

10
Relevance to Biomedicine
11
Enzyme Binding Pocket
-

Nature Reviews Drug Discovery 2 879-890 (2003)
doi10.1038/nrd1225
12
Relevance to Biomedicine
http//www.nist.gov/public_affairs/images/06MSEL01
1_BoneCementCellsAttachP_HR.jpg
13
Bone is rigid due to ion pairs
PO43-
Ca2
http//humor.plein.nl/files/images/thanksgiving_do
g_gets_bone.jpg
14
Types of Bonds
15
Types of Bonds
  • Ionic bond
  • Covalent bond
  • Metallic bond

16
Covalent Bond Theories
  • Lewis Theory (before quantum theory)
  • Octet rule atoms share electrons until they
    reach a noble-gas configuration

F F ? F F (F-F)
17
Covalent Bond Theories
  • Lewis Theory (before quantum theory)
  • Octet rule atoms share electrons until they
    reach a noble-gas configuration

?
F F ? F F (F-F)
18
Covalent Bond Theories
  • Valence bond theory (quantum based)

s
s
s-bond
19
Covalent Bond Theories
  • Valence bond theory (quantum based)

s
pz
s-bond
20
Covalent Bond Theories
  • Valence bond theory (quantum based)

pz
pz
s-bond
21
Covalent Bond Theories
  • Valence bond theory (quantum based)

px
px
p-bond
22
Hybrid orbitals
  • VB theory in CH4
  • Promote the electron
  • sp3 hybrids
  • h1spxpypz
  • h2s-px-pypz
  • h3s-pxpy-pz
  • h4spx-py-pz
  • Other hybrids
  • sp
  • sp2
  • sp3d2

23
The problem.
O O
http//www.superphysics.netfirms.com/t047413a.jpg
24
Covalent Bond Theories
  • Molecular orbital theory
  • The molecular orbital, ?, is formed by a linear
    combination of atomic orbitals (LCAO) and is
    called an LCAO-MO.
  • ? ?A1s ? B1s
  • ?A1s is a 1s-orbital centred on atom (A)
  • ? B1s is a 1s-orbital centred on atom (B)

25
Constructive interference bonding MO
? ?A1s ? B1s Between the nuclei the waves
interfere constructively so the total amplitude
increases. In this region the electrons interact
with both nuclei, so there is a consequent
lowering of the energy. ? is a bonding molecular
orbital
26
Destructive interference antibonding MO
  • ? ?A1s - ? B1s
  • Between the nuclei the waves can interfere
    destructively so the total amplitude decreases.
    There is a nodal surface between the atoms where
    the electrons are excluded from the region where
    they would have a strong interaction with the
    nuclei and hence the energy is higher than in the
    atomic orbitals.
  • ? is an antibonding molecular orbital

27
Hydrogen MOs
28
Where shall we put the electrons?
29
Hydrogen MOs
  • Building-up principle
  • Start with lowest energy
  • Pauli exclusion principle
  • Hund rule

30
What do the MOs look like?
31
What do the MOs look like?
32
Li2 to N2 p2p lower than s2p
O2 and F2 p2p higher than s2p
33
N2?
F2?
O2?
34
N2 configuration s2s2s2s2p2p4s2p2
Atkins Jones
35
  • F2 s2s2s2s2s2p2 p2p4 p2p4

Atkins Jones
36
O2 s2s2s2s2s2p2 p2p4 p2p1 p2p1
Atkins Jones
37
The problem is solved!
O O
O O
http//www.superphysics.netfirms.com/t047413a.jpg
38
Bond Order
  • BOnet number of bonds allowing for the
    cancellation of bonds by antibonds.
  • Bond order ½ x (number of electrons in bonding
    orbitals the number of electrons in
    antibonding orbitals)
  • BO ½(N N)

39
Heteronuclear Diatomic Molecules
Y cAYA cBYB
  • The electron is shared unequally between the two
    atoms
  • Born interpretation

40
Heteronuclear Diatomic Molecules
Y cAYA cBYB
  • The electron is shared unequally between the two
    atoms
  • Born interpretation
  • If cA2 is large, then Y looks more like YA, the
    electron density is greater near A and vice versa
  • Scenarios

41
Heteronuclear Diatomic Molecules
Y cAYA cBYB
  • The electron is shared unequally between the two
    atoms
  • Born interpretation
  • If cA2 is large, then Y looks more like YA, the
    electron density is greater near A and vice versa
  • Scenarios
  • Nonpolar covalent bond cAcB
  • Ionic bond cA0 (or cB0)
  • Polar covalent bond cA gt cB

42
Types of Bonds
  • Ionic bond
  • Covalent bond
  • Metallic bond
  • Polar covalent bond
  • Electronegativity
  • Partial charges
  • Electric dipole moment
  • Ionic character
  • Hydrogen bond

43
Examples in Biomolecules
http//users.rcn.com/jkimball.ma.ultranet/BiologyP
ages/B/BasePairing.gif
http//tainano.com/Molecular20Biology20Glossary.
files/image006.gif
44
Summary
  • What is a chemical bond?
  • Bonding types
  • Ionic
  • Covalent
  • Metallic
  • In between
  • Bonding theories
  • Lewis
  • Valence bond
  • Molecular orbital
  • Bonding and antibonding orbitals
  • Building up principle
  • Bond order
  • Diatoms
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