What we have learned so far toward molecular structure and properties.
Model of the atom
Quantum theory
Hydrogen atom
(one electron atoms)
The nuclear model of atom
Thompson’s model
Rutherford’s model
Atomic spcetra -- Bohr’s model
Wave-particle duality
Uncertainty principle
Wave function – particle in a box
Schroedinger equation
Principle quantum number
Atomic orbitals: radial wave function
angular wave function
orbital angular momentum
magnetic quantum numbers
radial distribution function
shape of atomic orbitals
electron spin
Many electron atoms orbital energy split
shielding effect
effective nuclear charge
Pauli exclusion principle
Hund’s rule
valence shell (electrons)
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Periodicity of atomic properties
Atomic radius
Ionic radius
Ionization energy
Electron affinity
Periodic table
What we have learned so far toward molecular structure and properties.
Chemical bond Interaction between two electrons
Ionic bond
Lewis structure
Covalent bond
electronegativity
Octet rule
Exceptions to octet rule
Resonance
Formal charge
Oxidation number
Ionic v.s. covalent
Dipole moment
Polar bond
Nonpolar bond
Bond strength
Bond length
IR(infrared) spectroscopy
MOLECULAR SHAPE AND STRUCTURE
Stability, reactivity, color, size, polarity, solubility, function etc…
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3D structure of a molecule is crucial for its property.
Sophisticated quantum mechanical calculations are needed
to predict the structure.
⇒ Drugs by Design and Discovery
Box 3.1
1) Identification of key enzymes
2) Molecular structure determination
3) Hints from Nature --- Natural Products
4) Computer-aided design of molecules
with structures fitting into the active site
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Chapter 3.
MOLECULAR SHAPE AND STRUCTURE
THE VSEPR MODEL (전자쌍 반발 모델)
3.1 The Basic VSEPR Model
3.2 Molecules with Lone Pairs on the Central Atom
3.3 Polar Molecules
VALENCE-BOND THEORY (원자가 결합 이론)
3.4 Sigma and Pi Bonds
3.5 Electron Promotion and the Hybridization of Orbitals
(혼성궤도 함수)
3.6 Other Common Types of Hybridization
3.7 Characteristics of Multiple Bonds
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THE VSEPR MODEL (Sections 3.1-3.3)
Lewis structure:
showing the linkages between atoms and the presence of lone pairs,
but not the 3D arrangement of atoms
BeCl2
H 2O
SF4
XeF4
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BF3
NH3
PCl5
ClF3
IF5
CH4
SF6
Estimating the 3D structure: THE VSEPR MODEL
3.1 The Basic VSEPR Model
Valence Shell Electron-Pair Repulsion theory
Electron pairs (lone pairs & bonding pairs) repel each other.
Proposed by R. J. Gillespie in 1959.
Rule 1: Electron pairs move as far apart as possible.
VSEPR structures for AXn with no lone pair
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BeCl2
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BF3
CH4
PCl5
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SF6
Rule 2: (Almost) No distinction between single and multiple
bonds.
BeCl2
BF3
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CO2
CO32-
3.2 Molecules with Lone Pairs on the Central Atom
 Rule 3 All regions of high electron density, lone pairs and bonds, are included in a
description of the electronic arrangement,
But only the positions of atoms are considered when identifying the shape of a molecule.
NH3
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CH4
98
 Rule 4 The strength of repulsions are in the order
lone pair-lone pair > lone pair-atom > atom-atom
NH3
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H2O
99
ClF3
PCl5
axial
SF4
equatorial
axial
T-shaped
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equatorial
seesaw shaped
more stable
 Predicting a molecular shape of XeF4
Step 1 Draw the Lewis structure.
Step 2 Assign the electron arrangement
around the central atom.
Step 3 Identify the molecular shape. AX4E.
Step 4 Allow for distortions.
Square planar
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AXE method
A; central atom
X; outside atom
E; lone pair
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3.3 Polar Molecules
 Polar molecule: a molecule with a nonzero dipole moment
i.e. HCl with a dipole moment of 1.1 D
HCl, H2O, CHCl3, cis-dichloroethane, ···
- A polyatomic molecule is polar if it has polar bonds arranged in
space in such a way that the dipole moments associated with
the bonds do not cancel.
polar
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polar
102
3.3 Polar Molecules
 Nonpolar molecule: a molecule with a net zero dipole moment
Homonuclear diatomic molecules
Polyatomic molecules with symmetry;
CO2, BF3, CH4, CCl4, trans-dichloroethane, ···
nonpolar
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nonpolar
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VALENCE-BOND THEORY (Sections 3.4-3.7)
105
Lewis model of the chemical bond; localized electron model
Valence-bond theory; Walter Heitler, Fritz London (1927)
Linus Pauling (1931)
Quantum mechanical description of the distribution of electrons in bonds
Valence electrons are localized either between pairs of atoms or on atoms as lone pairs.
1) Hybridization of atomic valence orbitals with proper symmetry
that are localized between pairs of atoms.
2) Placing valence electrons in the hybridized orbitals as pairs (↑↓) or leaving them
localized in lone-pair orbitals on individual atoms in the molecule.
VSEPR theory is a simplified one : powerful way of predicting the shape of simple
molecules. --- does not explain many things including multiple bond, bond angles
……..
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3.4 s(Sigma) and p(Pi) Bonds: description of covalent bond
H2
Walter Heitler, Fritz London (1927)
1) Two hydrogen 1s-orbitals merge (overlap) to form a s-orbital between the two
hydrogen atoms.
2) A s-bond is formed as two electrons (↑↓) fill the s-orbital.
s-bond ;
cylindrically symmetrical with no nodal planes containing the intermolecular
axis.
i.e. H2, 1s-1s
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HF, 1s-2pz
N2, 2pz-2pz
105
106
overlap with 1:1 match of orbitals
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overlap with 1:1 match of orbitals
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 p-bond
nodal plane containing the interatomic (bond) axis
- two cylindrical shapes (lobes), one above and the other below the nodal plane
N2
one s-bond
with two
perpendicular
p-bonds
- multiple bonds: single bond (one s-bond),
double bond (one s- and one p-bond)
triple bond (one s- and two p-bonds)
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Polyatomic molecules
Linus Pauling (1931)
BeH2
3.5 Electron Promotion and the Hybridization of Orbitals
Why do we have to make hybrid orbitals?
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not real.
localization problem
Linear combination of orbitals
sp hybrid
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Linear molecule
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BH3
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sp2 hybrid orbitals
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CH4
promotion
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hybridization
sp3
107
hybrids
h1 = s + px + py + pz h = s - p - p + p
2
x
y
z
h3 = s - px + py - pz h = s + p - p - p
4
x
y
z
similar ideas to VSEPR
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NH3
hybrid orbitals can be determined
by the steric number
based on the VSEPR model.
steric number =
# of atoms bonded to the central atom
+
# of lone pairs
H2O
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- sp3d hybrid orbitals in PCl5
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- sp3d2 hybrid orbitals in SF6 and XeF4
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C2H6
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3.7 Characteristics of Multiple Bonds
CO2
Carbon
Steric # = 2
Oxygen
Steric # = 3
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3.7 Characteristics of Multiple Bonds
CO2
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3.7 Characteristics of Multiple Bonds
- ethene, CH2=CH2
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C-C s bond, s(C2sp2, C2sp2)
C-C p bond, p(C2p, C2p)
each C-H bond formed as s(C2sp2, H1s)
restricted rotation
111
112
- ethyne (acetylene), C2H2
free rotation
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- benzene, C6H6
Now, delocalization has the meaning !
Still, there are many properties that can not be explained by the current model.
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111
CO32-
resonance hybrid
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3.8 The Limitations of Lewis’s Theory
& Valence Bond Theory
Paramagnetic O2; unpaired electron(s)
Lewis's theory;
Valence-bond theory;
bond and
bond
2 lone pairs on each O occupying the sp2 hybrid orbitals
Paramagnetic: tendency to move into the magnetic field.
When there are unpaired electrons in the molecule.
Diamagnetic: tendency to move out of the magnetic field.
When all the electrons in the molecules are paired.
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113s
3.8 The Limitations of Lewis’s Theory
& Valence Bond Theory
Shortcomings of the Valence Bond Model
1) Inadequate treatment of odd-electron molecules and resonances
2) Magnetism of molecules
• Paramagnetic: molecules with
unpaired electrons
• Diamagnetic: weakly repelled
by a magnetic field
N
N
both are expected to be diamagnetic!!
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O2
N2
3.8 The Limitations of Lewis’s Theory
& Valence Bond Theory
113
Electron deficient diborane, B2H6
First published by H. C. Lunguet-Higgins,
a 2nd year undergraduate student !
does not have enough electrons !
At least seven bonds (= 14 electrons) are required,
but only 12 valence electrons.
- No simple explanation for spectroscopic properties of compounds
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MOLECULAR ORBITAL THEORY
(Sections 3.8-3.12)
3.9 Molecular Orbitals
3.10 Electron Configurations of Diatomic Molecules
3.11 Bonding in Heteronuclear Diatomic Molecules
3.12 Orbitals in Polyatomic Molecules
 Molecular Orbital (MO) theory advantages
-
Addresses all of the above shortcomings of VB theory
Provides a deeper understanding of electron-pair bonds
Accounts for the structure and properties of metals and semiconductors
Universally used in calculations of molecular structures
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115s
H2+: Prototype Molecular Orbital System
• Atomic orbital(AO) theory → successful for orbital structures of all atoms
with both even and odd numbers of electrons
• Assume that molecule H2+ ~ as an united atom with a fragmented
nucleus if the nuclei in molecule were fused together
• construct the one-electron orbital corresponding to the arrangement of
nuclear charges presented by the molecule
Coulomb interactions in H2+
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3.9 Molecular Orbitals
Quantum mechanics : the ideal solution to the problem, but…….
Even for the smallest molecule, H2
Schroedinger equation will look like…..
and way too complex and complicated… So, need simplification !
Simplification 1 (Born - Oppenheimer Approximation)
Simplification 2 (Orbital Approximation)
Simplification 3 (LCAO Approximation)
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3.9 Molecular Orbitals
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The valence-bond (VB) and molecular orbital (MO) theories are both procedures for
constructing approximate wavefunctions of electrons.
- In VB theory, bonding electrons are localized on atoms or between pairs of
atoms.
 Molecular orbitals (MOs)
The MO theory can account for electron-deficient compounds, paramagnetic O2, and
many other properties by focusing on electrons delocalized over the whole molecule.
 MOs formed by linear combination of atomic orbitals (LCAO-MO)
Approximate molecular wavefunctions
of N atomic orbitals
cij and Ej are determined
by solving the Schrödinger equation
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by superimposing (mixing)
Trial wavefunctions for H2 using two 1s atomic orbitals of H
Increased amplitude in the internuclear region
Larger volume for electrons
lower kinetic energy
(particle-in-a-box)
Decreased amplitude in the internuclear
region & nodal plane
antibonding
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bonding
 Molecular orbital energy-level diagram
- relative energies of original AOs and resulting MOs
- arrows to show electron spin and location of the electrons
- In H2, two 1s-orbitals merge to form
the bonding orbital s1s and the antibonding orbital s1s*
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3.10 Electron Configurations of Diatomic Molecules
Building-up principle for MO
 Valence electrons in molecular orbitals
1. Electrons are accommodated in the lowest-energy MO, then in
orbitals of increasingly higher energy.
2. Pauli exclusion principle:
each MO can accommodate up to two electrons.
If two electrons are present in one orbital, they must be paired.
3. Hund’s rule:
If more than one MO of the same energy is available,
the electrons enter them singly and adopt parallel spins.
H2:
The energy of H2 is lower than
that of the separate H atoms.
Even the energy of H2+ is lower than
that of the separate H atoms.
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H2
He2
Bond order = 0
Bond order = 1
Bond order = ½( # of bonding electrons - # of antibonding electrons)
H2+
Bond order = 1/2
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He2+
Bond order = 1/2
 For other homonuclear diatomic molecules of Period 2 elements,
Linear combination of 10 atomic orbitals;
1. No mixing between AO's of the same atom
2. Significant mixing only between AO's of similar energies and substantial overlap
⇒ Negligible mixing between the core 1s and the valence 2s and 2p orbitals
⇒ No
MO from 2s–2p mixing due to symmetry
- two 2s orbitals (one on each atom) overlap to form two s orbitals,
one bonding (s2s-orbital) and the other antibonding (s2s*-orbital)
- six 2p orbitals (three on each atom) overlap to form six MOs,
two 2pz orbitals to form bonding and antibonding (s2p, s2p*)
four 2px, 2py orbitals to form two p2p and two p2p* orbitals
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four 2px, 2py orbitals to
form two p2p and
two p2p* orbitals
two 2pz orbitals to form
bonding s2p and
antibonding s2p* orbitals
one bonding (s2s-orbital)
and the other
antibonding (s2s*-orbital)
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- From Li2 to N2, the energy levels of 2s and 2p are close, and thus
the 2s orbital also participates in forming s2p orbitals.
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- For O2 and F2, the energy levels of 2s and 2p are separated well.
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- In N2, each atom supplies five valence electrons.
A total of ten electrons fill the MOs.
The ground configuration is,
 Bond order (b): net number of bonds
b = ½(8-2) = 3
- In O2, each atom supplies six valence electrons.
A total of twelve electrons fill the MOs.
The ground configuration is,
b = ½(8-4) = 2
accounts for paramagnetism of O2
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118
 Bond order (b) = 1
0
1
does not exist
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2
3
paramagnetic
2
1
Second-Row MO Diagrams
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3.11 Bonding in Heteronuclear Diatomic Molecules
 A diatomic molecule built from atoms of two different elements
in polar, with the electrons shared unequally by the two atoms.
- In a nonpolar covalent bond, cA2 = cB2
- In an ionic bond, the coefficient belonging to one ion is zero.
-In a polar covalent bond,
the AO belonging to the more electronegative atom has the lower energy,
and so it makes the larger contribution to the lowest energy (bonding) MO.
Conversely, the contribution to the highest-energy (most antibonding)
orbital is greater for the higher-energy AO, which belongs to the less
electronegative atom.
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HF
No net overlap between H1s and (F2px or F2py) ⇒ 2 "nonbonding" orbitals
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orbital mainly of F2pz (energy level close to F2pz)
orbital mainly of H1s (energy level close to H1s)
⇒
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CO and NO
CO
from 2p-2p mixing only
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most stable
diatomic molecule
NO
3.12 Orbitals in Polyatomic Molecules
- The MOs spread over all atoms in the molecule.
experimentally studied by using ultraviolet and visible spectroscopy
too complex --- qualitative assessment
- A water molecule with six atomic orbitals
(one O2s, three O2p, and two H1s)
1b1; nonbonding, mainly O2py, lone pair effect
2a1; almost nonbonding
⇒
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121
antibonding orbitals
O2px
nonbonding orbital
H1s-O2py-H1s
bonding orbitals
H1s-(O2s,2pz)-H1s
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121s
MO and energy levels of a linear triatomic dihydride HXH
LUMO
Reversed the
energy levels σ2s*
-σ2p (cf. Fig. 7.7)
energy – no. of nodes relationship
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121s
• 8 valence electrons of water → (σ2s)2(σ2p)2(nπ2p)4
O
H
H
• By bending ;
σ2s→ favorable since of constructive overlap
between the end hydrogens.
σ2p→ destabilizes since 1s orbitals have opposite signs
n2p→ depends on their orientation
e.g. bending occurs in the xz plane 
py – little change;
px – can overlap with H 1s orbital: lowing its energy
 2 orbitals go down in energy(σ2s, n2px),
1 goes up (σ2p), and 1 remains same (n2py)
→ water is favorable to be bent geometry
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MO of water
LUMO
HOMO
Energy decrease;
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Energy increase
121s
CH4 ; 1 of the 4 electron pairs is slightly lower in energy.
from photoelectron spectroscopy
VB-theory; all eight electrons have the same energy.
MO-theory; (1a1)2(1t1)6
⇒ Lower energy for the 1a1 electron pair
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 benzene, C6H6
122
- All thirty C2s-, C2p-, and H1s-orbitals contribute MOs.
- The orbitals in the ring plane:
C2s-, C2px, C2py, and six H1s-orbitals → delocalized s-orbitals for C-C and C-H
- six C2pz-orbitals perpendicular to the ring → delocalized p-orbitals spreading
the ring
- consider the two separately !!
From VB, each C atom with sp2 hybrid orbitals forming s-bonds and 120° angles.
From MO, the six C2pz-orbitals form six delocalized p-orbitals.
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6 p-orbital shapes from fully bonding to fully antibonding
antibonding
bonding
great stability: the p-electrons occupy
only orbitals with a net bonding effect
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MO does not require electron pair for each bonding or octet rule for a particular atom
as all electrons are spread over all the atoms in the molecule.
 Hypervalent compounds
- From VB, SF6 with sp3d2 hybridization
- From MO, four orbitals of S and six of F,
a total of 10 AOs → 10 MOs
12 electrons occupy bonding and nonbonding
orbitals.
- Average bond order of each S-F is 2/3.
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124
 Colors of vegetation
for benzene p-electrons
Unoccupied
MO
hn
LUMO
excitation
Occupied
MO
HOMO
- lowest unoccupied molecular orbital (LUMO)
- highest occupied molecular orbital (HOMO)
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 Colors of vegetation
124
b-carotene
lycopene
Retinal (vitamin A)
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 Particle in a box (one dimensional)
ULTRAVIOLET AND VISIBLE SPECTROSCOPY
 The Technique
- The electrons in the molecule can be excited to a higher energy state,
by electromagnetic radiation.
Bohr frequency condition, DE = hn
- UV-vis absorption gives us information about the electronic energy
levels of molecules.
i.e. Chlorophyll absorbs red and blue
light, leaving the green light present
in white light to be reflected.
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131
 Chromophores
- Characteristic groups of atoms in the molecules absorbing certain
bands in visible and ultraviolet spectra
- p-to-p* transition in conjugated double bonds ~ 160 nm
- n-to-p* transition in the carbonyl group ~ 280 nm
- d-to-d transition in d-metal complexes in visible ranges
- charge transfer transition in d-metal complexes electrons migrate
from the ligands to the metal atom or vice versa
i.e. deep purple color of MnO42012 General Chemistry I
Model of the atom
The nuclear model of atom
Thompson’s model
Rutherford’s model
Atomic spectra -- Bohr’s model
Quantum theory
Quantization: M. Plank
E = hn
Wave-particle duality: de Broglie
Uncertainty principle: Heisenberg
Wave function – Schroedinger equation
particle in a box
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Solution:
particle in a box
Solution:
Hydrogen atom (one electron atoms)
n= principal quantum number
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Hydrogen atom (one electron atoms) Principal quantum number
Atomic orbitals: orbital angular momentum --- shape
magnetic quantum number -- orientation
spin magnetic quantum number – spin direction
Periodicity of atomic properties
Many-electron atoms
orbital energy
shielding effect
effective nuclear charge
Pauli exclusion principle
valence shell (electrons)
Hund’s rule
Atomic radius
Ionic radius
Ionization energy
Electron affinity
Periodic table
 Toward molecules…...
 Chemical bond is the link between atoms.
Ionic bond; electron transfer + electrostatic attraction
Covalent bond; sharing electrons
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Lewis structure
Octet rule ---- ---- coordinate covalent bond
Resonance
Formal charge
Oxidation number
toward molecular structure and properties.
115
The valence-bond (VB) and molecular orbital (MO) theories are both procedures for
constructing approximate wavefunctions of electrons.
- In VB theory, bonding electrons are localized on atoms or between pairs of
atoms.
 Molecular orbitals (MOs)
The MO theory can account for electron-deficient compounds, paramagnetic O2, and
many other properties by focusing on electrons delocalized over the whole molecule.
 MOs formed by linear combination of atomic orbitals (LCAO-MO)
Approximate molecular wavefunctions
of N atomic orbitals
cij and Ej are determined
by solving the Schrödinger equation
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by superimposing (mixing)
Building-up principle for MO
 Valence electrons in molecular orbitals
1. the lowest-energy MO first then in orbitals of increasingly higher energy.
2. Pauli exclusion principle:
3. Hund’s rule:
1. No mixing between AO's of the same atom
2. Significant mixing only between AO's of similar energies and substantial overlap
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3.11 Bonding in Heteronuclear Diatomic Molecules
CO and NO
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