Atomic structure, bonding

Chapter 2: Atomic Structure & Interatomic Bonding
These notes have been prepared by Jorge Seminario from the textbook material
1

• Basic idea … properties of materials are a
consequence of
– Identity of the atoms
– Spatial arrangement of the atoms
– Interactions between the atoms
• Thus, we need to study atomic structure/bonding!

Chapter 2: Atomic Structure &
Interatomic Bonding
ISSUES TO ADDRESS...
• What promotes bonding?
• What types of bonds are there?
• What properties are inferred from bonding?

2.2 Atomic Structure (Freshman Chem.)
• atom – electrons – 9.11 x 10 -31 kg
protons
} neutrons 1.67 x 10 -27 kg
• atomic number = # of protons in nucleus of atom
= # of electrons of neutral species
• A [=] atomic mass unit = amu = 1/12 mass of 12 C
Atomic wt = wt of 6.022 x 10 23 molecules or atoms
C 12.011
H 1.008 etc.
1 amu/atom = 1g/mol
4

Atomic Structure
• Some of the following properties
1) Chemical
2) Electrical
3) Thermal
4) Optical
are determined by electronic structure

2.2 Fundamental Concepts
• Atoms consist of a small nucleus
containing
• Protons
+1.60 x 10 -19 C = e
1.67 x 10 -27 kg
• Neutrons
0 C (neutral)
1.67 x 10 -27 kg
• Electrons (which circle the
nucleus)
-1.60 x 10 -19 C = -e
9.11 x 10 -31 kg

2.2 Fundamental Concepts
• Atomic Number (Z)
• Number of protons in the nucleus
• Electrically neutral or complete
atom: Z = # electrons
• Atomic Mass (A)
• Sum of the masses of protons and
neutrons; atomic mass unit = amu =
1/12 mass of 12 C
• Isotopes
• Atoms of the same element with
different atomic masses due to varying
number of neutrons (e.g. 12 C, 13 C, 14 C

Basic concepts
– Atoms are made of protons, neutrons and electrons
• m e = 0.00091094x10 -27 = 9.1094x10 -31 kg = 0.511 MeV
• m p = 1.6726 x 10 -27 kg = 938.272 MeV
• m n = 1.6749 x 10 -27 kg = 939.566 MeV = m p + 1.293 MeV
– Charge of a proton and electron are the same: 1.6022x10 -19 C
– However p are +’ve and e are –’ve
– Since J = C x V (1 joule = 1 coulomb x 1 volt),
1 eV = 1.6022x10 -19 J
– mass is related to energy by E = mc 2

2.3 Electrons In Atoms
Bohr Atomic Model
• Early outgrowth of
quantum mechanics
• Electrons revolve
around nucleus in
discrete orbitals
• Electrons closer to
nucleus travel faster
then outer orbitals
• Principal quantum
number (n); 1 st shell,
n=1; 2 nd shell, n=2;
3 rd shell, n=3

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Quantum Numbers
For the H atom
Scaled for
hydrogen-like
atoms
Degenerate states
Same energy

Bohr Atom
Wave-mechanical atom
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Atomic Models
• Wave-Mechanical
Model
• Electron exhibits both
wave-like and particle-like
characteristics
• Position is now considered
to be the probability of an
electron being at various
locations around the
nucleus, forming an
electron cloud

Electron Configuration
• Pauli Exclusion Principle
• Stipulates that electron states (orbital or shell) can have no
more than two electrons, must have opposite spins
• Ground state
• All electrons occupy the lowest energies
• Electrons can move to higher states
• Filled shells are more stable

Electronic Structure
• Electrons have wave-like and particle-like properties (old view)
• We can better say that the wave-particle nature is the real
thing; individual wave and particle states are limiting cases,
observed in measurements (collapse of the wave function)
• To better understand electronic structure, we assume
– Electrons “reside” in orbitals.
– Each orbital, at a discrete energy level, is determined by
quantum numbers.
c
Quantum numbers
n = principal (energy level-shell)
Designation
K, L, M, N, O (1, 2, 3, etc.)
l = angular (orbitals) s, p, d, f (0, 1, 2, 3,…, n -1)
m l = magnetic
m s = spin ½, -½
1, 3, 5, 7 (-l to +l)
14

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Quantum Numbers
Relative electrons
energies (E) for shells
and subshells
if n↓ then E↓
Within each shell E↑
with quantum number
Overlapping in energy
of a state in one shell
with states in adjacent
shells, true of d and f
states

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Electron Configurations
• Valence electrons – those in unfilled shells
• Filled shells more stable
• Valence electrons are most available for
bonding and tend to control the chemical
properties
– example: C (atomic number = 6)
1s 2 2s 2 2p 2
valence electrons
17

Atomic Models
Quantum numbers
• Principal quantum number n, represents a
shell
• K, L, M, N, O correspond to n=1, 2, 3, 4,
5....
• Quantum number l, signifies the subshell
• Lowercase italics letter s, p, d, f; related to
the shape of the subshell
• Quantum number m l
, represents the
number of energy states
• s, p, d, f have 1, 3, 5, 7 states respectively
• Quantum number m s
, is the spin moment
• Each electron is a spin moment
• (+1/2) and (-1/2)

Electron Configuration
Silicon (Si)
• Electron configuration
represents the manner in
which the states are
occupied
• Valence electrons
• Occupy the outermost
shell
• Available for bonding
• Tend to control chemical
properties

Electron Configurations - Pauli Exclusion Principle
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Na Atom
Z = 11

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When some elements covalently
bond, they form sp hybrid bonds,
e.g., C, Si, Ge

Examples
Give the electron configurations for the following:
C
1s 2 2s 2 2p 2
Br
1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 5
Mn +2
1s 2 2s 2 2p 6 3s 2 3p 6 3d 5
F - 1s 2 2s 2 2p 6
Cr
1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 5

Electronic Configurations
ex: Fe - atomic # = 26
1s 2 2s 2 2p 6 3s 2 3p 6 3d 6 4s 2
4d
4p
3d
4s
N-shell n = 4
valence
electrons
Energy
3p M-shell n = 3
3s
2p
2s
Adapted from Fig. 2.4,
Callister & Rethwisch 3e.
L-shell n = 2
1s
K-shell n = 1
Notice that 2s and 2p do not have the same energy
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Electron Configuration
• “Stable electron configurations”
• States within the outermost or valence electron shell are
completely filled
• Some atoms of elements with unfilled shells assume
stable electron configurations by gaining or losing
electrons to form charged ions
• Sometimes s and p orbitals form hybrid sp n orbitals
• 3A, 4A, and 5A group elements typically
• Lower energy state for the valence electrons

SURVEY OF ELEMENTS
• Most elements: Electron configuration not stable.
Element
Hydrogen
Helium
Lithium
Beryllium
Boron
Carbon
...
Neon
Sodium
Magnesium
Aluminum
...
Argon
...
Krypton
Atomic #
1
2
3
4
5
6
10
11
12
13
18
...
36
Electron configuration
1s 1
1s 2
(stable)
1s 2 2s 1
1s 2 2s 2
1s 2 2s 2 2p 1
1s 2 2s 2 2p 2
...
1s 2 2s 2 2p 6 (stable)
1s 2 2s 2 2p 6 3s 1
1s 2 2s 2 2p 6 3s 2
1s 2 2s 2 2p 6 3s 2 3p 1
...
1s 2 2s 2 2p 6 3s 2 3p 6 (stable)
...
1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)
Adapted from Table 2.2,
Callister & Rethwisch 3e.
25

STABLE ELECTRON CONFIGURATIONS
Stable electron configurations...
• have complete s and p subshells
• tend to be unreactive.
Adapted from Table 2.2,
Callister 6e.
4

2.4 Periodic Table
• Elements classified according to electron configuration
• Elements in a given column or group have similar valence electron
structures as well as chemical and physical properties
• Group 0 – inert gases, filled shells and stable
• Group VIIA – halogen
• Group IA and IIA - alkali and alkaline earth metals
• Groups IIIB---IIB – transition metals
• Groups IIIA, IVA and VA – characteristics between the metals and
nonmetals

2.4

Electronegativity Values
• Electropositive:
• Capable of giving up their
valence electrons to become
positively charged
• Electronegative:
• Readily accept electrons to form
negatively charged ions
• Sometimes share electrons with
other atoms

Atomic Bonding
• Valence electrons determine all of the
following properties
1) Chemical
2) Electrical
3) Thermal
4) Optical
5) Deteriorative
6) etc.
30

Atomic Bonding in Solids

When 0 = F A + F R ,
equilibrium exists.
The centers of the
atoms will remain
separated by the
equilibrium spacing
r o .
2.5 Bonding Forces and
Energies
This spacing also
corresponds to the
minimum of the
potential energy
curve. The energy
that would be
required to
separate two
atoms to an infinite
separation is E o
F N = F A + F R
Figure 2.8
E N = E A + E R

2.5 Bonding Forces and Energies
• A number of material properties depend on E o ,
the curve shape, and bonding type
– Material with large E o typically have higher melting
points
– Mechanical stiffness is dependent on the shape of its
force vs. interatomic separation curve (F vs r)
– A material’s linear coefficient of thermal expansion
is related to the shape of its E vs. r curve

Bonding in Solids
• 2.5 Bonding forces and energies
– Far apart: atoms don’t know about each other
– As they approach one another, start to exert force on one
another
• two types of forces
– Attractive (F A ) – slowly changing with distance
– Repulsive (F R ) – typically short-range
– Net force is the sum of these
F N = F A + F R
– At some point the net force is zero; at that position a state of
equilibrium exists

Bonding forces and energies
F
E
E
dE
F
dr
F A
F R
N
N
r
E
F
A
A
dr
E
R
r
F
R
Bonding in Solids
dr
E
The interatomic separation at that point (r o ) corresponds
to the potential energy at that minimum
E o , it is also the bonding energy
E o is the energy needed to separate the atoms
Fdr
r
Fdr
& setting our ZERO ENERGY reference at ∞
r
Fdr
The point where the forces
are zero also corresponds
to the minimum potential
energy for the two atoms,
which makes sense because
-dE/dr = F = 0 at a minimum.

Examples
(book wrong sign of the F)
Calculate the force of attraction between ions X + and an Y - , the
centers of which are separated by a distance of 2.01 nm.
&

2.6 Primary Interatomic Bonds
• Types of chemical bonds found in solids
– Ionic
– Covalent
– Metallic
• As you might imagine, the type of bonding influences
properties – why?
• Bonding involves the valence electrons!!!

2.6 Primary Interatomic Bonds
• Ionic Bonding
– Compounds composed of metallic and nonmetallic
elements
– Coulombic Attractive Forces: positive and negative ions,
by virtue of their net electrical charge, attract one another
• E A = -A/r
• E R = B/r n
Coulombic bonding Force
A, B, n are
Cl
Na
constants -
+
– Bonding is nondirectional: the magnitude of the bond is
equal in all directions around an ion
– Properties: generally large bonding energies (600-1500
kJ/mol) and thus high melting temperatures, hard, brittle,
and electrically and thermally insulative

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2.6 Primary Interatomic Bonds

2.6 Primary Interatomic Bonds
• Ionic bonding
– Prototype example – sodium chloride (NaCl)
• Sodium gives up one its electrons to chlorine – sodium becomes
positively charged, chlorine becomes negatively charged
– The attraction energy is electrostatic in nature in ionic solids
(opposite charges attract)
– The attractive component of the potential energy (for 2 point
charges) is given by
– The repulsive term is given by
E
E
A
R
B
n
r
Z eZ
e
1 2
4
o
1
r
, n ~ 8 12

Ionic bond: metal + nonmetal
donates
electrons
accepts
electrons
Dissimilar electronegativities
ex: MgO Mg 1s 2 2s 2 2p 6 3s 2 O 1s 2 2s 2 2p 4
[Ne] 3s 2
Mg 2+ 1s 2 2s 2 2p 6 O 2- 1s 2 2s 2 2p 6
[Ne]
[Ne]
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Ionic Bonding
• Occurs between + and - ions.
• Requires electron transfer.
• Large difference in electronegativity required.
• Example: NaCl
Na (metal)
unstable
electron
Cl (nonmetal)
unstable
Na (cation)
stable
+ -
Coulombic
Attraction
Cl (anion)
stable
42

Ionic Bonding
• Energy – minimum energy most stable
– Energy balance of attractive and repulsive terms
E N = E A + E R =
A
r
B
r n
Repulsive energy E R
Interatomic separation r
Net energy E N
Adapted from Fig. 2.8(b),
Callister & Rethwisch 3e.
Attractive energy E A
43

Examples: Ionic Bonding
• Predominant bonding in Ceramics
NaCl
MgO
CaF 2
CsCl
Give up electrons
Acquire electrons
Adapted from Fig. 2.7, Callister & Rethwisch 3e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the
Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.
44

2.6 Primary Interatomic Bonds
• Covalent Bonding
– Stable electron configurations are assumed by
the sharing of electrons between adjacent atoms
– Bonding is directional: between specific atoms
and may exist only in the direction between one
atom and another that participates in electron
sharing
– Number of covalent bonds for a particular
molecule is determined by the number of
valence electrons
– Bond strength ranges from strong to weak
• Rarely are compounds purely ionic or
covalent but are a percentage of both.
Sharing 2
electrons
Sharing
4
electrons
%ionic character = {1 – exp[-(0.25)(X A -X B ) 2 ]} x 100
X A and X B are electronegatives

Covalent bonding
– Sharing of electrons between adjacent atoms
– Most nonmetallic elements and molecules containing
dissimilar elements have covalent bonds
– Polymers!
– Bonding is highly directional!
– Number of covalent bonds possible is guessed by the
number of valence electrons
• Typically is 8 – N, where N is the number of valence
electrons
• Carbon has 4 valence e’s – 4 bonds (ok!)

H
2.1
Li
1.0
Na
0.9
K
0.8
Rb
0.8
Cs
0.7
Fr
0.7
EXAMPLES: COVALENT BONDING
Be
1.5
Mg
1.2
Ca
1.0
Sr
1.0
Ba
0.9
Ra
0.9
H2
Ti
1.5
Cr
1.6
Fe
1.8
H2O
C(diamond)
SiC
Ni
1.8
Zn
1.8
Ga
1.6
column IVA
C
2.5
Si
1.8
As
2.0
GaAs
Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 is
adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright
1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.
Ge
1.8
Sn
1.8
Pb
1.8
O
2.0
F
4.0
Cl
3.0
Br
2.8
I
2.5
At
2.2
He
-
Ne
-
Ar
-
Kr
-
Xe
-
Rn
-
F2
Cl2
• Molecules with nonmetals
• Molecules with metals and nonmetals
• Elemental solids (RHS of Periodic Table)
• Compound solids (about column IVA)
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Covalent Bonding
• similar electronegativity share electrons
• bonds determined by valence – s & p orbitals
dominate bonding
• Example: CH 4
shared electrons
C: has 4 valence e - ,
needs 4 more
CH 4
H
from carbon atom
H: has 1 valence e - ,
needs 1 more
Electronegativities
are comparable.
H
C
H
H
shared electrons
from hydrogen
atoms
Adapted from Fig. 2.10, Callister & Rethwisch 3e.
48

Bonding in Solids
• Many materials have bonding that is both ionic and
covalent in nature (very few materials actually exhibit pure
ionic or covalent bonding)
• Easy (empirical) way to estimate % of ionic bonding
character:
%ionic character
2
1exp
(0.25)(
X ) x
100
A
X B
X A , X B are the electronegativities of atoms A and B involved
Notice: this is a very very very empirical formula

Primary Bonding
• Ionic-Covalent Mixed Bonding
% ionic character =
x ( 100 %)
where X A & X B are Pauling electronegativities
Ex: MgO X Mg = 1.3
X O = 3.5
1 e (X AX B ) 2
4
(3.5
% ionic character 1
e 4
1.3)
2
x (100%)
70.2%ionic
50

Example
Compute the percentage ionic character of the interatomic bond for
zinc oxide (ZnO). Refer to the periodic Table for electronegativity
values. Note: Electronegativity values in slides differ slightly from
those in book.
% ionic character = {1-exp[-(0.25)*(X Zn -X O ) 2 ]}*100
= {1-exp[-(0.25)*(1.7-3.5) 2 ]}*100
= 55.51%

2.6 Primary Interatomic Bonds
• Metallic Bonding
– Found in metals and their alloys
– 1 to 3 valence electrons that form a
“sea of electrons” or an “electron
cloud” because they are more or
less free to drift through the entire
metal
– Nonvalence electrons and atomic
nuclei form ion cores
– Bonding energies range from weak
to strong
– Good conductor of both electricity
and heat
– Most metals and their alloys fail in
a ductile manner
+
+
+
Ion
Cores
+
- -
+
- -
+
Sea of Valence
Electrons
+
+
+

METALLIC BONDING
• Arises from a sea of donated valence electrons
(1, 2, or 3 from each atom).
Adapted from Fig. 2.11, Callister 6e.
• Primary bond for metals and their alloys
12

• Metallic bonding
Bonding in Solids
– Most metals have one, two, or at most three valence electrons
– These electrons are highly delocalized from a specific atom – have
a “sea of valence electrons”
– Free electrons shield positive core of
ions from one another (reduce E R )
– Metallic bonding is also nondirectional
– Free electrons also act to hold
structure together
– Wide range of bonding energies,
typically good conductors (why?)

2.7 Secondary Bonding or van der
Walls Bonding
• Also known as physical bonds
• Weak in comparison to primary or chemical
bonds
• Exist between virtually all atoms and molecules
• Arise from atomic or molecular dipoles
– bonding that results from the coulombic attraction
between the positive end of one dipole and the
negative region of an adjacent one
– a dipole may be created or induced in an atom or
molecule that is normally electrically symmetric

2.7 Secondary Bonding or van der
Waals Bonding
• Fluctuating Induced Dipole Bonds
– A dipole (whether induced or instantaneous)
produces a displacement of the electron distribution
of an adjacent molecule or atom and continues as a
chain effect
– Liquefaction and solidification of inert gases
– Weakest Bonds
– Extremely low boiling and melting point
Atomic nucleus
Electron
cloud
Instantaneous
Fluctuation
Atomic nucleus
Electron
cloud

2.7 Secondary Bonding or van der Waals Bonding
• Polar Molecule-Induced Dipole Bonds
– Permanent dipole moments exist by virtue of an
asymmetrical arrangement of positively and negatively
charged regions
– Polar molecules can induce dipoles in adjacent nonpolar
molecules
– Magnitude of bond greater than for fluctuating induced
dipoles
+ -
Atomic nucleus
Electron Cloud
Polar
Molecule
Induced
Dipole

2.7 Secondary Bonding or van der
Waals Bonding
• Permanent Dipole Bonds
– Stronger than any secondary bonding with induced
dipoles
– A special case of this is hydrogen bonding: exists
between molecules that have hydrogen as one of the
constituents
Hydrogen Bond
H Cl H Cl

Permanent dipoles
Hydrogen-bonds
These interactions are fairly strong, very
complex, and surprisingly not well understood!
van der Waals
interactions between
polar molecules
2.82 Å
109.47°
Best known example
hydrogen bonding

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MATERIAL OF IMPORTANCE
Water
Many molecules do not have a
symmetric distribution/arrangement
of positive and negative charges
(e.g. H 2 O, HCl)
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