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3) Metallic Bond
The outer electrons are weakly bound. They roam freely in the space between the atoms
and thus are able to conduct electricity. They can be approximated by free electrons in a
constant, attractive “inner potential” V0 (typically -15 eV).
Isotropic bonding.
Examples: Alkali metals, aluminum.
Various approximations for describing electrons in metals, starting with the simplest:
E=0
jellium model =
particle in a box
V0
muffin tin potential
valence levels
core level
equivalent
single-electron
pseudopotential
full potential
Wave functions of the outer electrons
versus distance (in Å = 0.1 nm) for
nickel, a transition metal. The 4s
electrons are truly metallic, extending
well beyond the nearest neighbor atoms
(at r1, r2, r3). The 3d electrons are
concentrated at the central atom and
behave almost like a core level.
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Electronegativity
The goal: Find a simple number for each element that tells us the type of bonding
(covalent, ionic, metallic).
The electronegativity  quantifies the ability of an atom to bind electrons. There
are various definitions. The simplest is:
 = 0.184  (I + A)
I = ionization energy,
A = electron affinity (in eV)
The electron affinity is the binding energy of an added electron (= ionization energy of
the negative ion). An atom with high ionization energy is able to keep its electrons, and
an atom with high electron affinity is able to attract more electrons.
The electronegativities A , B of two atoms A, B and their difference Δχ = |A  B|
can be used to qualitatively predict the type of bonding in the compound AB :
Ionic:
Δχ large
Covalent: Δχ ≈ 0
Metallic:
Δχ ≈ 0
CsF ( = 0.8, 4.0)
χ mediumlarge
C  C ( = 2.5)
χ small
AlAl ( = 1.5)
In an ionic bond, atom A holds electrons weakly, and atom B holds them strongly. In a
covalent bond, both atoms hold electrons strongly. In a metallic bond, both atoms hold
electrons weakly. The transitions between the three types of bonding are continuous,
since the electronegativities vary gradually (see the table below).
The charge transfer between the two atoms in an ionic bond is proportional to Δχ . The
absolute charge transfer is hard to define and often subject to controversy. It depends on
how one defines the volume of each atom/ion.
Electronegativity Table
H 2.1
Li 1.0 Be 1.5 B 2.0 C 2.5 N 3.0 O 3.5 F 4.0
Na 0.9 Mg 1.2 Al 1.5 Si 1.8 P 2.1 S 2.5 Cl 3.0
K 0.8 Ca 1.0 Ga 1.8 Ge 1.8 As 2.0 Se 2.4 Br 2.8
Rb 0.8 Sr 1.0 In 1.8 Sn 1.8 Sb 1.9 Te 2.1 I 2.5
Cs 0.8 Ba 0.9 Tl 1.6 Pb 2.3 Bi 2.0
The overall trend is an increase of the electronegativity from the lower left to the upper
right of the Periodic Table.
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4) Hydrogen Bond
Attraction between static dipoles; polar molecules (containing electric dipoles).
A shared proton is attracted to two negative ions (e.g. oxygens from two H2O molecules).
||2
+
--
Can be symmetric
or asymmetric.
--
(Compare the covalent bond in H2 : A shared electron is attracted to two protons )
5) Molecular (van der Waals) Bond
Attraction between dynamic (oscillating) dipoles; non-polar molecules.
+
j
A temporary electric dipole is created at molecule i
j
by zero point oscillations at its optical resonance
-
+
-
+
creates an electric field E at a neighbor molecule j.
j
i
frequency (h  Egap , in the ultraviolet). This dipole
+
The dipole j lowers its energy by lining up parallel
to the electric field.
+
j
Electric dipole field:
E  1/rij3
Induced dipole moment  on molecule j:
  E  1/rij3
Energy of the induced dipole in the electric field:
UC  E  1/rij6
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Hydrogen Bonding in Ice
O2
H+
Tetrahedral arrangement of the oxygens. Each oxygen has two short and two long OH
bonds. That leads to many possible combinations (N) and a large entropy S = kB  ln(N) .
Hydrogen Bonding between Base Pairs in DNA
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Hydrophilic versus Hydrophobic
The hydrogen bond and the van der Waals bond are mutually exclusive, since they have
opposite requirements (polar vs. non-polar molecules). This leads to the distinction
between hydrophilic (charged) and hydrophobic (neutral) groups of atoms, for example
OH and CH3 . Hydrophilic groups bond to other hydrophilic groups, and likewise
hydrophobic to hydrophobic, but there is no bonding between hydrophilic and
hydrophobic.
This competition leads to intricate self-assembled structures which are discussed in the
next lecture.
Amphiphilic Molecules, Surfactants
Hydrophilic and hydrophobic groups can be stitched together by
covalent bonds, leading to amphiphilic molecules (= surfactants). An
example is the class of phospholipids, which consist of a charged
phosphate group stitched to neutral alkane chains (right side). They form
the cell walls of all living beings.
Block Copolymers
The same effect can be achieved in block-copolymers by stitching a
hydrophilic polymer block to a hydrophobic block. A common
combination is PMMA (=Plexiglas)  Polystyrene, as shown below.
Block copolymers are used in nano-lithography for fabricating patterns
with molecular precision.
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