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 “innerpotential” V0(typically -15 eV). Isotropic bonding.
Examples: Alkali metals, aluminum.
Various approximations for describing electrons in metals, starting with the simplest:
jellium model =
particle in a box
muffin tin potential
valence levels
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.
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 CsF(=0.8, 4.0)
Covalent: Δχ≈0χ mediumlarge CC(=2.5)
Metallic: Δχ≈0χ small AlAl(=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. Thetransitions 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 Ge1.8 As 2.0 Se 2.4 Br2.8
Rb 0.8 Sr 1.0 In 1.8 Sn 1.8 Sb1.9 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.
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
(Compare the covalent bond in H2 : A shared electron is attracted to two protons)
5) Molecular (van der Waals) Bond
Attraction betweendynamic (oscillating) dipoles; non-polar molecules.
A temporary electric dipole is created atmoleculei by zero point oscillations at its optical resonance frequency (h Egap , in the ultraviolet). This dipole creates an electric field E at a neighbor moleculej. The dipole j lowers its energy by lining up parallel to the electric field.
Electric dipole field:
E 1/rij3
Induced dipole moment on moleculej:
E 1/rij3
Energy of the induced dipole in the electric field:
UCE1/rij6
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
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 blockto a hydrophobic block. A common combination is PMMA (=Plexiglas)Polystyrene, as shownbelow. Block copolymers are used in nano-lithography for fabricating patterns with molecular precision.
1