Chapter 29
Molecules and Solids
Chapter 29
• Bonding in Molecules
• Potential­Energy Diagrams for Molecules
• Weak (van der Waals) Bonds
• Molecular Spectra
• Bonding in Solids
• Electronic Energy Bands in Solids
• Semiconductors and Doping
Bonding in Molecules
Molecule: two or more atoms strongly held together to function as a unit
This attachment is called a chemical bond
Two main types of bond:
• Covalent ­ shared electrons, often directional
• Ionic ­ oppositely charged ions, non­directional
Bonding in Molecules
Hydrogen molecule, H2, is bound covalently. If the atoms have e− spins in the same direction, S = 1 the atoms will not bond due to the exclusion principle.
The molecule will only form if S = 0. The two electrons can then be shared by the two atoms.
S = 1
no bond
S = 0
How does angular momentum add ?
Two particles have s1 and s2 as quantum numbers for L.
What are the possible states Total L and Lz when combined ?
Total L for {S,M}: S from |s1­s2| to s1+s2 in integral steps
Then Lz can give M from –S to S in integer steps, as usual
If initial m’s are given then its more restricted: M = +/­ m1 +/­ m2
Expl: s1=1 and s2=1 Total of three S values are then possible
Total S = 2 or S = 1 or S = 0
Allowed M = 2
M = 1
M = 0
1 0
0 ­1
­1
Bonding in Molecules
Ionic bonds ­ created by the attraction of ions.
For example, the outer electron in the sodium atom spends most of its time around the chlorine atom in NaCl. Na+ and Cl­ are closed shell ions.
Bonding in Molecules
Mixed bonding: Pure covalent bonds are found in molecules consisting of only one type of atom. Otherwise, electrons are likely to spend more time around one type of atom than another, giving a partial ionic character. Water is one such molecule.
Potential­Energy Diagrams for Molecules
For the hydrogen molecule, the force between the atoms is attractive at large distances. If the atoms are too close, the electrons are too squeezed; therefore there is a minimum in the potential.
Weak (van der Waals) Bonds
Weak bonds are electrostatic bonds between molecules (and not between atoms within a molecule). The binding energy is much less than that of the main bond types, about 0.04 to 0.3 eV.
Van der Waals bonds are the result of attraction between electric dipoles.
Molecular Spectra
Orbital overlap alters energy levels in molecules: N atoms give N levels for each atomic state. More types of energy levels are possible due to rotations and vibrations. The result is a band of closely spaced energy levels.
Molecular Spectra: Rotational States
A diatomic molecule can rotate around a vertical axis. The rotational energy is quantized.
Molecular Spectra: Rotational States
These are some rotational energy levels and allowed transitions for a diatomic molecule.
Each level adds to previous energy
EL = EL­1+ L h2/4π 2I
Molecular Spectra: Vibrational States
Small­amplitude vibrations of a molecule or in a solid will be simple harmonic. Again, energy is quantized. Thermal expansion of solids is due to anharmonic effects.
anharmonic
approximately harmonic
Molecular Spectra
m =
Here are some vibrational energy levels in a diatomic molecule, with some allowed transitions.
This set of levels is modeled as a simple harmonic oscillator.
Em = (m+1/2) hf
Bonding in Solids
Some solids are amorphous, but most are crystalline, having their molecules arranged in a regular lattice.
Here are the three possible cubic crystal lattices:
simple cubic face­centered body centered (SC) 6 nn
(FCC) 12 nn
(BCC) 8 nn
29. Bonding in Solids
The NaCl lattice is face­centered cubic; here is what it looks like, with the atoms in their actual “packed” configuration.
Band Theory of Solids
The more atoms that are bound together with overlapping wave functions, the more continuous the energy bands become. Each atomic energy level becomes an energy band in a solid. Here is what happens with two, six, and many atoms:
Bond length
Band Theory of Solids
A metal has a band partly filled. An insulator has a large gap between a filled band and an empty one. A semiconductor also has its valence band filled, but a small gap to the next level (conduction band). Empty
Occupied
Gap
Semiconductors and Doping
Phosphorous­ or arsenic­doped silicon becomes an n­type semiconductor; current is carried by negative charges (electrons in the conduction band).
P or As have 5 valence electrons to 4 for Si. The extra e­ is very weakly bound and easily goes to conduction band.
Semiconductors and Doping
Gallium­doped silicon is a p­type semiconductor – the current is carried by “holes,” or spots in the valence band that are missing an electron – act like a positive charge moving in a filled valence band.
Ga has only 3 valence electrons
Semiconductors and Doping
The dopants provide additional energy states to the semiconductor that lie very close to band edges; these dopants ionize very easily. Semiconductor devices (diodes, transistors, IC’s, etc) require both n and p type material in finely controlled structures.
Summary of Chapter 29
• Molecules form either covalent or ionic bonds
• Electron wave functions overlap to form a bond
• Weak (van der Waals) bonds are dipole attractions between molecules
• Energy levels in molecules are altered from an atom
• Additional energy levels correspond to rotational and vibrational states of the molecule
•Rotational or vibrational energies are quantized
Summary of Chapter 29
• Electron energy levels in crystals become bands of allowed states, with gaps in the bands. • Metal ­ highest occupied band is only partially full
• Insulator ­ the highest occupied band is totally full, and there is a large gap to the next band
• Semiconductors ­ the highest band is also full, but the energy gap is fairly small • Doped semiconductors ­ small amounts of doping allow conductivity to be very precisely controlled; can be n­type (dopant is ‘donor’) or p­type (or ‘acceptor’)