Title: Molecular Bonding and Spectra
1CHAPTERS 37 38Molecules and Solids
- Molecular Bonding and Spectra
- Structural Properties of Solids
Johannes Diderik van der Waals (1837 1923)
2Motion in atoms and molecules
- Electrons vibrate in their motion around nuclei
- High frequency 1014 - 1017 cycles per
second. - Nuclei in molecules vibrate with respect to each
other - Intermediate frequency 1011 - 1013
cycles per second. - Nuclei in molecules rotate
- Low frequency 109 - 1010 cycles per second.
3Molecular Bonding and Spectra
- The Coulomb force is the only one to bind atoms.
- The combination of attractive and repulsive
forces creates a stable molecular structure. - Force is related to potential energy F -dV /
dr, where r is the distance separation. - It is useful to look at molecular binding using
potential energy V. - Negative slope (dV / dr lt 0) with repulsive
force. - Positive slope (dV / dr gt 0) with attractive
force.
4Molecular Bonding and Spectra
- An approximation of the force felt by one atom
in the vicinity of another atom is - where A and B are positive constants.
- Because of the complicated shielding effects of
the various electron shells, n and m are not
equal to 1.
A stable equilibrium exists with total energy E lt
0. The shape of the curve depends on the
parameters A, B, n, and m. Also n gt m.
5Molecular Bonding and Spectra
Vibrations are excited thermally, so the exact
level of E depends on temperature.
- A pair of atoms is joined.
- One would have to supply energy to raise the
total energy of the system to zero in order to
separate the molecule into two neutral atoms. - The corresponding value of r of a minimum value
is an equilibrium separation. The amount of
energy to separate the two atoms completely is
the binding energy which is roughly equal to the
depth of the potential well.
6Molecular Bonds
- Ionic bonds
- The simplest bonding mechanism.
- Example Sodium (1s22s22p63s1) readily gives up
its 3s electron to become Na, while chlorine
(1s22s22p63s23p5) easily gains an electron to
become Cl-.
7Molecular Bonds
- Covalent bonds
- The atoms are not as easily ionized.
- Example Diatomic molecules formed by the
combination of two identical atoms tend to be
covalent. - Larger molecules are formed with covalent bonds.
Diamond
8Molecular Bonds
- Van der Waals bond
- Weak bond found mostly in liquids and solids at
low temperature. - Ex in graphite, the van der Waals bond holds
together adjacent sheets of carbon atoms. As a
result, one layer of atoms slides over the next
layer with little friction. The graphite in a
pencil slides easily over paper.
9Molecular Bonds
- Hydrogen bond
- Holds many organic molecules together in solution.
10Molecular Bonds
- Metallic bond
- Free valence electrons may be shared by a number
of atoms. - Drude model for a metal a free-electron gas!
11Rotational States
- Molecular spectroscopy
- We can learn about molecules by studying how
molecules absorb, emit, and scatter light. - From the equi-partition theorem, a diatomic
molecule may be thought of as two atoms held
together with a massless, rigid rod (rigid
rotator model). - In a purely rotational system, the kinetic energy
is expressed in terms of the angular momentum L
and rotational inertia I.
12Rotational States
- L is quantized.
- The energy levels are
- Erot varies only as a function of the quantum
number l.
13Vibrational States
- A vibrational energy mode can also be excited.
- Thermal excitation of a vibrational mode can
occur. - It is also possible to stimulate vibrations in
molecules with light. - Assume that the two atoms are point masses
connected by a massless spring with simple
harmonic motion.
14Vibrational States
- The energy levels are those of a
quantum-mechanical oscillator. - The frequency of a two-particle oscillator is
- where the reduced mass is m m1m2 / (m1 m2)
and the spring constant is ?. - If its a purely ionic bond, we can compute ? by
assuming that the force holding the masses
together is Coulomb.
and
15Vibration and Rotation Combined
- Its possible to excite rotational and
vibrational modes simultaneously. - Total energy of simple vibration-rotation system
- Vibrational energies are spaced at regular
intervals. - Transition from l 1 to l
- Photons will have an energies at regular
intervals
16Vibration and Rotation Combined
- An emission-spectrum spacing that varies with l.
- The higher the starting energy level, the
greater the photon energy. - Vibrational energies are greater than rotational
energies. This energy difference results in the
band spectrum.
17Vibration and Rotation Combined
- The positions and intensities of the observed
bands are ruled by quantum mechanics. Note two
features in particular - 1) The relative intensities of the bands are due
to different transition probabilities. - 2) Some transitions are forbidden by the
selection rule that requires ?l 1. - Absorption spectra
- Within ?l 1 rotational state changes,
molecules can absorb photons and make transitions
to a higher vibrational state when
electromagnetic radiation is incident upon a
collection of a particular kind of molecule.
18Vibration and Rotation Combined
- ?E increases linearly with l.
19Vibration and Rotation Combined
- In the absorption spectrum of HCl, the spacing
between the peaks can be used to compute the
rotational inertia I. The missing peak in the
center corresponds to the forbidden ?l 0
transition. - The central frequency
20Vibration and Rotation Combined
- A transition from l to l 2
- Let hf be the Raman-scattered energy of an
incoming photon and hf is the energy of the
scattered photon. The frequency of the scattered
photon can be found in terms of the relevant
rotational variables - Raman spectroscopy is used to study the
vibrational properties of liquids and solids.
21Structural Properties of Solids
- Condensed matter physics
- The study of the electronic properties of solids.
- Crystal structure
- The atoms are arranged in extremely regular,
periodic patterns. - Max von Laue proved the existence of crystal
structures in solids in 1912, using x-ray
diffraction. - The set of points in space occupied by atomic
centers is called a lattice.
22Structural Properties of Solids
- Most solids are polycrystalline theyre made up
of many small crystals. - Solids lacking any significant lattice structure
are called amorphous and are referred to as
glasses. - Why do solids form as they do?
- When the material changes from the liquid to the
solid state, the atoms can each find a place that
creates the minimum-energy configuration.
In the sodium chloride crystal, the spatial
symmetry results because there is no preferred
direction for bonding. The fact that different
atoms have different symmetries suggests why
crystal lattices take so many different forms.
23Structural Properties of Solids
- Each ion must experience a net attractive
potential energy. - where r is the nearest-neighbor distance, and a
is the Madelung constant and it depends on the
type of crystal lattice. - In the NaCl crystal, each ion has 6 nearest
neighbors. - There is a repulsive potential due to the Pauli
exclusion principle - The value e-r /? diminishes rapidly for r gt ?.
- ? is roughly regarded as the range of the
repulsive force.
24Structural Properties of Solids
- The net potential energy is
- At the equilibrium position (r r0), F -dV /
dr 0. - therefore,
- and
- The ratio ? / r0 is much less than 1.