Covalent
A covalent bond between two atoms: electrons supplied by either one or both atoms are shared by the two atoms
Covalent bonds can be described in terms of overlapping atomic wave functions
Example: two hydrogen atoms forming H2 molecule
The probability is higher that the electrons associated with the atoms will be located between them
This can be modelled as if there were a fixed negative charge between the atoms, exerting attractive Coulomb forces on both nuclei
The result is an overall attractive force between the atoms, resulting in the covalent bond
Bonding between molecule themselves
Van der Waals
Two neutral molecules are attracted to each other by weak electrostatic forces called van der Waals forces
Atoms that do not form ionic or covalent bonds are also attracted to each other by van der Waals forces
The van der Waals force is due to the fact that the molecule has a charge distribution with positive and negative centers at different positions in the molecule
Van der Waals forces are weak but are often the only attractive force between molecules.
As a result of this charge distribution, the molecule may act as an electric dipole
Because of the dipole electric fields, two molecules can interact such that there is an attractive force between them
Remember, this occurs even though the molecules are electrically neutral
Hydrogen bond
An hydrogen atom in a molecule can also form a hydrogen bond (weaker than other bonds)
Example: water (H2O):
There are two covalent bonds in the molecule
Electrons from the hydrogen atoms are more likely to be found near the oxygen atom than the hydrogen atoms
Bare protons at positions of the hydrogen atoms
Hence, the negative end of another molecule can come very close to the proton
Hydrogen bond strong enough to form a solid crystalline structure
Hydrogen bonding is a critical mechanism for the linking of biological molecules and polymers
DNA is an example
Energy States of Molecules
Molecules also have characteristic discrete energy levels
The energy of a molecule can be divided into four categories
Electronic energy
interactions between molecule’s electrons and nuclei
Translational energy (unrelated to internal structure)
Due to motion of the molecule through space
Rotational energy
Due to the rotation of the molecule about its center of mass
Vibrational energy
Due to the vibration of the molecule’s constituent atoms
Rotational Motion of Molecules
A diatomic model will be used, but the same ideas can be extended to polyatomic molecules
A diatomic molecule aligned along an x axis has only two rotational degrees of freedom
Corresponding to rotations about the y and x axes
Rotational energy given by
Moment of inertia of the molecule
(µ is called the reduced mass of the molecule)
Rotational Spectrum
In classical mechanics, the angular momentum (L=Iω) can take any value. In quantum mechanics, it is quantized
As a result, rotational energy is also quantized
For most molecules, transitions result in radiation in the microwave spectrum
l= 0, 1, 2, … (quantum numbers)