What is the meaning of σ and π bonds in molecules quantum mechanically?

[hokhani]

Bonds in molecules

What is the meaning of the bonds σ and π in molecules quantum mechanically?

 

[DrClaude]

What is the meaning of the bonds σ and π in molecules quantum mechanically?

Consider a molecular orbital in a diatomic molecule. The projection of the angular momentum of an electron in that orbital on the internuclear axis is designated by the quantum number $\lambda$. In analogy with hydrogenic orbitals, the value of this quantum number is expressed with a letter according to
$$
| \lambda | = 0 \Rightarrow \sigma \\
| \lambda | = 1 \Rightarrow \pi \\
| \lambda | = 2 \Rightarrow \delta \\
\vdots
$$
(note the absolute value, as the projection can be positive or negative).

For polyatomic molecules, a similar concept is applied in LCAO-MO theory where the molecular orbitals are built two atoms at a time.

An easy way to identify the value of $| \lambda |$ is to look along the bond and count the number of nodal planes. A $\sigma$ bond will look circular, a $\pi$ bond will be in the shape of a 8, similar to a p orbital in an atom.

 

[hokhani]

Consider a molecular orbital in a diatomic molecule. The projection of the angular momentum of an electron in that orbital on the internuclear axis is designated by the quantum number $\lambda$. In analogy with hydrogenic orbitals, the value of this quantum number is expressed with a letter according to
$$
| \lambda | = 0 \Rightarrow \sigma \\
| \lambda | = 1 \Rightarrow \pi \\
| \lambda | = 2 \Rightarrow \delta \\
\vdots
$$
(note the absolute value, as the projection can be positive or negative).

For polyatomic molecules, a similar concept is applied in LCAO-MO theory where the molecular orbitals are built two atoms at a time.

An easy way to identify the value of $| \lambda |$ is to look along the bond and count the number of nodal planes. A $\sigma$ bond will look circular, a $\pi$ bond will be in the shape of a 8, similar to a p orbital in an atom.

Thank you very much. I like to know how to calculate angular momentum in molecular orbitals. Could you please give me a reference for that?

 

[DrDu]

Landau Lifgarbagez, Quantum Mechanics, has a good discussion of the states of diatomic molecules apt for physicists.

 

[hokhani]

Landau Lifgarbagez, Quantum Mechanics, has a good discussion of the states of diatomic molecules apt for physicists.

Thank you. I will get it.

 

[ycheff]

Read also: Enrico Fermi "Molecules, Crystals and Quantum Statistics".