The discussion centers on the quantum mechanical interpretation of σ and π bonds in molecules, exploring their definitions, characteristics, and the underlying principles of molecular orbitals, particularly in diatomic and polyatomic molecules.
Participants generally agree on the definitions and characteristics of σ and π bonds, but there is no explicit consensus on the methods for calculating angular momentum or the implications of these bonds in more complex molecular systems.
The discussion does not resolve the complexities involved in calculating angular momentum in molecular orbitals, nor does it clarify the assumptions underlying the definitions of the bonds.
hokhani said:What is the meaning of the bonds σ and π in molecules quantum mechanically?
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?DrClaude said: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. I will get it.DrDu said:Landau Lifgarbagez, Quantum Mechanics, has a good discussion of the states of diatomic molecules apt for physicists.