What are radial knots and planar knots



Under a node In quantum chemistry (zero crossing) one understands a flat or curved surface on which the sign of a wave function changes. The vicinity of a node clearly corresponds to a low probability of presence for electrons.


Atomic orbitals always have n-1 nodal areas (n = principal quantum number). Of these, n-l-1 nodes (l = secondary quantum number) are in the radial part and l nodes are in the angle-dependent part of the wave function. The latter run through the atomic nucleus.

Examples:

In the case of s orbitals, all nodes are in the radial part of the wave function. Since the wave functions belonging to s orbitals do not show any angle dependence, there are no related nodal surfaces that run through the atomic nucleus. This is important when forming covalent bonds. s orbitals can only participate in sigma bonds.

In the case of p orbitals, a nodal surface is stirring always from the angle-dependent part, and the remaining nodes are found in the radial part. Depending on the relative orientation, p orbitals can form sigma or pi bonds.

In the case of d orbitals, the angle-dependent part always contains two nodal surfaces, and all remaining nodes can be found in the radial part. Accordingly, d orbitals can be involved in sigma, pi, or delta bonds.

Finally, f orbitals always have three nodal surfaces in the angle-dependent part of the wave function and can even form phi bonds.

Category: Physical Chemistry