Knot (chemistry)

The three p orbitals (each ); an (angle-dependent) node or a node surface is z. B. in the py orbital the xz plane ${\displaystyle l=1}$

The orbital has node areas in the radial part (circular) and node areas in the angle-dependent part (lines along conical surfaces). ${\displaystyle (n{=}5,l{=}3,m{=}0)}$ ${\displaystyle n-1-l=1}$ ${\displaystyle l=3}$

In quantum chemistry, a node is understood to be a flat or curved surface on which the sign of a wave function changes ( zero point of the wave function). The vicinity of a node clearly corresponds to a low probability of being for electrons .

Atomic orbitals always have a total of n-1  nodal areas (n = principal quantum number ). Of which lie

• l node in the angle-dependent part of the wave function ( secondary quantum number l <n). These knots run through the atomic nucleus and are important in the formation of covalent bonds .
• the remaining (n-1) -l = n _r  nodes in the radial part of the wave function ( radial quantum number n _r ≥ 0):

Orbital	shape	Secondary quantum number = No. Node in angular Part of the WF ${\displaystyle l\,}$	radial QZ = no. Node in radius-dependent Part of the WF ${\displaystyle n_{r}=(n-1)-l\,}$	covalent bonds
s	spherically symmetrical	0	${\displaystyle n-1}$	σ
p	dumbbell shaped	1	${\displaystyle n-2}$	σ, π
d	crossed double dumbbell	2	${\displaystyle n-3}$	σ, π, δ
f	rosettes shaped	3	${\displaystyle n-4}$	σ, π, δ, φ [1]

Remarks:

^[1] An example of a φ-bond is the side-on coordination of O ₂ to UO ₂ ⁺ .