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If two $\mathrm d_{xy}$ orbitals approach each other on $x=y,$ $z=0$, would a σ bond be formed? I would think so.
Can $\mathrm d_{z^2}$ form π bond with another $\mathrm d_{z^2}?$ (As all others can on $x$ or $y$ or $z$ as internuclear axis?) I am not sure but overlapping similar to p could be observed.
I would assume all except $\mathrm d_{z^2} - \mathrm d_{z^2}$ form δ bond. (both of same type like $\mathrm d_{xy}$ with $\mathrm d_{xy}.)$
What are the faults in my logic?
Sigma, pi and delta denote how many planar nodes are in the bond. Sigma bonds have no node, pi bonds have one and delta bonds have two. You can tell what kind of bond forms by how the orbitals overlap. Two single lobes form a sigma bond, two pairs of lobes form a pi bond and two quartets form a delta bond.
σ bond: $\mathrm s - \mathrm s;$ $\mathrm s - \mathrm p_x;$ $\mathrm s - \mathrm d_{x^2 - y^2};$ $\mathrm s - \mathrm d_{x^2};$ $\mathrm p_x - \mathrm p_x;$ $\mathrm p_x - \mathrm d_{x^2 - y^2};$ $\mathrm p_x - \mathrm d_{z^2};$ $\mathrm d_{x^2 - y^2} - \mathrm d_{x^2 - y^2}.$
π bond: $\mathrm p_y - \mathrm p_y;$ $\mathrm p_z - \mathrm p_z;$ $\mathrm p_y - \mathrm d_{xy};$ $\mathrm p_z - \mathrm d_{xz};$ $\mathrm d_{xy} - \mathrm d_{xy};$ $\mathrm d_{xz} - \mathrm d_{xz}.$
δ bond: $\mathrm d_{yz} - \mathrm d_{yz}.$
$x$ is between atoms line. Other configurations are impossible. So there is only one δ bond configuration (if not count $\mathrm f$ orbitals). There also exists hypothetical φ bond. P.S. This https://commons.wikimedia.org/wiki/File:Quintuple_bond_orbital_diagram2.png is absolutely incorrect, even for the fact that names of orbitals are duplicated ($d_{z^2}$) and those π bonds (both) are impossible.
