When we are talking about hybridization, in $\mathrm{sp/sp^2/sp^3}$ hybridization, does s stand for sigma bond and p for pi bond ?
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2 Answers
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You got it backwards.
The $\mathrm{s}$, $\mathrm{p}$, $\mathrm{d}$, $\mathrm{f}$ orbitals stand for sharp, principal, diffuse, and fundamental. Wikipedia: Electron Configuration § Notation:
The choice of letters originates from a now-obsolete system of categorizing spectral lines as "sharp", "principal", "diffuse" and "fundamental" (or "fine"), based on their observed fine structure: their modern usage indicates orbitals with an azimuthal quantum number, l, of $0$, $1$, $2$ or $3$ respectively.
Then, $\sigma$, $\pi$, $\delta$, $\phi$, being the Greek equivalents of $\mathrm{s}$, $\mathrm{p}$, $\mathrm{d}$, $\mathrm{f}$ respectively, came to designate bonds or molecular orbital symmetry, because $\mathrm{s}$ is the first orbital to form $\sigma$ bonds, $\mathrm{p}$ the first orbital to form $\pi$ bonds, $\mathrm{d}$ the first orbital to form $\delta$ bonds, and $\mathrm{f}$ the first orbital to form $\phi$ bonds.
The $\mathrm{s}$ and $\mathrm{p}$ in $\mathrm{sp^3}$ are precisely the $\mathrm{s}$ orbital and the $\mathrm{p}$ orbital. $\mathrm{sp^3}$ means that $1$ $\mathrm{s}$ orbital mixes with $3$ $\mathrm{p}$ orbitals to create $4$ hybrid orbitals known as $\mathrm{sp^3}$ orbitals.
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4$\begingroup$ The last part is a bit incorrect and only applies to ideal tetrahedral molecules like methane strictly. The notation for hybrid orbitals is more accurately $$\ce{sp^{n} {=} s^{\frac{1}{n+1}}p^{\frac{n}{n+1}}}.$$ Therefore one part $\ce{s}$ mixes with one part $\ce{p}$ to form one hybrid orbital $\ce{sp^3}$. There can be different types of hybrid orbitals at the same atom. $\endgroup$– Martin - マーチン ♦Oct 16, 2016 at 7:49
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It is important to note that while s orbitals cannot form π bonds, p orbitals are very capable at forming σ bonds. Similarly, neither of those two can form δ bonds but d-orbitals can and will form σ and π bonds.
An s orbital does not have a nodal plane. A p orbital has exactly one and a d orbital exactly two. (Note: I am not counting the ‘inner nodes’, e.g. inside a 2s orbital.) This definition was interpreted for bonds to determine whether a bond has zero, one or two nodal planes that fully contain the bond axis. A σ bond is rotation symmetric and does not have a nodal plane. A π bond has exactly one and a δ bond exactly two.
The $\ce{Cl-Cl}$ bond in chlorine, for example, is a σ bond formed by two p orbitals. And similarly, in transition metal complexes $\mathrm{d}^\unicode[Times]{x3c0}\mathrm{p}^\unicode[Times]{x3c0}$ bonds are common.
The $\mathrm{sp}^n$ nomenclature stands for hybrid orbitals; others have already described them.