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In internet resources, only $p_z$ orbitals are shown to overlap with $s$ orbitals to form sigma bond. But my teacher says that according to Valence Bond Theory, $s$ orbital overlaps with all three $p_x$, $p_y$ and $p_z$ orbitals to form sigma bonds. I am really confused about this. I heard that the concept changes when it comes to molecular orbital theory. Only similar orbitals (like $1s$-$1s$,$2p_x$-$2p_x$,$3p_y$-$3p_y$) form bonds but ($2s$-$2p_z$) do not. Please clarify if there is any difference in concepts of overlapping between 'Molecular orbital theory' and 'Valence Bond Theory'.

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    $\begingroup$ The axis of orientation is used so we can designate one orbital from another. But since each orbital is equal, the assignment of the axis is arbitrary, so it doesn't really matter which is $P_x$ and which is $P_y$ or $P_z$. So if there can be an overlap of an $S$ and $P$ orbital, it is us who decide if it is $x$, $y$ or $z$. $\endgroup$ – LDC3 May 10 '14 at 20:00
  • $\begingroup$ Certainly. An example of a s-p sigma overlap is the bonds between hydrogen and the halogen in hydrogen halides. $\endgroup$ – Tan Yong Boon Jan 28 '18 at 2:03
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$\ce{Px}$, $\ce{Py}$, and $\ce{Pz}$ orbitals can all overlap with an $\ce{S}$ orbital to form a bond. It simply depends upon along which axis (X, Y or Z) the bond will be directed. These concepts of overlap do not change between Molecular Orbital theory and Valence Bond theory.

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    $\begingroup$ As an additional note here: The choice of the coordinate system is completely arbitrary. Orbitals can also be rotated, linar combined, ..., to form bonds. $\endgroup$ – Martin - マーチン May 12 '14 at 14:37
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Of course there is only one concept of bonding which never differ in either cases.

Now that here you have a doubt about the bonding between s and p orbital. First of all you should know that s orbital can form bond between with p orbital on any axis (x,y or z axis) and all forms bond in sigma bond.

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