# WHICH IS CORRECT ABOUT DIRECTIONAL ORIENTATIONS OF THE ORBITAL AND HOW  ???   P>SP      P

SAGAR SINGH - IIT DELHI
878 Points
13 years ago

Dear Raj,

The basic s, px, py, and pz orbitals are unsatisfactory for two reasons. First, these orbitals are not directed in a particular direction; instead, they tend to spread out in all directions (or at least multiple directions). Second, to the extent that the orbitals have an orientation (the px along the x axis, for example), the geometry is often inconsistent with the molecular geometry. For example, in methane (CH4) the carbon is at the center of the molecule and the hydrogens lie on the points of a tetrahedron. Each H-C-H bond angle is 109.5o. The carbon 2s orbital is spherical and as such extends toward all four hydrogen atoms. The carbon 2px, 2py, and 2pz extend along the x, y, and z axes and as such form 90o angles with each other. This geometry does not provide for effective overlap with the hydrogen atoms.

The solution to this problem is to create a new set of atomic orbitals. Recall that the Schrödinger equation for the hydrogen atom is a linear  differential equation. Any linear combination of solutions to this equation is also a solution. Thus for n = 2, there are an infinite number of solutions, not just the 2s, 2px, 2py, and 2pz wave functions. The carbon atom, in the example given above, will choose the set of wave functions that minimizes its energy. For an isolated carbon, the 2s, 2px, 2py, and 2pz wave functions are optimal, but in the presence of other atoms, where chemical bonding can occur, an alternate set of orbitals may be preferred.

Valence Bond Theory manages this situation by creating hybrid orbitals that are linear combinations of the s, px, py, and pz orbitals in the valence shell. (The d orbitals may also be included, if necessary.) The hybrid orbitals have energies intermediate between those of the basic orbitals used to construct them. Basic atomic orbitals not employed in constructing the hybrid orbitals are unaffected by the hybridization process.

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All the best.

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