What is linear combination of atomic orbitals for CO2?

1 Answer
Truong-Son N.
Feb 9, 2018

They are shown in its molecular orbital diagram.

Inorganic Chemistry, Miessler, Fischer, and Tarr, pg. 148

For example, consider the overlap of the carbon #2s# with the #2p_z# group orbitals of #2xx"O"#. That is labeled #3a_g#, and is given by

#Psi_(3a_g) = 1/sqrt3[psi_((2s)(C)) + psi_((2p_z)(O_((1)))) - psi_((2p_z)(O_((2))))]#

where #psi# is each atomic orbital wave function and #Psi# is the molecular orbital wave function.

The left-hand #psi_(2p_z)# is positive and the right-hand #psi_(2p_z)# is negative, so that there is constructive overlap with the carbon #2s# on both sides.

(I assumed the atomic orbitals were all the same relative contribution, but they might not be.)

Or, consider the overlap of the #2p_x# of carbon with the #2p_x# group orbitals of #2 xx "O"#. That is labeled #1b_(3u)# and is given by:

#Psi_(1b_(3u)) = 1/sqrt3[psi_((2p_x)(C)) + psi_((2p_x)(O_((1)))) + psi_((2p_x)(O_((2))))]#

Clearly, all of these are the same phase, so they are all #+#.

(I assumed the atomic orbitals were all the same relative contribution, but they might not be.)

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