Hybrid orbitals

[905022356]

In the textbook, hybrid orbitals are described as a linear mix of atomic orbitals, as given by the following formulas
h1 =s +px +py +pz, h2= s -px -py +pz, h3= s -px +py -pz, but I don't understand what the formulas tell us, can someone explain them to me? Thank you!

[Victoria Draper 1G]

When I first read the textbook I was a bit confused as well with regards to what those equations meant and how they related to hybrid orbitals. After reading it a few times, I think the textbook uses those equations better explain how they derive a hybridized molecule. The signs of each of the orbitals such as in h2=s-px-py=pz represent the wavefunction of each orbital. When the orbitals of each of the subshells have different signs, it results in the formation of new wavefunction patterns (showing difference in energy levels) giving each of the equations in the textbook its own unique wavefunction pattern. In the end, the different signs that are present in each of the four equations are averaged together to give a hybridized form of the molecule showing that the hybridized molecule is an average of the energies of the two subshells. I hope this helps answer your question!

[Camille Ng 1D]

The formula basically explains that new hybrid orbitals are made of old atomic oribtials like s px, py, pz, etc. For example the sp^2 hybrid orbitals are made of one s orbital and two p orbitals (px and py orbitals)

[VahagnAldzhyan]

The formula basically explains that new hybrid orbitals are made of old atomic oribtials like s px, py, pz, etc. For example the sp^2 hybrid orbitals are made of one s orbital and two p orbitals (px and py orbitals)

Does this refer to the formation of sigma and pi bonds? Because I know that the pi bonds form between p orbitals and on the py axis.

[905022356]

When I first read the textbook I was a bit confused as well with regards to what those equations meant and how they related to hybrid orbitals. After reading it a few times, I think the textbook uses those equations better explain how they derive a hybridized molecule. The signs of each of the orbitals such as in h2=s-px-py=pz represent the wavefunction of each orbital. When the orbitals of each of the subshells have different signs, it results in the formation of new wavefunction patterns (showing difference in energy levels) giving each of the equations in the textbook its own unique wavefunction pattern. In the end, the different signs that are present in each of the four equations are averaged together to give a hybridized form of the molecule showing that the hybridized molecule is an average of the energies of the two subshells. I hope this helps answer your question!

Yes! This helps a lot thank you! So basically the equations represent the shape of the hybrid orbitals, as compared to the atomic orbitals?