Question

Write the valence bond spatial wavefunction for the bonds in the CH4 molecule using sp3 hybrid orbitals on C and the 4 H1s orbitals. What does this predict for the H-C-H bond angles?

Answer 1

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The wave bond function for methane is difficult to determine because it depends on 10 electrons, but I've found some papers in which they describe some alternatives. Here's one:

Ψ=C1(s2s*2p6)+C2(s2s*2p5d)+C3(s2s*fp6)+C4(s2s*2p5f′)+C5(s2s*2p5g)

source: "A One‐Center Wave Function for the Methane Molecule". Antony F. Saturno1 and Robert G. Parr1

You can look for another approach more elaborated in:

Ian M. Mills (1958) Wave functions for the methane molecule, Molecular Physics: An International Journal at the Interface Between Chemistry and Physics, 1:2, 99-106.

Where they describe an spherical aproximation and is really more complex.

Hope this helps!