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    $\begingroup$ Are you asking how to evaluate those bra-kets? Or do you want your homework assigned checked? $\endgroup$ Commented Nov 25 at 23:07
  • $\begingroup$ Your current rendition of the question has nothing to do with the $R$ hydrocarbon nor with the three $H$ atoms. It seems to be completely the same basic hybridisation as would happen in diamond (nicer because there is no asymmetry), and worse, there is no consideration of any orbital from other atoms, which should have been taken into account. It is not clear how we could help when this is so rudimentary. $\endgroup$ Commented Nov 25 at 23:18
  • $\begingroup$ @naturallyInconsistent It (now) does. In methyl carbocations, there is hyperconjugation that drives electron density from $\sigma$-bond to empty/partially-filled $p$-orbital. And I wanted to show that this depends on dihedral angle $\theta$ by computing the overlap integral. $\endgroup$ Commented Nov 25 at 23:23
  • $\begingroup$ You have completely failed to incorporate anything that could remotely show this dependence. You are extremely far away from what you set out to do. $\endgroup$ Commented Nov 25 at 23:32
  • $\begingroup$ If the carbon is positively charged then what is R? Are you talking about a radical? $\endgroup$ Commented Nov 26 at 0:16