Is trans-2-butene IR active with regard to its C=C bond?

To be IR active, the vibration of a bond must result in a substantial change in dipole moment. Since trans-2-butene is symmetrical, will the C=C stretch show up on IR?

Something tells me no because if the C=C bond vibrates, there will be no net change in the bond dipole moment, unlike in cis-2-butene. Any polarization one way in trans-2-butene is cancelled out by a polarization in the opposite direction in trans-2-butene. Cis-2-butene, however, has a permanent dipole and any vibration only exacerbates this dipole.

• What about the C-H bonds? They will show in the IR.
– LDC3
Sep 8 '14 at 2:52
• I was thinking specifically of the C=C bond. Sep 8 '14 at 2:53
• How come something such as 2-butyne is IR inactive according to my book? Couldn't the methyls be moving in different directions here too? Sep 8 '14 at 3:11
• – LDC3
Sep 8 '14 at 3:27
• Dissenter I think Martin has answered your first comment below. If you would, add a separate question about what you and @LDC3 came up with in chat. I'm going to leave the second comment for now. Sep 8 '14 at 20:12

The $\ce{C=C}$ stretch will not show in IR. The frequency is $\nu_{\ce{C=C}}=1700~\mathrm{cm^{-1}}$ and has A gerade symmetry (DF-BP86/def2-SVP). There is no change in the dipole moment.
However, some bending frequencies involving the $\ce{C=C}$ double bond will show up. For example $\nu_{\ce{HC=CH}}=963~\mathrm{cm^{-1}}$ with a medium intensity.