Why is a C–D bond stronger than a C–H bond?

I have heard that the carbon–deuterium bond is stronger than the carbon–hydrogen bond. What are the possible reasons for it? Is this also the reason that C–H bonds participate more in hyperconjugation than C–D bonds? Please explain.

• I sincerely recommend to look at the matter from a slightly different angle. C-D bonds are not stronger; for most purposes they are identical. Only if you measure the energies with really high precision, you might notice some very small, very insignificant difference, so small that most people don't even care which way is it. That's the difference you want to discuss. No, I don't think it has anything to do with hyperconjugation. My bet is on lower zero vibrational level for C-D because of higher equivalent mass. – Ivan Neretin Mar 9 '17 at 17:59
• The lesser contribution of C-D to hyperconjugation is the cause of some secondary kinetic isotope effects; it is related to the very slightly different bond strengths. See for example p 12 of this MacMillan group meeting (The classic text, Anslyn/Dougherty, doesn't actually mention it. I haven't checked Lowry/Richardson yet.) Warning: organic chemists' explanations tend to be a bit handwavy. However, the KIE is indeed there for all to see, so it's not fake. – orthocresol Mar 9 '17 at 19:46
• While it is true that the C-D strength will have only very minute effects on reactions, it is worth noting that many many systems if placed in D2O will switch any protium that leaves at a reasonable pace with a deuterium. And like the answer given below indicates, this is almost solely due to a lower zero point vibrational energy because electronically the systems are the same. – jheindel Mar 10 '17 at 1:11
• @IvanNeretin No need to bet on it. That is exactly correct. :) You don't need to measure the energy with the precision you suggest those. The lower ZPE results in a measurable difference in the rate of bond cleavage. – Zhe Apr 5 '17 at 19:14

Since energy is proportional to the frequency of vibration, the energy of the C–D system is less (lower). This table lists the C–D bond dissociation energy as $\pu{341.4 kJ/mol}$ and C–H as $\pu{338 kJ/mol}$. Since this is the energy to break the bond, the C–D bond is stronger.