With the help of molecular orbital theory we can easily calculate the bond energy and bond length of both CN and CN  species. The basic thing we need to calculate is the electronic Configuration of  CN.

Total no of electrons in CN are 13. i.e.So, the EC of CN is :

CN: KK σ (2s)2 σ*(2s)2π (2py)2σ (2pz)1

We know

Bond order = [number of bonding electrons – number of anti-bonding electrons]/ 2

So the bond order will become :
Hence, Bond order = 1/2(7–2) =2.5

If we consider the electronic configuration of CN then one electron will shift to σ(2pz) 1

After the electron shifting the electronic configuration will be

CN-:  KKσ(2s)2σ*(2s)2π(2py)2σ (2pz)2

So, bond order   = 1/2 (8–2) = 3

From the above discussion it is clear that CN-  is having the higher value of bond order. Bond energy is in direct proportion to bond order. As the bond order will increase bond energy will  also increase. So CN- will have high bond order and bond energy than CN+.  But the bond length of CN-  will be less as compared to CN+.