# Order by bond length? #"NO"#, #"NO"^(+)#, #"NO"^(-)#

##### 1 Answer

The bond *strength* **increases** going from *length* consequently **shortens** going from

#r_("N"-"O")^("NO"^(-)) > r_("N"-"O")^("NO") > r_("N"-"O")^("NO"^(+))#

To start with,

#color(red)(["*"])# -except forthe orbital ordering below the#pi^"*"# (the#2b_1,2b_2# ) of these species

To prove this, here is the **MO diagram** of *Miessler et al.*, Answer Key):

(The original was this; I added the orbital depictions and symmetry labels.)

Quick overview of what the labels correspond to what MOs:

#1a_1# is the#sigma_(2s)# bonding MO.#2a_1# is the#sigma_(2s)^"*"# antibonding MO.#1b_1# is the#pi_(2p_x)# bonding MO.#1b_2# is the#pi_(2p_y)# bonding MO.#3a_1# is the#sigma_(2p_z)# bonding MO, but it's relatively nonbonding with respect to oxygen.#2b_1# is the#pi_(2p_x)^"*"# antibonding MO.#2b_2# is the#pi_(2p_y)^"*"# antibonding MO.#4a_1# is the#sigma_(2p_z)^"*"# antibonding MO.

Note that for

#"NO"^(+)# has#bb0# #pi^"*"# antibonding electrons.#"NO"# has#bb(1)# #pi^"*"# antibonding electron.#"NO"^(-)# has#bb(2)# #pi^"*"# antibonding electrons.

As the number of antibonding electrons ** increases**, the

**, having acquired**

*weakens**antibonding*character (which as the name suggests, goes against making a bond).

Thus, the bond *strength* **increases** going from *length* consequently **shortens** going from