Basicities of nitrogen atoms in purine


> 
> Arrange the sites in purine in order of basicity.
> 
> 
> [![Purine numbering system](https://i.stack.imgur.com/5Gsgx.png)](https://i.stack.imgur.com/5Gsgx.png)
> 
> 
> 


I feel that **9 is the least basic** as nitrogen's lone pair is delocalised. However, I am unable to rank 1, 3, and 7 in a particular order. Is there a particular theory to decide basicity of sites?




I don't think that question is trivial and except for what you have already deduced, I would not have an idea how to solve that without employing computational chemistry.


![structure of purine](https://i.stack.imgur.com/5Gsgx.png)


The problems already start that I suspect that the proton from position 9 readily exchanges to position 7 in any kind of polar solvent (and in absence why not with itself).


Well from that point on forward, I'd say you need at least a lot of acid to protonate 9, as the π system is aromatic and will most likely not react first.


After that you could probably deduce from the approximate bond angles which of the nitrogen would have the largest s- and p- character, then rank them from highest to lowest p contribution. The one with the most will probably be the HOMO and therefore react first. To be honest though, this is just guessing.  

I have absolutely no clue what the lesson with this exercise it, except for: "They're pretty much the same." 


Let's have a closer look anyway. I have computed the neutral molecule at the DF-B97D3/def2-TZVPP level of theory, and used NBO6.0 for the partial charges:


[![NBO charges of purine at DF-B97D3/def2-TZVPP](https://i.stack.imgur.com/I436J.jpg)](https://i.stack.imgur.com/I436J.jpg)


As expected, there is not much of a difference; I'd even go as far and say they are the same. Position 9 is a little bit more negative, because it has a hydrogen to draw from.


Next up, let's have a look at the highest molecular orbital, as we would assume to protonate there:


[![HOMO of purine at DF-B97D3/def2-TZVPP](https://i.stack.imgur.com/SrIRI.jpg)](https://i.stack.imgur.com/SrIRI.jpg)


Again, there is only little to no difference. Or in numbers (contributions > 3%):



```
Alpha occ 31 OE=-0.217 is 
N1-p=0.3635 N1-s=0.0382
N3-p=0.2551 
N7-p=0.0667 
C5-p=0.0563 
C4-p=0.0473 
C2-p=0.0452 
C6-p=0.0382 

```

From this we would conclude that since `N1` has the largest contribution, the proton is most likely to go there. 


Therefore I also calculated all the protonated species, and their relative energies are:
\begin{array}{lr}\hline
\text{Position} & \Delta G(\pu{298.15 K}, \pu{1 atm})/(\pu{kJ/mol})\\\hline
1 & 0.0 \\
3 & 41.2 \\
7 & 26.1 \\
9 & 196.8 \\\hline
\end{array}


From this we conclude that the most likely position to be protonated is `N1`, followed closely by `N7`, and also `N3`. Off the charts is, as expected, `N9` as it breaks the aromaticity.


**TL;DR**: Order of protonation $1 > 7 > 3 > 9$, calculated at DF-B97D3/def2-TZVPP.


 10