Wow, ok! Thank you. Do you got some references for me where you got equation (4) and (5) from? — Andrea Aug 5 at 11:35

The most common form of Equations 4/5 I would say is the more common protonation using H3O+ rather than H+? — B. Kelly Aug 5 at 11:50

@Andrea These basically follow from definition. Just think of the reaction "(explicitly solvated) A- + (explicitly solvated) H+ -> (explicitly solvated) AH", and add a suitable number of water molecules to balance the reaction, then calculate the Gibbs free energy change of the reaction. — wzkchem5 Aug 5 at 14:27

@B.Kelly Exactly. My terminology may be a bit loose, but $H^+ (H_2O)_k$ is just another way of writing $H_3O^+ (H_2O)_{k-1}$. — wzkchem5 Aug 5 at 14:28

OK, there is plenty of information so maybe I missed it. But I do not understand why I can do all calculations with the same amount of water molecules? Will the (m-n-k) not useless when I use the same amount? And the other question is: where does l comes from? — Andrea 2 days ago

"l" means liquid, as opposed to "aq" which means aqueous solution. The former stresses that the standard state of water is the pure liquid of water, not a 1 mol/L solution. I don't know what you mean by "the same amount of water molecules", but if you mean the m=n+k case, then yes, you should treat the $(m-n-k)G(H_2O)$ or $G((H_2O)_{m-n-k}$ terms as zero. — wzkchem5 2 days ago

Ok, so for example: I want to make my first try with catechol. There are two OH- groups on the structure. So I would simulate my [HA] with 2 explicit water molecules because two hydrogen bonds are possible. For [A-] I would use one explicit water molecule because on OH groups is left? And for my [H+]I use k=4. For m-n-k is the result than: -3? So I have to reduce k? To get a positive number for my water cluster ? - I am a little bit confused. — Andrea 2 days ago

OK I get your point. The point is m-n-k is not required to be non-negative, just that I didn't explicitly mention what to do when m-n-k<0. I have edited my answer and included the formula for the m-n-k<0 case. Besides, in your example one water molecule is not necessarily enough for [A-], because water molecules can act not only as hydrogen bond acceptors, but also as hydrogen bond donors. That is, the hydrogen atoms of water molecules can form hydrogen bonds with the oxygens of catechol. — wzkchem5 2 days ago

This is good discussion! — Nike Dattani 2 days ago

OK, thank you for given the additional equation. I understand what I are saying with [A-]. So I got one OH and one O in my [A-], so I need minimum 2 explicit water molecules there. But am I right that my [HA] also needs then 2 explicit water molecules? I am new to this. For sure I know about H bonding but never needed to made thoughts like this about it. Or can an O Atom accept and donor at one time? — Andrea yesterday

2 explicit water molecules may or may not be enough. On one hand, catechol can probably form hydrogen bonds with more than 2 water molecules at the same time, as a hydroxyl group can simultaneously act as hydrogen bond donor and acceptor. On the other hand, sufficiently weak hydrogen bonds can be reliably described by implicit solvation models, so not all hydrogen bonds between the solute and the solvent need to be described by explicit solvent molecules. — wzkchem5 yesterday

OK to make it easy and get in to it I made a calculation now without water to get stick to the eq. 1-3. So when I got my three Gibbs energies can I use: pKa = -dG/RxT? (Sorry I can't find how to use math symbols in comments). Or how do I go from the dG Gibbs Energy of the reaction to my pka value? — Andrea yesterday

Not quite, because Eq. (1) uses logarithm with base 10, not with base e. This introduces an additional factor of lg10 = 2.303. So pKa = -dG/(2.303RT). — wzkchem5 yesterday

Ah ok. I did the lg(exp(...)) so I got the same result as with your equation. Thanks very much for all your effort. Helps me a lot. So know I got a pKa value, but it is far away from literature. As energies to calculate dG I used the electronic energy (EE) from gaussian and added it with the Thermal Correction to Free Energy (named in GaussView). I think it is the correction to free Gibbs energy?! May I used the wrong energies for it? — Andrea yesterday

I would suggest using the "science and math of matter modeling" chat room if this needs a lot more back-and-forth discussion. — Nike Dattani yesterday

There are a lot of possible reasons for getting a wrong pKa. Without the complete input file, output file and a detailed description of your workflow, it is impossible to elucidate the reason. @NikeDattani: No problem, if the OP also agrees. — wzkchem5 yesterday

@NikeDattani good idea. How to get into it? — Andrea 2 hours ago