# Understanding derivation of geminal based methods [closed]

I have been reading through  to get a better understanding of geminal based methods. This is one of two questions that I'm asking about that paper on this site, the other one being: Understanding the complexity of geminal-based wavefunctions. This question is: How does expression (1) relate to Eqs. (3) and (7)?

#### References

1. P. Tecmer & K. Boguslawski Phys. Chem. Chem. Phys., 2022,24, 23026-23048 DOI
• Welcome to the site! I tried to make a few small edits to make the post clearer. For future posts 1. It's ideal to limit to one specific question per post, even if they are related 2. You should try to quote just the relevant portions of your reference and reproduce the relevant equations using mathjax.
– Tyberius
Feb 21 at 13:51
• +1 and welcome to our new community! Thank you for contributing your question here and we hope to see much more of you in the future!!! As Tyberius said, ideally each post will be limited to one question, so I've commented out your second question and you can ask that separately if you want. Feb 21 at 15:28
• Could you clarify what you don't understand about the explanation in your reference? It seems clear to me from the text that (3) is obtained from (1) by diagonalizing it, while (7) is obtained from (1) by setting $C_{pq}^i\equiv C_{pq}\, \forall i$. Is it the notation $\sum_{p<q}$ in the double sum that is confusing, or something else? Feb 22 at 3:11
• It's a short form for $\sum_{q=1}^{2K}\sum_{p=1}^{q-1}$ Feb 24 at 7:53
• Your question was "what's the relationship between (3) and (1)". The answer is that when you diagonalize (1) you get (3). How to diagonalize is a different question. We can discuss it in the "math and science of matter modeling" chat room. Feb 25 at 14:35