T1 and T2 condition

Here is my memory of T1/T2 conditions by Braams of JCP2004 (actually he reformulated from Erdahl's 1978 paper).

After I finished two papers, I was not sure where I go. I applied more N-representability condition like: Weinhold-Wilson inequality (this is a subset of Davidson's inequality) but energy gain were only order of 1e-4 hartree. Totally exhausted and want to take some rest. I moved to Tokyo Univ. as post doc (and there, I was really exhausted).

But I was very lucky - otherwise I cannot win my Ph.D - because Braams and Percus are also trying to do variational calculation on 2-RDM for realistic molecules via semi-definite programming around 2000. Especially when I saw Braams' NFS fund proposal, what he's trying to do was almost the same as what I did. I think he was also very very surprised :)
Fukuda-san (specialist of optimization) were also at there of course after JCP 2001 paper was out. Note that Erdahl and Jin had already done by their SDP in 2000 or so, this was included in Cioslowski's density matrix book.

In 2004, Fukuda-san send me a preprint. Incorporating T1/T2 conditions in the variational space and results were surprisingly good. With PQG, we cannot do chemistry due to lack of accuracy but now it is comparable to CCSD(T). I thought that it was a great breakthrough in this field...

Then I visited New York University for one month. and started collaboration.

I met Braams there. He is really smart person I ever met. I asked why he did notice 2-RDM
method, and he replied as just he saw on some books. Oh how smart he is.

Also, I never thought that someone will find a really effective and applicable N-representability
condition in 10 years. And Braams did find it just three years.