Paul A Johnson

Connections between Richardson-Gaudin States, Perfect-Pairing, and Pair Coupled-Cluster Theory Slater determinants underpin most electronic structure methods, but orbital-based approaches often struggle to describe strong correlation efficiently. Geminal-based theories, by contrast, naturally c...

arxiv.org/abs/2510.06144 #compchem

secret lair x toothpaste for dinner

Richardson–Gaudin states of non-zero seniority. II. Single-reference treatment of strong correlation Strongly correlated systems are well described as a configuration interaction of Slater determinants classified by their number of unpaired electrons. This trea

pubs.aip.org/aip/jcp/arti...

"very small claims court" aka academic conferences

Fully Analytic Nuclear Gradients for the Bethe--Salpeter Equation The Bethe-Salpeter equation (BSE) formalism, combined with the $GW$ approximation for ionization energies and electron affinities, is emerging as an efficient and accurate method for predicting optica...

arxiv.org/abs/2507.02160 #compchem

Richardson-Gaudin states of non-zero seniority II: Single-reference treatment of strong correlation Strongly correlated systems are well described as a configuration interaction of Slater determinants classified by their number of unpaired electrons. This treatment is however unfeasible. In this man...

Very short follow-up after the ridiculous part I. Short excitation-based CI of RG states converges quickly.

(ordinarily, I'd reply to a post from @titouloos.bsky.social )

arxiv.org/abs/2506.09379

no joke some frogs freeze/unfreeze

Richardson–Gaudin states of non-zero seniority: Matrix elements Seniority-zero wave functions describe bond-breaking processes qualitatively. As eigenvectors of a model Hamiltonian, Richardson–Gaudin states provide a clear p

Finally. This was quite a struggle.

In short: can add missing structure from a seniority-zero state with single-reference methods.

Parts 2 and 3 to come.

pubs.aip.org/aip/jcp/arti...

Scheduling a meeting at 6:30, google calendar assumes it's in the evening 😂

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number of pairs of states times one linear algebra operation

Next paper will clean up Slater-Condon rules.

This was meant to be a short project at the start of my sabbatical. Here we are, almost two years later...

Seniority-based CI works well for strongly correlated systems at an exponential cost. The goal here is to replace it with a short excitation-based CI of correlated states. Here all the required matrix elements are computed. In every case, a single linear algebra operation per pair of states.