Coulomb interaction operator

This record was searched and did not deepen. That is the finding, not a gap in the search.

There is no primary research paper whose subject is $V = \tfrac{1}{2}\sum h_{pqrs}\,a^\dagger_p a^\dagger_q a_r a_s$. It is the standard second-quantized form of an interaction that was already known, written in the formalism of second quantization that was already established — textbook composition rather than a result. Nothing beyond the definition and the formula could be honestly added, so nothing was.

Two near misses were checked and rejected, and the reasons are the useful part.

The integral literature is about the coefficients, not the operator. There is a substantial and genuinely primary literature on evaluating the numbers $h_{pqrs}$ — Gaussian basis functions and the recurrence schemes built on them. Those papers are about computing matrix elements. Citing one here would claim this record documents an evaluation algorithm, which it does not.

The analytic literature is about a different representation of the same physics. The Coulomb cusp condition — the constraint the $1/|\mathbf{r}_i - \mathbf{r}_j|$ singularity imposes on exact wavefunctions — is a real theorem and it is not about this object. It concerns the first-quantized operator in real space; what this record holds is the already-integrated orbital-basis form, in which the singularity has been integrated away. The connection is real but indirect: the cusp is why finite orbital-basis expansions converge slowly. Citing it as though it were about this operator is precisely the slippage the catalog's sourcing rule forbids.

So the record keeps its shared citation and its two authored strings, and adds this note about why. A search that returns nothing is worth recording once so the next person does not repeat it, and an object that genuinely cannot carry more than a formula should not be padded until it looks like one that can.