Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytical two-center integrals over Slater geminal functions   We present analytical formulas for the calculation of the two-center
two-electron integrals in the basis of Slater geminals and products of Slater
orbitals. Our derivation starts with establishing a inhomogeneous fourth-order
ordinary differential equation that is obeyed by the master integral, the
simplest integral with inverse powers of all interparticle distances. To solve
this equation it was necessary to introduce a new family of special functions
which are defined through their series expansions around regular singular
points of the differential equation. To increase the power of the interparticle
distances under the sign of the integral we developed a family of open-ended
recursion relations. A handful of special cases of the integrals is also
analysed with some remarks on simplifications that occur. Additionally, we
present some numerical examples of the master integral that validate the
usefulness and correctness of the key equations derived in this paper. In
particular, we compare our results with the calculations based on the series
expansion of the exp(-\gamma r12) term in the master integral.

11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol