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I am trying to solve a Hamiltonian of one electron and 10 stationary nuclear centers. here, the electron is treated quantum mechanically and nuclear centers are treated classically objects. The Hamilton is as follows, $$H=-\frac{1}{2}\nabla^{2}-\sum_{i=1}^{10}\frac{1}{|\vec{r}-\vec{R_{i}}|}$$. Charge on each nuclear center is one. For the given set of locations of nuclear centers I tried to solve the Hamiltonian using MO theory by mixing $1s$, $2px$,$2py$,$2pz$ of all the 10 centers making a total basis of 40 with arbitrary coefficients to be determined.

Now I have used STO -3G to compute the one electron attraction integral by using the existing algorithm and wrote my own code. My question is whether there any software package to compute all the integrals (one electron integral) using slater type orbital in python. Because STO-3G is not an accurate representation of slater type orbital. Do I need to go for FORTRAN for slater type orbital basis set calculations?

Also is there any reference books or papers where I can find the algorithm for slater type orbitals one-electron integrals?

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    $\begingroup$ I would argue that in order to get accurate results, using several GTOs on each center will probably get you farther than one fixed STO. Nonetheless, en.wikipedia.org/wiki/… lists DFTB+ as having STOs. The integral code is likely to be Fortran still. $\endgroup$ – TAR86 Feb 23 at 14:41
  • $\begingroup$ Thank you so much.What GTO basis set would be appropriate for the above Hamiltonian. I already used STO-3G to solve the above Hamiltonian. How do I verify my answers? and how do I know how much, the answers are deviating from the right answers? @TAR86 $\endgroup$ – user135580 Feb 23 at 16:04
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    $\begingroup$ Any sufficiently sized basis set will do, check bse.pnl.gov/bse/portal for candidates. Given that you have a single electron, Hartree-Fock is exact in the given basis set. You could run your calculation in e.g. ORCA to verify your code. To assess the quality of the solution, observe the rate of convergence when using subsequently larger sets, such as cc-pVXZ, where X = D, T, Q, 5 ... $\endgroup$ – TAR86 Feb 23 at 16:19
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    $\begingroup$ The write-up on wikipedia is not entirely bad, for detailed derivation and mathematics have a look at Szabo, mentioned on wiki. ORCA is closed source, but would do all that I think you try to do here. The point is that HF is the same and exact for one electron in any quantum chemistry package - so why program it (unless that's the point). $\endgroup$ – TAR86 Feb 23 at 18:41
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    $\begingroup$ There is a google site: sites.google.com/site/orcainputlibrary/home and the manual is not bad (I wrote parts of it). You would set up a "molecule" consisting of 10 hydrogen, multiplicity 2, charge +9. Choose HF, a basis set and let it rip. $\endgroup$ – TAR86 Feb 23 at 18:59

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