PySEQM — closed forms and frame convention for the sp two-centre integrals
==========================================================================

  Repository: https://github.com/lanl/PYSEQM
  License:    BSD 3-Clause — full text in this directory as LICENSE.
              (c) 2020 Triad National Security, LLC. Produced under U.S.
              Government contract 89233218CNA000001 for Los Alamos National
              Laboratory.
  Citation:   G. Zhou, B. Nebgen, N. Lubbers, W. Malone, A. M. N. Niklasson,
              S. Tretiak, "Graphics Processing Unit-Accelerated Semiempirical
              Born Oppenheimer Molecular Dynamics Using PyTorch",
              J. Chem. Theory Comput. 16, 4951 (2020).


What was taken
--------------

The s/p-block two-centre Dewar-Sabelli-Klopman multipole integrals in
src/integrals.rs follow the closed forms PySEQM uses, together with two
conventions that go with them and are not otherwise deducible:

  * `rotation_to_x_g` (src/integrals.rs:25) — the local frame that rotates the
    interatomic unit vector onto +x, marked in the source as a port of PySEQM's
    `rotate_with_quaternion`.
  * the sign of the two-electron frame vector, `v = -x_ij`
    (src/integrals.rs:211), which is PySEQM's convention rather than MOPAC's.

Everything around them is original: the Rust code, the generic scalar
abstraction that lets the same kernels be instantiated at f64 for energies and
at a dual number for exact analytic derivatives, the d-orbital extension
(src/integrals_d.rs, which follows MNDO-d rather than PySEQM), and the
removable-singularity handling that keeps the derivatives finite where the
closed forms are 0/0.

Nothing from PySEQM is vendored, linked, or redistributed here; the shared
material is mathematical expression and frame convention. No PySEQM parameter
data is used — the parameters come from MOPAC, see ../mopac/NOTICE.


License compatibility
---------------------

BSD-3-Clause is one-way compatible with GPL-3.0-or-later. The upstream license
text is retained as LICENSE in this directory, including the attribution and
disclaimer clauses it requires. See ../../THIRD_PARTY_NOTICES.md for the
complete picture.
