ORCA 6.1.1 orbital-localization and block-canonicalization examples

In allocated CPU resources, run:
  bash run.sh
  bash analyze.sh work
  /public/toolkit/miniconda3/envs/ase-3.29.0/bin/python plot_results.py

The workflow first makes one HF/def2-SVP water single point (full input in
inputs/water.inp), then performs ten native localizations and three block
diagonalizations. Main ORCA is launched once by its full path, with one MPI
process and one CPU thread. It is the vendor precompiled ORCA 6.1.1 package,
paired with OpenMPI 4.1.8 built using GCC 13.3; no new ORCA compilation/GPU.
Use a new extraction directory to repeat the complete workflow.

Native methods 1-8: PM, FB, IAOIBO, IAOBOYS, NEWBOYS, AHFB, PMVVO, LIVVO.
The first six localize all occupied orbitals 0-4. The VVO methods receive the
entire virtual range 5-23 and select two valence virtual orbitals (5-6).
Two additional cases localize the full virtual space with PM and FB.
All native input parameters are in inputs/settings.json and generated
work/<method>/localize.in. Randomization is off and tolerance is 1e-8.
The IAO reference is STO-3G. Standalone native orbital-spread output is off:
this optional route requires the original case.SHARKINP.tmp. The package
computes spreads independently from analytic Gaussian position integrals.

Density invariance is tested for this RHF closed-shell occupied/virtual
rotation; do not generalize that statement to arbitrary CASSCF rotations.
Native localized orbitals need not diagonalize the Fock operator. Do not
interpret inherited GBW orbital energies as canonical LMO eigenvalues.

The two selected VVOs are orthonormal and orthogonal to occupied orbitals.
The remaining original virtuals are retained and may overlap the VVOs.
Do not pass the entire unadjusted VVO-output file to a downstream method
requiring a complete orthonormal virtual space. The checker tests the actual
selected subspace, including an independent STO-3G IAO/SVD construction.

The three blockf examples recanonicalize PM occupied, FB occupied and PM
virtual spaces against the original canonical Fock operator. The checker
verifies the full MO metric, density, target Fock block, eigenvalues and
projector; localized orbitals outside the chosen block are not assumed to
be canonicalized by that operation.

Reference text inputs, native JSON orbital coefficients, and scientific
figures are in reference/. No GBW, software binaries or density-container
files are distributed. Check reference data without new SCF:
  bash analyze.sh

The analysis uses the ORCA 6.1.1 unit convention, 1 bohr = 0.5291772083 A.
It analytically integrates normalized contracted s/p/d functions; no PySCF
installation or external basis service is required. Public formulas for IAO
projectors are independently implemented, using the exported native STO-3G.
Figures come from actual coefficients and validated moments; plot_results.py
defaults to the supplied reference data. Edit its input path for other data.

Official utility and units documentation:
https://orca-manual.mpi-muelheim.mpg.de/contents/utilitiesvisualization/utilities.html
https://www.faccts.de/docs/orca/6.1/manual/contents/orcaarchitecture/conversionfactors.html
IAO reference: Knizia, JCTC 9, 4834 (2013); implementation reference:
https://pyscf.org/_modules/pyscf/lo/iao.html
