Draft: ResHF Hessian (part 2)

As preliminary step to calculating the inverse Hessian via a Krylov space algorithm, I am building a function that will apply a Hessian matrix onto a vector.

(Merged back into master prematurely due to The Big Rename from qtensor to qleve happening midway through development. Couldn't figure out how to reopen the original merge request, so this is a duplicate/pick-up of where I left off.)

Goal #1: Implement an explicitly built Hessian to be able to verify my Hessian derivation

• Sketch out approach to explicit Hessian builder
• Set up src/resmf/reshf.cpp to generate input for Hessian builder
  • Relabel variables and access functions so that the determinant of S_AB_ is distinct from the actual overlap matrix S_AB_
  • Compute and store (vir, occ) (occ, vir) and (vir, vir) blocks for S_AB_ in addition to the current (occ, occ) block
  • Store condensed inverse matrix results from SVD (occ,occ block of S_AB only!) and send it to Hessian builder
  • Separate and store 1 electron and 2 electron components of the energy expectation value between two Slater determinants (H_AB_1e and H_AB_2e)
• Build Hessian matrix explicitly in src/resmf/hessian.cpp
  • Modify sdets_ in order to account for orthonormal generic MO basis in Hessian derivation
  • Set up loop(s) to iterate through all second derivatives
  • Compartmentalize portions of Hessian equations to minimize repetitive calculations
• Multiply Hessian matrix with step input vector in src/resmf/hessian.cpp
  • Decide how to treat gradient output vector and whether step should be a constant or not
• Troubleshoot to make sure equations to build Hessian matrix are correct

Goal #2: Implement an on-the-fly version of the Hessian, for the sake of memory demands