Add initial orbital guess for DMRG CI/SCF

[lcyyork]

Description

This PR adds DMRG initial orbitals based on localization (active space only) + reordering from Fiedler vector, which is controlled by keyword DMRG_REORDER_INIT_ORBS. This reordering appears effective to pseudo-1D molecules (see test case dmrg-ci-2). For less obvious molecules like N2 or Cr2, this option should be disabled and orbitals should be adjusted based on orbital characters (σ, σ*, π, π*, δ, δ*, ...). This reordering is also performed only once when entering Forte, which seems to be enough to have a good DMRG-SCF results for Cr2 and acene.

A test case (dmrg-ci-2) on H20 chain is added to test the effect of various orbital localization schemes and Fiedler reordering. I leave dmrg-ci-1 to the test case of PR #413.

Other changes that I considered to be minor includes:

• The Cholesky orbitals are added directly inside Localize such that CholeskyLocal is removed.

• I modified proc/orbital_helpers.py, although it is subject to reallocation to somewhere else in the future.

• The infamous die_if_not_converged is reintroduced to ActiveSpaceSolver and ActiveSpaceMethod to speed up CI of MCSCF.

• Improve printing for permanent dipole in ActiveSpaceSolver.

User Notes

• Orbital localization and Fiedler reordering for DMRG-CI.
• Add Cholesky orbitals inside Localize class.

Checklist

• Added/updated tests of new features and included a reference output.ref file
• Removed comments in code and input files
• Documented source code
• Checked for redundant headers
• Checked for consistency in the formatting of the output file
• Documented new features in the manual
• Ready to go!

[brianz98]

@lcyyork is this PR now ready for review? Happy to take a look if it is!

[lcyyork]

@lcyyork is this PR now ready for review? Happy to take a look if it is!

I think it is. Maybe there will be other tweaks. But I am using it to run acene jobs.

[fevangelista]

I think this can be merged if tests pass. We need to do a follow up PR to move the DMRG-specific functions outside of the psi4 module. This function should go in the driver instead.