Sella-Style Optimizer

The Sella optimizer (Algorithm sella or Sella task token) provides a quasi-Newton geometry optimization backend with explicit Cartesian and internal-coordinate execution paths, combining:

1. TS-BFGS Hessian update (maintains order negative eigenvalues)

2. P-RFO or MMF step computation

3. Sigma-based trust-radius schedule: multiplicative update driven by the model-quality ratio $\rho =\Delta E_{\text{actual}}/\Delta E_{\text{predicted}}$:

   Condition	Action
   $\rho \ge \text{rho\_inc}$	$\delta \times ={\sigma }_{\text{inc}}$ (grow)
   $\rho <1/\text{rho\_dec}$	$\delta \times ={\sigma }_{\text{dec}}$ (shrink)
   otherwise	unchanged

4. Adaptive Hessian eigenvalue correction: every nsteps_per_diag steps, the Hessian eigenspectrum is inspected and corrected if the number of negative eigenvalues deviates from order:

   • Too few negative eigenvalues → flip the smallest positive ones to −0.2 a.u.
   • Too many negative eigenvalues → flip the least-negative ones to +0.2 a.u.

5. Initial TS Hessian: TS startup uses Davidson partial eigensolver refinement when available; if refinement is unavailable, fallback initialization sets the order softest modes to −0.2 a.u. so that P-RFO/MMF has a well-defined ascent direction from the first step.

6. Coordinate-space support:

   • Coord cartesian: native Cartesian Sella engine path
   • Coord primitive: native internal-coordinate Sella path
   • Coord dlc / Coord tric: reduced-space internal step path

Default Parameters

Relationship to Existing Optimizers

Usage

Sella minimum optimisation:

task: SELLA RHF STO-3G

GEOMETRY
  ...
END

Sella TS search with MMF step (more robust on flat surfaces):

task: TS SELLA RHF STO-3G

GEOMETRY
  ...
END

OPT
  Step     mmf
  Coord    dlc
  SellaOrder 2
  MaxCycle 100
END