Hessian Update Variants for TS Optimization

The Update keyword selects the Hessian update formula.

Bofill Update with TS Search

OPT
  TransitionState true
  Update bofill
END

`Update=`	Description
`bfgs`	Standard BFGS (minima)
`psb`	Powell–Symmetric–Broyden, rank-2 (TS)
`ms`	Murtagh–Sargent, rank-1 (TS, allows negative curvature)
`bofill`	φ·PSB + (1-φ)·MS, blends PSB and MS (TS)
`sr1`	Symmetric rank-1 (naturally indefinite)
`dfp`	Davidon–Fletcher–Powell (positive-definite)
`bfgs_powell`	Auto: BFGS for minima, Bofill for TS
`ts-bfgs`	TS-BFGS: BFGS in \|H\| space (saddle points)

Bofill with TS search:

OPT
  TransitionState true
  Update bofill
END

Bofill with primitive internal coordinates:

OPT
  TransitionState true
  Update bofill
  Coord primitive
END

Bofill with DLC coordinates:

OPT
  TransitionState true
  Update bofill
  Coord dlc
  MaxCycle 100
END

PSB with TS search:

OPT
  TransitionState true
  Update psb
END

PSB with TRIC coordinates:

OPT
  TransitionState true
  Update psb
  Coord tric
END

MS with TS search:

OPT
  TransitionState true
  Update ms
END

BFGS/Powell mixed for minimum:

OPT
  Update bfgs_powell
END

BFGS/Powell mixed for TS (auto Bofill):

OPT
  TransitionState true
  Update bfgs_powell
END

Combined GEDIIS + Bofill for TS:

OPT
  TransitionState true
  Update bofill
  Diis true
  MaxCycle 150
END

Sella + Bofill:

OPT
  Algorithm       sella
  TransitionState true
  Update          bofill
  MaxCycle        100
END

Sella + Bofill + DLC:

OPT
  Algorithm       sella
  TransitionState true
  Update          bofill
  Coord           dlc
  MaxCycle        100
END