Internal Coordinates Optimization

Berny RFO Optimization — Water, RHF/STO-3G

task: OPT RHF STO-3G

GEOMETRY
  O   0.000000   0.000000   0.100000
  H   0.750000   0.000000  -0.450000
  H  -0.750000   0.000000  -0.450000
END

OPT
  Algorithm  berny
  MaxCycle   50
END

Primitive Internal Coordinates

task: OPT RHF STO-3G

GEOMETRY
  O   0.000000   0.000000   0.100000
  H   0.750000   0.000000  -0.450000
  H  -0.750000   0.000000  -0.450000
END

OPT
  Algorithm  berny
  Coord      primitive
  MaxCycle   50
END

Delocalized Internal Coordinates (DLC)

OPT
  Algorithm  berny
  Coord      dlc
  MaxCycle   50
END

TRIC (Translation-Rotation Internal Coordinates)

OPT
  Algorithm  berny
  Coord      tric
  MaxCycle   50
END

GeomeTRIC Native TRIC Optimizer

The geometric backend runs a quasi-Newton optimizer directly in TRIC coordinates, with rigid-body translation/rotation as first-class internals and an adaptive trust radius:

task: OPT RHF STO-3G

GEOMETRY
  O   0.000000   0.000000   0.100000
  H   0.750000   0.000000  -0.450000
  H  -0.750000   0.000000  -0.450000
END

OPT
  Algorithm  geometric    # aliases: geomet, tric
  Coord      tric         # tric-p drops the rigid-body modes
  MaxCycle   200
END

For transition-state searches add TransitionState true (or use the TS task token); the engine switches to RS-P-RFO with Bofill Hessian updates. Seeding the initial Hessian via CartHessian is recommended for TS runs.

Notes

• Primitive IC: Full redundant primitive set (bonds, angles, dihedrals, OOP, linear-angle)
• DLC: Non-redundant delocalized basis from SVD of B-matrix
• TRIC: DLC + rigid-body translational/rotational modes removed via modified Gram-Schmidt
• GeomeTRIC backend: native TRIC quasi-Newton; per-fragment rotations are encoded as exponential maps with analytic B-matrix derivatives, and the internal-to-Cartesian back-transform is iterative with periodic-aware residuals
• For floppy molecules or systems with near-linear geometries, TRIC is recommended
• The default algorithm for internal coordinates is Berny RFO
• When Coord != cartesian, the optimizer automatically uses the IC back-transform