Geometry Optimization Algorithms

OpenQuantum provides a comprehensive suite of geometry optimization algorithms for minima and transition-state searches.

Overview of Chapters

Primitive Internal Coordinates — Topology, B-matrix, Lindh Hessian, TRM step
Delocalized & TRIC Coordinates — SVD rank detection, rigid-body removal
GeomeTRIC Optimizer — Native TRIC quasi-Newton minimizer / RS-P-RFO TS engine
IRC — Intrinsic Reaction Coordinate — Gonzalez–Schlegel mass-weighted predictor-corrector
Transition-State Search — P-RFO, Bofill update, TS-specific trust radius
Quasi-Newton Hessian Updates — MSP, BFGS, TS-BFGS, SR1, DFP, Bofill, PSB, MS, BFGS/Powell
NEB — Nudged Elastic Band — Henkelman–Jónsson with climbing image
Davidson Partial Eigensolver — Rayleigh–Ritz for lowest eigenvalues
Minimum Mode Following — Alternative TS step with |λ| denominator
Sella-Style Optimizer — TS-BFGS, sigma-trust, adaptive eigenvalue correction

Optimizer Selection

The optimizer is selected via the OPT section:

OPT
  Algorithm  bfgs | berny | rberny | sella | geometric
  Coord      cartesian | primitive | dlc | hdlc | tric | tric-p
  ...
END

Algorithm	Description	Use Case
`bfgs`	Cartesian BFGS	Simple minima, small systems
`berny`	Berny RFO (internal coordinates)	Standard minima, robust
`rberny`	Rust Berny backend	High performance, native IC
`sella`	Saddle-point-aware IC optimizer	TS searches, difficult surfaces
`geometric`	GeomeTRIC TRIC quasi-Newton (RS-P-RFO for TS)	Floppy systems, multi-fragment, TS searches

Coordinate Models

Model	Key	Description
Cartesian	`cartesian`	Direct 3N optimization, no IC back-transform
Primitive IC	`primitive`	Full redundant primitive set (bonds, angles, dihedrals, OOP, linear)
DLC	`dlc`	Non-redundant delocalized basis from SVD of B-matrix
HDLC	`hdlc`	Hybrid DLC with Cartesian components
TRIC	`tric`	DLC + rigid-body translational/rotational modes removed
TRIC-p	`tric-p`	TRIC with projected Cartesian components

Transition-State Search

Activate with TransitionState true or the TS task token. Two TS step engines are available, depending on the optimizer backend:

P-RFO (Berny / Sella) partitions the Hessian into a TS mode (maximize) and minimization modes.
RS-P-RFO (GeomeTRIC) is the restricted-step partitioned RFO variant; it applies a positive metric scaling and a damped Hebden iteration to keep the step inside the trust radius. See GeomeTRIC Optimizer for details.

GEDIIS Acceleration

Geometry-space DIIS (GDIIS/GEDIIS) extrapolates from previous geometry/gradient points. Enable with Diis true in the OPT section. Most effective for difficult optimizations near flat PES regions.

Between optimization cycles the molecular geometry changes only slightly, so the converged orbitals from one cycle are an excellent initial guess for the SCF at the next. By default the optimizer carries the previous cycle's density matrix forward and uses it as the SCF guess, which typically reduces the SCF iteration count markedly after the first cycle. The first cycle has no prior orbitals and uses the configured SCF guess (core Hamiltonian by default).

This warm-start applies to RHF, UHF, and ROHF and to every optimizer backend and run mode (minimization, TS, IRC, NEB). Disable it with MOGuess false in the OPT section to force a fresh guess at every geometry.

Convergence Criteria

5-criterion Gaussian-style check:

Energy change ΔE
Gradient RMS
Gradient max
Displacement RMS
Displacement max

Presets: Gauss default, Gauss loose, Gauss tight, or customize with Tighten N (tightens all by 10⁻ᴺ).