IRC — Intrinsic Reaction Coordinate

The Gonzalez–Schlegel (1990) algorithm for mass-weighted IRC following:

Algorithm

1. Mass-weight the input Hessian: $${\mathbf{H}}_{\text{mw}}={\mathbf{M}}^{-1/2}\mathbf{H}{\mathbf{M}}^{-1/2}$$

2. Diagonalize to find the mode of largest imaginary frequency

3. Displace along that mode (forward and reverse) to get two starting points

4. For each direction: predictor (mass-weighted steepest descent) + corrector (constrained optimization orthogonal to the path tangent)

   • The corrector uses a proper Gonzalez–Schlegel corrector sub-loop (up to 10 iterations per IRC step)
   • The gradient is projected orthogonal to the radial (path tangent) direction in mass-weighted coordinates
   • A constrained steepest-descent step is taken on the hypersphere
   • Iterates until the perpendicular gradient norm is below $10^{-6}$

5. Convergence by max-gradient norm; output is a list of IrcPoint (arc, geometry, energy)

Bidirectional IRC

The IRC true directive triggers bidirectional IRC from the provided geometry. Restrict to one direction with IRCDir +1 (forward) or IRCDir -1 (reverse).

Requirements

• Starting geometry should be a pre-converged transition state (imaginary frequency expected)
• The initial Hessian must have at least one negative eigenvalue for the reaction mode

Usage

task: RHF STO-3G

GEOMETRY
  ...
END

OPT
  IRC     true
  IRCDir  +1
END

The output includes per-step energies, geometries, and a formatted path summary.