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Mathematics for Nerds: Coordinate Scan

This section formalizes what a relaxed coordinate scan actually computes — from the geometric definitions of bond, angle, and dihedral coordinates, through the constrained-optimization problem solved at every scan point, to the full algorithm.

  • The PES in Internal Coordinates — writing the energy as a function of bond lengths, angles, and dihedrals.
  • The Relaxed Scan as a Constrained Optimization — the Lagrange-multiplier picture behind holding one coordinate fixed.
  • Bond Length, Bond Angle, and Dihedral Coordinates — the geometric formulas for each coordinate type.
  • Specifying a Scan: Step Count and Step Size — how the start, nsteps, and stepsize parameters build the scan grid.
  • Rigid vs. Relaxed Scans — a formal comparison of the two approaches.
  • The Reaction Coordinate Approximation and Its Limitations — why a scan is not a rigorous reaction path.
  • Complete Relaxed Scan Algorithm — the full procedure, start to finish.