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, andstepsizeparameters 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.