Relaxed potential-energy surface scans

A relaxed scan maps how the energy changes along one chosen coordinate (a bond, angle, or dihedral) while every other degree of freedom relaxes at each step. Unlike a rigid scan, which freezes the whole geometry, a relaxed scan traces the true minimum-energy path along that coordinate: the right tool for a dissociation curve, a torsional profile, or a one-dimensional reaction coordinate.

Running a scan

relaxed_scan takes the molecule, a basis, the coordinate to drive, and the values to step through. The remaining coordinates are optimised at each point:

import vibeqc as vq

mol = vq.Molecule([vq.Atom(8, [0, 0, 0]),
                   vq.Atom(1, [0,  1.43, -0.98]),
                   vq.Atom(1, [0, -1.43, -0.98])])

scan = vq.relaxed_scan(
    mol, "sto-3g",
    coordinate=("bond", 0, 1),           # the O-H(1) bond
    values=[1.4, 1.6, 1.8, 2.0, 2.2],    # bond length in bohr
    method="RHF",
)
for r, e in zip(scan.values, scan.energies):
    print(f"{r:.2f} bohr   {e:.6f} Ha")

1.40 bohr   -74.845508 Ha
1.60 bohr   -74.934691 Ha
1.80 bohr   -74.964215 Ha
2.00 bohr   -74.961050 Ha
2.20 bohr   -74.939884 Ha

The minimum sits near 1.8 bohr (about 0.95 Angstrom), the equilibrium O-H distance. The relaxed scan recovers it because the other coordinates (the second O-H and the H-O-H angle) relax at every step; a rigid scan of a distorted starting geometry would not.

The result object

relaxed_scan returns a ScanResult with:

  • values and energies: the scan coordinate and the relaxed energy at each point.

  • geometries: the optimised structure at each point, for export or restart.

  • converged_flags: whether each constrained optimisation converged.

The coordinate argument also takes ("angle", i, j, k) and ("dihedral", i, j, k, l), and a periodic system can be scanned the same way by passing kpoints=.

See also