A 1752‑molecule benchmark set for molecular geometry optimizers on the GFN2‑xTB potential energy surface

Changelog v2.1 (June 2026) — optimizer geometries regenerated with the current aiopt release, two corrected reference minima, a duplicate-minimum map, and accurate soft-mode counts. (1) The aiopt-converged geometries, full optimization trajectories, cycle counts, and the energies and frequencies evaluated at the aiopt geometry were regenerated with the current development version of the TURBOMOLE built-in tight-binding optimizer (GFN2-xTB, gas phase). Of the 1752 cases, 1739 reproduce the previous geometry, energy and cycle count exactly; 13 differ by a flat-mode reorientation at the same energy; and one case (g55_mb16-43__36) now converges to a genuine minimum (lowest vibrational frequency +26.88 cm-1) where it previously stopped at a low saddle (-24 cm-1). Twelve cases whose first-pass gradient sat just above the convergence criterion (1.0-1.3×10^-4 Ha/Bohr) were re-optimized to a clean minimum (max gradient < 1×10^-5 Ha/Bohr); one floppy ion-water cluster (g55_water27__H3OpH2O62d) remains at a ~1.0×10^-4 Ha/Bohr gradient floor set by its flat intermolecular libration modes. The xtb 6.7.1 Hessian-verified reference minima (true_min) are unchanged. (2) g55_sie4x4__h2o2+_1.75: its v2 true minimum was the dissociated optimization endpoint (the two water fragments ~39 A apart); it is replaced by the bound water-dimer-cation minimum (O-O 2.006 A, 2.0 mHa lower, lowest vibrational frequency 179 cm-1, no imaginary modes), Hessian-verified with xtb 6.7.1. (3) Re-examined every case whose v2 Hessian showed a small spurious imaginary mode and re-optimized it at tighter accuracy (xtb --acc 1e-4), resolving four (g55_fh51__2-pentyne, g55_hal59__NCH_PhBr, g55_rg18__c2h2Ar, g55_s66__49); the remaining 13 have a lowest mode below the resolution of a GFN2 numerical Hessian and stay flagged n_imag_significant = 0. After v2.1, 1739 of 1752 cases are strictly positive-definite. (4) Added tables/duplicate_minima.tsv, mapping the 79 sets of cases that relax to a shared minimum from different starting geometries. v2 (May 2026) — Hessian-verified true minima, vibrational frequencies, full optimization trajectories. Replaces v1. For every case the archive now provides four items: the distorted starting geometry, the aiopt-converged stationary point with its full per-cycle optimization trajectory, and the Hessian-verified true local minimum together with its vibrational frequencies and normal modes from xtb 6.7.1. 1745 of 1752 cases have strictly positive-definite Hessian; the remaining 7 have sub-3 cm⁻¹ residual modes from intrinsic free-rotor / soft-libration physics and are flagged in the manifest. Energies are reported at both engines (TURBOMOLE tb at the aiopt geometry, xtb 6.7.1 at the same geometry, xtb 6.7.1 at the refined geometry); manifest.tsv carries same-engine and cross-engine ΔE plus imaginary-mode counts at both aiopt and refined geometries. v1 (March 2026) — initial deposit; subsequently superseded by v2. Description A Cartesian-coordinate benchmark set of 1752 molecules (4–110 atoms) for evaluating molecular geometry optimizers on the semiempirical tight-binding GFN2-xTB potential energy surface. It collects molecules from the Baker geometry-optimization test set, a broad selection of GMTKN55 subsets (conformers, reactions, non-covalent complexes, main-group and heavy-element species), the 130 transition-metal complexes of the tmQM database, organic and TURBOMOLE test molecules, and larger flexible drug-like systems (Birkholz–Schlegel). The set spans 215 charged species and 114 open-shell doublets. For each molecule the archive provides four items: (a) a distorted starting geometry, generated by perturbing the reference minimum, which serves as the optimizer input; (b) the corresponding aiopt-converged stationary point on the GFN2-xTB surface (TURBOMOLE tb engine); (c) the complete per-cycle optimization trajectory from the starting geometry to that stationary point; and (d) the Hessian-verified true local minimum, with associated vibrational frequencies and normal modes computed with standalone xtb 6.7.1. The two static geometries are given in .xyz format (Ångström) and in native TURBOMOLE coord format (atomic units / Bohr); the trajectory is a multi-frame .xyz file whose first frame is the starting geometry and whose final frame is the aiopt stationary point, with every frame annotated by its energy (Ha). Frequencies are deposited in TURBOMOLE vibspectrum format (cm⁻¹) and as Gaussian-98-format normal modes written natively by xtb 6.7.1. The file tables/manifest.tsv lists, for every molecule, its group, case name, atom count, charge, spin multiplicity, the number of trajectory frames and optimization cycles, the energies at both engines (TURBOMOLE tb at the aiopt geometry, xtb 6.7.1 at the same geometry, xtb 6.7.1 at the refined geometry), both same-engine and cross-engine ΔE, the lowest vibrational frequency and imaginary-mode count at both aiopt and refined geometries, and the refinement source. tables/per_group.tsv aggregates these per group. tables/COLUMNS.md documents every column. Charges and multiplicities correspond to the automatic GFN2-xTB low-spin state (singlet for an even electron count, doublet for an odd one); the 130 tmQM complexes are closed-shell singlets matching the tmQM database. Optimization to the stationary point was performed on the GFN2-xTB surface as implemented in TURBOMOLE's built-in tight-binding module (not the standalone xtb program), in the gas phase. The convergence criterion is a maximum gradient component below 1×10⁻⁴ Ha/Bohr, an RMS gradient below 1×10⁻⁴ Ha/Bohr, and an energy change below 1×10⁻⁶ Ha between successive steps; every deposited aiopt geometry satisfies these criteria. Hessian verification and the optional mode-follow refinement that produces the true minimum were performed with standalone xtb 6.7.1 at --ohess extreme --acc 0.001 (max gradient < 5×10⁻⁵ Ha/Bohr, energy ΔE < 5×10⁻⁸ Ha). Optimizer cost is measured as the number of GFN2-xTB energy-and-gradient evaluations, equal to the trajectory length and listed per molecule in the manifest. Contents: cases/ (per-case directories with initial, aiopt_min, true_min in xyz + TURBOMOLE coord, plus aiopt_trajectory.xyz, true_min.vibspectrum, true_min.g98, true_min.energy, aiopt_min.energy, and provenance.txt), tables/ (manifest.tsv, per_group.tsv, COLUMNS.md), docs/METHODOLOGY.md (engine and convergence settings used at each stage), README.md, and LICENSE. Released under the Creative Commons Attribution 4.0 International (CC-BY-4.0) license.