Does Blackmon and Closser's near-uniform sulfamethoxazole ensemble survive a thermal correction?

Abstract

Blackmon and Closser, in Determination of Ground-State Structure and Electronic Excitations of Sulfamethoxazole Using Density Functional Theory (Comput. Theor. Chem. 1264, 2026, 115931), optimize sulfamethoxazole to four unique solvated minima, A–D, spanning 0.202 kJ/mol, and assign 298 K Boltzmann populations of roughly one quarter each from electronic energies alone.¹ Their paper states that frequency calculations confirmed all four structures as minima, but neither the frequencies nor a thermally corrected ordering appears in the paper or its supplement. This note adds that correction independently, under a protocol frozen before the first calculation: each published geometry is re-optimized with GFN2-xTB in ALPB water, a harmonic Hessian is computed, and the xTB thermochemical correction is added to the source’s own electronic energies, in two arms that differ only in the low-frequency rotor cutoff. The preregistered hypothesis — that the near-uniform ensemble is robust, with no conformer’s population moving more than 10.0 percentage points and the effective conformer count staying at or above 3.5 in both arms — was falsified. The maximum population shift is 19.7 percentage points in the pure-RRHO arm and 12.7 percentage points in the 50 cm⁻¹ modified-RRHO arm; conformer A’s population moves from 26.3% on the source’s electronic energies to 45.9% and 39.0% in the two arms, and the effective conformer count falls from four to 3.00 and 3.57. Conformer A remains the lowest structure throughout. The corrected populations bound the robustness of the published electronic-only population vector; they do not determine the source’s unreported same-level thermochemistry.

Introduction

Conformer populations are equilibrium quantities, so the observable mixture of a flexible molecule follows from free energies, not electronic energies. For minima separated by more than a few kJ/mol the distinction rarely changes a qualitative story, but zero-point and thermal contributions routinely differ between conformers of one molecule by tenths of a kJ/mol and more — the treatment of low-frequency torsions alone can move relative free energies by that much, which is why modified rigid-rotor–harmonic-oscillator schemes exist at all.²

Blackmon and Closser optimize the antibiotic sulfamethoxazole (SMX) to four unique minima, A–D, in implicit water, and find them separated by 0.202 kJ/mol in total, with A lowest by 0.137 kJ/mol over B.¹ Their Table 1 assigns 298 K Boltzmann populations of 26.3, 24.9, 24.7 and 24.2%, and its footnote states that zero-point and thermal corrections are excluded. Recomputing a Boltzmann factor over the supplement’s electronic energies reproduces those populations — the values enter this note’s tables as 26.3%, 24.9%, 24.7% and 24.2% — so the published populations are an electronic-energy projection of a 0.2 kJ/mol-spaced quartet at a temperature where \(kT\) is 2.48 kJ/mol. The paper reports that frequency calculations were run to confirm all four structures are minima, so same-level frequencies existed; a corrected ordering is the analysis their own data supports that the paper never prints.

An energy separation this far below the typical conformer-to-conformer spread of thermal corrections could resolve either way. The corrections could be as degenerate as the electronic energies — four conformers of one molecule share most of their vibrational structure, and near-perfect cancellation is a reasonable default expectation — or they could exceed the electronic span by an order of magnitude and redraw the ensemble. I therefore state the hypothesis before the experiment, on the side of the published picture: under an independently calculated 298.15 K thermochemical correction, the near-uniform ensemble is robust — in both registered arms, no conformer’s population moves more than 10.0 percentage points from the source’s electronic-energy baseline, and the effective conformer count \(1/\sum_i p_i^2\) stays at or above 3.5. The falsifier, fixed in advance: both arms fail at least one of those gates. If the arms disagree, or any preregistered method-fidelity check fails, the result is inconclusive rather than repaired. Either outcome is worth publishing: robustness would bound how much the near-degeneracy matters for anyone selecting a single SMX conformer for excited-state work, and a falsification would mean the published population vector is a property of the electronic surface rather than of the molecule at temperature.

Computational Methods

Source inputs. The A–D Cartesian coordinates and electronic energies were transcribed from the source’s supplement and frozen, with checksums, in the experiment’s inputs.json before any calculation ran. The published relative energies reproduce from those transcribed values to ±0.002 kJ/mol. The source authors’ program (Q-Chem), their PCM solvation, and their excited-state calculations were not used or reproduced; nothing in this note reruns any calculation of theirs. The atom order of the rendered B and C coordinate lists differs from the article’s numbering in the position of one sulfonyl oxygen; that atom is moved ahead of the hydrogens to restore the common order, without changing any coordinate.

Protocol. The full protocol was frozen in the experiment’s PREREGISTRATION.md before the first SMX calculation. For each conformer and each arm: (1) optimize from the source geometry with GFN2-xTB 6.7.1 in ALPB water, tight convergence, SCC accuracy 0.2, single-threaded;^3,4 (2) compute the numerical Hessian on the optimized structure; (3) retain the thermochemical free-energy correction \(G_\mathrm{xTB} - E_\mathrm{xTB}\) at 298.15 K; (4) form the composite free energy

\[ G_i \;=\; E_i^{\mathrm{source\ DFT}} \;+\; \bigl[\,G_i^{\mathrm{xTB}} - E_i^{\mathrm{xTB}}\,\bigr], \]

and (5) compute normalized Boltzmann populations at 298.15 K. The two arms differ only in xTB’s low-frequency rotor cutoff: rrho uses \(s_\mathrm{thr} = 0\) cm⁻¹ (pure RRHO) and mrrho50 uses \(s_\mathrm{thr} = 50\) cm⁻¹ (Grimme’s modified-RRHO interpolation).² The imaginary-mode threshold is −20 cm⁻¹, the frequency scale factor 1.0. Native all-xTB free energies are retained as a secondary sensitivity result and do not enter the verdict.

Method-fidelity gate. The verdict is automatically inconclusive if any run terminates abnormally, any optimized structure has a mode below −20 cm⁻¹, any A–D pair of optimized structures falls below 0.10 Å heavy-atom aligned RMSD in either arm, or the two arms’ optimized geometries for one conformer differ by more than 0.02 Å heavy-atom aligned RMSD.

Environment. The registered run executed 2026-07-25 on macOS (Darwin 25.5.0, Apple M1, arm64) with CPython 3.14.6, NumPy 2.5.0, and conda-forge xTB 6.7.1, serialized to a single thread throughout; the explicit conda lock is committed. The analysis layer regenerates deterministically from the committed raw xTB outputs without rerunning quantum chemistry, and its canonical serialization rounds floats to 12 significant digits so the regeneration check is architecture-independent; the committed analysis was re-verified on linux-x86_64. The bars in Figure 1 are emitted from the same canonical result rather than typed by hand, and a check mode fails if the committed figure and the canonical populations disagree. The experiment bundle — preregistration, frozen inputs, raw outputs, runner, analysis, and metrics — is published under research/smx-conformer-thermochemistry/. The reproducibility level this earns is end-to-end reproducible on osx-arm64, and analysis-reproducible from the committed outputs elsewhere.

Results

Every registered method-fidelity check passed: all eight conformer/arm runs terminated normally, no optimized structure has a mode below −20 cm⁻¹, all optimized A–D pairs are separated by at least 0.10 Å heavy-atom RMSD in both arms, and the two arms’ optimized geometries agree within 0.02 Å for each conformer.

Table 1 reports the composite populations. The maximum absolute population shift from the source baseline is 19.7 percentage points in the rrho arm and 12.7 percentage points in the mrrho50 arm, against the registered ceiling of 10.0. The effective conformer count is 3.00 in the rrho arm and 3.57 in the mrrho50 arm, against the registered floor of 3.5. The rrho arm fails both gates; the mrrho50 arm fails the shift gate and passes the count gate. Both arms fail at least one gate.

Table 1. Boltzmann populations of the four SMX conformers at 298.15 K: from the source’s electronic energies, and from the composite free energies of the two registered thermochemistry arms.

Figure 1. The populations of Table 1 as grouped bars: the source’s electronic-energy baseline in gray, the two composite thermochemistry arms in blue.

The composite free-energy ordering is A < B < C < D in both arms, with C and D separated by 0.02 kJ/mol in the mrrho50 arm and 0.24 kJ/mol in the rrho arm. Conformer A has the lowest composite free energy in both arms. Among the secondary sensitivity results, the native all-xTB free energies also order the re-optimized structures A < B < C < D in both arms, matching the source’s electronic ordering, while the native xTB electronic energies alone order them B < C < A < D, spanning 0.148 kJ/mol.

As a separate audit of the transcribed source data: all eight relaxation-energy magnitudes recomputed from the supplement’s energies agree with the source’s main-table values to within 0.005 kJ/mol, and the recomputed signs differ from the table footnote’s stated \(E_\mathrm{vertical} - E_\mathrm{adiabatic}\) formula in 8 of the eight rows.

Discussion

The preregistered hypothesis was falsified. Both registered arms exceeded the 10.0-percentage-point ceiling on population shift, and the pure-RRHO arm additionally dropped the effective conformer count below the registered floor of 3.5. The registered decision rule reads two failing arms as a falsification rather than an inconclusive split, and both arms failed.

What this does and does not establish needs stating carefully, in both directions. The falsified quantity is the robustness of the published population vector to an independently calculated thermochemical correction — not the source’s own thermochemistry. The corrections here are GFN2-xTB free-energy corrections evaluated on GFN2-xTB re-optimized geometries in ALPB water; the source’s surface is a hybrid-DFT PCM surface, and its harmonic frequencies, which the paper states were computed, were never published for comparison. A same-level correction could well land differently in detail. What the experiment establishes is narrower: the thermochemical term, at a level of theory routinely used for exactly this purpose, is an order of magnitude larger than the 0.202 kJ/mol electronic span it is being added to, and it does not cancel across the quartet. A population statement inherited from electronic energies spaced at a hundredth of \(kT\) has no protection against a correction of ordinary conformer-to-conformer size, and this one did not survive it.

In the other direction, the correction strengthens the source’s central structural claim. Blackmon and Closser’s contribution is the identification of conformer A as the global minimum against earlier SMX studies that used a different geometry; in both registered arms A keeps the lowest composite free energy, by a margin far larger than its published 0.137 kJ/mol electronic lead. Under this protocol the thermal correction promotes their preferred structure from first-among-equals to a distinctly dominant conformer. The rotor-cutoff comparison behaves as expected for corrections dominated by low-frequency modes: the modified-RRHO arm, which damps the harmonic entropy of exactly those modes, moves every population in the same direction as pure RRHO but less far.

The sign audit is reported with our hands up. The recomputed relaxation-energy magnitudes agree with the source’s table to within transcription precision, and the systematic sign opposition is consistent with the footnote’s formula being stated in the reverse order of the one applied — or with us misreading which states the footnote’s symbols name. It changes nothing in this note’s analysis, which uses only ground-state energies; it is recorded so that a reader of the supplement is not surprised by it, and we invite correction if the convention is ours to fix.

The main limitations are the ones the boundary conditions above imply. The composite free energy mixes two electronic-structure levels, which is a standard low-cost construction but not a controlled approximation to either level alone. The corrections are harmonic-based with an empirical rotor treatment, at 298.15 K only, for the four published minima only — no conformer search was run, so a fifth minimum, if one exists, is outside the frozen scope. And the populations are equilibrium statements about an implicit-solvent model, not predictions of what any experiment on aqueous SMX would measure.

Conclusion

The published near-uniform SMX ensemble is a property of the electronic surface, not a demonstrated property of the molecule at temperature: an independent thermochemical correction concentrates the ensemble onto the source’s own global minimum in both registered arms. How far it concentrates depends on the rotor treatment — pure RRHO roughly halves the C and D populations, while the modified-RRHO arm cuts them by about a quarter. For anyone using the paper’s structures, the practical reading is that selecting conformer A alone is better supported after thermal correction than before it, while any workflow that weights all four conformers equally inherits a population vector this experiment measured to be fragile.

The next experiment is the same-level version of this one: harmonic frequencies for the four published geometries at a hybrid-DFT level with implicit water — a calculation within reach of the tools used on this site — to test whether the concentration of the ensemble survives when the correction and the electronic energies come from one surface. That question is now on the research shelf.

References