11 KiB
Nitrogenase N2-Binding Source Audit and Regression Dataset
Source audit
The core numeric point checks out. The four Bjornsson values you flagged from the later Ryde paper — +69, +41, +8, and −17 kJ/mol for the best (N_2)-binding energies of E_0, E_1, E_2, and E_4 — do appear in Jiang and Ryde’s introduction as their summary of Pang and Bjornsson’s newer study, and those numbers match the more explicit Pang/Bjornsson values once the reported kcal/mol numbers are converted to kJ/mol. One source entry in your list, however, needs correction: the 2005 Kästner/Hemmen/Blöchl paper is 10.1063/1.2008227, while 10.1063/1.2042456 is an unrelated paper on quantum control. citeturn54view0turn32search2turn31search1
Pang and Bjornsson values
For regression purposes, Pang and Bjornsson’s terminology matters. In that paper, “binding energy” means binding relative to the lowest-energy isomer of a given E_n manifold, while “single-step N_2 binding energy” means binding to a specific precursor isomer. They also state explicitly that these are 0 K electronic energies without ZPVE or entropy, so they are not free energies of binding. citeturn18search0turn27search0
| Redox state | Regression-safe Pang/Bjornsson value | Pang/Bjornsson structural reference |
|---|---|---|
E_0 |
+69.45 kJ/mol | best QM-VI (N_2)-bound minimum at Fe6, (E_0)-(N_2)@Fe6-BS147 |
E_1 |
+41.42 kJ/mol | best QM-VI (N_2)-bound minimum at Fe6 |
E_2 |
+7.95 kJ/mol | best-isomer (E_2)-hyd value, referenced to the most stable (E_2)-hyd precursor |
E_4 |
−17.15 kJ/mol | best-isomer (E_4)-SP value, referenced to the most stable E_4 precursor |
These values come directly from Pang and Bjornsson’s large-QM discussion: E_0 binding to Fe6 is 16.6 kcal/mol, E_1 binding to Fe6 is 9.9 kcal/mol, (E_2)-hyd best-isomer binding is +1.9 kcal/mol, and (E_4)-SP best-isomer binding is −4.1 kcal/mol. Converting with 1\ \text{kcal mol}^{-1}=4.184\ \text{kJ mol}^{-1} gives the four regression values above. citeturn24search0turn23search0turn27search0
Two caveats are especially important before fitting anything. First, the alternative single-step values are much more favorable than the best-isomer values for E_2 and E_4: Pang and Bjornsson report −9.8 kcal/mol for direct binding to the alternative (E_2)-hyd-SH(^{-})@Fe2 precursor and −15.2 kcal/mol for (E_4)-SP-SH(^{-})@Fe2 (\rightarrow E_4)-SP-(N_2)@Fe6. Second, the paper stresses that these energies are meant to compare electronic trends, not room-temperature binding free energies. Mixing those single-step values with the best-isomer series would create a category error in any regression. citeturn18search0turn27search0
Jiang and Ryde comparison
A key clarification: in the published Dalton Transactions paper, Table 2 is not the cross-state summary table. Table 2 is the set of ten E_2 structures without (N_2). The cross-state (N_2)-binding comparison is spread across Table 1 (E_0/E_1), Table 3 (E_2), Table 5 (E_3), and Table 7 (E_4), with additional best-structure checks in ESI Tables S1–S3. If you want the paper’s most systematic state-by-state comparison in the final published version, those are the tables to read together. citeturn47view0turn49view0turn50view0turn48view0turn45view0
Ryde’s methodological framework is broader than Pang’s. The paper compares four functionals — TPSS, r2SCAN, TPSSh, and B3LYP — and distinguishes different energetic measures, including the ordinary (N_2)-binding energy \Delta E_{N_2} and a direct binding energy \Delta E_{db} referenced to the same structure with N_2 in the second coordination sphere. That means a Pang-style regression and a Ryde-style cross-functional survey are not interchangeable unless the metric is harmonized up front. citeturn49view0turn54view0
The broad conclusion of Jiang and Ryde is unusually clear even though the tables are method-sensitive. In the abstract and the conclusion, they state that TPSS gives the strongest bonding and is the only functional that reproduces the experimental pattern of unfavorable binding for (E_0)–E_2 and favorable binding for E_3 and (E_4). r2SCAN gives favorable binding only to E_4, while TPSSh and B3LYP do not yield favorable binding to any E_n state in the final comparison. They also emphasize that B3LYP strongly favors triply protonated carbide states and that structures with two hydrides bridging Fe2/Fe6 and a partially dissociated S2B ligand are the best (E_4)-type models for TPSS, r2SCAN, and TPSSh. citeturn12search3turn54view0turn3view2
The paper also gives an important warning for anyone doing quantitative fitting. When Jiang and Ryde add entropy corrections, the picture softens materially: with the larger entropy correction, no E_n state gives favorable N_2 binding; with the smaller correction, TPSS still gives favorable binding for E_3 and E_4, whereas r2SCAN gives favorable binding only to E_4. In the ESI they further note that some basis-set changes alter relative energies by more than 20 kJ/mol, and Table S2 shows cases where the electronic structure itself changes extensively on the larger basis. That is exactly the sort of hidden heterogeneity that can flatten or distort a regression if all points are pooled indiscriminately. citeturn3view2turn36view1
Hallmen and Kästner in context
For the paywalled 2015 paper, the abstract-level record is still useful. Hallmen and Kästner state that they examined N_2 binding to a reduced and protonated FeMo-cofactor including the central carbon ligand, found that the central ligand stabilizes the cluster, and concluded that N_2 can bind either Fe or Mo, with Fe preferred and exo modes more stable than endo modes. That makes the paper mechanistically relevant as a bridge between the older pre-carbide DFT literature and the later carbide-aware Fe-site binding work. citeturn29search3turn29search4
What the accessible sources do not safely provide is a trustworthy numeric extraction comparable to Pang’s or Ryde’s tabulated series. For that reason, Hallmen and Kästner is a sound context source, but not a safe regression datapoint source unless the full paper is opened and its energetic definitions are checked directly. citeturn29search4
Earlier Kästner trajectory
The older Kästner/Blöchl sequence is still useful, but it sits on an older structural footing. In the 2003 JACS study, Schimpl, Petrilli, and Blöchl modeled the FeMo cofactor with a central nitrogen ligand, found that the Fe–Mo cage opens on N_2 binding, identified both axial and bridged binding modes, and concluded that Mo binding is less favorable than Fe-site binding. That paper is historically important because it already places sulfur-bridge opening and Fe-site coordination at the center of the mechanism, but it predates the 2011 structural assignment of the interstitial carbide in modern FeMoco descriptions. citeturn29search1turn53search0turn53search1
The corrected 2005 JCP paper by Kästner, Hemmen, and Blöchl then pushed the mechanism one step further. Its central quantitative result is that bridging N_2, activated by bonding to two Fe sites, lowers the energy for the first hydrogen transfer by 123 kJ/mol, while an axial mode with an open sulfur bridge is 30 kJ/mol less reactive. It also reports that the energetic ordering of axial and bridged binding modes reverses in favor of the bridged dinitrogen upon first protonation. citeturn32search2
The 2007 JACS paper continued the same DFT trajectory from monoprotonated bound dinitrogen all the way to ammonia release. Its abstract says that during the modeled catalytic conversion, nitrogen bridges two Fe atoms, a cis-to-trans diazene rearrangement occurs, N–N bond cleavage is strongly exothermic, and release of the second ammonia is facilitated by re-closure of the sulfur bridge after an intramolecular proton transfer. In other words, it is best read as a continuation of the 2003–2005 Fe-site, sulfur-lability, Fe-bridged pathway picture. citeturn34search0turn34search1
The short 2005 ChemPhysChem paper, Towards an understanding of the workings of nitrogenase from DFT calculations, is best treated as a bibliographic waypoint rather than a data source in this exercise. PubMed provides the citation but no abstract, so it is not a reliable place to mine numbers or detailed mechanistic constraints unless the full text is opened separately. citeturn52search0
Regression-ready takeaways
If the immediate goal is a clean regression input, the most defensible numeric series is the Pang/Bjornsson best-isomer QM/MM set: E_0 = +69.45, E_1 = +41.42, E_2 = +7.95, and E_4 = -17.15\ \text{kJ mol}^{-1}. Those four points are internally consistent in definition, level of discussion, and structural framing. Jiang and Ryde can then be used as the sensitivity analysis layer that tells you how much those energies move with functional choice, alternative structural manifolds, and entropy treatment. citeturn24search0turn23search0turn27search0turn12search3turn3view2
The main thing not to do is pool together four different categories of numbers: Pang best-isomer values, Pang single-step values, Ryde (\Delta E_{N_2}) values, and Ryde (\Delta E_{db}) values. Those are different observables. A second thing not to do is treat Hallmen 2015 as numerically commensurate until the full text is in hand. A third is to ignore the structural regime change: the Pang sequence is not simply “binding gets linearly better with reduction.” It also crosses from resting-state-like manifolds (E_0/E_1) into hydride-bearing, S2B-hemilabile manifolds (E_2/E_4), which is exactly why both Pang and Ryde keep emphasizing hydride ligation, low-spin Fe configurations, and local coordination change as the real drivers of favorable binding. citeturn18search0turn12search3turn54view0
If a purely descriptive fit is still useful, an ordinary least-squares line through the four Pang best-isomer points gives approximately (E_{\text{bind}}(\text{kJ/mol}) = 63.26 - 21.63,E_n) with (R^2 \approx 0.95). That fit is fine as a compact summary of the monotonic trend in this one internally consistent series, but it should be treated as descriptive only, not mechanistic, because two of the four points already sit on different electronic and structural manifolds than the first two. citeturn24search0turn23search0turn27search0turn18search0turn12search3