A Showcase of Using the Partial-Structure R1 to Assemble Small-Molecule Crystal Structures

Xiaodong Zhang

REVIEW 3 major objections 5 minor 7 references

A Showcase of Using the Partial-Structure R1 to Assemble Small-Molecule Crystal Structures

T0 review · 3 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read The partial-structure R1 method can assemble small-molecule crystal structures fragment by fragment, without traditional phasing.

desk verdict A genuine but mostly qualitative showcase of the pR1 assembly method; worth refereeing after the authors add a self-contained definition and quantitative validation. read the letter →

arxiv 2607.13836 v1 pith:KI6XRBOH submitted 2026-07-15 physics.comp-ph cond-mat.mtrl-sci

Xiaodong Zhang This is my paper · ORCID

classification physics.comp-phcond-mat.mtrl-sci

keywords partial-structureR1pcrystalstructuresolutionfragmentassemblyresidualreflectionintensitiesphasing-freemethodsmall-moleculecrystallography

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that a function called the partial-structure R1 (pR1) can assemble a small-molecule crystal structure from a few idealized molecular fragments, bypassing traditional phasing. It works by first orienting and placing large fragments or fragments containing heavy atoms, then attaching smaller fragments to the growing model by optimizing only their orientation. When the remaining fragments contain only light atoms, the paper shows they cannot be found directly because heavy-atom scattering overwhelms them; instead, the heavy-atom contribution must be subtracted from the reflection data to make residual intensities. Demonstrated on one main example and two supporting ones, the claim is that in favorable situations pR1 is a useful, if not universal, route to structure solution.

What carries the argument

The pR1 function is an approximate R1 factor defined by taking the traditional crystallographic R1 and removing its dependence on the locations of atoms not yet in the model, so that it depends only on the orientation and position of the fragment being added. In practice a full six-dimensional search is split into two three-dimensional searches: orientation first, using a 'free-standing' fragment whose position in the cell is irrelevant, then translation. Attaching a fragment to an existing partial model reduces the search to orientation alone. Residual reflection intensities, formed by subtracting the calculated contribution of the known heavy-atom partial model from observed intensities, p

What would settle it

Take a crystal structure whose correct solution is already known and that contains a light-atom-only fragment plus heavy atoms. Run the pR1 calculation with the heavy-atom partial model subtracted, and check whether the correct orientation of the light-atom fragment appears among the low pR1 minima and leads to a model that does not fall apart on tweaking. If the correct orientation is absent from the ranked minima, the method's claim of usefulness in that case is falsified; more decisively, a direct computation of pR1 with and without the 'removal' of other atoms would show whether the approx

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is a set of practical observations about how to use the pR1 function to solve crystal structures: start with large fragments or fragments with heavy atoms, whose correct orientations appear as low-lying local minima of the pR1 surface; attach new fragments to the known partial model so that only a three-dimensional orientation search remains; and, for light-atom-only fragments in heavy-atom structures, search residual reflection intensities after removing the heavy-atom model. The author states that these observations indicate pR1 is a useful tool for solving some small-molecule crystal structures.

Load-bearing premise

The pR1 function is assumed to genuinely depend only on the fragment's orientation and location once the other undetermined atoms are 'removed'; this paper relies on that definition from prior work and does not reproduce the proof, yet the entire search strategy stands or falls on it.

Editorial extensions

If this is right

Solving a small-molecule structure can proceed by assembling idealized fragments, so prior chemical knowledge of fragment geometry replaces the need for direct phasing.
pR1 orientation ranking provides a natural way to order candidate placements; low pR1 values indicate correct orientation in favorable cases.
For heavy-atom structures, a two-stage workflow—build and tweak the heavy-atom partial model, then subtract it to generate residual intensities—makes light-atom fragments findable.
The method reduces computational cost when fragments are attached: only orientation needs optimizing, a 3-dimensional search instead of a 6-dimensional one.
If a full 6-dimensional search became feasible, the author suggests pR1 could become a general tool, not just for favorable cases.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The residual-intensity trick may generalize to any weak structural feature hidden behind a known strong partial model, such as locating disordered solvent or guest molecules after subtracting the ordered framework.
The ordering of pR1 minima behaves like a scoring function; one could automate fragment assembly by greedily trying top-ranked orientations and validating with a tweak step, which the paper does by hand.
A testable extension is to benchmark pR1 assembly on a library of known small-molecule structures, measuring how often the correct orientation appears within the top few pR1 minima; this would map the boundary of 'favorable situations.'
For fragments that are small and light, the paper's own example 3 shows residual intensities may still rank wrong orientations first, implying the method's reliability depends on fragment size and scattering power; a quantitative criterion for when the method is safe remains open.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this paper does what it says — it shows pR1 assembling small-molecule structures in three examples — but the evidence is mostly visual and the method's definition lives in the prior paper. I'd send it to referees, but I'd expect major revision.

The genuinely new piece is the residual-intensity workaround for light-atom-only fragments, and Example 1 (JPD1252) is a nice walk-through of building a fragment in situ. The paper is honest about what pR1 can and cannot do right now ('only some favorable structures'), and the GitHub code is a real plus: someone could rerun the calculations without reverse-engineering the method. That is more than many crystallography papers offer.

The soft spots are the ones you'd expect. The pR1 function is never defined in this paper; the reader is pointed to Zhang & Donahue (2024). For a 'showcase' paper, that's awkward but not disqualifying — the prior work is citable, and the code ties the definition down. More serious: every success is verified by 'no fragments fall apart after tweak' and visual inspection. No final R1, no Rfree, no r.m.s.d. to the known structures, even though the heavy-atom example has a known answer. Example 3 (JPD1249) is transparently a trial-and-error story — orientations 0/1 fail, then 2/3 work; later a second OC4 fails, and only after recalculating residuals does 'new orientation 1' work. With no score attached to accepted vs. rejected orientations, the reader cannot tell whether the reported successes are the result of a meaningful ranking or post-hoc selection. The 'no fall apart' criterion is also too weak: a locally stable but wrong packing could pass it.

I don't think the central claim is circular. The method is not fitting the answer; the fragments are assembled using pR1 minima, and the residual-intensity trick is a sensible adaptation. But the lack of quantitative diagnostics makes the claim weaker than it needs to be.

Whom is this for? Practicing small-molecule crystallographers curious about phasing alternatives. It deserves a serious referee, not a desk reject, but the authors should be pushed to define pR1 inline, report conventional R-factors for the final models, compare coordinates to deposited structures where available, and tabulate pR1 values for accepted and rejected orientations. If that revision lands, this becomes a solid, citable application note.

Referee Report

3 major / 5 minor

Summary. The manuscript presents a showcase of the partial-structure R1 (pR1) method for assembling small-molecule crystal structures. The method, introduced in prior work by the same author, is an approximate R1 that supposedly depends only on the orientation and location of a fragment to be added to a partial model. The paper describes one main example (JPD1252, C2/c) in which a SiPh2tBuMoO4 fragment is built in situ, four such fragments are oriented and placed, and four NnPr4 fragments are added using residual reflection intensities to overcome heavy-atom interference. Two further examples (RAP119 and JPD1249) are given in the supporting information. The central claim is that pR1 is a useful tool for solving some small-molecule crystal structures.

Significance. If the claim is correct, pR1 would be a phasing-free alternative for structure assembly, particularly useful for structures containing heavy atoms where light-atom fragments are otherwise overwhelmed. A positive aspect is that the Python code is available on GitHub. However, the evidence presented is largely qualitative: the paper does not report any numerical R-factors, coordinate accuracies, or comparisons with independently determined structures, and the selection of fragment orientations appears to involve post-hoc trial and error in at least one example. Thus the significance is potentially real but not yet established.

major comments (3)

[§1] The pR1 function is not defined in this paper. Section 1 states only that pR1 is defined 'via modifying the traditional R1 by removing its dependence on the location of these other atoms' and that it 'only depends on the orientation and location of the defining fragment.' This is the mathematical foundation for the 3-d orientational search used throughout. The paper should restate the definition from Zhang & Donahue (2024) or provide a self-contained derivation of the removal step. As written, a reader cannot check whether the approximation is valid for the examples or reproduce the method without going to the cited paper.
[§6, §8, SI S5] The success criterion is entirely qualitative: 'no fragments fall apart after tweak' (Sections 6 and 8), with final models shown visually. No final R1, aR1, Rfree, coordinate r.m.s.d., or comparison to a deposited/known structure is reported for any example, even though pR1 is an R1-derived quantity. Because tweaking can stabilize an incorrect but locally stable packing, this criterion does not establish that the assembled model is the correct crystal structure. The paper should report, at minimum, the final aR1/R1 for the accepted model and, where the structure is known, the coordinate deviation from the reference.
[§5, SI S5] The selection of orientations appears post hoc. In SI S5, OC8 orientations 0 and 1 are tried and fail; only orientations 2 and 3 'are correct'. For OC4, orientation 0 works for the first fragment, orientation 3 is 'not acceptable', and after recalculating residuals a 'new orientation 1' works. No pR1 minima or any score are given for tried and rejected orientations. Likewise §5 chooses 'orientations 0 and 1' as a 'best guess' simply because four fragments are needed. To substantiate that pR1 systematically identifies correct orientations, the paper must give the full list of candidate orientations with their pR1 values and an a priori selection rule.

minor comments (5)

[Synopsis] The synopsis says 'one concrete example' but the manuscript plus supporting information give three examples; align the summary.
[Figures 1 and 2] Figures 1 and 2 are referenced in the text but do not appear to be embedded in the manuscript; only captions are present. Please include the actual figure panels.
[§1] 'For examples' should be 'For example'.
[§2] The abbreviation 'NnPr4' is unusual; define it as N(n-Pr)4 or tetra-n-propylammonium at first use.
[§6] The discussion of aR1/sR1/pR1 naming is confusing: 'if the partial model contains an undetermined fragment, the aR1 is called the pR1' seems to contradict the earlier definition of pR1 as a function of a fragment to be added. Please clarify the terminology.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the pR1 method is applied to new data and the paper's conclusions are empirical rather than equivalent to its inputs.

full rationale

The paper's central claim is that the partial-structure R1 (pR1) can be used to assemble crystal structures from fragments. This is not a derived mathematical result but an empirical demonstration on three datasets. The pR1 concept is cited from the authors' prior work (Zhang & Donahue, 2024), but the current examples are new external test cases; no parameter is fitted to make the examples succeed. The success criterion ('no fragments fall apart') is qualitative and applied after the fact, and Example 3 involves trial-and-error among ranked orientations, which weakens the evidence but does not make the conclusion equivalent to the input. The failure of orientations 0/1 in Example 3 shows that the top-ranked pR1 minima are not automatically treated as correct by construction—the method can be wrong and requires external judgment. No equation in the paper reduces a predicted orientation to a fitted constant, and the aR1 tweaking is a refinement step, not a hidden fit of the claimed result. The self-citation is present but not load-bearing: the prior paper supplies the method and the code is on GitHub, so the method is reproducible and the examples provide independent, if qualitative, validation. Thus no circular step is identifiable.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities or fitted constants. It relies on the prior pR1 definition, a set of heuristic search assumptions, and a qualitative success criterion. The idealized bond lengths (1.72 Å, 1.8 Å, 1.39 Å, etc.) are standard chemical inputs, not data-fitted parameters, so they are not counted as free parameters.

assumptions (5)

domain assumption The pR1 function, defined in Zhang & Donahue (2024), depends only on the fragment's orientation and location after removing dependence on other atoms.
Section 1 states this is the basis of the method, but the definition is not reproduced or proved in the paper.
domain assumption Global minimization of pR1 in orientation space yields correct orientations for large or heavy-atom-containing fragments.
This is the core premise tested by the examples; the paper does not provide a theoretical proof.
domain assumption Subtracting the partial model's contribution (residual intensities) reveals the signal of light-atom-only fragments in a heavy-atom structure.
Section 7 and SI S3 assume this difference-Fourier-like approach works for orientation search; it is plausible but not rigorously justified.
domain assumption The 'no fragments fall apart after tweaking' criterion indicates a correct structure.
Section 6 uses this as validation for examples where the true structure is not independently known; this is an unproven heuristic.
standard math Standard crystallographic equations (structure factors, R1) are valid and the datasets' space groups and cell parameters are correct.
The paper relies on standard crystallographic background without proof.

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Cite this review

Pith. "Pith review of A Showcase of Using the Partial-Structure R1 to Assemble Small-Molecule Crystal Structures." pith.science (2026). https://pith.science/paper/KI6XRBOH

@misc{pith2026260713836,
  author       = {Pith},
  title        = {Pith review of: A Showcase of Using the Partial-Structure R1 to Assemble Small-Molecule Crystal Structures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KI6XRBOH}},
  note         = {Machine review of arXiv:2607.13836}
}

read the original abstract

Using a few concrete examples this paper has demonstrated a few observations on using the partial-structure R1 (pR1) to assemble small-molecule crystal structures. (1) Assembling can start with orienting and/or placing large fragments or small fragments containing heavy atom(s). (2) It is handy to attach a fragment to a partial model as only the orientation needs to be optimized. (3) In a structure containing heavy atoms it is impossible to directly calculate the orientations of a light-atom-only fragment. Instead, it is necessary to use residual reflection intensities in which the contribution of the partial model containing all heavy atoms is deducted away. These observations indicate that pR1 is a useful tool for solving some small-molecule crystal structures.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

7 extracted references

[1]

C., Carrozzini, B., Cascarano, G

Burla, M. C., Carrozzini, B., Cascarano, G. L., Giacovazzo, C. & Polidori, G. (2018). Acta Cryst. A74, 123-130

2018
[2]

T., Weeks, C

DeTitta, G. T., Weeks, C. M., Thuman, P., Miller, R. & Hauptman, H. A. (1994). Acta Cryst. A50, 203-210

1994
[3]

Giacovazzo, C. (2014). Phasing in Crystallography – A Modern Perspective. Oxford: Oxford University Press

2014
[4]

T., Jones, R., Langs, D

Miller, R., DeTitta, G. T., Jones, R., Langs, D. A., Weeks, C. M. & Hauptman, H. A. (1993). Science, 259, 1430-1433

1993
[5]

M., DeTitta, G

Weeks, C. M., DeTitta, G. T., Miller, R. & Hauptman, H. A. (1993). Acta Cryst. D49, 179-181

1993
[6]

& Donahue, J

Zhang, X. & Donahue, J. P. (2024). Acta Cryst. A80, 237-248

2024
[7]

intensity

Zhang, X. (2026). Acta Cryst. A82, 331-334. 8 Supporting information S1. Set up an idealized model of the NnPr4 fragment This model is shown below together with the choice of the local cartesian system. All bonds have 1.5 Å bond length. All bond angles are 109.5º. All atoms are either in x-y plane or in x-z plane. S2. Tweaking the positions of the atoms i...

2026

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.

[1] [1]

C., Carrozzini, B., Cascarano, G

Burla, M. C., Carrozzini, B., Cascarano, G. L., Giacovazzo, C. & Polidori, G. (2018). Acta Cryst. A74, 123-130

2018

[2] [2]

T., Weeks, C

DeTitta, G. T., Weeks, C. M., Thuman, P., Miller, R. & Hauptman, H. A. (1994). Acta Cryst. A50, 203-210

1994

[3] [3]

Giacovazzo, C. (2014). Phasing in Crystallography – A Modern Perspective. Oxford: Oxford University Press

2014

[4] [4]

T., Jones, R., Langs, D

Miller, R., DeTitta, G. T., Jones, R., Langs, D. A., Weeks, C. M. & Hauptman, H. A. (1993). Science, 259, 1430-1433

1993

[5] [5]

M., DeTitta, G

Weeks, C. M., DeTitta, G. T., Miller, R. & Hauptman, H. A. (1993). Acta Cryst. D49, 179-181

1993

[6] [6]

& Donahue, J

Zhang, X. & Donahue, J. P. (2024). Acta Cryst. A80, 237-248

2024

[7] [7]

intensity

Zhang, X. (2026). Acta Cryst. A82, 331-334. 8 Supporting information S1. Set up an idealized model of the NnPr4 fragment This model is shown below together with the choice of the local cartesian system. All bonds have 1.5 Å bond length. All bond angles are 109.5º. All atoms are either in x-y plane or in x-z plane. S2. Tweaking the positions of the atoms i...

2026