GEMS: Molecular Structure Elucidation as Learned Search over Isomer Graphs

Utku Umur Acikalin; Yingheng Wang; Goncalo J. Gouveia; Tyler J. Schwertfeger; Frank C. Schroeder; Carla P. Gomes

cs.AIOct 16, 2026

GEMS: Molecular Structure Elucidation as Learned Search over Isomer Graphs

Authors: Utku Umur Acikalin, Yingheng Wang, Goncalo J. Gouveia, Tyler J. Schwertfeger, Frank C. Schroeder, Carla P. Gomes

Organizations: Department of Computer Science, Cornell University · Department of Chemistry and Chemical Biology, Cornell University · Boyce Thompson Institute, Cornell University

Abstract

Identifying small-molecule structures from molecular formulas and tandem mass spectra remains a bottleneck in untargeted metabolomics and natural-product discovery. Even when database retrieval or de novo prediction misses the exact structure, the resulting candidates can provide starting points for exploring nearby structures through a few bond edits. We introduce GEMS (Guided Editing of Molecular Structures), which refines candidates through learned 2-switch bond edits that preserve the molecular formula and each atom's total valence. GEMS uses MIST, a pretrained spectrum-to-fingerprint model, to predict fingerprint probabilities once per spectrum. A neural policy compares each candidate's fingerprint with these predictions, links present features to the atoms and bonds that generate them, and scores all valid edits in one forward pass. The policy is trained on shortest edit paths between structures, so it can be pretrained on PubChem isomers without spectra and then fine-tuned with spectrum-predicted fingerprints. At inference, GEMS searches from multiple initial candidates matching the supplied molecular formula and ranks candidates by fingerprint agreement and multi-start consensus. With the target structure excluded from PubChem initialization, three edit rounds achieve Hit@1/Hit@10 of 29.64%/50.81% on NPLIB1 and 30.22%/41.33% on MassSpecGym, exceeding published baselines under comparable settings. On NPLIB1, GEMS achieves higher identification accuracy in about 3.3 minutes end to end, compared with 26.2 hours for our FRIGID run. GEMS also improves identification from generated candidates, including those refined by FRIGID. Experiments with exact target fingerprints identify fingerprint prediction error as a bottleneck in target recovery and final ranking. Deeper search recovers additional targets without retraining, with larger gains from weaker initial candidates.

Figures & tables

Figure 1: GEMS: fingerprint-guided search over molecular isomers. (a) MIST predicts fingerprint probabilities

q

once from the MS 2 spectrum and molecular formula

\mathcal{F}

. Fingerprint likelihood selects five same-formula seeds, excluding the target. (b) Supported present bits have

x_{i}=1

and high

q_{i}

, unsupported present bits have

x_{i}=1

and low

q_{i}

, and likely missing bits have

x_{i}=0

and high

q_{i}

. Present bits are mapped to the atoms and bonds that generate them, while missing bits have no local occurrence. One policy evaluation scores all valid 2-switch edits. For Seed 5, the four highest-ranked edits receive 96.4% of policy probability, and each begins a shortest three-edit path to the reference structure. The illustrated path (purple) starts with

a_{2}

. (c) Initial and retained states are pooled and ranked by

s(m;q)+16\log(1+c(m))

, where

s(m;q)

measures fingerprint agreement and

c(m)

counts the distinct seeds whose searches reach

m

, including through their initial states. The target ranks first among 33 distinct candidate structures. Panel (c) omits Seeds 3 and 4, which still vote. NPLIB1 query CCMSLIB00001058451 . The example uses

K=5

starts, proposal and beam widths

P=B=4

, and depth

D=3

. The main experiments use

P=B=16

Figure 2: Formula- and valence-preserving 2-switch edits. (a) Type-A exchanges hydroxyl and amino attachments to reach tyrosine. (b) Type-B exchanges one carbonyl bond unit and one C–H bond for a new C–O bond and a new C–H bond, forming a four-membered ring. This is action

a_{1}

from Seed 5 in Figure 1 . Each affected atom loses and gains one bond unit. Orange marks removed bond units, teal marks added ones, and purple marks the moving hydrogen.

NPLIB1
Method	H@1	MCES@1	Tani.@1	H@10	MCES@10	Tani.@10
MIST + MolForge	2.24	14.16	0.40	5.11	10.96	0.47
DiffMS	8.34	10.46	0.35	15.44	8.54	0.47
FRIGID-base	19.80	7.88	0.54	24.41	6.20	0.61
FRIGID	25.03	7.10	0.58	33.37	5.56	0.64
MS-GPT †	21.05	18.49	0.50	28.64	17.79	0.54

Table 1: Known-formula structure elucidation (H@

k

in %). GEMS rows use

K=5

P=B=16

D=3

, and

\lambda=16

. PubChem starts exclude the target connectivity, and Tani.

<0.7

also excludes starts with target similarity

\geq 0.7

(Appendix H.2 ). Generator

\to

GEMS starts from MIST-selected outputs, which may contain the target.

\dagger

: our same-split reproduction. Bold marks the best per dataset. Lower maximum common edge subgraph (MCES) distance and higher Tanimoto similarity are better. Empty outputs receive MCES 100. Baselines are from Liu et al. (2026) and Bohde et al. (2026) .

Figure 3: Finding the target and ranking it first. Dark bars show Hit@1, total bar length gives reach, and ticks show Hit@10 for rows ranked with MIST. Labels specify navigation/ranking fingerprints. Exact FP is computed from the target as an oracle. Each dataset uses fixed starts and checkpoint,

K=5

P=B=16

D=3

, and

\lambda=16

. All 803 NPLIB1 and 17,556 MassSpecGym queries count, including queries without starts. Table 15 gives the values.

Appendix figures & tables22 assets

Supplementary material from the paper’s appendix.

Appendix

Identity	Representations merged	Use
Literal integer-bond graph	Atom renumberings preserving elements, bond orders, and attached hydrogens. The chosen Kekulé assignment is retained.	Training path joins and distance labels
Canonical stereo-free aromatic SMILES	Atom renumberings and alternative Kekulé assignments. Tautomers remain distinct.	Search deduplication and consensus votes
InChIKey14	Structures assigned the same connectivity block by InChI, including some tautomeric forms	Target exclusion, recovery, and final connectivity ranking

Appendix

Table 2: Identity conventions. Training exclusions additionally restrict admissible intermediate states.

Method	H@1	MCES@1	Tani.@1	H@10	MCES@10	Tani.@10
Spec2Mol	0.00	48.57	0.12	0.00	17.58	0.16
MADGEN	2.10	20.56	0.22	2.39	12.69	0.27
MIST + Neuraldecipher	2.32	10.26	0.35	6.11	8.53	0.43
MIST + MolForge	2.24	14.16	0.40	5.11	10.96	0.47
MIST + MSNovelist	5.40	13.10	0.34	11.04	8.57	0.44
MS-BART	7.45	9.66	0.44	10.99	8.31	0.51

Appendix

Table 3: NPLIB1 known-formula baselines and GEMS variants. Non-MS-GPT published values come from FRIGID Table 1 ( Bohde et al., 2026 ) .

\dagger

: our best-effort same-split MS-GPT reproduction with corrected masking and retraining.

\ddagger

: published MS-GPT values are contextual comparisons with protocol qualifications in this section ( Zhao et al., 2026 ) . All GEMS variants use up to five starts,

P=B=16

D=3

, and

\lambda=16

. PubChem starts exclude the target connectivity. The one-edit row additionally excludes every target-specific one-edit neighbor connectivity group, without a Tanimoto filter. Generator and Tanimoto-filtered starts follow Table 1 . Our evaluations retain all test queries. Best displayed values are bold, including ties.

Method	H@1	MCES@1	Tani.@1	H@10	MCES@10	Tani.@10
MIST + MSNovelist	0.00	39.84	0.06	0.00	18.83	0.15
Spec2Mol	0.00	36.78	0.12	0.00	36.02	0.16
MIST + Neuraldecipher	0.00	22.93	0.14	0.00	21.76	0.16
MADGEN	1.31	27.47	0.20	1.54	16.84	0.26
MS-BART	1.07	16.47	0.23	1.11	15.12	0.28
DiffMS	2.30	13.96	0.28	4.25	11.68	0.39

Appendix

Table 4: MassSpecGym known-formula baselines and GEMS variants. Non-MS-GPT published values come from MassSpecGym in the Wild Table 9 ( Liu et al., 2026 ) , with FRIGID-base from FRIGID Table 1 ( Bohde et al., 2026 ) .

\dagger

: our best-effort same-split MS-GPT reproduction with corrected masking and retraining.

\ddagger

: published MS-GPT values are contextual comparisons with protocol qualifications in this section ( Zhao et al., 2026 ) . All GEMS variants use up to five starts,

P=B=16

D=3

, and

\lambda=16

Dataset	Policy	H@1	H@10	Reach
NPLIB1	Random weights	$4.61\pm 2.90$	$7.97\pm 4.98$	$8.30\pm 5.29$
NPLIB1	RL from scratch (exact-FP reward)	24.78	42.59	47.20
NPLIB1	Supervised from scratch	28.02	47.45	52.80
NPLIB1	Pretrained only	28.89	46.82	50.06
NPLIB1	Pretrained + fine-tuned	29.64	50.81	57.78
MassSpecGym	Supervised from scratch	29.14	39.46	44.20

Appendix

Table 5: Evaluation of random-weight and trained policies with

K=5

P=B=16

D=3

, MIST fingerprints for navigation and ranking, and

\lambda=16

. All 803 NPLIB1 and 17,556 MassSpecGym queries count. Pretrained only uses the PubChem checkpoint without downstream fine-tuning. Pretraining uses exact target fingerprints as inputs. REINFORCE uses MIST inputs and exact target fingerprints for its training reward. The random-weight row reports mean

\pm

sample standard deviation across three weight initializations. Each trained setting uses one training random seed. Training schedules and selection details are given in the text.

	NPLIB1					MassSpecGym
Search (Params.)	H@1	H@10	Reach	Search (s)	Runtime (s)	H@1	H@10	Reach	Search (s)	Runtime (s)
E&S, $B=1$	25.40	43.84	44.21	770.01	802.88	28.03	37.98	38.57	25,250.45	25,351.17
E&S, $B=2$	25.65	47.57	50.19	1,364.69	1,397.98	28.18	39.25	41.55	47,022.92	47,131.94
E&S, $B=4$	26.03	49.07	54.17	2,491.07	2,524.59	28.16	39.05	44.24	87,247.68	87,372.32
GEMS, $P=B=4$	27.65	47.07	49.07	47.14	81.11	29.18	39.39	41.35	1,333.48	1,456.71
GEMS, $P=B=16$	29.64	50.81	57.78	129.28	200.12	30.22	41.33	46.88	3,869.90	4,091.00

Appendix

Table 6: GEMS versus Enumerate & Score (E&S), with

K=5

D=3

and

\lambda=16

. Each search task uses 32 physical CPU cores and 32 workers; GEMS also uses one H100. NPLIB1 GEMS at

P=B=16

reports end-to-end wall time, including loading and output writing. Other runtime entries report accumulated processing time for preprocessing, retrieval, search, and final ranking (Appendix K.2 ). MassSpecGym search covers 16 tasks.

Initialization	$D$	MIST			Exact FP (oracle)
Initialization	$D$	H@1	H@10	Reach	H@1	H@10	Reach
Full-catalog MIST, up to 5	3	29.64	50.81	57.78	68.99	72.73	72.85
	5	29.76	50.56	58.78	73.23	77.58	77.96
	10	29.64	50.81	59.90	79.45	84.43	84.93
Sampled-250 MIST, up to 5	3	26.15	43.46	50.44	61.15	64.38	64.51
	5	27.90	46.20	53.80	68.99	73.23	73.60

Appendix

Table 7: NPLIB1 query-level Hit@1, Hit@10, and reach (%) across initialization and depth, with

P=B=16

\lambda=16

, and the same trained checkpoint. All 803 queries count, including 17 without starts. MIST and Exact FP specify both navigation and ranking. Starts are fixed across guidance conditions. Random, up to 5 uses the first five starts of the random-100 searches. The ten-repeat random-five comparison is reported separately in the text.

	NPLIB1			MassSpecGym
Starts removed	H@1	H@10	Reach	H@1	H@10	Reach
Target only (reported)	29.64	50.81	57.78	30.22	41.33	46.88
Tanimoto $\geq 0.9$	29.39	50.44	57.04	29.94	40.62	46.07
Tanimoto $\geq 0.8$	29.27	49.07	55.79	28.49	38.29	42.61
Tanimoto $\geq 0.7$	27.90	46.45	52.18	23.93	31.75	34.64
Tanimoto $\geq 0.6$	25.16	42.84	47.95	–	–	–

Appendix

Table 8: Hit@1, Hit@10, and reach (%) at

D=3

, with

P=B=16

\lambda=16

, and up to five MIST-ranked starts after exclusion. Tanimoto rows keep only starts below the cutoff. One-edit exclusion removes every starting connectivity one valid edit from the target. Target-connectivity exclusion applies throughout. MassSpecGym Tanimoto filtering was evaluated at cutoffs of 0.7 and above. All test queries count, including those without starts.

	FRIGID-base		FRIGID after refinement		MS-GPT (ours)
Maximum edits	Queries	%	Queries	%	Queries	%
D0	192	23.91	242	30.14	221	27.52
D1	319	39.73	377	46.95	344	42.84
D2	$\geq$ 420	$\geq$ 52.30	$\geq$ 453	$\geq$ 56.41	$\geq$ 410	$\geq$ 51.06
D3	$\geq$ 484	$\geq$ 60.27	$\geq$ 517	$\geq$ 64.38	$\geq$ 461	$\geq$ 57.41

Appendix

Table 9: NPLIB1 queries with at least one selected start within D edits of the target. Each generator pool supplies up to five MIST-selected starts. All 803 queries count, including those without starts. D0/D1 are exact. D2/D3 are lower bounds combining exhaustive one-edit coverage with saved MIST- and oracle-guided paths. MS-GPT (ours) is our best-effort reproduction. These counts measure proximity, independently of final ranking.

Dataset	Initializer	Stage	H@1	H@10	Reach
NPLIB1	FRIGID-base	Selected (D0)	20.42	23.91	23.91
NPLIB1	FRIGID-base	GEMS (D3)	28.02	43.34	46.20
NPLIB1	FRIGID	Original ranking	24.03	33.13	–
NPLIB1	FRIGID	Selected (D0)	22.54	30.14	30.14
NPLIB1	FRIGID	GEMS (D3)	28.27	46.82	50.31
NPLIB1	MS-GPT (ours)	Original ranking	21.05	28.64	–

Appendix

Table 10: Generator outputs and GEMS refinement. FRIGID-base and FRIGID are the initial and final pools of the same NPLIB1 run. MS-GPT (ours) is our best-effort reproduction with corrected masking and retraining. Original ranking uses the generator output order. Selected (D0) and GEMS (D3) use the same up-to-five MIST-ranked starts and

\lambda=16

. All 803 NPLIB1 and 17,556 MassSpecGym queries count. Oracle results are separate in Table 11 .

Dataset	Initializer	Stage	H@1	H@10	Reach
NPLIB1	FRIGID-base	GEMS (D3)	57.91	59.90	60.15
NPLIB1	FRIGID	GEMS (D3)	61.52	64.38	64.38
NPLIB1	MS-GPT (ours)	Selected (D0)	27.27	27.52	27.52
NPLIB1	MS-GPT (ours)	GEMS (D3)	55.17	57.41	57.41
MassSpecGym	MS-GPT (ours)	Selected (D0)	26.13	26.68	26.68
MassSpecGym	MS-GPT (ours)	GEMS (D3)	41.05	42.87	42.92

Appendix

Table 11: Oracle diagnostics for generated starts. Exact target fingerprints guide navigation and ranking, using the same MIST-selected starts as Table 10 . Search uses up to

K=5

starts,

P=B=16

D=3

, and

\lambda=16

. MS-GPT (ours) is our best-effort reproduction. All 803 NPLIB1 and 17,556 MassSpecGym queries count, including missing starts.

Figure 4: Width and depth affect recovery differently. Per-seed reach on NPLIB1 from up to five MIST-ranked starts or up to 100 random starts per query. Each curve uses

P=B

and the same trained checkpoint. The vertical line marks the main depth

D=3

. Exact FP uses fingerprints computed from the known targets and is an oracle diagnostic. Denominators are 3,888 ranked and 68,811 random seed–target pairs. Queries without starts contribute no pairs. Table 13 gives the numerical values.

Initialization	Fingerprints	$P=B$	$D=1$	$D=3$	$D=5$	$D=10$
MIST-ranked, up to 5	MIST	1	23.54 / 32.38	25.16 / 36.74	25.78 / 37.24	26.03 / 37.48
		3	26.03 / 40.35	28.02 / 45.58	28.39 / 45.95	29.02 / 47.07
		5	26.15 / 43.09	28.52 / 47.95	28.89 / 48.32	28.89 / 48.19
		10	26.65 / 45.70	29.89 / 49.56	29.76 / 50.06	30.14 / 50.56
		16	27.02 / 46.82	29.64 / 50.81	29.76 / 50.56	29.64 / 50.81
MIST-ranked, up to 5	Exact FP	1	54.55 / 55.29	66.00 / 68.12	68.99 / 71.61	74.10 / 76.71

Appendix

Table 12: Query-level Hit@1 / Hit@10 (%) on NPLIB1 for the width–depth settings in Table 13 . All 803 queries count, including 17 without starts. Each run uses

P=B

and

\lambda=16

consensus with initial-seed support. Fingerprints specify both navigation and ranking. Exact FP uses the known target structure and is an oracle diagnostic. Candidates and consensus votes are restricted to depth

D

Starts	Guidance	$P=B$	$D=1$	$D=3$	$D=5$	$D=10$
MIST-ranked, up to 5	MIST	1	13.94	22.25	23.84	24.31
		3	19.19	32.43	34.93	37.22
		5	21.01	35.75	38.32	40.82
		10	23.61	38.79	41.67	43.96
		16	25.10	41.31	44.14	45.99
MIST-ranked, up to 5	Exact FP	1	25.51	48.20	54.48	59.95

Appendix

Table 13: Per-seed reach (%) on NPLIB1 for the searches in Figure 4 . A seed–target pair succeeds when its own retained lineage contains the target by depth

D

. Denominators are 3,888 pairs for MIST-ranked starts and 68,811 pairs for random starts. Queries without starts contribute no pairs. All runs use

P=B

and the same trained checkpoint. Exact FP is an oracle diagnostic.

Dataset	Guidance	Queries	D1	D2	D3	D5	D10
NPLIB1	MIST	803	51.56	56.66	57.78	58.78	59.90
NPLIB1	Exact FP	803	59.03	69.49	72.85	77.96	84.93
MassSpecGym	MIST	17556	43.30	45.94	46.88	47.30	47.82
MassSpecGym	Exact FP	17556	48.18	53.86	56.07	58.40	65.03

Appendix

Table 14: Queries with a witnessed path of at most D edits from at least one MIST-ranked starting isomer. All queries remain in the denominator, including queries without starts. Percentages are recovery, independent of final ranking. These provide lower bounds on the fraction of queries having a seed within D edits. Failures do not establish a larger shortest distance. Exact FP is an oracle diagnostic.

			NPLIB1			MassSpecGym
Navigation	Ranking	$\lambda$	H@1	H@10	Reach	H@1	H@10	Reach
MIST	MIST	0	28.02	50.56	57.78	29.47	40.94	46.88
MIST	MIST	16	29.64	50.81	57.78	30.22	41.33	46.88
MIST	Exact FP	0	55.54	57.66	57.78	44.76	46.74	46.88
MIST	Exact FP	16	56.66	57.53	57.78	45.12	46.79	46.88
Exact FP	MIST	0	29.39	58.78	72.85	31.19	47.10	56.07

Appendix

Table 15: Fingerprint replacement during navigation and ranking at

K=5

P=B=16

, and

D=3

, with pure Bernoulli ranking (

\lambda=0

) or consensus (

\lambda=16

). All rows use the same MIST-selected starts. Changing only the ranking fingerprint preserves the candidate pool and reach. Metrics are percentages. MassSpecGym includes both adducts. Rows with

\lambda=16

give the values in Figure 3 .

Ranking	NPLIB1	MassSpecGym
GEMS	29.64	30.22
GEMS + ICEBERG	31.88	31.60
Gain [95% interval]	+2.24 [0.62, 3.96]	+1.38 [0.40, 2.80]

Appendix

Table 16: ICEBERG reranking of the fixed GEMS top-ten lists. Hit@1 is reported in percent. Gains and their paired 95% bootstrap intervals, grouped by target connectivity, are in percentage points.

Component	NPLIB1 (s)	MassSpecGym (s)
Spectrum preprocessing	0.57	0.40
Peak annotation	0.61	3.04
MIST prediction	0.40	4.91
Build fingerprint database from SMILES	28.01	77.41
Retrieve top-5 seeds	0.32	1.50
GEMS search	129.28	3,869.90

Appendix

Table 17: Runtime measurements for

K=5

P=B=16

, and

D=3

, using one H100 and 32 physical CPU cores. NPLIB1 reports median end-to-end wall time, including startup, loading, and output writing. MassSpecGym reports accumulated processing time excluding this overhead; its search covers 16 tasks. Component rows show in-memory processing costs. Per-spectrum values divide the reported runtimes by 803 or 17,556 spectra.

Figure 5: NPLIB1 paths from seeds at certified distances D1–D3. MIST-guided search reaches the target in one, two, and three edits, respectively, matching the minimum distance from each displayed seed. The examples show side-chain rearrangement, changes in substituent attachment, and ring expansion followed by contraction. All use the reported checkpoint, ranked PubChem starts, and

P=B=16

. A/B denote edit types. Magenta highlights mark bond-order decreases in the outgoing edit, and teal marks increases in the incoming edit. These are graph-edit paths, not proposed chemical reactions.

Figure 6: MassSpecGym paths from seeds at certified distances D1–D3. MIST-guided search follows a shortest path from each displayed seed. The examples include ring expansion, rearrangement through a larger-ring intermediate, and redistribution of substituents between aromatic rings. All use the reported checkpoint, ranked PubChem starts, and

P=B=16

. Display conventions follow Figure 5 .

Figure 7: A five-edit MIST path and a three-edit exact-guided path on NPLIB1. Both paths start from Seed 3 of CCMSLIB00000846601 . They share their first edit and then diverge. Exact guidance reaches the target in the certified minimum of three edits, while MIST first reaches it after five. Search uses

P=B=16

with a ten-round budget. The displayed paths stop at the first hit from this seed. Dashed boxes repeat the preceding row’s final state to continue the same path.

Figure 8: A six-edit MIST path and a three-edit exact-guided path on MassSpecGym. Both paths start from Seed 4 of MassSpecGymID0214184 and end at the same target structure. Exact guidance follows a shortest path. MIST takes three additional edits in this search before its first retained target hit from this seed. Search uses

P=B=16

with a ten-round budget. Display conventions follow Figure 7 .

Figure 9: A ten-edit MIST-guided path from a random seed. Seed 60 of the 100-seed random pool first reaches the target at depth ten for NPLIB1 query CCMSLIB00001058417 . Every displayed transition is a replayed retained edge from the

P=B=16

D=10

search. The example illustrates substantial structural rearrangement along a successful lineage, rather than a certified ten-edit distance or a requirement for ten rounds across all seeds.

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Molecular Generation Mass Spectrometry

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Untargeted tandem mass spectrometry (MS/MS) detects thousands of small molecules per biological sample, yet most go unidentified because they are absent from spectral libraries. These uncharacterized metabolites and natural products are precisely the compounds that matter for drug discovery, biomarker research, and exposomics. Computational de novo structure elucidation could close this gap, but almost all state-of-the-art methods assume the ground-truth molecular formula is known, an oracle that does not exist for genuinely novel compounds and is itself predicted with substantial error. We present MARLIN, a de novo method that elucidates structures directly from a spectrum with no molecular formula at any stage. A self-supervised encoder predicts a molecular fingerprint from the raw peaks, and a block-diffusion language model generates candidate structures conditioned only on the fingerprint and the instrument-measured precursor mass. A provably safe mass-shell constraint keeps every candidate consistent with the measured mass without fixing the atom inventory, and candidates are accepted by exact parts-per-million mass agreement. A symmetric noise objective absorbs encoder error, and a candidate-diversity mechanism keeps the candidates from collapsing to a single structure. On the NPLIB1 benchmark, MARLIN is the strongest method evaluated without a ground-truth formula across exact-match accuracy, structural distance, and fingerprint similarity, and it recovers the correct molecular formula as a byproduct about as often as a dedicated predictor without ever using one. MARLIN enables reliable de novo structure elucidation in the realistic discovery regime where the molecular formula is unavailable.

Abstract

Mass Spectrometry

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