Rapid formation of gaseous benzoic sulfuric anhydride and its key role in urban-industrial sulfuric acid-ammonia nucleation

Guo, Xiaokai; Li, Yaogeng; Su, Rui; Yang, Yanlong; Feng, Xueping; Wang, Guane; Zuo, Yuan; Wang, Rui; Zhang, Tianlei

doi:10.5194/egusphere-2026-2831

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https://doi.org/10.5194/egusphere-2026-2831

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14 Jul 2026

| 14 Jul 2026

Status: this preprint is open for discussion and under review for Atmospheric Chemistry and Physics (ACP).

Rapid formation of gaseous benzoic sulfuric anhydride and its key role in urban-industrial sulfuric acid-ammonia nucleation

Xiaokai Guo, Yaogeng Li, Rui Su, Yanlong Yang, Xueping Feng, Guane Wang, Yuan Zuo, Rui Wang, and Tianlei Zhang

Abstract. Carboxylic sulfuric anhydrides are key aerosol constituents. Among these, benzoic sulfuric anhydride (BSA) has been predicted to reach up to 10⁷ molecules·cm^–3 in urban industrial regions and has been identified as a potential precursor for new particle formation (NPF). However, its formation mechanism and role in sulfuric acid-ammonia (SA-A) nucleation are unclear. Here, we employ quantum chemical (QC) calculations and atmospheric cluster dynamics simulations (ACDC) to investigate the gaseous mechanism of BSA formation and its key role in SA-A nucleation. QC calculations show that BSA forms via fast cycloaddition between BA and SO₃ (barrier of 1.5 kcal·mol^–1). Within 280.0-320.0 K, this route can effectively compete with the SO₃ + (H₂O)₂ reaction at [BA] > 10¹⁰ molecules·cm^–3 and RH < 60 %. ACDC simulations further reveal that at [BSA] = 10⁸ molecules·cm^–3, the SA‑A cluster formation rate increases by six orders of magnitude as temperature decreases from 298.15 K to 278.15 K. In high-BSA industrial regions (e.g., Beijing), the BSA-SA-A ternary pathway contributes 99 % to total cluster formation. Notably, despite its lower concentration, BSA exhibits stronger nucleation potential than its precursor BA in the SA-A system. These findings clarify the atmospheric sources of BSA and help explain frequent NPF events in urban-industrial regions.

Received: 17 May 2026 – Discussion started: 14 Jul 2026

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Xiaokai Guo, Yaogeng Li, Rui Su, Yanlong Yang, Xueping Feng, Guane Wang, Yuan Zuo, Rui Wang, and Tianlei Zhang

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RC1:
'Comment on egusphere-2026-2831', Anonymous Referee #1, 02 Aug 2026 reply
This manuscript combines quantum chemical calculations with a computational model of atmospheric cluster dynamics to systematically investigate the reaction mechanism of sulfur trioxide (SO₃) with benzoic acid (BA) to form benzoic sulfonic anhydride (BSA) in the gas phase, as well as the effect of BSA on the formation of new sulfate-ammonia (SA-A) particles. The results indicate that BSA is formed via a low-energy-barrier cycloaddition pathway; under conditions of low humidity and high BA concentrations, it can effectively compete with the hydrolysis of SO₃, and BSA significantly enhances the formation rate of SA-A ternary clusters in urban areas.
The topic is highly relevant to current frontiers in atmospheric chemistry and aerosol science, with particular significance in the exploration of non-traditional organic sulfur/anhydride nucleating agents in polluted urban environments. However, the manuscript currently contains numerous obvious errors, with considerable room for improvement regarding the description of methodology, the rationale behind calculation setups, and the quality of discussion/logical derivation. Therefore, I recommend Major Revision. The authors must thoroughly address the core issues outlined below before the manuscript can be considered for publication.

Major Comments
The author lists species such as HOMs, nitric acid, water, polyhydroxy compounds, and organic acids. Please clarify the logical relationships and distinctions among these species. Is there any conceptual overlap among them (e.g., between organic acids and certain HOMs)? If they are cited solely to illustrate that “These species can stabilize SA-A clusters by enhancing hydrogen bonding interactions, facilitating proton transfer, and reducing cluster volatility, thereby promoting particle formation.”, given that many components in the atmosphere have been shown to have similar effects, please explain the specific scientific rationale for listing them together in this context.

Lines 52–54：“…the nucleation rates predicted by current mechanisms remain than those observed in field measurements, indicating that key nucleating species and pathways have yet to be fully unidentified.”, this sentence not only omits the comparative term (is it an overestimation—“higher”—or an underestimation—‘lower’?), but the double negative construction (“have yet to be fully unidentified”) also causes semantic confusion. Please completely rewrite this sentence.

All of the research on CSAs in this paper is based on the theoretical predictions of CSA concentrations by Smith et al. (2019) (which assume concentrations of up to 10⁷ molecules cm^-3). Is there any other experimental or field observation evidence that further confirms that CSA concentrations in the actual atmosphere can indeed reach 10⁷ molecules cm^-3 or higher?

Lines 118–126 & 163–165: In Section 2.1, the authors state that the number of molecules included in the cluster conformation search is limited to 0 ≤ y ≤ x + z ≤ 3. However, in Section 2.3, the authors define the boundary clusters as (SA)₄·(A)₃, (SA)₄·(A)₄, and (SA)₁·(A)₃·(BSA)₃. The sizes of these boundary clusters clearly exceed the spatial range set in the initial search. Please specify the exact sizes of the simulated clusters, resolve the internal contradiction in the definition of the boundary clusters, and fully explain why truncating the system to only 3 acid molecules is sufficient to accurately simulate the nucleation process at different temperatures (258.15–298.15 K).

In the n × 100 structures search, the authors used the 6-31+G(d,p) basis set with a diffuse function. However, in the higher-level n × 10 structures optimization, they instead used the 6-311G(2d,2p) basis set without a diffuse function. What were the considerations behind omitting the diffusion function in the higher-level calculations? For cluster systems involving hydrogen bonding and proton transfer, would the absence of the diffusion function have a negative impact on the global minimum energy structures found?

Lines 131–132: the author mentions the use of the PLUMED package for metadynamics (MTD) simulations in the Methods section of the main text. Please clearly state the specific scientific purpose of incorporating MTD simulations into the overall research framework of this paper.

The author compared the competitive reactions of SO₃ with BA and (H₂O)₂. Why was the reaction of gaseous water monomers (H₂O) not included in the comparison? Given that both monomers and dimers are important forms of gaseous water, omitting water monomers may affect the accuracy of the assessment of the competitive rate ratio.

Lines 179–185: After presenting the low energy barrier (1.5 kcal mol^-1) and Gibbs free energy change (ΔG = -4.9 kcal mol^-1) for the reaction between BA and SO₃, the author merely draws the redundant conclusion that “this reaction is exothermic”. Readers can intuitively infer the exothermic nature of the reaction from these numerical values; the authors should have conducted a more in-depth analysis from the perspective of “thermodynamic favorability”. Furthermore, in the Introduction, the authors mention that Zhang et al. (2023) reported that the energy barrier for this reaction is only 0.34 kcal mol^-1, which is significantly lower than the calculated value in this study (1.5 kcal mol^-1). Please thoroughly discuss the underlying reasons for this quantitative discrepancy (e.g., differences in methods, basis sets, or single-point energy corrections).

Lines 182–185: “Additionally, compared to cycloaddition-hydrogen abstraction between SO₃ and HCOOH, the SO₃ + BA introduction of the phenyl ring not only effectively lowers the reaction barrier but also enhances the product’s stability due to the aromatic conjugation effect (Fig. S2(a)).”. This sentence lacks a clear concluding point. Please clarify what specific scientific hypothesis this comparison is intended to demonstrate.

Lines 186–196: The author used MTD simulations to confirm that SO₃ reacted with BA. However, quantum chemical calculations have already demonstrated that the reaction occurs. Does the MTD simulation provide additional kinetic information? If the two approaches are based on different theoretical principles, please explain why they yield highly consistent results and highlight the irreplaceable nature of the MTD simulation in this context.

Lines 201–208: The authors set low, intermediate, and high BA concentrations, respectively. Please provide evidence from field observations to demonstrate that this selected concentration range is consistent with real-world atmospheric conditions (particularly in polluted areas).

Lines 241–243: The ΔG value for (SA)₁·(A)₃·(BSA)₂ (-56.93 kcal mol^-1) was slightly lower than that of the most stable binary cluster (SA)₃·(A)₃ (-55.04 kcal mol^-1). Is an energy difference of only 1.89 kcal mol^-1 within the margin of error of quantum chemical calculation methods? Can such a minute difference provide strong support for the corresponding scientific conclusions?

Lines 310–313: The authors claim that in regions with low sulfuric acid concentrations (e.g., Beijing, Nanjing, Atlanta), the BSA-involved pathway contributes 100% to cluster formation. This logic is flawed: low sulfuric acid concentration does not imply high BSA concentration, nor does it guarantee that the BSA pathway will dominate. The pathway contribution depends on the relative ratios of all precursor species. Please re-evaluate and tone down this statement.

Minor Comments
In the Abstract, the full names of BA, SO₃, and RH are missing in their first mentions. The sentence “In high-BSA industrial regions (e.g., Beijing), the BSA-SA-A ternary pathway contributes 99% to total cluster formation” contains semantic ambiguity and an invalid inference. The concluding sentence, “Notably, despite its lower concentration, BSA exhibits stronger nucleation potential than its precursor BA in the SA-A system” lacks logical connection to the preceding text; please improve the transition.

Line 45: “In response to this, …” has a rather colloquial tone; it is recommended to replace it with a more academic expression, such as “To address this uncertainty, …”.

Lines 65–67: The description of the formation of acetic sulfuric anhydride from acetic acid and SO₃ in Leipzig lacks the necessary references.

Line 178: When describing the intermolecular interactions between BA and SO₃ and analyzing bond formation, the three references cited here should be moved to the Methods section if they pertain to the Methods section, rather than being included in the Results and Discussion section.

Lines 172–185: The author classifies the mechanisms of SO₃ and BA as “cycloaddition-H abstraction” However, Mackenzie et al. (2015) refer to it simply as a cycloaddition mechanism. Considering the synergistic process shown in Fig. 1(a, b), this reaction is more consistent with a “cycloaddition-H shift mechanism” rather than “cycloaddition-H abstraction”. Please correct the description of the mechanism.

Lines 216–219: “This work first analyzed…. It then …” This phrasing is too colloquial and please rephrase it using the passive voice or an academic style.

Lines 224–227: The description of the details regarding proton transfer is rather wordy and colloquial, please rewrite it in a more concise manner.

Lines 309–310: “…clear negative correlated with [SA] …” contains a grammatical error; “correlated” should be changed to the noun “correlation.”

In Fig. 1 (a), the “G” in ΔG should be in italics.

In Table S1, two values are listed for SO₃·H₂O at 298 K. What does the superscript “a” in (5.80 × 10^-20)^a represent? The same applies to the superscript “b” in Table S2. The authors must provide detailed explanations for all special symbols in the table notes.

Page S15 of the Supporting information is completely blank and please fix the formatting.

The symbol k representing the rate constant in Table S5 should be in italics. If the elevation for the selected temperature range is 0 km, please delete this redundant row and column directly from the table header.

The citation format in Part S4 is inconsistent with that in the preceding sections of the Supporting information. Please standardize the reference format throughout the entire manuscript.

There are numerous figure callout errors throughout the manuscript: (1) Line 223: Fig. 2 should be changed to Fig. 3; (2) Line 250: Fig. 3a should be changed to Fig. 4a; (3) Line 270: Fig. 4a should be changed to Fig. 5a; (4) Lines 325–353: Fig. 7 is repeatedly cited but does not exist in the manuscript, it should be changed to Fig. 6.

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Citation: https://doi.org/10.5194/egusphere-2026-2831-RC1

Xiaokai Guo, Yaogeng Li, Rui Su, Yanlong Yang, Xueping Feng, Guane Wang, Yuan Zuo, Rui Wang, and Tianlei Zhang

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https://doi.org/10.5194/egusphere-2026-2831-supplement

Xiaokai Guo, Yaogeng Li, Rui Su, Yanlong Yang, Xueping Feng, Guane Wang, Yuan Zuo, Rui Wang, and Tianlei Zhang

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Short summary

Benzoic sulfuric anhydride is a potential precursor to atmospheric new particle formation. We used calculations and kinetic modeling to investigate how it forms and influences sulfuric acid-amine particle formation. It forms readily in the gas phase and is a previously unrecognized sulfur-containing species that stabilizes molecular clusters more effectively than benzoic acid. Thus, it promotes particle formation in polluted cities and helps explain why these events occur so frequently.


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