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Computational investigation on mechanisms and kinetics of gas-phase reactions of 4-hydroxy-2-pentanone (4H2P) with hydroxyl radicals and subsequent reactions of CH3C(O)CH2C·(OH)CH3 radical

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Abstract

The mechanistic, thermochemical, and kinetic study of the 4-hydroxy-2-pentanone (4H2P) + OH radical reaction is performed for the first time by employing quantum theoretical calculations. The potential energy diagram was evaluated for five possible reaction pathways at the CCSD(T)/cc-pVTZ//BH&HLYP/cc-pVTZ level of theory. Theoretical rate coefficients of five abstraction pathways are computed as a function of temperature (210–350 K) utilizing the canonical variational transition state theory (CVT) with small-curvature tunneling (SCT). A three-parameter modified Arrhenius equation is used to fit rate coefficients. The thermodynamic quantities like reaction enthalpy and Gibbs free energy are calculated at the BH&HLYP/cc-pVTZ level of theory. According to thermodynamic analysis, the hydrogen abstraction from the –CH group adjacent to the hydroxyl group occurs more favorably and is the dominant pathway with minimum barrier height. The structure–activity relationship is explored by comparing rate coefficients of the titled reaction with the literature values of similar species. The subsequent fate of the alkyl radical (CH3C(O)CH2C·(OH)CH3) is further studied in a NO-rich environment resulting in the formation of acetone, NO2, and oxygen as the major final products.

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References

  1. Atkinson R (1986) Kinetics and mechanisms of the gas-phase reactions of the hydroxyl radical with organic compounds under atmospheric conditions. Chem Rev 86:69–201. https://doi.org/10.1021/cr00071a004

    Article  CAS  Google Scholar 

  2. Atkinson R (1994) Gas-phase tropospheric chemistry of volatile organic compounds. J Phys Chem Ref Data 21:1–216. https://doi.org/10.1063/1.556012

    Article  Google Scholar 

  3. Hudzik M, Bozzelli JW (2012) Thermochemistry and bond dissociation energies of ketones. J Phys Chem A 116:5707–5722. https://doi.org/10.1021/jp302830c

    Article  CAS  Google Scholar 

  4. Sebbar N, Bozzelli J, Bockhorn H (2011) Thermochemistry and kinetics for 2-Butanone-1-yl radical (CH2·C(=O)CH2CH3) reactions with O2. J Phys Chem A 18:21–37. https://doi.org/10.1021/jp408708u

    Article  CAS  Google Scholar 

  5. Hanson RK, Seitzman JM, Paul PH (1990) Planar laser-fluorescence imaging of combustion gases. Appl Phys B 50:441–454. https://doi.org/10.1007/BF00408770

    Article  Google Scholar 

  6. Schulz C, Sick V (2005) Tracer-LIF diagnostics: quantitative measurement of fuel concentration, temperature and fuel/air ratio in practical combustion systems. Prog Energy Combust Sci 31:75–121. https://doi.org/10.1016/j.pecs.2004.08.002

    Article  CAS  Google Scholar 

  7. Pepiot-Desjardins P, Pitsch H, Malhotra R, Kirby S, Boehman AL (2008) Structural group analysis for soot reduction tendency of oxygenated fuels. Combust Flame 154:191–205. https://doi.org/10.1016/j.combustflame.2008.03.017

    Article  CAS  Google Scholar 

  8. Hong Z, Davidson D, Vasu S, Hanson R (2009) The effect of oxygenates on soot formation in rich heptane mixtures: a shock tube study. Fuel 88:1901–1906. https://doi.org/10.1016/j.fuel.2009.04.013

    Article  CAS  Google Scholar 

  9. Aschmann SM, Arey J, Atkinson R (2000) Atmospheric chemistry of selected hydroxycarbonyls. J Phys Chem A 104:3998–4003. https://doi.org/10.1021/jp9939874

    Article  CAS  Google Scholar 

  10. Atkinson R, Arey J (2003) Atmospheric degradation of volatile organic compounds. Chem Rev 103:4605–4638. https://doi.org/10.1021/cr0206420

    Article  CAS  Google Scholar 

  11. Monks PS (2005) Gas-phase radical chemistry in the troposphere. Chem Soc Rev 34:376–395. https://doi.org/10.1039/B307982C

    Article  CAS  Google Scholar 

  12. de Andrade M, Pinheiro H, Pereira P, de Andrade J (2002) Atmospheric carbonyl compounds: sources, reactivity, concentration levels, and toxicologic effects. Quím Nova 25:1117–1131. https://doi.org/10.1590/S0100-40422002000700013

    Article  Google Scholar 

  13. Ciccioli P, Brancaleoni E, Frattoni M, Cecinato A, Brachetti A (1993) Ubiquitous occurrence of semi-volatile carbonyl compounds in tropospheric samples and their possible sources. Atmos Environ A Gen Top 27:1891–2190. https://doi.org/10.1016/0960-1686(93)90294-9

    Article  Google Scholar 

  14. Rivas B, Torre P, Manuel DJ, Perego P, Converti A, Carlos Parajó J (2003) Carbon material and bioenergetic balances of xylitol production from corncobs by debaryomyces hansenii. Biotechnol Prog 19:706–713. https://doi.org/10.1021/bp025794v

    Article  CAS  Google Scholar 

  15. Ichikawa N, Sato S, Takahashi R, Sodesawa T (2005) Synthesis of 3-buten-2-one from 4-hydroxy-2-butanone over anatase-TiO2 catalyst. Catal Commun 6:19–22. https://doi.org/10.1016/j.catcom.2004.10.004

    Article  CAS  Google Scholar 

  16. Řezanka T, Libalova D, Votruba J, Viden I (1994) Identification of odorous compounds from Streptomyces avermitilis. Biotechnol Lett 16:75–78. https://doi.org/10.1007/BF01022627

    Article  Google Scholar 

  17. Knudsen JT, Eriksson R, Gershenzon J, Ståhl B (2006) Diversity and distribution of floral scent. Bot Rev 72:1–120. https://doi.org/10.1663/0006-8101(2006)72[1:DADOFS]2.0.CO;2

    Article  Google Scholar 

  18. Nishanth T, Praseed K, Rathnakaran K, Kumar MS, Krishna RR, Valsaraj K (2012) Atmospheric pollution in a semi-urban, coastal region in India following festival seasons. Atmos Environ 47:295–306. https://doi.org/10.1016/j.atmosenv.2011.10.062

    Article  CAS  Google Scholar 

  19. Bethel HL, Atkinson R, Arey J (2003) Hydroxycarbonyl products of the reactions of selected diols with the OH radical. J Phys Chem A 107:6200–6205. https://doi.org/10.1021/jp027693l

    Article  CAS  Google Scholar 

  20. Saunders SM, Jenkin ME, Derwent R, Pilling M (2003) Protocol for the development of the master chemical mechanism, MCM v3 (part A): tropospheric degradation of non-aromatic volatile organic compounds. Atmos Chem Phys 3:161–180. https://doi.org/10.5194/acp-3-161-2003

    Article  CAS  Google Scholar 

  21. Chia M, Schwartz TJ, Shanks BH, Dumesic JA (2012) Triacetic acid lactone as a potential biorenewable platform chemical. Green Chem 14:1850–1853. https://doi.org/10.1039/C2GC35343A

    Article  CAS  Google Scholar 

  22. Arnold F, Bürger V, Droste-Fanke B, Grimm F, Krieger A, Schneider J, Stilp T (1997) Acetone in the upper troposphere and lower stratosphere: impact on trace gases and aerosols. Geophys Res Lett 24:3017–3020. https://doi.org/10.1029/97GL02974

    Article  CAS  Google Scholar 

  23. Ziemann PJ, Atkinson R (2012) Kinetics, products, and mechanisms of secondary organic aerosol formation. Chem Soc Rev 41:6582–6605. https://doi.org/10.1039/C2CS35122F

    Article  CAS  Google Scholar 

  24. Perring A, Pusede S, Cohen R (2013) An observational perspective on the atmospheric impacts of alkyl and multifunctional nitrates on ozone and secondary organic aerosol. Chem Rev 113:5848–5870. https://doi.org/10.1021/cr300520x

    Article  CAS  Google Scholar 

  25. Wang C, Wania F, Goss K-U (2018) Is secondary organic aerosol yield governed by kinetic factors rather than equilibrium partitioning? Environ Sci Process Impacts 20:245–252. https://doi.org/10.1039/C7EM00451F

    Article  CAS  Google Scholar 

  26. Hehre W, Radom L, Schleyer PR, Pople JA (1986) Ab initio molecular orbital theory. Wiley, New York

    Google Scholar 

  27. Becke AD (1993) A new mixing of Hartree-Fock and local density-functional theories. J Chem Phys 98:1372–1377. https://doi.org/10.1063/1.464304

    Article  CAS  Google Scholar 

  28. Dunning TH Jr (1989) Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J Chem Phys 90:1007–1023. https://doi.org/10.1063/1.456153

    Article  CAS  Google Scholar 

  29. Gour NK, Gupta S, Mishra BK, Singh HJ (2014) A computational study on kinetics, mechanism, and thermochemistry of gas-phase reactions of 3-hydroxy-2-butanone with OH radicals. J Chem Sci 126:1789–1801. https://doi.org/10.1007/s12039-014-0733-6

    Article  CAS  Google Scholar 

  30. Priya AM, El Dib G, Senthilkumar L, Sleiman C, Tomas A, Canosa A, Chakir A (2015) An experimental and theoretical study of the kinetics of the reaction between 3-hydroxy-3-methyl-2-butanone and OH radicals. RSC Adv 5:26559–26568. https://doi.org/10.1039/C4RA15664A

    Article  CAS  Google Scholar 

  31. Guleria K, Subramanian R (2022) Theoretical study of mechanisms and kinetics of reactions of the O(3P) atom with alkyl hydroperoxides (ROOH) where (R=CH3 & C2H5). Comput Theor Chem 1208:113547. https://doi.org/10.1016/j.comptc.2021.113547

    Article  CAS  Google Scholar 

  32. Helgaker T, Klopper W, Koch H, Noga J (1997) Basis-set convergence of correlated calculations on water. J Chem Phys 106:9639–9646. https://doi.org/10.1063/1.473863

    Article  CAS  Google Scholar 

  33. Halkier A, Helgaker T, Jørgense P, Klopper W, Koch H, Olsen J, Wilson AK (1998) Basis-set convergence in correlated calculations on Ne, N2, and H2O. Chem Phys Lett 286:243–252. https://doi.org/10.1016/S0009-2614(98)00111-0

    Article  CAS  Google Scholar 

  34. Gonzalez C, Schlegel HB (1989) An improved algorithm for reaction path following. J Chem Phys 90:2154–2161. https://doi.org/10.1063/1.456010

    Article  CAS  Google Scholar 

  35. Gonzalez C, Schlegel HB (1990) Reaction path following in mass-weighted internal coordinates. J Phys Chem 94:5523–5527. https://doi.org/10.1021/j100377a021

    Article  CAS  Google Scholar 

  36. Pople JA, Head-Gordon M, Raghavachari K (1987) Quadratic configuration interaction. A general technique for determining electron correlation energies. J Chem Phys 87:5968–5975. https://doi.org/10.1063/1.453520

    Article  CAS  Google Scholar 

  37. Lee TJ, Taylor PR (1989) A diagnostic for determining the quality of single-reference electron correlation methods. Int J Quantum Chem 36:199–207. https://doi.org/10.1002/qua.56036084

    Article  Google Scholar 

  38. Rienstra-Kiracofe JC, Allen WD, Schaefer HF (2000) The C2H5 + O2 reaction mechanism: high-level ab initio characterizations. J Phys Chem A 104:9823–9840. https://doi.org/10.1021/jp001041k

    Article  CAS  Google Scholar 

  39. Dennington R, Keith T, Millam JG (2009) Version 5 Semichem Inc. Shawnee Mission KS

  40. Frisch M, Trucks G, Schlegel H, Scuseria G, Robb M, Cheeseman J, Scalmani G, Barone V, Petersson G, Nakatsuji H (2016) Gaussian 16, Revision A03 Gaussian Inc, Wallingford

  41. Zheng J, Bao JR, Meana-Pañeda R, Zhang S, Lynch GC, Corchado JC, Chuang YY, Fast PL, Hu WP, Liu YP et al (2018) Polyrate 2017-C. University of Minnesota, Minneapolis, MN

    Google Scholar 

  42. Garrett BC, Truhlar DG (1979) Generalized transition state theory. Bond energy-bond order method for canonical variational calculations with application to hydrogen atom transfer reactions. J Am Chem Soc 101:4534–4548. https://doi.org/10.1021/ja00510a019

    Article  CAS  Google Scholar 

  43. Garrett BC, Truhlar DG (1979) Criterion of minimum state density in the transition state theory of bimolecular reactions. J Chem Phys 70:1593–1598. https://doi.org/10.1063/1.437698

    Article  CAS  Google Scholar 

  44. Garrett BC, Truhlar DG, Grev RS, Magnuson AW (1980) Improved treatment of threshold contributions in variational transition-state theory. J Phys Chem 84:1730–1748. https://doi.org/10.1021/j100450a013

    Article  CAS  Google Scholar 

  45. Kuppermann A, Truhlar DG (1971) Exact tunneling calculations. J Am Chem Soc 93:1840–1851. https://doi.org/10.1021/ja00737a002

    Article  CAS  Google Scholar 

  46. Fernandez-Ramos A, Ellingson BA, Garrett BC, Truhlar DG (2007) Variational transition state theory with multidimensional tunneling. Rev Comput Chem 23:125–232. https://doi.org/10.1002/9780470116449.ch3

    Article  CAS  Google Scholar 

  47. Truhlar DG, Isaacson AD, Garrett BC (1985) Generalized transition state theory. Theory Chem React Dyn 4:65–137

    Google Scholar 

  48. Isaacson AD, Truhlar DG, Rai SN, Steckler R, Hancock GC, Garrett BC, Redmon MJ (1987) POLYRATE: a general computer program for variational transition state theory and semiclassical tunneling calculations of chemical reaction rates. Comput Phys Commun 47:91–102. https://doi.org/10.1016/0010-4655(87)90069-5

    Article  CAS  Google Scholar 

  49. Lu D, Truong TN, Melissas VS, Lynch GC, Liu Y-P, Garrett BC, Steckler R, Isaacson AD, Rai SN, Hancock GC (1992) Polyrate 4: a new version of a computer program for the calculation of chemical reaction rates for polyatomics. Comput Phys Commun 71:235–262. https://doi.org/10.1016/0010-4655(92)90012-N

    Article  CAS  Google Scholar 

  50. Liu YP, Lynch GC, Truong TN, Lu DH, Truhlar DG, Garrett B (1993) Molecular modeling of the kinetic isotope effect for the [1,5]-sigmatropic rearrangement of cis-1,3-pentadiene. J Am Chem Soc 115:2408–2415. https://doi.org/10.1021/ja00059a041

    Article  CAS  Google Scholar 

  51. Srinivasulu G, Vijayakumar S, Rajakumar B (2018) Kinetic Investigations on the gas phase reaction of 2,2, 2-trifluoroethylbutyrate with OH radicals: an experimental and theoretical study. ChemistrySelect 3:4480–4489. https://doi.org/10.1002/slct.201703113

    Article  CAS  Google Scholar 

  52. Dib GE, Aazaad B, Lakshmipathi S, Laversin H, Roth E, Chakir A (2018) An experimental and theoretical study on the kinetics of the reaction between 4-hydroxy-3-hexanone CH3CH2C(O)CH(OH)CH2CH3 and OH radicals. Int J Chem Kinet 50:556–567. https://doi.org/10.1002/kin.21181

    Article  CAS  Google Scholar 

  53. Priya AM, Lakshmipathi S, Chakir A, El Dib G (2016) First experimental and theoretical kinetic study of the reaction of 4-hydroxy-4-methyl 2-pentanone as a function of temperature. Int J Chem Kinet 48:584–600. https://doi.org/10.1002/kin.21017

    Article  CAS  Google Scholar 

  54. Skodje RT, Truhlar DG, Garrett BC (1982) Vibrationally adiabatic models for reactive tunneling. J Chem Phys 77:5955–5976. https://doi.org/10.1063/1.443866

    Article  CAS  Google Scholar 

  55. Truhlar DG, Brown FB, Steckler R, Isaacson AD (1986) The representation and use of potential energy surfaces in the wide vicinity of a reaction path for dynamics calculations on polyatomic reactions. Theory of chemical reaction dynamics. Springer, pp 285–329

    Google Scholar 

  56. Truhlar DG, Garrett BC (1987) Dynamical bottlenecks and semiclassical tunneling paths for chemical reactions. J Chim Phys 84:365–369. https://doi.org/10.1051/jcp/1987840365

    Article  Google Scholar 

  57. Marcus R (1966) On the analytical mechanics of chemical reactions. Quantum mechanics of linear collisions. J Chem Phys 45:4493–4499. https://doi.org/10.1063/1.1727528

    Article  CAS  Google Scholar 

  58. Truhlar DG, Garrett BC (1984) Variational transition state theory. Annu Rev Phys Chem 35:159–189. https://doi.org/10.1146/annurev.pc.35.100184.001111

    Article  CAS  Google Scholar 

  59. Marcus R, Coltrin ME (1977) A new tunneling path for reactions such as H + H2 → H2 + H. J Chem Phys 67:2609–2613. https://doi.org/10.1063/1.435172

    Article  CAS  Google Scholar 

  60. Skodje RT, Truhlar DG, Garrett BC (1981) A general small-curvature approximation for transition-state-theory transmission coefficients. J Phys Chem 85:3019–3023. https://doi.org/10.1021/j150621a001

    Article  CAS  Google Scholar 

  61. Moberly JG, Bernards MT, Waynant KV (2018) Key features and updates for Origin 2018. J Cheminformatics 10:1–2. https://doi.org/10.1186/s13321-018-0259-x

    Article  Google Scholar 

  62. Flynn J (1990) Temperature dependence of the rate of reaction in thermal analysis: the Arrhenius equation in condensed phase kinetics. J Therm Anal Calorim 36:1579–1593. https://doi.org/10.1007/bf01914077

    Article  CAS  Google Scholar 

  63. Guleria K, Subramanian R (2022) Quantum chemical and chemical kinetic investigation on hydrogen abstraction reactions of CF3CF2C(O)OCH3 and CHF2CF2C(O)OCH3 with OH radicals and fate of haloalkoxy radicals. ACS Earth Space Chem 6:1596–1611. https://doi.org/10.1021/acsearthspacechem2c00069

    Article  CAS  Google Scholar 

  64. Hammond GS (1955) A correlation of reaction rates. J Am Chem Soc 77:334–338. https://doi.org/10.1021/ja01607a027

    Article  CAS  Google Scholar 

  65. Aslan L, Laversin H, Coddeville P, Fittschen C, Roth E, Tomas A, Chakir A (2017) Kinetics of the photolysis and OH reaction of 4-hydroxy-4-methyl-2-pentanone: atmospheric implications. Atmos Environ 150:256–263. https://doi.org/10.1016/j.atmosenv.2016.11.059

    Article  CAS  Google Scholar 

  66. Wallington TJ, Kurylo MJ (1987) Flash photolysis resonance fluorescence investigation of the gas-phase reactions of hydroxyl radicals with a series of aliphatic ketones over the temperature range 240–440 K. J Phys Chem 91:5050–5054. https://doi.org/10.1021/j100303a033

    Article  CAS  Google Scholar 

  67. Alvarez-Idaboy JR, Cruz-Torres A, Galano A, Ruiz-Santoyo ME (2004) Structure-reactivity relationship in ketones + OH reactions: a quantum mechanical and TST approach. J Phys Chem A 108:2740–2749. https://doi.org/10.1021/jp036795o

    Article  CAS  Google Scholar 

  68. Baasandorj M, Griffith S, Dusanter S, Stevens PS (2009) Experimental and theoretical studies of the kinetics of the OH + hydroxyacetone reaction as a function of temperature. J Phys Chem A 113:10495–10502. https://doi.org/10.1021/j100303a033

    Article  CAS  Google Scholar 

  69. Galano A (2006) Theoretical study on the reaction of tropospheric interest: hydroxyacetone + OH. Mechanism and kinetics. J Phys Chem A 110:9153–9160. https://doi.org/10.1021/jp061705b

    Article  CAS  Google Scholar 

  70. Gao Y, Zhao Y, Guan Q, Wang F (2020) Ab initio kinetics predictions for the role of pre-reaction complexes in hydrogen abstraction from 2-butanone by OH radicals. RSC Adv 10:33205–33212. https://doi.org/10.1039/D0RA05332E

    Article  CAS  Google Scholar 

  71. Atkinson R, Tuazon EC, Aschmann SM (2000) Atmospheric chemistry of 2-pentanone and 2-heptanone. Environ Sci Technol 34:623–631. https://doi.org/10.1021/es9909374

    Article  CAS  Google Scholar 

  72. Zhang S, Sun J, Cao H, Qiao Q, He M (2017) Computational study on the mechanism and kinetics of Cl-initiated oxidation of ethyl acrylate. Struct Chem 28:1831–1842. https://doi.org/10.1007/s11224-017-0967-2

    Article  CAS  Google Scholar 

  73. Ji Y, Zheng J, Qin D, Li Y, Gao Y, Yao M, Chen X, Li G, An T, Zhang R (2018) OH-initiated oxidation of acetylacetone: implications for ozone and secondary organic aerosol formation. Environ Sci Technol 52:11169–11177. https://doi.org/10.1021/acs.est.8b03972

    Article  CAS  Google Scholar 

  74. Colmenar I, Martin P, Cabanas B, Salgado S, Martinez E (2018) Analysis of reaction products formed in the gas phase reaction of E, E-2,4-hexadienal with atmospheric oxidants: reaction mechanisms and atmospheric implications. Atmos Environ 176:188–200. https://doi.org/10.1016/j.atmosenv.2017.12.027

    Article  CAS  Google Scholar 

  75. Paul S, Gour NK, Deka RC (2019) Oxidation pathways, kinetics and branching ratios of chloromethyl ethyl ether (CMEE) initiated by OH radicals and the fate of its product radical: an insight from a computational study. Environ Sci Process Impacts 21:1519–1531. https://doi.org/10.1039/C9EM00104B

    Article  CAS  Google Scholar 

  76. Hein R, Crutzen PJ, Heimann M (1997) An inverse modeling approach to investigate the global atmospheric methane cycle. Glob Biogeochem Cycles 11:43–76. https://doi.org/10.1029/96GB03043

    Article  CAS  Google Scholar 

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Acknowledgements

Kanika Guleria thanks the Indian Institute of Technology Patna for providing financial support and research facilities to accomplish this work.

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This study was funded by Indian Institute of Technology, Patna.

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  1. Department of Chemistry, Indian Institute of Technology Patna, Patna, 801103, India

    Kanika Guleria & Ranga Subramanian

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KG contributed to the conceptualization, methodology, analysis, and writing─original draft. RS contributed to writing─review and editing and supervision.

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Guleria, K., Subramanian, R. Computational investigation on mechanisms and kinetics of gas-phase reactions of 4-hydroxy-2-pentanone (4H2P) with hydroxyl radicals and subsequent reactions of CH3C(O)CH2C·(OH)CH3 radical. Theor Chem Acc 141, 77 (2022). https://doi.org/10.1007/s00214-022-02938-x

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