Molecular dynamics of combustion reactions in supercritical carbon dioxide. Part 4: boxed MD study of formyl radical dissociation and recombination


Fossil fuel oxy-combustion is an emergent technology where habitual nitrogen diluent is replaced by high pressure (supercritical) carbon dioxide. The supercritical state of CO2 increases the efficiency of the energy conversion and the absence of nitrogen from the reaction mixture reduces pollution by NOx. However, the effects of a supercritical environment on elementary reactions kinetics are not well understood at present. We used boxed molecular dynamics simulations at the QM/MM theory level to predict the kinetics of dissociation/recombination reaction HCO + [M] ↔ H + CO + [M], an important elementary step in many combustion processes. A wide range of temperatures (400–1600 K) and pressures (0.3–1000 atm) were studied. Potentials of mean force were plotted and used to predict activation free energies and rate constants. Based on the data obtained, extended Arrhenius equation parameters were fitted and tabulated. The apparent activation energy for the recombination reaction becomes negative above 30 atm. As the temperature increased, the pressure effect on the rate constant decreased. While at 400 K the pressure increase from 0.3 atm to 300 atm accelerated the dissociation reaction by a factor of 250, at 1600 K the same pressure increase accelerated this reaction by a factor of 100.

Formyl radical surrounded by carbon dioxide molecules

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  1. 1.

    Howlett KE (1952) The pyrolisis of 1,2-dichloroethane. Trans Faraday Soc 48:23–34

    Google Scholar 

  2. 2.

    Horner ECA, Style DWG, Summers D (1954) The oxidation of formaldehyde. Part 2.—General discussion and mechanism of the reaction. Trans Faraday Soc 50:1201–1212

    CAS  Article  Google Scholar 

  3. 3.

    Hidaka Y, Taniguchi T, Kamesawa T, Masaoka H, Inami K, Kawano H (1993) High-temperature pyrolysis of formaldehyde in shock-waves. Int J Chem Kinet 25(4):305–322

    CAS  Article  Google Scholar 

  4. 4.

    Dorman FH, Buchanan AS (1956) The photolysis of gaseous aldehydes. II. The decomposition of formyl and acetyl radicals. Aust J Chem 9(1):34–40

    CAS  Article  Google Scholar 

  5. 5.

    Cribb PH, Dove JE, Yamazaki S (1992) A kinetic-study of the pyrolysis of methanol using shock-tube and computer-simulation techniques. Combust Flame 88(2):169–185

    CAS  Article  Google Scholar 

  6. 6.

    Bernstein JS, Song XM, Cool TA (1988) Detection of the formyl radical in a methane oxygen flame by resonance ionization. Cheml Phys Lett 145(3):188–192

    CAS  Article  Google Scholar 

  7. 7.

    Peters J, Mahnen G (1973) Reaction mechanism and rate constants of elementary steps in methane-oxygen flames. 14th international symposium on combustion. Combust Inst 14:133–146

  8. 8.

    Hennessy RJ, Peacock SJ, Smith DB (1984) Flame structure studies by high resolution quadrupole mass spectrometry. Combust Flame 58:73–75

    CAS  Article  Google Scholar 

  9. 9.

    Jeffries JB, Crosley DR, Wysong IC, Smith GP (1990) Laser-induced fluorescence detection of HCO in a low pressure flame. 23rd symposium (international) on combustion. Combust Inst 23:1847–1854

  10. 10.

    Diau EW-G, Smith GP, Jeffries JB, Crosley DR (1998) HCO concentration in flames via quantitative laser-induced fluorescence. 27th symposium (international) on combustion. Combust Inst 27:453–460

  11. 11.

    Cheskis S (1995) Intracavity laser-absorption spectroscopy detection of HCO radicals in atmospheric-pressure hydrocarbon flames. J Chem Phys 102(4):1851–1854

    CAS  Article  Google Scholar 

  12. 12.

    Lozovsky VA, Cheskis S, Kachanov A, Stoeckel F (1997) Absolute HCO concentration measurements in methane/air flame using intracavity laser spectroscopy. J Chem Phys 106(20):8384–8391

    CAS  Article  Google Scholar 

  13. 13.

    Scherer JJ, Rakestraw DJ (1997) Cavity ringdown laser absorption spectroscopy detection of formyl (HCO) radical in a low pressure name. Cheml Phys Lett 265(1-2):169–176

    CAS  Article  Google Scholar 

  14. 14.

    McIlroy A (1999) Laser studies of small radicals in rich methane flames: OH, HCO, and (CH2)-C-1. Israel J Chem 39(1):55–62

    CAS  Article  Google Scholar 

  15. 15.

    Friedrichs G, Herbon JT, Davidson DF, Hanson RK (2002) Quantitative detection of HCO behind shock waves: The thermal decomposition of HCO. Phys Chem Chem Phys 4(23):5778–5788

    CAS  Article  Google Scholar 

  16. 16.

    Manion J, Huie R, Levin R, Burgess Jr D, Orkin V, Tsang W, McGivern W, Hudgens J, Knyazev V, Atkinson D (2017) NIST chemical kinetics database, NIST standard reference database 17, version 7.0 (web version), release 1.6.8, data version 2017.07. National Institute of Standards and Technology, Gaithersburg Web address: Accessed 2 Dec 2017

  17. 17.

    Trenwith AB (1963) The thermal decomposition of acetaldehyde: the formation of hydrogen. J Chem Soc (0):4426–4430.

  18. 18.

    Tsuboi T (1976) Mechanism for homogeneous thermal oxidation of methane in gas-phase. Jpn J Appl Phys 15(1):159–168

    CAS  Article  Google Scholar 

  19. 19.

    Wagner AF, Bowman JM (1987) The addition and dissociation reaction H + CO reversible HCO. 1. Theoretical RRKM studies. J Phys Chem 91(20):5314–5324

    CAS  Article  Google Scholar 

  20. 20.

    Tsang W, Hampson RF (1986) Chemical kinetic database for combustion chemistry. 1. Methane and related-compounds. J Phys Chem Ref Data 15(3):1087–1279

    CAS  Article  Google Scholar 

  21. 21.

    Hikida T, Eyre JA, Dorfman LM (1971) Pulse radiolysis studies. 20. Kinetics of some addition reactions of gaseous hydrogen atoms by fast Lyman-Alpha absorption spectrophotometry. J Chem Phys 54(8):3422–3428

    CAS  Article  Google Scholar 

  22. 22.

    Wang HY, Eyre JA, Dorfman LM (1973) Activation-energy for gas-phase reaction of hydrogen-atoms with carbon-monoxide. J Chem Phys 59(9):5199–5200

    CAS  Article  Google Scholar 

  23. 23.

    Ahumada JJ, Osborne DT, Michael JV (1972) Pressure-dependence and third body effects on rate constants for H+O2, H+NO, and H+CO. J Chem Phys 57(9):3736–3745

    CAS  Article  Google Scholar 

  24. 24.

    Timonen RS, Ratajczak E, Gutman D, Wagner AF (1987) The addition and dissociation reaction H + CO reversible HCO. 2. Experimental studies and comparison with theory. J Phys Chem 91(20):5325–5332

    CAS  Article  Google Scholar 

  25. 25.

    Langford AO, Moore CB (1984) Reaction and relaxation of vibrationally excited formyl radicals. J Chem Phys 80(9):4204–4210

    CAS  Article  Google Scholar 

  26. 26.

    Reed RI (1956) Studies in electron impact methods. Trans Faraday Soc 52:1195–1200

    CAS  Article  Google Scholar 

  27. 27.

    Browne WG, Porter RP, Verlin JD, Clark AH (1969) A study of acetylene-oxygen flames. Symposium (international) on combustion. 12(1):1035–1047

  28. 28.

    Bowman JM, Bittman JS, Harding LB (1986) Ab initio calculations of electronic and vibrational energies of HCO and HOC. J Chem Phys 85(2):911–921

    CAS  Article  Google Scholar 

  29. 29.

    Hippler H, Krasteva N, Striebel F (2004) The thermal unimolecular decomposition of HCO: effects of state specific rate constants on the thermal rate constant. Phys Chem Chem Phys 6(13):3383–3388

    CAS  Article  Google Scholar 

  30. 30.

    Krasnoperov LN, Chesnokov EN, Stark H, Ravishankara AR (2004) Unimolecular dissociation of formyl radical, HCO -> H plus CO, studied over 1-100 bar pressure range. J Phys Chem A 108(52):11526–11536

    CAS  Article  Google Scholar 

  31. 31.

    Peters PS, Duflot D, Wiesenfeld L, Toubin C (2013) The H + CO reversible arrow HCO reaction studied by ab initio benchmark calculations. J Chem Phys 139(16):164310-1 164310-15

    Google Scholar 

  32. 32.

    Bjorklund GC, Levenson MD, Lenth W, Ortiz C (1983) Frequency-modulation (FM) spectroscopy - theory of lineshapes and signal-to-noise analysis. Appl Phys B-Photo 32(3):145–152

    Article  Google Scholar 

  33. 33.

    Field MJ, Bash PA, Karplus M (1990) A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations. J Comput Chem 11(6):700–733

    CAS  Article  Google Scholar 

  34. 34.

    Potoff JJ, Siepmann JI (2001) Vapor-liquid equilibria of mixtures containing alkanes, carbon dioxide, and nitrogen. Aiche J 47(7):1676–1682

    CAS  Article  Google Scholar 

  35. 35.

    Zhong HM, Lai SH, Wang JY, Qiu WD, Ludemann HD, Chen LP (2015) Molecular dynamics simulation of transport and structural properties of CO2 using different molecular models. J Chem Eng Data 60(8):2188–2196

    CAS  Article  Google Scholar 

  36. 36.

    Brooks BR, Brooks CL, Mackerell AD, Nilsson L, Petrella RJ, Roux B, Won Y, Archontis G, Bartels C, Boresch S et al (2009) CHARMM: the biomolecular simulation program. J Comput Chem 30(10):1545–1614

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  37. 37.

    Brooks BR, Bruccoleri RE, Olafson BD, States DJ, Swaminathan S, Karplus M (1983) CHARMM - a program for macromolecular energy, minimization, and dynamics calculations. J Comput Chem 4(2):187–217

    CAS  Article  Google Scholar 

  38. 38.

    Essmann U, Perera L, Berkowitz ML, Darden T, Lee H, Pedersen LG (1995) A smooth particle mesh Ewald method. J Chem Phys 103(19):8577–8593

    CAS  Article  Google Scholar 

  39. 39.

    Shavitt I, Stevens RM, Minn FL, Karplus M (1968) Potential-Energy Surface for H3. J Chem Phys 48(6):2700

    CAS  Article  Google Scholar 

  40. 40.

    Dewar MJ, Thiel W (1977) Ground states of molecules. 38. The MNDO method. Approximations and parameters. J Am Chem Soc 99(15):4899–4907

    CAS  Article  Google Scholar 

  41. 41.

    Schaftenaar G, Noordik JH (2000) Molden: a pre- and post-processing program for molecular and electronic structures. J Comput Aid Mol Des 14(2):123–134

    CAS  Article  Google Scholar 

  42. 42.

    Glowacki DR, Paci E, Shalashilin DV (2009) Boxed molecular dynamics: a simple and general technique for accelerating rare event kinetics and mapping free energy in large molecular systems. J Phys Chem B 113(52):16603–16611

    CAS  PubMed  Article  Google Scholar 

  43. 43.

    Glowacki DR, Paci E, Shalashilin DV (2011) Boxed molecular dynamics: decorrelation time scales and the kinetic master equation. J Chem Theory Comput 7(5):1244–1252

    CAS  PubMed  Article  Google Scholar 

  44. 44.

    Glowacki DR, Orr-Ewing AJ, Harvey JN (2015) Non-equilibrium reaction and relaxation dynamics in a strongly interacting explicit solvent: F + CD3CN treated with a parallel multi-state EVB model. J Chem Phys 143(4):044120

    PubMed  Article  CAS  Google Scholar 

  45. 45.

    Glowacki DR, Rodgers WJ, Shannon R, Robertson SH, Harvey JN (2017) Reaction and relaxation at surface hotspots: using molecular dynamics and the energy-grained master equation to describe diamond etching. Philos T Roy Soc A 375(2092):0206

    Article  CAS  Google Scholar 

  46. 46.

    Linstrom PJ, Mallard WG (2001) The NIST Chemistry WebBook: a chemical data resource on the internet. J Chem Eng Data 46(5):1059–1063

    CAS  Article  Google Scholar 

  47. 47.

    Khavrutskii IV, Dzubiella J, McCammon JA (2008) Computing accurate potentials of mean force in electrolyte solutions with the generalized gradient-augmented harmonic Fourier beads method. J Chem Phys 128(4):044106

    PubMed  Article  CAS  Google Scholar 

  48. 48.

    Masunov A, Lazaridis T (2003) Potentials of mean force between ionizable amino acid side chains in water. J Am Chem Soc 125(7):1722–1730

    CAS  PubMed  Article  Google Scholar 

  49. 49.

    Henin J, Chipot C (2004) Overcoming free energy barriers using unconstrained molecular dynamics simulations. J Chem Phys 121(7):2904–2914

    CAS  PubMed  Article  Google Scholar 

  50. 50.

    Neumann RM (1980) Entropic Approach to Brownian-Movement. Am J Phys 48(5):354–357

    CAS  Article  Google Scholar 

  51. 51.

    Sangwan M, Krasnoperov LN (2013) Kinetics of the gas phase reaction CH3 + HO2. J Phys Chem A 117(14):2916–2923

    CAS  PubMed  Article  Google Scholar 

  52. 52.

    Benson SW (1983) Molecular-models for recombination and disproportionation of radicals. Can J Chem 61(5):881–887

    CAS  Article  Google Scholar 

  53. 53.

    Revell LE, Williamson BE (2013) Why are some reactions slower at higher temperatures? J Chem Ed 90(8):1024–1027

    CAS  Article  Google Scholar 

  54. 54.

    Masunov AE, Atlanov AA, Vasu SS (2016) Molecular dynamics study of combustion reactions in a supercritical environment. Part 1: carbon dioxide and water force field parameters refitting and critical isotherms of binary mixtures. Energy Fuels 30(11):9622–9627

    CAS  Article  Google Scholar 

  55. 55.

    Krasnoperov LN, Chesnokov EN, Stark H, Ravishankara AR (2005) Elementary reactions of formyl (HCO) radical studied by laser photolysis - transient absorption spectroscopy. P Combust Inst 30:935–943

    Article  CAS  Google Scholar 

  56. 56.

    Li J, Zhao ZW, Kazakov A, Chaos M, Dryer FL, Scire JJ (2007) A comprehensive kinetic mechanism for CO, CH2O, and CH3OH combustion. Int J Chem Kinet 39(3):109–136

    Article  CAS  Google Scholar 

  57. 57.

    Kee RJ, Rupley FM, Miller JA (1989) Chemkin-II: a Fortran chemical kinetics package for the analysis of gas-phase chemical kinetics. Sandia National Labs, Livermore, p 127

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The authors are grateful to Dr. Glowacki for his assistance with AXD program module. This work was supported in part by the Department of Energy (grant number: DE-FE0025260). The authors also acknowledge the National Energy Research Scientific Computing Center (NERSC), and the University of Central Florida Advanced Research Computing Center ( for providing computational resources and support. A.E.M. acknowledges support by the Act 211 Government of the Russian Federation (contract no. 02.A03.21.0011) and by the “improving of the competitiveness” program of the National Research Nuclear University MEPhI.

Disclaimer: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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Panteleev, S.V., Masunov, A.E. & Vasu, S.S. Molecular dynamics of combustion reactions in supercritical carbon dioxide. Part 4: boxed MD study of formyl radical dissociation and recombination. J Mol Model 25, 35 (2019).

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  • Molecular dynamics
  • Combustion kinetics