Supporting Information for the article Numerical Study of the Superadiabatic Flame Temperature Phenomenon in HN3 Flame by *O.P. Korobeinicheva, A.A. Paletskya, T.A.Bolshovaa and V.D Knyazevb a b Institute of Chemical Kinetics and Combustion SB RAS, Novosibirsk, Russia The Catholic University of America, Washington, D. C., United States of America 1 Table 1S. Kinetics mechanism of HN3 decomposition (k = A T**b exp(-E/RT)) A units: mole-cm-sec-K, E units Joules/mole REACTIONS CONSIDERED 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. N3H+N2=N2+NH+N2 N3H+N3H=N2+NH+N3H N3H+AR=N2+NH+AR N3H+H=N2+NH2 N3H+N=N2+NNH N3H+NH=NH2+N3 N3H+NH2=NH3+N3 H+H+M=H2+M H2 Enhanced H+H+H2=H2+H2 N2+M=N+N+M N2 Enhanced NH+M=N+H+M NH+H=N+H2 NH+N=N2+H NH+NH=NH2+N NH+NH=N2+H2 NH+NH=N2+H+H NH2+M=NH+H+M NH+H2=NH2+H NH2+N=N2+H+H NH2+NH=N2H2+H NH2+NH=NH3+N NH3+NH=NH2+NH2 NH2+NH2=N2H2+H2 NH3+M=NH2+H+M NH3+M=NH+H2+M NH3+H=NH2+H2 NH3+NH2=N2H3+H2 NNH=N2+H NNH+M=N2+H+M NNH+H=N2+H2 NNH+N=NH+N2 NNH+NH=N2+NH2 NNH+NH2=N2+NH3 NNH+NNH=N2H2+N2 N2H2+M=NNH+H+M N2 Enhanced H2 Enhanced N2H2+M=NH+NH+M N2 Enhanced H2 Enhanced N2H2+H=NNH+H2 N2H2+N=NNH+NH N2H2+NH=NNH+NH2 N2H2+NH2=NH3+NNH N2H3+M=NH2+NH+M N2H3+M=N2H2+H+M N2H3+H=N2H2+H2 A by by b E 2.14E+26 6.67E+26 7.55E+25 3.71E+07 1.87E+08 7.83E+02 5.88E+00 6.50E+17 -3.0 -2.9 -3.0 1.9 1.5 3.2 3.5 -1.0 195151.0 201280.0 191551.0 13754.0 14500.0 41700.0 -2900.0 0.0 1.00E+17 1.00E+28 -0.6 -3.3 0.0 942030.0 2.65E+14 3.20E+13 9.00E+11 5.95E+02 1.00E+08 2.54E+13 3.16E+23 1.00E+14 6.90E+13 1.50E+15 1.00E+13 3.16E+14 1.00E+13 2.20E+16 6.30E+14 5.42E+05 1.00E+11 3.00E+08 1.00E+13 1.00E+14 3.00E+13 2.00E+11 1.00E+13 1.00E+13 5.00E+16 0.0 0.0 0.5 2.9 1.0 0.0 -2.0 0.0 0.0 -0.5 0.0 0.0 0.0 0.0 0.0 2.4 0.5 0.0 0.5 0.0 0.0 0.5 0.0 0.0 0.0 316100.0 1360.0 0.0 -8370.0 0.0 0.0 382670.0 84030.0 0.0 0.0 8370.0 112080.0 6280.0 391340.0 391000.0 41530.0 90430.0 0.0 12810.0 0.0 8370.0 8370.0 0.0 16750.0 209340.0 3.16E+16 0.0 416170.0 8.50E+04 1.00E+06 1.00E+13 8.80E-02 5.00E+16 1.00E+17 1.00E+13 2.6 2.0 0.0 4.0 0.0 0.0 0.0 -963.0 0.0 25120.0 -6740.0 251210.0 138160.0 0.0 0.000E+00 5.000E+00 by by 2.000E+00 2.000E+00 by by 2.000E+00 2.000E+00 2 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. N2H3+H=NH2+NH2 5.00E+13 0.0 N2H3+H=NH+NH3 1.00E+11 0.0 N2H3+N=N2H2+NH 1.00E+06 2.0 N2H3+NH=N2H2+NH2 2.00E+13 0.0 N2H3+NH2=N2H2+NH3 1.00E+11 0.5 N2H3+NNH=N2H2+N2H2 1.00E+13 0.0 N2H3+N2H3=NH3+NH3+N2 3.00E+12 0.0 N2H3+N2H3=N2H4+N2H2 1.20E+13 0.0 N2H4(+M)=NH2+NH2(+M) 5.00E+14 0.0 Low pressure limit: 0.15000E+16 0.00000E+00 0.16328E+06 N2 Enhanced by 2.400E+00 NH3 Enhanced by 3.000E+00 N2H4 Enhanced by 4.000E+00 N2H4+M=N2H3+H+M 1.00E+15 0.0 N2 Enhanced by 2.400E+00 NH3 Enhanced by 3.000E+00 N2H4 Enhanced by 4.000E+00 N2H4+H=N2H3+H2 7.00E+12 0.0 N2H4+H=NH2+NH3 2.40E+09 0.0 N2H4+N=N2H3+NH 1.00E+10 1.0 N2H4+NH=NH2+N2H3 1.00E+09 1.5 N2H4+NH2=N2H3+NH3 1.80E+06 1.7 N3+N3=N2+N2+N2 8.43E+11 0.0 H+N3=N2+NH 6.03E+13 0.0 N3+N=N2+N2 8.43E+13 0.0 8370.0 0.0 0.0 0.0 0.0 16750.0 0.0 0.0 251210.0 266280.0 10470.0 12980.0 8370.0 8370.0 -5780.0 0.0 0.0 0.0 3 Table 2S. Results of the quantum chemical study. Units are Å, amu, hartree, and cm-1. hn3 Structures BH&HLYP/aug-cc-pvdz[Opt] N X Y 7 -1.706458 -2.322950 1 -2.603872 -2.190261 7 -0.810269 -1.879217 7 0.094694 -1.522562 N X Y 7 -0.023544 0.000073 1 -0.002753 0.000023 7 1.171020 -0.000173 7 2.182935 -0.001512 Electronic energy (hartree): Z -0.066073 0.386900 0.660744 1.211232 Z -0.001217 1.024502 -0.406034 -0.932441 BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz -164.7059545 -164.4115719 -164.5505160 CCSD/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz -164.3881483 -164.4150842 Vibrational frequencies (cm^-1) BH&HLYP/aug-cc-pvdz[Opt] 555 3606 634 1246 1356 2391 CCSD/aug-cc-pvdz[Opt] 504 3499 575 1180 1315 2234 - - h_hn3_2 Structures BH&HLYP/aug-cc-pvdz[Opt] N X Y 7 1.102971 -0.340121 1 1.634233 0.358120 7 -0.053258 -0.416761 7 -1.080145 -0.732823 1 2.049278 -1.734053 - Electronic energy (hartree): Z -0.089828 -0.595311 -0.551534 -0.877814 -0.323691 - BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz - -165.1982569 CCSD/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz - Barrier width 1.5565676 Vibrational frequencies (cm^-1) BH&HLYP/aug-cc-pvdz[Opt] -954 1216 347 1349 485 2314 575 3625 665 - - - n_hn3_1 Structures BH&HLYP/aug-cc-pvdz[Opt] N X Y 7 2.010879 -0.248341 7 0.955204 0.065514 7 -0.011866 0.421508 1 2.007258 -1.540181 7 1.909707 -2.733608 - Electronic energy (hartree): Z -0.521358 -1.028341 -1.502013 -0.348293 -0.229858 - BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz CCSD/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz -219.2540176 -218.8587230 -219.0291815 - Barrier width 0.9160000 Vibrational frequencies (cm^-1) BH&HLYP/aug-cc-pvdz[Opt] 124 1099 494 1356 622 2108 661 -2281 735 - - - n_hn3_2 Structures BH&HLYP/aug-cc-pvdz[Opt] N X Y 7 -1.505783 -2.497576 1 -2.442477 -2.667215 7 -0.916439 -1.638695 7 0.032458 -1.292811 7 -0.793466 -4.207487 Electronic energy (hartree): Z -0.071051 0.275842 0.683738 1.220495 -0.099963 BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz CCSD/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz -219.2496336 -218.8568686 -219.0247802 - Vibrational frequencies (cm^-1) BH&HLYP/aug-cc-pvdz[Opt] -713 1044 160 1294 460 2022 495 3504 565 - 4 n_hn3_3 Structures BH&HLYP/aug-cc-pvdz[Opt] N X Y 7 -1.878382 -1.829296 1 -2.362847 -2.679099 7 -0.693578 -2.135091 7 0.309036 -1.618969 7 -0.479411 -3.794201 Electronic energy (hartree): Z 0.295537 0.027056 0.626188 1.012083 0.466229 BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz CCSD/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz -219.2217627 -218.8279226 -218.9954454 Vibrational frequencies (cm^-1) BH&HLYP/aug-cc-pvdz[Opt] 379 1384 452 1645 530 3584 652 -920 1162 - -219.2511860 -218.8566856 -219.0262522 Vibrational frequencies (cm^-1) BH&HLYP/aug-cc-pvdz[Opt] -772 1279 197 1298 243 1940 612 3583 639 - - n_hn3_4 Structures BH&HLYP/aug-cc-pvdz[Opt] N X Y 7 -0.702392 -0.266554 1 -1.594370 0.196080 7 -0.601042 -1.260260 7 -0.028628 -2.193256 7 1.535557 -2.346723 Electronic energy (hartree): Z 0.784730 0.925780 1.507759 1.916252 1.149526 BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz CCSD/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz - n3 Structures BH&HLYP/aug-cc-pvdz[Opt] N X Y 7 -1.684422 -2.214041 7 -0.788677 -1.879702 7 0.107458 -1.543966 Electronic energy (hartree): Z -0.080242 0.591313 1.262012 BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz -164.0651137 -163.7673419 -163.8995360 Vibrational frequencies (cm^-1) BH&HLYP/aug-cc-pvdz[Opt] 510 633 1456 1728 - n2 Structures BH&HLYP/aug-cc-pvdz[Opt] N X Y 7 0.000000 0.000000 7 0.000000 0.000000 Electronic energy (hartree): Z 0.545239 -0.545239 BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz -109.4827318 -109.2927886 -109.3803583 Vibrational frequencies (cm^-1) BH&HLYP/aug-cc-pvdz[Opt] 2586 - -55.2097946 -55.1055657 -55.1451107 Vibrational frequencies (cm^-1) BH&HLYP/aug-cc-pvdz[Opt] 3387 - nh Structures BH&HLYP/aug-cc-pvdz[Opt] N X Y 7 -0.228139 0.329319 1 -0.617555 1.288335 Electronic energy (hartree): Z 0.000000 0.000000 BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz nh2 Structures BH&HLYP/aug-cc-pvdz[Opt] N X Y 7 -0.233123 0.333362 1 -0.612708 1.282105 1 0.778305 0.479003 Electronic energy (hartree): Z 0.000000 0.000000 0.000000 BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz -55.8589788 -55.7515947 - Vibrational frequencies (cm^-1) BH&HLYP/aug-cc-pvdz[Opt] 1562 3484 3579 - 5 hn2 Structures BH&HLYP/aug-cc-pvdz[Opt] N X Y 7 -1.663195 -2.374856 1 -2.613410 -2.236869 7 -0.856767 -1.580019 Electronic energy (hartree): Z 0.022341 0.432509 0.311898 BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz -109.9870695 -109.7855721 -109.8742071 Vibrational frequencies (cm^-1) BH&HLYP/aug-cc-pvdz[Opt] 1145 1975 3047 - nh2_hn3_01 Structures BH&HLYP/aug-cc-pvdz[Opt] N X Y 7 1.607868 -0.412746 7 1.172506 -0.130162 7 0.752344 0.206485 1 2.072061 -1.523122 7 2.151989 -2.797767 1 1.981652 -3.098026 1 1.377313 -3.162446 Electronic energy (hartree): Z -0.064990 -1.164312 -2.157440 -0.025595 -0.079546 -1.036203 0.469102 BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz -220.5560701 -220.1570836 - CCSD/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz - Barrier width 0.7027000 Vibrational frequencies (cm^-1) BH&HLYP/aug-cc-pvdz[Opt] -2191 630 1433 80 719 1591 134 741 2235 423 1173 3540 530 1369 3639 - - - nh2_hn3_02 Structures BH&HLYP/aug-cc-pvdz[Opt] N X Y 7 -2.390141 -4.483745 1 -2.409975 -5.492715 7 -2.631509 -3.994644 7 -2.455769 -3.248017 7 -0.638388 -4.291570 1 -0.225558 -3.761106 1 -0.905682 -3.584836 Electronic energy (hartree): Z 0.515325 0.561830 1.668493 2.513343 -0.221254 0.542984 -0.900607 BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz -220.5395300 -220.1431575 - CCSD/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz - Vibrational frequencies (cm^-1) BH&HLYP/aug-cc-pvdz[Opt] -790 644 1564 121 838 2133 190 937 3533 483 1089 3632 511 1363 3658 - - - nh2_hn3_04 Structures BH&HLYP/aug-cc-pvdz[Opt] N X Y 7 -1.469754 -2.442214 1 -2.141690 -2.289311 7 -0.384739 -2.808879 7 0.752612 -3.007981 7 1.466966 -2.206627 1 2.440077 -2.404734 1 1.339307 -1.228997 Electronic energy (hartree): Z 1.954357 2.699345 2.437027 2.358065 0.882422 1.098599 1.138486 BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz -220.5399100 -220.1417915 - CCSD/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz - Vibrational frequencies (cm^-1) BH&HLYP/aug-cc-pvdz[Opt] -661 625 1564 126 883 1982 198 925 3526 438 1275 3582 576 1326 3632 - - - 6 nh3 Structures BH&HLYP/aug-cc-pvdz[Opt] N X Y 7 -0.326768 0.333321 1 -0.642533 1.146389 1 0.681352 0.332325 1 -0.644543 -0.478587 Electronic energy (hartree): Z -0.033723 -0.540309 -0.065660 -0.540900 BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz CCSD/aug-cc-pvdz[Opt] -56.5305369 -56.4249954 -56.4804577 - Vibrational frequencies (cm^-1) BH&HLYP/aug-cc-pvdz[Opt] 1044 3720 1693 1694 3588 3720 - hn3_ar_vdw01 Structures BH&HLYP/aug-cc-pvdz[Opt] N X Y 7 -0.691015 0.179463 1 -0.273725 1.083969 7 -1.922392 0.284774 7 -3.038841 0.236043 18 1.709333 3.132014 N X Y 7 1.174069 0.878088 1 0.281006 0.374015 7 2.096761 0.018498 7 3.039813 -0.622743 18 -2.469750 -0.127273 Electronic energy (hartree): Z -0.494832 -0.304913 -0.488047 -0.511388 0.103180 Z -0.000719 0.007429 0.000295 -0.000299 -0.000132 BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz -692.2438213 -691.3824559 - CCSD/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz -691.3563365 -691.3860023 Vibrational frequencies (cm^-1) BH&HLYP/aug-cc-pvdz[Opt] 26 1247 40 1359 58 2390 557 3607 634 CCSD/aug-cc-pvdz[Opt] 10 1180 51 1317 108 2236 505 3510 576 - - hn3_ar_vdw02 Structures BH&HLYP/aug-cc-pvdz[Opt] N X Y 7 -0.628971 0.165343 1 -0.314412 1.111210 7 -1.864528 0.143001 7 -2.969501 0.019615 18 -1.553831 3.828000 N X Y 7 0.044913 0.000000 1 0.179743 0.000000 7 1.188344 0.000000 7 2.138326 0.000000 18 2.598803 0.000000 Electronic energy (hartree): Z -0.494702 -0.308218 -0.513562 BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz -0.557945 0.202038 Z 0.161893 1.178845 -0.369644 -1.000883 2.921386 CCSD/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz -692.2438163 -691.3826030 - -691.3565038 -691.3862001 Vibrational frequencies (cm^-1) BH&HLYP/aug-cc-pvdz[Opt] 18 1248 35 1358 102 2390 555 3604 634 - CCSD/aug-cc-pvdz[Opt] 28 1181 58 1316 74 2234 503 3502 574 - - - 7 n Electronic energy (hartree): BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz -54.5812562 -54.4869816 -54.5169239 h Electronic energy (hartree): BH&HLYP/aug-cc-pvdz[Opt] -0.4980784 ar Electronic energy (hartree): BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz CCSD/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz -527.5375827 -526.9696846 -526.9671591 -526.9696846 Table 3S. Reaction energy barriers and Ho0 (kJ mol-1, ZPE included). HN3+H=N2+NH2 BH&HLYP/aug-cc-pvdz[Opt] Final model (fitted to experiment) Energy barrier 19.87 23.57 Ho0 -352.95 -323.33 HN3+N=N2+NNH (Attack on the 2-nd atom (N)) BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz Final model (fitted to experiment) Energy barrier 99.58 110.36 112.92 18.60 Ho0 -485.57 -478.26 -497.48 HN3+N=Products (Attack on the 3-rd atom (N)) BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz Energy barrier 171.84 185.45 189.03 Ho0 8 HN3+N=N2+NNH (Attack on the 4-th atom (N)) BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz Energy barrier 94.61 109.95 108.16 Ho0 -485.57 -478.26 -497.48 HN3+N=NH+N3 (Attack on the 1-st atom (H)) BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz CCSD(T)/aug-cc-pvtz Energy barrier 71.67 89.10 84.97 Ho0 16.11 51.15 43.66 Energy barrier 22.22 14.92 14.92 Ho0 -76.22 -72.16 -72.16 HN3+NH2=NH3+N3 BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz Final model HN3+NH2=Products (Attack on the 2-nd atom (N)) BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz Energy barrier 80.34 66.18 Ho0 HN3+NH2=Products (Attack on the 4-th atom (N)) BH&HLYP/aug-cc-pvdz[Opt] CCSD(T)/aug-cc-pvdz Energy barrier 79.13 69.55 Ho0 Comments on individual reactions N + HN3 → Products Two channels are possible: N + HN3 → NH + N3 N + HN3 → N2H + N2 → H + N2 + N2 The first channel results from an abstraction of H atom by N. The second channel can result from N atom attack on the N of HN3 nearest to H (HN(…N)NN) or the farthest from H 9 (HNNN(…N)). There is only one experimental study of this reaction, performed by Le Bras and Combourieu [1]. The rate constant obtained at 298 K was 2.7×109 cm3 mol-1 s-1. The energy barriers obtained in quantum chemical calculations are large. The room temperature overall rate constant calculated using transition state theory and the above results is much lower than the experimental value of Le Bras and Combourieu, with many orders of magnitude difference. In modeling, the energy of the transition state of the second channel were fitted to reproduce the rate constant of Le Bras and Combourieu. The first channel was not used because of the endothermicity exceeding the barrier required for fitting the experimental rate constant. NH2 + HN3 → Products No experimental data are available for this reaction. An earlier computational study was performed by Henon and Bohr [2]. In the current work, quantum chemical calculations were performed for the reaction of N atoms with HN3. The methods were BH&HLYP/aug-cc-pvdz for geometry optimization and vibrational frequencies and CCSD(T)/aug-cc-pvtz for single-point energy calculations. Radical attack on the H atom (atom 1) and nitrogen atoms 2 and 4 were studied. Energy barrier for attack on H (producing NH3 + N3) is only 14.9 kJ mol-1, whereas those for the other two reaction channels are 66.2 and 69.6 kJ mol-1, making these two channels unimportant. Rate constants obtained in transition state theory calculations are larger than those derived by Henon and Bohr by approximately two orders of magnitude, due to the lower energy barrier but also due to the fact that calculations performed in that earlier study did not include the partition function of the hindered internal rotation about the forming H2N-H bond, as described in their article, which resulted in too low rate constant values. References [1] G. Le Bras, J. Combourieu, Int. J. Chem. Kinet. 5 (1973) 559-576. [2] E. Henon, F. Bohr, J. Molec. Struc. - Theochem. 531 (2000) 283-299. 10