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Fig3-10: The comparison for the major channel of trans-ONONO2 + N2H4 reaction optimized by B3LYP/6-311++G(3df,2p) and PW91PW91/
6-311++G(3df,2p).
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Table3-16: Moments of inertia (IA, IB, IC) and vibration frequencies of the species in trans-ONONO2 + N2H4 and cis-ONONO2 + N2H4 reactions computed at B3LYP/6-311++G(3df,2p).
Species or
Transition States Moments of inertia Ii(a.u) Vibrational Frequency υj (cm-1)
N2O4 273.2, 500.4, 773.7 87, 222, 293, 446, 490, 704, 760, 850, 1307, 1450, 1787, 1826 trans-ONONO2 151.2, 773.8, 925.0 9, 131, 209, 294, 486, 647, 786, 801, 945, 1330, 1709, 1934 cis-ONONO2 244.9, 605.7, 632.1 73, 135, 179, 285, 542, 564, 693, 862, 909, 1360, 1683, 1845
N2H4 12.4, 74.2, 74.3 439, 801, 974, 1114, 1294, 1323, 1674, 1686, 3462, 3471, 3562, 3568
Cs-Complex1 508.6, 1412.0, 1695.8 48, 64, 101, 135, 205, 240, 262, 301, 324, 405, 665, 712, 727, 822, 833, 899, 1057, 1153, 1190, 1242, 1299, 1455, 1544, 1660, 1707, 1886, 2481, 3445, 3510, 3551
Cs-Complex2 439.1, 2040.2, 2195.3 22, 41, 85, 106, 110, 134, 204, 345, 455, 584, 616, 675, 794, 853, 909, 928, 988, 1196, 1333, 1351, 1397, 1411, 1617, 1690, 1746, 3449, 3494, 3523, 3539
Cs-Complex3 484.4, 1854.4, 1965.1 24, 39, 43, 64, 92, 120, 130, 172, 246, 283, 450, 538, 551, 714, 814, 878, 912, 989, 1115, 1297, 1327, 1364, 1656, 1675, 1687, 1867, 3458, 3472, 3557, 3568
Cs-Complex4 485.2, 2398.5, 2638.5 17, 29, 49, 71, 109, 137, 216, 319, 354, 482, 613, 663, 776, 800, 805, 834, 857, 988, 1223, 1311, 1365, 1399, 1441, 1694, 1705, 1763, 3481, 3518, 3559, 3588
Cs-Complex5 615.6, 1318.9, 1727.1 51, 62, 103, 142, 169, 186, 214, 285, 302, 385, 465, 507, 622, 823, 876, 1005, 1019, 1169, 1309, 1338, 1451, 1489, 1619, 1669, 1688, 1931, 3035, 3376, 3465, 3543 Cs-Complex6 666.8, 1856.0, 2280.3 35, 56, 74, 94, 152, 164, 166, 201, 342, 427, 506, 540, 635, 698, 825, 864, 892, 964,
1069, 1188, 1348, 1461, 1497, 1687, 1749, 1797, 3415, 3468, 3509, 3578
Cs-Complex7 722.8, 1126.3, 1485.2 21, 47, 76, 117, 158, 211, 241, 260, 307, 330, 474, 490, 651, 824, 866, 998, 1010, 1175, 1304, 1342, 1446, 1487, 1602, 1651, 1681, 1902, 3173, 3360, 3460, 3538 Cs-Complex8 299.3, 4559.1, 4857.4 10, 18, 20, 54, 61, 71, 134, 138, 180, 186, 542, 297, 684, 685, 862, 873, 908, 949,
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1277, 1350, 1427, 1444, 1546, 1680, 1682, 1753, 3199, 3260, 3340, 3494
Cs-TS1 492.1, 1449.5, 1727.3 224i, 38, 67, 140, 173, 239, 257, 288, 319, 440, 681, 712, 730, 830, 838, 882, 995, 1087, 1188, 1231, 1409, 1497, 1569, 1606, 1696, 1736, 1872, 3452, 3490, 3557 Cs-TS2 660.0, 1301.4, 1608.6 184i, 29, 59, 94, 121, 200, 233, 241, 278, 382, 454, 521, 766, 817, 854, 900, 1031,
1124, 1194, 1237, 1309, 1469, 1533, 1559, 1676, 1794, 3178, 3449, 3504, 3556
Cs-TS3 434.3, 1522.1, 1651.2 773i, 69, 83, 99, 183, 202, 236, 261, 283, 310, 512, 590, 644, 741, 774, 843, 908, 1012, 1124, 1207, 1216, 1408, 1466, 1635, 1695, 1928, 3013, 3478, 3561, 3576
Cs-TS4 791.8, 1144.0, 1804.4 427i, 58, 81, 145, 158, 195, 232, 250, 293, 358, 451, 498, 620, 787, 843, 899, 990, 1097, 1175, 1283, 1375, 1475, 1592, 1672, 1687, 1750, 1957, 3435, 3471, 3556
Cs-TS5 422.1, 1464.3, 1550.0 779i, 43, 66, 105, 159, 177, 233, 247, 301, 344, 496, 539, 637, 738, 757, 868, 923, 1063, 1149, 1172, 1197, 1389, 1469, 1624, 1701, 1918, 3274, 3482, 3557, 3576
Cs-TS6 681.6, 1171.9, 1623.1 1061i, 59, 92, 120, 135, 193, 240, 281, 324, 417, 459, 521, 652, 711, 796, 863, 1020, 1079, 1153, 1293, 1387, 1417, 1541, 1600, 1634, 1728, 1783, 3319, 3427, 3506
HONO2 137.8, 149.0, 286.8 493, 589, 655, 787, 904, 1325, 1350, 1756, 3734
H2NN(H)NO 79.4, 271.1, 340.5 151, 212, 332, 583, 674, 901, 978, 1168, 1285, 1433, 1630, 1672, 3504, 3567, 3600 H2NN(H)NO2 155.4, 34.6, 534.8 173, 313, 330, 499, 591, 790, 795, 852, 976, 1236, 1315, 1367,
1430, 1663, 1705, 3471, 3562, 3576
H2NN(H)ONO 80.4, 672.2, 687.1 96, 187, 323, 438, 501, 555, 612, 832, 967, 1042, 1189, 1335, 1504, 1687, 1766, 3453, 3515, 3584
cis-N2H2 6.1, 45.6, 51.8 1281, 1361, 1555, 1651, 3102, 3195 trans-HONO 19.0, 143.1, 162.1 590, 621, 819, 1303, 1783, 3773 cis-HONO 21.1, 135.9, 157.0 635, 695, 876, 1342, 1716, 3597
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Table3-17: Relative energies of species in trans-ONONO2 + N2H4 reaction and cis-ONONO2
+ N2H4 reaction predicted at various theoretical levels. a ZPE b B3LYP/
b: The ZPE is determined by B3LYP/6-311++G(3df,2p) level, and the energy unit is kcal/mol for every species.
c: The energies are including single-point energies, based on geometries of B3LYP/6-311++G(3df,2p), and ZPE.
d:The heat of reaction in the experimental result is calculated by species of the reactants and products, whose heat of formation are from the reference (23).
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Table3-18: Moments of inertia (IA, IB, IC) and vibration frequencies of the species in the major channel of trans-ONONO2 + N2H4 reaction computed at PW91PW91/6-311++G(3df,2p).
Species or Transition States
Moments of inertia
Ii(a.u) Vibrational Frequency j (cm-1)
N2H4_PW91PW91 12.6, 74.6, 74.7 434, 766, 958, 1097, 1260, 1290, 1626, 1639, 3367, 3379, 3474, 3480 N2O4_PW91PW91 278.4, 526.5, 804.9 86, 190, 264, 401, 449, 641, 727, 851, 1264, 1407, 1738, 1773
trans-ONONO2_PW91PW91 157.8, 792.9, 947.7 26, 13, 191, 289, 424, 582, 746, 766, 895, 1287, 1686, 1850
Cs-TS1_PW91PW91 495.2, 1481.3, 1811.2 607i, 34, 67, 135, 149, 222, 239, 271, 332, 414, 497, 680, 702, 743, 783, 850, 869, 1002, 1153, 1205, 1325, 1390, 1475, 1516, 1609, 1639, 1753, 3337, 3408, 3469
Cs-omplex1_PW91PW91 521.3, 1411.3, 1713.4
41, 68, 123, 149, 203, 232, 264, 295, 354, 396, 623, 682, 698, 756, 790, 901, 1004, 1107,
1160, 1181, 1208, 1408, 1483, 1614, 1655, 1781, 2536, 3329, 3450, 3465
Cs-Complex2-_PW91PW91 425.4, 2021.8, 2257.7
28, 44, 83, 104, 115, 134, 299, 359, 474, 570, 594, 632, 746, 748, 830, 868, 887, 943, 1160,
1278, 1291, 1342, 1367, 1513, 1612, 1694, 3311, 3317, 3415, 3455
H2NN(H)NO_PW91PW91 87.0, 246.5, 327.0 223, 343, 399, 579, 844, 902, 998, 1165, 1277, 1368, 1488, 1618, 3294, 3417, 3521 HONO2_PW91PW91 140.5, 153.4, 293.9 482, 554, 600, 750, 844, 1267, 1302, 1717, 3629
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Table3-19: Relative energies of species in the major channel of the trans-ONONO2 + N2H4 reaction at various theoretical levels. a
ZPE b PW91PW91
/6-311++G(3df,2p)
CCSD(T)
/6-311+G(d,p) c G2M(CC3) c N2O4+N2H4 46.51 -522.0717000000 -520.9408055 -521.3819786
trans-ONONO2+N2H4 45.23 14.74 6.18 5.88
Cs-Complex1_PW91PW91 47.11 -2.17 -1.48 -3.27
Cs-Complex2_PW91PW91 47.51 -10.25 -17.61 -19.76
Cs-TS1-new_PW91PW91 44.71 -3.28 -7.44 -8.66
H2NN(H)NO+HONO2 46.57 -6.58 -12.37 -14.56
a: The relative energy (kcal/mol) is calculated with the energy of N2O4 (D2h)+N2H4 as reference, whose total energy unit is hartree/molecule.
b: The ZPE is determined by PW91PW91/6-311++G(3df,2p) level, and the energy unit is kcal/mol for every species.
c: The energies are including single-point energies, based on geometries of PW91PW91/6-311++G(3df,2p), and ZPE.
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3.3.2 Decomposition of H2NN(H)NO molecule
The H2NN(H)NO molecule is the product of the lowest-energy path in the N2H4 + isomeric N2O4 reactions, as discussed in the previous section. This molecule can be formed the combination of NO and N2H3 radicals, and we want to know whether there is another lower-energy path to produce highly reactive products in the decomposition reaction. The optimized geometries of stationary points, such as intermediates, transition states, and product molecules, in the reaction are determined at the B3LYP/ 6-311++G(3df,2p) level, as shown in Fig3-11. Further, the full potential energy surface of decomposition reaction is represented in Fig.3-12, and the energies of species are predicted by the G2M(CC1) single-point calculation.
Since this is the decomposition reaction of H2NN(H)NO, we add a notation d in front of the complexes and TSs for easy recognition. The moments of inertia and vibrational frequencies of all species are listed in Table3-20, and the energies by G2M(CC1), CCSD(T)/6-311+G(d,p), and CCSD(T)/6-311++G(3df,2p) are shown in Table3-21.
The H2NN(H)NO molecule is a stable structure, and we separate H2NN(H)NO into three groups, including NH2, NH, and NO for conveniently explaining geometries. Since the two hydrogen atoms of NH2 turn upward to NO tail, the hydrogen bonding makes molecule more stable. However, if the molecule undergoes a dissociation reaction to produce the N2H3+NO radicals, the hydrogen bonding will retard this reaction. Therefore, the possible path to dissociate into two radicals may be that H2NN(H)NO molecule first undergoes NH2
rotation, to form d-Complex1 via d-TS1, turning the two H atoms into the opposite direction, and the energy of d-Complex1 raises as the hydrogen bonding disappears. Furthermore, d-Complex1 undergoes the dissociation reaction producing N2H3 and NO. The energy barrier of d-TS1 is 6.28 kcal/mol, which is the same as d-Complex1 at the G2M(CC1) level. At
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CCSD(T)/6-311++G(3df,2p), it is 6.82 kcal/mol which is higher than d-Complex1 by 0.54 kcal/mol. Moreover, the dissociation from d-Complex1 to N2H3+NO radicals needs 21.55 and 24.06 kcal/mol by G2M(CC1) and CCSD(T), respectively. Comparing the other channels in the H2NN(H)NO molecule decomposition, the channel producing the N2H3+NO radicals is most likely with the lowest-energy path.
Another path is the hydrogen transfer from NH2 group to the oxygen atom of the NO group in the H2NN(H)NO molecule via d-TS2; the energy barrier is only 18.75 and 19.17 kcal/mol with G2M(CC1) and CCSD(T)/6-311++G(3df,2p) methods, respectively. The d-TS2 has a five-member ring structure for hydrogen transfer, which is the major motion in this path, and the imaginary frequency is 1395 cm-1 as shown in Table3-20. However, the N-N bond between the NO and NH group is as short as 1.279Å with an N=N double bond character; the dissociation of d-Complex2 to HON+cis-N2H2 requires very high energy, 62.45 kcal/mol above d-Complex2. In addition, the unstable HON molecule raises the system energy.
Therefore, the formation of d-Complex2 does not lead to another lower-energy path for the decomposition of H2NN(H)NO. Even though the energy of initial hydrogen transfer is low, the high dissociation energy makes this reaction channel be very hard to occur kinetically. On the other hand, the d-Complex2 may undergo a hydrogen transfer reaction via d-TS6, and the d-complex6 dissociates to highly active products, N3H2 + OH radicals, without a barrier.
However, the energy barrier of the hydrogen transfer via d-TS6 is 37.6 kcal/mol computed at G2M(CC1) level. Since the N3H2 radical is highly unstable, the dissociation energy from d-Complex5 to N3H2 + OH is 58.3 kcal/mol. Therefore this channel seems to be difficult to occur kinetically.
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The third reaction is also the hydrogen transfer via d-TS3, whose energy barrier is as high as 43.79 and 44.18 kcal/mol at the G2M(CC3) and CCSD(T)/6-311++G(3df,2p) levels, respectively, and the hydrogen atom is from nitrogen atom of the NH group to that of NO group to form d-Complex3. The d-Complex3 is as stable as the H2NN(H)NO molecule, since this complex also obeys by the Octet rule. However, it needs very high energy to dissociate the d-Complex3 into HNO and H2NN molecules, similar to d-Complex2. The dissociation energy is 53.01 kcal/mol with respect of the d-Complex3, and it is too high to happen. The product, H2NN, is an unstable molecule, which increases the system energy, therefore, we seek another reaction channel from d-Complex3 to produce the N2H2 and HNO. However, in order to form the d-Complex4, it should overcome d-TS4, whose energy barrier is 63.16 kcal/mol at the G2M(CC1) level. Even though d-TS5 is only higher than d-Complex4 by 8.32 kcal/mol, the final products HNO+trans-N2H2 are still controlled by the high barrier of d-TS4.
In conclusion, these decomposition reaction channels cannot compete with the dissociation to NO+N2H3 radicals kinetically.
In the present case, the CCSD(T)/6-311++G(3df,2p) method has been used for comparison with the values of G2M(CC1), since the total number of atom is only seven. The energy differences between CCSD(T)/6-311++G(3df,2p) and G2M(CC1) methods are smaller than 1 kcal/mol for all species except for NO+N2H3, whose G2M value is lower than CCSD(T) by 2.55 kcal/mol. The reason causing the larger energy difference for NO+N2H3 may be the spin contamination on the doublet molecules, since the G2M method use the projection method of MPn and higher level corrections to correct the problem of spin contamination. The other species in this decomposition reaction are all singlet, so the spin-contamination does not affect the energies of G2M and CCSD(T) methods. Therefore, the G2M(CC1) can generally provide good predictions as CCSD(T)/6-311++G(3df,2p) does, and it can also save the
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computational resource. On the other hand, comparing with the CCSD(T)/6-311++G(3df,2p) and G2M(CC1) methods, the CCSD(T)/6-311+G(d,p) method underpredicts the energies of product molecules, and there is no systematic correlation for complexes and transition states.
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91
92
Fig3-11: The stationary points in the PES of H2NN(H)NO decomposition are optimized by B3LYP/6-311++G(3df,2p)
93
Fig3-12: Potential Energy Surface of H2NN(H)NO decomposition, whose energies are calculated by G2M(CC1) // B3LYP/6-311++G(3df,2p).
0 kcal/mol
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Table3-20: Moments of inertia (IA, IB, IC) and vibration frequencies of the species in H2NN(H)NO decomposition computed at B3LYP/6-311++G(3df,2p).
Species or
Transition States Moments of inertia Ii(a.u) Vibrational Frequency υj (cm-1)
H2NN(H)NO 85.7, 251.3, 327.5 38, 288, 324, 589, 871, 901, 1042, 1219, 1330, 1411, 1585, 1695, 3454, 3515, 3634 d-complex1 79.4, 271.1, 340.5 151, 212, 332, 583, 674, 901, 978, 1168, 1285, 1433, 1630, 1672, 3504, 3567, 3600 d-complex2 86.3, 228.8, 315.1 378, 444, 586, 667, 815, 871, 1037, 1169, 1317, 1430, 1522, 1620, 3421, 3485, 3547 d-complex3 82.4, 236.4, 317.5 366, 496, 580, 627, 798, 858, 1128, 1247, 1325, 1493, 1562, 1617, 3439, 3471, 3672 d-complex4 79.7, 251.6, 331.3 178, 316, 515, 651, 847, 852, 1084, 1228, 1376, 1502, 1541, 1592, 3420, 3530 d-complex5 907, 386.8, 470.9 129, 161, 224, 360, 368, 565, 1305, 1307, 1534, 1572, 1582, 1686, 2960 3120, 3284 d-complex6 86.1, 236.9, 320.3 353, 416, 545, 574, 813, 911, 1031, 1130, 1342, 1469, 1507, 1565, 3470, 3503, 3580 d-TS1 81.5, 259.2, 334.4 205, 177, 340, 538, 766, 923, 967, 1178, 1314, 1436, 1586, 1648, 3469, 3585, 3609 d-TS2 91.9, 201.7, 291.8 1395i, 479, 573, 693, 796, 935, 1098, 1160, 1177, 1266, 1373, 1546, 2125, 3564, 3583 d-TS3 85.6, 231.8, 310.4 1570i, 374, 393, 598, 654, 786, 890, 1087, 1268, 1299, 1403, 1545, 2012, 3399, 3690 d-TS4 84.1, 244.2, 323.0 1700i, 335, 503, 624, 681, 853, 914, 1095, 1252, 1382, 1435, 1520, 2614, 3331, 3455 d-TS5 89.2, 266.3, 349.4 375i, 265, 392, 555, 726, 1069, 1152, 1184, 1346, 1434, 1529, 1637, 2965, 3042, 3397 d-TS6 88.1, 225.5, 307.6 1607i, 354, 605, 700, 773, 876, 926, 1061, 1138, 1356, 1428, 1527, 2165, 3183, 3516 N2H3 8.8, 58.6, 66.5 548, 696, 1136, 1238, 1479, 1658, 3425, 3488, 3632
NO 0, 34.9, 34.9 1979
HON 2.8, 45.2, 48.0 1282, 1489, 3107
HNO 3.2, 41.9, 45.1 1562, 1672, 2876
H2NN 5.4,46.0, 51.4 100.8, 1329, 1612, 1733, 2998, 3036 trans-N2H2 5.9, 45.4, 51.3 1341, 1351, 1588, 1652, 3235, 3036
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cis-N2H2 6.1, 45.6, 51.8 1281, 1361, 1555, 1651, 3102, 3195
N3H2 11.2, 153.1, 163.1 556, 642, 725, 1197, 1249, 1356, 1660, 3439, 3445
OH 0.0, 3.2, 3.2 3722
Table3-21: Relative energies of species in H2NN(H)NO decomposition computed at various theoretical levels. a
ZPE b B3LYP
/6-311++G(3df,2p) c
CCSD(T) /6-311+G(d,p) c
CCSD(T)
/6-311++G(3df,2p) c G2M(CC1) c
H2NN(H)NO 31.3 -151368.1213 -150999.8933 -151090.8409 -151137.0469
d-complex1 31.01 5.57 6.02 6.32 6.28
d-complex2 31.89 14.85 16.05 14.22 13.8
d-complex3 32.42 -1.09 1.45 0.06 -0.37
d-complex4 31.57 28.16 34.29 30.64 29.82
d-complex5 28.82 25.51 25.13 28.29 28.01
d-complex6 31.7 5.74 5.88 6.02 5.89
N2H3+NO 27.56 31.07 26.48 30.38 27.83
HON+cis-N2H2 25.76 78.02 73.68 76.19 76.25
HNO+H2NN 25.79 53.27 49.31 52.76 52.69
HNO+trans-N2H2 26.51 32.83 29.37 33.43 33.31
N3H2+OH 25.72 53.62 56.52 60.49 64.16
d-TS1 30.79 5.96 6.9 6.86 6.28
d-TS2 29.12 18.76 20.05 19.17 18.75
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d-TS3 27.73 44.18 45.11 44.18 43.79
d-TS4 28.58 66.61 68.04 66.15 65.33
d-TS5 29.58 36.17 38.56 38.75 38.15
d-TS6 28.03 52.02 52.24 51.88 51.4
a: The relative energy (kcal/mol) is based on the energy of N2O4 (D2h)+N2H4 as reference, whose energy unit is hartree/molecule.
b: The ZPE is determined by B3LYP/6-311++G(3df,2p) level, and the energy unit is kcal/mol for every species.
c: The energies are including single-point energies, based on geometries of B3LYP/6-311++G(3df,2p), and ZPE.
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3.3.3 N2H4+N2O4 (D2h) reaction
We consider the reaction of N2O4(D2h) and N2H4 in this section. Since high-symmetry N2O4 (D2h) molecule is less reactive than the monomer NO2, the reaction channels in N2H4+N2O4 (D2h) are not as many intuitively. The products are the same as those in the previous reactions, such as H2NN(H)NO2, H2NN(H)ONO, NO2, trans-HONO, cis-HONO, and N2H3 radical. All geometries of species in this potential energy surface are optimized at the B3LYP/6-311++G(3df,2p) level, and the details of bond lengths and angles are shown in Fig3-13. The potential energy surface is based on the single-point energies determined by G2M(CC3) in Fig3-14. It is easier to recognize the species in PES from other reactions, if we add a notation D2h in front of the complexes and TSs. The information, including the moments of inertia and vibrational frequencies, are listed in Table3-22; moreover, the energies by different computational methods with the zero-point energy (ZPE) of B3LYP/6-311++G(3df,2p) are compared in Table3-23
The N2O4(D2h) and N2H4 form an intermediate, D2h-Complex1, due to the physical attraction and hydrogen bonding, and the energy is lower than the reactants by 6.98 kcal/mol at the G2M(CC3) level. Basically the N2O4 and N2H4 molecules in the D2h-Complex1 have the same geometries as those in the individual molecules, the nearest distance between these two molecules is 2.662Å. There are three channels starting from D2h-Complex1 in the PES, and the lowest-energy path is to produce the H2NN(H)NO2 and trans-HONO molecules via D2h-TS1. The structure of five-member ring in D2h-TS1 connects the two nitrogen and one oxygen atoms of N2O4 with one nitrogen atom and one hydrogen atom of N2H4, as in Fig.3-13.
The N-N bond of N2O4 twists to make the planes of two NO2 group be perpendicular, and the nitrogen atom of the NO2 group connects with the one of nitrogen atoms of the N2H4 molecule as the two oxygen atoms is parallel with the N-N bond of N2H4 upwardly. The
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structure of N2H4 in the D2h-TS1 makes two hydrogen atoms point upward to one oxygen atom, and it forms the hydrogen bonds and reduces the system energy as in Cs-TS1 and Cs-TS2. The major motion of D2h-TS1 is the hydrogen transfer to form the trans-HONO with the concerted formation of H2NN(H)NO2. The energy barrier is 14.16 and 21.14 kcal/mol above the reactants and D2h-Complex1 at the G2M(CC3) level. The products H2NN(H)NO2
and trans-HONO, from D2h-Complex2, have appeared in the N2H4+cis-ONONO2 reaction;
therefore, we will discuss further about the decomposition reaction of H2NN(H)NO2 molecule in the next section. The D2h-TS4 has the a six-member ring structure, as shown in Fig.3-13.
The hydrogen transfer reaction from N2H4 to one of the NO2 groups is accompanied by the formation N-O bond between N2H4 and the other NO2 group, and the breaking of the N-N bond of N2O4, producing trans-HONO and H2NN(H)ONO. However, the energy barrier is higher than D2h-TS1 by 6.7 kcal/mol. Comparing with the structure between two transition states, it is apparent that the D2h-TS1 has tight connection with each element in the ring, whereas the ring structure of D2h-TS4 is relatively loose. The N-N bond length of the N2O4 molecule is 2.257 and 2.672 Å in D2h-TS1 and D2h-TS4, respectively. The motion of breaking the N-N bond in D2h-TS1 is more drastic than that in D2h-TS4, which means that it needs to elongate the N-N bond before reaching the D2h-TS4. Therefore, the barrier of D2h-TS3 is higher than the D2h-TS1. On the other hand, the products of the D2h-TS4 are H2NN(H)ONO and trans-HONO molecules, dissociated from D2h-Complex5, have also appeared in the cis-ONONO2+N2H4 reaction, we will not discuss the decomposition of the H2NN(H)ONO molecule due to the higher energy for its formation.
D2h-TS3 is the transition state which is not originated from the D2h-Complex1 but directly from the reactants, N2H4 and N2O4, attributable to the unique structure of the D2h-TS3, which is the ball-like geometries with C2 symmetry, and it is difficult to achieve this structure from other intermediates. Every oxygen atoms of N2O4 molecule connects with the hydrogen
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atoms of N2H4 molecule without repetition, and the dihedral angle of four nitrogen atoms is 4o, which means nearly on one plane. Due to the C2 symmetry, the distances between hydrogen atom and oxygen atom on the diagonal position are the same. One pair of N-O distance is short as 1.836Å, whereas the other pair of N-O distance is long as 2.406Å. This structure indicates that the two hydrogen transfer reaction occur concurrently in the D2h-TS3 with the breaking N-N bond of the N2O4 molecule, and its energy barrier is 21.37 and 25.07 kcal/mol obtained at G2M(CC3) and CCSD(T)/6-311+G(d,p) levels. The reaction via the D2h-TS3 produces the D2h-Complex4, including two cis-HONO and one trans-N2H2 molecules, with 11.8 kcal/mol exothermally.
The last reaction channel in the N2H4+N2O4(D2h) reaction is the transfer of only one hydrogen atom to an oxygen atom of N2O4 via D2h-TS2, whose geometry is shown in Fig3-13.
The seven-member ring is constructed by the H-N-N-N atoms of N2H4 and the O2N group of N2O4 molecule; D2h-TS2 has the C1 symmetry. The distance between oxygen and hydrogen atoms on the side not being transferred is 2.255 Å, and the connection is built up by the hydrogen bond. On the other side of the seven-member ring, the hydrogen atom is 1.515Å far from the nitrogen atom of N2H4 and much closer to the oxygen atom of N2O4, 1.062 Å. The position of hydrogen atom in D2h-TS2 is different comparing with the other transition states of hydrogen transfer, which is much closer to the bonding N atom of N2H4 and far away from the N or O atoms of N2O4 isomers. Therefore, it is believed that the high energy barrier predicted by B3LYP/6-311++G(3df,2p) is reasonable, since the hydrogen atom needs to elongate the N-H bond by raising energy. However, the prediction of CCSD(T)/6-311+G(d,p) and G2M(CC3) methods are very low, which is the contrary result to that of B3LYP, as shown in Table3-23. The IRC calculation confirms the large difference of energy between D2h-Complex1 and D2h-TS2. Therefore, we assume the strange results in CCSD(T) and G2M(CC3) single-point energy calculations are caused by the incorrect prediction in the
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electronic energy instead the geometry optimized by B3LYP/6-311++G(3df,2p). Since the G2M methods are based on the correction with CCSD(T)/6-311G(d,p), it is understandable that the G2M and CCSD(T) have problems at the same time. On the other hand, the D2h-Complex3, composed of a N2H3 radical and cis-HONO molecule, forms with the breaking N-N bond of N2O4 after passing over the D2h-TS2. The total energy of D2h-Complex3 and NO2 should be lower than that of D2h-TS2, therefore, it is another proof that the single-point energies of CCSD(T) and G2M are incorrect.
In Table3-23, comparing with the energies determined by CCSD(T)/6-311+G(d,p) and G2M(CC3), it is difficult to summarize a systematic relationship. Most of the energies at CCSD(T)/6-311+G(d,p) level is lower than those at G2M(CC3), but it has a opposite relationship in transition states. Therefore, the difference of intermediate and transition states at CCSD(T) is larger than those at G2M. This is not consistent with the relationship in section3.3.1. Moreover, if we compare the heat of reaction with experimental results, it is apparent that the G2M(CC3) performs well for the production of cis-N2H2+ 2 cis-HONO only, whereas the CCSD(T)/6-311+G(d,p) performs bad at both cases. Therefore, it is very important to decide which lower single-point energy computation can perform well for this larger system, and we will discuss this topic in section 3.3.5.
Observing the full PES of N2H4 with N2O4 isomers, it is consistent that all of the complexes passing over the TSs, including Cs-Complex2, 4, 6, 8 and D2h-Complex2, 3, 4, 5, still need high energy to separate the product molecules. The dissociation energy of these complexes are 3~8 kcal/mol for two-molecular cases and 11~14 kcal/mol for three-molecular cases at the G2M(CC3) level. This phenomenon of high complexation energies is caused by the strong hydrogen bonds as appears in the NO2 reaction, discussed in section 3.1. Even though these dissociation energies from complexes to molecules are high, most of the energies of final products are lower than the reactants, N2H4+N2O4; they are all formed exothermically.
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Fig3-13: The stationary points in the PES of N2O4 (D2h) + N2H4 reaction are optimized by B3LYP/6-311++G(3df,2p)
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Fig3-14: Potential Energy Surface of the N2O4 (D2h) + N2H4 reaction, whose energies are calculated by G2M(CC3) // B3LYP/6-311++G(3df,2p).
N2H4+N2O4(D2h)
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Table3-22: Moments of inertia (IA, IB, IC) and vibration frequencies of the species in the N2O4 (D2h) + N2H4 reaction computed at B3LYP/6-311++G(3df,2p).
Species or Transition States
Moments of inertia
Ii(a.u) Vibrational Frequency υj (cm-1)
N2H4 12.4, 74.2, 74.3 439, 801, 974, 1114, 1294, 1323, 1674, 1686, 3462, 3471, 3562, 3568 N2O4 273.2, 500.4, 773.7 87, 222, 293, 446, 490, 704, 760, 850, 1307, 1450, 1787, 1826
D2h-Complex1 776.6, 1229.5, 1435.3 30, 53, 61, 74, 107, 115, 164, 234, 302, 451, 463, 505, 701, 767, 822, 853, 995, 1116, 1295, 1311, 1331, 1448, 1673, 1686, 1787, 1823, 3455, 3471, 3555, 3564
D2h-Complex2 516.9, 2021.0, 2135.4 38, 57, 64, 92, 135, 163, 221, 318, 381, 482, 607, 673, 767, 801, 815, 841, 869, 989, 1223, 1320, 1368, 1412, 1439, 1693, 1703, 1763, 3477, 3520, 3549, 3573
D2h-Complex3 190.8, 649.9, 839.4 82, 149, 191, 206, 256, 268, 496, 717, 735, 1032, 1056, 1146, 1308, 1468, 1504, 1623, 1663, 2802, 3488, 3494, 3625
D2h-Complex4 267.9, 4696.8, 4964.6 9, 21, 33, 40, 40, 87, 121, 150, 179, 181, 255, 315, 678, 896, 902, 936, 937, 1332, 1346, 1427, 1432, 1579, 1677, 1687, 1690, 3284, 3313, 3330, 3354
D2h-Complex5 666.4, 1857.8, 2282.0 35, 55, 74, 94, 152, 164, 166, 201, 342, 427, 506, 540, 635, 698, 825, 865, 892, 964, 1069, 1188, 1349, 1461, 1497, 1687, 1749, 1797, 3415, 3468, 3509, 3578
D2h-TS1 717.6, 1072.4, 1381.5 223i, 48, 126, 144, 205, 213, 255, 287, 354, 388, 488, 551, 769, 814, 867, 883, 1134, 1196, 1231, 1275, 1309, 1437, 1596, 1626, 1695, 1712, 2613, 3466, 3515, 3569
D2h-TS2 503.1, 1969.7, 2073.4 246i, 28, 34, 79, 88, 143, 163, 205, 236, 270, 315, 427, 498, 720, 766, 828, 886, 1099, 1144, 1249, 1346, 1457, 1479, 1588, 1652, 1677, 1987, 3457, 3490, 3694
D2h-TS3 840.0, 981.8, 1277.8 198i, 101, 111, 140, 151, 158, 191, 194, 254, 260, 323, 467, 473, 716, 795, 815, 905, 1142, 1227, 1253, 1351, 1450, 1533, 1565, 1642, 1678, 3055, 3094, 3573, 3586 D2h-TS4 1051,6, 1084.9, 2055.5 1332i, 31, 54, 79, 108, 123, 154, 189, 222, 244, 268, 299, 538, 633, 710, 740, 849,
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1129, 1204, 1224, 1325, 1416, 1546, 1599, 1613, 1659, 1678, 3493, 3554, 3618
H2NN(H)NO2 155.4, 34.6, 534.8 173, 313, 330, 499, 591, 790, 795, 852, 976, 1236, 1315, 1367, 1430, 1663, 1705, 3471, 3562, 3576 H2NN(H)ONO 80.4, 672.2, 687.1 96, 187, 323, 438, 501, 555, 612, 832, 967, 1042, 1189, 1335, 1504, 1687, 1766, 3453, 3515, 3584 trans-HONO 19.0, 143.1, 162.1 590, 621, 819, 1303, 1783, 3773
cis-N2H2 6.1, 45.6, 51.8 1281, 1361, 1555, 1651, 3102, 3195
NO2 7.4, 137.6, 145.0 767, 1395, 1703
N2H3 8.8, 58.6, 66.5 548, 696, 1136, 1238, 1479, 1658, 3425, 3488, 3632
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Table3-23: Relative energies of species in N2O4 (D2h) + N2H4 reaction computed at various theoretical levels. a ZPE b B3LYP/
6-311++G(3df,2p)
CCSD(T)/
6-311+G(d,p) c G2M(CC3) c ∆HExpd
N2O4+N2H4 48.02 -522.173728 -520.938139 -521.3804132
D2h-Complex1 48.91 -3.03 -7.34 -6.98
D2h-Complex2 49.11 -17.74 -24.86 -24.94
D2h-Complex3 + NO2 39.04 3.73 2.18 8.28
D2h-Complex4 45.62 -16.87 -29.36 -26.26
D2h-Complex5 47.75 -1.98 -13.27 -11.33
H2NN(H)NO2+trans-HONO 47.93 -15.26 -19 -19.73
cis-N2H2+ 2 cis-HONO 42.69 -3.96 -13.66 -11.75 -11.75
H2NN(H)ONO+trans-HONO 46.42 3.31 -5.39 -3.83
trans-HONO+N2H3+NO2 42.92 13.94 12.64 19.05 15.94
D2h-TS1 48.27 12.82 16.25 14.16
D2h-TS2 44.24 38.18 -9.27 1.16
D2h-TS3 45.98 23.67 25.07 21.37
D2h-TS4 43.32 36.57 19.94 20.86
a: The relative energy (kcal/mol) is taken the energy of N2O4 (D2h)+N2H4 as reference, whose energy unit is hartree/molecule.
b: The ZPE is determined by B3LYP/6-311++G(3df,2p) level, and the energy unit is kcal/mol for every specie.
c: The energies are including single-point energies, based on geometries of B3LYP/6-311++G(3df,2p), and ZPE.
d:The heat of reaction in the experimental result is calculated by species of the reactants and products, whose heat of formation are from the reference (23).
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3.3.4 Decomposition of H2NN(H)NO2 molecule
The H2NN(H)NO2 molecule is the product of lowest-energy path via D2h-TS1 in the N2H4+N2O4(D2h) reaction; it also appears in the lowest-energy path via Cs-TS2 in the N2H4+cis-ONONO2 (Cs) reaction. In this section, we denote this molecule separately into three groups, including NH2, NH, and NO2, for describing the geometries in the PES conveniently. This molecule can be formed by the combination of NO2 and N2H3 radicals.
The products H2NN(H)NO2 + trans-HONO are energetically more stable than that of H2NN(H)NO + HONO2. However, the oxygen atoms of NO2 group may provide more possibilities to generate the active and exothermic products in different channels of the decomposition reaction. All geometries of the optimized species, such as intermediates, transition states, and products, are shown in Fig3-15. To distinguish the complexes and TSs in this reaction, we make a notation “d2” in front of them. The PES represents all decomposition channels in Fig.3-16, and the relative energies of the species are determined by G2M(CC1) method. Moreover, the moments of inertia and vibrational frequencies of the species are listed in Table3-24, and the energies calculated by different methods as shown in Table3-25.
Since H2NN(H)NO2 is the most stable configuration on the PES, all of reaction channels start from this molecule, and there is no other configurations of the molecule appearing in the PES. The first decomposition path is to form the NO2 and N2H3 radicals directly, with this dissociation energy of 38.23 kcal/mol at the G2M(CC1) level. Unlike the decomposition reaction of H2NN(H)NO, whose dissociation energy is 27.86 kcal/mol, the
Since H2NN(H)NO2 is the most stable configuration on the PES, all of reaction channels start from this molecule, and there is no other configurations of the molecule appearing in the PES. The first decomposition path is to form the NO2 and N2H3 radicals directly, with this dissociation energy of 38.23 kcal/mol at the G2M(CC1) level. Unlike the decomposition reaction of H2NN(H)NO, whose dissociation energy is 27.86 kcal/mol, the