DFT Studies on the Acid Catalyzed Curtius Reaction: The Schmidt Reaction
Rita Kakkar*, Ritu Arora & Sheza Zaidi
Computational Chemistry Group, Department of Chemistry, University of Delhi, Delhi-110007
S.1Parent Compound
Scheme S.1
Figure S.1.1 Energy profile for the protonated formyl azide rearrangement in the gas phase (solid lines) and the aqueous phase (dotted lines)
Table S.1.1 NBO analysis
a) Interaction energy between donor and acceptor orbitals for protonated isocyanate ion
NBO donor / NBO acceptor / E (kcal mol-1)Gas phase / Aqueous phase
σ(C-O) / σ*(C-N) / 6.3 / 6.1
π1(C-O) / π1*(C-O) / 1.2 / 1.3
π2(C-O) / σ*(H1-N) / 2.4 / 2.1
π2(C-O) / σ*(N-H) / 2.4 / 2.1
σ(C-N) / σ*(C-O) / 5.9 / 5.9
σ(H1-N) / σ*(C-O) / 4.7 / 5.0
σ(H1-N) / π2*(C-O) / 8.7 / 9.5
σ(N-H2) / σ*(C-O) / 4.7 / 5.0
σ(N-H2) / π2*(C-O) / 8.7 / 9.5
n(O) / σ*(C-N) / 10.4 / 10.1
n(N) / π1*(C-O) / 91.1 / 100.6
b) Occupancy of donor and acceptor orbitals for protonated isocyanate ion
NBO / OccupancyGas phase / Aqueous phase
σ(C-O) / 1.99670 / 1.99687
π1(C-O) / 1.99881 / 1.99883
π2(C-O) / 1.99012 / 1.99136
σ(C-N) / 1.99579 / 1.99579
σ(H1-N) / 1.96208 / 1.95756
σ(N-H2) / 1.96206 / 1.95755
n(O) / 1.97905 / 1.97963
n(N) / 1.66111 / 1.63068
σ*(C-O) / 0.00968 / 0.01022
π1*(C-O) / 0.32587 / 0.35570
π2*(C-O) / 0.06263 / 0.07051
σ*(C-N) / 0.01203 / 0.01153
σ*(H1-N) / 0.00520 / 0.00466
σ*(N-H2) / 0.00520 / 0.00466
Table S.1.2NBO analysis
a) Interaction energy between donor and acceptor orbitals for formylnitrenium ion
NBO donor / NBO acceptor / E (kcal mol-1)Gas phase / Aqueous phase
σ(C-O) / π*(C-O) / 1.3 / 1.0
σ(C-O) / σ*(C-H1) / 0.8 / 0.8
σ(C-O) / σ*(O-N) / 3.6 / 3.5
π(C-O) / σ*(C-O) / 1.0 / 0.7
π(C-O) / π*(C-O) / 1.7 / 1.3
π(C-O) / σ*(N-H2) / 3.9 / 3.2
σ(C-N) / σ*(C-H1) / 0.8 / 0.7
σ(C-N) / σ*(O-N) / 5.2 / 5.4
σ(O-N) / σ*(C-O) / 8.2 / 8.2
σ(O-N) / π*(C-O) / 2.7 / 1.7
σ(O-N) / σ*(C-H1) / 17.9 / 16.4
σ(O-N) / π*(C-N) / 8.0 / 7.8
σ(N-H2) / σ*(C-O) / 1.1 / 0.9
σ(N-H2) / π*(C-O) / 5.2 / 6.7
n(O) / σ*(C-H1) / 0.9 / 0.7
n(O) / σ*(O-N) / 0.6 / 0.6
n(N) / π*(C-O) / 15.5 / 12.8
n(N) / σ*(C–H1) / 1.1 / 1.0
n(N) / σ*(O-N) / 0.5 / 0.6
n(N) / σ*(N-H2) / 1.5 / 1.4
π*(C-O) / σ*(C-O) / 4.2 / 2.1
π*(C-O) / σ*(C-N) / 0.6 / -
π*(C-O) / σ*(N-H2) / 1.1 / 0.8
b) Occupancy of donor and acceptor orbitals for formyl nitrenium ion
NBO / OccupancyGas phase / Aqueous phase
σ(C-O) / 1.98425 / 1.98462
π(C-O) / 1.98847 / 1.99094
σ(C-H1) / 1.99684 / 1.99692
σ(C-N) / 1.97545 / 1.97484
σ(O-N) / 1.94678 / 1.95012
σ(N-H2) / 1.94395 / 1.94239
n(O) / 1.99253 / 1.99297
n(N) / 1.86656 / 1.89109
σ*(C-O) / 0.01931 / 0.01509
π*(C-O) / 0.16803 / 0.14931
σ*(C-H1) / 0.03066 / 0.02739
σ*(C-N) / 0.00953 / 0.00898
σ*(O-N) / 0.03338 / 0.03449
σ*(N–H2) / 0.01394 / 0.01194
Table S.1.3NBO analysis
a) Interaction energy between donor and acceptor orbitals for TS4
NBO donor / NBO acceptor / E (kcal mol-1)Gas phase / Aqueous phase
π(C-O) / n*(N) / 32.2 / 42.9
π(C-O) / n*(N) / 12.4 / -
σ(C-H1) / π*(C-O) / 3.0 / -
σ(C-H1) / σ*(N-H2) / 1.2 / 1.3
σ(C-N) / n*(N) / 2.1 / -
σ(N-H2) / π*(C-O) / 2.5 / 2.3
σ(N-H2) / σ*(C-H1) / 1.9 / 2.6
σ(N-H2) / σ*(C-N) / 1.1 / 0.9
n2(O) / π*(C-O) / 1.5 / 0.6
n2(O) / σ*(C-H1) / 17.3 / 15.7
n2(O) / σ*(C-N) / 25.1 / 27.3
n(N) / σ*(C–O) / 7.2 / 6.1
n(N) / π*(C-O) / 0.5 / 0.7
n(N) / σ*(C-H1) / 1.7 / 1.1
n*(N) / π*(C-O) / 10.2 / 6.7
n*(N) / σ*(C-H1) / 0.6 / -
n*(N) / σ*(C-N) / 2.6 / -
b) Occupancy of donor and acceptor orbitals for TS4
NBO / OccupancyGas phase / Aqueous phase
σ(C-O) / 1.99931 / 1.99896
π(C-O) / 1.75545 / 1.73656
σ(C-H1) / 1.88943 / 1.98776
σ(C-N) / 1.99528 / 1.99614
σ(O-N) / - / -
σ(N-H2) / 1.98170 / 1.98158
n(O) / 1.98684 / 1.98768
n2(O) / 1.79664 / 1.87271
n(N) / 1.97352 / 1.97190
n*(N) / 0.40285 / 0.27279
σ*(C-O) / 0.02163 / 0.01979
π*(C-O) / 0.01395 / 0.01103
σ*(C-H1) / 0.05150 / 0.04789
σ*(C-N) / 0.09062 / 0.07489
σ*(O-N) / - / -
σ*(N–H2) / 0.00676 / 0.00716
Table S.1.4aInteraction energy between donor and acceptor orbitals for the transition state (TS2) for the concerted Schmidt rearrangement in the gas phase
NBO donor / NBO acceptor / Eσ(N-H2) / π*(C-O) / 8.3
σ(N-H2) / σ*(N1-N2) / 1.4
σ(N-H2) / σ*(N1-O) / 17.7
σ(C-N1) / σ*(N1-N2) / 158.2
σ(C-N1) / σ(N1-O) / 391.0
n(N3) / σ*(N1-N2) / 2.5
σ(N1-N2) / σ*(N1-N2) / 24.0
σ(N1-N2) / σ(N1-O) / 106.4
π(N2-N3) / σ*(N1-N2) / 1.1
σ(C-H1) / σ*(N1-N2) / 24.1
σ(C-H1) / σ*(N1-O) / 13.1
n(N1) / σ*(C-O) / 9.1
n(N1) / σ*(N1-O) / 5.6
σ*(N1-O) / π(C-O) / 3.1
σ*(N1-O) / σ(N1-N2) / 50.3
σ*(N1-O) / σ(N1-O) / 46.4
π*(C-O) / σ*(N1-N2) / 3.0
σ*(N1-N2) / σ*(N1-O) / 397.2
σ*(N1-N2) / σ*(C-N1) / 16.7
Table S.1.4bInteraction energy between donor and acceptor orbitals for the transition state (TS2) for the concerted Schmidt rearrangement in the aqueous phase
NBO donor / NBO acceptor / E (kcal mol-1)σ(N-H2) / σ*(C-O) / 8.1
σ(N-H2) / σ*(N1-N2) / 0.7
σ(N-H2) / σ*(N2-N3) / 1.3
σ(C-N1) / π*(C-O) / 3.4
σ(C-N1) / σ*(N1-N2) / 1.0
n(N3) / σ*(N1-N2) / 5.3
σ(N1-N2) / π*(N2-N3) / 4.3
π(N2-N3) / σ*(N1-N2) / 1.0
σ(C-H1) / σ*(N1-N2) / 54.8
n(N1) / π*(C-O) / 19.2
n2(O) / σ*(C-H1) / 27.3
n2(O) / σ*(C-N1) / 18.5
n2(O) / σ*(N1-N2) / 1.8
σ(C-O) / σ*(C-N1) / 2.8
σ(C-O) / σ*(C-H1) / 1.4
π(C-O) / σ*(C-H1) / 1.1
π(C-O) / σ*(C-N1) / 1.2
π*(C-O) / σ*(C-N1) / 7.8
σ*(N1-N2) / π2*(N2-N3) / 6.7
Table S1.5 Calculated vibrational wavenumbersa (cm−1) and intensities (km mol-1) at the B3LYP/6-311+G(d,p) level for the stationary points of protonated formyl azide. Figures in parentheses are the computed intensities in km mol-1.
Syn / Anti / TS1 / TS2 / TS3 / TS4 / NHCHO+ +N2 / OCNH2+ +N23480
(230) / 3459
(230) / 3446
(201) / 3387
(178) / 3383
(151) / 3249
(155) / 3370
(153) / 3498
(341)
3107
(9) / 3095
(2) / 3140
(14) / 2444
(47) / 3152
(15) / 2840
(220) / 3170
(32) / 3128
(1501)
2359
(93) / 2343
(137) / 2345
(148) / 2416
(196) / 2436
(82) / 1570
(47) / 2445
(44) / 2456
(15)
1917
(210) / 1934
(321) / 1972
(270) / 2001
(218) / 1720
(42) / 1285
(18) / 1681
(50) / 2421
(564)
1411
(122) / 1406
(77) / 1384
(37) / 1218
(28) / 1310
(8) / 1135
(124) / 1344
(5) / 1588
(110)
1342
(2) / 1331
(2) / 1265
(2) / 1161
(7) / 1200
(9) / 931
(52) / 1167
(15) / 1240
(0)
1136
(128) / 1170
(67) / 1158
(109) / 912
(17) / 1045
(44) / 789
(64) / 1045
(11) / 1138
(8)
964
(2) / 962
(2) / 974
(30) / 860
(14) / 1019
(42) / 601
(69) / 965
(114) / 706
(183)
801
(43) / 848
(276) / 662
(227) / 632
(124) / 689
(92) / 709i
(216) / 723
(91) / 577
(43)
645
(232) / 529
(21) / 588
(28) / 552
(5) / 398
(113) / 408
(144) / 502
(1)
538
(1) / 480
(121) / 496
(9) / 463
(15) / 257
(22) / 195
(14) / 305
(43)
396
(17) / 433
(23) / 380
(179) / 193
(11) / 215
(9) / 158
(16) / 176
(46)
306
(120) / 388
(151) / 331
(39) / 155
(10) / 114
(4) / 119
(36) / 147
(11)
227
(35) / 182
(15) / 173
(8) / 93
(7) / 112
(10) / 96
(9) / 126
(2)
146
(4) / 111
(4) / 168i
(42) / 512i
(365) / 127i
(219) / 77
(48) / 57
(5)
aScaled by 0.9679
Isomers of formyl nitrenium ion
The potential surface of singlet formyl nitrenium ion has been explored by means of DFT calculations at the B3LYP/6-311+G(d,p) level. The potential energy surface of [H2, C, N, O]+ has been already studied by means of high-level ab initiocalculations at G2 theory[1]. They found 13 isomers on the singlet potential energy surface of [H2, C, N, O]+ whereas we found a total of 14 isomers.The isomers and some of the possible transition states connecting these isomers are given in Figure S.1.2. Since we are interested in the Schmidt rearrangement, the potential energy surface relative to the gas phase Gibbs energy of syn conformer is considered. The isomers are labelled from 1 to 14 in the order of increasing gas phaseGibbs energy. The formyl nitrenium ion (I) holds position 7 and the product of Schmidt rearrangement, N-protonated isocyanate ion (labelled 1) is the global minimum both in the gas phase and the aqueous phase.The overall activation energies of the possible isomerization pathways from 7 to 1 are quite high and are unlikely to take place under the near thermal conditions. From the point of view of thermal Schmidt rearrangement, these pathways can only be considered at very high temperature or under photolytic conditions.
Figure S.1.2 Energy profile for the formyl nitrenium ion rearrangement in the gas phase and the aqueous phase (parenthesized values)
Note – The isomer 12 was not found to be stable in the aqueous phase and therefore, the corresponding values are missing in the figure.
S.2Methyl Substitution
Scheme S.2
Figure S.2.1 Energy profile for the protonated acetyl azide rearrangement in the gas phase (solid lines) and the aqueous phase (dotted lines)
Table S.2.1 Structural parameters (Å and degrees) and rotational constants (GHz) of the stationary points on the potential energy surface on methyl substitution in the gas phase and the aqueous phase (parenthesized values)
Parametersa / Syn / Anti / TS1 / TS2 / TS3 / TS4 / NHC(CH3)O+Bond Lengths
C1-N1 / 1.619
(1.508) / 1.654
(1.515) / -
(1.681) / 1.374
(1.361) / 1.430
(1.413) / -
(1.370) / 1.354
(1.357)
N1-N2 / 1.273
(1.269) / 1.268
(1.269) / -
(1.263) / 1.848
(1.848) / 1.821
(1.863) / - / -
N2-N3 / 1.113
(1.109) / 1.115
(1.110) / -
(1.114) / 1.097
(1.095) / 1.098
(1.095) / - / -
C1=O / 1.166
(1.188) / 1.161
(1.867) / -
(1.166) / 1.175
(1.186) / 1.206
(1.216) / -
(1.210) / 1.252
(1.254)
C1-C2 / 1.482
(1.480) / 1.480
(1.480) / -
(1.466) / 1.598
(1.567) / 1.471
(1.458) / -
(1.456) / 1.444
(1.432)
N1-H / 1.021
(1.027) / 1.023
(1.027) / -
(1.028) / 1.031
(1.037) / 1.030
(1.036) / -
(1.047) / 1.034
(1.037)
N1-C2 / 2.533
(2.457) / 1.654
(1.515) / -
(2.552) / 2.211
(2.178) / 2.609
(2.592) / -
(2.205) / 2.657
(2.640)
O-N1 / 2.359
(2.311) / 2.337
(2.264) / -
(2.415) / 2.363
(2.355) / 1.998
(1.975) / -
(2.026) / 1.642
(1.657)
Bond Angles
C1N1N2 / 116.9
(118.8) / 127.1
(124.3) / -
(117.6) / 110.0
(109.0) / 117.6
(113.4) / - / -
N1N2N3 / 170.9
(173.9) / 174.3
(176.9) / -
(174.4) / 158.5
(161.3) / 157.0
(159.1) / - / -
N1C1O / 114.8
(117.6) / 111.1
(113.4) / -
(114.9) / 135.9
(135.1) / 98.2
(97.1) / -
(117.3) / 78.0
(78.7)
N1C1C2 / 109.4
(110.6) / 112.2
(115.3) / -
(108.2) / 95.8
(95.8) / 128.1
(129.1) / -
(102.6) / 143.5
(142.5)
Dihedral Angles
N2N1C1O / 0.0
(0.0) / 180.0
(180.0) / -
(75.2) / -7.5
(8.6) / -173.0
(-175.8) / - / -
Rotational Constants
A / 9.606
(9.888) / 8.288
(8.556) / -
(7.464) / 8.979
(9.108) / 7.921
(7.965) / -
(13.025) / 20.062
(19.667)
B / 2.405
(2.443) / 2.372
(2.509) / -
(2.328) / 2.066
(2.082) / 2.108
(2.146) / -
(9.177) / 7.360
(7.477)
C / 1.947
(1.983) / 1.866
(1.964) / -
(2.045) / 1.717
(1.729) / 1.697
(1.724) / -
(5.703) / 5.669
(5.713)
aSee SchemeS.2 for numbering
Table S.2.2 Optimized geometry of the final product of the Schmidt rearrangement in the gas phase and the aqueous phase (parenthesized values)
Bonda / [OCNH(CH3)...N2]+ / OCNH(CH3)+Bond Lengths
C1-N1 / 1.260 / 1.264
(1.499)
N2-N3 / 1.095 / -
C1=O / 1.134 / 1.133
(1.136)
N1-C2 / 1.511 / 1.514
(1.499)
N1-H / 1.035 / 1.022
(1.025)
N2-H / 1.978 / -
Bond Angles
N1C1O / 179.1 / 178.6
(178.6)
HN1C2 / 117.5 / 119.2
(119.8)
Dihedral Angles
C2N1C1O / 0.2 / 0.0
(0.0)
HN1C1O / -179.8 / -180.0
(-180.0)
Rotational Constants
A / 5.169 / 38.087
(38.043)
B / 1.384 / 4.696
(4.757)
C / 1.099 / 4.297
(4.346)
aSee Scheme S.2 for numbering
Table S.2.3NBO charges on the various atoms and dipole moments (Debye) of the stationary points on the potential energy surface for methyl substitution in the gas phase and the aqueous phase (parenthesized values)
Atoma / Syn / Anti / TS1 / TS2 / TS3 / TS4 / NHC(CH3)
O+ / M / OC
NH
(CH3)+ / [OCNH
(CH3)
...N2]+
H / 0.462
(0.510) / 0.466
(0.507) / -
(0.487) / 0.438
(0.485) / 0.433
(0.465) / -
(0.453) / 0.419
(0.444) / 0.441 / 0.480
(0.509) / 0.487
C1 / 0.758
(0.763) / 0.771
(0.769) / -
(0.813) / 0.679
(0.718) / 0.715
(0.751) / -
(0.660) / 0.763
(0.804) / 0.433 / 0.990
(1.035) / 0.986
C2 / -0.695
(-0.692) / -0.705
(-0.708) / -
(-0.699) / -0.576
(-0.587) / -0.696
(-0.703) / -
(-0.643) / -0.707
(-0.707) / 0.180 / -0.343
(-0.345) / -0.343
O / -0.408
(-0.525) / -0.372
(-0.508) / -
(-0.433) / -0.389
(-0.496) / -0.308
(-0.381) / -
(-0.419) / -0.193
(-0.233) / -0.395 / -0.240
(-0.345) / -0.254
N1 / -0.478
(-0.426) / -0.482
(-0.423) / -
(-0.470) / -0.331
(-0.311) / -0.323
(-0.299) / -
(-0.048) / -0.201
(-0.231) / -0.570 / -0.615
(-0.600) / -0.632
N2 / 0.264
(0.315) / 0.256
(0.306) / -
(0.296) / 0.080
(0.122) / 0.086
(0.119) / - / - / - / - / -0.102
N3 / 0.276
(0.241) / 0.239
(0.235) / -
(0.165) / 0.265
(0.206) / 0.257
(0.193) / - / - / - / - / 0.137
/ 4.52
(6.52) / 1.98
(4.19) / -
(3.63) / 4.29
(5.99) / 2.36
(3.08) / -
(5.97) / 2.94
(3.62) / 7.51 / 2.88
(3.52) / 3.36
aSee Scheme S.2 for numbering
Table S.2.4 Calculated Wiberg bond orders for methyl substitution in the gas phase and the aqueous phase (parenthesized values)
Bond* / Syn / Anti / TS1 / TS2 / TS3 / TS4 / NHC(CH3)O+ / OC
NH
(CH3)+ / [OCNH
(CH3)
...N2]+
C1-O / 2.018
(1.870) / 2.042
(1.864) / -
(2.018) / 1.936
(1.844) / 1.703
(1.628) / -
(1.706) / 1.401
(1.382) / 2.242
(2.175) / 2.225
C1-N1 / 0.676
(0.827) / 0.641
(0.826) / -
(0.608) / 1.136
(1.169) / 1.006
(1.033) / -
(1.106) / 1.163
(1.142) / 1.479
(1.514) / 1.495
C1-C2 / 1.064
(1.055) / 1.072
(1.063) / -
(1.097) / 0.779
(0.813) / 1.075
(1.092) / -
(1.030) / 1.139
(1.151) / 0.026
(0.027) / 0.026
N1-N2 / 1.278
(1.274) / 1.302
(1.277) / -
(1.330) / 0.480
(2.972) / 0.514
(0.471) / - / - / - / 0.015
N2-N3 / 2.584
(2.604) / 2.547
(2.587) / -
(2.544) / 2.959
(2.972) / 2.942
(2.965) / - / - / - / 3.021
N1-H / 0.753
(0.708) / 0.749
(0.709) / -
(0.727) / 0.781
(0.739) / 0.790
(0.760) / -
(0.765) / 0.791
(0.769) / 0.729
(0.701) / 0.675
O-N1 / 0.119
(0.109) / 0.118
(0.108) / -
(0.094) / 0.250
(0.184) / 0.460
(0.474) / -
(0.383) / 0.927
(0.913) / 0.178
(0.177) / 0.182
N1-N3 / 0.322
(0.301) / 0.350
(0.309) / -
(0.367) / 0.052
(0.048) / 0.066
(0.054) / - / - / - / 0.001
*See Scheme S.2 for numbering
Table S.2.5 Calculated vibrational wavenumbersa (cm−1) and intensities (km mol-1) at the B3LYP/6-311+G(d,p) level for the stationary points of the methyl homologue. Figures in the parentheses are the computed intensities in km mol-1.
Syn / Anti / TS2 / TS3 / NHC(CH3)O+ / M / OC
NH(CH3)+ / [OC
NH(CH3)
...N2]+
3499
(181) / 3476
(203) / 3407
(124) / 3420
(127) / 3359
(148) / 3579
(167) / 3480
(241) / 3246
(1096)
3154
(9) / 3151
(10) / 3145
(22) / 3153
(8) / 3149
(19) / 3480
(168) / 3183
(2) / 3183
(0)
3109
(4) / 3110
(4) / 3137
(18) / 3096
(7) / 3067
(29) / 3278
(19) / 3183
(3) / 3181
(2)
3041
(20) / 3041
(15) / 3029
(54) / 3034
(24) / 2996
(80) / 3158
(6) / 3076
(1) / 3077
(0)
2346
(143) / 2326
(162) / 2420
(107) / 2407
(72) / 1754
(197) / 2261
(57) / 2398
(585) / 2455
(15)
1966
(205) / 2031
(340) / 1949
(241) / 1820
(118) / 1442
(15) / 1757
(99) / 1509
(44) / 2392
(661)
1456
(13) / 1459
(24) / 1455
(17) / 1453
(20) / 1424
(17) / 1586
(16) / 1474
(19) / 1522
(48)
1455
(21) / 1454
(6) / 1400
(36) / 1448
(14) / 1373
(43) / 1448
(30) / 1472
(52) / 1477
(19)
1396
(30) / 1396
(33) / 1343
(11) / 1397
(42) / 1305
(36) / 1350
(7) / 1427
(52) / 1476
(19)
1375
(122) / 1374
(60) / 1216
(25) / 1274
(8) / 1103
(88) / 1143
(14) / 1244
(0) / 1446
(28)
1186
(69) / 1198
(48) / 1099
(7) / 1209
(96) / 1076
(39) / 1060
(0) / 1136
(31) / 1267
(3)
1082
(188) / 1072
(143) / 978
(23) / 1058
(14) / 941
(24) / 964
(9) / 1131
(0) / 1138
(30)
1055
(8) / 1053
(9) / 934
(11) / 1004
(9) / 864
(62) / 911
(237) / 860
(23) / 1131
(1)
975
(35) / 948
(133) / 780
(82) / 810
(33) / 847
(45) / 208
(0) / 635
(11) / 873
(21)
660
(4) / 664
(54) / 652
(3) / 736
(52) / 576
(34) / 155
(5) / 566
(30) / 693
(104)
552
(0) / 542
(12) / 544
(2) / 485
(29) / 410
(20) / 113
(0) / 496
(112) / 644
(8)
511
(3) / 504
(4) / 530
(31) / 464
(19) / 377
(2) / 113
(9) / 226
(4) / 569
(19)
492
(122) / 496
(97) / 327
(6) / 398
(18) / 84
(3) / 67
(17) / 98
(0) / 238
(13)
356
(177) / 360
(16) / 287
(6) / 284
(16) / 160
(0)
330
(19) / 329
(127) / 186
(8) / 219
(6) / 138
(2)
242
(124) / 275
(169) / 169
(0) / 123
(3) / 119
(16)
137
(1) / 139
(21) / 104
(2) / 103
(4) / 96
(0)
111
(1) / 129
(1) / 82
(5) / 102
(1) / 85
(1)
81
(0) / 61
(2) / 501i
(483) / 362i
(271) / 42
(4)
aScaled by 0.9679
Table S.2.6NBO analysis
a) Interaction energy between donor and acceptor orbitals for synand anticonformers of protonated acetyl azide
NBO donor / NBO acceptor / Syn / AntiGas phase / Aqueous phase / Gas phase / Aqueous phase
σ(C1-O) / σ*(C1-C2) / 1.7 / 1.8 / 1.6 / 1.7
σ(C1-N1) / σ*(N2-N3) / 4.1 / 4.6 / 4.2 / 4.7
σ(C1-N1) / π2*(N2-N3) / 8.8 / 6.3 / 7.8 / 5.1
σ(C1-C2) / σ*(C1-O) / 2.0 / 1.8 / 2.1 / 1.9
σ(C1-C2) / σ*(C1-N1) / 0.5 / - / 0.7 / -
σ(C1-C2) / σ*(N2-N1) / - / 2.6 / - / -
σ(N2-N3) / σ*(N2-N1) / 5.5 / 5.5 / 5.8 / 5.6
π2(N2-N3) / σ*(C1-N2) / 3.3 / 3.1 / 3.7 / 3.4
π2(N2-N3) / σ*(N1-H) / 3.8 / 3.6 / 4.0 / 3.7
σ(N2-N1) / σ*(N2-N3) / 4.6 / 4.8 / 4.8 / 4.9
σ(N1-H) / σ*(N2-N3) / 5.7 / 5.7 / 5.6 / 5.3
σ(N1-H) / π2*(N2-N3) / 4.3 / 5.4 / 5.9 / 6.7
σ(C2-H1) / σ*(C1-O) / 3.6 / 3.4 / 3.6 / 3.2
σ(C2-H1) / π*(C1-O) / 6.3 / 6.5 / 6.2 / 6.5
σ(C2–H2) / σ*(C1-O) / 3.6 / 3.4 / 3.6 / 3.2
σ(C2–H2) / π*(C1-O) / 6.3 / 6.5 / 6.2 / 6.5
σ(C2-H3) / σ*(C1-N1) / 7.0 / 5.8 / 8.0 / 6.9
n2(N3) / σ*(N2-N1) / 15.1 / 14.4 / 15.5 / 14.7
n1(O) / σ*(C1-C2) / 3.7 / 3.1 / 3.8 / 3.2
n2(O) / σ*(C1-N1) / 67.8 / 45.5 / 70.9 / 43.0
n2(O) / σ*(C1-C2) / 13.8 / 14.8 / 12.7 / 14.1
n(N1) / π*(C1-O) / 15.1 / 24.6 / 12.7 / 22.8
n(N1) / π*(N2-N3) / 72.4 / 74.6 / 78.0 / 75.9
σ*(C1-N1) / σ*(N1-H1) / 2.3 / 1.9 / 0.5 / 0.8
b) Occupancy of donor and acceptor orbitals for syn and anti conformers of protonated acetyl azide
Occupancy / Syn / AntiGas phase / Aqueous phase / Gas phase / Aqueous phase
σ(C1-O) / 1.99626 / 1.99592 / 1.99501 / 1.99445
π(C1-O) / 1.99073 / 1.98927 / 1.98899 / 1.98599
σ(C1-N1) / 1.94514 / 1.95960 / 1.94196 / 1.96236
σ(C1-C2) / 1.97701 / 1.97824 / 1.98131 / 1.98555
σ(N2-N3) / 1.99626 / 1.99583 / 1.99557 / 1.99562
π(N2-N3) / 1.99435 / 1.99346 / 1.99437 / 1.99352
π2(N2-N3) / 1.98270 / 1.98478 / 1.98151 / 1.98401
σ(N2-N1) / 1.99397 / 1.99372 / 1.99437 / 1.99396
σ(N2-H) / 1.97134 / 1.96670 / 1.96487 / 1.96300
σ(C2–H1) / 1.95928 / 1.95719 / 1.95979 / 1.95778
σ(C2–H2) / 1.95929 / 1.95720 / 1.95992 / 1.95777
σ(C2–H3) / 1.96823 / 1.97489 / 1.96738 / 1.97555
n(N3) / 1.97386 / 1.97556 / 1.97351 / 1.97492
n1(O) / 1.97548 / 1.97760 / 1.97522 / 1.97768
n2(O ) / 1.73441 / 1.81279 / 1.70283 / 1.80180
n(N1) / 1.65890 / 1.62840 / 1.64012 / 1.62458
σ*(C1-O) / 0.01334 / 0.01399 / 0.01311 / 0.01321
π*(C1-O) / 0.11584 / 0.14765 / 0.10802 / 0.14378
σ*(C1-N) / 0.24383 / 0.15876 / 0.26311 / 0.15573
σ*(C1-C2) / 0.03661 / 0.03880 / 0.03555 / 0.03889
σ*(N2-N3) / 0.01053 / 0.01062 / 0.01131 / 0.01085
π*(N2-N3) / 0.28443 / 0.28928 / 0.31031 / 0.29853
π2*(N2-N3) / 0.08085 / 0.06560 / 0.09981 / 0.07389
σ*(N2-N1) / 0.02556 / 0.02703 / 0.03360 / 0.03185
σ*(N1-H) / 0.01281 / 0.01078 / 0.01039 / 0.01092
σ*(C2–H1) / 0.00429 / 0.00421 / 0.00448 / 0.00442
σ*(C2–H2) / 0.00429 / 0.00421 / 0.00448 / 0.00442
σ*(C2–H3) / 0.00332 / 0.00295 / 0.00343 / 0.00295
Table S.2.7 NBO analysis
a) Interaction energy between donor and acceptor orbitals for the intermediate
NBO donor / NBO acceptor / NHC(CH3)O+Gas phase / Aqueous phase
σ(C1-O) / σ*(C1-C2) / 2.2 / 2.3
σ(C1-O) / σ*(O-N) / 3.5 / 3.4
σ(C1-O) / σ*(H-N) / 4.0 / 3.4
σ(C1-N) / σ*(O-N) / 4.6 / 4.8
σ(O-N) / σ*(C1-O) / 7.3 / 7.4
σ(O-N) / σ*(C1-N) / 7.3 / 7.1
σ(O-N) / σ*(C1-C2) / 17.4 / 16.8
σ(N-H) / π*(C1-O) / 5.5 / 7.1
σ(C2–H1) / σ*(C1-O) / 3.7 / 3.4
σ(C2–H1) / π*(C1-O) / 8.7 / 11.2
σ(C2–H2) / σ*(C1-O) / 4.1 / 5.1
σ(C2–H2) / π*(C1-O) / 9.3 / 8.5
σ(C2-H3) / σ*(C1-N) / 7.7 / 8.0
n1(O) / σ*(C1-C2) / 2.3 / 2.4
n(N) / π*(C1-O) / 13.7 / 11.5
b) Occupancy of donor and acceptor orbitals for the intermediate
Occupancy / NHC(CH3)O+Gas phase / Aqueous phase
σ(C1-O) / 1.98461 / 1.98488
π(C1-O) / 1.98575 / 1.98784
σ(C1-N) / 1.97462 / 1.97398
σ(C1-C2) / 1.99588 / 1.99578
σ(O-N) / 1.95427 / 1.95574
σ(N-H) / 1.94957 / 1.94669
σ(C2–H1) / 1.94402 / 1.92987
σ(C2–H2) / 1.91710 / 1.92080
σ(C2–H3) / 1.97068 / 1.97210
n1(O) / 1.98852 / 1.98863
n(N) / 1.88554 / 1.90273
σ*(C1-O) / 0.03619 / 0.03339
π*(C1-O) / 0.25820 / 0.25431
σ*(C1-N) / 0.02778 / 0.02797
σ*(C1-C2) / 0.02670 / 0.02597
σ*(O-N) / 0.03053 / 0.03166
σ*(N-H) / 0.01264 / 0.01120
σ*(C2–H1) / 0.00388 / 0.00380
σ*(C2–H2) / 0.00343 / 0.00349
σ*(C2–H3) / 0.00365 / 0.00376
Table S.2.8NBO analysis
a) Interaction energy between donor and acceptor orbitals for the product
NBO donor / NBO acceptor / OCNH(CH3)+Gas phase / Aqueous phase
σ(C1-O) / σ*(C1-N) / 7.0 / 6.8
π2(C1-O) / σ*(N-H) / 2.6 / 2.3
π2(C1-O) / σ*(N-C2) / 2.0 / 1.9
σ(C1-N) / σ*(C1-O) / 6.2 / 6.2
σ(N-H) / σ*(C1-O) / 4.7 / 5.0
σ(N-H) / π2*(C1-O) / 9.1 / 9.8
σ(N-C2) / σ*(C1-O) / 5.1 / 5.2
σ(N-C2) / π2*(C1-O) / 7.5 / 7.6
σ(N-C2) / σ*(C1-N) / 1.3 / 1.5
σ(C2-H1) / σ*(N-H) / 2.8 / 2.8
σ(C2-H2) / σ*(C1-N) / 1.7 / 1.7
σ(C2-H3) / σ*(C1-N) / 1.7 / 1.7
n(O) / σ*(C1-N) / 10.4 / 10.0
n(N) / π*(C1-O) / 98.8 / -
n(N) / σ*(C2-H2) / 2.7 / -
n(N) / σ*(C2-H3) / 2.7 / -
b) Occupancy of donor and acceptor orbitals for the product
Occupancy / OCNH(CH3)+Gas phase / Aqueous phase
σ((C1-O) / 1.99605 / 1.99618
π(C1-O) / 1.99873 / 1.99141
π2(C1-O) / 1.99045 / -
σ(C1-N) / 1.99321 / 1.99287
π(C1-N) / - / 1.98697
σ(N-H) / 1.95735 / 1.95308
σ(N-C2) / 1.95985 / 1.95932
σ(C2-H1) / 1.99079 / 1.99125
σ(C2-H2) / 1.98435 / 1.98406
σ(C2-H3) / 1.98435 / 1.98406
n1(O) / 1.97929 / 1.98010
n2(O) / - / 1.61203
n(N) / 1.62327 / -
σ*(C1-O) / 0.01031 / 0.01066
π*(C1-O) / 0.36516 / 0.07546
π2*(C1-O) / 0.07181 / -
σ*(C1-N) / 0.01794 / 0.01726
π*(C1-N) / - / 0.38831
σ*(N-H) / 0.01346 / 0.01275
σ*(N-C2) / 0.00716 / 0.00629
σ*(C2-H1) / 0.00204 / 0.00214
σ*(C2-H2) / 0.00577 / 0.00631
σ*(C2-H3) / 0.00577 / 0.00631
Table S.2.9 Structural parameters (Å and degrees) and rotational constants (GHz) of the stationary points on the potential energy surface of C-H insertion product M
Parameters / MBond Lengthsa
C1-N1 / 3.679(0.020)
C1=O / 1.122(2.355)
C1-C2 / 2.961(0.053)
N1-H / 1.019(0.781)
N1-C2 / 1.278(1.774)
O-N1 / 4.756(0.001)
Bond Angles
N1C1O / 161.4
N1C1C2 / 18.4
Dihedral Angles
NC2C1O / 3.879
Rotational Constants
A / 34.542
B / 2.098
C / 2.030
aBond orders are given in parentheses
S.3 Phenyl Substitution
Scheme S.3
Figure S.3.1 Energy profile for the protonated benzoyl azide rearrangement in the gas phase (solid lines) and the aqueous phase (dotted lines)
Table S.3.1 Structural parameters (Å and degrees) and rotational constants (GHz) of the stationary points on the potential energy surface of phenyl homologue in the gas phase and the aqueous phase (parenthesized values)
Parametersa / Syn / Anti / TS1 / TS2 / TS3 / TS4 / NHC(Ph)O+Bond lengths
C-N1 / 1.668
(1.507) / 3.087
(1.529) / -
(1.619) / 1.431
(1.403) / 1.463
(1.430) / 1.351 / 1.366
(1.363)
N1-N2 / 1.271
(1.270) / 1.251
(1.273) / -
(1.266) / 1.685
(1.718) / 1.703
(1.775) / - / -
N2-N3 / 1.114
(1.109) / 1.124
(1.110) / -
(1.112) / 1.103
(1.098) / 1.100
(1.097) / - / -
C=O / 1.172
(1.195) / 1.127
(1.191) / -
(1.183) / 1.184
(1.195) / 1.213
(1.225) / 1.232 / 1.278
(1.278)
C-C1 / 1.443
(1.459) / 1.382
(1.457) / -
(1.445) / 1.497
(1.493) / 1.433
(1.434) / 1.387 / 1.387
(1.388)
N1-H / 1.020
(1.026) / 1.022
(1.028) / -
(1.028) / 1.024
(1.032) / 1.029
(1.035) / 1.030 / 1.031
(1.034)
C1-N1 / 2.558
(1.507) / 3.626
(1.529) / -
(1.619) / 2.207
(1.403) / 2.629
(2.619) / 2.429 / 1.366
(1.363)
O-N1 / 2.387
(2.306) / 3.160
(2.280) / -
(2.376) / 2.346
(2.341) / 2.016
(1.987) / 2.079 / 1.607
(1.628)
Bond angles
CN1N2 / 114.2
(117.1) / 120.9
(123.1) / -
(117.2) / 110.7
(109.7) / 123.1
(119.2) / - / -
N1N2N3 / 170.5
(174.7) / 172.2
(178.3) / -
(175.0) / 143.1
(151.1) / 151.4
(153.2) / - / -
N1CO / 113.3
(116.7) / 83.3
(113.4) / -
(115.1) / 127.4
(128.4) / 97.3
(96.6) / 107.0 / 74.8
(76.0)
N1CC1 / 110.4
(113.3) / 101.6
(116.1) / -
(111.9) / 97.9
(98.8) / 130.4
(132.3) / 145.4 / 145.4
(144.9)
Dihedral angle
N2N1C1O / 2.0
(2.2) / 72.1
(144.2) / -
(72.3) / -16.1
(-16.2) / 178.8
(-176.9) / - / -
N1CC1C2 / -162.5
(178.2) / -0.6
(153.4) / -
(-176.9) / -81.5
(-75.6) / 160.1
(-158.3) / 27.1 / 174.6
(177.6)
Rotational Constants
A / 3.368
(3.451) / 2.028
(1.878) / -
(2.435) / 3.231
(3.195) / 1.864
(1.829) / 3.998 / 4.476
(4.467)
B / 0.606
(0.610) / 0.547
(0.871) / -
(0.693) / 0.586
(0.578) / 0.795
(0.804) / 1.211 / 1.142
(1.147)
C / 0.518
(0.523) / 0.454
(0.653) / -
(0.575) / 0.554
(0.542) / 0.573
(0.577) / 0.960 / 0.912
(0.916)
aSee Scheme S.3 for numbering
Table S.3.2 Structural parameters (Å and degrees) and rotational constants (GHz) of the stationary points on the potential energy surface of benzoyl nitrenium ion in aqueous phase
Parameters / A / TSIA / TSAB / TSAP / B / TSBPBond lengths
C-N / 1.373 / 1.351 / 1.410 / 1.393 / 1.423 / 1.407
C=O / 1.208 / 1.238 / 1.195 / 1.192 / 1.189 / 1.167
C-C1 / 1.519 / 1.434 / 1.540 / 1.472 / 1.561 / 1.952
N-H / 1.015 / 1.034 / 1.017 / 1.029 / 1.019 / 1.020
C1-N / 2.026 / 2.440 / 1.410 / 2.848 / 2.091 / 2.207
O-N / 2.377 / 2.055 / 2.390 / 2.401 / 2.390 / 2.385
N-C6 / 1.479 / 2.877 / 1.431 / 2.050 / 1.345 / 1.407
C6-H6 / 1.111 / 1.083 / 1.247 / 1.082 / 2.130 / 2.166
C1-H6 / 2.126 / 2.181 / 1.449 / 2.199 / 1.103 / 1.092
Bond angles
NCO / 134.0 / 105.0 / 133.0 / 136.4 / 132.2 / 147.3
NCC1 / 88.8 / 122.3 / 90.2 / 80.6 / 88.9 / 82.4
CNC6 / 94.1 / 57.9 / 90.5 / 84.2 / 92.6 / 97.4
C6C1C / 88.4 / 117.3 / 85.2 / 107.7 / 82.1 / 72.7
C1C6N / 86.6 / 57.9 / 93.6 / 61.2 / 42.9 / 102.3
HNC / 130.5 / 110.9 / 123.9 / 116.0 / 133.9 / 128.9
Dihedral angle
N1CC1C2 / -140.5 / -147.4 / -155.0 / -101.7 / -124.4 / -128.9
NCC1C6 / 11.2 / 28.5 / 5.2 / 50.1 / -7.8 / -16.2
H6C6NC / -98.4 / - / -59.2 / -86.1 / -93.9 / -44.6
H6C1CN / 40.0 / 32.0 / 55.1 / 66.1 / 100.6 / -58.5
HNCO / 17.1 / 118.7 / 41.7 / 76.9 / 5.419 / 13.5
HNCC1 / -165.5 / -65.3 / -139.6 / -111.0 / -176.3 / -170.3
Rotational Constants
A / 3.856 / 4.022 / 3.994 / 4.008 / 3.700 / 3.687
B / 1.435 / 1.209 / 1.414 / 1.352 / 1.483 / 1.376
C / 1.081 / 0.961 / 1.055 / 1.103 / 1.107 / 1.079
Table S.3.3 Optimized geometry of the product of the Schmidt rearrangement
Bonda / [OCNH(Ph)...N2]+ / OCNH(Ph)+Bond Lengths
C-N1 / 1.263 / 1.265
(1.265)
N2-N3 / 1.095 / -
C=O / 1.135 / 1.134
(1.134)
N1-H / 1.033 / 1.022
(1.028)
N1-C1 / 1.492 / 1.493
(1.458)
N2-H1 / 1.998 / -
Bond Angles
N1CO / 178.1 / 177.6
(179.7)
HN1C1 / 119.7 / 119.4
(115.5)
Dihedral Angles
H1N1CO / -179.9 / -180.0
(179.9)
C1N1CO / 0.1 / 0.0
(-0.1)
C2C1NC / 90.5 / 90.4
(0.0)
Rotational Constants
A / 1.270 / 4.161
(4.729)
B / 0.62 / 1.022
(1.017)
C / 0.489 / 0.914
(0.837)
aSee SchemeS.3 for numbering
Table S.3.4NBO charges on the various atoms and dipole moments (Debye) of the stationary points on the potential energy surface of protonated benzoyl azide in the gas phase and the aqueous phase (parenthesized values)
Atom* / Syn / Anti / TS1 / TS2 / TS3 / TS4 / NHC(Ph)
O+ / OC
NH
(Ph)+ / [OC
NH(Ph)
...N2]+
H / 0.452
(0.509) / 0.389
(0.503) / -
(0.494) / 0.432
(0.474) / 0.427
(0.463) / 0.402 / 0.395
(0.430) / 0.475
(0.521) / 0.485
C / 0.745
(0.733) / 0.915
(0.745) / -
(0.754) / 0.682
(0.710) / 0.690
(0.713) / 0.592 / 0.682
(0.719) / 0.995
(1.041) / 0.994
C1 / -0.228
(-0.193) / -0.316
(-0.205) / -
(-0.211) / -0.110
(-0.113) / -0.215
(-0.204) / -0.085 / -0.222
(-0.216) / 0.085
(0.134) / 0.090
O / -0.435
(-0.541) / -0.243
(-0.506) / -
(-0.476) / -0.433
(-0.528) / -0.362
(-416) / -0.301 / -0.245
(-0.272) / -0.255
(-0.289) / -0.266
N1 / -0.477
(-0.416) / -0.624
(-0.422) / -
(-0.449) / -0.418
(-0.373) / -0.367
(-0.326) / -0.240 / -0.229
(-0.249) / -0.614
(-0.592) / -0.631
N2 / 0.264
(0.315) / 0.226
(0.302) / -
(0.301) / 0.121
(0.158) / 0.120
(0.137) / - / - / - / -0.093
N3 / 0.247
(0.244) / 0.027
(0.234) / -
(0.184) / 0.259
(0.221) / 0.255
(0.210) / - / - / - / 0.124
/ 4.06
(7.38) / 4.35
(6.83) / -
(5.62) / 3.53
(5.30) / 3.37
(4.75) / 2.46 / 2.00
(2.60) / 3.99
(6.28) / 1.80
*See Scheme S.3 for numbering
Table S.3.5NBO charges on the various atoms and dipole moments (Debye) of the stationary points on the potential energy surface of protonated benzoyl azide in aqueous phase
Atom* / A / TSIA / TSAB / TSAP / B / TSBP / TSBPH / 0.454 / 0.431 / 0.449 / 0.458 / 0.475 / 0.489 / 0.457
H6 / 0.326 / 0.260 / 0.432 / 0.286 / 0.336 / 0.324 / 0.311
C / 0.673 / 0.633 / 0.728 / 0.696 / 0.772 / 0.883 / 0.830
C1 / 0.141 / -0.089 / -0.053 / 0.059 / -0.385 / -0.346 / -0.368
C6 / -0.137 / -0.083 / 0.026 / -0.006 / 0.434 / 0.290 / -0.300
O / -0.618 / -0.365 / -0.545 / -0.520 / -0.540 / -0.448 / -0.370
N / -0.585 / -0.231 / -0.625 / -0.471 / -0.549 / -0.587 / -0.606
/ 9.67 / 3.08 / 7.74 / 6.79 / 5.80 / 3.81 / 2.98(gas)
*See Scheme S.3 for numbering
Table S.3.6 Calculated Wiberg bond orders in the gas phase and aqueous phase#
Bond* / Syn / Anti / TS1 / TS2 / TS3 / TS4 / NHC(Ph)O+ / OC
NH(Ph)+ / [OCNH(Ph)
...N2]+
C-O / 1.948
(1.801) / 2.300
(1.826) / -
(1.886) / 1.902
(1.815) / 1.632
(1.567) / 1.515 / 1.251
(1.250) / 2.226
(2.204) / 2.214
C-N1 / 0.622
(0.831) / 0.012
(0.807) / -
(0.678) / 0.998
(1.061) / 0.944
(1.007) / 1.222 / 1.111
(1.113) / 1.469
(1.457) / 1.482
C-C1 / 1.133
(1.088) / 1.273
(1.089) / -
(1.139) / 0.916
(0.925) / 1.155
(1.144) / 1.079 / 1.300
(1.281) / 0.035
(0.022) / 0.033
N1-N2 / 1.295
(1.271) / 1.460
(1.272) / -
(1.312) / 0.639
(0.604) / 0.641
(0.561) / - / - / - / 0.014
N2-N3 / 2.567
(2.607) / 2.422
(2.590) / -
(2.560) / 2.844
(2.904) / 2.879
(2.925) / - / - / - / 3.022
N1-H / 0.760
(0.706) / 0.806
(0.711) / -
(0.719) / 0.789
(0.751) / 0.795
(0.761) / 0.810 / 0.812
(0.782) / 0.722
(0.006) / 0.673
O-N1 / 0.116
(0.108) / 0.005
(0.104) / -
(0.089) / 0.149
(0.141) / 0.388
(0.423) / 0.560 / 0.924
(0.915) / 0.179
(0.162) / 0.182
N1-N3 / 0.338
(0.299) / 0.554
(0.311) / -
(0.352) / 0.084
(0.076) / 0.104
(0.078) / - / - / - / 0.001
*See Scheme S.3 for numbering#Figures in the parentheses are the computed Wiberg bond orders in the aqueous phase
Table S.3.7 Calculated Wiberg bond orders of the isomers of benzoyl nitrenium ion in the aqueous phase
Bond* / A / TSIA / TSAB / TSAP / B / TSBP(aq) / TSBP(gas)C-O / 1.681 / 1.485 / 1.789 / 1.825 / 1.837 / 1.939 / 2.008
C-N / 1.198 / 1.205 / 1.088 / 1.072 / 1.106 / 1.278 / 1.188
C-C1 / 0.951 / 1.094 / 0.923 / 0.938 / 0.901 / 0.438 / 0.504
C1-C6 / 1.025 / 1.223 / 1.084 / 1.079 / 1.014 / 1.187 / 1.146
C6-N / 0.946 / 0.077 / 1.017 / 0.418 / 1.284 / 1.037 / 1.066
N-H / 0.759 / 0.785 / 0.767 / 0.752 / 0.735 / 0.716 / 0.745
C1-H6 / 0.014 / 0.002 / 0.260 / 0.002 / 0.801 / 0.824 / 0.828
C6-H6 / 0.787 / 0.901 / 0.448 / 0.889 / 0.010 / 0.007 / 0.008
O-N / 0.195 / 0.559 / 0.141 / 0.144 / 0.116 / 0.145 / 0.136
*See Scheme S.3 for numbering
Table S.3.8 Calculated vibrational wavenumbersa (cm−1) and intensities (km mol-1) at the B3LYP/6-311+G(d,p) level for the stationary points of phenyl homologue. Figures in the parentheses are the computed intensities in km mol-1.
Syn / Anti / TS2 / TS3 / TS4 / NHC(Ph)O+ / OCNH(Ph)+ / [OCNH(Ph)...N2]+3500
(121) / 3474
(71) / 3479
(76) / 3432
(116) / 3416
(313) / 3380
(111) / 3464
(213) / 3267
(1074)
3212
(1) / 3214
(0) / 3211
(0) / 3214
(2) / 3214
(1) / 3214
(1) / 3211
(0) / 3211
(0)
3208
(1) / 3209
(15) / 3207
(2) / 3210
(1) / 3211
(8) / 3211
(4) / 3206
(1) / 3206
(1)
3200
(1) / 3201
(8) / 3198
(1) / 3202
(2) / 3200
(4) / 3196
(2) / 3197
(0) / 3198
(0)
3193
(2) / 3197
(41) / 3191
(0) / 3198
(2) / 3195
(4) / 3193
(1) / 3193
(1) / 3193
(1)
3188
(1) / 3191
(10) / 3176
(1) / 3190
(0) / 3191
(2) / 3189
(0) / 3189
(0) / 3189
(0)
2336
(270) / 2297
(725) / 2330
(13) / 2367
(25) / 1652
(55) / 1744
(884) / 2381
(737) / 2455
(14)
1949
(383) / 2287
(615) / 1891
(287) / 1764
(543) / 1599
(109) / 1632
(217) / 1632
(5) / 2377
(771)
1626
(87) / 1619
(146) / 1610
(191) / 1629
(156) / 1535
(16) / 1589
(0) / 1608
(0) / 1633
(6)
1606
(22) / 1586
(2) / 1578
(1) / 1603
(27) / 1496
(64) / 1505
(21) / 1506
(25) / 1611
(0)
1516
(1) / 1498
(2) / 1496(
0) / 1518
(1) / 1456
(23) / 1481
(45) / 1487
(9) / 1509
(28)
1479
(31) / 1472
(47) / 1470
(25) / 1479
(35) / 1388
(30) / 1390
(23) / 1389
(64) / 1487
(9)
1369
(31) / 1373
(9) / 1367
(14) / 1370
(16) / 1373
(30) / 1355
(2) / 1348
(6) / 1426
(60)
1355
(74) / 1336
(6) / 1333
(1) / 1345
(4) / 1305
(8) / 1292
(32) / 1338
(7) / 1348
(5)
1340
(45) / 1309
(28) / 1245
(23) / 1335
(16) / 1210
(1) / 1223
(9) / 1223
(1) / 1337
(6)
1234
(72) / 1242
(46) / 1213
(2) / 1274
(170) / 1188
(4) / 1205
(4) / 1199
(2) / 1242
(2)
1206
(81) / 1205
(10) / 1198
(2) / 1210
(38) / 1148
(41) / 1188
(106) / 1196
(0) / 1199
(2)
1200
(4) / 1202
(62) / 1150
(144) / 1201
(2) / 1117
(10) / 1125
(2) / 1112
(1) / 1196
(0)
1181
(218) / 1201
(230) / 1115
(5) / 1123
(3) / 1032
(0) / 1058
(94) / 1105
(6) / 1118
(16)
1122
(4) / 1118
(6) / 1035
(0) / 1048
(7) / 1017
(18) / 1043
(1) / 1038
(6) / 1105
(6)
1044
(1) / 1043
(0) / 1033
(4) / 1038
(0) / 1014
(12) / 1032
(10) / 1034
(0) / 1040
(7)
1037
(0) / 1037
(2) / 1008
(15) / 1020
(25) / 1003
(33) / 1025
(90) / 1012
(17) / 1033
(0)
1012
(10) / 1026
(0) / 1006
(1) / 1012
(7) / 994
(148) / 1015
(0) / 999
(0) / 1013
(17)
1008
(2) / 1004
(7) / 964
(0) / 1008
(4) / 968
(9) / 1006
(11) / 946
(1) / 999
(0)
964
(1) / 987
(1) / 910
(10) / 964
(1) / 843
(1) / 981
(2) / 837
(0) / 946
(1)
860
(111) / 861
(0) / 860
(34) / 850
(12) / 796
(14) / 848
(0) / 814
(26) / 839
(0)
850
(1) / 775
(48) / 843
(1) / 839
(66) / 760
(79) / 787
(23) / 758
(59) / 820
(19)
787
(31) / 772
(1) / 783
(4) / 774
(67) / 715
(87) / 781
(28) / 694
(25) / 760
(62)
692
(47) / 668
(29) / 764
(96) / 726
(21) / 648
(16) / 657
(41) / 656
(3) / 698
(28)
684
(36) / 642
(16) / 682
(60) / 680
(33) / 596
(3) / 637
(62) / 624
(1) / 662
(2)
667
(36) / 605
(26) / 677
(3) / 628
(9) / 543
(43) / 617
(2) / 580
(15) / 653
(68)
626
(6) / 598
(14) / 614
(20) / 614
(43) / 499
(2) / 553
(36) / 491
(64) / 624
(1)
571
(182) / 582
(0) / 600
(62) / 559
(13) / 422
(15) / 509
(2) / 472
(18) / 583
(22)
525
(12) / 537
(7) / 512
(1) / 495
(35) / 380
(0) / 394
(0) / 465
(5) / 477
(18)
472
(1) / 456
(3) / 394
(23) / 412
(1) / 347
(5) / 390
(0) / 413
(0) / 469
(7)
415
(11) / 394
(1) / 370
(23) / 398
(1) / 171
(3) / 380
(5) / 333
(33) / 414
(0)
402
(0) / 387
(0) / 347
(12) / 382
(3) / 135
(26) / 151
(1) / 242
(11) / 375
(5)
375
(78) / 269
(100) / 325
(4) / 315
(9) / 81
(7) / 136
(7) / 94
(0) / 249
(15)
312
(58) / 165
(2) / 230
(3) / 236
(5) / 188i
(204) / 122
(2) / 33
(3) / 126
(4)
229
(111) / 133
(0) / 200
(11) / 170
(5) / 125
(0)
194
(37) / 108
(4) / 109
(21) / 156
(1) / 123
(4)
162
(7) / 75
(0) / 95
(2) / 129
(12) / 86
(1)
108
(4) / 57
(5) / 56
(4) / 95
(0) / 57
(2)
74
(7) / 34
(2) / 43
(4) / 38
(0) / 25
(0)
54
(1) / 14
(1) / 532i
(879) / 511i
(301) / 25
(1)
aScaled by 0.9679
Table S.3.9NBO analysis
a) Interaction energy between donor and acceptor orbitals for syn conformer of protonated benzoyl azide
Gas phase / Aqueous phaseNBO donor / NBO acceptor / E(kcal mol-1) / NBO donor / NBO acceptor / E(kcal mol-1)
σ(C-O) / σ*(C-C1) / 2.8 / σ(C-O) / σ*(C-C1) / 2.8
σ(C-N1) / σ*(N2-N3) / 3.0 / σ(C-N1) / σ*(N2-N3) / 4.6
σ(C-N1) / π2*(N2-N3) / 10.5 / σ(C-N1) / π2*(N2-N3) / 6.4
σ(C-C1) / σ*(C-O) / 3.1 / σ(C-C1) / σ*(C-O) / 2.7
σ(C-C1) / σ*(N2-N1) / 0.7 / σ(C-C1) / σ*(N2-N1) / 1.8
σ(N2-N3) / σ*(N2-N1) / 5.3 / σ(N2-N3) / σ*(N2-N1) / 5.5
π2(N2-N3) / σ*(C1-N2) / 0.5 / π2(N2-N3) / σ*(C1-N2) / 3.1
π2(N2-N3) / σ*(N1-H) / 3.6 / π2(N2-N3) / σ*(N1-H) / 3.4
σ(N2-N1) / σ*(N2-N3) / 4.6 / σ(N2-N1) / σ*(N2-N3) / 4.8
σ(N1-H) / σ*(N2-N3) / 4.9 / σ(N1-H) / σ*(N2-N3) / 5.4
σ(N1-H) / π2*(N2-N3) / 4.8 / σ(N1-H) / π2*(N2-N3) / 5.5
n2(N3) / σ*(N2-N1) / 15.3 / n2(N3) / σ*(N2-N1) / 14.6
n1(O) / σ*(C-C1) / 4.1 / n1(O) / σ*(C-C1) / 3.0
n2(O) / σ*(C-N1) / 74.1 / n2(O) / σ*(C-N1) / 44.2
n2(O) / σ*(C-C1) / 12.0 / n2(O) / σ*(C-C1) / 14.8
n(N1) / π*(C-O) / 9.5 / n(N1) / π*(C-O) / 22.4
n(N1) / π*(N2-N3) / 43.7 / n(N1) / π*(N2-N3) / 66.4
σ*(C-N1) / σ*(N1-H1) / 1.7 / σ*(C-N1) / σ*(N1-H1) / 2.2
π(C1-C6) / π*(C-O) / 30.9 / σ(C1-C2) / π*(C-O) / 2.9
π(C1-C6) / π*(C2-C3) / 19.8 / σ(C1-C2) / π*(C-C1) / 1.9
π(C1-C6) / π*(C4-C5) / 14.3 / σ(C1-C2) / π*(C-O) / 26.9
π(C2-C3) / π*(C1-C6) / 18.4 / π(C1-C6) / σ*(C-N1) / 3.0
π(C2-C3) / π*(C4-C5) / 19.9 / π(C1-C6) / σ*(C-C1) / 2.2
π(C4-C5) / π*(C1-C6) / 29.3 / π(C2-C3) / σ*(C-C1) / 3.6
π(C4-C5) / π*(C2-C3) / 18.0 / π(C5-C6) / σ*(C-C1) / 2.8
π2*(C-O) / π*(C1-C2) / 65.8 / π2*(C-O) / π*(C1-C2) / 57.4
b) Occupancy of donor and acceptor orbitals for syn conformer of protonated benzoyl azide
Occupancy / SynGas phase / Aqueous phase
σ(C-O) / 1.99481 / 1.99434
π(C-O) / 1.98615 / 1.98371
σ(C-N) / 1.91816 / 1.95883
σ(C1–C) / 1.97070 / 1.97156
σ(N2-N3) / 1.99607 / 1.99584
π(N2–N3) / 1.99385 / 1.99325
π2(N2-N3) / 1.98262 / 1.98512
σ(N2–N1) / 1.99367 / 1.99340
σ(N-H) / 1.95794 / 1.96135
σ(C1-C6) / 1.97224 / 1.96660
σ(C1-C2) / 1.96001 / 1.97331
π(C1-C2) / 1.61351 / 1.63196
σ(C5–C6) / 1.97865 / 1.97871
π(C5-C6) / 1.65502 / 1.64234
σ(C2–C3) / 1.97784 / 1.97871
σ(C5-C4) / 1.98080 / 1.98085
σ(C3–C4) / 1.98128 / 1.98086
π(C3-C4) / 1.56945 / 1.60545
n(N3) / 1.97366 / 1.97522
n(O) / 1.97596 / 1.97896
n2(O) / 1.71249 / 1.81508
n(N1) / 1.68056 / 1.63642
σ*(C-O) / 0.00996 / 0.00994
π*(C-O) / 0.21581 / 0.22383
σ*(C-N1) / 0.27382 / 0.15107
σ*(C-C1) / 0.04853 / 0.05407
σ*(N2–N3) / 0.01858 / 0.01162
π*(N2–N3) / 0.28783 / 0.28900
π2*(N2–N3) / 0.09404 / 0.06238
σ*(N2–N1) / 0.02369 / 0.02489
σ*(N1–H) / 0.01724 / 0.01449
σ*(C1–C6) / 0.02477 / 0.02289
σ*(C1–C2) / 0.02343 / 0.02399
π*(C1–C2) / 0.42395 / 0.40570
σ*(C6-C5) / 0.01436 / 0.01408
π*(C6–C5) / 0.27240 / 0.26480
σ*(C2–C3) / 0.01366 / 0.01461
σ*(C5–C4) / 0.01507 / 0.01586
σ*(C3–C4) / 0.01512 / 0.01562
π*(C3–C4) / 0.27509 / 0.29478
Table S.3.10NBO analysis
a) Interaction energy between donor and acceptor orbitals for the global minimum of protonated benzoyl azide in the gas phase
Gas phaseNBO donor / NBO acceptor / E(kcal mol-1)
π(C-C1) / π*(C-C1) / 18.2
π(C-C1) / π*(C2-C3) / 21.5
π(C-C1) / σ*(N2-N1) / 21.8
σ(C2-C1) / σ*(C-O) / 4.7
σ(C6-C1) / σ*(C-O) / 4.9
σ(C6-C1) / σ*(C-O) / 4.2
σ(C6-C1) / σ*(C2-C1) / 4.6
π(C2-C3) / n*(C4) / 58.4
π(C2-C3) / π*(C-C1) / 15.4
π(C6-C5) / n*(C4) / 54.4
n2(O) / π*(C-C1) / 128.0
n*(C4) / π*(C2-C3) / 49.4
n*(C4) / π*(C2-C3) / 51.6
π*(C-C1) / π*(C2-C3) / 22.8
π*(C-C1) / π*(C6-C5) / 22.5
σ(N1-H) / π2*(N2-N3) / 13.7
n(N3) / σ*(N2-N1) / 16.8
n(N1) / σ*(N2-N3) / 12.1
n(N1) / π2*(N2-N3) / 10.8
n2(N1) / π*(N2-N3) / 105.9
b) Interaction energy between donor and acceptor orbitals for the global minimum of protonated benzoyl azide in the aqueous phase
Aqueous phaseNBO donor / NBO acceptor / E(kcal mol-1)
σ(C-O) / σ*(C-C1) / 2.6
σ(C-O) / σ*(C2-C1) / 1.0
π(C-O) / σ*(N2-N1) / 1.2
π(C-O) / π*(C2-C1) / 3.0
σ*(C-N1) / σ*(N2-N3) / 4.2
σ*(C-N1) / π*(N2-N3) / 1.6
σ*(C-N1) / π2*(N2-N3) / 5.0
σ*(C-N1) / σ*(C1-C6) / 1.5
σ(C-C1) / σ*(C-O) / 2.7
σ(C-C1) / σ*(C2-C1) / 2.5
σ(C-C1) / σ*(C6-C1) / 1.7
σ(C-C1) / σ*(C2-C3) / 1.7
σ(C-C1) / σ*(C5-C6) / 2.0
σ*(N2-N3) / σ*(N2-N1) / 5.3
π2*(N2-N3) / σ*(C-N1) / 3.1
π2*(N2-N3) / σ*(N1-H) / 3.5
σ(N2-N1) / σ*(N2-N3) / 4.7
σ(C1-C2) / σ*(C-O) / 3.0
σ(C1-C2) / σ*(C-C1) / 1.9
π(C1-C2) / π*(C-O) / 23.5
π(C1-C2) / σ*(C-N1) / 2.0
σ(C1-C6) / σ*(C-N1) / 2.9
σ(C5-C6) / σ*(C-C1) / 2.9
π*(C1-C2) / σ*(C-N1) / 2.0
π*(C-O) / π*(C2-C1) / 73.8
σ*(C-N1) / σ*(N2-N1) / 1.8
n(N3) / σ*(N2-N1) / 15.0
n(O) / σ*(C-C1) / 3.2
n2(O) / σ*(C-N1) / 43.4
n2(O) / σ*(C-C1) / 13.9
n(N1) / π*(C-O) / 15.3
n(N1) / σ*(N2-N3) / 2.5
n(N1) / π*(N2-N3) / 52.9
n(N1) / σ*(N1-H) / 1.0
c) Occupancy of donor and acceptor orbitals for the global minimum of protonated benzoyl azide
Gas phase / Aqueous phaseOccupancy / Anti / Occupancy / Anti
σ(C-O) / 1.99364 / σ(C-O) / 1.99380
π(C-O) / 1.98768 / π(C-O) / 1.98091
σ(C-N) / 1.97458 / σ(C-N) / 1.95249
σ(C1–C) / 1.91379 / σ(C1–C) / 1.97614
σ(N2-N3) / 1.99751 / σ(N2-N3) / 1.99593
π(N2–N3) / 1.99356 / π(N2–N3) / 1.99394
π2(N2-N3) / 1.98846 / π2(N2-N3) / 1.98404
σ(N2–N1) / 1.97008 / σ(N2–N1) / 1.99389
σ(N-H) / 1.97128 / σ(N-H) / 1.95342
σ(C1-C6) / 1.96672 / σ(C1-C2) / 1.97204
σ(C1-C2) / 1.97026 / π(C1-C2) / 1.64056
π(C3-C2) / 1.65055 / σ(C1-C6) / 1.96658
σ(C5–C6) / 1.97538 / σ(C2–C3) / 1.97854
π(C5-C6) / 1.63824 / σ(C5–C6) / 1.97885
σ(C2–C3) / 1.97588 / π(C5-C6) / 1.64085
σ(C5-C4) / 1.98169 / σ(C3-C4) / 1.98089
σ(C3–C4) / 1.98150 / π(C3–C4) / 1.60569
n(N3) / 1.97497 / σ(C4–C5) / 1.98084
n(O) / 1.97602 / n(N3) / 1.97423
n2(O) / 1.79690 / n(O) / 1.97869
n(N1) / 1.84649 / n2(O) / 1.79511
n(C1) / 1.01381 / n(N1) / 1.65341
n(C4) / 0.86127 / σ*(C-O) / 0.01311
σ*(C-O) / 0.02220 / π*(C-O) / 0.19808
π*(C-O) / 0.14603 / σ*(C-N1) / 0.15957
σ*(C-N1) / 0.13046 / σ*(C-C1) / 0.05356
σ*(C-C1) / 0.08495 / σ*(N2–N3) / 0.01480
σ*(N2–N3) / 0.03803 / π*(N2–N3) / 0.29135
π*(N2–N3) / 0.03441 / π2*(N2–N3) / 0.07663
π2*(N2–N3) / 0.08855 / σ*(N2–N1) / 0.03098
σ*(N2–N1) / 0.34085 / σ*(N1–H) / 0.01384
σ*(N1–H) / 0.01002 / σ*(C1–C2) / 0.02460
σ*(C1–C6) / 0.02446 / π*(C1–C2) / 0.40780
σ*(C1–C2) / 0.02488 / σ*(C1–C6) / 0.02340
π*(C3–C2) / 0.25785 / π*(C3–C2) / 0.01467
σ*(C6-C5) / 0.01396 / σ*(C6-C5) / 0.01402
π*(C6–C5) / 0.23350 / π*(C6–C5) / 0.26536
σ*(C2–C3) / 0.01470 / σ*(C3–C4) / 0.01557
σ*(C5–C4) / 0.01471 / σ*(C3–C4) / 0.29279
σ*(C3–C4) / 0.01464 / σ*(C4–C5) / 0.01579
Table S.3.11NBO analysis
a) Interaction energy between donor and acceptor orbitals for the intermediate
Gas phase / Aqueous phaseNBO donor / NBO acceptor / NHC(Ph)O+ / NBO donor / NBO acceptor / NHC(Ph)O+
σ(C-O) / σ*(C-C1) / 3.6 / σ(C-O) / σ*(C-C1) / 3.5
σ(C-O) / σ*(O-N) / 3.6 / σ(C-O) / σ*(O-N) / 3.6
σ(C-N) / σ*(C-C1) / 3.9 / σ(C-N) / σ*(C-C1) / 3.9
σ(C-N) / σ*(O-N) / 3.7 / σ(C-N) / σ*(O-N) / 3.8
π(C-C1) / π*(C2-C3) / 21.2 / σ(C-C1) / π*(C1-C6) / 2.5
π(C-C1) / π*(C5-C6) / 20.7 / σ(C-C1) / π*(C1-C2) / 2.6
σ(O-N) / σ*(C-O) / 7.2 / σ(O-N) / σ*(C-O) / 7.4
σ(O-N) / σ*(N-C) / 6.5 / σ(O-N) / σ*(N-C) / 6.3
σ(O-N) / σ*(C-C1) / 17.4 / σ(O-N) / σ*(C-C1) / 17.2
σ(N-H) / π*(C-C1) / 7.3 / σ(N-H) / n*(C1) / 10.8
σ(C2-C1) / σ*(C-O) / 5.0 / σ(C6-C1) / σ*(C-O) / 4.9
σ(C6-C1) / σ*(N-C) / 4.9 / σ(C6-C1) / σ*(N-C) / 2.9
σ(C6-C1) / σ*(C-C1) / 2.9 / π(C6-C1) / n*(C1) / 147.0
σ(C6-C1) / σ*(C2-C1) / 4.2 / σ(C1-C2) / σ*(N-C) / 4.7
σ(C2-C3) / σ*(C-C1) / 2.9 / σ(C1-C2) / σ*(C-C1) / 2.9
σ(C2-C3) / σ*(C2-C1) / 2.4 / σ(C5-C6) / σ*(C-C1) / 2.9
π(C2-C3) / n*(C4) / 57.2 / σ(C2-C3) / σ*(C-C1) / 2.9
π(C2-C3) / π*(C-C1) / 16.1 / n*(C1) / σ*(N-H) / 3.8
π(C5-C6) / n*(C4) / 57.6 / n*(C1) / σ*(C1-C6) / 35.2
π(C5-C6) / π*(C-C1) / 16.2 / n(O) / π*(C-C1) / 2.4
n2(O) / π*(C-C1) / 59.1 / n2(O) / π*(C-C1) / 112.9
n(N) / π*(C-C1) / 11.1 / n(N) / π*(C-C1) / 15.4
n*(C4) / π*(C2-C3) / 47.5 / n(N) / π*(C2-C3) / 2.5
n*(C4) / π*(C5-C6) / 46.2 / n(N) / σ*(C-O) / 1.2
π*(C-C1) / π*(C2-C3) / 20.0 / π*(C1-C6) / π*(C2-C3) / 91.6
π*(C-C1) / π*(C5-C6) / 19.1 / π*(C1-C6) / π*(C5-C4) / 146.0
b) Occupancy of donor and acceptor orbitals for the intermediate
Gas phase / Aqueous phaseOccupancy / NHC(Ph)O+ / Occupancy / NHC(Ph)O+
σ(C-O) / 1.98405 / σ(C-O) / 1.98412
σ(C-N) / 1.97506 / σ(C-N) / 1.97529
σ(C1–C) / 1.98503 / σ(C1–C) / 1.98488
π(C-C1) / 1.52376 / π(C-C1) / -
σ(O-N) / 1.95818 / σ(O-N) / 1.95792
σ(N-H) / 1.95865 / σ(N-H) / 1.95406
σ(C1-C6) / 1.96843 / σ(C1-C6) / 1.96916
σ(C1-C2) / 1.96901 / π(C1-C6) / 1.53860
σ(C5–C6) / 1.98057 / σ(C1-C2) / 1.96880
π(C5-C6) / 1.63846 / σ(C5–C6) / 1.98036
σ(C2–C3) / 1.98056 / σ(C2–C3) / 1.98037
π(C3-C2) / 1.63956 / π(C3-C2) / 1.63939
σ(C5-C4) / 1.98198 / σ(C5-C4) / 1.98175
σ(C3–C4) / 1.98191 / σ(C3–C4) / 1.98169
n*(C) / - / n*(C) / 0.71149
n(N) / 1.91213 / n(N) / 1.91699
n(O) / 1.98971 / n(O) / 1.99004
n2(O) / 1.72273 / n2(O) / 1.72700
σ*(C-O) / 0.02065 / σ*(C-O) / 0.02077
σ*(C-N) / 0.01948 / σ*(C-N) / 0.01884
σ*(C-C1) / 0.03946 / σ*(C-C1) / 0.03983
π*(C-C1) / 0.32726 / π*(C-C1) / -
σ*(O-N) / 0.02889 / σ*(O-N) / 0.02960
σ*(N–H) / 0.01195 / σ*(N–H) / 0.01101
σ*(C1–C2) / 0.02386 / σ*(C1–C6) / 0.02356
σ*(C4–C6) / 0.02446 / π*(C1–C6) / 0.44404
σ*(C6-C5) / 0.01289 / σ*(C1-C2) / 0.02423
π*(C6–C5) / 0.20268 / σ*(C6–C5) / 0.01307
σ*(C2–C3) / 0.01304 / σ*(C2–C3) / 0.01301
π*(C3–C2) / 0.21091 / π*(C3–C2) / 0.21118
σ*(C5–C4) / 0.01484 / σ*(C5–C4) / 0.01531
σ*(C3–C4) / 0.01480 / σ*(C3–C4) / 0.01535
Table S.3.12NBO analysis
a) Interaction energy between donor and acceptor orbitals for the product in the gas phase
Gas phaseNBO donor / NBO acceptor / NH(Ph)CO+
σ(C-O) / σ*(C-N) / 6.5
π(C-O) / σ*(H-N) / 2.5
σ(C-N) / σ*(C-O) / 5.8
σ(H-N) / σ*(C-O) / 4.5
σ(H-N) / π*(C-O) / 8.4
σ(C1-N) / σ*(C-O) / 6.3
σ(C1-N) / π*(C-O) / 7.0
σ(C6-C1) / σ*(C2-C1) / 4.8
σ(C2-C1) / σ*(C6-C1) / 4.8
π(C6-C1) / σ*(C-N) / 2.4
π(C6-C1) / σ*(H-N) / 3.4
π(C2-C1) / σ*(C6-C5) / 19.3
π(C2-C1) / π*(C3-C4) / 14.4
σ(C6-C5) / σ*(N-C1) / 5.9
π(C6-C5) / π*(C2-C1) / 22.4
π(C6-C5) / π*(C3-C4) / 19.1
π(C2-C3) / σ*(N-C1) / 5.9
π(C4-C3) / π*(C2-C1) / 27.1
π(C4-C3) / π*(C6-C5) / 20.2
n1(O) / σ*(C-N) / 10.7
n2(O) / n*(C) / 260.1
n(N) / n*(C) / 204.6
π*(C2-C1) / π*(C5-C6) / 112.1
π*(C2-C1) / π*(C3-C4) / 84.7
π*(C-C1) / π*(C3-C4) / 208.9
b) Interaction energy between donor and acceptor orbitals for the global minimum of protonated benzoyl azide in the aqueous phase
Aqueous phaseNBO donor / NBO acceptor / NH(Ph)CO+
σ(C-O) / σ*(C-N) / 6.4
π(C-O) / σ*(H-N) / 2.3
σ(C-N) / σ*(C-O) / 5.9
σ(H-N) / σ*(C-O) / 4.6
σ(H-N) / π*(C-O) / 10.5
σ(C1-N) / σ*(C-O) / 5.3
σ(C1-N) / π*(C-O) / 4.7
σ(H-N) / σ*(C6-C1) / 2.6
σ(C6-C1) / σ*(H-N) / 1.6
σ(C6-C5) / σ*(C1-N) / 5.6
σ(C1-C2) / σ*(C-N) / 2.4
π(C2-C1) / π*(N-C) / 11.8
π(C2-C3) / σ*(C1-N) / 4.9
n1(O) / σ*(C-N) / 10.2
n2(O) / π*(N-C) / 142.3
π*(C-N) / π*(C1-C2) / 10.7
c) Occupancy of donor and acceptor orbitals for the product
Occupancy / NH(Ph)CO+Gas phase / Aqueous phase
σ(C-O) / 1.99589 / 1.99619
π(C-O) / 1.99112 / 1.99109
σ(C-N) / 1.99128 / 1.99014
π(C-N) / - / 1.96084
σ(C1-N) / 1.95353 / 1.96532
σ(N-H) / 1.95899 / 1.94899
σ(C1-C6) / 1.97442 / 1.97488
σ(C1-C2) / 1.97447 / 1.97218
π(C1-C2) / 1.71652 / 1.68148
σ(C5–C6) / 1.97017 / 1.97334
π(C5-C6) / 1.63495 / 1.65890
σ(C3-C4) / 1.98099 / 1.98048
π(C3–C4) / 1.59939 / 1.64169
n(N) / 1.62698 / -
n(O) / 1.97869 / 1.98007
n2(O) / 1.57884 / 1.59892
n(C) / 0.77904 / -
σ*(C-O) / 0.01107 / 0.01057
π*(C-O) / 0.08775 / 0.06511
σ*(C-N) / 0.02112 / 0.01745
π*(C-N) / - / 0.41299
σ*(C1-N) / 0.04361 / 0.03767
σ*(N-H) / 0.02271 / 0.01151
σ*(C1-C6) / 0.02400 / 0.02245
σ*(C1-C2) / 0.02415 / 0.02118
π*(C1-C2) / 0.42251 / 0.39308
σ*(C5–C6) / 0.01434 / 0.01407
π*(C5-C6) / 0.29749 / 0.31559
σ*(C2–C3) / 0.01435 / 0.01377
σ*(C4–C5) / 0.01457 / 0.01535
σ*(C3-C4) / 0.01457 / 0.01535
π*(C3–C4) / 0.27785 / 0.30908
S.4 Methoxy Substitution
Scheme S.4
Figure S.4.1 Energy profile for the rearrangement of methoxy substituted precursor in the gas phase (solid lines) and the aqueous phase (dotted lines)
Table S.4.1 Structural parameters (Å and degrees) and rotational constants (GHz) of the stationary points on the potential energy surface for methoxy substitution in the gas phase and the aqueous phase (parenthesized values)
Parametersa / Syn / Anti / TS1 / TS2 / TS3 / TS4 / NHC(OCH3)O+Bond lengths
C1-N1 / 1.524
(1.470) / 1.520
(1.468) / 1.597
(1.532) / 1.413
(1.401) / 1.405
(1.396) / 1.355
(1.353) / 1.352
(1.353)
N1-N2 / 1.274
(1.269) / 1.277
(1.273) / 1.275
(1.273) / 1.959
(1.931) / 1.886
(1.908) / - / -
N2-N3 / 1.111
(1.108) / 1.111
(1.108) / 1.113
(1.109) / 1.096
(1.095) / 1.100
(1.095) / - / -
C1=O1 / 1.180
(1.193) / 1.178
(1.192) / 1.176
(1.188) / 1.167
(1.175) / 1.217
(1.223) / 1.190
(1.199) / 1.265
(1.266)
C1-O2 / 1.291
(1.297) / 1.294
(1.298) / 1.283
(1.291) / 1.366
(1.358) / 1.268
(1.264) / 1.327
(1.312) / 1.234
(1.232)
N1-H / 1.022
(1.027) / 1.021
(1.026) / 1.023
(1.029) / 1.032
(1.037) / 1.031
(1.036) / 1.038
(1.043) / 1.033
(1.036)
N1-O2 / 2.233
(2.218) / 2.272
(2.252) / 2.294
(2.270) / 1.921
(1.934) / 2.360
(2.361) / 2.110
(2.142) / 2.432
(2.425)
O1-N1 / 2.340
(2.319) / 2.304
(2.288) / 2.391
(2.363) / 2.402
(2.394) / 2.007
(1.998) / 2.251
(2.222) / 1.664
(1.681)
Bond angles
C1N1N2 / 117.7
(118.4) / 122.9
(121.4) / 117.4
(117.0) / 107.0
(106.6) / 113.7
(111.5) / - / -
N1N2N3 / 174.8
(177.5) / 175.7
(178.5) / 175.2
(175.8) / 161.5
(160.9) / 157.6
(160.6) / - / -
N1C1O1 / 119.2
(120.8) / 116.8
(118.3) / 118.4
(120.2) / 137.0
(136.5) / 99.7
(99.2) / 124.1
(120.9) / 78.9
(79.8)
N1C1O2 / 104.7
(106.4) / 107.4
(118.9) / 105.0
(106.8) / 87.4
(89.0) / 124.0
(125.0) / 103.7
(107.0) / 140.2
(139.5)
Dihedral angle
N2N1C1O1 / 0.0
(0.0) / -180.0
(-180.0) / -74.6
(-74.0) / -170.4
(16.1) / 175.0
(176.4) / - / -
N1C1O2C2 / -180
(-180.0) / 180.0
(-180.0) / 177.7
(178.3) / 17.1
(-114.0) / -172.0
(-172.8) / -115.9
(-120.7) / -171.6
(-175.3)
Rotational Constants
A / 9.808
(10.002) / 5.038
(5.142) / 6.528
(6.730) / 7.187
(7.262) / 4.844
(4.829) / 9.986
(10.237) / 16.282
(16.014)
B / 1.486
(1.502) / 1.950
(1.987) / 1.531
(1.556) / 1.341
(1.358) / 1.633
(1.653) / 4.374
(4.363) / 3.739
(3.802)
C / 1.301
(1.317) / 1.419
(1.446) / 1.402
(1.430) / 1.198
(1.216) / 1.239
(1.250) / 3.327
(3.334) / 3.133
(3.169)
aSee Scheme S.4 for numbering
Table S.4.2 Optimized geometry of the product of the Schmidt rearrangement for methoxy substitution in the gas phase and the aqueous phase (parenthesized values)
Bonda / [OCNH(OCH3)...N2]+ / OCNH(OCH3)+Bond Lengths
C1-N1 / 1.271 / 1.274
(1.268)
N2-N3 / 1.095 / -
C1=O1 / 1.132 / 1.131
(1.132)
N1-H / 1.037 / 1.024
(1.027)
N1-O2 / 1.406 / 1.403
(1.394)
N2-H / 1.945 / -
Bond Angles
N1C1O / 178.3 / 177.8
(178.5)
HN1O2 / 118.9 / 119.0
(119.9)
Dihedral Angles
HN1C1O1 / 161.8 / 166.0
(-149.6)
O2N1C1O1 / -37.6 / -33.3
(24.2)
Rotational Constants
A / 2.825 / 18.935
(17.745)
B / 1.253 / 2.782
(2.879)
C / 0.898 / 2.650
(2.715)
aSee Scheme S.4 for numbering
Table S.4.3 NBO charges on the various atoms* and dipole moments (Debye) of the stationary points on the potential energy surface for methoxy substitution in both the gas phase and the aqueous phase (parenthesized values)
Atom / Syn / Anti / TS1 / TS2 / TS3 / TS4 / NHC
(OCH3)
O+ / OC
NH
(OCH3)+ / [OC
NH
(OCH3)
...N2]+
H / 0.478
(0.516) / 0.478
(0.517) / 0.462
(0.506) / 0.430
(0.471) / 0.428
(0.463) / 0.412
(0.443) / 0.412
(0.441) / 0.467
(0.501) / 0.472
O1 / -0.496
(-0.579) / -0.465
(-0.567) / -0.450
(-0.536) / -0.410
(-0.493) / -0.356
(-0.415) / -0.298
(-0.374) / -0.245
(-0.269) / -0.214
(-0.268) / -0.228
O2 / -0.507
(-0.502) / -0.529
(-0.518) / -0.479
(-0.482) / -0.410
(-0.405) / -0.465
(-0.455) / -0.367
(-0.362) / -0.396
(-0.393) / -0.334
(-0.360) / -0.337
C1 / 0.947
(0.970) / 0.950
(0.972) / 0.940
(0.968) / 0.892
(0.931) / 0.902
(0.933) / 0.840
(0.875) / 0.929
(0.962) / 0.975
(1.019) / 0.972
C2 / -0.201
(-0.213) / -0.200
(-0.212) / -0.204
(-0.216) / -0.196
(-0.199) / -0.206
(-0.212) / -0.197
(-0.197) / -0.193
(-0.197) / -0.209
(-0.212) / -0.209
H1 / 0.213
(0.212) / 0.222
(0.219) / 0.225
(0.219) / 0.219
(0.225) / 0.229
(0.225) / 0.222
(0.227) / 0.215
(0.224) / 0.240
(0.224) / 0.198
H2 / 0.223
(0.218) / 0.214
(0.212) / 0.214
(0.214) / 0.233
(0.228) / 0.216
(0.220) / 0.246
(0.244) / 0.239
(0.231) / 0.200
(0.204) / 0.198
H3 / 0.213
(0.212) / 0.214
(0.212) / 0.212
(0.214) / 0.233
(0.234) / 0.217
(0.220) / 0.258
(0.252) / 0.236
(0.231) / 0.200
(0.203) / 0.237
N1 / -0.443
(-0.411) / -0.440
(-0.408) / -0.444
(-0.425) / -0.272
(-0.271) / -0.279
(-0.269) / -0.115
(-0.110) / -0.197
(-0.230) / -0.326
(-0.310) / -0.343
N2 / 0.272
(0.315) / 0.269
(0.311) / 0.259
(0.304) / 0.0490
(0.101) / 0.0715
(0.108) / - / - / - / -0.102
N3 / 0.302
(0.263) / 0.289
(0.261) / 0.266
(0.232) / 0.232
(0.178) / 0.241
(0.182) / - / - / - / 0.142
/ 3.65
(5.13) / 2.85
(4.29) / 2.32
(3.55) / 3.28
(4.32) / 1.67
(2.15) / 2.70
(3.38) / 2.02
(2.47) / 2.68
(3.45) / 2.05
*See Scheme S.4 for numbering
Table S.4.4 Calculated Wiberg bond orders for methoxy substitution in both the gas phase and the aqueous phase (parenthesized values)
Bond* / Syn / Anti / TS1 / TS2 / TS3 / TS4 / NHC(OCH3)O+ / OC
NH
(OCH3)+ / [OC
NH(OCH3)
...N2]+
C1-O1 / 1.851
(1.766) / 1.855
(1.752) / 1.899
(1.811) / 1.959
(1.880) / 1.553
(1.504) / 1.749
(1.671) / 1.277
(1.267) / 2.265
(2.221) / 2.249
C1-O2 / 1.164
(1.153) / 1.151
(1.150) / 1.207
(1.192) / 0.885
(0.910) / 1.247
(1.262) / 0.974
(1.025) / 1.394
(1.397) / 0.067
(0.062) / 0.066
C1-N1 / 0.767
(0.848) / 0.777
(0.865) / 0.681
(0.766) / 0.985
(1.017) / 1.019
(1.033) / 1.127
(1.133) / 1.118
(1.107) / 1.430
(1.453) / 1.446
C2-O2 / 0.797
(0.816) / 0.797
(0.816) / 0.794
(0.811) / 0.787
(0.788) / 0.788
(0.763) / 0.801
(0.802) / 0.753
(0.760) / 0.850
(0.852) / 0.855
N1-N2 / 1.260
(1.263) / 1.255
(1.255) / 1.278
(1.277) / 0.394
(0.408) / 0.452
(0.428) / - / - / - / 0.018
N2-N3 / 2.605
(2.619) / 2.594
(2.612) / 2.580
(2.599) / 2.979
(2.982) / 2.959
(2.976) / - / - / - / 3.021
N1-N3 / 0.304
(0.294) / 0.306
(0.293) / 0.334
(0.323) / 0.043
(0.044) / 0.054
(0.047) / - / - / - / 0.002
N1-H / 0.738
(0.702) / 0.741
(0.703) / 0.751
(0.708) / 0.792
(0.755) / 0.795
(0.763) / 0.802
(0.775) / 0.800
(0.777) / 0.737
(0.708) / 0.681
O1-N1 / 0.099
(0092) / 0.096
(0.087) / 0.082
(0.071) / 0.124
(0.121) / 0.469
(0.473) / 0.415
(0.426) / 0.889
(0.882) / 0.162
(0.162) / 0.166
O2-N1 / 0.031
(0.030) / 0.029
(0.030) / 0.026
(0.025) / 0.439
(0.423) / 0.050
(0.049) / 0.458
(0.414) / 0.069
(0.065) / 0.981
(0.987) / 0.002
*See Scheme S.4 for numbering
Table S.4.5 Calculated vibrational wavenumbersa (cm−1) and intensities (km mol-1) at the B3LYP/6-311+G(d,p) level for the stationary points of methoxy homologue. Figures in the parentheses are computed intensities in km mol-1.
Syn / Anti / TS1 / TS2 / TS3 / TS4 / NHC(OCH3)O+ / OC
NH(OCH3)+ / [OC
NH(OCH3)...N2]+
3491
(226) / 3501
(247) / 3465
(213) / 3401
(127) / 3416
(126) / 3328
(249) / 3367
(142) / 3449
(216) / 3201
(1139)
3211
(0) / 3211
(0) / 3212
(0) / 3209
(4) / 3217
(2) / 3194
(25) / 3216
(5) / 3166
(9) / 3165
(17)
3183
(0) / 3185
(0) / 3182
(0) / 3166
(6) / 3188
(0) / 3135
(15) / 3207
(3) / 3156
(3) / 3153
(1)
3082
(2) / 3083
(2) / 3080
(1) / 3064
(7) / 3083
(0) / 3026
(119) / 3085
(2) / 3052
(5) / 3052
(5)
2367
(130) / 2355
(128) / 2352
(165) / 2433
(106) / 2421
(82) / 1761
(41) / 1912
(617) / 2383
(534) / 2455
(18)
1950
(356) / 1960
(450) / 1966
(438) / 2008
(335) / 1822
(468) / 1469
(52) / 1483
(39) / 1490
(25) / 2376
(578)
1482
(20) / 1483
(20) / 1482
(20) / 1473
(17) / 1485
(21) / 1429
(29) / 1459
(19) / 1463
(22) / 1494
(30)
1480
(16) / 1482
(18) / 1476
(17) / 1460
(8) / 1475
(15) / 1412
(31) / 1450
(13) / 1451
(2) / 1466
(25)
1472
(21) / 1473
(19) / 1469
(15) / 1447
(13) / 1469
(14) / 1231
(17) / 1344
(21) / 1414
(30) / 1463
(8)
1397
(193) / 1415
(60) / 1408
(65) / 1179
(40) / 1376
(149) / 1172
(1) / 1213
(21) / 1227
(3) / 1447
(4)
1255
(221) / 1247
(269) / 1257
(243) / 1164
(6) / 1218
(71) / 1088
(43) / 1155
(2) / 1174
(9) / 1239
(2)
1203
(34) / 1193
(16) / 1194
(13) / 1128
(7) / 1204
(3) / 1005
(60) / 1110
(161) / 1158
(3) / 1179
(11)
1164
(1) / 1167
(1) / 1162
(2) / 1019
(210) / 1162
(1) / 967
(46) / 1036
(36) / 948
(4) / 1160
(3)
1160
(365) / 1146
(359) / 1136
(417) / 977
(21) / 1011
(85) / 736
(27) / 1026
(74) / 868
(45) / 954
(8)
898
(66) / 940
(21) / 888
(16) / 925
(82) / 915
(62) / 667
(89) / 777
(51) / 647
(4) / 874
(52)
824
(212) / 825
(203) / 823
(41) / 790
(43) / 839
(39) / 640
(43) / 615
(4) / 554
(2) / 703
(68)
729
(6) / 721
(30) / 772
(220) / 675
(39) / 646
(21) / 512
(1) / 551
(37) / 491
(93) / 638
(20)
728
(25) / 685
(0) / 582
(14) / 577
(8) / 603
(15) / 214
(19) / 473
(40) / 368
(63) / 546
(42)
530
(5) / 525
(8) / 510
(16) / 401
(36) / 390
(57) / 160
(11) / 214
(11) / 261
(23) / 416
(9)
429
(43) / 460
(16) / 467
(19) / 298
(11) / 279
(22) / 86
(1) / 183
(13) / 181
(1) / 274
(33)
377
(3) / 375
(30) / 392
(62) / 234
(15) / 259
(8) / 302i
(38) / 38
(0) / 91
(2) / 182
(5)
289
(125) / 316
(123) / 296
(76) / 207
(19) / 195
(4) / 151
(0)
249
(30) / 258
(21) / 232
(37) / 166
(19) / 175
(14) / 141
(1)
178
(7) / 175
(13) / 209
(16) / 93
(4) / 109
(3) / 124
(7)
133
(0) / 132
(0) / 123
(1) / 76
(4) / 85
(1) / 88
(2)
81
(4) / 92
(0) / 75
(0) / 74
(0) / 36
(0) / 64
(5)
72
(1) / 76
(0) / 103i
(12) / 271i
(287) / 283i
(314) / 37
(2)
aScaled by 0.9679
Table S.4.6 NBO analysis
a) Interaction energy between donor and acceptor orbitals for syn and anti conformers of the methoxy homologue
NBO donor / NBO acceptor / Syn / AntiGas phase / Aqueous phase / Gas phase / Aqueous phase
σ(C1-N1) / σ*(N2-N3) / 4.4 / 4.7 / 4.4 / 4.7
σ(C1-N1) / π2*(N2-N3) / 6.4 / 5.3 / 5.4 / 4.4
σ(N2-N3) / σ*(N2-N1) / 5.5 / 5.7 / 5.4 / 5.5
π2(N2-N3) / σ*(C1-N2) / 3.4 / 3.4 / 3.7 / 3.6
σ(N2-N1) / σ*(N2-N3) / 4.6 / 4.9 / 4.5 / 4.8
σ(N1-H) / σ*(N2-N3) / 4.6 / 5.3 / 5.1 / 5.1
σ(N1-H) / σ*(N2-N3) / 4.9 / 5.3 / 5.4 / 6.2
n(N3) / σ*(N2-N1) / 15.3 / 14.7 / 15.4 / 14.8
n2(O1) / σ*(C1-N1) / 49.1 / 37.8 / 46.3 / 35.5
n2(O1) / σ*(C1-O2) / 23.6 / 24.8 / 23.7 / 24.5
n(N1) / π*(C1-O1) / 22.8 / 31.4 / 22.2 / 30.6
n(N1) / π*(N2-N3) / 71.2 / 73.7 / 71.1 / 72.7
n1(O2) / σ*(C1-O) / 11.4 / 10.7 / 11.2 / 10.8
n1(O2) / σ*(C1-N1) / 3.7 / 3.2 / 4.1 / 3.8
n2(O2) / π*(C1-O1) / 61.2 / 60.9 / 59.1 / 60.5
σ*(C1-N1) / σ*(O2-C2) / 4.7 / - / 7.2 / -
b) Occupancy of donor and acceptor orbitals for syn and anti conformers of the methoxy homologue
Occupancy / Syn / AntiGas phase / Aqueous phase / Gas phase / Aqueous phase
σ(C1-O1) / 1.99600 / 1.99613 / 1.99434 / 1.99447
π(C1-O1) / 1.99473 / 1.99438 / 1.99109 / 1.99085
σ(C1-N1) / 1.95666 / 1.96381 / 1.95795 / 1.96476
σ(C1-O2) / 1.98997 / 1.99063 / 1.99163 / 1.99257
σ(N2-N3) / 1.99643 / 1.99636 / 1.99627 / 1.99623
π(N2-N3) / 1.99484 / 1.99413 / 1.99471 / 1.99406
π2(N2-N3) / 1.98335 / 1.98457 / 1.98326 / 1.98461
σ(N2-N1) / 1.99408 / 1.99361 / 1.99459 / 1.99408
σ(N2-H) / 1.97082 / 1.96648 / 1.96891 / 1.96557
σ(O2–C2) / 1.97600 / 1.98026 / 1.97929 / 1.98308
σ(C2–H1) / 1.99361 / 1.99359 / 1.99125 / 1.99159
σ(C2–H2) / 1.99135 / 1.99175 / 1.99397 / 1.99381
σ(C2–H3) / 1.99357 / 1.99359 / 1.99398 / 1.99381
n(N1) / 1.97368 / 1.97503 / 1.97339 / 1.97468
n1(O1) / 1.97634 / 1.97903 / 1.97627 / 1.97906
n2(O1) / 1.76180 / 1.80578 / 1.74436 / 1.79457
n(N4) / 1.66208 / 1.63833 / 1.66148 / 1.64093
n1(O2) / 1.95112 / 1.95424 / 1.95238 / 1.95315
n2(O 2) / 1.75489 / 1.75522 / 1.76587 / 1.76114
σ*(C1-O1) / 0.02212 / 0.02210 / 0.02089 / 0.02100
π*(C1-O1) / 0.27825 / 0.29745 / 0.26990 / 0.29448
σ*(C1-N) / 0.18199 / 0.13539 / 0.17595 / 0.13087
σ*(C1-O2) / 0.07770 / 0.07784 / 0.08053 / 0.07962
σ*(N2-N3) / 0.01007 / 0.01009 / 0.01052 / 0.01036
π*(N2-N3) / 0.28372 / 0.28817 / 0.28429 / 0.28508
π2*(N2-N3) / 0.05506 / 0.04839 / 0.06906 / 0.05852
σ*(N2-N1) / 0.02582 / 0.02447 / 0.03389 / 0.03050
σ*(N1-H) / 0.01266 / 0.01104 / 0.01003 / 0.00926
σ*(O2-C2) / 0.01253 / 0.01158 / 0.01263 / 0.01187
σ(C2–H1) / 0.00743 / 0.00830 / 0.00522 / 0.00582
σ(C2–H2) / 0.00530 / 0.00595 / 0.00735 / 0.00815
σ(C2–H3) / 0.00743 / 0.00830 / 0.00735 / 0.00815
Table S.4.7NBO analysis
a) Interaction energy between donor and acceptor orbitals for the intermediate
NBO donor / NBO acceptor / NHC(OCH3)O+Gas phase / Aqueous phase
σ(C1-O1) / σ*(C1-O2) / 3.2 / 3.4
π2(C1-O1) / σ*(O1-N) / 3.1 / 3.0
π2(C1-N) / σ*(C1-O2) / 5.2 / 5.1
σ(C1-N) / σ*(O1-N) / 3.8 / 4.1
σ(C1-N) / σ*(C2-O2) / 3.3 / 3.4
σ(O1-N) / σ*(C1-O1) / 7.9 / 7.8
σ(O1-N) / σ*(C1-N) / 6.7 / 6.7
σ(O1-N) / σ*(C1-O2) / 29.1 / 28.2
σ(N–H) / π*(C1-O2) / 8.9 / 10.1
σ(O2–C2) / σ*(C1-N) / 7.4 / 7.5
σ(C2–H1) / σ*(C1-O2) / 2.7 / 2.3
n1(O1) / σ*(C1-O2) / 3.6 / 3.7
n1(O1) / π*(C1-O2) / 81.2 / 79.0
n(N) / σ*(C1-O2) / 3.8 / 3.3
n(N) / π*(C1-O2) / 13.6 / 11.8
n1(O2) / σ*(C1-O1) / 15.3 / 15.3
π*(C1-O2) / σ*(N–H) / 2.3 / 1.7
b) Occupancy of donor and acceptor orbitals for the intermediate
Occupancy / NHC(OCH3)O+Gas phase / Aqueous phase
σ(C1-O1) / 1.98672 / 1.98679
σ(C1-N) / 1.97267 / 1.97203
σ(C1-O2) / 1.99636 / 1.99644
π(C1-O2) / 1.99069 / 1.99070
σ(O1-N) / 1.93022 / 1.93189
σ(N-H) / 1.95741 / 1.95486
σ(O2–C2) / 1.97174 / 1.97242
σ(C2–H1) / 1.99478 / 1.99493
σ(C2–H2) / 1.98839 / 1.98954
σ(C2–H3) / 1.98872 / 1.98837
n1(O1) / 1.98947 / 1.98978
n2(O1) / 1.72308 / 1.73308
n(N) / 1.90749 / 1.91886
n1(O2) / 1.93380 / 1.93479
σ*(C1-O1) / 0.05073 / 0.04981
σ*(C1-N) / 0.03932 / 0.03823
σ*(C1-O2) / 0.05638 / 0.05321
π*(C1-O2) / 0.38331 / 0.36864
σ*(O1-N) / 0.02672 / 0.02776
σ*(N-H) / 0.01014 / 0.00907
σ*(O2–C2) / 0.01791 / 0.01657
σ*(C2–H1) / 0.00465 / 0.00478
σ*(C2–H2) / 0.00454 / 0.00451
σ*(C2–H3) / 0.00446 / 0.00477
Table S.4.8NBO analysis
a) Interaction energy between donor and acceptor orbitals for the product
NBO donor / NBO acceptor / OCNH(OCH3)+Gas phase / Aqueous phase
σ(C1-O1) / σ*(C1-N) / 5.9 / 5.4
π2(C1-O1) / σ*(O2-N) / 3.8 / 3.8
π2(C1-O1) / σ*(N-H) / 2.2 / 2.1
σ(C1-N) / σ*(O1-C) / 5.1 / 6.6
σ(H-N) / σ*(C1-O1) / 3.4 / 5.0
σ(H-N) / π*(C1-O1) / 3.0 / 6.6
σ(H-N) / π2*(C1-O1) / 5.9 / -
σ(N-O2) / π*(C1-O1) / 1.0 / 5.2
σ(N-O2) / π2*(C1-O1) / 5.9 / -
n(O1) / σ*(C1-N) / 10.0 / 8.8
n2(O1) / σ*(C1-O1) / - / 4.1
n2(O1) / π*(C1-N) / - / 123.1
n(N) / σ*(C1-O1) / 5.5 / -
n(N) / π*(C1-O1) / 49.0 / -
n2(O2) / π2*(C1-O1) / 2.1 / 2.0
n2(O2) / σ*(C1-N) / 4.1 / 6.0
n2(O2) / σ*(N-H) / 4.6 / 3.8
π2*(C1-O1) / σ*(C1-O1) / 23.6 / 2.1
π2*(C1-O1) / σ*(C1-N) / 3.1 / 15.4
b) Occupancy of donor and acceptor orbitals for the product
Occupancy / OCNH(OCH3)+Gas phase / Aqueous phase
σ(C1-O) / 1.99503 / 1.99572
π(C1-O1) / 1.99626 / 1.98609
π2(C1-O1) / 1.98573 / -
σ(C1-N) / 1.99340 / 1.98841
π(C1-N) / - / 1.98645
σ(N-H) / 1.96833 / 1.97171
σ(N-O2) / 1.96840 / 1.97308
σ(C2-O2) / 1.98851 / 1.98858
σ(C2-H1) / 1.97233 / 1.97712
σ(C2-H2) / 1.99474 / 1.99528
σ(C2-H3) / 1.99577 / 1.99626
n1(O1) / 1.98038 / 1.98131
n(N) / 1.65008 / 1.59571
n1(O2) / 1.97982 / 1.98000
n2(O2) / 1.93083 / 1.93687
σ*(C1-O1) / 0.05522 / 0.01490
π*(C1-O1) / 0.31355 / 0.05750
π2*(C1-O1) / 0.06299 / 0.05894
σ*(C1-N) / 0.02188 / 0.37772
σ*(N-H) / 0.02504 / 0.01881
σ*(O2-N) / 0.03265 / 0.02981
σ*(O2–C2) / 0.00838 / 0.00857
σ*(C2–H1) / 0.00465 / 0.00495
σ*(C2–H2) / 0.01013 / 0.01032
σ*(C2–H3) / 0.00982 / 0.01023
S.5 Amino Substitution
Scheme S.5
Figure S.5.1 Energy profile for the rearrangement of amine substituted precursor in the gas phase (solid lines) and the aqueous phase (dotted lines)
Table S.5.1 Structural parameters (Å and degrees) and rotational constants (GHz) of the stationary points on the potential energy surface in the gas phase and the aqueous phase (parenthesized values)
Parametersa / Syn / Anti / TS1 / TS2 / TS3 / TS4 / NHC(NH2)O+Bond Lengths
C-N1 / 1.590
(1.500) / 1.608
(1.507) / -
(1.569) / 1.444
(1.411) / 1.441
(1.423) / 1.347
(1.349) / 1.357
(1.359)
N1-N2 / 1.276
(1.266) / 1.277
(1.271) / -
(1.272) / 1.810
(1.815) / 1.716
(1.769) / - / -
N2-N3 / 1.111
(1.109) / 1.114
(1.110) / -
(1.110) / 1.097
(1.096) / 1.100
(1.096) / - / -
C=O / 1.179
(1.204) / 1.175
(1.202) / -
(1.196) / 1.176
(1.191) / 1.213
(1.232) / 1.203
(1.218) / 1.271
(1.279)
C-N4 / 1.327
(1.322) / 1.329
(1.322) / -
(1.315) / 1.387
(1.370) / 1.316
(1.301) / 1.373
(1.345) / 1.283
(1.274)
N1-H / 1.022
(1.027) / 1.024
(1.026) / -
(1.028) / 1.031
(1.034) / 1.029
(1.034) / 1.036
(1.039) / 1.032
(1.034)
N1-N4 / 2.378
(2.322) / 2.415
(2.380) / -
(2.350) / 2.040
(2.084) / 2.456
(2.453) / 2.218
(2.244) / 2.512
(2.501)
O-N1 / 2.362
(2.322) / 2.348
(2.283) / -
(2.377) / 2.400
(2.350) / 2.050
(2.017) / 2.218
(2.192) / 1.630
(1.645)
Bond Angles
CN1N2 / 114.3
(117.4) / 122.3
(124.3) / -
(116.9) / 107.8
(108.0) / 119.7
(116.4) / - / -
N1N2N3 / 172.8
(176.2) / 175.3
(177.4) / -
(175.6) / 160.4
(156.3) / 154.6
(155.9) / - / -
N1CO / 116.3
(118.0) / 114.2
(114.4) / -
(118.0) / 132.1
(129.0) / 100.8
(98.7) / 120.8
(117.3) / 76.6
(77.1)
N1CN4 / 108.9
(110.7) / 110.2
(114.4) / -
(108.9) / 92.2
(96.9) / 125.8
(128.4) / 109.3
(112.8) / 144.3
(143.6)
Dihedral Angles
N2N1CO / 3.0
(-0.2) / 131.7
(153.0) / -
(76.5) / 17.9
(-30.7) / -174.1
(-178.5) / - / -
Rotational Constants
A / 10.075
(10.368) / 8.64
(9.419) / -
(8.097) / 8.972
(9.501) / 8.998
(8.946) / 12.537
(12.768) / 21.756
(21.306)
B / 2.533
(2.542) / 2.439
(2.492) / -
(2.453) / 2.177
(2.178) / 2.170
(2.173) / 10.400
(10.413) / 8.105
(8.185)
C / 2.029
(2.042) / 2.012
(2.007) / -
(2.156) / 1.811
(1.801) / 1.766
(1.770) / 5.900
(5.934) / 6.019
(6.035)
aSee Scheme S.5 for numbering
Table S.5.2 Optimized geometry of the product of the Schmidt rearrangement in the gas phase and the aqueous phase (parenthesized values)
Bonda / [OCNH(NH2)...N2]+ / OCNH(NH2)+Bond Lengths
C-N1 / 1.274 / 1.278
(1.267)
N2-N3 / 1.095 / -
C=O / 1.130 / 1.128
(1.132)
N1-H / 1.036 / 1.025
(1.027)
N1-N4 / 1.424 / 1.419
(1.426)
N2-H / 1.976 / -
Bond Angles
N1CO / 179.8 / 179.2
(179.3)
N4N1H / 125.2 / 125.7
(124.4)
Dihedral Angles
HN1CO / 178.0 / 178.8
(179.9)
N4N1CO / -1.94 / -1.181
(-0.130)
Rotational Constants
A / 5.765 / 38.907
(40.941)
B / 1.332 / 5.020
(4.979)
C / 1.089 / 4.603
(4.550)
aSee Scheme S.5 for numbering
Table S.5.3 NBO charges on the various atoms* and dipole moments (Debye) of the stationary points on the potential energy surface in the gas phase and the aqueous phase (parenthesized values)
Atom / Syn / Anti / TS1 / TS2 / TS3 / TS4 / NHC(NH2)
O+ / OC
NH
(NH2)+ / OCNH
(NH2)+
…N2
H / 0.459
(0.511) / 0.468
(0.508) / -
(0.498) / 0.430
(0.464) / 0.435
(0.462) / 0.417
(0.438) / 0.409
(0.432) / 0.461
(0.495) / 0.470
(-)
C / 0.824
(0.825) / 0.828
(0.831) / -
(0.827) / 0.777
(0.796) / 0.776
(0.791) / 0.702
(0.726) / 0.780
(0.803) / 1.007
(1.043) / 1.004
(-)
N4 / -0.773
(-0.760) / -0.783
(-0.770) / -
(-0.740) / -0.704
(-0.663) / -0.744
(-0.724) / -0.602
(-0.581) / -0.677
(-0.663) / -0.596
(-0.621) / -0.598
(-)
O / -0.482
(-0.625) / -0.438
(-0.597) / -
(-0.571) / -0.417
(-0.544) / -0.385
(-0.483) / -0.284
(-0.389) / -0.231
(-0.286) / -0.218
(-0.286) / -0.231
(-)
N1 / -0.465
(-0.416) / -0.460
(-0.418) / -
(-0.441) / -0.356
(-0.329) / -0.351
(-0.331) / -0.155
(-0.159) / -0.210
(-0.249) / -0.462
(-0.450) / -0.479
(-)
N2 / 0.267
(0.315) / 0.252
(0.301) / -
(0.303) / 0.101
(0.134) / 0.111
(0.143) / - / - / - / -0.104
(-)
N3 / 0.295
(0.243) / 0.259
(0.239) / -
(0.214) / 0.266
(0.202) / 0.276
(0.216) / - / - / - / 0.138
(-)
/ 5.33
(7.85) / 2.98
(4.91) / -
(5.36) / 4.40
(7.60) / 3.59
(4.94) / 3.920
(5.18) / 4.22
(5.36) / 3.82
(4.99) / 2.19
(-)
*See Scheme S.5 for numbering
Table S.5.4 Calculated Wiberg bond orders in the gas phase and the aqueous phase (parenthesized values)
Bond* / Syn / Anti / TS1 / TS2 / TS3 / TS4 / NHC(NH2)
O+ / OC
NH(NH2)+ / OC
NH(NH2)+
…N2
C-O / 1.851
(1.682) / 1.878
(1.687) / -
(1.740) / 1.920
(1.784) / 1.580
(1.461) / 1.669
(1.565) / 1.249
(1.204) / 2.283
(2.218) / 2.267
(-)
C-N1 / 0.696
(0.821) / 0.677
(0.816) / -
(0.725) / 0.937
(1.023) / 0.960
(0.992) / 1.180
(1.173) / 1.119
(1.098) / 1.415
(1.462) / 1.432
(-)
C1-N4 / 1.291
(1.330) / 1.286
(1.332) / -
(1.372) / 1.025
(1.065) / 1.335
(1.412) / 1.064
(1.173) / 1.495
(1.548) / 0.047
(0.039) / 0.045
(-)
N1-N2 / 1.265
(1.281) / 1.277
(1.275) / -
(1.288) / 0.532
(0.510) / 0.625
(0.567) / - / - / - / 0.016
(-)
N2-N3 / 2.603
(2.601) / 2.570
(2.588) / -
(2.586) / 2.953
(2.950) / 2.899
(2.933) / - / - / - / 3.021
(-)
N1-H / 0.754
(0.706) / 0.748
(0.710) / -
(0.715) / 0.791
(0.763) / 0.799
(0.764) / 0.798
(0.779) / 0.803
(0.784) / 0.729
(0.703) / 0.679
(-)
O-N1 / 0.114
(0.100) / 0.106
(0.096) / -
(0.086) / 0.128
(0.133) / 0.378
(0.403) / 0.483
(0.487) / 0.909
(0.901) / 0.163
(0.165) / 0.166
(-)
N1-N3 / 0.312
(0.309) / 0.332
(0.314) / -
(0.332) / 0.061
(0.061) / 0.094
(0.075) / - / - / - / 0.001
(-)
*See Scheme S.5 for numbering
Table S.5.5 Calculated vibrational wavenumbersa (cm−1) and intensities (km mol-1) at the B3LYP/6-311+G(d,p) level for the stationary points of amino homologue. Figures in the parentheses are computed intensities in km mol-1.
Syn / Anti / TS2 / TS3 / TS4 / NHC(NH2)O+ / OC
NH(NH2)+ / OC
NH(NH2)+…N2
3675(138) / 3661(124) / 3622(175) / 3674(117) / 3559(212) / 3597(218) / 3589(85) / 3587(75)
3556(221) / 3545(170) / 3493(329) / 3549(200) / 3440(312) / 3489(250) / 3481(66) / 3481(55)
3482(163) / 3463(207) / 3406(118) / 3432(125) / 3359(267) / 3370(124) / 3417(176) / 3217(967)
2362(128) / 2332(161) / 2420(98) / 2377(50) / 1719(43) / 1922(392) / 2402(475) / 2454(15)
1992(397) / 2010(484) / 1955(335) / 1857(397) / 1578(64) / 1613(45) / 1678(19) / 2396(534)
1636(106) / 1636(92) / 1584(75) / 1630(57) / 1344(13) / 1396(23) / 1458(16) / 1679(20)
1407(131) / 1404(47) / 1218(7) / 1386(73) / 1108(21) / 1159(106) / 1323(3) / 1493(13)
1274(158) / 1270(161) / 1170(65) / 1309(33) / 993(3) / 1088(16) / 1237(13) / 1323(3)
1183(160) / 1152(172) / 1069(23) / 1100(4) / 907(76) / 1053(55) / 1029(36) / 1256(22)
1122(23) / 1115(42) / 968(5) / 933(45) / 679(17) / 951(15) / 822(113) / 1026(26)
714(17) / 769(20) / 827(61) / 833(30) / 626(241) / 665(233) / 620(50) / 842(136)
689(7) / 682(128) / 630(10) / 645(33) / 511(48) / 623(23) / 611(0) / 740(60)
568(163) / 566(116) / 627(56) / 548(125) / 440(11) / 586(21) / 534(104) / 628(41)
517(58) / 546(85) / 549(160) / 522(29) / 390(16) / 504(34) / 324(77) / 580(62)
501(55) / 515(6) / 487(51) / 426(23) / 377i(39) / 435(3) / 227(3) / 325(55)
419(67) / 455(140) / 364(1) / 415(99) / 238(8)
375(177) / 433(83) / 257(6) / 300(16) / 157(2)
371(44) / 373(50) / 212(4) / 248(16) / 138(2)
210(61) / 354(42) / 117(5) / 113(6) / 120(18)
151(4) / 149(8) / 93(3) / 105(9) / 86(6)
76(3) / 58(13) / 485i(414) / 462.5i(301) / 40(6)
aScaled by 0.9679
Table S.5.6 NBO analysis
a) Interaction energy between donor and acceptor orbitals for syn and anti conformers of amino homologue
NBO donor / NBO acceptor / Syn / AntiGas phase / Aqueous phase / Gas phase / Aqueous phase
σ(C1-O) / σ*(C1-N4) / 3.4 / - / 3.2 / 3.0
σ(C1-N1) / σ*(N2-N3) / 3.8 / 4.8 / 3.2 / 4.3
σ(C1-N1) / π2*(N2-N3) / 8.1 / 5.9 / 7.2 / 2.0
σ(C1-N4) / σ*(C1-O) / 3.2 / 2.8 / 3.1 / 2.7
σ(N2-N3) / σ*(N2-N1) / 5.3 / 5.7 / 5.1 / 5.4
π2(N2-N3) / σ*(N1-H) / 3.6 / 3.6 / 3.6 / 3.6
σ(N2-N1) / σ*(N2-N3) / 4.5 / 5.0 / 5.1 / 4.8
σ(N1-H) / σ*(N2-N3) / 5.0 / 5.6 / 4.5 / 5.0
σ(N1-H) / π2*(N2-N3) / 4.7 / 5.8 / 4.4 / 6.8
n2(N3) / σ*(N2-N1) / 15.3 / 14.7 / 15.6 / 14.8
n2(O) / σ*(C1-N4) / 61.0 / 41.4 / 4.6 / 3.4
n2(O) / σ*(C1-N1) / 18.6 / 18.9 / 60.2 / 39.1
n(N1) / π*(C1-O) / 15.6 / 29.0 / 10.4 / 22.1
n(N1) / π*(N2-N3) / 54.1 / 76.6 / 43.7 / 64.9
n(N2) / π*(C1-O) / 60.7 / 84.8 / 65.8 / 80.3
b) Occupancy of donor and acceptor orbitals for syn and anti conformers of amino homologue
Occupancy / Syn / AntiGas phase / Aqueous phase / Gas phase / Aqueous phase
σ(C1-O) / 1.99449 / 1.99406 / 1.99413 / 1.99281
π(C1-O) / 1.99485 / 1.99535 / 1.99084 / 1.99029
σ(C1-N1) / 1.94606 / 1.96299 / 1.93073 / 1.95950
σ(C1-N4) / 1.98862 / 1.98956 / 1.99006 / 1.99170
σ(N2-N3) / 1.99664 / 1.99582 / 1.99688 / 1.99596
π(N2-N3) / 1.99487 / 1.99465 / 1.99478 / 1.99454
π2(N2-N3) / 1.98322 / 1.98418 / 1.98334 / 1.98402
σ(N2-N1) / 1.99421 / 1.99382 / 1.99465 / 1.99424
σ(N2-H) / 1.96537 / 1.96677 / 1.95636 / 1.95853
n(N3) / 1.97339 / 1.97517 / 1.97303 / 1.97480
n1(O) / 1.97590 / 1.97892 / 1.97554 / 1.97870
n2(O) / 1.72823 / 1.80640 / 1.70343 / 1.79156
n(N1) / 1.68682 / 1.63602 / 1.69233 / 1.64880
n(N4) / 1.70323 / 1.66605 / 1.71301 / 1.67385
σ*(C1-O) / 0.02607 / 0.01314 / 0.01342 / 0.01528
π*(C1-O) / 0.30675 / 0.37699 / 0.30049 / 0.36471
σ*(C1-N1) / 0.22741 / 0.15047 / 0.23650 / 0.14987
σ*(C1-N4) / 0.05194 / 0.05026 / 0.05174 / 0.05039
σ*(N2-N3) / 0.01440 / 0.01039 / 0.01725 / 0.01226
π*(N2-N3) / 0.27515 / 0.30398 / 0.29131 / 0.30069
π2*(N2-N3) / 0.06470 / 0.05362 / 0.08933 / 0.06894
σ*(N2-N1) / 0.02301 / 0.02282 / 0.03147 / 0.03242
σ*(N1-H) / 0.01589 / 0.01149 / 0.01272 / 0.01124
Table S.5.7NBO analysis
a) Interaction energy between donor and acceptor orbitals for the intermediate
NBO donor / NBO acceptor / NHC(NH2)O+Gas phase / Aqueous phase
σ(C1-O) / σ*(C1-N4) / 3.4 / 3.5
σ(C1-O) / σ*(O-N1) / 3.4 / 3.3
σ(C1-N1) / σ*(O-N1) / 3.5 / 3.6
σ(O-N1) / σ*(C1-O) / 7.5 / 7.6
σ(O-N1) / σ*(C1-N1) / 6.7 / 6.4
σ(O-N1) / σ*(C1-N4) / 23.9 / 22.3
σ(O-N1) / π*(C1-N4) / 4.5 / 3.8
σ(N1-H) / π*(C1-N4) / 9.2 / 10.3
σ(N1-H1) / σ*(C1-O) / 7.9 / 8.9
σ(N1-H2) / σ*(C1-N1) / 7.4 / 8.0
n2(N1) / π *(C1-N4) / 6.2 / 6.1
n2(O) / σ*(C1-N4) / 2.4 / 1.5
n2(O) / π*(C1-N4) / 53.5 / 53.1
n(N1) / σ*(C1-N4) / 6.9 / 5.5
n(N1) / π*(C1-N4) / 6.2 / 6.1
π*(C1-N4) / σ*(C1-N4) / 23.9 / 13.4
b) Occupancy of donor and acceptor orbitals for the intermediate
Occupancy / NHC(NH2)O+Gas phase / Aqueous phase
σ(C1-O) / 1.98267 / 1.98308
σ(C1-N1) / 1.97462 / 1.97479
σ(C1-N4) / 1.99110 / 1.99326
π(C1-N4) / 1.98959 / 1.99223
σ(O-N1) / 1.94316 / 1.94711
σ(N1-H) / 1.95977 / 1.95892
n1(O) / 1.98971 / 1.99028
n2(O) / 1.74632 / 1.77394
n(N1) / 1.91362 / 1.92729
σ*(C1-O) / 0.02602 / 0.02827
σ*(C1-N1) / 0.02380 / 0.02478
σ*(C1-N4) / 0.08771 / 0.06474
π*(C1-N4) / 0.31001 / 0.28862
σ*(O-N1) / 0.02649 / 0.02733
σ*(N1-H) / 0.01022 / 0.00912
Table S.5.8 NBO analysis
a) Interaction energy between donor and acceptor orbitals for the product
NBO donor / NBO acceptor / NHC(NH2)O+Gas phase / Aqueous phase
σ(C1-O) / σ*(C1-N1) / 6.0 / 6.1
π2(C1-O) / σ*(H-N1) / 2.3 / 2.1
π2(C1-O) / σ*(N4-N1) / 2.6 / 2.6
σ(C1-N1) / σ*(C1-O) / 5.4 / 5.6
σ(H-N1) / σ*(C1-O) / 4.7 / 5.0
σ(O-N1) / π2*(C1-O) / 6.4 / 7.6
σ(N1-N4) / σ*(C1-O) / 4.4 / 4.3
σ(N1-N4) / π2*(C1-O) / 5.8 / 5.9
n(O) / π*(C1-N4) / 9.9 / 9.6
n1(N1) / π*(C1-O) / 88.1 / 97.6
n1(N4) / σ*(N4-H) / 8.1 / 6.7
b) Occupancy of donor and acceptor orbitals for the product
Occupancy / NHC(NH2)O+Gas phase / Aqueous phase
σ(C1-O) / 1.98267 / 1.99663
π(C1-O) / 1.99888 / 1.99895
π2(C1-O) / 1.98994 / 1.99016
σ(C1-N1) / 1.99363 / 1.99352
σ(N1-H) / 1.97358 / 1.96772
σ(N1-N4) / 1.97546 / 1.97332
n1(O) / 1.97954 / 1.98061
n(N1) / 1.64875 / 1.61966
n(N4) / 1.94625 / 1.96357
σ*(C1-O) / 0.00962 / 0.01002
π*(C1-O) / 0.33455 / 0.36625
π2*(C1-O) / 0.05505 / 0.05482
σ*(C1-N1) / 0.02226 / 0.02074
σ*(N1-H) / 0.03108 / 0.02412
σ*(N1-N4) / 0.00860 / 0.00842
Reference
[1]F. Ijjaali, M. Alcamí, O. Mó andM. Yáñez,Mol. Phys.,99, 1129-1137 (2001).
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