Supplementary Information

Supplementary Information
Thermochemistry of Disputed Soot Formation Intermediates C4H3 and C4H5
Steven E. Wheeler, Wesley D. Allen, and Henry F. Schaefer
Table S1. Open-shell T1 diagnostics92 and maximum T1 and T2
amplitudes for isomers of C4H3 and C4H5 at the cc-pVTZ ROCCSD
level.a
Species
a
T1 Diagnostic
Largest T1
Largest T2
Amplitude
Amplitude
i-C4H3
0.024
0.111
0.105
Z-n-C4H3
0.015
0.050
0.092
E-n-C4H3
0.015
0.048
0.093
i-C4H5
0.024
0.124
0.089
Z-n-C4H5
0.014
0.039
0.107
E-n-C4H5
0.014
0.037
0.108
Computed at frozen-core TZ(2d1f,2p1d) ROCCSD(T) geometries using Psi3.111
Table S2. Incremental valence focal point table (kcal mol–1) for the energy of the C2v-symmetric
structure 5 relative to i-C4H3.a
Basis Set
∆Ee[ROHF]
+δ[ZAPT2]
+δ[CCSD]
+δ[CCSD(T)]
+δ(CCSDT)
∆Ee[CCSDT]
i-C4H3 (4) → C2v-C4H3 (5)
a
cc-pVDZ
2.609
–3.814
+1.966
–0.200
+0.071
0.633
cc-pVTZ
2.587
–4.213
+2.122
–0.248
[+0.071]
[0.320]
cc-pVQZ
2.592
–4.344
+2.177
–0.260
[+0.071]
[0.236]
cc-pV5Z
2.599
–4.342
[+2.147]
[–0.265]
[+0.071]
[0.211]
cc-pV6Z
2.601
[–4.341]
[+2.147]
[–0.265]
[+0.071]
[0.214]
CBS limit
[2.602]
[–4.340]
[+2.147]
[–0.265]
[+0.071]
[0.216]
Fit
a + be −cX
a + bX −3
a + bX −3
a + bX −3
additive
Points (X=)
4,5,6
4,5
3,4
3,4
Cut-off
none
none
5
5
See footnote a of Table IV. The extrapolated core-correlation correction is –0.044 kcal mol–1, resulting in a final
extrapolated energy separation of 0.172 kcal mol–1.
Table S3. Incremental core-correlation focal point tables (kcal mol–1) for isomerization
reactions of C4H3.a
Basis Set
∆fp(core)[ZAPT2]
+δ[CCSD]
+δ[CCSD(T)]
∆fp(core)[CCSD(T)]
i-C4H3 → Z-n-C4H3
cc-pVDZ
0.118
–0.015
+0.007
0.110
cc-pVTZ
0.140
–0.028
+0.009
0.120
cc-pVQZ
0.152
[–0.028]
[+0.009]
[0.132]
cc-pV5Z
[0.156]
[–0.028]
[+0.009]
[0.136]
CBS limit
[0.160]
[–0.028]
[+0.009]
[0.141]
i-C4H3 → E-n-C4H3
a
cc-pVDZ
0.121
–0.015
+0.007
0.112
cc-pVTZ
0.132
–0.029
+0.008
0.112
cc-pVQZ
0.144
[–0.029]
[+0.008]
[0.124]
cc-pV5Z
[0.148]
[–0.029]
[+0.008]
[0.128]
CBS limit
[0.152]
[–0.029]
[+0.008]
[0.132]
Fit
a + bX −3
additive
additive
Points (X=)
3,4
Cut-off
none
See footnote a of Table IV for notation. This table pertains to the core correlation correction [∆fp(core)]
to the reaction energy.
Table S4. Incremental core-correlation focal point tables (kcal mol–1) for
isomerization reactions of C4H5.a
Basis Set
∆fp(core)[ZAPT2]
+δ[CCSD]
+δ[CCSD(T)]
∆fp(core)[CCSD(T)]
i-C4H5 → Z-n-C4H5
cc-pVDZ
0.161
–0.020
–0.000
0.141
cc-pVTZ
0.182
–0.020
–0.003
0.159
cc-pVQZ
0.198
[–0.020]
[–0.003]
[0.175]
cc-pV5Z
[0.205]
[–0.020]
[–0.003]
[0.181]
CBS limit
[0.211]
[–0.020]
[–0.003]
[0.188]
i-C4H5 → E-n-C4H5
a
cc-pVDZ
0.159
–0.020
–0.000
0.139
cc-pVTZ
0.173
–0.020
–0.003
0.150
cc-pVQZ
0.189
[–0.020]
[–0.003]
[0.167]
cc-pV5Z
[0.195]
[–0.020]
[–0.003]
[0.173]
CBS limit
[0.201]
[–0.020]
[–0.003]
[0.179]
Fit
a + bX −3
additive
additive
Points (X=)
3,4
Cut-off
none
See footnote a of Table IV. This table pertains to the core correlation correction [∆fp(core)] to the
reaction energy.
Table S5. Incremental core-correlation focal point tables (kcal mol–1) for
decomposition reactions of C4H4 and C4H6.a
Basis Set
∆fp(core)[MP2]
+δ[CCSD]
+δ[CCSD(T)]
∆ fp(core)[CCSD(T)]
C4H4 + C2H6 → C3H6 + C3H4
cc-pVDZ
–0.004
–0.000
+0.004
–0.001
cc-pVTZ
–0.028
–0.003
+0.006
–0.025
cc-pVQZ
–0.041
[–0.003]
[+0.006]
[–0.038]
cc-pV5Z
[–0.045]
[–0.003]
[+0.006]
[–0.042]
CBS limit
[–0.050]
[–0.003]
[+0.006]
[–0.047]
C4H6 + C2H6 → C3H6 + C3H6
a
cc-pVDZ
0.009
–0.000
+0.001
0.010
cc-pVTZ
–0.009
–0.003
+0.000
–0.012
cc-pVQZ
–0.017
[–0.003]
[+0.000]
[–0.020]
cc-pV5Z
[–0.020]
[–0.003]
[+0.000]
[–0.022]
CBS limit
[–0.021]
[–0.003]
[+0.000]
[–0.025]
Fit
a + bX −3
additive
additive
Points (X=)
3,4
Cut-off
none
See footnote a of Table IV. This table pertains to the core correlation correction [∆fp(core)] to the
reaction energy.
Table S6. Incremental core-correlation focal point tables (kcal mol–1) for isodesmic
reaction of i-C4H3 and i-C4H5.a
Basis Set
∆ fp(core)[ZAPT2]
+δ[CCSD]
+δ[CCSD(T)]
∆ fp(core)[CCSD(T)]
i-C4H3 + CH4→ C4H4 + CH3
cc-pVDZ
0.117
–0.005
+0.008
0.120
cc-pVTZ
0.112
–0.014
+0.012
0.110
cc-pVQZ
0.121
[–0.014]
[+0.012]
[0.119]
cc-pV5Z
[0.125]
[–0.014]
[+0.012]
[0.123]
CBS limit
[0.129]
[–0.014]
[+0.012]
[0.126]
i-C4H5 + CH4→ C4H6 + CH3
a
cc-pVDZ
0.161
–0.010
+0.002
0.152
cc-pVTZ
0.153
–0.006
+0.001
0.148
cc-pVQZ
0.168
[–0.006]
[+0.001]
[0.162]
cc-pV5Z
[0.173]
[–0.006]
[+0.001]
[0.167]
CBS limit
[0.178]
[–0.006]
[+0.001]
[0.172]
Fit
a + bX −3
additive
additive
Points (X=)
3,4
Cut-off
none
See footnote a of Table IV. This table pertains to the core correlation correction [∆fp(core)] to the
reaction energy.
Table S7. Harmonic vibrational frequencies (cm–1) for C4H4 and
isomers of C4H3, computed at the cc-pVDZ ROCCSD(T) level of
theory. IR intensities (km mol–1) are in parentheses.
Species
a′
a′′
C4H4 (vinylacetylene,1)
206 (2)
297 (4)
524 (1)
670 (0)
883 (3)
914 (25)
1097 (4)
979 (23)
1304 (1)
1432 (2)
1655 (6)
2146 (1)
3167 (3)
3186 (7)
3271 (8)
3461 (56)
E-n-C4H3 (2)
209 (5)
306 (14)
511 (3)
571 (55)
616 (34)
662 (16)
816 (18)
784 (0)
1015 (8)
1252 (3)
1609 (3)
2148 (1)
3094 (5)
3255 (1)
3462 (57)
Z-n-C4H3 (3)
199 (0)
314 (1)
491 (6)
567 (33)
613 (40)
663 (16)
875 (11)
860 (46)
997 (21)
1253 (1)
1594 (4)
2139 (0)
3166 (3)
3250 (1)
3461 (57)
i-C4H3 (4)
149 (4)
245 (2)
378 (7)
509 (9)
435 (37)
575 (28)
871 (1)
8501 (37)
983 (1)
1428 (1)
1722 (5)
1962 (7)
3104 (4)
3209 (3)
3451 (74)
Table S8. Harmonic vibrational frequencies (cm–1) for 1,3-butadiene-2-yl, computed at
the cc-pVDZ ROCCSD(T) level of theory. IR intensities (km mol–1) are in parentheses.
Species
1,3-butadiene-2-yl (5)
a1
870 (0)
b1
118i
b2
214 (4)
1436 (0)
96 (12)
464 (6)
1754 (1)
351 (15)
564 (31)
1927 (2)
976 (0)
844 (40)
3102 (5)
3158 (5)
3450 (82)
Table S9. Harmonic vibrational frequencies (cm–1) for C4H6, computed at the cc-pVDZ
ROCCSD(T) level of theory. IR intensities (km mol–1) are in parentheses.
ag
au
bg
bu
C4H6
506 (0)
172 (0)
748.1 (0)
289 (2)
(1,3-butadiene,6)
898 (0)
524 (9)
898.1 (0)
989 (1)
1219 (0)
896 (59)
970.7 (0)
1299 (3)
1300 (0)
1027 (32)
Species
1402 (3)
1468 (0)
1638 (9)
1701 (0)
3154 (18)
3151 (0)
3168 (13)
3164 (0)
3256 (27)
3255 (0)
Table S10. Harmonic vibrational frequencies (cm–1) for isomers of C4H5, computed at
the cc-pVDZ ROCCSD(T) level of theory. IR intensities (km mol–1) are in parentheses.
Species
E-n-C4H5 (7)
a′
a′′
199 (6)
171 (4)
544 (4)
488 (0)
849 (41)
507 (3)
892 (1)
711 (33)
1064 (1)
917 (19)
1173 (1)
983 (1)
1360 (1)
3192 (6)
1489 (2)
1866 (3)
3109 (12)
3160 (7)
3172 (5)
3283 (7)
Z-n-C4H5 (8)
287 (1)
155 (0)
480 (2)
562 (0)
871 (27)
695 (24)
937 (7)
886 (27)
1164 (0)
895 (26)
1245 (1)
1000 (28)
1301 (2)
1431 (1)
1597 (3)
1669 (4)
3141 (4)
3156 (8)
3177 (8)
3238 (1)
3258 (12)
i-C4H5 (9)
292 (6)
165 (0)
505 (3)
550 (40)
817 (13)
713 (9)
947 (2)
815 (0)
1181 (3)
897 (30)
1238 (1)
1002 (17)
1300 (1)
1433 (1)
1602 (3)
1680 (3)
3074 (9)
3156 (7)
3184 (6)
3250 (1)
3258 (12)
1,3-butadiene-2-yl (10)
231 (1)
72 (1)
472 (1)
388 (4)
868 (0)
692 (2)
971 (1)
840 (38)
1149 (2)
909 (26)
1285 (1)
968 (19)
1390 (5)
1440 (0)
1634 (10)
1700 (0)
3083 (5)
3107 (13)
3166 (4)
3213 (4)
3267 (8)

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