Supporting Information On the Viability of Small Endohedral Hydrocarbon Cage Complexes: X@C4H4, X@C8H8, X@C8H14, X@C10H16, X@C12H12 and X@C16H16 Damian Moran, H. Lee Woodcock, Zhongfang Chen, Henry F. Schaefer III and Paul v. R. Schleyer S 1. C4v geometry optimization of Be@C16H16, leads to spontaneous dissociation into (cyclobutadiene)Be(nido-C12H12 fragment). H
H H
H
CC
CC
Be H
H
H
C C
H
C
H
C
H
CC C
C
C
C C
C
H H
H
H
1
H
S 2. The B3LYP/6-31G(d) energy, ZPE (kcal/mol) and first harmonic vibrational frequency (cm-1) for cubane, bicyclo[2.2.2]octane and their endohedral complexes.
X@C8H8 (Oh)
Energy
ZPE
w1
X@C8H14 (D3h)
Energy
ZPE
w1
C8H8
-309.46047
84.22
EU (628)
C8H14
-313.28991
130.07
A1"(39)
He@
-311.83968
85.25
T1U (448 )
He@
-315.85592
130.28
A1'(136)
Li+@
-316.35359
83.74
T1U (286 )
Li@
-320.49112
127.11
A1"(189)
Be2+@
-323.21916
81.22
T1U (131 )
Li+@
-320.40927
130.12
A1"(127)
Be2+@
-327.27452
130.39
A1"(148)
S 3. The B3LYP/6-31G(d) energy, ZPE (kcal/mol) and first harmonic vibrational frequency (cm-1) for adamantane, truncated tetrahedrane and their endohedral complexes.
X@C10H16 (Td)
Energy
ZPE
w1
X@C12H12 (Td)
Energy
ZPE
w1
C10H16
-390.72601
154.09
!T1(343)
C12H12
-464.38473
130.97
T1(414)
H@
-391.06503
154.09
T2(326)
H@
-464.75148
133.56
T1(415)
He@
-393.38129
156.02
T1(328)
He@
-467.10775
134.78
T1(433)
Ne@
-519.02649
145.97
T2(223)
Ne@
-592.81864
129.08
T2(413)
Li@
-397.98536
153.67
T1(349)
Li@
-471.64116
127.15
T1(395)
T1(334)
+
Li @
-471.59255
132.99
T1(416)
+
+
Li @
-397.91807
156.03
Na@
-552.42135
146.34
T2(208)
Na @
-626.08505
129.18
T2(383)
Na+@
-552.34361
147.87
T2(209)
Be2+@
-478.36315
154.48
T2(361)
Be@
-405.00892
137.34
T2 (338)
Mg2+@
-663.53546
127.93
T2(359)
Be+@
-404.95576
144.68
T1 (349)
Be2+@
-404.75424
154.48
T1(328)
2
Mg2+@
-589.84402
148.20
T2(200)
S 4. The B3LYP/6-31G(d) energy, ZPE (kcal/mol) and first harmonic vibrational frequency (cm-1) for D4d symmetric C16H16 and its endohedral complexes.
X@C16H16 (D4d)
Energy
ZPE
w1
X@C16H16 (D4d)
Energy
ZPE
w1
C10H16
-619.29382
178.16
E1(495)
Na@
-781.18900
174.54
B2(446)
H@
-619.69364
180.52
E2(493)
Na+@
-781.12117
177.14
B2(451)
He@
-622.06462
181.13
E(498)
Be+@ (C4v)
-633.57334
172.01
E(142)
Ne@
-747.85169
177.04
B1(481)
Be2+@ (C4v)
-633.32234
176.45
E(334)
-818.57772
175.95
B2(386)
Ar@
-1145.92351
167.44
B1(294)
Li@
-626.60771
173.41
B2(183)
Li+@
-626.55482
179.52
B2(378)
2+
Mg @
S 5. B3LYP/6-31G(d) computed properties of Oh symmetric endohedral X@C8H8. See Figure 1 for an explanation of atom labels.
Natural Charges (electrons)
Internuclear Distances (Å)
X
H/L (eV)
Xb
Cb
Hb
C-Xc
C-Cc
C-Hc
-
9.14
-
-0.24
0.24
-
1.570
1.092
He
8.01
0.13
-0.24
0.22
1.482
1.712
1.096
+
Li
7.34
0.60
-0.24
0.29
1.521
1.756
1.084
Be2+
7.26
1.46
-0.29
0.35
1.532
1.769
1.086
3
S 6. B3LYP/6-31G(d) computed properties of D3d symmetric X@C8H14. See Figure 1 for an explanation of atom labels.
Natural Charges (electrons)
Internuclear Distances (Å)
X
H/L (eV)
X
CA
CB
HA
HB
CA-X
CB-X
CA-CB
CB-CB'
CA-H
CB-H
-
9.40
-
-0.26
-0.46
0.25
0.23
-
-
1.542
1.559
1.097
1.097
He
9.63
0.09
-0.26
-0.47
0.22
0.23
1.473
1.741
1.649
1.686
1.104
1.096
Li
1.33
0.33
-0.33
-0.53
0.27
0.25
1.533
1.744
1.672
1.692
1.088
1.095
Li+
9.51
0.75
-0.31
-0.52
0.31
0.28
1.540
1.749
1.664
1.728
1.085
1.090
Be2+
10.38
1.63
-0.41
-0.58
0.38
0.32
1.539
1.748
1.661
1.731
1.086
1.089
S 7. B3LYP/6-31G(d) computed properties of Td symmetric X@C10H16. See Figure 1 for an explanation of atom labels.
Natural Charges (electrons)
Internuclear Distances (Å)
X
H/L (eV)
X
CA
CB
HA
HB
CA-X
CB-X
C-C
CA-H
CB-H
-
9.32
-
-0.26
-0.46
0.25
0.23
-
-
1.544
1.098
1.099
H
5.05
0.23
-0.32
-0.46
0.23
0.24
1.824
1.572
1.577
1.113
1.099
He
9.90
0.09
-0.27
-0.47
0.24
0.23
1.627
1.849
1.610
1.098
1.098
Ne
9.83
0.12
-0.24
-0.46
0.22
0.23
1.977
1.777
1.735
1.100
1.097
Li
1.04
0.25
-0.32
-0.50
0.27
0.24
1.644
1.849
1.616
1.092
1.098
Li+
9.62
0.72
-0.32
-0.50
0.31
0.28
1.650
1.858
1.624
1.087
1.093
4
Na
0.87
0.15
-0.29
-0.49
0.26
0.24
1.794
1.983
1.745
1.090
1.095
Na+
9.36
0.76
-0.29
-0.49
0.29
0.27
1.800
1.990
1.750
1.087
1.092
Be
1.86
1.51
-0.43
-0.55
0.24
0.21
1.645
1.848
1.616
1.127
1.116
Be+
1.83
1.58
-0.44
-0.54
0.31
0.26
1.645
1.856
1.620
1.103
1.103
Be2+
10.99
1.69
-0.45
-0.53
0.37
0.32
1.646
1.868
1.627
1.087
1.092
Mg2+
10.17
1.75
-0.39
-0.55
0.34
0.31
1.802
1.997
1.755
1.085
1.091
S 8. B3LYP/6-31G(d) computed properties of Td symmetric X@C12H12. See Figure 1 for an explanation of atom labels.
Natural Charges (electrons)
Internuclear Distances (Å)
X
H/L (eV)
X
C
H
C-X
CA-CB
CB-BB'
C-H
-
7.61
-
-0.26
0.26
-
1.499
1.522
1.087
H
7.45
0.15
-0.27
0.25
1.797
1.539
1.525
1.091
He
9.06
0.07
-0.26
0.25
1.816
1.552
1.544
1.087
Ne
8.87
0.12
-0.26
0.25
1.900
1.607
1.636
1.088
Li
0.57
0.21
-0.28
0.26
1.819
1.552
1.551
1.090
Li+
8.68
0.73
-0.29
0.31
1.827
1.555
1.562
1.082
Na+
8.23
0.80
-0.28
0.30
1.915
1.607
1.664
1.082
Be2+
8.74
1.75
-0.35
0.37
1.830
1.548
1.576
1.084
Mg2+
8.47
1.77
-0.33
0.35
1.923
1.601
1.685
1.082
5
S 9. B3LYP/6-31G(d) computed properties of D4d symmetric X@C16H16. See Figure 1 for an explanation of atom labels.
Natural Charges (electrons)
Internuclear Distances (Å)
X
H/L (eV)
X
CA
CB
HA
HB
CA-X
CB-X
CA-CA'
CA-CB
CB-CB'
CA-H
CB-H
-
8.44
-
-0.24
-0.26
0.25
0.25
-
-
1.563
1.544
1.562
1.094
1.095
H
7.15
0.13
-0.24
-0.27
0.25
0.25
2.099
1.842
1.570
1.553
1.583
1.094
1.099
He
9.36
0.06
-0.25
-0.26
0.25
0.25
2.094
1.869
1.573
1.558
1.602
1.093
1.094
Ne
9.69
0.12
-0.25
-0.25
0.25
0.24
2.115
1.947
1.597
1.585
1.669
1.093
1.094
Ar
7.85
0.46
-0.27
-0.26
0.25
0.23
2.180
2.073
1.648
1.637
1.789
1.096
1.101
Li
0.76
0.28
-0.25
-0.29
0.25
0.26
2.104
1.865
1.574
1.561
1.604
1.099
1.098
Li+
9.11
0.70
-0.26
-0.30
0.29
0.30
2.113
1.872
1.580
1.567
1.610
1.089
1.087
Na
0.58
0.16
-0.26
-0.28
0.26
0.26
2.124
1.952
1.598
1.590
1.676
1.094
1.092
+
8.83
0.75
-0.27
-0.28
0.29
0.29
2.131
1.956
1.604
1.594
1.681
1.088
1.087
2+
9.21
1.65
-0.30
-0.33
0.33
0.34
2.143
1.956
1.606
1.600
1.684
1.087
1.085
Na Mg
6
S 10. B3LYP/6-31G(d) computed geometries of C4v Be+@C16H16 (left) and Be2+@C16H16 (right). HH
H
H
H H
H
C 1.563Å C C
C
H
C 1.576ÅC
C
1.556Å
1.552Å C
C
H
C
C H
1.589Å
2.003Å H
C
C
1.830Å
C
C
Be
H
CH
C
H
H
H
H
H
C
C
1.966Å C 1.815ÅBe C
1.602Å C
C
H
1.803Å C C
1.578Å
1.859Å
1.675Å
C
C
C C
H
1.599Å
H
S 11. The B3LYP/6-31G(d) energy and ZPE (kcal/mol) for cubane and bicyclo[2.2.2]octane exohedral complexes.
Energy
ZPE
C8H14He
-312.36750
84.34
C8H14Li+
-316.78893
C8H14Be2+
-323.46809
Energy
ZPE
C8H14He
-316.19710
130.27
85.15
C8H14Li
-320.78129
130.27
85.22
C8H14Li+
-320.61803
131.13
C8H14Be2+
-327.30694
128.93
7
C
C
H
H
H
1.601Å
H
H
H
H
H
H
S 12. The B3LYP/6-31G(d) energy and ZPE (kcal/mol) for adamantane, truncated tetrahedrane and C16H16 exohedral complexes.
Energy
ZPE
Energy
ZPE
Energy
ZPE
C10H17
-391.22588 153.54
C12H13
-464.89102 131.26
C16H17
-619.79407
178.33
C10H16He
-393.63244 153.47
C12H12He
-467.29242 131.27
C16H16He
-622.20076
178.32
C10H16Ne
-519.62403 153.89
C12H12Ne
-593.28365 131.53
C16H16Ne
-748.19186
178.47
C10H16Li
-398.21656 153.33
C12H12Li
-471.88244 131.60
C16H16Ar
-1146.81055 178.02
C10H16Li+
-398.04904 154.40
C12H12Li+
-471.74794 132.68
C16H16Li
-626.78479
178.01
C10H16Na
-553.00542 153.36
C12H12Na+
-626.51619 131.53
C16H16Li+
-626.63091
178.96
C10H16Na+
-552.82946 153.25
C12H12Be2+
-478.50185 132.70
C16H16Na
-781.57375
178.12
C10H16Be
-405.39398 153.37
C12H12Mg2+
-663.85919 131.40
C16H16Na+
-781.40855
178.41
+
-405.14018 152.75
C16H16Be (C4v)
-633.73030
179.07
C10H16Be2+
-404.76707 153.03
C16H16Be2+ (C4v)
-633.35486
179.02
C10H16Mg2+
-590.13785 152.15
C16H16Mg2+
-818.72808
177.38
C10H16Be
+
8
S 13. Relationship between cage dimensions. Cage, face and bond correspond to the distance between a cage center and the closest cage atom, cage face midpoint and CC bond midpoint. Cage volume is calculated using the cage center to bond midpoint distance.
9
C20H20
C16H16
C12H12
C10H16
C8H14
C8H8
Cage (Å) Face (Å) Bond (Å) Volume (Å^3)
C4H4
9 8 7 6 5 4 3 2 1 0
