Supporting Information for Valence Charge Concentrations ... · Lithium Alkyls: Negative...
Transcript of Supporting Information for Valence Charge Concentrations ... · Lithium Alkyls: Negative...
Copyright Wiley−VCH Verlag GmbH, 69451 Weinheim, 2002
Chem. Eur. J. 2002
Suppor ting Information
for
" Valence Charge Concentrations and Electron Delocalization in
L ithium Alkyls: Negative Hyperconjugation and Agostic Bonding"
Wolfgang Scherer,* Peter Sirsch, Dmitry Shorokhov, G. Sean McGrady,
Sax A. Mason, and Michael G. Gardiner
Contents:
S1 − Topological analysis and geometrical parameters
S2 − Fractional atomic coordinates and mean−square atomic displacement parameters
S3 − Kappa and multipole parameters
S4 − Local coordinate systems
S5 − Model deformation and residual density maps after multipole refinement
S6 − Comparison of multipole models with different flexibility
S7 − Geometrical and topological parameters of the calculated model systems
1, 2, 3, 4, 5, 10 and 11
S8 − Geometrical and topological parameters of the calculated model systems
6, 6a, 7 and 9
S9 − Ellipticity angle along the C1−Si2 bondpath of 8
S1: Topological analysis and geometr ical parameters of [{2−(Me3Si)2C(Li)C5H4N}2] 8.
Unit Methoda Distance [Å] ρ(r c) [e/Å3] ∇2ρ(r c) [e/Å5] Ellipticity ε
Li···N_a Experiment 1.9508 0.215(2) 5.201(2) 0.02
Theory I 1.9636 0.24 5.07 0.05
Theory II 0.24 4.76 0.04
Li−C1 Experiment 2.2049 0.150(2) 2.521(1) 0.12
Theory I 2.1757 0.19 2.76 0.10
Theory II 0.19 2.52 0.11
C1−Si2 Experiment 1.8592(4) 0.859(14) 1.73(3) 0.13
Theory I 1.8819 0.79 4.72 0.11
Theory II 0.80 3.16 0.11
C1−Si1 Experiment 1.8552(4) 0.756(15) 4.25(3) 0.19
Theory I 1.8798 0.77 4.69 0.12
Theory II 0.78 3.16 0.12
C1−C11 Experiment 1.4798(5) 1.78(2) −11.29(5) 0.12
Theory I 1.4783 1.73 −13.60 0.12
Theory II 1.73 −13.38 0.11
Si1−C2 Experiment 1.8804(6) 0.693(17) 4.63(3) 0.22
Theory I 1.9050 0.78 4.54 0.01
Theory II 0.79 2.92 0.01
Si1−C3 Experiment 1.8930(8) 0.758(14) 2.73(3) 0.20
Theory I 1.9197 0.75 4.50 0.01
Theory II 0.76 2.99 0.01
Si1−C4 Experiment 1.8781(7) 0.765(16) 4.23(3) 0.14
Theory I 1.9023 0.78 4.65 0.01
Theory II 0.79 3.01 0.01
Si2−C5 Experiment 1.8888(6) 0.735(16) 4.41(3) 0.07
Theory 1.9094 0.77 4.46 0.01
Theory II 0.78 2.89 0.02
Si2−C6 Experiment 1.8811(5) 0.714(16) 5.39(3) 0.12
Theory 1.9083 0.77 4.52 0.01
Theory II 0.78 2.91 0.01a The experimental values were obtained by multipole refinement of the experimental charge density, the theoretical
calculations were performed at the B3LYP/6−311G(d,p)//B3LYP/6−31G(d) (I) and the B3LYP/6–311G(3d,3p)//
B3LYP/6−31G(d) (II) level of theory, respectively.
Unit Methoda Distance [Å] ρ(r c) [e/Å3] ∇2ρ(r c) [e/Å5] Ellipticity ε
Si2−C7 Experiment 1.8947(7) 0.717(16) 3.84(3) 0.03
Theory I 1.9180 0.75 4.50 0.01
Theory II 0.76 2.97 0.01
N−C11 Experiment 1.3636(6) 2.17(3) −17.34(13) 0.23
Theory I 1.3729 2.13 −21.91 0.09
Theory II 2.16 −22.96 0.10
C11−C12 Experiment 1.4168(6) 2.06(2) −16.48(5) 0.21
Theory I 1.4223 2.00 −19.18 0.19
Theory II 2.01 −18.88 0.18
C12−C13 Experiment 1.3834(7) 2.165(19) −19.03(4) 0.23
Theory I 1.3846 2.12 −21.28 0.22
Theory II 2.13 −21.06 0.21
C13−C14 Experiment 1.3948(7) 2.133(19) −18.090(0) 0.24
Theory I 1.4000 2.06 −20.43 0.18
Theory II 2.07 −20.04 0.17
C14−C15 Experiment 1.3821(7) 2.20(3) −20.68(6) 0.24
Theory I 1.3858 2.13 −21.47 0.24
Theory II 2.13 −21.20 0.23
N−C15 Experiment 1.3454(7) 2.39(3) −22.34(12) 0.22
Theory I 1.3450 2.24 −22.76 0.11
Theory II 2.27 −24.80 0.13
C7−H7c Experiment 1.0981 1.71(4) −12.85(11) 0.08
Theory I 1.1009 1.76 −19.68 0.03
Theory II 1.78 −20.03 0.03
C3−H3b Experiment 1.1003 1.73(5) −13.01(17) 0.05
Theory I 1.0987 1.78 −20.08 0.02
Theory II 1.80 −20.48 0.02
C3−H3c Experiment 1.0919 1.65(4) −12.64(11) 0.08
Theory I 1.1001 1.78 −19.89 0.02
Theory II 1.79 −20.25 0.03
C3−Li_a Experiment 2.5107 0.082(1) 0.828(1) 0.69
Theory I 2.4793 0.06 1.30 1.16
Theory II 0.06 1.30 0.98a The experimental values were obtained by multipole refinement of the experimental charge density, the theoretical
calculations were performed at the B3LYP/6−311G(d,p)//B3LYP/6−31G(d) (I) and the B3LYP/6–311G(3d,3p)//
B3LYP/6−31G(d) (II) level of theory, respectively.
Selected angles [deg] for [{2−(Me3Si)2C(Li)C5H4N}2] 8.a
C1−Li−N_a Experiment 145.90 Li_a−N−C11 Experiment 104.12
Theory 142.9 Theory 110.4
Li_a−Li−C1 Experiment 65.55 Li−C1−Si1 Experiment 104.51
Theory 70.6 Theory 105.1
Li−Li_a−N Experiment 104.46 Li−C1−Si2 Experiment 88.92
Theory 95.7 Theory 90.6
Li_a−N−C15 Experiment 135.39 Li−C1−C11 Experiment 123.15
Theory 128.6 Theory 116.5a The experimental values were obtained by multipole refinement of the experimental charge density, the theoretical
calculations were performed at the B3LYP/6−31G(d) level of theory.
S2a: Fractional atomic coordinates and mean−square atomic displacement parameters for
the non−hydrogen atoms of 8.
Fractional atomic coordinates
Atom x/a y/b z/c
Si(2) 0.302283(9) 0.263099(13) −0.086250(9)
Si(1) 0.360087(10) 0.364467(12) 0.142651(9)
N 0.32170(4) 0.65175(5) 0.01422(4)
C(1) 0.34445(3) 0.40747(4) 0.00109(3)
C(2) 0.21836(5) 0.35769(7) 0.20396(4)
C(3) 0.44800(8) 0.49177(8) 0.22359(5)
C(4) 0.43410(5) 0.19839(7) 0.16947(5)
C(5) 0.25199(5) 0.31911(7) −0.22208(4)
C(6) 0.18768(5) 0.14550(5) −0.04195(5)
C(7) 0.43079(6) 0.15207(8) −0.10675(7)
C(11) 0.27294(3) 0.53035(4) −0.01261(3)
C(12) 0.15600(4) 0.52954(5) −0.04788(4)
C(13) 0.09272(4) 0.64778(5) −0.05310(4)
C(14) 0.14460(4) 0.77001(5) −0.02328(4)
C(15) 0.25923(4) 0.76603(5) 0.00900(3)
Li 0.519190 0.392970 −0.052800
Mean−square atomic displacement parameters [Å2]Atom U11 U22 U33 U12 U13 U23
Si(2) 0.01521(4) 0.01959(5) 0.02321(5) −0.00064(3) −0.00003(3) −0.00526(4)
Si(1) 0.01713(4) 0.02092(5) 0.01712(4) 0.00037(4) −0.00047(3) 0.00369(4)
N 0.01575(14) 0.01575(16) 0.02033(15) 0.00046(12) −0.00024(12) −0.00178(13)
C(1) 0.01391(12) 0.01611(14) 0.01614(13) 0.00126(11) 0.00004(10) −0.00010(11)
C(2) 0.0262(2) 0.0590(4) 0.02440(18) 0.0003(2) 0.00801(16) 0.0090(2)
C(3) 0.0428(3) 0.0346(3) 0.01996(19) −0.0082(3) −0.0073(2) −0.0005(2)
C(4) 0.0370(3) 0.0277(2) 0.0389(3) 0.0071(2) −0.0079(2) 0.01062(19)
C(5) 0.0315(2) 0.0485(3) 0.02199(18) −0.0046(2) −0.00559(16) −0.00591(19)
C(6) 0.02615(19) 0.02222(18) 0.0453(3) −0.00720(16) 0.00334(18) −0.00462(17)
C(7) 0.0243(2) 0.0278(3) 0.0458(3) 0.0046(2) 0.0023(2) −0.0152(3)
C(11) 0.01226(12) 0.01619(14) 0.01658(13) 0.00037(11) 0.00075(10) 0.00121(11)
C(12) 0.01265(12) 0.01972(16) 0.0349(2) 0.00008(11) −0.00214(12) 0.00216(13)
C(13) 0.01447(13) 0.02391(19) 0.0407(2) 0.00346(13) −0.00146(14) 0.00497(16)
C(14) 0.01988(16) 0.01992(17) 0.03251(19) 0.00554(13) 0.00302(13) 0.00352(14)
C(15) 0.02103(16) 0.01679(16) 0.02521(17) 0.00222(14) 0.00148(12) −0.00099(12)
Li 0.015314 0.040846 0.029042 0.002015 0.001001 −0.001989
S2b: Fractional atomic coordinates and mean−square atomic displacement parameters for
the hydrogen atoms of 8.
Fractional atomic coordinates
Atom x/a y/b z/c
H(2a) 0.229000 0.335210 0.287310
H(2b) 0.163710 0.278590 0.168450
H(2c) 0.171690 0.452050 0.194260
H(3a) 0.450260 0.461780 0.306060
H(3b) 0.411360 0.594320 0.220820
H(3c) 0.536830 0.498040 0.202810
H(4a) 0.442330 0.182190 0.254950
H(4b) 0.520350 0.197010 0.141910
H(4c) 0.388230 0.111860 0.135300
H(5a) 0.239740 0.230740 −0.272890
H(5b) 0.311180 0.383330 −0.258120
H(5c) 0.170370 0.370720 −0.226310
H(6a) 0.173660 0.063050 −0.099050
H(6b) 0.106420 0.196770 −0.036710
H(6c) 0.210030 0.099030 0.034400
H(7a) 0.402480 0.062230 −0.150680
H(7b) 0.475150 0.117940 −0.034470
H(7c) 0.494710 0.199020 −0.154600
H(12) 0.114500 0.433840 −0.068030
H(13) 0.001910 0.644630 −0.080100
H(14) 0.097350 0.865670 −0.026700
H(15) 0.304520 0.859320 0.031140
Mean−square atomic displacement parameters [Å2]Atom U11 U22 U33 U12 U13 U23
H(2a) 0.067080 0.164801 0.034814 −0.003406 0.009672 0.021281
H(2b) 0.047008 0.081276 0.079196 −0.016445 0.010400 0.003484
H(2c) 0.055653 0.081146 0.087919 0.021593 0.022022 −0.000689
H(3a) 0.094991 0.081263 0.031538 −0.016757 −0.015509 0.007878
H(3b) 0.096174 0.044382 0.054717 −0.000286 −0.001248 −0.011193
H(3c) 0.044499 0.086294 0.065182 −0.020605 −0.005018 0.001261
H(4a) 0.099086 0.069472 0.050050 0.012987 −0.013806 0.023413
H(4b) 0.045786 0.070382 0.088751 0.020397 0.000429 0.008541
H(4c) 0.082173 0.035113 0.085800 0.000611 −0.016757 0.001105
H(5a) 0.116987 0.079859 0.050388 −0.007358 −0.007397 −0.027638
H(5b) 0.106028 0.134680 0.057291 −0.066417 −0.019838 0.035802
H(5c) 0.083603 0.146861 0.055549 0.055107 −0.017472 −0.000637
H(6a) 0.073671 0.050557 0.077285 −0.022880 0.006214 −0.026130
H(6b) 0.036673 0.054730 0.118404 0.001027 0.019331 0.002782
H(6c) 0.074074 0.062699 0.066157 −0.017563 −0.000026 0.016354
H(7a) 0.057889 0.054730 0.122005 −0.000741 0.003042 −0.051857
H(7b) 0.066599 0.079599 0.070369 0.035776 −0.007059 0.001885
H(7c) 0.050544 0.063453 0.088972 0.002964 0.027404 −0.011037
H(12) 0.031213 0.032019 0.090012 −0.005473 −0.010699 −0.004979
H(13) 0.024466 0.051389 0.091546 0.004589 −0.011609 0.003991
H(14) 0.042510 0.033111 0.073983 0.015418 0.003081 0.003926
H(15) 0.041054 0.028977 0.069667 −0.003393 −0.006409 −0.008476
S3: Kappa and multipole parameters for [{2−(Me3Si)2C(Li)C5H4N}2] 8.
Symmetry forbidden multipoles are denoted by an asterisk (* )
Atom κ’ κ’ ’ Pv P11+ P11− P10
Si(2) 1.051(7) 1.00b 3.26(10) −0.05(2) 0.13(2) 0.06(2)
Si(1) 1.031(7) 1.00b 3.23(11) 0.07(2) −0.01(2) 0.02(2)
N 0.983(2) 1.00b 5.33(5) −0.009(13) −0.064(12) 0.004(11)
C(1) 0.966b 1.00b 4.52(4) 0.024(13) −0.024(13) −0.019(13)
C(2)a 0.986(3) 1.00b 4.44(6) * * 0.018(12)
C(3) 0.984b 1.00b 4.46(4) 0.06(2) 0.025(16) 0.029(17)
C(5)a 0.984(3) 1.00b 4.59(7) * * 0.014(12)
C(7) 0.985(5) 1.00b 4.54(10) 0.10(2) 0.006(17) 0.024(17)
C(11) 1.030(4) 1.00b 3.79(5) 0.000(11) 0.028(13) −0.040(14)
C(12)a 1.009(2) 1.00b 4.13(3) 0.005(11) −0.019(10) *
C(15) 1.009(2) 1.00b 4.02(4) 0.036(15) 0.040(15) *
a The multipole population coefficients of C(2), C(5) and C(12) were set equal to the corresponding coefficients of
C(4), C(6) and C(13) / C(14), respectively (chemically constrained model).
b Fixed values.
Atom P20 P21+ P21− P22+ P22−
Si(2) −0.02(2) 0.00(2) −0.01(2) −0.03(2) −0.11(2)
Si(1) −0.07(2) 0.17(2) −0.03(2) 0.05(2) 0.02(2)
N −0.119(13) 0.018(11) 0.006(11) 0.022(12) 0.019(12)
C(1) −0.029(13) −0.014(12) −0.021(12) −0.002(13) −0.045(12)
C(2)a 0.043(12) * * * *
C(3) 0.052(16) −0.042(19) 0.005(14) 0.012(16) 0.077(19)
C(5)a 0.049(11) * * * *
C(7) 0.019(16) −0.007(19) 0.049(15) 0.014(18) 0.053(19)
C(11) 0.044(15) −0.006(12) 0.016(13) −0.143(12) 0.011(11)
C(12)a −0.193(9) * * 0.007(10) 0.002(8)
C(15) −0.182(15) * * −0.021(14) 0.021(15)
a The multipole population coefficients of C(2), C(5) and C(12) were set equal to the corresponding coefficients of
C(4), C(6) and C(13) / C(14), respectively (chemically constrained model).
Atom P30 P31+ P31− P32+ P32− P33+ P33−
Si(2) −0.01(3) −0.22(3) −0.30(3) 0.06(3) 0.01(2) 0.36(3) −0.01(2)
Si(1) −0.09(3) −0.21(3) −0.43(3) 0.13(2) −0.09(3) 0.28(3) 0.04(3)
N 0.002(11) −0.013(11) −0.018(11) −0.004(10) 0.015(10) 0.137(11) 0.014(11)
C(1) −0.035(14) −0.054(13) −0.097(13) −0.015(13) 0.091(13) 0.107(13) 0.000(13)
C(2)a 0.175(13) * * * * 0.004(11) 0.127(12)
C(3) 0.176(16) −0.039(17) 0.003(14) −0.007(15) 0.006(17) −0.017(16) 0.225(16)
C(5)a 0.236(12) * * * * 0.020(11) 0.144(11)
C(7) 0.179(19) −0.065(16) 0.007(15) 0.005(17) −0.033(17) −0.047(16) 0.163(17)
C(11) 0.184(16) 0.013(14) −0.004(15) 0.180(14) −0.022(13) 0.032(12) −0.013(12)
C(12)a * 0.032(10) 0.029(9) * * 0.249(8) −0.018(11)
C(15) * 0.009(14) 0.021(14) * * 0.300(15) −0.005(15)
a The multipole population coefficients of C(2), C(5) and C(12) were set equal to the corresponding coefficients of
C(4), C(6) and C(13) / C(14), respectively (chemically constrained model).
Li H(2a)a H(3b) H(3c) H(7b) H(7c) H(12)a
κ’ 1.20b 1.20b 1.20b 1.20b 1.20b 1.20b 1.20b
κ’ ’ 1.20b 1.20b 1.20b 1.20b 1.20b 1.20b 1.20b
Pv 0.90(11) 0.888(10) 0.83(3) 0.91(3) 0.82(3) 0.94(3) 0.888(12)
P10 0.099(6) 0.06(2) 0.10(2) 0.11(2) 0.17(2) 0.125(9)
a The multipole population coefficients of all methyl group hydrogens, except for H(3b), H(3c), H(7b) and H(7c),
were set equal to H(2a) and all aromatic hydrogens equal to H(12) (chemically constrained model).
b Fixed values.
S4: Local coordinate systems for [{2−(Me3Si)2C(Li)C5H4N}2] 8 before normalization.
C1 Li*
C11
C12
C13 C14
C15
Nz
y
y x
x y
x y
x
y x
y
The following local coordinate systems (right handed setting) were adapted:C11 [z axis: C11 � N; y axis: C11 � C12], C12 [x axis: C12 � C11; y axis: C12 � C13], C13 [x axis: C13 � C12; y axis: C13 � C14], C14 [x axis: C14 � C13; y axis: C14 � C15], C15 [x axis: C15 � C14; y axis: C15 � N], N [x axis: N � C11; y axis: N � C15].For the carbon atoms C12, C13, C14 and C15 the z−axes are located perpendicular to a pseudo mirror plane.
C11
C1Li
Si2
C7 C6
C5
y x
Si1
y x
x
y
z
z
y
y z
y
C3
C3
C1
Li
Si1
C3 C2
C4
y
x
Si2
y
x
x
y
z
z
y
y
z y
C3
C3
C11
The following local coordinate systems (right handed setting) were adapted:Li [x axis: Li � C1; y axis: Li � Si2], C1 [x axis: C1 � Si2; y axis: C1 � Si1], Si2 [x axis: Si2 � C7; y axis: Si2 � C1], Si1 [x axis: Si1 � C3; y axis: Si1 � C1], C2 [z axis: C2 � Si1; y axis: C2 � C1], C3 [z axis: C3 � Si1; y axis: C3 � C1], C4 [z axis: C4 � Si1; y axis: C4 � C1], C5 [z axis: C5 � Si2; y axis: C5 � C1], C6 [z axis: C6 � Si2; y axis: C6 � C1], C7 [z axis: C7 � Si2; y axis: C7 � C1].For the carbon atoms C5, C6, C2 and C4 the z−axes are oriented along the pseudo 3−fold axes.
S5a: Model deformation density maps after multipole refinement for
[{2−(Me3Si)2C(Li)C5H4N}2] 8.
Contour level: 0.05 e Å−3
C1C12
C13
C14
C15
N
H15
H14
H13
H12
C11
Si2
C1
Li
S5b: Residual density maps after multipole refinement for [{2−(Me3Si)2C(Li)C5H4N}2] 8.
Data cut−off at sinΘ/λ = 0.8 Å−1; contour level: 0.05 e Å−3.
Li Si2
C1
C1
C11
C12
C13
C14
C15
N
H15
H14
H13
H12
S6: Compar ison of multipole models for [{2−(Me3Si)2C(Li)C5H4N}2] with different flexibility.
• Model 1:
as described in the Experimental Part
• Model 2:
as Model 1 but without chemical constraints and without imposing selection picking rules for
the multipoles.
Topological analysis and geometr ical parameters of the agostic fragment
Unit Distance [Å] ρ(r c) [e/Å3] ∇2ρ(r c) [e/Å5] Ellipticity ε
Li···N_a 1.9509 0.210(2) 5.202(2) 0.02
Li−C1 2.2050 0.142(2) 2.515(1) 0.10
C1−Si2 1.8592(4) 0.855(15) 1.83(3) 0.17
Si2−C7 1.8946(6) 0.686(17) 4.81(3) 0.04
C7−H7c 1.0981 1.72(5) −13.06(11) 0.09
• Model 3:
as Model 1 but with hexadecapole refinement, in addition.
Topological analysis and geometr ical parameters of the agostic fragment
Unit Distance [Å] ρ(r c) [e/Å3] ∇2ρ(r c) [e/Å5] Ellipticity ε
Li···N_a 1.9510 0.210(4) 5.110(4) 0.06
Li−C1 2.2049 0.147(4) 2.449(3) 0.33
C1−Si2 1.8591(4) 0.870(17) 1.93(3) 0.24
Si2−C7 1.8940(6) 0.733(18) 4.97(3) 0.08
C7−H7c 1.0981 1.74(5) −15.81(15) 0.10
S7: Topological analysis and geometr ical parameters of the calculated model systems 1, 2, 3,
4, 5, 10 and 11.
System Basisa d(C−Y)b
[Å]ρ(r c)[e/Å3]
∇2ρ(r c)[e/Å5]
Ellipticity L(CC1) / L(CC2)[e/Å5]
CH3−CH3 1 I 1.531 1.60 −12.79 0.00 25.5 / 20.0
II 1.531 1.60 −12.79 0.00 25.4 / 19.9
III 1.531 1.63 −13.38 0.00 26.5 / 19.8
CH2CH3− 2 I 1.535 1.53 −10.97 0.14 22.0 / 14.0
II 1.531 1.56 −11.55 0.10 18.0 / 15.5
III 1.525 1.60 −12.31 0.10 17.0 / 16.4
CH2=CH2 3 I 1.327 2.32 −24.86 0.33 − / 27.6
II 1.329 2.32 −24.78 0.33 − / 27.6
III 1.324 2.41 −27.15 0.33 − / 29.3
CH2−SiH3− 4 I 1.783 0.90 7.89 0.29 15.5 / 15.6
II 1.790 0.89 7.66 0.25 14.4 / 15.9
III 1.781 0.93 6.45 0.27 17.0c
EtLi 5 I 1.543 1.53 −11.26 0.06 18.9 / 16.3
II 1.544 1.53 −11.23 0.06 18.8 / 16.3
III 1.540 1.56 −11.81 0.06 18.8 / 16.8
CH2=SiH2 10 I 1.707 0.99 12.99 0.49 − / 20.3
II 1.708 0.99 12.92 0.49 − / 20.2
III 1.702 1.03 11.05 0.50 − / 20.3
CH3−SiH3 11 I 1.885 0.80 4.86 0.00 24.1 / 18.8
II 1.885 0.80 4.85 0.00 24.0 / 18.7
III 1.878 0.83 3.56 0.00 25.1 / 18.5a The theoretical calculations were performed at the B3LYP/6−311G(d,p) (I), the B3LYP/6–311+G(d,p) (II) and the
B3LYP/6–311++G(3df,3pd) (III) level of theory, respectively. b Y = C, Si. c At this level of theory charge
concentrations CC(1) and CC(2) are merged into one broad feature as observed in the experimental study of 8.
S8a: Geometr ical and topological parameters of the calculated model system 6
[B3LYP/6−311G(d,p) and B3LYP/6−311+G(d,p) in square brackets, respectively].
Li−C1 1.991 [1.993] Li−C1−Si 88.0 [88.0]C1−Si 1.834 [1.834] C1−Si−C2 107.8 [107.8]Si−C2 1.946 [1.947] Si−C2−H2a 111.9 [112.0]C2−H2a 1.093 [1.094] Si−C2−H2b 112.6 [112.6]C2−H2b 1.104 [1.104] Si−C2−H2c 112.6 [112.6]C2−H2c 1.104 [1.104] Li−C1−Si−C2 0.0 [0.0]
2.258 [2.256] Li−Si−C2−H2a 180.0 [180.0]Li···H2c 2.258 [2.256]
Selected distances [Å] and angles [deg]
Li···H2b
Unit EllipticityLi−C1 0.28 [0.28] 4.76 [4.68] 0.09 [0.09]C1−Si 0.85 [0.85] 5.85 [5.88] 0.17 [0.17]Si−C2 0.70 [0.70] 4.40 [4.36] 0.02 [0.01]
ρ(rc) [e/Å3] ∇2ρ(r
c) [e/Å5]
Li
SiC1
H2b
H2aC2
H2c
CC(2):L(r) = 14.91 [14.93] e/Å5
ρ(r) = 1.62 [1.62] e/Å3
CC(1):L(r) = 16.14 [16.03] e/Å5
ρ(r) = 1.66 [1.66] e/Å3
S8b: Geometr ical and topological parameters of the calculated model system 6a.
I 14.56 1.64 16.16 1.70II 16.81 1.73III 18.03 1.79
Basisa L(CC1) [e/Å5] ρ(CC1) [e/Å3] L(CC2) [e/Å5] ρ(CC2) [e/Å3]
b b
b b
Si
C1
C2CC(2)
CC(1)
Unit Ellipticity
C1−Si I 1.773 0.91 8.55 0.29II 1.778 0.90 8.55 0.26III 1.771 0.94 7.12 0.27
Si−C2 I 1.953 0.69 4.01 0.02II 1.942 0.71 4.06 0.02III 1.933 0.74 3.03 0.03
Basisa Distance [Å] ρ(rc) [e/Å3] ∇2ρ(rc) [e/Å
5]
a The theoretical calculations were performed at the B3LYP/6−311G(d,p) (I), the B3LYP/6−311+G(d,p) (II)
and the B3LYP/6−311++G(3df,3pd) (III) level of theory, respectively. b At these levels of theory charge
concentrations CC(1) and CC(2) are merged into one broad feature as observed in the experimental study of 8.
S8c: Geometr ical and topological parameters of the agostic fragment
in the calculated system Li[HC(SiMe3)2] 7 [B3LYP/6−311G(d,p)].
Li−C1 2.00 C2−H2c 1.10 Si1−C1−Si2 128.0C1−Si1 1.83 Li···H2b 2.35 Si1−C2−H2a 110.4C1−Si2 1.83 Li···H2c 2.17 Si1−C2−H2b 113.9Si1−C2 1.95 Li−C1−Si1 87.4 Si1−C2−H2c 113.5Si1−C3 1.90 Li−C1−Si2 87.4 Li−C1−Si1−C2 7.2Si1−C4 1.89 C1−Si1−C2 107.5 Li−Si1−C2−H2a −173.8C2−H2a 1.09 C1−Si1−C3 119.6C2−H2b 1.10 C1−Si1−C4 111.6
Selected distances [Å] and angles [deg]
Unit EllipticityLi−C1 0.26 4.54 0.11C1−Si1 0.84 6.39 0.14Si1−C2 0.70 4.30 0.02Si1−C3 0.78 4.77 0.01Si1−C4 0.79 4.96 0.01
ρ(rc) [e/Å3] ∇2ρ(r
c) [e/Å5]
Li
C1
Si1
C4
C2
C3
H2c
H2b
Si2
H2a
CC(2):L(r) = 14.90 e/Å5
ρ(r) = 1.65 e/Å3
CC(1):L(r) = 13.59 e/Å5
ρ(r) = 1.60 e/Å3
S8d: Geometr ical and topological parameters
of the calculated model system 9 [B3LYP/6−311G(d,p)].
Li−C1 2.00 C2−H2c 1.10 Si−C4−H4a 110.8C1−Si 1.85 Li···H2c 2.61 Si−C4−H4b 113.9Si−C4 1.95 C1−C2 1.55 Si−C4−H4c 113.4C4−H4a 1.09 C1−C3 1.53 C1−C2−H2b 111.6C4−H4b 1.11 Si−C5 1.91 C1−C2−H2c 113.9C4−H4c 1.10 Si−C6 1.90 Li−C1−Si−C4 −17.0
2.11 Li−C1−Si 85.3 Li−Si−C4−H4a 172.8Li···H4c 2.31 C1−Si−C4 105.5 Li−C1−C2−H2c 38.7
Selected distances [Å] and angles [deg]
Li···H4b
Unit EllipticityLi−C1 0.29 4.33 0.10C1−Si 0.88 3.99 0.19Si−C4 0.70 3.20 0.03Si−C5 0.77 4.66 0.01Si−C6 0.78 4.95 0.02C1−C2 1.52 −10.54 0.09C1−C3 1.57 −11.59 0.07
ρ(rc) [e/Å3] ∇2ρ(r
c) [e/Å5]
Li
C1 Si
C4
C2
C3 C5
C6
H4b
H4c H4a
H2c
H2b
CC(1):L(r) = 18.01 e/Å5
ρ(r) = 1.73 e/Å3
CC(2):L(r) = 16.03 e/Å5
ρ(r) = 1.66 e/Å3
S9: Ellipticity angle along the C1−Si2 bondpath of 8 (theo).
(the eigenvector v2 of the Hessian matrix of ρ(r ) corresponds to the major axis of curvature)
0
20
40
60
80
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6
BCPSi2C1
0 0.2 0.6−0.6 −0.2−1.0
0
20
40
60
80
Distance from the Bond Critical Point / Å
Ang
le b
etw
een
v 2
and
the
plan
e Li
,C1,
Si2
/ de
g