By Anna Rita Campanelli and Aldo Domenicano

A computational study of 4-substituted biphenyls in their minimum energy conformation: twist angles, structural variation, and substituent effects

By Anna Rita Campanelli and Aldo Domenicano

SUPPLEMENTARY MATERIAL

Table S1 Selected internal coordinates of benzene ring B in the equilibrium conformation of p-Ph-C6H4-X molecules, from HF/6-31G* calculationsa,b
Substituentc / Molecular symmetryd / α / β / γ / δ / a / r(CA-CB)e
H / D2 / 118.331 / 120.857 / 120.243 / 119.468 / 1.3928 / 1.4911
Li / C2 / 117.966 / 121.056 / 120.311 / 119.300 / 1.3938 / 1.4900
BH2(c) / C2 / 118.464 / 120.778 / 120.217 / 119.545 / 1.3928 / 1.4899
BH3-(o) / C1 / 117.298 / 121.391 / 120.486 / 118.946 / 1.3965 / 1.4868
CH2+(c) / C2 / 118.685 / 120.564 / 119.895 / 120.373 / 1.4028 / 1.4571
CH2-(c) / C2 / 115.135 / 122.260 / 121.351 / 117.639 / 1.4116 / 1.4552
Me(o) / C1 / 118.271 / 120.890 / 120.255 / 119.439 / 1.3929 / 1.4905
CF3(o) / C1 / 118.526 / 120.746 / 120.211 / 119.560 / 1.3924 / 1.4905
Ph(e) / C2h / 118.319 / 120.863 / 120.245 / 119.466 / 1.3929 / 1.4902
CHO(c) / C1 / 118.508 / 120.754 / 120.212 / 119.562 / 1.3927 / 1.4901
COMe(c) / C1 / 118.478 / 120.772 / 120.218 / 119.543 / 1.3926 / 1.4900
COCl(c) / C1 / 118.602 / 120.699 / 120.194 / 119.611 / 1.3925 / 1.4894
COO-(c) / C2 / 117.666 / 121.209 / 120.392 / 119.132 / 1.3949 / 1.4897
COOH(c) / C1 / 118.506 / 120.755 / 120.213 / 119.557 / 1.3926 / 1.4901
Table S1, continued
COOMe(c) / C1 / 118.480 / 120.770 / 120.217 / 119.545 / 1.3926 / 1.4902
CCH / C2 / 118.411 / 120.809 / 120.232 / 119.509 / 1.3927 / 1.4901
CN / C2 / 118.588 / 120.708 / 120.200 / 119.596 / 1.3924 / 1.4899
NH-(c) / C1 / 115.698 / 122.057 / 121.087 / 118.007 / 1.4069 / 1.4644
NH2(p) / C1 / 118.119 / 120.969 / 120.287 / 119.367 / 1.3934 / 1.4895
NMe2(p) / C1 / 118.088 / 120.985 / 120.295 / 119.352 / 1.3935 / 1.4887
NF2(p) / C1 / 118.480 / 120.772 / 120.220 / 119.537 / 1.3925 / 1.4904
NH3+(o) / C1 / 119.043 / 120.445 / 120.112 / 119.843 / 1.3923 / 1.4878
NO2(c) / C2 / 118.648 / 120.673 / 120.189 / 119.628 / 1.3924 / 1.4896
NC / C2 / 118.482 / 120.769 / 120.220 / 119.541 / 1.3926 / 1.4903
N2+ / C2 / 119.128 / 120.368 / 120.046 / 120.038 / 1.3946 / 1.4793
O- / C2 / 116.077 / 121.918 / 120.917 / 118.246 / 1.4038 / 1.4712
OH(c) / C1 / 118.209 / 120.922 / 120.270 / 119.408 / 1.3931 / 1.4901
OMe(c) / C1 / 118.199 / 120.927 / 120.271 / 119.404 / 1.3932 / 1.4900
OH2+(p') / C1 / 119.100 / 120.409 / 120.102 / 119.876 / 1.3923 / 1.4876
F / C2 / 118.351 / 120.845 / 120.243 / 119.473 / 1.3927 / 1.4909
Na / C2 / 117.872 / 121.106 / 120.332 / 119.251 / 1.3941 / 1.4897
Table S1, continued
MgCl / C2 / 118.313 / 120.866 / 120.244 / 119.468 / 1.3929 / 1.4903
SiH3(o) / C1 / 118.404 / 120.815 / 120.230 / 119.506 / 1.3927 / 1.4904
SiMe3(c) / C1 / 118.349 / 120.846 / 120.239 / 119.480 / 1.3928 / 1.4904
PH2(p') / C1 / 118.415 / 120.809 / 120.229 / 119.511 / 1.3927 / 1.4904
PH3+(o) / C1 / 119.048 / 120.434 / 120.094 / 119.895 / 1.3930 / 1.4846
S- / C2 / 117.130 / 121.459 / 120.549 / 118.851 / 1.3976 / 1.4834
SH(o) / C1 / 118.437 / 120.796 / 120.226 / 119.518 / 1.3926 / 1.4906
Cl / C2 / 118.441 / 120.794 / 120.229 / 119.515 / 1.3925 / 1.4905
ClO3(o) / C1 / 118.755 / 120.612 / 120.173 / 119.673 / 1.3922 / 1.4898
Br / C2 / 118.449 / 120.789 / 120.226 / 119.522 / 1.3926 / 1.4904
Range / 3.993 / 1.892 / 1.456 / 2.734 / 0.0194 / 0.0359
a Whenever necessary, the geometry of ring B has been made consistent with C2v symmetry by averaging appropriate geometrical parameters. Bond distances and angles are labelled according to Fig. 2.
b Angles are in degrees, bond distances in Å.
c The conformation of the substituent with respect to ring A is denoted as (c), (o), (p), (p'), and (e) according to the definitions given in Ref. [4]. Adherence to definitions is only approximate (see the text).
d Symmetry constraint imposed in the optimization of molecular geometry.
e Length of the C-C bond connecting ring A with ring B.
Table S2 Selected internal coordinates of benzene ring B in the equilibrium conformation of p-Ph-C6H4-X molecules, from B3LYP/6-311++G** calculationsa,b
Substituentc / Molecular symmetryd / α / β / γ / δ / a / r(CA-CB)e
H / D2 / 118.147 / 120.943 / 120.260 / 119.447 / 1.4029 / 1.4856
Li / C2 / 117.797 / 121.139 / 120.319 / 119.286 / 1.4040 / 1.4845
BH2(c) / C2 / 118.269 / 120.862 / 120.238 / 119.529 / 1.4032 / 1.4834
BH3-(o) / C1 / 116.926 / 121.578 / 120.544 / 118.829 / 1.4082 / 1.4783
CH2+(c) / C2 / 118.194 / 120.742 / 120.036 / 120.232 / 1.4169 / 1.4499
CH2-(c) / C2 / 114.963 / 122.386 / 121.286 / 117.690 / 1.4241 / 1.4509
Me(o) / C1 / 118.079 / 120.979 / 120.275 / 119.413 / 1.4031 / 1.4849
CF3(o) / C1 / 118.350 / 120.822 / 120.230 / 119.546 / 1.4026 / 1.4848
Ph(e) / C2h / 118.106 / 120.963 / 120.267 / 119.436 / 1.4032 / 1.4841
CHO(c) / C1 / 118.285 / 120.852 / 120.237 / 119.536 / 1.4032 / 1.4836
COMe(c) / C1 / 118.255 / 120.872 / 120.242 / 119.518 / 1.4031 / 1.4837
COCl(c) / C1 / 118.363 / 120.805 / 120.225 / 119.577 / 1.4031 / 1.4827
COO-(c) / C2 / 117.391 / 121.351 / 120.421 / 119.065 / 1.4057 / 1.4826
COOH(c) / C1 / 118.276 / 120.859 / 120.237 / 119.531 / 1.4031 / 1.4840
Table S2, continued
COOMe(c) / C1 / 118.247 / 120.878 / 120.245 / 119.507 / 1.4030 / 1.4841
CCH / C2 / 118.183 / 120.914 / 120.258 / 119.474 / 1.4032 / 1.4839
CN / C2 / 118.353 / 120.814 / 120.229 / 119.559 / 1.4029 / 1.4838
NH-(c) / C1 / 115.362 / 122.238 / 121.108 / 117.943 / 1.4200 / 1.4573
NH2(p) / C1 / 117.876 / 121.085 / 120.318 / 119.317 / 1.4039 / 1.4833
NMe2(p) / C1 / 117.799 / 121.124 / 120.334 / 119.285 / 1.4043 / 1.4823
NF2(p) / C1 / 118.306 / 120.845 / 120.239 / 119.525 / 1.4028 / 1.4843
NH3+(o) / C1 / 118.773 / 120.551 / 120.156 / 119.812 / 1.4032 / 1.4804
NO2(c) / C2 / 118.388 / 120.792 / 120.224 / 119.580 / 1.4029 / 1.4832
NC / C2 / 118.292 / 120.852 / 120.240 / 119.524 / 1.4028 / 1.4842
N2+ / C2 / 118.532 / 120.612 / 120.099 / 120.032 / 1.4100 / 1.4636
O- / C2 / 115.849 / 122.040 / 120.917 / 118.232 / 1.4162 / 1.4632
OH(c) / C1 / 118.020 / 121.009 / 120.288 / 119.385 / 1.4033 / 1.4844
OMe(c) / C1 / 117.987 / 121.027 / 120.294 / 119.371 / 1.4035 / 1.4842
OH2+(p') / C1 / 118.826 / 120.516 / 120.150 / 119.840 / 1.4033 / 1.4800
F / C2 / 118.183 / 120.921 / 120.261 / 119.454 / 1.4027 / 1.4853
Na / C2 / 117.773 / 121.154 / 120.324 / 119.270 / 1.4040 / 1.4845
Table S2, continued
MgCl / C2 / 118.138 / 120.948 / 120.257 / 119.453 / 1.4030 / 1.4848
SiH3(o) / C1 / 118.193 / 120.914 / 120.253 / 119.474 / 1.4029 / 1.4848
SiMe3(c) / C1 / 118.176 / 120.927 / 120.259 / 119.452 / 1.4030 / 1.4852
PH2(p') / C1 / 118.191 / 120.916 / 120.254 / 119.470 / 1.4029 / 1.4848
PH3+(o) / C1 / 118.705 / 120.572 / 120.145 / 119.855 / 1.4047 / 1.4761
S- / C2 / 116.452 / 121.771 / 120.720 / 118.563 / 1.4121 / 1.4701
SH(c) / C1 / 118.104 / 120.960 / 120.275 / 119.425 / 1.4032 / 1.4840
Cl / C2 / 118.220 / 120.898 / 120.254 / 119.477 / 1.4028 / 1.4849
ClO3(o) / C1 / 118.491 / 120.736 / 120.213 / 119.611 / 1.4024 / 1.4844
Br / C2 / 118.230 / 120.892 / 120.252 / 119.482 / 1.4028 / 1.4848
Range / 3.863 / 1.870 / 1.250 / 2.542 / 0.0217 / 0.0357
a Whenever necessary, the geometry of ring B has been made consistent with C2v symmetry by averaging appropriate geometrical parameters. Bond distances and angles are labelled according to Fig. 2.
b Angles are in degrees, bond distances in Å.
c The conformation of the substituent with respect to ring A is denoted as (c), (o), (p), (p'), and (e) according to the definitions given in Ref. [4]. Adherence to definitions is only approximate (see the text).
d Symmetry constraint imposed in the optimization of molecular geometry.
e Length of the C-C bond connecting ring A with ring B.

Table S3 Selected internal coordinates of the benzene ring and SFBCO parameters for some Ph-C(CH2-CH2)3C-X molecules, from HF/6-31G* and B3LYP/6-311++G** calculationsa,b

Substituentc

Level of calculation

a

b

g

/ SFBCO

NH-

/ HF / 116.134 / 122.078 / 120.608 / 118.492 / 1.3969 / -0.77
B3LYP / 116.387 / 121.980 / 120.490 / 118.671 / 1.4050 / -0.63

NMe2

/ HF / 116.756 / 121.735 / 120.492 / 118.788 / 1.3949 / 0.08
B3LYP / 116.903 / 121.679 / 120.417 / 118.904 / 1.4031 / 0.09

/ HF / 116.828 / 121.691 / 120.486 / 118.818 / 1.3948 / 0.18
B3LYP / 116.965 / 121.640 / 120.413 / 118.930 / 1.4030 / 0.17
a Bond angles and SFBCO parameters are in degrees, bond distances in Å. The SFBCO parameters have been calculated by the equation SFBCO = c0 + c1Da + c2Db + c3Dg + c4Dd (where Da = a - 120°, etc) using the appropriate coefficients from Table 1 of Ref. [7].
b The molecules have been imposed Cs symmetry, with the benzene ring perpendicular to the symmetry plane.
c The NH- substituent lies in the symmetry plane of the molecule, with the N-H bond antiperiplanar to a C-C bond of the cage. The NMe2 substituent has a pyramidal bond configuration, with the lone pair of electrons antiperiplanar to a C-C bond of the cage.

Table S4 Selected internal coordinates of the benzene ring and SE and SR parameters for some Ph-X molecules, from HF/6-31G* and B3LYP/6-311++G** calculationsa,b

Substituent

Level of calculation

/ SE / SR

NH-(c)c

/ HF / 113.37 / 122.56 / 122.52 / 116.46 / 1.4425 / -7.72 / -4.19
B3LYP / 113.60 / 122.70 / 121.98 / 117.04 / 1.4473 / -7.52 / -3.28

NMe2(p)

/ HF / 117.22 / 121.02 / 121.29 / 118.15 / 1.4007 / -3.25 / -2.11
B3LYP / 117.30 / 120.96 / 121.19 / 118.39 / 1.4123 / -3.04 / -1.83

/ HF / 121.35 / 119.05 / 120.37 / 119.83 / 1.3827 / 1.85 / -0.45
B3LYP / 121.45 / 118.93 / 120.47 / 119.76 / 1.3918 / 2.04 / -0.50
a Bond angles and SE and SR parameters are in degrees, bond distances in Å. The SE and SR parameters have been calculated from the internal ring angles by using the equations given in Tables 3 and 4 of Ref. [4].
b The Ph-NH- and Ph-NMe2 molecules have been imposed Cs symmetry, with the benzene ring coplanar and orthogonal to the symmetry plane, respectively. The Ph-Br molecule has been imposed C2v symmetry.
c The benzene ring of the Ph-NH- molecule has been treated has having idealized C2v symmetry by averaging appropriate bond distances and angles.

Table S5 Comparison of the twist angles j for pairs of 4-substituted biphenyls with protonated/deprotonated substituents. Also given are the SR and SFBCO parameters,a measuring the resonance and field effects of the substituents, respectivelyb
Substituents / j (°) / SR (°) / SFBCO (°)
CH2- / 21.7 / -4.79 / -0.70
Me / 44.9 / -0.17 / 0.02
COO- / 42.7 / -0.05 / -0.53
COOH / 44.7 / 0.53 / 0.12
NH- / 26.7 / -4.19 / -0.77
NH2 / 44.5 / -1.40 / 0.06
NH3+ / 44.2 / 0.04 / 0.79
O- / 30.4 / -3.51 / -0.81
OH / 45.1 / -1.22 / 0.08
OH2+ / 44.3 / -0.08 / 0.89
PH2 / 44.9 / 0.29 / 0.09
PH3+ / 41.6 / 0.76 / 0.75
S- / 38.0 / -1.75 / -0.59
SH / 45.1 / 0.11 / 0.11
a SR values refer to Ph-X molecules and are taken from Table 5 of Ref. [4] and Table S4 of the present paper. SFBCO values refer to Ph-C(CH2-CH2)3C-X molecules and are taken from Table 2 of Ref. [7] and Table S3 of the present paper.
b All entries in this table are from HF/6-31G* calculations.

Table S6 Selected internal coordinates of the phenyl probe and SFBIPH(o) parameters for some p-Ph-C6H4-X molecules in the orthogonal conformation, from HF/6-31G* and B3LYP/6-311++G** calculationsa

Substituent

Level of calculation

/ SFBIPH(o)

NH-(c)b

/ HF / 116.988 / 121.688 / 120.250 / 119.136 / 1.3961 / -2.31
B3LYP / 117.036 / 121.667 / 120.221 / 119.188 / 1.4053 / -2.24

NMe2(p)b,c

/ HF / 118.511 / 120.802 / 120.153 / 119.579 / 1.3913 / -0.29
B3LYP / 118.430 / 120.834 / 120.169 / 119.566 / 1.4006 / -0.38

Brd

/ HF / 118.874 / 120.583 / 120.147 / 119.666 / 1.3904 / 0.19
B3LYP / 118.817 / 120.594 / 120.172 / 119.652 / 1.3997 / 0.14
a Bond angles and SFBIPH(o) parameters are in degrees, bond distances in Å. The SFBIPH(o) parameters have been calculated from the internal ring angles by using the equations given in Table 1 of Ref. [8].
b The p-Ph-C6H4-NH- and p-Ph-C6H4-NMe2 molecules have been imposed Cs symmetry.
c The phenyl probe has been treated as having idealized C2v symmetry by averaging appropriate bond distances and angles.
d The p-Ph-C6H4-Br molecule has been imposed C2v symmetry.

Table S7 Selected internal coordinates of the phenyl probe and SFBIPH(c) parameters for some p-Ph-C6H4-X molecules in the coplanar conformation, from HF/6-31G* and B3LYP/6-311++G** calculationsa

Substituent

Level of calculation

/ SFBIPH(c)

NH-(c)b,c

/ HF / 114.776 / 122.474 / 121.406 / 117.464 / 1.4108 / -2.89
B3LYP / 114.836 / 122.496 / 121.255 / 117.663 / 1.4219 / -2.78

NMe2(p)b

/ HF / 116.679 / 121.719 / 120.602 / 118.680 / 1.3968 / -0.19
B3LYP / 116.614 / 121.758 / 120.568 / 118.735 / 1.4069 / -0.31

Brd

/ HF / 116.924 / 121.606 / 120.496 / 118.874 / 1.3960 / 0.18
B3LYP / 116.902 / 121.620 / 120.466 / 118.927 / 1.4056 / 0.11
a Bond angles and SFBIPH(c) parameters are in degrees, bond distances in Å. The SFBIPH(c) parameters have been calculated from the internal ring angles by using the equations given in Table 1 of Ref. [8].
b The p-Ph-C6H4-NH- and p-Ph-C6H4-NMe2 molecules have been imposed Cs symmetry.
c The phenyl probe has been treated as having idealized C2v symmetry by averaging appropriate bond distances and angles.
d The p-Ph-C6H4-Br molecule has been imposed C2v symmetry.