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A Theoretical study of 13C NMR chemical shifts in a series of rigid bicyclo[m.n.o.] alkanes
124 (1985) 25-40 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
Journal of Molecular Structure (Theochem),
A THEORETICAL STUDY OF 13C NMR CHEMICAL SHIFTS IN A SERIES OF RIGID BICYCLO[m.n. o. ] ALKANES
RUTH PACHTER and PHILIPPUS L. WESSELS
Natiorud Chemical Research Labomtory, of South Africa)
CSIR, P.O. Box 395, Pretoria, 0001 (Republic
(Received 26 July 1984)
ABSTRACT The INDO-FPT calculated 13C NMR shielding constants, using GIAO’s and at the London approximation, were analysed in a series of rigid bicyclo[m.n.o. ] alkanes (m = 2, 3, 4; n = 2, 3; 0 = 1, 2), and adamantane. The trends in the experimental ‘“C chemical shifts values in this series of compounds are reasonably reproduced, and improved upon by the correction of the (r-Y integrals with the use of Mulliken populations. The discrepancy observed between the experimental and calculated 13C chemical shifts of the C(2) carbon atoms in bicyclo[2.2.l]heptane and bicyclo[3.2.1]octane, and the C(7) carbon atom in bicyclo[ 4.2.11 nonane, can be explained on the basis of a changed charge distribution resulting from nonbonded interactions in these highly strained five-membered rings, which, in turn, affect the one-center paramagnetic contribution to the shielding constant. The problem can be circumvented for C(2) in bicyclo[ 2.2.llheptane and bicyclo[ 3.2.lloctane by regarding a more rigorous method for calculating charge distributions within molecules than the Mulliken population analysis. INTRODUCTION
The detailed theoretical analysis of NMR chemical shifts has severely lagged behind developments in other areas of NMR. A major breakthrough in the application of SCF-MO chemical shift theory to molecules of general interest is represented by the ab initio Gauge Invariant Atomic Orbital (GIAO) method of Ditchfield [l-3], assuring origin independence of the results. This method was further applied by Prado et al. [4-81 and by Tse [9, lo] . However, the complexity of calculations using this technique restricts its applicability to molecules containing a limited number and types of atoms. Therefore, the relative computational simplicity of a semi-empirical approach which employs GIAO basis sets and wave functions that include all electrons, e.g., CNDO/INDO, seems attractive, and has indeed proved to be the most promising among the present methods of calculating nuclear magnetic shielding for larger molecules. In the INDO Finite Perturbation Theory (FPT) of nuclear magnetic shielding constants employing GIAO basis sets, originally introduced by Ellis, Maciel and McIver [ 111, MO’s are calculated with a magnetic field included 0166-1280/85/$03.30
0 1985 Elsevier Science Publishers B.V.
26
the Hamiltonian, the shielding is computed nuclear magnetic with the MO’s. At effects of invariance and magnetic field two-center part of perturbed Hamiltonian
the interaction INDO levels, up only the
3 is external magnetic and $, 2, R,, 2, the distance from the origin of molecular coordinate to the on which basis functions XV are $M is magnetic moment nucleus M; N is the number of electrons and ZK is the charge of the K-th nucleus; ? and i$ are the distance vectors to the electron from the arbitrary origin of the coordinate system and nucleus K, respectively. The origin independence of the theory is maintained as long as approximations are made only to terms which a_ppearinside the integral in eqn. (1). Care must also be taken to ensure that H remains Hermitian, since the perturbed energies E(s’zM) are real quantities. Expanding the exponential inside the integral and keeping only those terms which are relevant in chemical shift calculations one gets
+ higher order terms
1
(Y,p = x, y, z
c-3
Ho,, is appropriate for the calculation in the absence of the perturbations and is given in the INDO method by: HOW= l/2@: + fiz)S”,, where the p’s are atomic parameters and S$, is the overlap integral when PP and x0, are on different atoms. The operators in the remaining integrals are defined in ref. 11. Retaining only the leading term or first order term in 3 in this expansion is equivalent to the Londoz approximation, and there are two ways to keep the Hermitian property of H in such a case: (a) To assume that, with the exception of Hi,, all the integrals in eqn. (2) are zero if J$ and x”, are centered on different atoms. This approach was first suggested by Ellis et al. [ 111, and with different parametrization also by Fukui [ 121, Kondo et al. [13], and recently by Chesnut et al. [14] and by Galasso [ 151.
27
(b) However, the inclusion of two- and three-center terms in the calculations of chemical shifts, which are neglected in approach (a), has recently been proved essential [ 16,171. To retain the Hermitian property of H at the INDO and London levels of approximation in such a case, the restrictions resulting from writing explicitly [HJh_ = 1/2[H, + H&,1 should be taken into account. Such a formalism for the calculation of mono-, di-, and triatomic terms of u was developed by Vauthier, Tonnard and Odiot [17,X3]. Another extension of the original INDO model was presented by Garber et al. [ 191. In this approach H, was not truncated at the level of the London approximation, but the dipole integral term and the two-center angular momentum terms in eqn. (2) were retained. However, the three-center terms were not included in this work, so that those terms which include the contribution to the shielding of atom A as a result of the induced current density between atoms C and D where A # C # D were neglected. Inclusion of the three-center terms in Hc, was subsequently reported by Dobosh, Ellis and Chou for proton [16] and boron [20] chemical shifts. NMR shielding calculations were performed using an adapted version of the NMR CINDO-80 program [21], which follows the theoretical approach outlined in (b). This program seems to be suitable for a more advanced theoretical study of chemical shifts as it retains two- and three-center contributions, and thus reveals the relative importance of “local” and “distant” electron densities on the magnetic shielding of a given nucleus. The various contributions to the total shielding a(M) of nucleus M following this approach and in the notation of Vauthier et al. [ 181 are: 1: ad(M)= local diamagnetic shielding from AO’s centered on M; 2: ad(K) = diamagnetic contribution of all atoms but M, from AO’s centered on K; 3: up(M)= local paramagnetic shielding, from AO’s centered on M; 4: up(K) = paramagnetic contribution of all atoms but M, from AO’s centered on K; 5 + 6 + 7: u(MK) = ud(MK) + ut(MK) + ujj(MK)= total (dia plus paramagnetic) contribution of all the MK pairs of atoms involving M, from AO’s centered on M and K; 8 + 9 + 10: u(M,AB) = ud(M,AB)+ &M,AB) + ug(M,AB)= contributionofallpairs AB but those involving atom M, from AO’s centered on atoms A and B. The total shielding of atom M is then expressed by the sum u = ud(M)+ ud(K)+ up(M)+ up(K)+ u(MK)f u(M,AB), which is calculated from the appropriate expressions described in ref. 17. The INDO-FPT methods employing GIAO’s, as described above, were applied to calculate “C chemical shifts in model compounds [18, 221. We have undertaken a theoretical investigation of the “C chemical shifts in a series of rigid bicyclo[m.n.o.] alkanes (m = 2, 3, 4; II = 2, 3; o = 1, 2) (see Fig. 1); in order to determine if the experimental trends in the 13C chemical shifts can be theoretically reproduced, and to delineate the various contributions to the 13C chemical shift values.
I:BiCYCLO
[2.2.1]
HEPTANE
II’BICYCLO
[2.2.2]
OCTANE
IX.
WCYCLO
[3
2 I]
OCTANE
FOREIORNANE]
l!Z : BICYCLO
[3 3.11
NONANE
P
m
BICYCLO
[3.2.2]
NONANE
p1: BICYCLO
[4.2.1]
NONANE
: ADAMANTANE
Fig. 1. Series of rigid bicyclo[m.n.o.] tane.
alkanes (m = 2, 3, 4; n = 2, 3; o = 1, 2) and adaman-
RESULTS
13C chemical shifts were calculated for compounds I-VII using experimental geometry parameters [23] as well as empirical Molecular Mechanics (MM) optimized structures, e.g., by applying MM2 [24] and EnglerSchleyer [25] force-fields. An experimental geometry is not always available for all molecules considered, and if available for a relatively strained molecule, e.g., in norbomane, such structures can differ in important details [23a] . Calculated 13C shielding constants trends vary only slightly by using an MM optimized geometry (MM2 or Eng. Sch.) rather than an experimental one (exp.), as is demonstrated, for example, in norbomane [exp.: a(C1) = 14.51, a(C2) = 10.32, o(C7) = 10.91; MM2: u(C1) = 13.18, u(C2) = 11.70, u(C7) = 11.72; Eng. Sch.: u(C1) = 15.73, o(C2) = 13.88, u(C7) = 14.54 (ppm)], and
29
bicyclo[2.2.2] octane [exp.: o(C1) = 18.08, a(C2) = 14.46; MM2: o(C1) = 17.59, o(C2) = 13.69; Eng. Sch.: u(C1) = 19.06, u(C2) = 15.14 (ppm)]. All reported r3C chemical shifts results given in the following are therefore based on MM2 optimized geometries. Table 1 summarizes the calculated u shielding constants, and Table 2 the calculated vs. experimental shifts values. Except for the basic considerations mentioned in the introduction, there are differences between the INDO models also in the parameters used, since it is well known that semi-empirical theories suffer from the fact that although one set of parameters may be good for reproducing one class of physical observables, reparametrization to reproduce a second class may avoid the ability to apply the theory to the first. This reparametrization problem with respect to 13C chemical shifts was approached by Ellis, Maciel and McIver [ 111, and by Kondo et al. [ 131. Maciel and Seidman have also in
TABLE
1
Calculated ‘W shielding constants (in ppm) of molecules I-VII Terma
1
2
4
5+6+7
S+StlO
Total (l-7)
Total (l-10)
BicycIo[2.2.llheptaneI C(l) C(2) C(7)
57.38 57.52 57.60
3.81 3.50 3.55
-61.13 -64.49 -65.91
1.00 0.37 0.79
12.32 14.80 15.69
2.62 2.22 1.53
13.18 11.70 11.72
15.80 13.92 13.25
Bicyclo12.2.21octaneII C(l) cczi
57.39 57.52
3.42 3.37
-55.30 -61.74
0.65 0.11
11.43 14.43
3.50 2.64
17.59 13.69
21.09 16.33
BicycIo[3.2.lloctaneIII C(l) C(2) C(5) C(6) C(8)
57.39 57.54 57.51 57.47 57.58
3.46 3.40 3.35 3.37 3.43
-62.15 -65.83 -62.59 -58.99 -66.89
1.01 0.70 0.21 0.23 0.61
11.76 14.74 14.35 14.09 15.38
3.13 2.42 2.63 2.85 1.99
11.47 10.55 12.83 16.17 10.11
14.60 12.97 15.46 19.02 12.10
Bicyclo[3.3.11nonaneIV C(l) C(2) C(3) C(S)
57.39 57.51 57.49 57.56
3.38 3.34 3.34 3.39
-57.56 -61.85 -59.17 -63.40
0.57 0.24 0.14 0.13
11.19 14.30 14.10 14.89
3.82 2.66 3.20 2.82
14.97 13.54 15.90 12.57
18.79 16.20 19.10 15.39
BicycIoC3.2.2lnonaneV C(l) C(2) C(3) C(6)
57.38 57.54 57.47 57.53
3.29 3.26 3.37 3.35
-57.67 -63.41 -58.71 41.49
0.98 0.45 0.32 0.31
11.18 14.49 14.20 14.44
3.77 3.01 3.32 2.76
14.96 12.33 16.65 14.14
18.73 15.34 19.97 16.90
BicycloC4.2.llnonaneVI C(l) C(2) C(3) C(7) C(9)
57.40 57.52 57.48 57.55 57.59
3.39 3.30 3.34 3.37 3.39
-64.09 -63.05 -59.41 -67.72 -67.85
1.38 0.29 0.40 0.88 1.10
11.64 14.34 14.11 14.84 15.22
3.45 2.99 3.05 2.46 2.21
9.72 12.40 15.92 8.92 9.45
13.17 15.39 18.97 11.38 11.66
Adamantane VII C(l) C(2)
57.3s 57.57
3.47 3.34
-58.20 -64.97
0.38 0.14
11.27 14.78
3.60 2.45
14.30 10.86
17.90 13.31
3
aDefinitions of the different terms contributing text.
to the shielding constant are given in the
30 TABLE 2 Calculated and experimentala “C! chemical shiftsb in the molecules I-VII 6 C% (cab. )”
gCH4 (caic.)d
6 CH4(exp.)
17.76 19.24 19.22
16.97 18.85 19.52
38.7 32.1 40.7
13.35 17.25
11.68 16.44
26.3 28.4
19.47 20.39 18.11 14.77 20.83
18.17 19.80 17.31 13.75 20.67
37.5 31.2 35.1 21.4 42.0
Bicyclo[ 3.3.11 nonane IV C(1) C(2) C(3) C(9)
15.97 17.40 15.04 18.37
13.98 16.57 13.67 17.38
30.2 33.9 24.8 37.4
Bicyclo[3.2.2]nonane C(1) C(2) C(3) C(6)
V 15.98 18.61 14.29 16.80
14.04 17.43 12.80 15.87
31.3 38.0 24.7 28.2
Bicyclo[4.2.l]nonane C(1) C(2) C(3) C(7) C(9)
VI 21.22 18.54 15.02 22.02 21.49
19.60 17.38 13.80 21.39 21.11
39.7 38.2 27.9 35.4 37.8
16.64 20.08
14.87 19.46
30.8 40.1
Bicyclo[2.2.l]heptane C(1) C(2) C(7)
I
Bicyclo[2.2.2]octane C(1) C(2)
II
Bicyclo[3.2.l]octane C(1) C(2) C(5) C(6) C(8)
III
Adamantane VII C(1) C(2)
aThe experimental values were taken from refs. 26-32 for compounds I-VII, respectively, and are given relative to methane. bin ppm and a positive sign means deshielding, i.e., 6 CH4 = e(CH,) - o(C-relevant). CChemical shifts are excluding the 3-center terms (8 + 9 + 10) and given relative to methane (a(CH,) = 30.94 ppm). dChemicai shifts are including the 3-center terms (8 + 9 + 10) and given relative to methane (o(CH,) = 32.77 ppm).
treated 13C shifts with different p parameters [22]. More recently, a modified least-squares procedure to find optimum p parameters was carried out [ 191. Optimal p’s obtained by this generalized procedure were also reported by Dobosh et al. [ 161 and Vauthier et al. [ 171. In addition, a variable-size
31
simplex optimization procedure was used [ 141 to reparametrize both (I + A) and p parameters. Table 3 lists the different parameters used in the above cited publications. The parameters summarized in Table 3 are derived from a basic set of small model hydrocarbons, and we therefore compared the shielding constants in the series of rigid molecules using these different parameter sets. The calculations for parameter set (5) were not done since the parameters are basically those of parameter set (3). The results for parameter set (7), the original parameter set of the NMRCINDOSO program, have already been reported in Table 1. Results of calculated 13Cshielding constants (excluding the threecenter terms), as well as the corresponding chemical shifts values by using different parameter sets, which are summarized in Table 4, prove that the original parameter set (7) is the most suitable for prediction of 13C chemical shifts. Specifically, no correlation between the calculated chemical shifts reported in Table 4 and the corresponding experimental values is found when using parameter sets (l), (4), (6) and (8). Although parameter sets (2) and (3) do yield a positive correlation between 6 22 and 6 %%, the magnitude of the correlation coefficients is smaller than when using the original parameter set (7). The results reported in Table 1 will, therefore, serve as the basis for the following discussion. DISCUSSION
Analysis of the calculated “C shielding constants presented in Tables 1 and 2 shows that the od(lM) local diamagnetic shielding is virtually constant for all carbon atoms, i.e., ad(M) = 57.5 & 0.1 ppm. The tricentric a(M, AB) contributions are small and fairly constant, too, i.e., o(&f,AB) = 2.8 + 1.3 ppm. Since the calculation of the tricentric terms is very time consuming, calculated chemical shfits excluding these contributions will be considered in all subsequent discussions. The relationship between the calculated and experimental 13C chemical shifts for the series of rigid bicyclic alkanes is TABLE 3 INDO parameters (in eV) Parameter set
l/2(1 + -4):
(1) (2)
7.18 7.18 7.18 7.18 7.18 7.18 7.18 6.00
(3) (4) (5) (6) (7) (8)
pH
l/2(2 + A):
l/2(1 + A);
-9.00
14.05 17.05 14.05 17.05 14.05 14.05 14.05 18.06
5.57 8.57 5.57 8.57 5.57 5.57 5.57 8.99
-21.00 -13.00 -13.00 -13.84 -11.82 -14.31 -a.43
Bc
Ref.
-21.00 -17.00 -15.00 -15.00 -15.14 -16.58 -16.57 -16.38
33 11 13 22 19 16 17 14
32 TABLE 4 Calculated “C shielding constant9 and chemical shiftsb in the molecules I-VII parameter sets (I), (2), (3), (4), (6), (3)’ Parameter set Methane C(1)
u(l)
3CH,
-1.31
D (3
3CH,
D 6)
40.43
17.90
Bicyclo[2.2.1lheptme I 36.06 -37.37 C(1) 17.13 -18.44 C(2) 18.67 -19.98 cm
13.85 13.50 12.63
26.58 -5.92 26.93 -5.60 27.80 -5.11
BicycloC2.2.2loctane II 34.81 -36.18 C(l) 16.74 -18.05 C(2)
18.99 15.73
BicycIo[3.2.1]octane III 32.16 -34.01 C(1) 15.54 -16.85 C(2) 16.43 -17.74 C(5) 18.51 -19.82 C(6) 15.86 -17.17 C(8)
$H,
(rw
3CH,
44.52
0 (6)
by using
gCH,
,,(8)
gCH,
11.53
33.36
23.82 -5.29 49.81 23.50 3.06 41.46 23.01 2.01 42.51
8.25 1.62 2.39
3.28 -2.04 9.91 -1.73 9.14 -2.04
21.44 -1.27 24.70 -3.59
19.17 -2.32 42.20 21.49 6.05 38.41
11.13 2.93
12.39 12.13 15.02 17.75 11.90
28.04 28.30 25.41 22.66 28.53
-1.98 -6.81 4.55 -1.07 -6.99
25.88 -6.43 24.71 1.62 22.45 5.16 18.97 8.18 24.39 1.42
50.95 42.90 39.36 36.34 43.10
5.97 5.56 -3.91 0.36 11.17 -3.48 2.18 9.35 -0.36 5.19 6.34 1.22 0.31 11.22 -2.83
31.33 36.84 33.72 32.14 36.19
BicycIo[3.3.1lnonaneIV 33.02 -34.33 C(l) 16.51 -17.82 C(2) 18.32 -19.63 C(3) 15.75 -17.06 C(9)
16.43 15.67 17.47 15.14
24.00 24.16 22.96 25.29
4.62 -3.88 -1.53 4.71
22.52 -1.20 21.78 5.97 19.43 7.15 22.61 5.46
45.72 38.55 36.11 39.06
8.36 2.65 4.84 1.92
3.17 -0.42 8.88 0.11 6.69 0.76 9.61 0.20
33.18 33.25 32.61 33.16
Bicyclo[3.2.2lnonaneV 34.13 -35.44 C(l) 16.95 -18.26 C(2) 19.60 -20.91 C(3) 16.97 -18.28 C(6)
15.89 14.16 17.96 15.94
24.54 4.57 26.27 -5.30 22.47 -0.55 24.49 -3.18
22.41 -2.44 23.20 3.51 18.45 8.15 21.08 5.47
46.96 41.01 36.37 39.05
8.18 1.82 5.85 3.31
2.75 -1.07 9.71 -1.61 5.68 1.33 8.22 0.02
34.43 34.97 32.03 33.34
Bicyclo[4.2.1lnonaneVI 31.28 -32.59 C(1) 16.71 -18.02 C(2) 19.20 -20.51 C(3) C(7) 14.21 -15.52 C(9) 14.50 -15.81
10.28 14.48 17.31 10.82 10.86
30.15 25.95 23.12 29.61 29.67
27.61 -8.82 22.82 4.45 19.39 7.09 26.21 0.22 25.73 0.09
53.34 4.21 7.26 -6.50 40.07 1.92 9.61 -0.76 5.17 6.36 0.64 31.43 44.30 -1.20 12.13 4.47 44.43 -0.5'7 12.10 4.62
39.86 34.12 32.72 37.83 37.98
AdmantaneVII C(1) 32.80 -34.11 C(2) 14.52 -15.83
16.73 13.50
24.70 -6.31 26.93 -6.53
-9.77 4.92 -1.49 -8.37 -7.83
23.21 -2.10 46.62 24.43 3.63 40.89
aIn ppm. bRelative to methane, i.e., 6 CH4 = u(CH,) - u(C-relevant),
CAssummarizedin Table3.
6%
= -1.06
0.40 8.60
3.20 30.16 0.10 33.26
7.91 3.62 -1.23 0.31 11.22 -1.47
in ppm.
+ 1.92 6222 (ppm), r2 = 0.64
However, the substantially larger deshielding observed experimentally for the carbon atoms C(2) in bicyclo[2.2.1] heptane, C(2) in bicyclo[3.2.1] octane and C(7) in bicyclo[4.2.l]nonane than for the corresponding methylenic bridgehead carbon atoms, is not exhibited by the calculated 13C chemical shifts. If these three results are excluded from the twenty-five points correlation 6 cu., = -8.42 _P.
+ 2.38 6 zzz(ppm), r2 = 0.80
35.40 35.09 35.40
34.59 34.83
It is often assumed, specifically according to the Pople-Karplus approximation (as reviewed in refs. 34 and 35), that the local paramagnetic term makes the dominant contribution to 13C!screening. Indeed, although the sum of o(MK) and the dia- and paramagnetic contributions to the shielding constant of atom M from AO’s centered on K, i.e., ad(K) + up(K) + o(MK), increases the overall correlation with the experimental chemical shifts trends in this series of rigid compounds by approximately 20%, the discrepancy regarding the chemical shifts of C(2) in I, C(2) in III, and C(7) in VI, emerges in the local paramagnetic contribution. Excluding these points from a correlation of up(M)evaluated relative to methane (u”(CH,) = -51.51 ppm), with the corresponding experimental chemical shifts yields: Sz = 18.17 + 1.50 uPcn,(ppm), r2 = 0.63, whereas no correlation is obtained when all points are included. The relevant five-membered rings of bicycle [ 2.2.11 heptane, bicyclo[3.2.1] octane, and bicyclo[4.2.l]nonane (with pseudorotation @2puckering and the six-membered rings of degrees of 144”, -36”) 125”) respectively), bicyclo[2.2.2] octane (boat: 0 2 90”, Q s 0”); bicyclo[3.3.1] nonane (chair: 8 z 180”, $J 2 120”); bicyclo[3.2.2]nonane (boat: 6 2 90”, 4 z 0”); and adamantane (chair: f3 = 0”, C$= 0'),have been investigated. The rings are indicated in bold lines in Fig. 1, and their puckering coordinates were derived by using the RING program [36], which is based on a general ring puckering theory [ 371. The five-membered rings of I and III, and to a lesser extent of VI, are conformations with unfavourable bond eclipsing between the two t-gaxial hydrogens, as shown by the position of the ring on the pseudorotation itinerary of a general five-membered ring. Nonbonded interactions in these five-membered ring systems (C’ symmetry) are also revealed by examining the nonequivalence of the exo-exo and endo-endo vicinal proton spin-spin coupling constants. This nonequivalence was experimentally demonstrated in norbornanes by Marchand et al. [38], and was considered remarkable since existing theories predicted equality for these cis (eclipsed) coupling constants. With the aid of semiempirical MO calculations Marshall et al. [39] and Barfield et al. [40, 411, and more recently de Leeuw et al. [ 421, have shown that this nonequivalence arises from nonbonded interactions between MO’s located about the bridgehead CH2 group and MO’s located at the C-C ethylene fragment. 3J(H,H) calculations were performed (unpublished results) at the INDO-FPT level of approximation [ 431 (summarized in Table 5) for bicycle [2.2.1] heptane, bicyclo[3.2.1] octane, bicyclo[4.2.1] nonane, and for bicyclo[2.2.2] octane and bicyclo[3.2.2]nonane. The difference between exo-exo and e&o-e&o 3J(H,H) can be extended to other bicyclic systems containing a five-membered ring, but is less pronounced in the comparable II and V six-membered rings with a boat conformation. The nonbonded interactions as described above cause an uneven partitioning of the overlap population between the bridgehead carbon atom and the ethylenic group carbon atom in norbornane, bicyclo[3.2.1] octane and
34 TABLE 5 INDO-FPT
calculations of 3J(H,H) coupling constants (in Hz)
Bicyclo[ 2.2.11 heptane Bicyclo[3.2.l]octane Bicyclo[4.2.1 Jnonane Bicyclo[2.2.2]octane Bicyclo[3.2.2]nonane
‘J[C(P)-H, V[ C(2)-H, 3J[C(7)-H, ‘J[C(2)_H, 3J[C(8)-H,
C(3)-H] C( 3)-H] C(S)-H] C(3kHl C(9)-H]
exo-exo
endo-endo
14.69 15.39 14.34 14.73 16.57
10.41 10.43 10.67 14.76 15.08
bicyclo[4.2.1]nonane, with a larger electron density anticipated about the ethylene bridge carbon atom than at the methylene carbon atom. Atomic charges calculations were performed at the ab initio [44] level using minimal STO-3G basis sets, and the Mulliken populations obtained in this manner for the carbon atoms in the series of rigid molecules I-VII is presented in Table 6. There is almost no indication of a difference in the electron densities between the methylenic bridgehead carbon atom and the ethylenic carbon atom in the five-membered rings of I, III and VI. However, the Mulliken population analysis [ 451 simply assigns all the molecular charge density in a molecule to the individual atoms, i.e., the charge belonging to a specific atom M is that arising entirely from the atomic orbitals of M and half of that arising from the overlap of atomic orbitals on M with those of all other atoms in the molecule. This is a physically unrealistic scheme, and has been repeatedly questioned [46, 471. In a recently developed method [48--511, the wavefunction is squared according to Born’s probabilistic interpretation and then integrated over the required volume, the coordinate origin being set each time at the center of the sphere. This method [CHARGES program: 521 was used with ab initio molecular wavefunctions [44] as a starting point, in order to obtain physically more accurate charges for the carbon atoms in the series of molecules I-VII, as summarized in Table 7. It is important to emphasize that the total charge within spheres of covalent radii centered on the atomic nuclei of the molecule amounts to less than the total number of electrons in the system, and approximately two or three electrons per main atom and one per hydrogen lie outside the spheres. According to the Mulliken population analysis the changes in 4 atomic charges between the bridgehead carbon atoms (C(7) in I and II and C(8) in VI) and the ethylenic carbon atoms (C(2) in I and III, and C(7) in VI) is approximately 0.5-2.5%. The CHARGES method yieldsdifferences (defined as (q(C2) - q(C7))/qC(2)) of about 400%, 100% and 50% for molecules I, III and VI, respectively, with the more negative charge on the ethylenic carbon. For comparison, the atom charges obtained from the diagonal elements of the bond-order matrices of semi-empirical methods are given in Table 8. Since these results are not comparable to the ab initio values, semi-empirical and ab initio methods are not to be used indiscriminately for a charge analysis.
35 TABLE 6 Mulliken orbital populations (in electrons) from STO-3G calculations 1s
2s
2P
1.9922 1.9922 1.9922
1.1816 1.1890 1.1873
2.8540 2.9157 2.9200
-0.0278 -0.0969 -0.0995
1.9921 1.9924
1.1763 1.2204
2.8624 2.8916
-0.0308 -0.1044
1.9921 1.9922 1.9921 1.9921 1.9922
1.1772 1.1883 1.1859 1.1835 1.1876
2.8581 2.9169 2.9142 2.9187 2.9165
-0.0274 -0.0974 -0.0922 -0.0943 -0.0963
1.9921 1.9921 1.9921 1.9921
1.1741 1.1852 1.1825 1.1844
2.8598 2.9155 2.9206 2.9181
-0.0260 -0.0928 -0.0952 -0.0946
G(l) G(2) G(3) G(6)
1.9921 1.9921 1.9921 1.9921
1.1753 1.1860 1.1824 1.1851
2.8578 2.9150 2.9172 2.9185
-0.0252 -0.0931 -0.0917 -0.0957
Bicyclo[ 4.2.11 nonane VI G(l) G(2) G(3) G(7) G(9)
1.9921 1.9922 1.9921 1.9921 1.9922
1.1771 1.1867 1.1838 1.1879 1.1874
2.8584 2.9114 2.9166 2.9170 2.9179
-0.0276 -0.0903 -0.0925 -0.0970 -0.0975
1.9921 1.9922
1.1745 1.1864
2.8629 2.9169
-0.0295 -0.0955
I
Bicyclo[2.2.1]heptane
(71) C(2)
G(7)
Bicyclo[2.2.2]octane G(1) G(2)
II
Bicyclo[3.2.l]octane
II
G(1) G(2) G(5) G(6) G(8) Bicyclo[3.3.1 G(1) G(2) G(3) G(9)
Atomic charge
Jnonane IV
Bicyclo[3.2.2]nonane
V
Adamantane VII G(l) G(2)
Some aspects of this problem were recently examined by Fliszar et al. [ 541, describing STO-3G wavefunctions to be adequate for deducing consistent atomic charges, although by no means unique in that respect. Flisz&r and co-workers also developed a modified Mulliken population analysis [ 55, 561, used with STO-3G wavefunctions, for an uneven partitioning of overlap in heteronuclear situations. However, this method does not differentiate between two -GH2 groups as is investigated in this study. The problem presented in the beginning of the discussion regarding the overall trend of aP(locaI) in the series of rigid molecules I-VII, involves the incorrect prediction of the local paramagnetic contribution to the shielding
36 TABLE 7 Charges within spheres centered on the carbon nuclei of molecules I-VII CHARGES CHARGE Bicyclo[2.2.l]heptane C(l) C(2) C(7)
I
Bicyclo[ 2.2.2loctane C(l) C(2)
II
Bicyclo[3.2.1] C(l) C(2) C(5) C(6) C(8)
calculated with
Modified CHARGE’
1.5601 1.5520 1.5744
0.0026 -0.0055 0.0169
1.5736 1.5564
0.0129 -0.0043
1.5710 1.5571 1.5711 1.5780 1.5677
0.0030 -0.0109 0.0031 0.0100 -0.0003
1.5798 1.5751 1.5798 1.5757
0.0026 -0.0021 0.0026 -0.0015
1.5793 1.5774 1.5919 1.5713
0.0026 0.0007 0.0152 -0.0054
1.5769 1.5767 1.5833 1.5658 1.5710
0.0018 0.0016 0.0082 -0.0093 -0.0041
1.5739
0.0056 -0.0038
octane III
Bicyclo[B.I.l]nonane C(l) C(2) C(3) C(9)
IV
Bicyclo[3.2.2]nonane C(l) C(2) C(3) C(6)
V
Bicyclo[4.2.1]nonane C(l) C(2) C(3) C(7) C(9)
VI
Adamantane VII C(l) C(2)
1.5645
aIn order to facilitate comparison of these charges with the usual definition of an atomic charge, the average value of the missing electrons was added to each charge.
of the ethylenic carbon atoms in the molecules I, III and explained on the basis of the electronic structure of these integrals of the type WY2, in the one-center paramagnetic the 13C shielding constant are related to the Slater exponent to c3), which is modified by the formula [57] {M = (z* - 0.35(&M
VI, and can be molecules. The contribution to c (proportional
- &))/n*,
where Z* is the effective nuclear charge; II* is the effective quantum number;
37 TABLE 8 Semi-empirical atomic charges calculations (in electrons) INDOa Bicyclo[2.2.l]heptane C(1) C(2) C(7)
MNDOCb
I
Bicyclo[2.2.2]octane C(1) C(2)
II
BicycIo[ 3.2.lloctane C(1) C(2) C(5) C(6) C(8)
III
Bicyclo[3.3.l]nonane C(l) C(2) C(3) C(9)
IV
Bicyclo[3.2.2]nonane C(1) C(2) C(3) C(6)
V
Bicyclo[4.2.1] C(1) C(2) C(3) C(7) C(9)
MNDOb
0.0370 0.0198 0.0106
-0.0676 -0.0495 -0.0106
-0.0494
0.0362 0.0201
-0.0534 -0.0040
-0.0339 0.0028
0.0361 0.0183 0.0214 0.0266 0.0125
-0.0578 -0.0078 0.0050 -0.0113 -0.0030
-0.0380 -0.0009 0.0122 0.0024 -0.0035
0.0366 0.0211 0.0236 0.0152
-0.0477 0.0039 -0.0103 0.0057
-0.0264 0.0109 0.0026 0.0054
0.0368 0.0180 0.0265 0.0188
-0.0448 0.0054 -0.0080 0.0000
-0.0236 0.0133 0.0056 0.0069
0.0351 0.0209 0.0252 0.0166 0.0116
-0.0520 0.0085 -0.0064 -0.0064 0.0028
-0.0315 0.0163 0.0058 0.0001 0.0028
0.0372 0.0143
-0.0557 0.0090
-0.0342 0.0101
-0.0022 -0.0109
nonane VI
Adamantane VII C(1) C(2)
aCalculated by the INDO finite perturbation theory of chemical shifts as described in the introduction [ 211. bAs described in ref. 53.
P sgkn
is the electronic density, and 2, that
oP(modified) = ~~(1.00 + 0.32308q
the core charge of atom M. It can be
+ 0.03479q2
+ 0.00125q3),
where q is the atomic charge in electrons. The INDO calculated electron densities are not suitable for an electronic structure description of the series
38
of rigid hydrocarbons, and their inclusion in the modified evaluation of op(local) does not increase the total overall agreement with the experimental chemical shifts. On the other hand, an inclusion of the Mulliken populations in the Slater exponents modification for the one-center paramagnetic contribution to the u shielding constants yields an overall better relationship: 6 2 = 0.66 + 2.05 &zg;(ppm), r2 = 0.68. The Mulliken population analysis does not account for the higher electron density at C(2) than at C(7), at C(2) than at C(8), and at C(7) than at C(9) carbon atoms in bicyclo[2.2.1] heptane, bicyclo[3.2.1] octane, and bicyclo[4.2.1] nonane, respectively, as has been proved by the relative trends of the sphere charges for these particular carbon atoms. To evaluate the effective charge on C(2) in I and III and C(7) in VI, ab initio electron densities at these atoms were multiplied by a CHARGES factor, defined as the change in electron density between the ethylenic and bridgehead carbon atoms normalized to the absolute average change of charge for the main atoms in the molecule. The factors from CHARGES values presented in Table 7 are 2.6880 for C(2) in I, 1.9273 for C(2) in III, and 1.0400 for C(7) in VI. The resulting changes in the calculated local paramagnetic contributions to the shielding constants of C(2) in I (-58.84 ppm) and C(2) in III (-61.55 ppm) do, indeed, mainly account for the discrepancy in the total correlation with the experimental chemical shifts. The modified correlation is: SE2 = 3.21 + 2.34 &zz;(ppm), r2 = 0.77, as shown in Fig. 2. In the more complex molecule of bicyclo[4.2.l]nonane, other interactions might be present since the discrepancy between the calculated and experimental 13C chemical shift value of C(7) is not yet fully explained. This and other deviations between calculated and experimental 13C chemical shifts of carbon atoms in the series of rigid molecules are further investigated.
44
Fig. 2. Relationship between experimental and calculated chemical shifts in the series of rigid bicyclo[m.n.o. ] alkanes (m = 2, 3, 4; n = 2, 3; o = 1, 2) and adamantane (relative to methane).
39 REFERENCES 1 R. Ditchfield, Mol. Phys., 27 (1974) 789. 2 R. Ditchfield, Chem. Phys. Lett., 15 (1972) 203. 3 R. Ditchfield, J. Chem. Phys., 56 (1972) 5688. 4 F. Ribas Prado, C. Giessner-Prettre, B. Pullman and J.-P. Daudey, J. Am. Chem. Sot., lOl(l979) 1737. 5 F. Ribas Prado, C. Giessner-Prettre, J.-P. Daudey, A. Pullman, J. F. Hinton, G. Young and D. Harpool, J. Magn. Reson., 37 (1980) 431. 6 F. Ribas Prado, C. Giessner-Prettre and A. Pullman, Theor. Chim. Acta (Berlin), 59 (1981) 55. 7 F. Ribas Prado and C. Giessner-Prettre, J. Magn. Reson., 47 (1982) 103. 8 C. Giessner-Prettre and S. Ferchiou, J. Magn. Reson., 55 (1983) 64. 9 J. S. Tse, Chem. Phys. Lett., 92 (1982) 144. 10 S. K. Garg and J. S. Tse, Chem. Phys. Lett., 92 (1982) 150. 11 P. D. Ellis, G. E. Maciel and J. McIver, Jr., J. Am. Chem. Sot., 94 (1972) 4069. 12H. Fukui, Bull. Chem. Sot. Jpn., 47 (1974) 751. 13 M. Kondo, I. Ando, R. Chfijo and A. Nishioka, J. Magn. Reson., 24 (1976) 315. 14 D. B. Chesnut and F. W. Whitehurst, J. Comput. Chem., 1 (1980) 36. 15 V. Galasso, Org. Magn. Reson., 12 (1979) 318. 16 P. A. Dobosh, P. D. Ellis and Y. C. Chou, J. Magn. Reson., 36 (1979) 439. 17 E. C. Vauthier, S. Odiot and F. Tonnard, Can. J. Chem., 60 (1982) 957. 18 E. C. Vauthier, S., FIiszC, F. Tonnard and S. Odiot, Can. J. Chem., 61 (1983) 1417. 19 A. R. Garber, P. D. Ellis, K. Seidman and K. Schade, J. Magn. Reson., 34 (1979) 1. 20 P. D. Ellis, Y. C. Chou and P. A. Dobosh, J. Magn. Reson., 39 (1980) 529. 21EI C. Vauthier, Q.C.P.E. Bull., 2 (1982) 441. 22 K. Seidman and G. E. Maciel, J. Am. Chem. Sot., 99 (1977) 659. 23 (a) Bicyclo[ 2.2.1 Jheptane: experimental geometry from an electron diffraction study of L. Doms, L. van den Enden, H. J. Geise and G. van Alsenoy, J. Am. Chem. Sot., 105 (1983) 108; (b) bicyclo[2.2.2]octane: bicyclo[2.2.2]octane has three rings fused together at the carbon atoms 1 and 4. In the structure with the highest symmetry, D,h, the rings are locked in a boat form, i.e., 7 = 0. However, a D, symmetry is also considered, with r = 7.2” or r = 12.8”. The experimental geometry is taken from an electron diffraction study by A. Yokozeki, K. Kutchitsu and Y. Morino, Bull. Chem. Sot. Jpn., 43 (1970) 2017; (c) bicyclo[3.2.l]octane: the geometry to be optimized
is taken as an average of the three experimental geometries derived from: (1) cisdibromo-2,4 bicyclo[3.2.1 Joctanone-3 (P. M. van Meerssche, G. Germain and J. P. Declerq, Acta Crystallogr., Sect. B, 35 (1979) 491); (2) 2,4-dimethyl-2-methoxy-3,8dioxabicyclo[3.2.l]octane (D. M. Walba, R. C. Haltiwanger, M. D. Wand and M. C. Wilkes, Tetrahedron, 37 (1981) 1663); (3) syn-bicyclo[3.2.1]octa-2,6-dien-8-71 tosylate (F. G. K. Smit and C. H. Stam, Cryst. Struct. Commun., 7 (1978) 499). (d) bicyclo[3.3.1]nonane: experimental geometry is taken from an electron diffraction investigation by E. L. Osima, V. S. Mastryukov, L. V. Vilkov and N. A. Belikova, J. Chem. Sot., Chem. Commun., (1976) 12; (e) bicyclo[3.2.2]nonane: experimental geometry derived from a study on 3-aza bicyclo[3.2.2]nonane by L. M. Amzel, S. Baggio, R. F. Baggio and L. N. Becka, Acta Crystallogr., Sect. B, 30 (1974) 2494; (f) bicyclo[4.2.1 Jnonane: the geometry to be optimised is derived from an X-ray structure of 3-bromo-4-chloro bicyclo[ 4.2. l] non-3-ene-2-one by W. Kraus, H. Patzelt,
40 H. Sadlo, G. Sawitzki and G. Schwinger, Liebigs Ann, Chem., (1981) 1826; (g) admantane: experimental geometry by J. Donohue and S. H. Goodman, Acta Crystahogr., 22 (1967) 352. 24 N. L. Allinger and Y. H. Yuh, Q.C.P.E., 13 (1981) 395. 25 D. J. Iverson and K. Mislow, Q.C.P.E., 13 (1981) 410. 26 G. S. Poindexter and P. J. Kropp, J. Org. Chem., 41(1976) 1215. 27 H. Brouwer, J. B. Stothers and C. T. Tan, Org. Magn. Reson., 9 (1977) 360. 28 J. B. Stothers, J. R. Swenson and C. T. Tan, Can. J. Chem., 53 (1975) 581. 29 J. B. Stothers and C. T. Tan, Can. J. Chem., 55 (1977) 841. 30 J. R. Wiseman and H. 0. Krabbenhoft, J. Org. Chem., 42 (1977) 2240. 31 K. B. Becker, Helv. Chhn. Acta, 60 (1977) 81. 32 H. Duddeck and P. Wolff, Org. Magn. Reson., 9 (1977) 528. 33 J. A. Pople and D. L. Beveridge, Approximate Molecular Orbital Theory, McGraw Hill, New York, 1970. 34G. J. Martin, M. L. Martin and S. Odiot, Org. Magn. Reson., 7 (1975) 2. 35 G. L. Nelson and E. A. Williams, Progr. Phys. Org. Chem., 12 (1976) 229. 36D. Cremer, Q.C.P.E., 10 (1974) 288. 37 D. Cremer and J. A. Pople, J. Am. Chem. Sot., 97 (1975) 1354. 38 A. P. Marchand, N. W. Marchand and A. L. Segre, Tetrahedron Lett., (1969) 5207. 39 J. L. Marshall, S. R. Walter, M. Bar-field, A. P. Marchand, N. W. Marchand and A. L. Segre, Tetrahedron, 32 (1976) 537. 40M. Barfield, A. M. Dean, C. J. Fahick, R. J. Spear, S. Sternhell and P. W. Westerman, J. Am. Chem. Sot., 97 (1975) 1482. 41M. Bar-field, J. Am. Chem. Sot., 102 (1980) 1. 42 F. A. A.M. de Leeuw, A. A. van Beuzekom and C. Altona, J. Comput. Chem., 4 (1983) 438. 43P. Dobosh, Q.C.P.E., 10 (1975) 281. 44 A modified version of the Gaussian-76 ab initio program which was made available to us by Professor Dieter Cremer was used. 45 R. S. Mulliken, J. Chem. Phys., 23 (1955) 1833. 46 F. A. Momany, J. Phys. Chem., 82 (1982) 592. 47 K. B. Wiberg, J. Am. Chem. Sot., 102 (1980) 1229. 48 S. M. Dean and W. G. Richards, Nature, 256 (1975) 473. 49 W. G. Richards and J. Wallis, Proc. R. Sot. London, Ser. B, 199 (1977) 291. 50 A. F. Marchington, S. C. R. Moore and W. G. Richards, J. Am. Chem. Sot., 101(1979) 5529. 51 V. Sackwild and W. G. Richards, J. Mol. Struct., Theochem, 89 (1982) 269. 52 J. Wallis, Q.C.P.E., 13 (1981) 411. 53 MNDO is described by M. J. S. Dewar and W. Thiel, J. Am. Chem. Sot., 99 (1977) 4899; MNDOC is described by W. Thiel, J. Am. Chem. Sot., 103 (1981) 1413,142O. Calculations were performed using the program of W. Thiel, Q.C.P.E. Bull., 2 (1982) 438. 54 M. T. Beraldin, E. Vauthier and S. Fliszar, Can. J. Chem., 60 (1982) 106. 55 S. Fliszk, G. Kean and R. Macaulay, J. Am. Chem. Sot., 96 (1974) 4353; S. Fliszar,, A. Goursot and H. Dugas, J. Am. Chem. Sot., 96 (1974) 4358. 56 S. Flisz&r, Charge Distributions and Chemical Effects, Springer-Verlag, New York, 1983. 57 M. Karplus and J. A. Pople, J. Chem. Phys., 38 (1963) 2803.
Journal of Molecular Structure (Theochem),
A THEORETICAL STUDY OF 13C NMR CHEMICAL SHIFTS IN A SERIES OF RIGID BICYCLO[m.n. o. ] ALKANES
RUTH PACHTER and PHILIPPUS L. WESSELS
Natiorud Chemical Research Labomtory, of South Africa)
CSIR, P.O. Box 395, Pretoria, 0001 (Republic
(Received 26 July 1984)
ABSTRACT The INDO-FPT calculated 13C NMR shielding constants, using GIAO’s and at the London approximation, were analysed in a series of rigid bicyclo[m.n.o. ] alkanes (m = 2, 3, 4; n = 2, 3; 0 = 1, 2), and adamantane. The trends in the experimental ‘“C chemical shifts values in this series of compounds are reasonably reproduced, and improved upon by the correction of the (r-Y integrals with the use of Mulliken populations. The discrepancy observed between the experimental and calculated 13C chemical shifts of the C(2) carbon atoms in bicyclo[2.2.l]heptane and bicyclo[3.2.1]octane, and the C(7) carbon atom in bicyclo[ 4.2.11 nonane, can be explained on the basis of a changed charge distribution resulting from nonbonded interactions in these highly strained five-membered rings, which, in turn, affect the one-center paramagnetic contribution to the shielding constant. The problem can be circumvented for C(2) in bicyclo[ 2.2.llheptane and bicyclo[ 3.2.lloctane by regarding a more rigorous method for calculating charge distributions within molecules than the Mulliken population analysis. INTRODUCTION
The detailed theoretical analysis of NMR chemical shifts has severely lagged behind developments in other areas of NMR. A major breakthrough in the application of SCF-MO chemical shift theory to molecules of general interest is represented by the ab initio Gauge Invariant Atomic Orbital (GIAO) method of Ditchfield [l-3], assuring origin independence of the results. This method was further applied by Prado et al. [4-81 and by Tse [9, lo] . However, the complexity of calculations using this technique restricts its applicability to molecules containing a limited number and types of atoms. Therefore, the relative computational simplicity of a semi-empirical approach which employs GIAO basis sets and wave functions that include all electrons, e.g., CNDO/INDO, seems attractive, and has indeed proved to be the most promising among the present methods of calculating nuclear magnetic shielding for larger molecules. In the INDO Finite Perturbation Theory (FPT) of nuclear magnetic shielding constants employing GIAO basis sets, originally introduced by Ellis, Maciel and McIver [ 111, MO’s are calculated with a magnetic field included 0166-1280/85/$03.30
0 1985 Elsevier Science Publishers B.V.
26
the Hamiltonian, the shielding is computed nuclear magnetic with the MO’s. At effects of invariance and magnetic field two-center part of perturbed Hamiltonian
the interaction INDO levels, up only the
3 is external magnetic and $, 2, R,, 2, the distance from the origin of molecular coordinate to the on which basis functions XV are $M is magnetic moment nucleus M; N is the number of electrons and ZK is the charge of the K-th nucleus; ? and i$ are the distance vectors to the electron from the arbitrary origin of the coordinate system and nucleus K, respectively. The origin independence of the theory is maintained as long as approximations are made only to terms which a_ppearinside the integral in eqn. (1). Care must also be taken to ensure that H remains Hermitian, since the perturbed energies E(s’zM) are real quantities. Expanding the exponential inside the integral and keeping only those terms which are relevant in chemical shift calculations one gets
+ higher order terms
1
(Y,p = x, y, z
c-3
Ho,, is appropriate for the calculation in the absence of the perturbations and is given in the INDO method by: HOW= l/2@: + fiz)S”,, where the p’s are atomic parameters and S$, is the overlap integral when PP and x0, are on different atoms. The operators in the remaining integrals are defined in ref. 11. Retaining only the leading term or first order term in 3 in this expansion is equivalent to the Londoz approximation, and there are two ways to keep the Hermitian property of H in such a case: (a) To assume that, with the exception of Hi,, all the integrals in eqn. (2) are zero if J$ and x”, are centered on different atoms. This approach was first suggested by Ellis et al. [ 111, and with different parametrization also by Fukui [ 121, Kondo et al. [13], and recently by Chesnut et al. [14] and by Galasso [ 151.
27
(b) However, the inclusion of two- and three-center terms in the calculations of chemical shifts, which are neglected in approach (a), has recently been proved essential [ 16,171. To retain the Hermitian property of H at the INDO and London levels of approximation in such a case, the restrictions resulting from writing explicitly [HJh_ = 1/2[H, + H&,1 should be taken into account. Such a formalism for the calculation of mono-, di-, and triatomic terms of u was developed by Vauthier, Tonnard and Odiot [17,X3]. Another extension of the original INDO model was presented by Garber et al. [ 191. In this approach H, was not truncated at the level of the London approximation, but the dipole integral term and the two-center angular momentum terms in eqn. (2) were retained. However, the three-center terms were not included in this work, so that those terms which include the contribution to the shielding of atom A as a result of the induced current density between atoms C and D where A # C # D were neglected. Inclusion of the three-center terms in Hc, was subsequently reported by Dobosh, Ellis and Chou for proton [16] and boron [20] chemical shifts. NMR shielding calculations were performed using an adapted version of the NMR CINDO-80 program [21], which follows the theoretical approach outlined in (b). This program seems to be suitable for a more advanced theoretical study of chemical shifts as it retains two- and three-center contributions, and thus reveals the relative importance of “local” and “distant” electron densities on the magnetic shielding of a given nucleus. The various contributions to the total shielding a(M) of nucleus M following this approach and in the notation of Vauthier et al. [ 181 are: 1: ad(M)= local diamagnetic shielding from AO’s centered on M; 2: ad(K) = diamagnetic contribution of all atoms but M, from AO’s centered on K; 3: up(M)= local paramagnetic shielding, from AO’s centered on M; 4: up(K) = paramagnetic contribution of all atoms but M, from AO’s centered on K; 5 + 6 + 7: u(MK) = ud(MK) + ut(MK) + ujj(MK)= total (dia plus paramagnetic) contribution of all the MK pairs of atoms involving M, from AO’s centered on M and K; 8 + 9 + 10: u(M,AB) = ud(M,AB)+ &M,AB) + ug(M,AB)= contributionofallpairs AB but those involving atom M, from AO’s centered on atoms A and B. The total shielding of atom M is then expressed by the sum u = ud(M)+ ud(K)+ up(M)+ up(K)+ u(MK)f u(M,AB), which is calculated from the appropriate expressions described in ref. 17. The INDO-FPT methods employing GIAO’s, as described above, were applied to calculate “C chemical shifts in model compounds [18, 221. We have undertaken a theoretical investigation of the “C chemical shifts in a series of rigid bicyclo[m.n.o.] alkanes (m = 2, 3, 4; II = 2, 3; o = 1, 2) (see Fig. 1); in order to determine if the experimental trends in the 13C chemical shifts can be theoretically reproduced, and to delineate the various contributions to the 13C chemical shift values.
I:BiCYCLO
[2.2.1]
HEPTANE
II’BICYCLO
[2.2.2]
OCTANE
IX.
WCYCLO
[3
2 I]
OCTANE
FOREIORNANE]
l!Z : BICYCLO
[3 3.11
NONANE
P
m
BICYCLO
[3.2.2]
NONANE
p1: BICYCLO
[4.2.1]
NONANE
: ADAMANTANE
Fig. 1. Series of rigid bicyclo[m.n.o.] tane.
alkanes (m = 2, 3, 4; n = 2, 3; o = 1, 2) and adaman-
RESULTS
13C chemical shifts were calculated for compounds I-VII using experimental geometry parameters [23] as well as empirical Molecular Mechanics (MM) optimized structures, e.g., by applying MM2 [24] and EnglerSchleyer [25] force-fields. An experimental geometry is not always available for all molecules considered, and if available for a relatively strained molecule, e.g., in norbomane, such structures can differ in important details [23a] . Calculated 13C shielding constants trends vary only slightly by using an MM optimized geometry (MM2 or Eng. Sch.) rather than an experimental one (exp.), as is demonstrated, for example, in norbomane [exp.: a(C1) = 14.51, a(C2) = 10.32, o(C7) = 10.91; MM2: u(C1) = 13.18, u(C2) = 11.70, u(C7) = 11.72; Eng. Sch.: u(C1) = 15.73, o(C2) = 13.88, u(C7) = 14.54 (ppm)], and
29
bicyclo[2.2.2] octane [exp.: o(C1) = 18.08, a(C2) = 14.46; MM2: o(C1) = 17.59, o(C2) = 13.69; Eng. Sch.: u(C1) = 19.06, u(C2) = 15.14 (ppm)]. All reported r3C chemical shifts results given in the following are therefore based on MM2 optimized geometries. Table 1 summarizes the calculated u shielding constants, and Table 2 the calculated vs. experimental shifts values. Except for the basic considerations mentioned in the introduction, there are differences between the INDO models also in the parameters used, since it is well known that semi-empirical theories suffer from the fact that although one set of parameters may be good for reproducing one class of physical observables, reparametrization to reproduce a second class may avoid the ability to apply the theory to the first. This reparametrization problem with respect to 13C chemical shifts was approached by Ellis, Maciel and McIver [ 111, and by Kondo et al. [ 131. Maciel and Seidman have also in
TABLE
1
Calculated ‘W shielding constants (in ppm) of molecules I-VII Terma
1
2
4
5+6+7
S+StlO
Total (l-7)
Total (l-10)
BicycIo[2.2.llheptaneI C(l) C(2) C(7)
57.38 57.52 57.60
3.81 3.50 3.55
-61.13 -64.49 -65.91
1.00 0.37 0.79
12.32 14.80 15.69
2.62 2.22 1.53
13.18 11.70 11.72
15.80 13.92 13.25
Bicyclo12.2.21octaneII C(l) cczi
57.39 57.52
3.42 3.37
-55.30 -61.74
0.65 0.11
11.43 14.43
3.50 2.64
17.59 13.69
21.09 16.33
BicycIo[3.2.lloctaneIII C(l) C(2) C(5) C(6) C(8)
57.39 57.54 57.51 57.47 57.58
3.46 3.40 3.35 3.37 3.43
-62.15 -65.83 -62.59 -58.99 -66.89
1.01 0.70 0.21 0.23 0.61
11.76 14.74 14.35 14.09 15.38
3.13 2.42 2.63 2.85 1.99
11.47 10.55 12.83 16.17 10.11
14.60 12.97 15.46 19.02 12.10
Bicyclo[3.3.11nonaneIV C(l) C(2) C(3) C(S)
57.39 57.51 57.49 57.56
3.38 3.34 3.34 3.39
-57.56 -61.85 -59.17 -63.40
0.57 0.24 0.14 0.13
11.19 14.30 14.10 14.89
3.82 2.66 3.20 2.82
14.97 13.54 15.90 12.57
18.79 16.20 19.10 15.39
BicycIoC3.2.2lnonaneV C(l) C(2) C(3) C(6)
57.38 57.54 57.47 57.53
3.29 3.26 3.37 3.35
-57.67 -63.41 -58.71 41.49
0.98 0.45 0.32 0.31
11.18 14.49 14.20 14.44
3.77 3.01 3.32 2.76
14.96 12.33 16.65 14.14
18.73 15.34 19.97 16.90
BicycloC4.2.llnonaneVI C(l) C(2) C(3) C(7) C(9)
57.40 57.52 57.48 57.55 57.59
3.39 3.30 3.34 3.37 3.39
-64.09 -63.05 -59.41 -67.72 -67.85
1.38 0.29 0.40 0.88 1.10
11.64 14.34 14.11 14.84 15.22
3.45 2.99 3.05 2.46 2.21
9.72 12.40 15.92 8.92 9.45
13.17 15.39 18.97 11.38 11.66
Adamantane VII C(l) C(2)
57.3s 57.57
3.47 3.34
-58.20 -64.97
0.38 0.14
11.27 14.78
3.60 2.45
14.30 10.86
17.90 13.31
3
aDefinitions of the different terms contributing text.
to the shielding constant are given in the
30 TABLE 2 Calculated and experimentala “C! chemical shiftsb in the molecules I-VII 6 C% (cab. )”
gCH4 (caic.)d
6 CH4(exp.)
17.76 19.24 19.22
16.97 18.85 19.52
38.7 32.1 40.7
13.35 17.25
11.68 16.44
26.3 28.4
19.47 20.39 18.11 14.77 20.83
18.17 19.80 17.31 13.75 20.67
37.5 31.2 35.1 21.4 42.0
Bicyclo[ 3.3.11 nonane IV C(1) C(2) C(3) C(9)
15.97 17.40 15.04 18.37
13.98 16.57 13.67 17.38
30.2 33.9 24.8 37.4
Bicyclo[3.2.2]nonane C(1) C(2) C(3) C(6)
V 15.98 18.61 14.29 16.80
14.04 17.43 12.80 15.87
31.3 38.0 24.7 28.2
Bicyclo[4.2.l]nonane C(1) C(2) C(3) C(7) C(9)
VI 21.22 18.54 15.02 22.02 21.49
19.60 17.38 13.80 21.39 21.11
39.7 38.2 27.9 35.4 37.8
16.64 20.08
14.87 19.46
30.8 40.1
Bicyclo[2.2.l]heptane C(1) C(2) C(7)
I
Bicyclo[2.2.2]octane C(1) C(2)
II
Bicyclo[3.2.l]octane C(1) C(2) C(5) C(6) C(8)
III
Adamantane VII C(1) C(2)
aThe experimental values were taken from refs. 26-32 for compounds I-VII, respectively, and are given relative to methane. bin ppm and a positive sign means deshielding, i.e., 6 CH4 = e(CH,) - o(C-relevant). CChemical shifts are excluding the 3-center terms (8 + 9 + 10) and given relative to methane (a(CH,) = 30.94 ppm). dChemicai shifts are including the 3-center terms (8 + 9 + 10) and given relative to methane (o(CH,) = 32.77 ppm).
treated 13C shifts with different p parameters [22]. More recently, a modified least-squares procedure to find optimum p parameters was carried out [ 191. Optimal p’s obtained by this generalized procedure were also reported by Dobosh et al. [ 161 and Vauthier et al. [ 171. In addition, a variable-size
31
simplex optimization procedure was used [ 141 to reparametrize both (I + A) and p parameters. Table 3 lists the different parameters used in the above cited publications. The parameters summarized in Table 3 are derived from a basic set of small model hydrocarbons, and we therefore compared the shielding constants in the series of rigid molecules using these different parameter sets. The calculations for parameter set (5) were not done since the parameters are basically those of parameter set (3). The results for parameter set (7), the original parameter set of the NMRCINDOSO program, have already been reported in Table 1. Results of calculated 13Cshielding constants (excluding the threecenter terms), as well as the corresponding chemical shifts values by using different parameter sets, which are summarized in Table 4, prove that the original parameter set (7) is the most suitable for prediction of 13C chemical shifts. Specifically, no correlation between the calculated chemical shifts reported in Table 4 and the corresponding experimental values is found when using parameter sets (l), (4), (6) and (8). Although parameter sets (2) and (3) do yield a positive correlation between 6 22 and 6 %%, the magnitude of the correlation coefficients is smaller than when using the original parameter set (7). The results reported in Table 1 will, therefore, serve as the basis for the following discussion. DISCUSSION
Analysis of the calculated “C shielding constants presented in Tables 1 and 2 shows that the od(lM) local diamagnetic shielding is virtually constant for all carbon atoms, i.e., ad(M) = 57.5 & 0.1 ppm. The tricentric a(M, AB) contributions are small and fairly constant, too, i.e., o(&f,AB) = 2.8 + 1.3 ppm. Since the calculation of the tricentric terms is very time consuming, calculated chemical shfits excluding these contributions will be considered in all subsequent discussions. The relationship between the calculated and experimental 13C chemical shifts for the series of rigid bicyclic alkanes is TABLE 3 INDO parameters (in eV) Parameter set
l/2(1 + -4):
(1) (2)
7.18 7.18 7.18 7.18 7.18 7.18 7.18 6.00
(3) (4) (5) (6) (7) (8)
pH
l/2(2 + A):
l/2(1 + A);
-9.00
14.05 17.05 14.05 17.05 14.05 14.05 14.05 18.06
5.57 8.57 5.57 8.57 5.57 5.57 5.57 8.99
-21.00 -13.00 -13.00 -13.84 -11.82 -14.31 -a.43
Bc
Ref.
-21.00 -17.00 -15.00 -15.00 -15.14 -16.58 -16.57 -16.38
33 11 13 22 19 16 17 14
32 TABLE 4 Calculated “C shielding constant9 and chemical shiftsb in the molecules I-VII parameter sets (I), (2), (3), (4), (6), (3)’ Parameter set Methane C(1)
u(l)
3CH,
-1.31
D (3
3CH,
D 6)
40.43
17.90
Bicyclo[2.2.1lheptme I 36.06 -37.37 C(1) 17.13 -18.44 C(2) 18.67 -19.98 cm
13.85 13.50 12.63
26.58 -5.92 26.93 -5.60 27.80 -5.11
BicycloC2.2.2loctane II 34.81 -36.18 C(l) 16.74 -18.05 C(2)
18.99 15.73
BicycIo[3.2.1]octane III 32.16 -34.01 C(1) 15.54 -16.85 C(2) 16.43 -17.74 C(5) 18.51 -19.82 C(6) 15.86 -17.17 C(8)
$H,
(rw
3CH,
44.52
0 (6)
by using
gCH,
,,(8)
gCH,
11.53
33.36
23.82 -5.29 49.81 23.50 3.06 41.46 23.01 2.01 42.51
8.25 1.62 2.39
3.28 -2.04 9.91 -1.73 9.14 -2.04
21.44 -1.27 24.70 -3.59
19.17 -2.32 42.20 21.49 6.05 38.41
11.13 2.93
12.39 12.13 15.02 17.75 11.90
28.04 28.30 25.41 22.66 28.53
-1.98 -6.81 4.55 -1.07 -6.99
25.88 -6.43 24.71 1.62 22.45 5.16 18.97 8.18 24.39 1.42
50.95 42.90 39.36 36.34 43.10
5.97 5.56 -3.91 0.36 11.17 -3.48 2.18 9.35 -0.36 5.19 6.34 1.22 0.31 11.22 -2.83
31.33 36.84 33.72 32.14 36.19
BicycIo[3.3.1lnonaneIV 33.02 -34.33 C(l) 16.51 -17.82 C(2) 18.32 -19.63 C(3) 15.75 -17.06 C(9)
16.43 15.67 17.47 15.14
24.00 24.16 22.96 25.29
4.62 -3.88 -1.53 4.71
22.52 -1.20 21.78 5.97 19.43 7.15 22.61 5.46
45.72 38.55 36.11 39.06
8.36 2.65 4.84 1.92
3.17 -0.42 8.88 0.11 6.69 0.76 9.61 0.20
33.18 33.25 32.61 33.16
Bicyclo[3.2.2lnonaneV 34.13 -35.44 C(l) 16.95 -18.26 C(2) 19.60 -20.91 C(3) 16.97 -18.28 C(6)
15.89 14.16 17.96 15.94
24.54 4.57 26.27 -5.30 22.47 -0.55 24.49 -3.18
22.41 -2.44 23.20 3.51 18.45 8.15 21.08 5.47
46.96 41.01 36.37 39.05
8.18 1.82 5.85 3.31
2.75 -1.07 9.71 -1.61 5.68 1.33 8.22 0.02
34.43 34.97 32.03 33.34
Bicyclo[4.2.1lnonaneVI 31.28 -32.59 C(1) 16.71 -18.02 C(2) 19.20 -20.51 C(3) C(7) 14.21 -15.52 C(9) 14.50 -15.81
10.28 14.48 17.31 10.82 10.86
30.15 25.95 23.12 29.61 29.67
27.61 -8.82 22.82 4.45 19.39 7.09 26.21 0.22 25.73 0.09
53.34 4.21 7.26 -6.50 40.07 1.92 9.61 -0.76 5.17 6.36 0.64 31.43 44.30 -1.20 12.13 4.47 44.43 -0.5'7 12.10 4.62
39.86 34.12 32.72 37.83 37.98
AdmantaneVII C(1) 32.80 -34.11 C(2) 14.52 -15.83
16.73 13.50
24.70 -6.31 26.93 -6.53
-9.77 4.92 -1.49 -8.37 -7.83
23.21 -2.10 46.62 24.43 3.63 40.89
aIn ppm. bRelative to methane, i.e., 6 CH4 = u(CH,) - u(C-relevant),
CAssummarizedin Table3.
6%
= -1.06
0.40 8.60
3.20 30.16 0.10 33.26
7.91 3.62 -1.23 0.31 11.22 -1.47
in ppm.
+ 1.92 6222 (ppm), r2 = 0.64
However, the substantially larger deshielding observed experimentally for the carbon atoms C(2) in bicyclo[2.2.1] heptane, C(2) in bicyclo[3.2.1] octane and C(7) in bicyclo[4.2.l]nonane than for the corresponding methylenic bridgehead carbon atoms, is not exhibited by the calculated 13C chemical shifts. If these three results are excluded from the twenty-five points correlation 6 cu., = -8.42 _P.
+ 2.38 6 zzz(ppm), r2 = 0.80
35.40 35.09 35.40
34.59 34.83
It is often assumed, specifically according to the Pople-Karplus approximation (as reviewed in refs. 34 and 35), that the local paramagnetic term makes the dominant contribution to 13C!screening. Indeed, although the sum of o(MK) and the dia- and paramagnetic contributions to the shielding constant of atom M from AO’s centered on K, i.e., ad(K) + up(K) + o(MK), increases the overall correlation with the experimental chemical shifts trends in this series of rigid compounds by approximately 20%, the discrepancy regarding the chemical shifts of C(2) in I, C(2) in III, and C(7) in VI, emerges in the local paramagnetic contribution. Excluding these points from a correlation of up(M)evaluated relative to methane (u”(CH,) = -51.51 ppm), with the corresponding experimental chemical shifts yields: Sz = 18.17 + 1.50 uPcn,(ppm), r2 = 0.63, whereas no correlation is obtained when all points are included. The relevant five-membered rings of bicycle [ 2.2.11 heptane, bicyclo[3.2.1] octane, and bicyclo[4.2.l]nonane (with pseudorotation @2puckering and the six-membered rings of degrees of 144”, -36”) 125”) respectively), bicyclo[2.2.2] octane (boat: 0 2 90”, Q s 0”); bicyclo[3.3.1] nonane (chair: 8 z 180”, $J 2 120”); bicyclo[3.2.2]nonane (boat: 6 2 90”, 4 z 0”); and adamantane (chair: f3 = 0”, C$= 0'),have been investigated. The rings are indicated in bold lines in Fig. 1, and their puckering coordinates were derived by using the RING program [36], which is based on a general ring puckering theory [ 371. The five-membered rings of I and III, and to a lesser extent of VI, are conformations with unfavourable bond eclipsing between the two t-gaxial hydrogens, as shown by the position of the ring on the pseudorotation itinerary of a general five-membered ring. Nonbonded interactions in these five-membered ring systems (C’ symmetry) are also revealed by examining the nonequivalence of the exo-exo and endo-endo vicinal proton spin-spin coupling constants. This nonequivalence was experimentally demonstrated in norbornanes by Marchand et al. [38], and was considered remarkable since existing theories predicted equality for these cis (eclipsed) coupling constants. With the aid of semiempirical MO calculations Marshall et al. [39] and Barfield et al. [40, 411, and more recently de Leeuw et al. [ 421, have shown that this nonequivalence arises from nonbonded interactions between MO’s located about the bridgehead CH2 group and MO’s located at the C-C ethylene fragment. 3J(H,H) calculations were performed (unpublished results) at the INDO-FPT level of approximation [ 431 (summarized in Table 5) for bicycle [2.2.1] heptane, bicyclo[3.2.1] octane, bicyclo[4.2.1] nonane, and for bicyclo[2.2.2] octane and bicyclo[3.2.2]nonane. The difference between exo-exo and e&o-e&o 3J(H,H) can be extended to other bicyclic systems containing a five-membered ring, but is less pronounced in the comparable II and V six-membered rings with a boat conformation. The nonbonded interactions as described above cause an uneven partitioning of the overlap population between the bridgehead carbon atom and the ethylenic group carbon atom in norbornane, bicyclo[3.2.1] octane and
34 TABLE 5 INDO-FPT
calculations of 3J(H,H) coupling constants (in Hz)
Bicyclo[ 2.2.11 heptane Bicyclo[3.2.l]octane Bicyclo[4.2.1 Jnonane Bicyclo[2.2.2]octane Bicyclo[3.2.2]nonane
‘J[C(P)-H, V[ C(2)-H, 3J[C(7)-H, ‘J[C(2)_H, 3J[C(8)-H,
C(3)-H] C( 3)-H] C(S)-H] C(3kHl C(9)-H]
exo-exo
endo-endo
14.69 15.39 14.34 14.73 16.57
10.41 10.43 10.67 14.76 15.08
bicyclo[4.2.1]nonane, with a larger electron density anticipated about the ethylene bridge carbon atom than at the methylene carbon atom. Atomic charges calculations were performed at the ab initio [44] level using minimal STO-3G basis sets, and the Mulliken populations obtained in this manner for the carbon atoms in the series of rigid molecules I-VII is presented in Table 6. There is almost no indication of a difference in the electron densities between the methylenic bridgehead carbon atom and the ethylenic carbon atom in the five-membered rings of I, III and VI. However, the Mulliken population analysis [ 451 simply assigns all the molecular charge density in a molecule to the individual atoms, i.e., the charge belonging to a specific atom M is that arising entirely from the atomic orbitals of M and half of that arising from the overlap of atomic orbitals on M with those of all other atoms in the molecule. This is a physically unrealistic scheme, and has been repeatedly questioned [46, 471. In a recently developed method [48--511, the wavefunction is squared according to Born’s probabilistic interpretation and then integrated over the required volume, the coordinate origin being set each time at the center of the sphere. This method [CHARGES program: 521 was used with ab initio molecular wavefunctions [44] as a starting point, in order to obtain physically more accurate charges for the carbon atoms in the series of molecules I-VII, as summarized in Table 7. It is important to emphasize that the total charge within spheres of covalent radii centered on the atomic nuclei of the molecule amounts to less than the total number of electrons in the system, and approximately two or three electrons per main atom and one per hydrogen lie outside the spheres. According to the Mulliken population analysis the changes in 4 atomic charges between the bridgehead carbon atoms (C(7) in I and II and C(8) in VI) and the ethylenic carbon atoms (C(2) in I and III, and C(7) in VI) is approximately 0.5-2.5%. The CHARGES method yieldsdifferences (defined as (q(C2) - q(C7))/qC(2)) of about 400%, 100% and 50% for molecules I, III and VI, respectively, with the more negative charge on the ethylenic carbon. For comparison, the atom charges obtained from the diagonal elements of the bond-order matrices of semi-empirical methods are given in Table 8. Since these results are not comparable to the ab initio values, semi-empirical and ab initio methods are not to be used indiscriminately for a charge analysis.
35 TABLE 6 Mulliken orbital populations (in electrons) from STO-3G calculations 1s
2s
2P
1.9922 1.9922 1.9922
1.1816 1.1890 1.1873
2.8540 2.9157 2.9200
-0.0278 -0.0969 -0.0995
1.9921 1.9924
1.1763 1.2204
2.8624 2.8916
-0.0308 -0.1044
1.9921 1.9922 1.9921 1.9921 1.9922
1.1772 1.1883 1.1859 1.1835 1.1876
2.8581 2.9169 2.9142 2.9187 2.9165
-0.0274 -0.0974 -0.0922 -0.0943 -0.0963
1.9921 1.9921 1.9921 1.9921
1.1741 1.1852 1.1825 1.1844
2.8598 2.9155 2.9206 2.9181
-0.0260 -0.0928 -0.0952 -0.0946
G(l) G(2) G(3) G(6)
1.9921 1.9921 1.9921 1.9921
1.1753 1.1860 1.1824 1.1851
2.8578 2.9150 2.9172 2.9185
-0.0252 -0.0931 -0.0917 -0.0957
Bicyclo[ 4.2.11 nonane VI G(l) G(2) G(3) G(7) G(9)
1.9921 1.9922 1.9921 1.9921 1.9922
1.1771 1.1867 1.1838 1.1879 1.1874
2.8584 2.9114 2.9166 2.9170 2.9179
-0.0276 -0.0903 -0.0925 -0.0970 -0.0975
1.9921 1.9922
1.1745 1.1864
2.8629 2.9169
-0.0295 -0.0955
I
Bicyclo[2.2.1]heptane
(71) C(2)
G(7)
Bicyclo[2.2.2]octane G(1) G(2)
II
Bicyclo[3.2.l]octane
II
G(1) G(2) G(5) G(6) G(8) Bicyclo[3.3.1 G(1) G(2) G(3) G(9)
Atomic charge
Jnonane IV
Bicyclo[3.2.2]nonane
V
Adamantane VII G(l) G(2)
Some aspects of this problem were recently examined by Fliszar et al. [ 541, describing STO-3G wavefunctions to be adequate for deducing consistent atomic charges, although by no means unique in that respect. Flisz&r and co-workers also developed a modified Mulliken population analysis [ 55, 561, used with STO-3G wavefunctions, for an uneven partitioning of overlap in heteronuclear situations. However, this method does not differentiate between two -GH2 groups as is investigated in this study. The problem presented in the beginning of the discussion regarding the overall trend of aP(locaI) in the series of rigid molecules I-VII, involves the incorrect prediction of the local paramagnetic contribution to the shielding
36 TABLE 7 Charges within spheres centered on the carbon nuclei of molecules I-VII CHARGES CHARGE Bicyclo[2.2.l]heptane C(l) C(2) C(7)
I
Bicyclo[ 2.2.2loctane C(l) C(2)
II
Bicyclo[3.2.1] C(l) C(2) C(5) C(6) C(8)
calculated with
Modified CHARGE’
1.5601 1.5520 1.5744
0.0026 -0.0055 0.0169
1.5736 1.5564
0.0129 -0.0043
1.5710 1.5571 1.5711 1.5780 1.5677
0.0030 -0.0109 0.0031 0.0100 -0.0003
1.5798 1.5751 1.5798 1.5757
0.0026 -0.0021 0.0026 -0.0015
1.5793 1.5774 1.5919 1.5713
0.0026 0.0007 0.0152 -0.0054
1.5769 1.5767 1.5833 1.5658 1.5710
0.0018 0.0016 0.0082 -0.0093 -0.0041
1.5739
0.0056 -0.0038
octane III
Bicyclo[B.I.l]nonane C(l) C(2) C(3) C(9)
IV
Bicyclo[3.2.2]nonane C(l) C(2) C(3) C(6)
V
Bicyclo[4.2.1]nonane C(l) C(2) C(3) C(7) C(9)
VI
Adamantane VII C(l) C(2)
1.5645
aIn order to facilitate comparison of these charges with the usual definition of an atomic charge, the average value of the missing electrons was added to each charge.
of the ethylenic carbon atoms in the molecules I, III and explained on the basis of the electronic structure of these integrals of the type WY2, in the one-center paramagnetic the 13C shielding constant are related to the Slater exponent to c3), which is modified by the formula [57] {M = (z* - 0.35(&M
VI, and can be molecules. The contribution to c (proportional
- &))/n*,
where Z* is the effective nuclear charge; II* is the effective quantum number;
37 TABLE 8 Semi-empirical atomic charges calculations (in electrons) INDOa Bicyclo[2.2.l]heptane C(1) C(2) C(7)
MNDOCb
I
Bicyclo[2.2.2]octane C(1) C(2)
II
BicycIo[ 3.2.lloctane C(1) C(2) C(5) C(6) C(8)
III
Bicyclo[3.3.l]nonane C(l) C(2) C(3) C(9)
IV
Bicyclo[3.2.2]nonane C(1) C(2) C(3) C(6)
V
Bicyclo[4.2.1] C(1) C(2) C(3) C(7) C(9)
MNDOb
0.0370 0.0198 0.0106
-0.0676 -0.0495 -0.0106
-0.0494
0.0362 0.0201
-0.0534 -0.0040
-0.0339 0.0028
0.0361 0.0183 0.0214 0.0266 0.0125
-0.0578 -0.0078 0.0050 -0.0113 -0.0030
-0.0380 -0.0009 0.0122 0.0024 -0.0035
0.0366 0.0211 0.0236 0.0152
-0.0477 0.0039 -0.0103 0.0057
-0.0264 0.0109 0.0026 0.0054
0.0368 0.0180 0.0265 0.0188
-0.0448 0.0054 -0.0080 0.0000
-0.0236 0.0133 0.0056 0.0069
0.0351 0.0209 0.0252 0.0166 0.0116
-0.0520 0.0085 -0.0064 -0.0064 0.0028
-0.0315 0.0163 0.0058 0.0001 0.0028
0.0372 0.0143
-0.0557 0.0090
-0.0342 0.0101
-0.0022 -0.0109
nonane VI
Adamantane VII C(1) C(2)
aCalculated by the INDO finite perturbation theory of chemical shifts as described in the introduction [ 211. bAs described in ref. 53.
P sgkn
is the electronic density, and 2, that
oP(modified) = ~~(1.00 + 0.32308q
the core charge of atom M. It can be
+ 0.03479q2
+ 0.00125q3),
where q is the atomic charge in electrons. The INDO calculated electron densities are not suitable for an electronic structure description of the series
38
of rigid hydrocarbons, and their inclusion in the modified evaluation of op(local) does not increase the total overall agreement with the experimental chemical shifts. On the other hand, an inclusion of the Mulliken populations in the Slater exponents modification for the one-center paramagnetic contribution to the u shielding constants yields an overall better relationship: 6 2 = 0.66 + 2.05 &zg;(ppm), r2 = 0.68. The Mulliken population analysis does not account for the higher electron density at C(2) than at C(7), at C(2) than at C(8), and at C(7) than at C(9) carbon atoms in bicyclo[2.2.1] heptane, bicyclo[3.2.1] octane, and bicyclo[4.2.1] nonane, respectively, as has been proved by the relative trends of the sphere charges for these particular carbon atoms. To evaluate the effective charge on C(2) in I and III and C(7) in VI, ab initio electron densities at these atoms were multiplied by a CHARGES factor, defined as the change in electron density between the ethylenic and bridgehead carbon atoms normalized to the absolute average change of charge for the main atoms in the molecule. The factors from CHARGES values presented in Table 7 are 2.6880 for C(2) in I, 1.9273 for C(2) in III, and 1.0400 for C(7) in VI. The resulting changes in the calculated local paramagnetic contributions to the shielding constants of C(2) in I (-58.84 ppm) and C(2) in III (-61.55 ppm) do, indeed, mainly account for the discrepancy in the total correlation with the experimental chemical shifts. The modified correlation is: SE2 = 3.21 + 2.34 &zz;(ppm), r2 = 0.77, as shown in Fig. 2. In the more complex molecule of bicyclo[4.2.l]nonane, other interactions might be present since the discrepancy between the calculated and experimental 13C chemical shift value of C(7) is not yet fully explained. This and other deviations between calculated and experimental 13C chemical shifts of carbon atoms in the series of rigid molecules are further investigated.
44
Fig. 2. Relationship between experimental and calculated chemical shifts in the series of rigid bicyclo[m.n.o. ] alkanes (m = 2, 3, 4; n = 2, 3; o = 1, 2) and adamantane (relative to methane).
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