Nature of transmission of polar substituent effects in γ -disposed bicyclo[2.2.1]heptane (norbornane) and adamantane ring systems as monitored by 19 F NMR: A DFT-GIAO and – NBO Analysis

An extensive series of mixtures of exo - and endo -6-substituted(X)- exo -2-fluorobicyclo[2.2.1] - heptanes ( 4 and 5 , respectively) were synthesized and characterized by 13 C NMR and their 19 F chemical shifts measured. Additionally, the latter parameters for a more limited series of 4 eq - and 4 ax -substituted (X) 2 eq -fluoroadamantanes ( 9 and 10 , respectively) were also obtained. The corollary from correlations of the 19 F substituent chemical shifts(SCS) of 4 and 5 versus the corresponding results for the known 4-substituted(X)bicyclo[2.2.1]hept-1-yl fluorides( 3 ) is that electronegativity effects ( σ χ effect) underly the SCS of 4 and 5 . Differences between the SCS of 4 and 5 as well as 9 and 10 indicate that there is a stereoelectronic component to the polar effect significantly determining the 19 F SCS of 4 and 9 . 19 F NMR shieldings of 3 , 4 , 5 , 3-substituted(X) adamant-1-yl fluorides ( 8 ), 9 and 10 for a common set of substituents (X = H , NO 2 , CN, NC, CF 3 , COOH, F, Cl, HO, NH 2 , CH 3 , Si(CH 3 ) 3 and Li) were calculated using the DFT-GIAO theoretical model. The level of theory, B3LYP/6-31+G*, was chosen based on trial calculations which gave good agreement with experimental values where known. By means of NBO analysis various molecular parameters were obtained from the optimized geometries. Linear regression analysis was employed to explore the relationship between the calculated 19 F SCS and polar field and group electronegativity substituent constants( σ F and σ χ , respectively) and also the NBO derived molecular parameters( fluorine natural charges(Q n ), electron occupancies on fluorine of lone pairs(n F ), and occupation number of the C-F antibonding orbital( σ CF *)). The key determining parameters appear to be n F and σ CF *(occup).


Introduction
Over the years we have reported systematic studies of polar substituent effects in several remotely substituted polycyclic alkanes utilizing 19 F chemical shifts as sensitive electronic probes. 1 The perturbation of these shifts resides in the dominant paramagnetic term(σ p ) to the shielding constant 2 and is generally expressed in a simplified form as shown in the equation for an atom A [where r = mean orbital radius term(related to effective nuclear charge), ∆E = mean excitation energy and Q AB = bond-order electron density term].
For a series of structurally similar compounds, it is generally assumed that ∆E remains constant and, therefore the charge dependence of the 19 F chemical shifts resides either in the <r - 3 > np or Σ Q AB terms, or both.Consequently, approximations are unavoidable in order to analyse 19 F SCS in terms that have proved useful in the case of chemical reactivity.Nevertheless, for remotely substituted aryl and vinyl fluorides, 19 F SCS have been successfully correlated against field-inductive (σ F ) and resonance parameters (σ R ). 3 Moreover, ab initio calculations of charge distributions in metaand parasubstituted fluorobenzenes suggest that the shifts reflect primarily changes in π-electron density. 4Thus, the latter parameter apparently dominates the decisive paramagnetic contribution to the shifts.
The relationship between the 19 F SCS of stereochemically well-defined polycyclic alkyl fluorides 1 and polar substituent parameters have been explored and, in stark contrast to the results from chemical reactivity probes (log 10 K X /K 0 or log 10 k X /k 0 ; energy monitors), which generally can be satisfactorily described in terms of an electrostatic field model (σ F effect), 5 the SCS parameters (charge density monitors) appear to respond sensitively to electronegativity influences (σ χ effect).Consequently, these studies provide a different perspective to reactivity investigations on the nature of transmission of polar substituent effects in saturated systems.Recently, 6 we presented computational studies (DFT-GIAO calculations) coupled with natural bond orbital (NBO) analyses of 4-substituted (X)bicyclo[2.2.2]oct-1-yl fluorides(1) and 3substituted(X)bicyclo[1.1.1]pent-1-ylfluorides(2) which confirmed deductions drawn from model system studies, 1k namely, that the 19 F chemical shifts of alkyl fluorides respond sensitively to the extent of electron delocalization into the antibonding MO of the C-F bond (σ CF *).
Consequently, shift trends are largely controlled by hyperconjugative (σ CF *-σ C-C(X) ) or extended hyperconjugative (σ CF *-σ C-C -σ C-X (or σ C-X *)) orbital interactions which, in turn, are governed by the σ-inductive effect of the substituent (σ χ effect).Furthermore, a decrease in the electron population of σ CF * by σ-electron-withdrawing substituents lead to negative 19 F SCS (upfield shifts).The converse holds for σ-electron-donor groups.Most importantly, the aforementioned computational study also suggested that the occupation number of the p-type fluorine lone pair (n F ) may also be pertinent.This is significant since in remotely substituted aryl fluorides where the 19 F SCS are known to be governed by the perturbation of the π -electrons on fluorine, 4 the shift trends are diametrically opposite to those encountered for the influence of substituents on the occupation number of σ CF *, namely, net electron-withdrawal leads to positive SCS and vice-versa for net electron-donation.Thus, the conundrum of the 19 F SCS trends previously noted for 4-substituted(X)-bicyclo[2.2.1]hept-1-yl fluorides (3), 1d namely, opposite signs to those for the corresponding derivatives of 1, may be a special case where perturbation of the π-electrons of fluorine of an alkyl fluoride is the dominant influence.
The major impetus of this study was to attempt to shed further light on the origin and nature of the 1,3 or γ-interactions in the norbornyl system underlying the 19 F SCS of 3. Consequently, we extended our studies in this system to two other γ-disposed orientations, namely, exoand endo-6-substituted(X)-exo-2-fluorobicyclo[2.2.1]heptanes (4 and 5, respectively) covering an extensive range of substituent electronic effects.These two systems are of particular interest since although the number of intervening bonds between F and X are the same, their arrangements are quite different; W(4)-versus a sickle(5)arrangement. Hence, any stereoelectronic component to the polar effect underlying the 19 F SCS in γ-dispositions should be exposed.As we shall see later, incidental to the synthesis and measurements of the 19 F SCS of 4 and 5 we also obtained the corresponding shift data for exoand endo-5-substituted(X)-exo-2-fluorobicyclo[2.2.1]heptanes (6 and 7, respectively).We were hopeful that application of DFT-GIAO calculations coupled with NBO analyses to the γdisposed BCH systems (3, 4, and 5) as well as 3-substituted(X)adamant-1-yl fluorides(8) 1e and two other similarly disposed adamantane ring systems, 4 eq -and 4 ax -substituted (X) 2 eqfluoroadamantanes (9 and 10, respectively), might provide some insight into the aforementioned problem.As stated previously 6 , the basic philosophy behind this approach is that if there is good agreement between the theoretical and experimental relative shielding effects, then confidence might be placed in an NBO analysis to provide molecular parameters which reveal the electronic interactions perturbing the local environment of the fluorine nucleus.With this in mind, in order to validate the calculated 19 F SCS of 9 and 10 we also report the 19 F SCS of a limited number of these larger systems (X=F, Cl, Br, I, OH, CH 3 , and Sn(CH 3 ) 3 ).All these compounds were available from previous studies 7 except for the methyl derivatives.A mixture of these (9/10, X=CH 3 ) was obtained specifically for this investigation.

Experimental Section
Synthesis of Compounds.Our synthetic strategy was similar to that previously employed for the preparation of most of the compounds of systems 1-3, 8 1d,e,f,8 as well (E)/(Z)-5substituted(X)adamant-2-yl fluorides 1g,h and (E)/(Z)-4-substituted(X) adamant-1-yl fluorides.1h Consequently, we set out to prepare the fluoro-carboxylic acids of 4 and 5(X=COOH) for appropriate functionalisation.However, after considerable initial exploratory work it quickly became apparent that the preparation of sufficient amounts of the isomeric acids in a pure form would be a protracted and difficult exercise.Hence, we decided to solve the problem using various mixtures of the isomeric fluoro -acids which, by established methodology, provided most of the desired compounds as isomeric mixtures covering a wide range of substituent effects(X = H, NO 2 , CN, COOH, COOCH 3 , CONH 2 , Cl, Br, I, NH 2 , OH, OCH 3 , OCOCH 3 , CH 3 , CH 2 OH, and Sn(CH 3 ) 3 ).The remaining mixtures(X = F, OH, OCH 3 , and OCOCH 3 ) were obtained as indicated in the supporting information.
All the fluoride mixtures were unambiguously characterized by 13 C and 19 F NMR in conjunction with GC-MS and VPC analyses.The 13 C NMR spectral assignments followed unequivocally from the characteristic 13 C -19 F coupling constants in the norbornane skeletal framework 9 as well as chemical shift additivity and APT technology.Relevant details of the syntheses together with the 13 C NMR data are available in the supporting information.
Most of the limited number of derivatives of 9 and 10 were available from other studies (X = F, Cl, Br, I, OH and Sn(CH 3 ) 3 ) 7 .The methyl derivatives of these adamantane systems(X = CH 3 )were obtained as a mixture(ca.9:10 = 58:42) by catalytic hydrogenation of 4 eq -fluoro-2methyleneadamantane 7b (30mg, 0.2mmol and 10% Pd/C(200mg) in absolute ethanol(10ml) was agitated with hydrogen(30 psi) for 8 hrs)which was characterized readily by 13 C NMR as described previously for the other aforementioned derivatives of 9 and 10 7 : 13  Computational Methods.Full geometry optimizations of 3-10 were carried out at the B3LYP/6-31+G* level of theory utilizing the GAUSSIAN 98 program package. 10The nuclear magnetic shielding constant calculations using GIAO and the NBO analyses were performed at the same level of theory.Initially, because of our previous success with calculations at a higher level (B3LYP/6-311+G (2d,p), we anticipated utilizing this level of theory in this investigation.However, trial calculations on 3, 4, and 5 (X=H, NO 2 , and CN) at this level as well as at the lower level of theory(B3LYP/6-31+G*) revealed that the latter provided calculated 19 F SCS(see Table 1) which are in as good as, or better, accord with the observed values(cyclohexane as solvent: 3 1d , 8.63(NO 2 ) and 3.10(CN); 4, -8.27(NO 2 ) and -2.95(CN); 5, -11.28(NO 2 ) and -8.68(CN) than the latter.Consequently, we adopted the more economical level (B3LYP/6-31+G*) for all calculations reported in this study.The NBO approach is described in detail by Weinhold and co-workers 11 and no detailed account is necessary here.A brief account was given in our earlier studies. 6

Results and Discussion
Empirical Analysis.The 19 F SCS (ppm) of the norbornyl fluorides 4 and 5 are listed in Table 2 together with the corresponding data for the previously published bridgehead fluorides (3) 1d .The latter are listed in order to facilitate comparisons between these γ -disposed systems.For the sake of completion the results for the δ-disposed systems (6 and 7) are also listed, however, we do not wish to focus much attention on the latter data except to point out that they span a very narrow range.This was to be expected given that the alignment of the intervening bonds are well removed from the preferred stereoelectronic requirement (antiperiplanarity of the participating orbitals) 12 for through-three-bond transmission of the polar effect (extended hyperconjugation; σ C-X -σ C-C -σ CF *) 1k .Note that this is particularly the case for 7.
Scrutiny of the data for the γ-disposed systems reveals that the SCS of systems 4 and 5 are diametrically opposite in sign to those of 3.However, despite this contrast correlations of the SCS of 4 and 5 versus the corresponding results for 3 expose a rough linear trend (r = 0.87 and 0.92, respectively) between the data.Thus, based on the previous detailed regression analyses of the 19 F SCS of 3 1d , an obvious corollary is that a σ χ effect(s) is the dominant factor underlying the SCS of 4 and 5 as well.Most importantly, although the latter two systems have the same number of intervening bonds between the substituent and probe, there are significant differences in magnitude for most of the shifts.Note, that a similar pattern is revealed on comparison of the SCS for the similarly orientated adamantane systems (9 and 10; see Table 3).Given the W-versus sickle-arrangement of the bonds between F and X in 4/9 and 5/10, respectively, the results suggests that there is a stereoelectronic component to the polar effect underlying the 19 F SCS of the former systems (orbital interactions optimally aligned) but not the latter.Because of the similar orientation between the fluorine probe and the substituent in 3 and 4, the possible importance of extended hyperconjugation 13 (coupling of the n-orbital of F and X with the σ*-orbital of the C-X and C-F bond via the C 3 -C 4 σ-bond; n F -σ C-C -σ C-X * and n X -σ C-C -σ C-F *, respectively) is implicated in the former system as well.
A result strongly signifying the operation of extended hyperconjugation (n F -σ C-C -σ C-X *) in 9 is the sign of the SCS for I.Note that it is positive (Table 3) implying that a typical electronegative substituent is a σ-electron-donor!This phenomenon was previously noted in another γ-disposed adamantane system (8; see Table 3) several years ago 1e .Confirmation of the origin of this apparent "anomaly" emerges from the relative ∆ 1 J C-F trends set out in Table 4 for the halogen series in 3, 4, 5, 9 and 10.Given that 1 J C-F couplings are sensitive to changes in the π-bond order of the C-F bond 14 , the considerably larger ∆ 1 J C-F values for the halogens in 3/4, 8 and 9 compared to those in 5 and 10, respectively, strongly signifies the operation of extended hyperconjugation (n F -σ C-C -σ C-X *) increasing the C-F π-bond order in the neutral ground state.Interestingly, Duddeck et al 15 has shown that the ∆ 1 J C-F values of 9 (X=F, Cl, Br, OH and CH3) but not the corresponding derivatives of 10 reflect intramolecular interactions n,σ* of substituents in a W-arrangement.This effect on the 19 F chemical shifts will be in the opposite direction to that of hyperconjugation involving σ CF * and the C3-C4(X) bonding orbital (σ CF *-σ C- C(X) ).Hence, unlike the SCS for 5 and 10, which are essentially controlled by the latter interaction, the SCS for 4, 8 and 9 are composite quantities determined by two different effects which are diametrically opposed; modulation of the donor ability of the C-C(X) bond by the σinductive influence(σ χ effect) of X(F>Cl>Br>I) and perturbation of the F π-electron population by extended hyperconjugation governed by the energy levels of σ C-X * (I>Br>Cl>F) 16 .A third factor to consider underlying the 19 F SCS of π-electron donor substituents in 4, 8, and 9 is a n Xσ C-C -σ C-F * interaction which acts to promote downfield shifts (X=NH2>HO>F>Cl>Br>I). 17 The positive SCS for I in 8 and 9 is therefore a case where the n F -σ C-C -σ C-X * interaction dominates.If this argument is extended to 3 then all the 19 F SCS of this system reflect the dominance of the n Fσ C-C -σ C-X * and n X -σ C-C -σ C-F * interactions over the competing hyperconjugation (σ CF *-σ C-C(X) ) and extended hyperconjugation (σ C-X -σ C-C -σ CF *).The latter being less than optimal as a result of the intervening bond alignments.
Theoretical analysis.The DFT-GIAO calculated isotropic 19 F SCS for 3 -10 are given in Table 5.A common basic set of twelve substituents, which were previously employed for the study of 1 and 2, were adopted so as to cover a wide range of electronic effects.An examination of the calculated shifts (Table 5) for the norbornyl fluorides (3 -7) reveals that there is good agreement between these and the available observed 19 F SCS (Table 2).This is exemplified by the very good to excellent linear correlations between them: r = 0.960, 0.994, 0.994, 0.998, and 0.947 for 3 -7, respectively.Although there are significantly greater deviations between the calculated and observed 19 F SCS for the larger adamantane systems (8 -10, Table 3), the parallel trends are unmistakeable.For 8, the only one of these larger systems for which there are a sufficient number of observed SCS available (n = 8) to effect a sensible regression, a strong linear trend is formally defined(r = 0.904).Thus, the level of theory employed in this study appears to define adequately the relative shielding trends (SCS).The calculated 19 F SCS of 3, 4, 5, 8, 9, and 10 (Table 5) were correlated against polar substituent parameters ( σ F and σ χ ) by means of regression analysis.A summary of the statistical analysis is set out in Table 6.It can be seen that except for the adamantane system 8 the electronegativity constant (σ χ ) is adequate in describing the 19 F SCS of the norbornyl fluorides (3 -5) as well as 9 and 10.The dual dependency ( σ F and σ χ ) of the observed shifts for 8 was previously reported and independently verified by a noncorrelative procedure 1e .The significant polar field contribution (ρ F σ F ) has been ascribed to the marked longitudinal polarizability of the C-F bond in adamant-1-yl fluorides 1e,h .It should be emphasized that the incomplete disproportionality (r = 0.831) between (σ F and σ χ ) for the substituent set may be responsible for the lack of statistical definition of σ F in the other systems.Nevertheless, it is clear that the correlations for 3-5 and 9-10 indicate that electrostatic effects play only a minor role at best.The relative magnitude of the electronegativity susceptibility parameters (ρ χ ) indicate that the σ χ effect is clearly more pronounced in the norbornyl (4 and 5) than the corresponding adamantane systems (9 and 10).
Evidently, the greater electron donor capacity of the strained C 1 -C 6 bond in norborn-2-yl fluoride is more responsive to σ-inductive effects than the unstrained C 3 -C 4 bond in adamant-2-yl fluoride.Significantly, the ρ χ values for 4 and 9 are less than those for 5 and 10, respectively.This quantitates our empirical deductions above that there appears to be an opposing influence (n F -σ C-C -σ C-X *) to hyperconjugation involving σ CF *(σ CF *-σ C-C(X) ) underlying the 19 F SCS of 4 and 9, which is not operative in the respective γ-disposed systems (5 and 10).Most importantly, it can be seen (Table 6) that the ρ χ value for 3 , as expected, has a sign opposite to the other γdisposed systems which we have attributed (see above) to the possible dominance of the n F -σ C-Cσ C-X * interaction.By means of regression analysis we explored the relationship between the calculated 19 F SCS of the γ-disposed systems (3-5 and 8-10) and the most pertinent NBO-derived molecular parameters (fluorine natural charge (Q n ), occupation numbers of the fluorine lone pairs (n F ), and occupancy of the C-F antibonding orbital (σ C-F *(occup)) (see Table 12 in the Supporting Information).The occupancy of the C-F bonding orbital (σ C-F (occup)) is essentially invariant to changes of the substituent, hence, it was not included in the analysis.A summary of the regression parameters are presented in Table 7.Before interpreting these results it should be borne in mind that there is a degree of interdependence of the molecular parameters that makes outcomes somewhat inconclusive.Nevertheless, it can be seen that most of the fits are extremely poor.This should not be too surprising since none of these parameters corresponds exclusively to a particular transmission mechanism.Exceptions are the fits for the 19 F SCS of 4, 5, 8, 9 and 10 versus σ CF *(occup) which clearly indicate linear trends.Multiple regression analysis of these shifts against σ CF *(occup) and n F (or Q n ) did not improve the precision of fits(smaller F values).Most noticeably, the corresponding correlation for 3(SCS versus σ CF *(occup)) indicates no sensible relationship at all.This was somewhat anticipated from the discussion above.The best of these very poor correlations is the regression of the 19 F SCS versus n F .However, if the strongest π-electron donors (F, HO, NH 2 and CH 3 ) are excluded from the data set for the correlation between the 19 F SCS of 3 and n F , the precision of fit dramatically improves(r 2 = 0.925 and F = 85.986).Clearly, this good linear relationship offers strong support for the idea expressed above that the 19 F SCS for most of the substituents in 3 are largely manifestations of the coupling of n F and σ C-X * via the intervening σ C-C (n F -σ C-C -σ C-X * ), perturbation of n F being dominant rather than the occupancy of σ CF *.The latter parameter is clearly important for πelectron donors (F, HO, NH 2 and CH 3 ) in 3 which can engage in a dominant n X -σ C-C -σ C-F * interaction.Strong support for this latter interaction in the γ-disposed systems with a W arrangement of the intervening bonds between F and X, comes from the calculated`1 9 F SCS of O - and NH -in 3, 4, 8 and 9 compared to those of the appropriate neutral congeners, OH or NH 2 .These calculations are listed in Table 8 together with the values for the latter substituents (see Table 5) in order to facilitate comparison.Note the pronounced downfield shifts induced by these powerful π-electron donors compared to the neutral congeners.This signifies the expected response to enhanced electron delocalization into the antibonding MO of the C-F bond (σ CF *) due to the increased n X -σ C-C -σ C-F * interaction (see σ CF *(occup) values in Table 12 in the Supporting information).
Finally, it is of interest to note that the electronic effect of the carbonyl group as monitored by the fluorine probe indicates that this group is more electron-withdrawing in the 2,6disposition (11,19 F SCS(ppm)= -14.45(cyclo-C 6 H 12 ), -15.12(CDCl 3 ); calculated 19 F SCS (ppm)= -12.34) compared to the 2,5-disposition (12,19 F SCS(ppm)= -2.29(cyclo-C 6 H 12 ), -3.14(CDCl 3 );   This result reflects the dominant influence of hyperconjugation involving σ CF * and the C1-C2(C=O) bonding orbital (σ CF *-σ C-C(C=O) ) over the possible n O -σ C-C -σ C-F * resonance interaction.By contrast, in substituted 2-norbornyl cations the carbonyl group appears to have an electron donor influence from the 6-position compared to the 5-position 13 .The result highlights that electron-donating resonance interactions are more pronounced in electron deficient species such as carbocations than in the neutral ground state as a result of high electron demand.

Conclusions
The results of this model system study coupled with a DFT-GIAO and DFT-NBO analysis reinforce the view that the dominant factor governing the electronic perturbation of the 19 F chemical shifts of alkyl fluorides is the electron population of the C-F antibonding orbital [σ CF *(occup)].However, in an exceptional case, namely, 4-substituted(X)bicyclo[2.2.1]hept-1yl fluorides(3), the electronically induced shift perturbations appear to reflect primarily changes in π-electron density(n F ).This insight provides an explanation for the diametrically opposite signs of the 19 F SCS for the latter system compared to those for all other model alkyl fluorides.

anF
= average occupation numbers of the fluorine lone pairs.b Q n = fluorine natural charge.c σ CF * = occupancy of the C-F antibonding orbital.d Multiplecorrelation coefficient squared.e Ftest of variance for overall correlation.
a Defined as the difference (in ppm) between the 19 F chemical shift of the substituted compound and that of the parent compound(X=H).A negative sign denotes shielding (upfield shift).b f Theoretical chemical shift : -189.08ppmrelative to CFCl 3 .g Isotropic shielding constant of CFCl 3 : 156.69 ppm at the GIAO-B3LYP/6-311+G (2d,p) level.

Table 2 .
19F substituent chemical shifts (SCS) a-c of norbornyl fluorides( 3-7 ) a See footnote a to Table 1.b Cyclohexane as solvent.Results in parenthesis are forCDCl 3 .c Accurate to ± 0.05 ppm.d Taken from Ref. 1d. e X=H [relative to internal f Not measured.g Compound not available.
a See footnote a to Table 1.b c Theoretical chemical shift: -177