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Electronic Substituent Effects in Bicyclo[1.1.1]pentane and [n]Staffane Derivatives: A Quantum Chemical Study Based on Structural Variation Anna Rita Campanelli Department of Chemistry, UniVersity of Rome “La Sapienza”, I-00185 Rome, Italy
Aldo Domenicano,* Giovanni Piacente, and Fabio Ramondo Department of Chemistry, Chemical Engineering and Materials, UniVersity of L’Aquila, I-67100 L’Aquila, Italy ReceiVed: October 5, 2009; ReVised Manuscript ReceiVed: March 15, 2010
The transmission of electronic substituent effects through one or more bicyclo[1.1.1]pentane units has been investigated by ascertaining how a variable substituent at a bridgehead position perturbs the geometry of a phenyl group at the opposite end of the molecule. We have analyzed the molecular structures of many bicyclo[1.1.1]pentane and [n]staffane derivatives of general formula Ph-[C(CH2)3C]n-X (n ) 1-5), as obtained from molecular orbital calculations at the HF/6-31G* and B3LYP/6-311++G** levels of theory. When n ) 1, the structural variation of the benzene ring is controlled primarily by the long-range polar effect of X, with significant contributions from electronegativity and π-transfer effects. The capability of the bicyclo[1.1.1]pentane framework to transmit these short-range effects originates from the rather high electron density inside the cage and the hyperconjugative interactions occurring between substituent and framework. A set of at least two bicyclo[1.1.1]pentane units appears to be necessary to remove most of the electronegativity and π-transfer effects. In higher [n]staffanes (n g 3), the very small variation of the benzene ring geometry is controlled entirely by the long-range polar effect of X. With charged groups and for n g 2, the potential energy of the ring deformation decreases linearly with n-3. In Ph-C(CH2)3C-X molecules, the relatively large deformation of the bicyclo[1.1.1]pentane cage is determined primarily by the electronegativity of X, similar to the electronegativity distortion of the benzene ring in Ph-X molecules. Transfer of π electrons from substituent to cage or vice versa also plays a role in determining the cage deformation. 1. Introduction Transmission of electronic substituent effects through cage polycyclic alkanes has received considerable attention during the last few decades.1–3 These rigid saturated frameworks are well suited to study the propagation of long-range polar effects because they are sterically well-defined and should not allow resonance interactions between the variable substituent and the probe measuring its effect (usually a carboxylic group undergoing deprotonation). We have recently investigated the transmission of polar substituent effects through the bicyclo[2.2.2]octane cage by means of a novel approach based on the geometrical changes that a variable substituent X at a bridgehead position causes on a phenyl group at the opposite bridgehead position.4 By using symmetry distortion coordinates from the B3LYP/6-311++G** geometries of 21 Ph-C(CH2-CH2)3C-X molecules (6 in Chart 1), we have shown that a linear combination of the internal angles of the benzene ring lettered in Figure 1, namely
SF ) 0.697∆R - 0.875∆β - 0.165∆γ + 0.342∆δ + 4.154° (1) (where ∆R ) R - 120°, etc.) is a reliable measure of the longrange polar effect of X relative to H. Progressive replacement of the three -CH2-CH2- bridges of 6 by pairs of hydrogen * Corresponding author. Fax: 39-0862-433753. E-mail: aldo.domenicano@ univaq.it.
atoms, leading eventually to a rigid assembly of two separate molecules, Ph-CH3 and CH3-X, has little effect on the SF parameter. This provides clear evidence that long-range polar effects in bicyclo[2.2.2]octane derivatives are actually field effects transmitted through space. We have also shown4 that the geometrical variation of the bicyclo[2.2.2]octane cage under substituent impact is controlled primarily by the electronegativity of X because it correlates well with the deformation of the benzene ring in Ph-X molecules caused by changes in the electronegativity of X.5,6 We have now investigated by quantum chemical calculations the transmission of polar effects through another polycyclic alkane, bicyclo[1.1.1]pentane, using again a phenyl group as a probe. As with bicyclo[2.2.2]octane derivatives, substituent and probe are located at opposite bridgehead positions (1a or 1b in Chart 1). Two or more bicyclo[1.1.1]pentane units may be linked together by C-C bonds; the resulting rod-shaped molecular systems, termed [n]staffanes7 (2-5 in Chart 1), provide regularly increasing spacings between substituent and probe. They are thus ideally suited to investigate the dependence of polar effects upon distance, undisturbed by angular orientation factors. They are also of special interest as rigid axial spacers in supramolecular assemblies.2f We have applied our approach to investigate the propagation of polar effects in [n]staffanes up to n ) 5. In addition, we report how the geometry of the bicyclo[1.1.1]pentane cage in Ph-C(CH2)3C-X molecules is affected by the presence of the variable substituent X.
10.1021/jp909530u 2010 American Chemical Society Published on Web 03/31/2010
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CHART 1
2. Selection of Substituents
3. Calculations
With bicyclo[1.1.1]pentane and [2]staffane derivatives, Ph-C(CH2)3C-X (1) and Ph-[C(CH2)3C]2-X (2), respectively, adequate coverage of electronic substituent effects was ensured by using 26 functional groups. These included many organic and inorganic moieties, a few charged groups, and H as a reference. They were chosen so as to allow validation of our results against the available experimental3j and computed3f gasphase acidities of HOOC-C(CH2)3C-X molecules and comparison of geometrical variation with that occurring in bicyclo[2.2.2]octane derivatives.4,8 With higher [n]staffanes (n g 3), the increasingly long distance between substituent and probe makes the benzene ring geometry less and less sensitive to the presence of the remote substituent X. In the case of [3]staffanes, we have thus reduced the number of substituents to 12 by excluding many dipolar groups while retaining all charged ones. In the case of [4]- and [5]staffanes, where the variation of the ipso angle of the benzene ring is merely a few tenths of a degree, we have further reduced the number of substituents to eight.
Molecular geometries of Ph-[C(CH2)3C]n-X species with n ) 1-3 have been determined by molecular orbital (MO) calculations at the HF/6-31G* and B3LYP/6-311++G** levels of theory with gradient optimization9 using the Gaussian 03 package of programs.10 Molecular species with n g 4 were only studied at the HF/6-31G* level. We have imposed Cs symmetry to the species investigated,11 with the benzene ring perpendicular to the symmetry plane (orthogonal conformation), as in our previous work on bicyclo[2.2.2]octane derivatives.4 Imposing a fixed conformation to the phenyl group keeps any steric effect at the ortho hydrogens essentially constant within a series of molecules, irrespective of the nature of the variable substituent X. Control of steric effect is necessary because it affects the geometryofthebenzenering.4,5a,6 Inthecaseofbicyclo[1.1.1]pentane derivatives, besides the orthogonal conformation 1a, we have studied the coplanar conformation 1b, with the benzene ring lying in the symmetry plane of the molecule. This was done to ascertain whether the sensitivity of the benzene ring geometry to the electronic effects of X is different in the two conformations. In all Ph-C(CH2)3C-X molecules considered in the present study, conformations 1a and 1b correspond to a firstorder saddle point and a minimum, respectively, in the potential energy hypersurface at the HF/6-31G* level of theory. The energy differences between the two conformations are small, not exceeding 1.2 kJ mol-1 at both levels of theory. All MO calculations were run at the CASPUR Supercomputing Center, Rome.
Figure 1. Lettering of the C-C bonds and C-C-C angles in a monosubstituted benzene ring of C2V symmetry.
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4. Internal and Symmetry Coordinates of the Benzene Ring In a monosubstituted benzene ring of C2V symmetry, the seven internal coordinates R, β, γ, δ, a, b, and c (Figure 1) are not independent. They are linked by two equations of geometrical constraints, expressing the conditions of planarity and ring closure
R + 2β + 2γ + δ ) 4π
(2)
a sin(R/2) + b sin(β + R/2 - π) ) c sin(δ/2)
(3)
In a statistical analysis of the internal coordinates, the geometrical constraints introduce correlation. Therefore, part of the correlation of β, γ, δ, and a with R observed in the present study is due to geometrical constraints. To form an orthogonal basis for describing the geometry of monosubstituted benzene rings, we have to make use of symmetry coordinates. If the distorted ring retains C2V symmetry, which is practically the case of molecular systems 1a and 2-5,12 five symmetry coordinates are required.13 Of these, only three involve the internal ring angles
D4 ) 3-1/2(R - β - γ + δ)
(4)
D5 ) 3-1/2(R + β - γ - δ)
(5)
D6 ) 6-1/2(R - 2β + 2γ - δ)
(6)
(The other two will not be considered here because bond distance variation is much less pronounced than angular variation). In molecular systems 1-5, the values of D5 span a much smaller range than D4 and D6.14 Therefore, the angular variation of the benzene ring can be represented in the D6D4 plane, as in the case of Ph-X5a,d and Ph-C(CH2-CH2)3C-X molecules.4 5. Results and Discussion 5.1. Analysis of the Benzene Ring Deformation. Selected internal coordinates of the benzene ring in molecular systems 1-5 are provided as Supporting Information to this article. They are reported in Tables S1-S5 and S6-S8, from HF/6-31G* and B3LYP/6-311++G** calculations, respectively. (All tables containing an S in their identification label are deposited in the Supporting Information; see the relevant paragraph at the end of the article.) Correlations between internal coordinates are presented and discussed in the Supporting Information. 5.1.1. Symmetry Coordinates. On the basis of our previous results on Ph-X5a,d and Ph-C(CH2-CH2)3C-X molecules,4 we expect important chemical information to be contained in the D4 versus D6 scattergram. In bicyclo[1.1.1]pentane derivatives, these symmetry coordinates are correlated (Figure 2a: the correlation coefficient is R ) 0.9768), although not so well as in bicyclo[2.2.2]octane derivatives (Figure 4 of ref 4; R ) 0.9985). However, the correlation improves substantially with [2]staffanes (Figure 2b; R ) 0.9978) and even more so with [3]staffanes (Figure 2c; R ) 0.9997). Unlike correlations between internal coordinates, these correlations do not contain contributions from geometrical constraints; they originate entirely from physical effects.
In simple monosubstituted benzene derivatives, Ph-X, where the variable substituent is attached directly to the benzene ring, the angular distortion is described in terms of three separate contributions, originated by the electronegativity, resonance, and steric effects of the substituent.5a All contributions act in the D6D4 plane. Therefore, the points corresponding to different substituents are widely scattered in the D4 versus D6 scattergram. (See Figures 5 and 6 of ref 5a.) In contrast, the data points of [2]- and especially [3]staffane derivatives are well aligned in the D6D4 plane, the mark of a single electronic substituent effect. As with bicyclo[2.2.2]octane derivatives,4 this is identified as the long-range polar effect (field effect) of X. The appreciable deviation of several data points from the least-squares line of Figure 2a indicates that in Ph-C(CH2)3C-X molecules, the long-range polar effect of X acting on the phenyl group is perturbed by some other effect, transmitted through the bicyclo[1.1.1]pentane cage. We show here that two other substituent effects contribute to the deformation of the benzene ring in these molecules: they are an electronegativity effect and a π-transfer effect, similar to the resonance effect in Ph-X molecules. The evidence presented below is confirmed by statistical analysis. (See Section 5.2.) 5.1.2. Transmission of ElectronegatiWity Effects through the Bicyclo[1.1.1]pentane Cage. The position of the data points X ) Li and ClO3 in the D4 versus D6 scattergram of Figure 2a is a clear sign of an electronegativity effect, superimposed onto the long-range polar effect. The electronegativities of the two groups are at opposite ends of Pauling’s scale. In particular, the electronegativity of Li (1.03)15 is close to those of the charged groups O- (0.98) and BH3- (1.21), whereas that of ClO3 (3.86) is substantially larger than that of PH3+ (2.93) and approaches that of NH3+ (4.32). Comparison with Figure 2b,c shows that in Figure 2a the Li and ClO3 data points are shifted toward the negatively and positively charged groups, respectively, because of their extreme electronegativity values. The deviation of the two data points on opposite sides of the regression line is a further sign of the electronegativity effect. If a least-squares line is traced through the 21 uncharged groups as in Figure 3 rather than through all groups as in Figure 2a, then the angular coefficient decreases from 2.02(9) to 1.40(8), approaching the value of 1.21(3) of the electronegativity line for Ph-X molecules, as obtained from B3LYP/6-311++G** calculations.16 The ability of the bicyclo[1.1.1]pentane cage to transmit electronegativity effects explains the dependence of 19F NMR chemical shifts on the nature of the variable substituent in F-C(CH2)3C-X molecules.3d,g It certainly originates from the very short nonbonded separation between the bridgehead carbons (1.79 to 1.95 Å in both 1a and 1b, from B3LYP calculations). This causes the electron density inside the small bicyclo[1.1.1]pentane cage to be much higher than that in larger polycyclic cages. The electronic charge distribution in bicyclo[1.1.1]pentane and many other hydrocarbons was investigated theoretically some years ago based on HF/6-31G* calculations.17 The charge density at the cage critical point was found to be 0.0983 e bohr-1, which is 39% of the charge density at the C-C bond critical point in ethane. The corresponding value for bicyclo[2.2.2]octane is much less, 0.0211 e bohr-1. 5.1.3. Transmissionofπ-EffectsthroughtheBicyclo[1.1.1]pentane Cage. Close inspection of the central area of Figure 2a, enlarged in Figure 3, shows that π-donor and π-acceptor groups are displaced on opposite sides of the least-squares line. Comparison with the corresponding plot for bicyclo[2.2.2]octanes4 indicates that the displacement has a component
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Figure 2. Scattergrams of the symmetry coordinate D4 versus D6 for the benzene ring of (a) Ph-C(CH2)3C-X (1a), (b) Ph-[C(CH2)3C]2-X, and (c) Ph-[C(CH2)3C]3-X molecules from B3LYP/6-311++G** calculations. The correlation coefficients are 0.9768, 0.9978, and 0.9997, on 26, 26, and 12 data points, respectively.
along the least-squares line. (This is plainly evident in Figure 2a for the strongest π-donor in the data set, X ) O-.) It is clear that the π-effect of X is transmitted by the bicyclo[1.1.1]pentane cage and acts on the geometry of the benzene ring. This is easily explained in terms of hyperconjugative interactions between the π-system of the substituent and the saturated polycyclic framework. Transfer of electron density may actually occur from a lone pair orbital of a π-donor substituent into a σ*(C-C) orbital of the bicyclo[1.1.1]pentane cage (negative hyperconjugation) or from a σ(C-C) orbital of the cage into an empty orbital of a π-acceptor substituent (hyperconjugation). Pictures of the HOMO of Ph-C(CH2)3C-NH2 in the orthogonal and coplanar conformation of the phenyl group (Figures 4a and 4b, respectively) show delocalization of the nitrogen lone pair into the bicyclo[1.1.1]pentane cage and even into the π-system of
the benzene ring when conformation permits. This perturbs the geometry of the probe, as determined by the long-range polar effect of the substituent. In the corresponding bicyclo[2.2.2]octane derivative, Ph-C(CH2-CH2)3C-NH2, the delocalization of the nitrogen lone pair into the cage is less pronounced and does not involve the benzene ring (Figure 4c). In the [2]staffane derivative, Ph-[C(CH2)3C]2-NH2, the nitrogen lone pair is again delocalized into the cage carrying the substituent, but the other cage and the benzene ring are less involved (Figure 4d). Therefore, the effect of π-transfer on the geometry of the benzene ring is marginal in these molecules. The excellent capability of the bicyclo[1.1.1]pentane cage to transmit π-interactions is well known.2f It is demonstrated by the rather large splitting (0.7 eV) in the π-orbital energies of HCtC-C(CH2)3C-CtCH and Br-C(CH2)3C-Br, as deter-
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Figure 3. Enlarged view of the central area of Figure 2a showing the positions of common functional groups for Ph-C(CH2)3C-X molecules (1a). The least-squares line has been traced through the 19 data points shown in the Figure plus Li and ClO3.
Campanelli et al. The resulting SF values are presented in Table 1 and Table S14. Correlations between SF values at different levels of theory and for different molecular systems are reported in Table S15 and Table 2, respectively. The quality of the correlations between SF values from HF and B3LYP calculations on the same molecular system is excellent for [2]staffane and especially [3]staffane derivatives, slightly less good for bicyclo[1.1.1]pentanes (Table S15 of the Supporting Information). In all systems, the SF values from HF calculations tend to be smaller than those from B3LYP calculations. The SF values for the orthogonal (1a) and coplanar (1b) conformations of the phenyl group in Ph-C(CH2)3C-X molecules are in close agreement at both levels of theory. (See Tables 1 and 2 and Table S14.) The correlations between SF values for [2]- or [3]staffanes and bicyclo[1.1.1]pentanes are less good because of the perturbations caused by electronegativity and π-transfer effects in bicyclo[1.1.1]pentanes. Table 2 shows that the SF values of [2]- and [3]staffane derivatives correlate well with those of bicyclo[2.2.2]octanes,4 indicating that the same long-range polar effect is acting in the three systems. The correlation is less satisfactory in the case of bicyclo[1.1.1]pentanes but improves significantly if the electronegativity and resonance parameters of Ph-X molecules, SE and SR,5a are added to SFBCO as explanatory variables. Regression statistics (Table 3 and Table S16 of the Supporting Information) conclusively demonstrates that the geometry of the benzene ring in Ph-C(CH2)3C-X molecules is controlled primarily by the long-range polar effect of X, with significant contributions from electronegativity and π-transfer effects.20 The multiple regression equation is
SFBCP ) 1.32(4)SFBCO + 0.022(3)SE + 0.077(9)SR 0.003(8)◦
(7)
from HF/6-31G* calculations (R ) 0.9989), and
SFBCP ) 1.33(6)SFBCO + 0.028(6)SE + 0.159(21)SR + 0.003(16)◦
Figure 4. View of the HOMO of (a) Ph-C(CH2)3C-NH2, orthogonal conformation, (b) Ph-C(CH2)3C-NH2, coplanar conformation, (c) Ph-C(CH2-CH2)3C-NH2, and (d) Ph-[C(CH2)3C]2-NH2, showing different extent of delocalization of the nitrogen lone pair into the hydrocarbon framework (from B3LYP/6-311++G** calculations).
mined by photoelectron spectroscopy.18 Replacement of -C(CH2)3C- with -C(CH2-CH2)3C- as a central unit gives only a very small splitting.19 5.2. Benzene Ring Deformation and Long-Range Polar Effects. A coordinate along the least-squares line in the D6D4 plane, SF, with the origin set at X ) H, will be used to measure the long-range polar effect of the substituent, in the same manner as with bicyclo[2.2.2]octane derivatives.4 The equations giving the structural substituent parameter SF for molecular systems 1-3 at the two levels of calculation are given in Table S13.
(8)
from B3LYP/6-311++G** calculations (R ) 0.9970). 5.2.1. Falloff of Long-Range Polar Effect with Distance. The angular coefficients of the regression lines given in Table 2 show that the transmission efficiency of the long-range polar effect through a system of two (three) bicyclo[1.1.1]pentane units is ∼40% (20%) of that through a single unit. But the falloff of long-range polar effect with distance is best seen when the deformation of the benzene ring in Ph-[C(CH2)3C]n-X molecules, expressed as R(X) - R(H), is plotted against n, the number of cages interposed between substituent and probe (Figure 5). The deformation is well determined even for n ) 5, when the probe is at 18 to 19 Å from the substituent. In the harmonic approximation, the deformation energy is proportional to the square of the deformation. We find that the square of the difference R(X) - R(H) is linearly related to n-3 for the five charged groups if the data point corresponding to n ) 1 is excluded. This dependence of energy on distance is neither that expected for the interaction between an ion and a permanent dipole (n-2) nor that between an ion and an induced dipole (n-4); rather, it corresponds to the interaction between permanent dipoles aligned in the same direction if the distance between them is much greater than their length.21
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TABLE 1: Structural Substituent Parameters SF for Molecular Systems 1-3 from B3LYP/6-311++G** Calculations SF (deg)a substituent
1a
1b
2
3
OBH3COOLi Me H NH2 SiMe3 OMe MgCl OH SiH3 Ph SH COMe COOMe F CHO Cl CF3 CN COCl NO2 ClO3 NH3+ PH3+
-1.68 -1.09 -0.83 -0.38 -0.06 0.00 -0.08 -0.01 -0.02 0.03 -0.02 0.07 0.00 0.12 0.10 0.10 0.13 0.17 0.23 0.26 0.27 0.28 0.38 0.79 1.16 1.15
-1.66 -1.08 -0.75 -0.38 -0.06 0.00 -0.06 -0.03 0.01 0.03 0.01 0.07 -0.03 0.12 0.12 0.13 0.16 0.19 0.25 0.24 0.28 0.30 0.40 0.78 1.19 1.17
-0.60 -0.49 -0.40 -0.15 -0.01 0.00 0.00 0.00 0.01 0.01 0.02 0.02 0.02 0.05 0.05 0.06 0.06 0.06 0.08 0.09 0.11 0.13 0.13 0.22 0.51 0.51
-0.30 -0.26 -0.22 -0.07
exptl gas-phase acidityb
calcd gas-phase acidityc
-1.7 0.0
-0.5 0.0 1.0
0.00
-0.1
2.7 2.8
0.01 0.9
4.6 3.6 3.2 4.6
0.03 0.03
6.1 6.5 9.6
6.1 6.4 6.9 8.2 10.4
0.06 0.09 0.28 0.28
10.8
12.1
a SF values have been calculated by the equation SF ) c0 + c1∆R + c2∆β + c3∆γ + c4∆δ from the internal angles of the benzene ring given in Tables S6-S8 of the Supporting Information using the appropriate coefficients from Table S13. b ∆GH - ∆GX values (kcal mol-1) for the dissociation of HOOC-C(CH2)3C-X acids at 300 K, measured by ion cyclotron resonance spectroscopy (from data given in Figure 1 of ref 3j). c ∆HH - ∆HX values (kcal mol-1) for the dissociation of HOOC-C(CH2)3C-X acids, calculated at the MP2/6-311++G** level using B3LYP/6-311+G* geometries (from data given in Table S5 of ref 3f).
TABLE 2: Linear Regressions between Structural Substituent Parameters SF in Different Molecular Systems (1-3 and 6a) from HF/6-31G* and B3LYP/6-311++G** Calculations molecular systems
number of data points
level of calculation
angular coefficient
intercept (deg)
correlation coefficient
1a vs 1b
26
2 vs 1a
26
3 vs 1a
12
3 vs 2
12
1a vs 6
21
2 vs 6
21
3 vs 6
12
HF B3LYP HF B3LYP HF B3LYP HF B3LYP HF B3LYP HF B3LYP HF B3LYP
1.001(5) 1.004(8) 0.399(10) 0.402(12) 0.201(11) 0.209(13) 0.504(10) 0.525(11) 1.585(45) 1.701(73) 0.642(8) 0.701(11) 0.324(10) 0.368(10)
-0.003(2) -0.013(4) -0.008(6) 0.002(7) -0.005(9) -0.005(11) 0.000(3) -0.001(4) -0.049(17) -0.068(27) -0.027(3) -0.027(4) -0.013(5) -0.016(5)
0.9998 0.9993 0.9920 0.9890 0.9841 0.9801 0.9981 0.9979 0.9925 0.9831 0.9985 0.9976 0.9954 0.9966
a SF values for molecular system 6 are taken from Tables 4 and 5 of ref 4. We have added one important molecule, Ph-C(CH2-CH2)3C-Li, for which MO calculations yield SF ) -0.26° at the HF/6-31G* level and -0.23° at the B3LYP/6-311++G** level.
5.2.2. Comparison with Gas-Phase Acidities of 3-Substituted Bicyclo[1.1.1]pentane-1-carboxylic Acids. The SF values of Table 1 and Table S14 correlate well with two independent measures of long-range polar effects in bicyclo[1.1.1]pentane derivatives, namely, the experimental3j and calculated3f gasphase acidities of 3-substituted bicyclo[1.1.1]pentane-1-carboxylic acids (Table S17 and Figures 6 and 7). The correlations are better when SF values from [2]staffanes are used rather than those from bicyclo[1.1.1]pentanes. This may arise from the fact that in 3-substituted bicyclo[1.1.1]pentane-1-carboxylic acids, the O-H bond of the carboxylic group is further away from the substituent than the ipso carbon of the phenyl group in 1. As in the case of bicyclo[2.2.2]octane derivatives,4 the geo-
metrical variation of the phenyl group and the gas-phase acidities of the associated carboxylic acids point to the importance of field effects, which are at times considered small and rapidly diminishing with distance.22 5.3. Cage Deformation and Short-Range Polar Effects in Ph-C(CH2)3C-X Molecules. A detailed analysis of the deformation of the bicyclo[1.1.1]pentane cage under the impact of a variable substituent at a bridgehead position is beyond the scope of the present study. It should be based on the geometries of an adequate number of H-C(CH2)3C-X molecules, unperturbed by the presence of a phenyl group at the other bridgehead position. Here we report the structural variation of the bicyclo[1.1.1]pentane cage in the 26 Ph-C(CH2)3C-X mol-
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TABLE 3: Regression Statistics for the Structural Substituent Parameter SFBCP versus Field, Electronegativity, and Resonance Parametersa,b level of calculation HF
B3LYP
explanatory variablesc SFBCO SFBCO, SFBCO, SFBCO, SFBCO SFBCO, SFBCO, SFBCO,
SE SR SE , SR SE SR SE , SR
R2d
Radj2e
Ff
Pg
0.9851 0.9876 0.9922 0.9978 0.9667 0.9717 0.9857 0.9941
0.9843 0.9862 0.9913 0.9974 0.9647 0.9681 0.9839 0.9929
1255.2 716.13 1145.9 2554.7 493.58 274.42 550.32 843.61
