Transmission of Electronic Substituent Effects through a Benzene

Article pubs.acs.org/JPCA

Transmission of Electronic Substituent Effects through a Benzene Framework: A Computational Study of 4-Substituted Biphenyls Based on Structural Variation Anna Rita Campanelli* Department of Chemistry, University of Rome “La Sapienza”, I-00185 Rome, Italy

Aldo Domenicano* and Fabio Ramondo Department of Chemistry, Chemical Engineering and Materials, University of L’Aquila, I-67100 L’Aquila, Italy S Supporting Information *

ABSTRACT: The transmission of substituent effects through a benzene framework has been studied by a novel approach, based on the structural variation of the Ph group in p-Ph−C6H4−X molecules. The molecular structures of many 4-substituted biphenyls were determined from MO calculations at the HF/6-31G* and B3LYP/6-311++G** levels of theory. The twist angle between the phenyl probe (ring B) and the benzene framework carrying the substituent (ring A) was set at 90° to prevent π-electron transfer from one ring to the other and at 0° to maximize it. The structural variation of the probe is best represented by a linear combination of the internal ring angles, termed SBIPH(o) and SBIPH(c) for the orthogonal and coplanar conformations of the molecules, respectively. F F Regression analysis of these parameters using appropriate explanatory variables reveals a composite field effect, a substantial proportion of which is originated by resonance-induced π-charges on the carbon atoms of ring A. Field-induced polarization of the π-system of ring A also contributes to the structural variation of the probe. Thus, the SBIPH(o) parameter is very well F reproduced by a linear combination of the π-charges on the ortho, meta, and para carbons of ring A, an uncommon example of a quantitative relationship between molecular geometry and electron density distribution. Comparison of SBIPH(o) with the gasF phase acidities of para-substituted benzoic acids shows that, while the deprotonating carboxylic probe is more sensitive to π-electron withdrawal than donation, the phenyl probe is equally sensitive to both. While the ability of the orthogonal biphenyl system to exchange π-electrons with the para substituent is the same as that of the benzene ring in Ph−X molecules, an increase by about 18% occurs when the conformation is changed from orthogonal to coplanar. The structural variation of the probe becomes more complicated, however. This is due to π-electron transfer from one ring to the other, which is shown to introduce quadratic terms in the regressions.

1. INTRODUCTION During the past few years, we have studied the transmission of long-range polar effects (field effects) through a number of hydrocarbon frameworks.1−3 The molecules investigated have general formula Ph−G−X, where X is a variable substituent, G the hydrocarbon framework, and Ph a phenyl group acting as a probe by virtue of its structural variation. The frameworks we have considered are cage polycyclic alkanes, namely, bicyclo[2.2.2]octane,1 bicyclo[1.1.1]pentane,2 [n]staffanes with n = 2−5,2 and cubane.3 The field effect of the substituent gives rise to a small variation in the geometry of the phenyl probe, which is reliably determined by MO calculations at the B3LYP/6-311++G** and HF/6-31G* levels of theory. The variation is best represented by a linear combination of the internal ring angles, termed SF, which, in bicyclo[2.2.2]octane derivatives, correlates well with experimental indicators of the field effect. In bicyclo[1.1.1]pentane and cubane derivatives, however, we have found evidence of electronegativity and/or πtransfer effects perturbing the field effect that acts on the phenyl probe. © 2012 American Chemical Society

We have now investigated the transmission of long-range polar effects through an aromatic framework, the benzene ring. Unlike polycyclic alkanes, benzene has a highly polarizable π-electron system that may also be involved in resonance interactions with the substituent. The molecules we have studied are the 4-substituted derivatives of biphenyl, p-Ph−C6H4−X, where the benzene ring carrying the variable substituent is the framework, while the other benzene ring is the probe. Substituted biphenyls have attracted much interest over the years, resulting in countless experimental and computational studies. Suffice it to mention the dependence of the twist angle and barriers to internal rotation on the position and nature of the substituents, the possible chirality of ortho-substituted biphenyls, and the environmental problems posed by the ubiquitous polychlorinated biphenyls. Quite recently, a number of single-molecule junctions and molecular rods based on Received: April 18, 2012 Revised: July 8, 2012 Published: July 11, 2012 8209

dx.doi.org/10.1021/jp303722w | J. Phys. Chem. A 2012, 116, 8209−8217

The Journal of Physical Chemistry A

Article

bond configuration with a lone pair of electrons at the top of the pyramid. The pyramidal conformation is denoted as (p) when the lone pair axis protrudes from the plane of ring A. It is denoted as (p′) when the lone pair axis lies in the plane of ring A. Molecular geometries were determined by molecular orbital (MO) calculations at the HF/6-31G* and B3LYP/6-311+ +G** levels of theory with appropriate symmetry constraints, using the Gaussian03 package of programs.8 The HF/6-31G* level was selected to check its suitability for this type of study. The optimized geometries of all the p-Ph−C6H4−X molecules considered here correspond to saddle points in the potential energy hypersurface, as shown by harmonic normal-mode analysis at the HF/6-31G* level. π-Charges on the carbon atoms of the benzene rings were determined by natural atomic orbital (NAO) analysis9 at both levels of theory. All MO calculations were run at the CASPUR Supercomputing Center, Rome. For nearly one-half of the 57 molecular species investigated, the symmetry of the two benzene rings is lowered from D6h to C2v. With the other species, further lowering of the ring symmetry occurs, but deviations from C2v symmetry are generally small, especially in the case of ring B. To simplify the analysis, we have treated the less symmetrical benzene rings as having idealized C2v symmetry by averaging appropriate bond distances, bond angles, and π-charges. Internal coordinates of rings A and B in the orthogonal and coplanar conformations of p-Ph−C6H4−X molecules are provided as Supporting Information to this article, Tables S1−S8. π-Charges brought about by the substituent on the carbon atoms of the benzene rings are reported in Tables S9−S14. (All tables and figures containing an S in their identification label are deposited in the Supporting Information; see the relevant paragraph at the end of the article).

biphenyl units have been constructed to investigate the dependence of conductance on the twist angle.4 Biphenyl is the simplest molecular system made up of benzene units where it is possible to study the dependence of physical properties on conformation. In the free molecule, the twist angle about the C−C bond connecting the two benzene rings is 44.4(12)° from an electron diffraction study,5,6 due to a delicate interplay between π-electron delocalization, which would cause the molecule to be planar, and H···H repulsions at the ortho bays, which would favor a twist angle of 90°. In the present study, the twist angle between ring A (the framework) and ring B (the probe, see Chart 1) has been set at Chart 1

90° to prevent π-electron transfer from one ring to the other and at 0° to maximize such transfer. Throughout the article, the two conformations are denoted as orthogonal and coplanar, respectively. The scope of this work is to investigate how the field effect of a variable substituent X is transmitted through benzene ring A in the orthogonal and coplanar conformations of p-Ph−C6H4− X molecules. We will show that the geometry of ring B is determined by the distribution of π-charge within ring A. In addition, the signal from the phenyl probe will be compared with the experimental and computed gas-phase acidities of parasubstituted benzoic acids, a traditional indicator of the propagation of field and resonance effects through a benzene framework.

3. ANALYSIS OF THE GEOMETRY OF THE PHENYL PROBE As in all our previous studies on substituent effects determined from the structural variation of a phenyl probe,1−3,7,10,11 the analysis of the benzene ring geometry was based on angular symmetry coordinates, which are appropriate linear combinations of the internal ring angles. Although bond distances have been used successfully to analyze intramolecular interactions in conjugated systems,12 we prefer to use bond angles because they undergo a larger relative variation, and are thus more sensitive to substituent effects. This is particularly important when, as in the present case, the phenyl probe is far from the variable substituent. Moreover, bond angles are related to ratios of distances and are, therefore, less affected by systematic errors as compared to bond distances. This applies to computed and experimental geometries as well.13 The use of symmetry coordinates is particularly advantageous because they are mutually orthogonal, while internal coordinates are linked by equations of geometrical constraint, which introduce correlation (for instance, the sum of the internal angles of a planar hexagon must be 720°). Thus, any correlation between symmetry coordinates originates entirely from physical or chemical effects, which is not the case of correlations between internal coordinates. If the benzene ring conforms to C2v symmetry, its angular variance can be described by the following symmetry coordinates:1,2,10

2. SELECTION OF SUBSTITUENTS AND CALCULATIONS The substituents considered in the present study were selected so as to be as much representative as practically possible of the different types of electronic effects. In addition to common dipolar groups, we have included extreme cases of field, electronegativity, and resonance effects, several charged groups, and H as a reference. Some groups have been considered in more than one conformation with respect to ring A, giving a total of 57 species for both orthogonal and coplanar biphenyls. To specify the conformation of a nonlinear group with respect to ring A, we make use of the following terms and abbreviations.7 Coplanar conformation (c): this term applies to planar substituents when they are coplanar with ring A. It also applies to nonplanar substituents having Cs or C3v symmetry, if their symmetry plane (or one of their symmetry planes) coincides with the plane of ring A. Orthogonal conformation (o): this term applies to planar substituents when the substituent plane is orthogonal to the plane of ring A and passes through the ipso and para carbons. It also applies to nonplanar substituents having Cs or C3v symmetry, if their symmetry plane (or one of their symmetry planes) is orthogonal to the plane of ring A. Pyramidal conformation (p and p′): we use this term when the first atom of the substituent has a pyramidal

D4 = 3−1/2 (α − β − γ + δ) 8210

(1)


The Journal of Physical Chemistry A D6 = 6−1/2(α − 2β + 2γ − δ)

Article

Strong π-donor and π-acceptor functional groups are then seen to deviate somewhat on opposite sides of the least-squares line. This implies that the geometry of the phenyl probe (ring B) is determined not only by the field effect of the variable substituent X but also by the resonance interactions occurring between X and ring A. Further evidence of the role that resonance interactions between X and ring A play in determining the structural variation of ring B comes from Figure 3, where the central area of Figure 2 is compared with the corresponding area of the D4 versus D6 scattergram for Ph−C(CH2−CH2)3C−X molecules. The structural variation of the phenyl probe in bicyclo[2.2.2]octane derivatives (Figure 3b) is originated by an essentially pure field effect, unperturbed by electronegativity and resonance contributions.1,3 In biphenyl derivatives (Figure 3a), π-donor and π-acceptor functional groups not only deviate slightly from the least-squares line but are also considerably shifted in opposite directions along it. 4.1.1. Deriving the Structural Substituent Parameter SBIPH(o) . A coordinate along the least-squares line in the D6D4 F plane, with the origin set at X = H, will be used to measure the overall electronic effect of the variable substituent on the geometry of ring B. We call this parameter SBIPH(o) , notF withstanding the fact that it contains contributions from both field and resonance effects. Although a slightly better fit is obtained with a second degree polynomial (see Figure 2), we use linear regression for the sake of simplicity. The regression equation is

(2)

where α, β, γ, and δ are the internal angles of the benzene ring as defined in Figure 1. The D4 versus D6 scattergram is then

Figure 1. Lettering of the C−C bonds and C−C−C angles in a monosubstituted benzene ring of C2v symmetry.

examined to see whether the distribution of data points reveals any distortional pathway originated by specific electronic effects.

4. RESULTS AND DISCUSSION 4.1. 4-Substituted Biphenyls in the Orthogonal Conformation. Scattergrams of D4 versus D6 for ring B of p-Ph−C6H4−X molecules in the orthogonal conformation (1 in Chart 1) are presented in Figures 2 and S1, from B3LYP/

D4 = 1.45(2)D6 − 0.35(1)°

(3)

from B3LYP/6-311++G** calculations. The correlation coefficient is 0.9989 for the 19 nonresonant substituents through which the least-squares line has been traced. The equations giving SBIPH(o) from the ring angles calculated F at the HF and B3LYP levels of theory are reported in Table 1. The SBIPH(o) values obtained from these equations for the F 57 substituents considered in the present study are given in Table 2. A good correlation (R = 0.9974) exists between HF and B3LYP values of SBIPH(o) ; however, the origin is shifted by F 0.05(1)°. 4.1.2. Substituent Effects as Disclosed by the Orthogonal Phenyl Probe. The dependence of SBIPH(o) on the field and F resonance effects of the variable substituent may be put on a quantitative basis by multiple regression analysis. In an approach based entirely on structural variation, the following parameters were used as explanatory variables: (i) SBCO F , the measure of an essentially pure field effect, from the benzene ring geometry of Ph−C(CH2−CH2)3C−X molecules;1,3,14 (ii) SR, a measure of the resonance effect, from the ring geometry of Ph− X molecules;7 and (iii) SE, a measure of the electronegativity effect, again from the ring geometry of Ph−X molecules.7 The results of the analysis are presented in Table 3: they are closely similar at the two levels of theory. The correlation of SBIPH(o) with SBCO is far from good (R = 0.9604 on 57 data F F points, from B3LYP/6-311++G** calculations), as expected, but improves substantially (R = 0.9949) when the resonance parameter SR is added to SBCO as an explanatory variable. The F introduction of SE as an additional explanatory variable gives only a marginal improvement (R = 0.9965). This is not surprising because electronegativity effects are unlikely to be transmitted beyond a couple of chemical bonds.15 Similar results are obtained if the regression analysis is based on experimental parameters traditionally used to measure field

Figure 2. Scattergram of the symmetry coordinate D4 versus D6 for ring B of p-Ph−C6H4−X molecules in the orthogonal conformation, from B3LYP/6-311++G** calculations. The 19 nonresonant substituents through which the least-squares line has been traced (R = 0.9996 for a second-degree polynomial) are marked with open squares.

6-311++G** and HF/6-31G* calculations, respectively. At first, the data points may appear to be well aligned in the D6D4 plane (R = 0.9921 for a linear regression through all the 57 data points of Figure 2), and their distribution has clearly the mark of the field effect. However, careful inspection reveals intriguing displacements. These are best seen and interpreted if, as in Figures 2 and S1, a regression line is traced using only nonresonant substituents: that is, the 19 data points for which the net charge transferred from the substituent into the π-system of the benzene ring, or vice versa, as obtained from NAO calculations on Ph−X molecules,7 does not exceed 0.01 electrons. 8211



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Figure 3. (a) Enlarged view of the central area of Figure 2 showing the positions of uncharged substituents for p-Ph−C6H4−X molecules in the orthogonal conformation. (b) The corresponding plot for Ph−C(CH2−CH2)3C−X molecules, based on data from ref 3 and Table S15 of the Supporting Information.

carbon atoms of ring A. The possibility that π-electron density changes caused by resonance may set up second-order field effects upon probe groups was mentioned by Reynolds in 1983 (see Table 8 of ref 18). The present results indicate that this resonance-induced field effect is important in p-Ph−C6H4−X molecules. This is because the π-charges on the ortho and para carbons of ring A act on the phenyl probe from a much shorter distance than any charge residing on the substituent itself. This does not occur in bicyclo[2.2.2]octane derivatives, where the saturated hydrocarbon framework is essentially insensitive to resonance effects. Field-induced polarization of the π-electron system of ring A15,18 (formerly referred to as π-inductive effect)19 also plays a role in determining the structural variation of ring B. Examples of π-charge distribution on the carbon atoms of ring A when the substituent is a strong, nonresonant polarizer are provided in Table 4. They show how electron density is transferred within ring A from the ipso to the meta and para carbons (or vice versa), while essentially no transfer occurs between the substituent and ring A. The polarization of the π-electron system of ring A in p-Ph−C6H4−X molecules makes the phenyl probe more sensitive to the field effect of the substituent than in Ph−C(CH2−CH2)3C−X molecules, although the separation between the carbon atoms carrying substituent and probe is slightly larger in benzene (about 2.8 Å) than in bicyclo[2.2.2]octane (about 2.6 Å). The coefficient of SBCO in all the F regression equations of Table 3 is indeed substantially larger than unity. 4.1.3. Structural Changes and π-Charge Distribution. The charge distribution in the π-electron system of ring A is determined by resonance and polarization effects. We therefore expect the structural variation of ring B to correlate with the π-charge distribution on the carbon atoms of ring A. Multiple regression analysis shows this to be the case. The structural is well reproduced (R > 0.995 on substituent parameter SBIPH(o) F 57 data points) by any linear combination of three out of the four π-charges brought about by the substituent on the carbon atoms of ring A (ΔqAipso, ΔqAortho, ΔqAmeta, and ΔqApara). This is not

Table 1. Coefficients of the Linear Combinations of the Internal Angles of Ring B, c0 + c1Δα + c2Δβ + c3Δγ + c4Δδ,a Giving the Structural Substituent Parameters SBIPH(o) and F SBIPH(c) for 4-Substituted Biphenyls in the Orthogonal and F Coplanar Conformations, Respectively parameter SBIPH(o) F SBIPH(c) F a

level of calculation

c0 (deg)

c1

c2

c3

c4

HF B3LYP HF B3LYP

1.628 1.617 4.096 4.047

0.705 0.707 0.649 0.660

−0.915 −0.939 −0.733 −0.760

−0.076 −0.012 −0.398 −0.359

0.286 0.244 0.481 0.460

Δα = α − 120°, etc.

and resonance effects of dipolar substituents, such as the field parameter σF, from 19F NMR chemical shifts of p-F−C6H4− C(CH2−CH2)3C−X molecules in cyclohexane solution,16 and the resonance parameter σ0R, from infrared intensities of Ph−X molecules.17 The regression equations are SFBIPH(o) = 0.64(3)σF + 0.62(3)σR0 − 0.02(1)°

(4)

from HF/6-31G* calculations and SFBIPH(o) = 0.57(4)σF + 0.59(3)σR0 − 0.06(1)°

(5)

from B3LYP/6-311++G** calculations. The correlation coefficients are R = 0.9936 and 0.9901, respectively, for 22 substituents. Note that the blend of electronic substituent effects emerging from the calculations is essentially the same at both levels of theory. The regression analysis indicates that the field effect of the substituent and its π-donor/acceptor properties are of comparable importance in determining the structural variation of the phenyl probe (ring B). Resonance interactions between ring A and the substituent give rise to accumulation/depletion of π-electron density on the ortho and para carbons of ring A, as exemplified in Table 4. Thus, ring B of orthogonal biphenyls experiences a composite field effect, a substantial proportion of which is originated by the resonance-induced π-charges on the 8212



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Table 2. Structural Substituent Parameters SBIPH(o) and SBIPH(c) (deg) for 4-Substituted Biphenyls, from HF/6-31G* and F F a B3LYP/6-311++G** Calculations SBIPH(o) F substituent

b,c

H Li BH2(c) BH2(o) BH3−(o) CH2+(c) CH2−(c) CH2−(o) CH2−(p′) Me(o) CF3(o) Ph(c) Ph(o) CHO(c) CHO(o) COMe(c) COMe(o) COCl(c) COCl(o) COO−(c) COO−(o) COOH(c) COOH(o) COOMe(c) CCH CN NH2(c) NH2(o)

SBIPH(c) F

SBIPH(o) F

HF

B3LYP

HF

B3LYP

substituent

0.00 −0.46 0.27 −0.01 −1.20 2.31 −2.56 −1.29 −1.30 −0.07 0.30 0.04 0.01 0.31 0.18 0.26 0.14 0.45 0.32 −0.81 −0.85 0.31 0.21 0.26 0.15 0.42 −0.36 −0.03

0.00 −0.49 0.26 −0.03 −1.30 2.05 −2.44 −1.27 −1.31 −0.12 0.27 −0.02 −0.01 0.27 0.13 0.19 0.07 0.39 0.25 −0.91 −0.98 0.22 0.14 0.17 0.09 0.32 −0.36 −0.05

0.00 −0.37 0.24 0.03 −1.23 1.60 −3.34 −1.30 −1.33 −0.01 0.28 0.12 0.04 0.26 0.17 0.25 0.13 0.42 0.28 −0.82 −0.95 0.28 0.18 0.24 0.13 0.36 −0.30 0.01

0.00 −0.37 0.21 0.00 −1.40 1.38 −3.08 −1.24 −1.35 −0.06 0.24 0.07 0.03 0.27 0.14 0.20 0.08 0.37 0.20 −0.94 −1.13 0.21 0.14 0.17 0.08 0.29 −0.35 −0.02

NH2(p) NH2(p′) NF2(p) NF2(p′) NH3+(o) NO2(c) NO2(o) NC N2+ O− OH(c) OH(o) OMe(c) OMe(o) OH2+(p) OH2+(p′) F Na MgCl SiH3(o) SiMe3(o) PH2(p) PH2(p′) PH3+(o) S− SH(c) SH(o) Cl ClO3(o)

b,c

SBIPH(c) F

HF

B3LYP

HF

B3LYP

−0.26 −0.03 0.22 0.33 1.15 0.51 0.40 0.24 1.72 −2.10 −0.15 −0.04 −0.17 −0.05 1.21 1.25 0.03 −0.57 0.02 0.14 0.05 0.07 0.15 1.31 −1.30 0.04 0.18 0.17 0.66

−0.33 −0.08 0.22 0.33 1.14 0.40 0.30 0.23 1.73 −2.05 −0.18 −0.06 −0.21 −0.09 1.21 1.23 0.01 −0.50 −0.02 0.06 −0.04 −0.01 0.10 1.25 −1.51 −0.05 0.09 0.07 0.51

−0.22 −0.01 0.22 0.28 1.03 0.46 0.33 0.24 1.33 −2.54 −0.12 −0.02 −0.12 −0.04 1.03 1.05 0.02 −0.48 0.06 0.15 0.08 0.09 0.17 1.12 −1.42 0.06 0.18 0.18 0.53

−0.30 −0.03 0.21 0.26 0.97 0.34 0.23 0.21 1.26 −2.47 −0.17 −0.06 −0.20 −0.08 0.99 0.99 0.00 −0.42 0.03 0.10 0.01 0.02 0.09 1.02 −1.82 −0.02 0.12 0.09 0.39

a BIPH(o) SF

and SBIPH(c) values have been obtained from the internal angles of ring B given in Tables S1−S4 of the Supporting Information, using the F appropriate coefficients from Table 1. bThe conformation of the substituent with respect to ring A is denoted as (c), (o), (p), and (p′) according to the definitions given in the text (section 2). cThe nonresonant substituents through which the least-squares lines have been traced are identified in bold.

with a correlation coefficient R = 0.9995 on 57 substituents (ΔqPhX values are taken from Table S1 of ref 7). 4.1.4. Electronic Substituent Effects As Seen by Different Probes: A Comparison of the Structural Parameter SBIPH(o) F with the Gas-Phase Acidities of para-Substituted Benzoic Acids. The gas-phase acidities of para-substituted benzoic acids have been used repeatedly to investigate the transmission of field and resonance effects through the benzene framework.20 The presence of the substituent modifies the stability of both the acid molecule and its anion, causing the gas-phase acidity to vary. The two changes are not necessarily related. Thus, a carboxylic group undergoing deprotonation is a more complex probe than the orthogonal phenyl group. For a given substituent, the signal from the deprotonating carboxylic group is the difference of two terms, one from the acid molecule, the other from its anion, while the signal from the phenyl probe comes from a single molecular species. The blend of electronic substituent effects in the acid and the anion makes the relative acidity more sensitive to π-electron withdrawal than donation.20e This is not the case of the orthogonal phenyl probe, which is equally sensitive to both. Plots of the structural substituent parameter SBIPH(o) versus F the experimental and computed gas-phase acidities of parasubstituted benzoic acids are reported in Figures 4 and 5, respectively. In both plots, a straight line can be traced through

surprising because some degree of correlation necessarily exists between π-charges. The best regression equations are A A A SFBIPH(o) = 5.4(5)Δqortho + 18.1(7)Δqmeta + 6.3(3)Δqpara

− 0.024(9)

(6)

from HF/6-31G* calculations (R = 0.9989) and A A A SFBIPH(o) = 3.8(8)Δqortho + 22.3(15)Δqmeta + 3.9(7)Δqpara

− 0.099(18)

(7)

from B3LYP/6-311++G** calculations (R = 0.9975). We stress the point that the dependence of SBIPH(o) on the π-charges of F ring A is proven at both levels of theory, notwithstanding some differences in the π-charges from HF and B3LYP calculations, see Tables S9 and S10, Supporting Information. The net π-charge brought about by the substituent on ring A, ΔqA = ΔqAipso + 2ΔqAortho + 2ΔqAmeta + ΔqApara, is hardly different from the corresponding charge in monosubstituted benzene derivatives, ΔqPhX. Regressing ΔqA against ΔqPhX gives the following equation: Δq A = 1.008(4)ΔqPhX − 0.0004(5)

(8) 8213



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Table 3. Multiple Regression Statistics for the Structural Substituent Parameter SBIPH(o) versus Field, Resonance, and F Electronegativity Parametersa,b level of calculation HF

B3LYP

regression equationc SBIPH(o) = 1.96(9)SBCO − F F 0.09(3)° BIPH(o) BCO = 1.56(3)SF + SF 0.26(1)SR − 0.02(1)° SBIPH(o) = 1.38(5)SBCO + F F 0.27(1)SR + 0.019(5)SE + 0.01(1)° SBIPH(o) = 1.92(8)SBCO − F F 0.17(3)° = 1.57(3)SBCO + SBIPH(o) F F 0.29(2)SR − 0.10(1)° SBIPH(o) = 1.37(5)SBCO + F F 0.31(1)SR + 0.022(5)SE − 0.06(1)°

Rd

Radj2e

Ff

0.9486

0.8979

484.9

0.9957

0.9911

3078.6

0.9967

0.9930

2618.3

0.9604

0.9209

653.4

0.9949

0.9895

2627.5

0.9965

0.9925

2486.6

Figure 4. Plot of the structural substituent parameter SBIPH(o) (from F B3LYP/6-311++G** calculations) versus the experimental gas-phase acidities of para-substituted benzoic acids (ΔG°H − ΔG°X values from Table 4 of ref 20a and Table 5 of ref 20b). The seven data points through which the least-squares line has been traced (R = 0.971) are marked with open squares.

values refer to p-Ph−C6H4−X molecules in the orthogonal conformation. bThe number of data points is 56 for HF/6-31G* and values refer to Ph− 57 for B3LYP/6-311++G** calculations. cSBCO F C(CH2−CH2)3C−X molecules and are taken from Table 2 of ref 3 and Table S15 of the present article (Supporting Information). SR and SE values refer to Ph−X molecules and are taken from Table 5 of ref 7. d Multiple correlation coefficient. eAdjusted multiple correlation coefficient, squared. fFisher test of variance for overall correlation. a BIPH(o) SF

Table 4. π-Charges Originated by the Substituent on the Carbon Atoms of Ring A in Some Orthogonal 4-Substituted Biphenylsa,b substituent

ΔqAipso

CH2−(c) O− NH2(p)

0.021 0.119 0.026

CH2+(c) N2+ BH2(c)

−0.029 −0.169 −0.038

COO−(c) NH3+(o) OH2+(p′)

0.057 −0.150 −0.178

ΔqAortho

ΔqAmeta

π-Donor Substituents −0.126 −0.032 −0.113 −0.032 −0.068 0.013 π-Acceptor Substituents 0.156 0.034 0.066 0.047 0.070 −0.004 Nonresonant Polarizers 0.035 −0.034 −0.008 0.048 0.002 0.047

ΔqApara

ΔqAc

−0.237 −0.191 −0.059

−0.532 −0.362 −0.143

0.250 0.152 0.038

0.601 0.209 0.132

−0.058 0.064 0.070

0.001 −0.006 −0.010

Figure 5. Plot of the structural substituent parameter SBIPH(o) (from F B3LYP/6-311++G** calculations) versus the computed gas-phase acidities of para-substituted benzoic acids, from B3LYP/6-311+G** calculations (ΔEH − ΔEX values derived from Table 1 of ref 20e). The six data points through which the least-squares line has been traced (R = 0.997) are marked with open squares.

π-acceptor substituents on opposite sides of the least-squares line is reversed and more pronounced, and the range of D6 values is much smaller, than in the orthogonal conformation. These differences originate from the fact that, in the coplanar conformation of p-Ph−C6H4−X molecules, ring B is directly involved in resonance interactions with ring A. Such interactions occur not only when X is a π-donor or a π-acceptor but also when it polarizes the π-electron systems of the two rings. Field-induced π-electron transfer between ring A and ring B, with little or no transfer to or from the substituent, is clearly revealed by the π-charges on the ring carbons; some examples are given in Table 5. 4.2.1. Deriving the Structural Substituent Parameter SBIPH(c) . To quantify the long-range effect of the variable F substituent on the geometry of the phenyl probe, we make use of a coordinate along the least-squares line of Figures 6 and S2, in the same manner as with the orthogonal conformation of the molecules. This coordinate will be termed SBIPH(c) . Of course, F SBIPH(c) does not span the entire structural variation of the F phenyl probe, but certainly, it covers the part of it originated by long-range effects, which is important in the present study. The remaining part (which would be measured by a coordinate

π-Charges are in electrons. They have been obtained from NAO analysis at the B3LYP/6-311++G** level of theory. bThe carbon atoms of ring A are labeled as ipso, ortho, meta, and para with reference to the variable substituent X. cΔqA = ΔqAipso + 2ΔqAortho + 2ΔqAmeta + ΔqApara is the net π-charge brought about by the substituent on ring A. a

all the π-acceptor substituents plus the unsubstituted acid, leaving the π-donor substituents on one side. The deviation from the straight line increases with the π-donor ability of the substituent, as expected. 4.2. 4-Substituted Biphenyls in the Coplanar Conformation. Scattergrams of D4 versus D6 for ring B of p-Ph− C6H4−X molecules in the coplanar conformation (2 in Chart 1) are presented in Figures 6 and S2, from B3LYP/6-311++G** and HF/6-31G* calculations, respectively. The least-squares lines have been traced through the same nonresonant substituents used with the orthogonal conformation; they make a sharp cut between π-donor and π-acceptor substituents. Comparison with Figures 2 and S1 shows that, in the coplanar conformation of the molecules, the scatter of π-donor and 8214



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The equations giving SBIPH(c) from the ring angles calculated F at the HF and B3LYP levels of theory are reported in Table 1. The SBIPH(c) values from these equations for the 57 substituents F considered in the present study are given in Table 2. The is good, correlation between HF and B3LYP values of SBIPH(c) F R = 0.9954, and improves to R = 0.9971 if the data points X = , CH2−(c) and S− are excluded. As in the case of SBIPH(o) F however, the origin is shifted by 0.05(1)°. 4.2.2. Substituent Effects as Disclosed by the Coplanar Phenyl Probe. Comparison of SBIPH(c) with SBIPH(o) shows that a F F surprisingly good quadratic relationship exists between these structural substituent parameters, see Figures 7 and S3. Since

Figure 6. Scattergram of the symmetry coordinate D4 versus D6 for ring B of p-Ph−C6H4−X molecules in the coplanar conformation, from B3LYP/6-311++G** calculations. The least-squares line has been traced through the 19 nonresonant substituents marked with open squares; its equation is D4 = 3.95(7)D6 + 3.42(12)°, with a correlation coefficient R = 0.9977.

Figure 7. Scattergram of the structural substituent parameter SBIPH(c) F versus SBIPH(o) for p-Ph−C6H4−X molecules, from B3LYP/6-311+ F +G** calculations. The equation of the quadratic regression line is = 0.938(8)SBIPH(o) − 0.132(5)(SBIPH(o) )2 + 0.020(7)°, with R = SBIPH(c) F F F 0.9985 on 57 data points.

Table 5. Field-Induced π-Electron Transfer Between Ring A and Ring B in Some Coplanar 4-Substituted Biphenyls with Nonresonant Substituents, and Its Effect on the Length of the C−C Bond Connecting the Two Benzene Rings substituent-induced π-charges on the benzene rings (electrons)a,b substituent COO−(c) NH3+(o) OH2+(p′) Na ClO3(o)

level of calculation

ΔqA

ΔqB

ΔqAB

Δr(CA−CB) (Å)c

HF B3LYP HF B3LYP HF B3LYP HF B3LYP HF B3LYP

0.036 0.033 −0.038 −0.049 −0.042 −0.057 0.029 0.029 −0.016 −0.021

−0.030 −0.040 0.042 0.063 0.047 0.066 −0.017 −0.023 0.022 0.020

0.006 −0.007 0.004 0.014 0.005 0.009 0.012 0.006 0.006 −0.001

−0.0026 −0.0044 −0.0059 −0.0080 −0.0058 −0.0078 −0.0026 −0.0019 −0.0019 −0.0019

is well reproduced by a linear combination of SBCO and SBIPH(o) F F 2 SR (see Table 3), we expect quadratic terms such as (SBCO F ) 2 and SR to be of importance in determining the values of SBIPH(c) . Indeed, multiple regression analysis yields the following F equations: SFBIPH(c) = 0.938(8)SFBIPH(o) − 0.22(3)(SFBCO)2 − 0.037(2)SR 2 + 0.026(7)°

(9)

from HF/6-31G* calculations (R = 0.9987) and SFBIPH(c) = 0.958(10)SFBIPH(o) − 0.30(3)(SFBCO)2 − 0.049(4)SR 2 + 0.024(8)°

(10)

from B3LYP/6-311++G** calculations (R = 0.9982). The origin of the quadratic terms in eqs 9 and 10 is easily explained. The SR2 term originates from the transfer of electron density from ring A to ring B (or vice versa) occurring with resonant substituents, which causes the C A−C B bond connecting the two benzene rings to become shorter by as much as 0.04−0.05 Å in extreme cases; see Tables S3 and S4 of the Supporting Information. This occurs irrespective of whether the substituent is a π-donor or a π-acceptor. The shortening of the CA−CB bond gives rise to a decrease of α and

π-Charges have been obtained by NAO analysis at the HF/6-31G* and B3LYP/6-311++G** levels of theory. bΔqA and ΔqB are the net substituent-induced π-charges on ring A and ring B, respectively; ΔqAB = ΔqA + ΔqB. cThe variation of the length of the C−C bond connecting the two benzene rings is defined as Δr(CA−CB) = r(CA− CB)X − r(CA−CB)H. a

orthogonal to the least-squares line, as in the case of Ph−X molecules7,10) is due to resonance effects acting directly on the geometry of the probe and will not be considered here. 8215



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involves the π-charges on all the carbon atoms of ring A plus the square of ΔqB (R = 0.9974 on 57 data points):

increase of β in ring B,10 in accordance with the VSEPR model.21 The equations in Table 1 indicate that the decrease of α and increase of β cause SBIPH(c) to become smaller, hence the F negative coefficient of the quadratic term. It should of course be considered that the shortening of the CA−CB bond may enhance the steric hindrance at the ortho bays. This would again cause a decrease of α and increase of β, as shown in Table 10 of ref 7. Thus, resonance and steric effects contribute jointly to the SR2 term in eqs 9 and 10; their contributions cannot be separated. 2 The (SBCO F ) term accounts for the fact that π-electron transfer from ring A to ring B, or vice versa, may also occur with nonresonant substituents if they polarize the π-electron system of the entire molecule. Field-induced π-electron transfer (extended π-polarization according to Reynolds18) makes the CA−CB bond shorter, irrespective of whether the π-transfer is from ring A to ring B, or vice versa (see Table 5). Thus, the geometry of ring B varies in the same manner as described above for the SR2 term. If only nonresonant substituents are used in the regression, then the explanatory variable SBCO and its square suffice to F reproduce the structural substituent parameter SBIPH(c) (R = F 0.9962 and 0.9956 on 19 data points from HF/6-31G* and B3LYP/6-311++G** calculations, respectively). Since resonance effects are now absent, SBCO accounts for the changes in F the geometry of the phenyl probe originated by the fieldinduced polarization of the π-electron system of ring A and 2 (SBCO F ) for the changes caused by the shortening of the CA−CB bond. 4.2.3. Structural Changes and π-Charge Distribution. Let us denote as ΔqAB the charge transferred from the substituent into the π-system of the coplanar biphenyl frame, or vice versa. This quantity will be considered as negative when the transfer occurs from the substituent to the biphenyl π-system, positive in the opposite case. Note that ΔqAB is the sum of the net π-charge variations occurring on ring A, ΔqA, and ring B, ΔqB. Values of ΔqA, ΔqB, and ΔqAB are given in Tables S11−S14 of the Supporting Information. Regressing ΔqAB against the corresponding quantity for monosubstituted benzene derivatives, ΔqPhX, yields the following equation: Δq AB = 1.179(8)ΔqPhX + 0.0012(9)

A A SFBIPH(c) = 1.06(17)Δqipso + 4.2(4)Δqortho A A + 29.0(12)Δqmeta + 7.8(4)Δqpara

− 12.2(5)(Δq B)2 + 0.015(17)°

SBIPH(o) , F

As in the case of the dependence of on π-charges is thus proven at both levels of theory. While the linear terms of eqs 12 and 13 account conjointly for the field and resonance effects of the substituent, the quadratic term accounts for the structural variation of ring B caused by the shortening of the CA−CB bond, which occurs irrespective of whether the substituent is a π-donor, a π-acceptor, or a nonresonant polarizer. 4.3. Structural Variation of Ring A. The changes in the geometry of ring A in 4-substituted biphenyls are closely related to those of the benzene ring in Ph−X molecules. Correlations between corresponding internal coordinates of the ipso and ortho regions, where structural variation is more pronounced, are reported in Table S16 of the Supporting Information. They are nearly perfect for orthogonal biphenyls and generally good for coplanar. Thus, the structural changes of ring A caused by the variable substituent are controlled primarily by the electronegativity, resonance, and steric effects of the substituent, as in the case of monosubstituted benzene rings.7,10 They are of course superimposed onto those originated by the phenyl probe (which should not be considered as constant, especially in the coplanar conformation of the molecules). Correlations between corresponding internal coordinates of the meta and para regions are indeed poorer, due to the relatively small range of values and the closeness of the phenyl probe.

5. CONCLUSIONS The structural variation of ring B in the orthogonal conformation of 4-substituted biphenyls (1), as measured by the structural substituent parameter SFBIPH(o), has been used successfully to investigate how electronic substituent effects propagate through a benzene framework (ring A). HF/6-31G* and B3LYP/6-311++G** calculations consistently show that the changes in the geometry of the phenyl probe are caused by a composite field effect, a substantial proportion of which originates from the resonance-induced π-charges on the carbon atoms of ring A. Field-induced polarization of the π-electron system of ring A also plays a role in determining the structural variation of the probe. Thus, the SBIPH(o) parameter is very well F reproduced by a linear combination of the π-charges brought about by the substituent on the carbon atoms of ring A, an uncommon example of a quantitative relationship between molecular geometry and electron density distribution. Comparison with the gas-phase acidities of para-substituted benzoic acids, where the probe is a carboxylic group undergoing deprotonation, shows an important difference in the response of the two probes to the resonance effects of the substituent. While the deprotonating carboxylic probe is more sensitive to π-electron withdrawal than donation, the phenyl probe is equally sensitive to both. The structural variation of the phenyl probe becomes more complicated when the two benzene rings are constrained to lie in the same plane. This is due to π-electron transfer from ring A to ring B, or vice versa, caused by resonance interactions with the para-substituent and field-induced polarization of the entire

(11)

with a correlation coefficient R = 0.9988 on 57 substituents (ΔqPhX values are taken from Table S1 of ref 7). Thus, the ability of the coplanar biphenyl system to exchange π-electrons with a para-substituent exceeds by about 18% that of the single benzene ring of a Ph−X molecule. At variance with orthogonal biphenyls, the geometrical variation of ring B in the coplanar conformation of p-Ph− C6H4−X molecules, as measured by the structural substituent parameter SBIPH(c) , depends on the π-charges in both ring A and F ring B. When π-charges and SBIPH(c) parameters are from HF/ F 6-31G* calculations, the best correlation involves ΔqAmeta, ΔqApara, and the square of ΔqB as explanatory variables (R = 0.9981 on 57 data points): A A SFBIPH(c) = 11.0(4)Δqmeta + 10.10(10)Δqpara

− 26.8(9)(Δq B)2 + 0.040(7)°

(13)

SBIPH(c) F

(12)

Introducing ΔqAipso or ΔqAortho as additional explanatory variables does not improve the quality of the fit. However, when the data are from B3LYP/6-311++G** calculations, the best correlation 8216



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π-electron system of the molecule. The π-electron transfer causes the CA−CB bond connecting the two benzene rings to shorten, irrespective of whether the substituent is a π-donor, a π-acceptor, or a nonresonant polarizer. As a result, the SBIPH(c) F parameter, measuring the structural variation of the coplanar phenyl probe, is linked to SBIPH(o) by a quadratic relationship. F The SBIPH(c) parameter is very well reproduced by a linear F combination of the π-charges brought about by the substituent on the carbon atoms of ring A, plus a quadratic term, the square of the π-charge accepted or released by ring B. While the ability of the orthogonal biphenyl system to exchange π-electrons with the para-substituent is the same as that of the benzene ring in Ph−X molecules, an increase by about 18% occurs when the conformation is changed from orthogonal to coplanar.

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M. S.; Steigerwald, M. L. Nature 2006, 442, 904−907. (c) Lörtscher, E.; Elbing, M.; Tschudy, M.; von Hänisch, C.; Weber, H. B.; Mayor, M.; Riel, H. ChemPhysChem 2008, 9, 2252−2258. (5) Almenningen, A.; Bastiansen, O.; Fernholt, L.; Cyvin, B. N.; Cyvin, S. J.; Samdal, S. J. Mol. Struct. 1985, 128, 59−76. (6) Here, and throughout this article, least-squares standard deviations are given in parentheses in units of the last digit of the respective parameter. (7) Campanelli, A. R.; Domenicano, A.; Macchiagodena, M.; Ramondo, F. Struct. Chem. 2011, 22, 1131−1141. (8) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; et al. Gaussian 03, revision C.02; Gaussian Inc.: Wallingford, CT, 2004. (9) (a) Reed, A. E.; Weinhold, F. J. Chem. Phys. 1985, 83, 1736− 1740. (b) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88, 899−926. (10) Campanelli, A. R.; Domenicano, A.; Ramondo, F. J. Phys. Chem. A 2003, 107, 6429−6440. (11) Campanelli, A. R.; Domenicano, A.; Ramondo, F.; Hargittai, I. J. Phys. Chem. A 2004, 108, 4940−4948. (12) Krygowski, T. M.; Stępień, B. T. Chem. Rev. 2005, 105, 3482− 3512 and references therein. (13) (a) Campanelli, A. R.; Domenicano, A.; Ramondo, F.; Hargittai, I. J. Phys. Chem. A 2008, 112, 10998−11008. (b) Campanelli, A. R.; Domenicano, A.; Ramondo, F.; Hargittai, I. Struct. Chem. 2012, 23, 287−295. (c) Domenicano, A. In Accurate Molecular Structures: Their Determination and Importance; Domenicano, A., Hargittai, I., Eds.; Oxford University Press: Oxford, U.K., 1992; Chapter 18, pp 437− 468. values used in the regression analysis are from (14) Most of the SBCO F Table 2 of ref 3. Those for X = BH2, CH2+, N2+, and Na are from Table S15 of the Supporting Information of the present article. We parameter is essentially independent of the point out that the SBCO F conformation of the substituent with respect to the bicyclo[2.2.2]octane framework.1 Thus, for substituents having different conformations with respect to benzene ring A (such as, e.g., NH2(c), value is used in the NH2(o), NH2(p), and NH2(p′)), the same SBCO F regression analysis. (15) Taft, R. W.; Topsom, R. D. Prog. Phys. Org. Chem. 1987, 16, 1−83. (16) Adcock, W.; Trout, N. A. Chem. Rev. 1999, 99, 1415−1435. (17) Katritzky, A. R.; Topsom, R. D. Chem. Rev. 1977, 77, 639−658. (18) Reynolds, W. F. Prog. Phys. Org. Chem. 1983, 14, 165−203. (19) Topsom, R. D. Prog. Phys. Org. Chem. 1976, 12, 1−20. (20) (a) McMahon, T. B.; Kebarle, P. J. Am. Chem. Soc. 1977, 99, 2222−2230. (b) Koppel, I. A.; Mishima, M.; Stock, L. M.; Taft, R. W.; Topsom, R. D. J. Phys. Org. Chem. 1993, 6, 685−689. (c) Decouzon, M.; Exner, O.; Gal, J.-F.; Maria, P.-C. J. Phys. Org. Chem. 1994, 7, 615− 624. (d) Wiberg, K. B. J. Org. Chem. 2002, 67, 4787−4794. (e) Exner, O.; Böhm, S. J. Org. Chem. 2002, 67, 6320−6327. (f) Vianello, R.; Maksić, Z. B. J. Phys. Org. Chem. 2005, 18, 699−705. (21) Gillespie, R. J.; Hargittai, I. The VSEPR Model of Molecular Geometry; Allyn and Bacon: Boston, MA, 1991.

ASSOCIATED CONTENT

* Supporting Information S

Internal coordinates of rings B and A in molecular systems 1 and 2, from HF/6-31G* and B3LYP/6-311++G** calculations; π-charges originated by the substituent on the carbon atoms of ring A in molecular system 1, from HF/6-31G* and B3LYP/6311++G** calculations; π-charges originated by the substituent on the carbon atoms of rings A and B in molecular system 2, from HF/6-31G* and B3LYP/6-311++G** calculations; selected internal coordinates of the benzene ring and SBCO F values for some Ph−C(CH2−CH2)3C−X molecules (X = BH2, CH2+, N2+, and Na), from HF/6-31G* and B3LYP/6-311+ +G** calculations; linear regressions between selected internal coordinates of ring A in molecular systems 1 and 2 and the corresponding coordinates in Ph−X molecules, from HF/631G* and B3LYP/6-311++G** calculations; scattergram of D4 versus D 6 for molecular system 1, from HF/6-31G* calculations; scattergram of D4 versus D6 for molecular system 2, from HF/6-31G* calculations; scattergram of SBIPH(c) versus F SFBIPH(o), from HF/6-31G* calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*(A.R.C.) Fax: 39-06-490631. E-mail: [email protected]. (A.D.) Fax: 39-0862-433003. E-mail: aldo.domenicano@ univaq.it. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the CASPUR Supercomputing Center, Rome, with Standard HPC Grant 2011 (“A combined X-ray absorption spectroscopy, molecular dynamics simulations, and quantum mechanics calculation procedure for the structural characterization of ill-defined systems”).

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REFERENCES

(1) Campanelli, A. R.; Domenicano, A.; Ramondo, F. J. Phys. Chem. A 2006, 110, 10122−10129. (2) Campanelli, A. R.; Domenicano, A.; Piacente, G.; Ramondo, F. J. Phys. Chem. A 2010, 114, 5162−5170. (3) Campanelli, A. R.; Domenicano, A.; Ramondo, F. Struct. Chem. 2011, 22, 449−457. (4) (a) Dadosh, T.; Gordin, Y.; Krahne, R.; Khivrich, I.; Mahalu, D.; Frydman, V.; Sperling, J.; Yacoby, A.; Bar-Joseph, I. Nature 2005, 436, 677−680. (b) Venkataraman, L.; Klare, J. E.; Nuckolls, C.; Hybertsen, 8217


Transmission of Electronic Substituent Effects through a Benzene

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