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Publicly Available Published by De Gruyter June 9, 2017

Computational study of the substituent effects on the gas-phase stabilities of phenylboranylmethyl anions

Kazuhide Nakata and Mizue Fujio

Abstract

The relative gas-phase stabilities of ring-substituted phenylboranylmethyl anions were computationally determined using isodesmic reactions. The energies of species included in the reactions were calculated at the B3LYP/6-311+G(2d,p) level of theory. The obtained substituent effects were analyzed by the extended Yukawa-Tsuno equation, and unexpectedly substantial r (0.59) and s (0.65) values were found for the fully-optimized planar anion. The substantial through-resonance effect quantified by the r value was observed, although it is not possible to draw a canonical form in which the negative charge is delocalized on the benzene ring. Substituent effects were also analyzed for the anions in which the dihedral angle (φ) between the side chain plane and the benzene ring was fixed. The r value decreased significantly by changing the φ from 0° to 90°, while the s value changed little. NBO analyses revealed that the r value is proportional to the sum of the π–π* and σ–π* orbital interactions between the side chain and the benzene ring. This fact shows that the through-resonance effect quantified by the r value is present at all φ, and therefore, the anion cannot become an ideal σ0-reference system. The constant saturation effect quantified by the s value can be explained by the constant charge distributed to the benzene ring. The combination of substituent-effect analysis and NBO analysis successfully revealed the nature of the anion.

Introduction

Linear free energy relationships (LFER) are powerful tools to reveal the structures of unstable species such as transition states and intermediates [1]. Among them, the Yukawa-Tsuno equation is well-known for the analysis of the substituent effects on the stabilities of cationic benzene derivatives [2].

(1) Δ E X = ρ ( σ 0 + r + Δ σ ¯ R + )

Many successful applications of the two-term eq. 1 have been seen to date [3], [4]. However, the establishment of LFER for anions has been slow because of experimental difficulties [5], [6]. In recent years, the development of computational chemistry has allowed us to compute highly accurate structures and energies of chemical species [7]. We have computationally determined the gas-phase stabilities of anionic benzene derivatives, and the obtained substituent effects were compared to reveal the electronic effects affecting the stabilities. As a result, we found three types of electronic effects that govern the stabilities of the anions, and proposed a ‘three-term’ extended Yukawa-Tsuno equation (2) [8].

(2) Δ E X = ρ ( σ 0 + r Δ σ ¯ R + s Δ σ ¯ S )

The normal substituent constant σ0, measures the general stabilizing or destabilizing capability of ring substituents, which were defined by the gas-phase stabilities of benzoate anions (1) [9]. The resonance substituent constant (Δσ¯R) and the saturation substituent constant (Δσ¯S) measure the additional stabilizing capabilities by the through-resonance effect for para +R groups and by the saturation effect for electron-donating groups (EDGs), respectively. Both substituent constants were defined by subtracting σ0 from σ defined by the gas-phase stabilities of phenoxide anions (2) [9]. The resultant r and s values reveal the degree of through-resonance and saturation effects, respectively. Each anion system has unique r and s values. We have reported some applications of eq. 2 previously [8], [9], [10], [11], [12]. In the course of our studies, a through-resonance effect was found in 1, although it was slight [12]. To estimate the degree of such additional effects precisely, it is desirable to determine an ideal σ0 constant that is completely free from any additional effects. For this reason, we chose the phenylboranylmethyl anion (3) to analyze the substituent effects. Both the through-resonance and saturation effects are expected to be negligible in this anion, because it is not possible to draw a canonical structure in which the negative charge is delocalized on the benzene ring. In this paper, we discuss if 3 is appropriate as an ideal σ0 reference system.

Method

The substituent effects on the gas-phase stabilities of phenylboranylmethyl anions were determined by computational methods. The gas-phase stabilities of ring-substituted phenylboranylmethyl anions (3(X)) relative to “ring-unsubstituted” 3(H) were determined by the energy difference (ΔEX) of the isodesmic reaction (3).

(3)

In the reaction, substituted benzenes were used as neutral species to extract electronic effects operating in the anions. The symbols for the energies (E) of the respective species and atom numbering are shown in reaction (3). The ΔEX of the reaction is given by eq. 4.

(4) Δ E X = E X ( ) + E H ( P h ) E H ( ) E X ( P h )

The geometries of all species were optimized at the B3LYP/6–311+G(2d,p) level of theory [13], [14], [15] using the Gaussian 09 suite of programs [16], which was installed on computers located at Hosei University. The optimized structures were confirmed to be energy-minimum structures by frequency calculations. Some different conformers were optimized, and the energies of the most stable conformers were used as E in eq. 4. Twenty-four kinds of electronically varied functional groups were employed as the ring substituents.

The obtained substituent effects were analyzed with eq. 2. Substituent constants used in the analyses were taken from a previous paper [9].

For a detailed interpretation of the resultant reaction constants (r and s values), geometry optimizations were performed for the phenylboranylmethyl anions (3(φ,X)) whose dihedral angle φ between the side chain plane and the benzene ring was frozen. The φ of 3(φ,X) was varied from 0° to 90° in steps of 10°. The substituent effects were also analyzed by eq. 2 in the same manner.

To discuss the origin of obtained reaction constants, we carried out natural population analyses (NPA) and second-order perturbative analyses of donor-acceptor interactions of the natural bond orbitals (NBO) for the ring-unsubstituted anions using the NBO 6.0 program [17], [18], [19].

In this paper, φ and X are added in parentheses to the reference numbers of chemical species to indicate the dihedral angle φ and the name of the ring substituent (X), respectively.

Results and discussion

Structures and energies

The gas-phase stabilities of the fully optimized anions (3(X)) and the φ-fixed anions (3(φ,X)) relative to the ring-unsubstituted anions (3(H) and 3(φ,H), respectively) are summarized in Table 1. The stabilities of 3(φ,H) relative to 3(H) are listed in the parentheses. The structures of 3(H), 3(p-NO2), and 3(p-Me2N) are shown in Fig. 1.

Table 1:

Relative gas-phase stabilities (ΔEX)a of ring-substituted phenylboranylmethyl anions (3).

Subst. ΔEX(3)b/kcal mol−1 ΔEX(3(φ))/kcal mol−1
φ=0° φ=10° φ=20° φ=30° φ=40° φ=50° φ=60° φ=70° φ=80° φ=90°
p-Me2N 2.62 2.67 2.67 2.71 2.75 2.78 2.75 2.75 2.76 2.76 2.80
p-NH2 2.93 2.99 2.99 3.01 3.01 3.00 2.97 2.94 2.90 2.85 2.85
m-Me2N 1.78 1.85 1.83 1.82 1.78 1.79 1.89 1.87 1.89 1.90 1.91
p-MeO 1.18 1.18 1.19 1.22 1.25 1.23 1.18 1.15 1.13 1.12 1.15
p,m-Me2 1.40 1.39 1.36 1.37 1.36 1.37 1.35 1.35 1.35 1.34 1.35
p-MeO-m-Cl −3.42 −3.42 −3.42 −3.43 −3.43 −3.43 −3.41 −3.41 −3.36 −3.34 −3.29
p-t-Bu 0.18 0.18 0.16 0.18 0.20 0.23 0.23 0.23 0.24 0.22 0.24
p-Me 0.82 0.82 0.83 0.85 0.87 0.88 0.86 0.85 0.84 0.83 0.84
m-MeO −0.79 −0.79 −0.79 −0.80 −0.81 −0.81 −0.80 −0.76 −0.73 −0.69 −0.64
m-Me 0.57 0.58 0.56 0.57 0.57 0.58 0.56 0.57 0.56 0.57 0.59
H 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
(0)c (0.00)c (0.06)c (0.23)c (0.58)c (1.12)c (1.82)c (2.59)c (3.28)c (3.76)c (3.92)c
p-Cl −5.26 −5.26 −5.26 −5.24 −5.22 −5.19 −5.15 −5.10 −5.06 −5.04 −5.02
m-F −4.38 −4.38 −4.38 −4.37 −4.34 −4.31 −4.26 −4.20 −4.15 −4.12 −4.10
m-Cl −5.80 −5.80 −5.80 −5.78 −5.75 −5.71 −5.64 −5.56 −5.49 −5.45 −5.41
m-CF3 −7.94 −7.92 −7.92 −7.92 −7.91 −7.87 −7.80 −7.72 −7.63 −7.56 −7.49
m-CHO −8.66 −8.66 −8.64 −8.58 −8.51 −8.44 −8.41 −8.36 −8.29 −8.24 −8.17
m-COMe −6.99 −6.99 −6.98 −6.96 −6.93 −6.87 −6.82 −6.76 −6.72 −6.70 −6.68
m-CN −10.94 −10.94 −10.94 −10.93 −10.89 −10.83 −10.74 −10.63 −10.52 −10.43 −10.36
m-NO2 −11.82 −11.82 −11.82 −11.81 −11.79 −11.74 −11.66 −11.57 −11.45 −11.35 −11.22
p-CF3 −9.19 −9.19 −9.19 −9.13 −9.06 −8.94 −8.82 −8.66 −8.51 −8.41 −8.35
p-CHO −11.62 −11.62 −11.60 −11.46 −11.26 −11.00 −10.65 −10.23 −9.80 −9.47 −9.30
p-COMe −9.24 −9.24 −9.23 −9.13 −8.98 −8.72 −8.42 −8.05 −7.70 −7.43 −7.30
p-CN −13.08 −13.08 −13.06 −12.98 −12.85 −12.64 −12.39 −12.10 −11.82 −11.64 −11.56
p-NO −16.93 −16.93 −16.88 −16.65 −16.29 −15.77 −15.19 −14.48 −13.70 −12.98 −12.58
p-NO2 −16.93 −16.93 −16.89 −16.71 −16.45 −16.04 −15.52 −14.90 −14.26 −13.73 −13.47

  1. aDetermined in kcal mol−1 using reaction 3. 1 cal=4.184 J.

  2. bFully optimized phenylboranylmethyl anions [H13B7C1C2 =0.0° and C14B7C1C2=179.9° (φ=0.1°), and HC14B7C1 =0.0°/180.0° in 3(H)].

  3. cStability of φ-fixed ring-unsubstituted phenylboranylmethyl anions (3(φ,H)) relative to fully optimized phenylboranylmethyl anion (3(H)).

Fig. 1: 
            Geometric parameters of 3(H), 3(p-NO2), and 3(p-Me2N).

Fig. 1:

Geometric parameters of 3(H), 3(p-NO2), and 3(p-Me2N).

The fully optimized 3 has a planar structure, independently of the ring substituents. The unsubstituted anion 3(H) becomes unstable with increasing dihedral angle, φ. The orthogonal 3(φ=90°,H) is 3.9 kcal mol−1 less stable than the planar 3(H). This shows that the through-resonance effect and/or the resonance effect between the boron atom and the benzene π-electron system are more important than the steric repulsion between the side chain and the benzene ring.

The insertion of EDGs caused the anion to become unstable, and 3(p-Me2N) is 2.6 kcal mol−1 less stable than 3(H). The insertion of meta electron-withdrawing groups (EWGs) caused the anion to become stable, and 3(m-NO2) is 11.8 kcal mol−1 more stable than 3(H). The amounts of stabilization by meta EWGs and destabilization by EDGs are very similar to one another in all the φ-fixed systems. The insertion of para +R groups caused the anion to become stable, and 3(p-NO2) is 16.9 kcal mol−1 more stable than 3(H). The amount of the stabilization decreased substantially with increasing φ. These facts imply that the through-resonance effect decreases with increasing φ, although the general and saturation effects are almost constant.

In 3(H), the B7–C14 (1.454 Å) bond distance is significantly shorter than that of the B–C bond of neutral BH2–CH3 (1.552 Å). This shows that the negative charge on C14 is delocalized to the vacant p-orbital on B7. On the introduction of a p-NO2 group to 3(H), the bond distances of B7–C14 and C1–B7 become longer and shorter, respectively, and the quinoid structure is more significant in 3(p-NO2). This implies the presence of through-resonance effect operating in 3. In 3(p-Me2N), the bond distances in the parent skeleton are almost the same with those in 3(H). The dihedral angle between the lone pair on the p-Me2N group and the benzene π-electron system is estimated to be 23.9°. This implies that there is a saturation effect in 3.

Substituent-effect analysis

The obtained substituent effects on ΔEX of 3 were compared to those of 1, as shown in Fig. 2. An unsatisfactory linear correlation was obtained as a whole, with the gradient (slopeall) equal to 1.161 and a correlation coefficient, R, of 0.985. However, an excellent linear correlation was found for meta EWGs (H, m-F, m-Cl, m-COMe, m-CF3, m-CHO, m-CN, and m-NO2), which are shown by closed circles, yielding a slopemeta of 1.054 and an R of 1.000. The plots for para +R groups (p-NO2, p-NO, p-CN, p-CHO, p-CF3, and p-COMe), which are shown by open squares, deviated upward from the correlation line. These deviations indicate that the degree of the through-resonance effect in 3 is larger than that in 1. The plots for the EDGs (p-Me2N, p-NH2, m-Me2N, p-MeO, p,m-Me2, p-Me, p-t-Bu, m-Me, m-MeO, p-MeO-m-Cl, and p-Cl), which are shown by open circles, also deviated upward from the correlation line. These deviations indicate that the degree of the saturation effect in 3 is larger than that in 1. The substituent effects of 3 were compared to those of 2, as shown in Fig. 3. Again, an unsatisfactory linear correlation was found as a whole, yielding a slopeall of 0.693 and an R of 0.995. The plots for meta EWGs gave a better correlation: slopemeta=0.780 and the R=0.997. Both of the plots for para +R groups and EDGs deviated downward from the correlation line. These deviations indicate that the degrees of the through-resonance and saturation effects in 3 are smaller than those in 2. The comparisons of the substituent effects shown in Figs. 2 and 3 reveal that the degrees of both the through-resonance and saturation effects decrease in the order of 2>3>1.

Fig. 2: 
            Substituent effects on ΔEX of 3 compared to those of 1.

Fig. 2:

Substituent effects on ΔEX of 3 compared to those of 1.

Fig. 3: 
            Substituent effects on ΔEX of 3 compared to those of 2.

Fig. 3:

Substituent effects on ΔEX of 3 compared to those of 2.

The substituent effects of 3 were then analyzed by eq. 2. The extended Yukawa-Tsuno (eY–T) plot is shown in Fig. 4. In the figure, the plots of σ¯, σ, and σ0 are represented by open squares, open circles, and closed circles, respectively. Regarding the para +R groups, the σ0 plots deviate leftward from the correlation line, and the corresponding σ plots deviate rightward. The best correlation was obtained for the case in which the apparent sigma constants (σ¯) were given by the internal division of the line segment of σ0σ in a ratio of 0.59 to 0.41. The σ0 and σ plots of the EDGs again deviate left- and rightward from the correlation line, respectively. The best correlation was obtained for the case in which the σ¯ constants were given by the internal division of the line segment of σ0σ in a ratio of 0.65 to 0.35. As a result, we obtained an excellent linear correlation, with ρ=16.59, r=0.59, s=0.65, and R=0.999. For 3, we cannot draw a canonical form in which the negative charge is delocalized on the benzene ring. Nevertheless, unexpectedly substantial r and s values were observed, which suggest significant through-resonance and saturation effects operating in 3.

Fig. 4: 
            Extended Y-T plot on ΔEX of 3.

Fig. 4:

Extended Y-T plot on ΔEX of 3.

The results of the substituent effect analyses of the φ-fixed anions (3(φ)) are summarized in Table 2, together with that of 3. The eY–T plot for 3(φ=90°) is depicted in Fig. 5. At all the φ, an excellent linear correlation was observed with an R value of more than 0.999. The ρ and s values were almost constant independently to the φ; the rates of change are −5% and −8%, respectively. The invariance in the s value is reflected in the eY-T plot of 3(φ=90°) (Fig. 5). In Fig. 5, the correlation line divides the line segment of σ0σ for EDGs in a similar ratio to that of fully optimized planar 3 in Fig. 4. On the other hand, the correlation line passes through the vicinity of the σ0 plots of para +R groups as shown in Fig. 5, which contrasts with the behavior in Fig. 4. This implies a significant change in the r value with the φ. Actually, the r value decreased substantially from r=0.59 in 3(φ=0°) to r=0.15 in 3(φ=90°) with increasing φ; the rates of change is −75%.

Table 2:

Results of substituent-effect analyses on ΔEX of 3 with the extended Yukawa-Tsuno eq. 2.a

Anions ρ r s R b SD c n d NC Ar e
3 16.59 0.59 0.65 0.999 0.32 25 −0.458
3(φ=0°) 16.60 0.59 0.64 0.999 0.31 25 −0.458
3(φ=10°) 16.59 0.58 0.64 0.999 0.31 25 −0.458
3(φ=20°) 16.56 0.56 0.63 0.999 0.30 25 −0.457
3(φ=30°) 16.51 0.52 0.62 0.999 0.28 25 −0.455
3(φ=40°) 16.42 0.47 0.62 0.999 0.27 25 −0.452
3(φ=50°) 16.30 0.41 0.62 1.000 0.25 25 −0.447
3(φ=60°) 16.16 0.33 0.62 1.000 0.24 25 −0.441
3(φ=70°) 16.02 0.26 0.61 1.000 0.23 25 −0.436
3(φ=80°) 15.92 0.18 0.61 1.000 0.22 25 −0.431
3(φ=90°) 15.82 0.15 0.59 1.000 0.21 25 −0.430

  1. aEquation 2: ΔEX=ρ(σ0+rΔσ¯R+sΔσ¯S).

  2. bCorrelation coefficient.

  3. cStandard deviation.

  4. dNumber of derivatives included in the analysis.

  5. eSum of natural charge on the phenyl ring in ring-unsubstituted anions.

Fig. 5: 
            Extended Y-T plot on ΔEX of 3(φ=90°).

Fig. 5:

Extended Y-T plot on ΔEX of 3(φ=90°).

The physical meaning of the r and s values

The obtained r and s values were compared to the geometrical parameters and charge distribution in the anion system to interpret their physical meaning. In Fig. 6, the distance of the bond between the C atom at the para position (C4) and the N atom of the p-NO2 group in 3(φ,p-NO2) is plotted against the r value, together with those in Meisenheimer complexes and benzylic anions [11]. All plots, which consist of a variety type of anions, are linearly correlated. This verifies that the r values of 3 tabulated in Table 2 reveal the degree of the through-resonance effects equivalently to other types of anions. In the last column of Table 2, the sums of natural charges on the benzene ring (NCAr) for 3(φ,H) are summarized. The rate of change in the NCAr is only −6%, showing a constant charge distribution in a series of 3(φ,H). This caused the constant saturation effect (s value) for EDGs independently to the φ.

Fig. 6: 
            Bond lengths C4-NO2 vs. the r− values.

Fig. 6:

Bond lengths C4-NO2 vs. the r values.

Mechanism of inducement of the through-resonance effect

NBO analyses were performed on 3(H) and 3(φ,H) to reveal the mechanism that results in the through-resonance effect quantified by the r value. The donor-acceptor interactions of the NBOs that are relevant to the electron transfer between the side chain and the benzene π-electron system were determined. Some representative NBO interactions are shown in Fig. 7. The left figure in Fig. 7 shows the NBO interaction between the π-orbital of the side chain and the π*-orbital of the benzene π-electron system in planar 3(H), and the energy of the electron transfer from the π-orbital of the B7–C14 bond to the π* orbital of the C1–C2 bond was estimated to be 11.06 kcal mol−1. The right two figures in Fig. 7 show the NBO interactions between the σ-orbitals of the side chain and the π*-orbital of the benzene π-electron system in orthogonal 3(φ=79°,H). The corresponding energy of the electron transfer from the σ-orbital of the B7–H13 bond to the π* orbital of the C1–C2 bond was estimated to be 4.00 kcal mol−1, and that from the σ-orbital of the B7–C14 bond to the π* orbital of the C1–C2 bond was estimated to be 0.57 kcal mol−1. As we can see in these examples, two kinds of orbital interactions between the side chain and the benzene π-electron system were observed in 3(φ,H) which cannot be expressed by a classical canonical form. It is conceivable that the electron transfer caused by these orbital interactions concerns the through-resonance effects in the anion.

Fig. 7: 
            Donor-acceptor interactions of NBOs observed in 3(H) and 3(φ=79°,H).

Fig. 7:

Donor-acceptor interactions of NBOs observed in 3(H) and 3(φ=79°,H).

In Fig. 8, these two kinds of orbital interactions are plotted against the φ. In the plots, the energy of electron transfer in the reverse direction was subtracted from that of the above-mentioned electron transfers. The π–π* orbital interaction (open circles) operates at maximum efficiency when the structure is planar (ca. 11 kcal mol−1) and decreases monotonically with increasing φ, vanishing in the orthogonal structure. The σ–π* orbital interaction (closed circles) operates at maximum efficiency when the structure is orthogonal (ca. 5 kcal mol−1) and decreases monotonically with the decreasing φ, vanishing in the planar structure.

Fig. 8: 
            Change in D-A interactions of NBOs in 3(φ,H) with the dihedral angle φ.

Fig. 8:

Change in D-A interactions of NBOs in 3(φ,H) with the dihedral angle φ.

In Fig. 9, the sum of the π–π* and σ–π* orbital interactions is plotted against the r value. A reasonable linear correlation was observed for the plots. This fact suggests that the through-resonance effect in this anion was induced through these non-classical orbital interactions. In this anion, the interaction energy of these orbitals is larger than 5 kcal mol−1; that is, the electron transfer caused by these interactions always operate at any φ, inducing a certain degree of through-resonance effect. Consequently, this anion cannot become an ideal σ0-reference system. The extrapolation of the correlation line to the x-axis (0 kcal mol−1 of the sum of D-A interactions) gives an r value of −0.34. An ideal σ0-reference system might show such the r value on the current scale. Further exploration of σ0-reference systems will be performed in the future.

Fig. 9: 
            Change in sum of D-A (π–π* and σ–π*) interactions in 3(φ,H) with the r− values.

Fig. 9:

Change in sum of D-A (π–π* and σ–π*) interactions in 3(φ,H) with the r values.

Conclusion

The relative gas-phase stabilities of ring-substituted phenylboranylmethyl anions (3(X)) were determined at the B3LYP/6-311+G(2d,p) level of theory. The obtained substituent effects were analyzed using the extended Yukawa-Tsuno equation (2). All ring-substituted 3(X) anions had planar structures and gave an unexpectedly substantial r value (0.59). The r value decreased substantially with increasing dihedral angle (φ) between the side chain plane and the benzene ring, yielding r=0.15 in the orthogonal 3(φ=90°,X). The s value was almost constant (ca. 0.6) independently to the φ. The constant saturation effect quantified by the s value can be explained by the constant charge distributed to the benzene ring. NBO analyses indicate that the through-resonance effects were induced through the electron transfer caused by two kinds of orbital interactions between the side chain and the benzene ring. The π–π* orbital interaction operates at maximum efficiency in the planar structure, and the σ–π* orbital interaction operates at maximum efficiency in the orthogonal structure. These orbital interactions are active at all φ; consequently, the anion cannot become an ideal σ0-reference system.


Article note

A collection of invited papers based on presentations at the 23rd IUPAC Conference on Physical Organic Chemistry (ICPOC-23), Sydney, Australia, 3–8 July 2016.


Acknowledgments

We would like to acknowledge the Organizing Committee of the 23rd IUPAC Conference on Physical Organic Chemistry (ICPOC23), who have put together an outstanding scientific program and given us the opportunity to present our research. KN wishes to acknowledge the Research Center for Computing and Multimedia Studies at Hosei University for its computational facilities. We are deeply grateful to Prof. Masaaki Mishima at Kyushu University for his support and encouragement.

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Published Online: 2017-06-09
Published in Print: 2017-10-26

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