Letter - spectral assignment Received: 24 January 2014

Revised: 22 August 2014

Accepted: 25 August 2014

Published online in Wiley Online Library: 23 October 2014

(wileyonlinelibrary.com) DOI 10.1002/mrc.4148

A QSPR correlation on the 13C NMR chemical shifts of bridge carbons for different series of aromatic Schiff bases Guanfan Chen,a,b,c* Xiangsi Wu,a,b,c Chenzhong Cao,a,b,c** Fengping Liu,a,b,c Rongjin Zenga,b,c and Wanqiang Liua,b,c

Introduction Nuclear magnetic resonance (NMR) spectroscopy has attracted immense attention because of playing an important role in not only determining molecular structures but also explaining reaction mechanisms, molecular dynamics, chemical equilibrium, etc.[1] With the advancement of NMR technology, there is more and more NMR experimental information obtained. Consequently, many efforts have been made to understand relationships between molecular structures and different kinds of NMR chemical shifts.[2–14] In investigations on 13C NMR of specific carbons for aromatic systems with a changing substituent, the chemical shift (δC) values are usually calculated with the single substituent parameter treatment or the dual substituent parameter treatment, [15] shown as Eqns (1) and (2), where σ, σ F (or σI) and σ R are the Hammett parameter, inductive parameter, and resonance parameter, respectively, and C is a constant. δC ¼ ρσ þ C δC ¼ ρI σ I ðorρF σ F Þ þ ρR σ R þ C

(1) (2)

When two substituents in aromatic systems change simultaneously, what will happen to the substituent effect on δC values of specific carbons? In Neuvonen’s studies on δC values of bridge carbons for para-disubstituted benzylidene anilines[7] (p-XBAY-p, shown in Scheme 1) and para-disubstituted phenyl benzoates, [6] Eqn (3) was recommended to correlate with the corresponding experimental dataset. Cao’s group synthesized successively a series of para-disubstituted cinnamyl anilines (p-XCAY-p)[16] and a series of para-disubstituted benzylidene N-(4-substituted styryl)anilines (p-XBSAY-p),[17] whose structures are shown in Scheme 1, and research results indicated that δC values of specific bridge carbons can be correlated well with Eqn (3). δC ¼ ρσ F ðXÞ þ ρσ R ðXÞ þ ρσ F ðYÞ þ ρσR ðYÞ þ C

(3)

172

On this basis, Cao et al. studied further the alteration of substituent effects on δC of different bridge carbons for p-XCAY-p[18] and on δC values of the same type of carbons for different series of aromatic Schiff bases.[19] Now, what is interesting for us is the regularity of

Magn. Reson. Chem. 2015, 53, 172–177

substituent effects on the chemical shifts of the previously mentioned two types of specific carbons. That is to say, what is the regularity of substituent effects on δC values of specific bridge carbons for different aromatic Schiff bases? Although the alteration of substituent effects was confirmed to associate with the distance between the substituent and the corresponding carbon, the forms of substituent parameters in two papers were different. In this paper, the connection between the strength of the substituent effect and the distance is further investigated, and it is helpful to understand the regularity of the substituent effect on δC values of specific bridge carbons for aromatic compounds.

Results and discussions The model establishment In the conventional chemistry theory, the strength of substituent inductive effect has long been considered to gradually decrease with chemical bonds. Cherkasov[20] ever recommended that the substituent inductive effect should change with the inverse square of the distance between the corresponding substituent and the reaction center, shown as Eqn (4), where σA is an overall empirical atomic value, and r is the distance between the corresponding atom of the substituent and the reaction center. However, for the strength of the substituent conjugative effect, it does not decrease by the length of the conjugated chain, but the charge signs of adjacent

* Correspondence to: Guanfan Chen, School of Chemistry and Chemical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China. E-mail: [email protected] **Correspondence to: Chenzhong Cao, School of Chemistry and Chemical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China. E-mail: [email protected] a School of Chemistry and Chemical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China b Key Laboratory of Theoretical Chemistry and Molecular Simulation of Ministry of Education, Hunan University of Science and Technology, Xiangtan, China c Hunan Provincial University Key Laboratory of QSAR/QSPR, Hunan University of Science and Technology, Xiangtan, China

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A QSPR correlation on the 13C NMR shifts for Schiff bases

Scheme 1. The structures of p-XBAY-p, p-XCAY-p and p-XBSAY-p.

atoms in conjugative system usually represent by alternations. Generally, an identification parameter, (1)m, is used to distinguish the charge signs of conjugative effects on adjacent atoms, where m expresses the bond number from the substituent to the corresponding atom. σ* ¼

n X σA

i

i¼1

r2i

(4)

As shown in Scheme 1, it is obvious that the distances between the marked carbons and substituents are variable. In studies of substituent effects on δC values of different bridge carbons for p-XCAY-p[18] and on δC values of the same type of carbons for different series of aromatic Schiff bases,[19] the inductive effects of substituents X and Y were confirmed consistently to be changed with the inverse square of the distance. However, the conclusions on the variations of the substituent conjugative effect were different. The key difference was whether the substituent parameter σR(X) should be considered to be changed with the inverse square of distance in the two papers. Therefore, the connection between the strength of the substituent effect and the distance is further studied, and the variation of substituent parameters must be made uniform. Firstly, in order to confirm the variation of the conjugative effect of substituent X, the δCðCC¼N Þ values of the previously mentioned kinds of aromatic Schiff base (p-XBAY-p, p-XCAY-p, and p-XBSAY-p) are correlated with adjusted or unadjusted σR(X), where the adjusted σR(X) is calculated with Eqn (4), where the σA is the conjugative parameter of substituent X. The corresponding correlation equations are shown in Table 1, where mX and mY values are the bond numbers from the substituents X or Y to the corresponding bridge carbon, respectively. Seen from the results of Eqns (5) and (6), it implies that the substituent parameter σ R(X) is hardly influenced by the distance between substituent X and the carbon CC¼N, which is consistent with the conventional chemistry theory. Why is the variation of the conjugative effect of substituent Y different from that of substituent X? It is all known that the π–π interaction is dominant in the conjugated system, and resonance

stabilization is always used to interpret the effects of substituents on conformations of stilbene-like species.[21] Although BA derivatives are noncoplanar, Burgi considered that the π–π interaction is still a main driving force on their conformations.[22] However, in Yu’s study,[23] he indicated that the nonbonded σ–σ interaction distorts BA derivatives away from their planar geometry, and the π–π interaction should not be the main driving force. Combining the fact that the N-terminal benzene ring is nonplanar with the bridge bond, but the C-terminal benzene ring is planar with the bridge bond for BA derivatives, we consider that for the δCðCC¼N Þ values, the C-terminal benzene ring is planar with the bridge bond in substituted BAs, where the π–π interaction is dominant, so the conjugative effect of substituent X follows the conventional chemistry theory; however, the N-terminal benzene ring is nonplanar with the bridge bond in substituted BAs, where the σ–σ interaction is dominant, so the conjugative effect of substituent Y decreases with the bond number, whose variation is similar to that of the inductive effect of substituent Y. Although Eqn (5) is suitable to correlate with δCðCC¼N Þ values of the previously mentioned aromatic Schiff bases, there are two disadvantages: (i) The coefficients in front of substituent parameters belong to different magnitudes, and it is easily misunderstood that the role of σR(X) is less than 1% those of other substituent parameters. (ii) In the common theory chemistry, when the bond number is beyond 3, the substituent inductive effect is generally considered to be very slight and can be ignored. For all investigated bridge carbons of compounds in Scheme 1, it is no doubt that the bond numbers between the substituents and the substituents and the corresponding carbon are beyond 3. The relative distance was recommended to scale the distance between substituents and the marked carbons in the investigation of δC values for p-XCAY-p,[18] i.e. the distance from the substituent to the nearest carbon acted as a reference, and then, all distance was processed to become the relative distance. For those compounds in Scheme 1, the shortest distances between substituents X and Y to the bridge carbon are in p-XBAY-p, and their bond numbers are 5 and 6, respectively, which act as the reference (m(ref)), and then, distances between substituents and bridge carbons in model compounds are processed to become the relative distance, m(rel), where mðrelÞ ¼ mmðrefÞ, and m is the bond number from the substituent to the corresponding bridge carbon. Thus, the adjusted substituent effect is expressed as Eqn (7).   σ F ðor σ R ðYÞÞ δcðcc¼N Þ σ ′F or σ ′R ðYÞ ¼ m2 ðrelÞ

(7)

For example, in p-XBSAY-p, the relative distance from substituent X to carbon CC¼N is 1, where m(rel) = 55 ¼ 1, while the relative distance between substituent Y to carbon CC¼N is 2, where m(rel) = 12 6 ¼ 2. In p-XBAY-p, both m(rel) values of substituents X and Y are 1. For all previously mentioned compounds, the

Table 1. The correlation equations between theδCðCC¼N Þ values and the adjusted or unadjusted σ R(X) for compounds p-XBAY-p, p-XCAY-p, and p-XBSAY-p (5)[19]

δCðCC¼N Þ ¼ 28:87 þ 1:18δC:parent  4:45 m12 σ F ðXÞ  1:07 m12 σ R ðXÞ þ 2:80 m12 σ F ðYÞ þ 4:99 m12 σ R ðYÞ X X Y Y R = 0.9895, s = 0.35, n = 181, F = 1638

(6)

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173

δCðCC¼N Þ ¼ 13:29 þ 1:08δC;parent  110:6 m12 σ F ðXÞ  1:00σ R ðX Þ þ 101:96 m12 σ F ðYÞ þ 179:25 m12 σ R ðYÞ X Y Y R = 0.9909, s = 0.33, n = 181, F = 1892

G. Chen et al. relative distances, m(rel), are not beyond 3. With the adjusted parameters σ′F and σ′R(Y), a new correlation equation is obtained. δCðCC¼N Þ ¼ 13:29 þ 1:08δC;parent  4:43 σ′F ðXÞ  1:00σ R ðX Þ þ2:83 σ ′F ðY Þ þ 4:98 σ ′R ðYÞ R ¼ 0:9909; s ¼ 0:33; n ¼ 181; F ¼ 1892

(8)

It is remarkable that the coefficients in front of substituent parameters all belong to the same magnitude in Eqn (8), so it is not misunderstood that the relative contribution of σR(X) is much less than those of other substituent parameters. In order to distinguish the signs of substituent effect on δCðCC¼N Þ , δCðCα Þ , and δCðCβ Þ for compounds p-XCAY-p, an identification item, (1)m, was introduced into the adjusted parameters σ F and σ R , shown as Eqn (9).   σ F ðor σ R Þ (9) σ F or σ R ¼ ð1Þm  m2 ðrelÞ

[18]

Now, what we want to know is if the substituent effects on δC of the same bridge carbons for the previously mentioned aromatic compounds are also scaled by σ F and σ R . When parameters σ′F and σ′R(Y) in Eqn (8) are replaced with σ F and σ R (Y), and σR(X) is replaced with (1)mσ R(X), the correlation equation is obtained, shown as the Eqn (10). δCðCC-N Þ ¼ 13:29 þ 1:08 δC;parent þ 4:43 σ F ðxÞ þ1:00ð1Þm σ R ðXÞþ 2:83 σ F ðYÞ þ 4:98 σ R ðYÞ R ¼ 0:9909; s ¼ 0:33; n ¼ 181; F ¼ 1892

compounds, δCðCC¼N Þ values are also suitable to be correlated with the adjusted parameters σ F and σ R . Secondly, according to the previously mentioned inference about the conjugative effects of substituents X and Y on δCðCC¼N Þ values, we consider that it should be no exception to δCðCα Þ and δCðCβ Þ for compounds p-XCAY-p. In order to confirm the variation

of the conjugative effect of substituent X on δCðCβ Þ , δCðCα Þ , and δCðCC¼N Þ values for compounds p-XCAY-p, the δC values of p-XCAY-p are correlated with σ R and (1)mσ R(X), respectively, and the corresponding correlation equations are shown in Table 2. Analyzed from the results of Eqns (11) and Eqns (12) it is found that the substituent parameter σ R(X) is hardly influenced by the distance between substituent X and the carbon Cα and Cβ too. The correlation results of Eqns (10) and (11) show that variation of all substituent effects on different bridge carbons in the same compounds and on the same type of bridge carbons in different compounds can be scaled with the same adjusted parameters. Next, out of 280 δC values in the pieces of literature Neuvonen et al.,[7] Chen et al.,[16] and Fang et al.,[17] they are randomly divided into the training set and the cross-validation set according to the method of Bosque.[24] Some XBAOMe, XCAMe and XBNBACN (X = MeO, H, Cl, and NO2) are selected randomly for the cross-validation set, and δC values of the remaining compounds comprise the training set. With δC,parent, σ F , σ R , and (1)mσ R(X), the δC values of different bridge carbons for the training set are correlated, and a correlation equation is obtained. δC ¼ 1:50 þ 0:99 δC;parent þ 3:84 σ F ðXÞ þ 2:43ð1Þm σ R ðXÞ

(10)

In comparison with results of Eqns (8) and (10), there is only a subtle difference between them, i.e. the coefficient signs in front of σ F (X) and (1)mσR(X) are opposite to those of σ′F(X) and σR(X) because of the identification parameter. The correlation result of Eqn (10) shows that for the same type of bridge carbons in different

þ3:27 σ F ðYÞ þ 4:29ðYÞ R ¼ 0:9972; s ¼ 0:97; n ¼ 267; F ¼ 9148

(13)

Although the correlation result of Eqn (13) is good, there is a large standard deviation. In many previous types of m

Table 2. The correlation equations between the δC values and the adjusted or (1) σR(X) for p-XCAY-p δC ¼ 2:03 þ 0:98 δC;parent þ 4:52 σFðrelÞ ðXÞ þ 3:20ð-1Þm σR ðXÞ þ 3:40 σFðrelÞ ðYÞ þ 3:92 σRðverÞ ðYÞ R = 0.9972, s = 1.07, n = 159, F = 5345

(11)

δC ¼ -1:25 þ 1:00 δC;parent þ 4:87 σFðrelÞ ðXÞ þ 3:88 σRðverÞ ðXÞ þ 3:15 σFðrelÞ ðYÞ þ 3:98 σRðverÞ ðYÞ

(12) [18]

R ¼ 0:9970; s ¼ 1:10; n ¼ 159; F ¼ 5052

174

Scheme 2. The structures of p-XSBAY-p, p-XBBAY-p and p-XBNBAY-p.

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Magn. Reson. Chem. 2015, 53, 172–177

A QSPR correlation on the 13C NMR shifts for Schiff bases Table 3. The experimental δC, calculated δC, and residuals of the cross-validation set C

Compound

δexp C

δcal C

CC = N

p-MeOBAOMe-p HBAOMe-p p-ClBAOMe-p p-NO2BAOMe-p p-MeOCAMe-p HCAMe-p p-MeOCAMe-p HCAMe-p p-MeOCAMe-p HCAMe-p

157.88 158.41 156.68 154.76 161.07 160.75 143.32 143.52 126.55 128.64

157.79 158.32 157.03 155.77 161.45 160.43 143.39 143.42 127.40 128.83

Cβ Cα

ΔδC 0.09 0.09 0.35 1.01 0.38 0.32 0.07 0.10 0.85 0.19

δexp C

δcal C

CC = N

p-ClCAMe-p p-NO2CAMe-p p-MeOBASBCN-p HBASBCN-p p-ClBASBCN-p p-NO2BASBCN-p p-ClCAMe-p p-NO2CAMe-p p-ClCAMe-p p-NO2CAMe-p

160.29 159.34 159.68 160.40 158.75 157.25 141.88 140.04 129.15 132.64

160.71 159.73 159.49 159.36 158.11 156.25 142.11 140.33 129.59 131.68



R

Here,ΔσF*2 = (σF (X) σF (Y))2, andΔσ*R 2 = ((1)mσR(X) σR (Y))2. When the interaction between substituents is considered further, a new correlation equation is obtained. δC ¼ 2:54 þ 0:98 δC:parent þ 4:83 σF ðXÞ þ 3:28ð-1Þm σR ðXÞ þ2:53 σF ðYÞ þ 3:16 σR ðYÞ þ 1:07ΔσF*2 -1:31ΔσR*2 R ¼ 0:9989; s ¼ 0:62; n ¼ 267; F ¼ 16 204

Compound



work,[13,16–19,25,26] it is confirmed that there is an interaction between substituents, and it cannot be ignored. In the investigation of δC values for p-XCAY-p,[18] the substituent interaction item, Δσ 2 was recommended to be divided into two parts: Δσ *2 and Δσ *2 . F

C

(14)

ΔδC 0.42 0.39 0.19 1.04 0.64 1.00 0.23 0.29 0.44 0.96

it is noted that the adjusted substituent parameters include the identification parameter, (1)m, and for the same carbon, when the m value between a substituent and the marked carbon is odd, the m value between the other substituent and the carbon is even. Therefore, for the same carbons, the substituents X and Y in the previously mentioned aromatic Schiff base have actually an opposite effect on δC values. No matter of inductive or resonance effect of substituent X, electron-withdrawing groups (EWGs) decrease the δC values of carbon CC¼N and carbon Cβ, while electron-donating groups (EDGs) behave oppositely. In contrast, for substituent Y, the EWGs increase the δC values, while the EDGs decrease δC values. However, substituent effects on δC values of carbon Cα are opposite to those on δC values of carbon CC¼N and carbon Cβ. Moreover, the coefficient in front of the substituent interaction item Δσ*2 is positive, F

Compared with the correlation result of the Eqn (13), that of Eqn (14) is improved obviously. The correlation coefficient R of Eqn (14) is raised to 0.9989 and F value to 16 204, and its stancal dard deviation s is only 0.62 ppm. The δexp C , δC , and residuals of the training set are given in Table S2 in Supporting Information. With Eqn (14), δC values of the cross-validation set are calculated, cal and the corresponding δexp C , δC , and residuals are listed in Table 3. The plot of the calculated values with the experimental ones of all bridge carbons for the previously mentioned compounds is shown in Fig. 1. In previous investigation results of aromatic Schiff base,[7,16,17] the coefficients in front of a substituent in the C-terminal benzene ring are opposite to those in front of the substituent in the N-terminal benzene ring. However, the coefficients in front of inductive effect parameters and conjugative effect parameters are positive in Eqn (14), which seems to be in conflict with the previous results. In fact,

Magn. Reson. Chem. 2015, 53, 172–177

The reliability and application of Eqn (14) for different sorts of aromatic Schiff bases The reliability of Eqn (14) for some para-disubstituted nonheterocyclic aromatic Schiff bases Further, to verify the reliability of Eqn(14) in this work, δC values of bridge carbons for five groups of Schiff bases are collected, including p-XCACF3-p(X = Me2N, MeO, Me, Cl, and NO2),[18] some p-XBSAYs-p, para-disubstituted (4-styryl) benzylidene anilines (p-XSBAY-p, shown in Scheme 2),[19] para-disubstituted (4-benzyl)benzylidene anilines (p-XBBAY-p, shown in Scheme 2),[19] and para-disubstituted benzylidene N-(4-benzyl)anilines (p-XBNBAY-p, shown in Scheme 2).[19]The δC values of bridge carbons in these compounds are predicted, cal and the δexp C , δC , and residuals are given in Tables S3 and S4 in Supporting Information. The predicted results in Tables S3 and S4 are all in good agreement with the experimental values, and the plot of the calculated values with the experimental ones is shown in Fig. 1. The mean standard deviation of experimental data in Tables S3 and S4 is 0.51 ppm, which is less than the standard value of deviation (0.62 ppm) in the literature[18] and larger than that (0.12 ppm) in the literature.[19] It indicates the Eqn (14) can be used to predict the different bridge carbons in different nonheterocyclic aromatic Schiff bases. It is remarkable that the used δC,parent values of XSBAY, XBBAY, and XBNBAY are 159.81, 159.91, and 160.19 ppm, respectively, which are δCðCC¼N Þ values of the corresponding parent compounds.

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175

Figure 1. Plot of the calculated versus the experiment values of bridge carbons for the training, cross-validation and prediction set δC values using Eqn (14).

and that of ΔσR*2 is negative. It indicated that the substituent interaction of the inductive effect and conjugative effect has an opposite effect on δC values.

G. Chen et al.

Scheme 3. The structures of three sorts of heterocyclic aromatic Schiff bases.

The application of Eqn (14) for some para-disubstituted heterocyclic aromatic Schiff bases For para-substituted nonheterocyclic aromatic Schiff bases, those δC values of bridge carbons can be precisely predicted. Can Eqn (14) predict the corresponding δC values for paradisubstituted heterocyclic aromatic Schiff bases? Here, δCðCC¼N Þ values for N-(phenyl substituted) pyridine-4-aldimines (PP4AY-p),[4] N-(phenyl substituted) pyridine-3-aldimines (PP3AY-p),[27] and N-(phenyl substituted) pyridine-2-aldimines (PP2AY-p)[27] are collected, whose structures are shown in Scheme 3. The δC values of bridge carbons in these compounds are precal dicted, and the δexp C , δC , and residuals are given in Table S5 in Supporting Information. The standard deviation of experimental data in Table S5 is 0.35 ppm, which implies that the Eqn (14) could also be used to predict the bridge carbons in different heterocyclic aromatic Schiff bases, and the plot of the calculated values with the experimental ones is shown in Fig. 1. It is notable that δC,parent values are 157.67 (PP4AH), 156.80 (PP3AH), and 160.33 ppm (PP2AH), respectively. The application of Eqn (14) to meta-substituted benzylidene anilines

176

The previously mentioned results show that the Eqn (14) can be used to predict the chemical shifts of corresponding bridge carbons in para-substituted Schiff bases. For meta-substituted Schiff bases, can Eqn (14) predict precisely the chemical shifts of corresponding bridge carbons too? We noted that, for a para-substituent, its electronic effect can actually transfer to the designated carbons with two symmetrical routes through the aromatic ring, but for a meta-substituent, there are two asymmetrical routes. In this case, we consider that the m 2 value should be an arithmetic mean, i.e. m ¼ m1 þm , where m1 2 and m2 are the bond numbers from the substituent to the corresponding carbon with different routes through the aromatic ring. For para-substituted compounds, m1 and m2 are equal, and then, m can be simply regarded as the bond number from the substituent to the corresponding carbon. For meta-substituted compounds, although m1 and m2 are not equal, the arithmetic mean is the same to the m value of the para-substituted compounds. For example, in m-MeBAOMe-p, m1 and m2 of substituent m-Me are 4 and 6, and m and m(ref) are 5 and 1, respectively, which is the same to m and m(ref) values of p-Me. That is to say, whether for meta-substituted or for para-substituted compounds with the same parent, the m and m(rel) are the same. This phenomenon is consistent with the result of literature.[13] Using the calculating method, we easily obtain the adjusted meta-substituent parameter. With Eqn (14), we predict the δC values of bridge carbons in some benzylidene anilines with a metasubstituent, [13,28] and the standard deviation of experimental data in Table S6 is 0.30 ppm. The predicted results in Table S6 are also all in good agreement with the experimental values, and the plot of the calculated values with the experimental ones is shown in Fig. 1 The predicted results listed in Tables S3, S4, S5, and S6 show that Eqn (14) is suitable to predict the δC values of bridge carbons for

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nonheterocyclic or heterocyclic aromatic Schiff bases and for para-substituted or meta-substituted aromatic Schiff bases. The standard deviation of 79 samples of the prediction set is 0.53 ppm, and the number of predicted δC values whose calculated errors are ≤0.5 ppm is 44 (55.7% of the total), ≤1.0 ppm is 67 (84.8%), and ≤1.5 ppm is 79 (100%).

Conclusions The 13C NMR chemical shift values can be expressed by a heptaparameter correlation equation for different kinds of aromatic Schiff base. The seven parameters include the δC values of the parent compounds, the adjusted conjugative effects, the adjusted inductive effects, and the substituent cross-interaction effects, where the substituent parameters are adjusted with the distances between substituents and the corresponding carbons. The reliability of the obtained equation is further confirmed with 20 samples of cross-validation set δC values and 79 samples of prediction set δC values. In Eqn (4), the coefficients in front of inductive effect parameters and conjugative effect parameters are positive because of the identification parameter, but substituent X in the C-terminal benzene ring and Y in N-terminal benzene ring actually have an opposite effect on δC values of all marked bridge carbons. For carbon CC¼N and carbon Cβ, when the X substituents in the C-terminal benzene ring are EDGs, their substituent effects increase δC values; while the substituent effects of EWGs decrease δC values. When the Y substituents in the N-terminal benzene ring are EDGs, their substituent effects decrease δC values, while the substituent effects of EWGs increase δC values. Moreover yet, substituent effects on δC values of carbon Cα are opposite to those on δC values of carbon CC¼N and carbon Cβ. Moreover, the substituent cross-interaction effect is verified to be an important and a factor not being ignored and can be scaled with parameters Δσ*2 and Δσ*2 . F

R

Acknowledgements This work is supported by the National Natural Science Foundation of China (No. 21202043, 21272063, and 21172065) and the Scientific Research Fund of the Hunan Provincial Education Department (11K024).

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A QSPR correlation on the 13C NMR chemical shifts of bridge carbons for different series of aromatic Schiff bases.

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