Toward the Physical Interpretation of Inductive and Resonance Substituent Effects and Reexamination Based on Quantum Chemical Modeling.

An application of a charge of the substituent active region concept to 1-Y,4-X-disubstituted derivatives of bicyclo[2.2.2]octane (BCO) [where Y = NO2, COOH, OH, and NH2 and X = NMe2, NH2, OH, OMe, Me, H, F, Cl, CF3, CN, CHO, COMe, CONH2, COOH, NO2, and NO] provides a quantitative information on the inductive component of the substituent effect (SE). It is shown that the effect is highly additive but dependent on the kind of substituents. An application of the SE stabilization energy characteristics to 1,4-disubstituted derivatives of BCO and benzene allows the definition of inductive and resonance contributions to the overall SE. Good agreements with empirical approaches are found. All calculations have been carried out by means of the B3LYP/6-311++G(d,p) method.

Introduction

The substituent effect (SE) is one of the most fruitful and effective concepts in organic chemistry and related fields of research. According to ISI Web of Science,[1] everyday there appears at least one paper with this term in the title, keywords, or in the abstract. An introduction of substituent constants (SCs) by Hammett[2,3] begins the development of ideas of quantitative description of the SE. From the beginning, it has been found that SCs based on the acid–base equilibria constants of substituted benzoic acids are not of universal use.[4] For reactions with negatively and positively charged reaction sites, they had to be modified.[5] The explanation of these deviations from the original Hammett SCs was formulated by Taft and Lewis.[6,7] They assumed that the SE is composed of two kinds of interactions: inductive and resonance. A separation of them was based on the empirical hypothesis that SCs in the para position, σp, contain resonance and inductive contributions in comparable amounts,[8] as presented in eq .

An application of the acid–base equilibrium constants of 4-substituted derivatives of bicyclo[2.2.2]octane-1-carboxylic acids allowed the definition of inductive SCs, σI.[9] Then, by the use of eq , one can easily estimate σR. Additionally, it was assumed that the distance between X in position 4 in bicyclo[2.2.2]octane (BCO) and in p-substituted benzoic acid derivatives is very similar, and hence, the inductive effect is similar in both reference reaction series. A similar procedure was applied by Swain and Lupton[10] who generated a table of SCs for ∼200 substituents, named F (for inductive/field) and R (for resonance), but not presented in the scale of the original SC σ. The F and R values are now accessible in the review[5] and normalized to this scale.

In view of the above information, the classical Hammett equation, defined originally for kinetic and equilibria data, may be modified to the form of 2.[8] Actually, lg K(k) is often replaced by various physicochemical properties.

Assuming approximate constant values for σI, eq may be applied for the estimation of resonance constants for other kinds of SCs such as σ+ and σ– working for reaction series with positively and negatively charged reaction sites, respectively.[5] In all these cases, the final results depend on a particular reference reaction and for systems in which interactions defining the SE differ from these reactions, the estimation of resonance SCs is not well-defined. It should also be mentioned that apart from inductive (field) and resonance contributions, properties such as polarization and electronegativity have also been taken into account.[11]

Till now, SCs are of a fundamental importance, and they are applied in countless studies in organic chemistry and related fields.[5,12−14] In last decades, for describing SEs, many approaches have been proposed in which various kinds of quantum chemistry models are applied (see below). However, almost always the obtained data have been confronted with the Hammett SCs or some of their modifications. For example, successful correlations have been found between molecular electrostatic potential of substituted benzene (BEN) and SCs[15−17] or between electrostatic potential at a particular nucleus and resonance and inductive SCs σR and σI, respectively.[18] The molecular electrostatic potential was successfully applied for the assessment of the inductive effect[19] as well as for the characterization of the resonance effect.[20] Moreover, in many cases, the application of electrostatic potentials at the ring carbon atoms or at atoms of a reaction site revealed their good correlation with SCs.[21−23] Recently, some quantification and classification of the SE from the view point of molecular electrostatic potential were published.[24] SEs were also characterized using the calculated gas-phase acidities of benzoic acid, phenol, and bicyclo[2,2,2]octane derivatives.[25−27] The energy decomposition analysis[28] (EDA) was also used successfully in the SE studies. It was shown that in the meta- and para-substituted benzylic cations and anions, the strength of the π conjugation (EDA component) correlates well with SCs.[29] The other very important issue of SE is its energetic characteristics, named SESE (substituent effect stabilization energy), obtained through the use of the isodesmic or homodesmotic reactions approach.[30−32] It was demonstrated in many cases that SESE values correlate well with SCs.[33−35] Recently, it was documented that the sum of charges at the substituent and the ipso carbon atom, named cSAR (charge of the substituent active region),[33−38] also correlates well with the Hammett SCs. Moreover, it is very important to note that the values of cSAR(X) calculated by means of various assessments of atomic charge are mutually well-correlated.[39]

The motivation of this paper is to present the inductive and resonance SEs in terms of physically defined descriptors as above-mentioned SESE and cSAR characteristics. They describe independently the energetic effects of the interaction between X and Y in X-R-Y reaction series as well as changes in the electronic structure. For this purpose, 1,4-disubsituted derivatives of BCO and BEN are chosen. As shown in Scheme , two types of fixed groups are considered: (i) electron-accepting (EA) NO2 and COOH and (ii) electron-donating (ED) OH and NH2, as well as a wide range of substituents (X) with different electronic properties.

Scheme 1

(a) 4-X-BCO-1-Y (X-BCO-Y) and (b) para-X,Y-BEN (X-BEN-Y) Derivatives, X = NMe2, NH2, OH, OMe, Me, H, F, Cl, CF3, CN, CHO, COMe, CONH2, COOH, NO2, and NO and Y = NO2, COOH, OH, and NH2

Results and Discussion

For clarity, this section is divided into three subsections. Results and Discussion dealing with pure inductive effects are presented in the first two parts. They are based on the analysis of the changes in the electronic structure of 1,4-disubstituted X-BCO-Y derivatives. Our previous research on 1-X-BCO systems[40] has already confirmed the usefulness of the cSAR concept for this purpose. The presence of a second substituent allows both a deeper analysis of the inductive effect (first part) as well as its additivity (second part). The last (third) subsection is devoted to the inductive and resonance SEs working together. Hence, both BCO and BEN disubstituted series (derivatives) have to be investigated (the partial results of the latter systems have recently been published[35,41−43]). For this purpose, the energetic characteristic of the SE (SESE) is best suited because in this way all changes in molecules are taken into account.

Inductive Substituent Effects

As shown very recently, dependences of cSAR(CH) or cSAR(CH2) on cSAR(X) for monosubstituted 1-X-BCO systems are linear, and moreover, their slopes fulfill the ideal 1:2:3 ratio for groups in the 4, 3, and 2 positions.[40] This is a typical relation assumed for the inductive effect.[44] The following question may be posed: how cSAR(CH2) is affected by substituents X in 1,4-disubstituted BCO derivatives with a fixed functional group Y in position 1 (4-X-BCO-1-Y). It has been found that linear equations can be used to describe the dependences of cSAR(CH2) on cSAR(X) or cSAR(Y) in all studied cases.

Let us begin with an effect of substituent X on the vicinal CH2 fragment. As shown in Figure , the relations of cSAR(CH2)[3] versus cSAR(X) have negative slopes which are ∼−0.185 with R2 > 0.94 for all Y-series. This means that the SE of X on vicinal CH2 is almost the same regardless of the type of the second substituent—the fixed group Y. For a more distant CH2 fragment but closer to a fixed group Y, the slopes are less steep and are in the range between −0.109 and −0.116 with R2 > 0.898 (see Figure S1). Thus, the inductive SE of X becomes significantly weaker. For monosubstituted BCO derivatives[40] (calculations performed using the same method), the values of the slopes were found to be equal to −0.190 for vicinal and −0.124 for more distant CH2 groups with respect to X. A comparison of the above given slope values reveals a similar weakening of the inductive SE of the substituent X by the second substituent—the fixed group Y (NO2, COOH, OH, and NH2). With respect to Y = H series, this weakening is greater for more distant CH2 fragments than those closer to X; in the latter case, this is ca. 2.5%, whereas for the former one: 11.7 and 6.9% for EA and ED Y, respectively.

Figure 1

Dependence of cSAR(CH2)[3] (near X) on cSAR(X) for 4-X-BCO-1-Y derivatives.

Thus, let us look at similar relationships but from the perspective of a fixed group. In this case, the cSAR(CH2) variation is considered to be influenced by Y whose properties are in turn dependent on the SE from X. The dependences of cSAR(CH2) on cSAR(Y) are also characteristic and, as expected, with positive slope values. For the CH2 group closer to Y[(CH2)[2]], their slopes are in the range of 0.924 and 1.311, with R2 > 0.945 (Figure ). However, two groups of Y series can be distinguished: for the EA Y (NO2 and COOH), the average value of the slopes is 0.950, whereas the average value is 1.265 for the ED one (Y = OH and NH2).

Figure 2

Dependence of cSAR(CH2)[2] (near Y) on cSAR(Y) for 4-X-BCO-1-Y derivatives.

The dependences of cSAR(CH2) in positions closer to X[(CH2)[3]] on cSAR(Y) characterize slopes in the range from 1.427 to 1.819 and R2 > 0.768 (Figure S2). Again, two groups of Y series should be noted. Average values of the slopes are 1.440 and 1.765 for EA and ED Y, respectively. The greater slope values than that found for cSAR(CH2)[2] versus cSAR(Y) relations confirm stronger SE from X. For Y = H series (monosubstituted BCO derivatives),[40] the slopes of cSAR(CH2)[2] or cSAR(CH2)[3] versus cSAR(H) relations are equal to 2.089 and 2.865, respectively. Therefore, for EA/ED Y, the obtained slopes are significantly smaller than that found for monosubstituted BCO.

The strength of intramolecular interactions between fixed Y groups and substituents X can be characterized by dependences of cSAR(Y) on cSAR(X), as shown in Figure . Their slopes are in the range between −0.088 and −0.118 (with R2 > 0.923 for all Y’s), which suggests weak interactions between X and Y. However, stronger interactions are for Y = NO2 and COOH with the mean slope value −0.115 than that for Y = OH and NH2 with the mean value −0.091, whereas for Y = H, the slope amounts −0.059.[40] Note that for cSAR(Y) versus cSAR(X) in disubstituted BEN derivatives, the slope is ∼−0.35,[35,41−43] that is, approximately 3 times the stronger interactions. This point will be discussed in more detail later.

Figure 3

Dependence of cSAR(Y) vs cSAR(X) for 1,4-disubstituted BCO derivatives.

The analysis of the dependence of cSAR(FRAG) (see Scheme ) on cSAR(X) reveals rather low dependences (slopes between −0.886 and −0.910) but a very high correlation (R2 > 0.997, see Table S3). This confirms weak changes in charges of the BCO fragment and again weaker ones for ED fixed groups.

Additivity of the Inductive Effect

The question of additivity of the inductive effect is of fundamental importance. This was studied for disubstituted BCO derivatives by the use of the appropriate cSAR(CH2) data in monosubstituted BCO and X-BCO-Y systems. Consider an example: for NH2-BCO-NO2 (Y = NO2 and X = NH2), its cSAR(CH2)[3] (equal to 0.0109, Table S2) should be compared with the sum of cSAR(CH2)[3] in BCO-NO2 (0.0167) and cSAR(CH2)[2] in BCO-NH2 (−0.0068) (see Table S4), as presented in Scheme . Therefore, the additivity parameter, δ, in our example reads as

Scheme 2

Comparison of cSAR(CH2)[2] and cSAR(CH2)[3] in Monosubstituted BCO and X-BCO-Y Systems

When we look at the values of δ for all studied systems (Table S6 in the Supporting Information), we can observe that the additivity parameter (δ values) decreases in line with a decrease of EA (and increase of ED) properties of substituents. This means that the additivity of inductive effects operating in X-BCO-Y systems is better realized for EA fixed groups (NO2 and COOH) than for the ED ones (OH and NH2) (Table S6 in the Supporting Information). A direct inspection of the data in Table S6 discloses that numerical characteristics of additivity, δ, are very small numbers, at the level of 10–3 electron. When such small numbers are taken for calculating % value of additivity, then for many individual cases, this percentage can become very large—even up to ∼1000% (Tables S7 and S8). For this purpose, instead of an application of individual values of cSAR(CH2)[2] and cSAR(CH2)[3] in monosubstituted BCO and X-BCO-Y systems, for calculating additivity descriptor δ in terms of percentage, only the averaged values for all substituents were taken from Tables S2, S5, and S6. Table presents the obtained data and the final results—the percentage of the additivity. A very interesting problem is worth a deeper discussion: there are substantial differences between averaged percentages of the additivity, δ/cSAR(CH2), in positions 2 and 3 as well as for the EA and ED properties of the fixed groups, Y. Hence, the additivity parameter δ for EA groups (NO2 and COOH) is smaller than that for ED groups (OH and NH2). Moreover, the additivity is better disclosed for CH2 closer to the substituents X than that closer to the fixed group.

Table 1

Mean Values of cSAR(CH2) and the Additivity Parameter δ and the Percentage of Additivity for 4-X-BCO-Y Series

	(CH2)[2]				(CH2)[3]
Y	NO2	COOH	OH	NH2	NO2	COOH	OH	NH2
cSAR(CH2)·102	2.24	1.60	0.56	0.16	2.26	1.35	1.15	0.79
δ·102	0.12	0.13	0.17	0.16	0.04	0.16	0.16	0.19
δ/cSAR(CH2)/%	5.3	8.1	30.3	100	1.8	11.8	13.9	24.1

One more problem worth a discussion is the difference between the averaged values of cSAR(CH2) in positions 2 and 3 for Y EA and ED fixed groups. In the first case, the sum of cSAR(CH2)[3] for NO2 and COOH for all X is equal to 0.0361, whereas that for NH2 and OH is 0.0194 (Table S2 in the Supporting Information). As could be expected, CH2 groups lose more negative charge because of the interactions with EA groups than with the ED ones. A similar effect is observed for the CH2 group near Y, with the appropriate values 0.0384 and 0.0105 (Table S2 in the Supporting Information). A very similar effect was observed for substituted methyl—the sEDA descriptor was decreasing with a decrease of EA (and then increase of ED) properties of substituents.[45]

Inductive and Resonance Effects Working Together

As presented in the previous subsection, the inductive SE is realized in aliphatic, that is, sigma-electron systems. The situation is different in pi-electron systems, where apart from the inductive effects, the resonance effects are also present. For illustrating these differences, SESE values for all substituents X estimated for X-BCO-Y and X-BEN-Y systems are presented in Table . Approximately, the differences in SESE(X) for BEN and BCO series, ΔSESE, for a given Y may be interpreted as a result of the resonance effect for a particular X-BEN-Y system. It is worth to emphasize that (i) for different Ys, both BEN and BCO derivatives have different SESE(X) values, and (ii) SESEBEN values are mostly greater (as absolute values) than SESEBCO and the only exceptions are X = F and Cl. Furthermore, in BEN series, the greatest SESE values (as absolute values) are for X and Y with strong EA or ED properties, and stabilization is observed when Y and X are of opposite EA/ED properties. Moreover, besides the case of para-NMe2-BCO-COOH, SESEs for BCO series have negative values always. This indicates that inductive interactions between X and Y in X-BCO-Y series decrease the stability of the systems in comparison with separated monosubstituted BCO derivatives. The strongest destabilization is observed for the cases when both X and Y are EA substituents. This is not the case for para-substituted X-BEN-Y derivatives where SESE values are positive when Y and X are of opposite electron properties. The variabilities of SESE values of BCO and BEN series estimated by ratios of estimated standard deviation (ESD) values are 0.345 (Y = NO2), 0.224 (COOH), 0.214 (OH), and 0.067 (NH2). It is important to note that ESD for BEN series changes between 1.45 and 2.41, whereas that for BCO series changes between 0.15 and 0.83. Interestingly, the variability for BCO series decreases with an increase of the ED properties of Y.

Table 2

Values of SESE (in kcal/mol) for 1,4-Disubstituted BEN (X-BEN-Y) and BCO Derivatives (X-BCO-Y) and Their Differences Δa

	NO2			COOH			OH			NH2
X	BEN	BCO	Δ	BEN	BCO	Δ	BEN	BCO	Δ	BEN	BCO	Δ
NO	–3.46	–1.91	–1.56	–1.90	–0.68	–1.22	2.08	–0.73	2.82	4.17	–0.36	4.54
NO2	–4.01	–2.77	–1.24	–2.08	–1.07	–1.01	1.26	–1.08	2.35	3.17	–0.54	3.71
CN	–3.12	–2.38	–0.75	–1.58	–1.00	–0.58	0.86	–0.82	1.68	2.25	–0.40	2.64
CF3	–2.58	–1.77	–0.80	–1.47	–0.64	–0.83	0.64	–0.67	1.30	1.56	–0.28	1.84
COMe	–1.72	–1.03	–0.69	–1.02	–0.26	–0.76	1.32	–0.31	1.63	2.30	–0.12	2.42
COOH	–2.08	–1.07	–1.01	–1.27	–0.37	–0.90	1.33	–0.43	1.76	2.45	–0.21	2.66
CHO	–2.46	–1.38	–1.09	–1.43	–0.48	–0.95	1.48	–0.48	1.96	2.80	–0.27	3.07
CONH2	–1.45	–0.96	–0.49	–0.80	–0.24	–0.56	0.88	–0.26	1.14	1.53	–0.29	1.83
Cl	–1.09	–1.90	0.81	–0.29	–0.79	0.50	–0.68	–0.80	0.12	–0.27	–0.40	0.13
F	–0.77	–1.87	1.09	0.01	–0.76	0.77	–1.35	–0.88	–0.47	–1.19	–0.48	–0.71
H	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
Me	0.87	–0.06	0.93	0.58	–0.01	0.59	–0.49	–0.12	–0.37	–0.65	–0.07	–0.58
OMe	1.74	–0.75	2.49	1.47	–0.25	1.72	–1.77	–0.45	–1.32	–2.05	–0.30	–1.76
OH	1.27	–1.08	2.35	1.33	–0.43	1.76	–1.85	–0.56	–1.29	–2.14	–0.30	–1.84
NH2	3.17	–0.54	3.71	2.45	–0.21	2.66	–2.14	–0.30	–1.84	–2.57	–0.20	–2.37
NMe2	4.23	–0.15	4.38	2.99	0.09	2.90	–2.05	–0.18	–1.87	–2.56	–0.09	–2.47
average	–0.72	–1.23	0.51	–0.19	–0.44	0.26	–0.03	–0.50	0.47	0.55	–0.27	0.82
ESD	2.41	0.83	1.85	1.56	0.35	1.36	1.45	0.31	1.55	2.24	0.15	2.29
range	8.24	2.77	5.94	5.07	1.16	4.12	4.22	1.08	4.68	6.74	0.54	7.01

Δ = ΔSESE = SESEBEN – SESEBCO; ESD—estimated standard deviation.

When COOH series are chosen as a reference (SCs were obtained based on the properties of the carboxylic group in benzoic acids and BCO-COOH derivatives),[2,9] then the resonance contribution to SEs and ΔSESE for NO2, OH, and NH2 systems plotted versus ΔSESECOOH results in well-correlated lines with R2 > 0.900 (Figure ). Important to note that for the NO2 group, the slope is positive (and has high R2 = 0.995), which can be explained by similar properties of the fixed groups (NO2 and COOH are both EA groups). In the case of ED functional groups, OH and NH2, the slopes are negative and the precision of regression lines is slightly lower with R2 equal to 0.93 and 0.90, respectively.

Figure 4

Dependence of ΔSESENO vs ΔSESECOOH for disubstituted BEN and BCO derivatives (a). Plots for X EA and ED are separated (b); ΔSESE in kcal/mol.

However, the scatter plot (the distribution of the points) for the latter series suggests a splitting of the substituents into two groups. If the regressions for Y = OH and NH2 series are done separately for EA and ED substituents, it appears that the slopes for EA substituents are −3.39 (Y = NH2) and −2.14 (Y = OH), that is, they are much greater (as absolute values) than the slopes obtained for all substituents. For ED substituents, the slopes are less steep and amount to −0.97 and −0.77, for NH2 and OH, respectively. In all cases, R2 > 0.862. These effects reveal how strongly the resonance effect is dependent on EA/ED properties of X and the nature of Y.

Figure presents linear dependences of SESEBCO (inductive effect), SESEBEN (inductive and resonance effects), and ΔSESE (resonance effect) on F, σp, and R constants, respectively. Despite different sensitivities and a character of the variability of SESEBCO, SESEBEN, and ΔSESE values, their dependences on empirical constants F, σp, and R are either very good (SESEBEN and ΔSESE) or at least acceptable for SESEBCO versus F. This is not only a mutual verification of empirical characteristics by theoretical modeling but also a justification of using SESE as a valuable descriptor of the above-mentioned SEs.

Figure 5

Dependences of SESEBCO, SESEBEN, and ΔSESE for Y = NO2, COOH, OH, and NH2 on SCs (a) F, (b) σp, and (c) R, respectively; SESE and ΔSESE in kcal/mol.

The regressions presented in Figure a reveal very important properties of the inductive effects:

as expected, the inductive effect estimated by the use of the SESE approach for X-BCO-Y series depends clearly on the nature of a substituent X and correlates well with empirical constant F;

in all cases, except for X = NMe2, SESE values are negative, it means that X···Y interactions are destabilizing in comparison with separated monosubstituted systems; and

the more EA (and less ED) Y, the stronger interactions between X and Y (the more negative slope) and a greater range of the variation of SESE values (Table ).

The dependences of SESE on σp values for X-BEN-Y series, shown in Figure b, disclose a very clear difference for the series with EA and ED functional groups, that is, COOH and NO2 on the one hand and OH and NH2 on the another hand. In the first case, the slopes are negative, indicating the destabilizing effect of EA substituents, whereas in the second case, the EA substituents stabilize X-BEN-Y systems.

Finally, the use of the ΔSESE concept to characterize the resonance effect of a substituent, R, in all systems studied (Y = NO2, COOH, OH, and NH2) is shown in Figure c. The obtained relationships between ΔSESE and R reveal symptoms similar to those for σ (σp are used), presented in Figure b. In both cases, the stronger interactions between X and Y are observed for the series with the most EA (NO2) and ED (NH2) fixed groups, documented by the slope values as well as by the ranges of variation of SESE and ΔSESE values (Table ). The mean SESE values for BEN series increase with a decrease of EA (an increase of ED) properties of the fixed group: for NO2, COOH, OH, and NH2, the values are −0.72, −0.19, −0.03, and 0.55, respectively (Table ).

A more general view is found while looking at the data in Table . Two important differences have to be indicated. The first one, the ranges for BCO series are much smaller than those for BEN series: from 0.0 to 2.23 and from 0.0 to 7.63, respectively (Table ). The mean values for these two kinds of ranges are 0.98 for BCO series and 4.04 for BEN series. This means that the variability of substituent’s interactions in BCO series is approximately 4 times weaker than that in BEN series. The next difference, the averaged values of SESE for BCO series are always negative and amount from 0.0 (H) to −1.37 (NO2), whereas the SESE for BEN series may be either negative, the lowest value is for X = F (−0.83), or positive for X = NMe2 (+0.65) (Table ).

Table 3

Values of Averages and Ranges of SESE (in kcal/mol) for All Obtained BCO and BEN Systems

	Y = NO2, COOH, OH, and NH2
	BCO		BEN
X	average	range	average	range
NO	–0.92	1.54	0.22	7.63
NO2	–1.37	2.23	–0.41	7.18
CN	–1.15	1.98	–0.40	5.37
CF3	–0.84	1.49	–0.46	4.13
COMe	–0.43	0.91	0.22	4.02
COOH	–0.52	0.86	0.11	4.52
CHO	–0.65	1.10	0.10	5.26
CONH2	–0.44	0.72	0.04	2.98
Cl	–0.97	1.50	–0.58	0.82
F	–1.00	1.39	–0.83	1.35
H	0.00	0.00	0.00	0.00
Me	–0.07	0.10	0.08	1.52
OMe	–0.43	0.50	–0.15	3.80
OH	–0.59	0.78	–0.35	3.47
NH2	–0.31	0.34	0.23	5.74
NMe2	–0.08	0.27	0.65	6.78
average	0.98		4.04

Conclusions

The application of cSAR and SESE concepts to describe SEs in 4-X-BCO-Y and 4-X-BEN-Y derivatives has enabled the investigation of the nature of X···Y intramolecular interactions, that is, their inductive and resonance contributions.

The analyses of the inductive SEs by the use of the cSAR(CH2) approach applied to X-BCO-Y systems revealed that the changes in the SE are qualitatively similar to those found in monosubstituted BCOs. However, the slopes for linear regressions of cSAR(CH2) versus cSAR(Y) or cSAR(X) are (as absolute values) greater for NH2 and OH derivatives than for the NO2 and COOH ones. This indicates a different mechanism of interactions between CH2 groups and Y differing in ED and EA properties.

The inductive SE exhibits a high level of additivity, which depends on the kind of substituents. This decreases with a decrease of EA (an increase of ED) properties of the substituents.

The SESE approach applied to X-BCO-Y series reveals a good correlation with the empirical F constants; similarly for X-BEN-Y series, the SESE values correlate well with the classical Hammett constants.

The difference, ΔSESE, between SESE values for X-BEN-Y and X-BCO-Y characterizes the resonance effect, and in consequence, follows a good correlation with resonance constants R.

Thus, the above-described results of the application of the SESE approach (to disubstituted BEN and BCO derivatives) have confirmed well the older concept of the SE based on the additivity of the inductive and resonance effects.

To sum up, the obtained results of quantum chemical modeling of the SE by means of SESE and cSAR approaches exhibit a good agreement with commonly accepted empirical concepts. The advantage of using these modeling is that they can be applied to any kind of molecules.

Theoretical Methods

Four series of X-BCO-Y derivatives with fixed group Y = NO2, COOH, OH, NH2, and the 16 substituents (Scheme ) were used to investigate the inductive and resonance SEs.

The substituent properties were characterized by SESE and cSAR parameters. SESE descriptors were obtained using the homodesmotic reaction (Scheme , eq )

Scheme 3

Homodesmotic Reaction Used To Obtain SESE Parameter

The cSAR parameter was calculated as a sum of charges at all atoms of the substituent X or Y and the charge at the ipso carbon atom; cSAR(CH2) was obtained as a mean value for CH2 fragments in the same position of BCO. Additionally, cSAR values for all CH2 groups inside the BCO ring, named cSAR(FRAG), by summing up the atomic charges of carbon and hydrogen was obtained. The Hirshfeld method[46] was applied to calculate all cSAR values.

For all analyzed structures, optimization was performed with the use of the Gaussian 09 program.[47] The B3LYP/6-311++G(d,p) method was used for all calculations as the one which was proven to give fine results.[35] The vibrational frequencies were calculated at the same level of theory to confirm that all calculated structures correspond to the minima on potential energy surface.