Compounds containing phenyl and heterocyclic radicals exist widely. They not only intimately relate to daily life and industrial production,but also closely impact the environment [1, 2, 3]. With respect to compounds containing phenyl,there have been a lot of reports about the sites of electrophilic attack [4, 5, 6, 7, 8, 9, 10]. Theoretically, many methods have been proposed for evaluating and rationalizing the sites of eletrophilic substitution reaction,such as Fukui function,molecular electrostatic potential (MEP),the HOMOdensity and the Laplacian of the electron density [6, 11]. All of them consider and treat the indices related to the electronic properties. These methods are fruitful for predicting the regioselectivity of the electrophilic substitution of cyclic compounds. In reality,electrophilic substitution involves a bond formation and a bond breaking simultaneously. Therefore,it relates to both the electronic properties of the attacked site and the bond strength of the broken bond. However,little attention has been paid to the latter. Usually,the electrophilic substitution reaction is rationalized within the context of electronic properties,while the nature of the bond strength of the broken bond is often neglected. Herein,we will show that the regioselectivity of the electrophilic substitution reaction can be also rationalized by the bond strength of the broken bond as evaluated by means of the Dpb value.
Strength of a bond,especially the C-H bond in organic and biological chemistry,is an indispensable component in understanding correlative molecular reactions,including reaction rate and yield of product [11, 12, 13, 14, 15]. Bond energy is a quantity to characterize the bond strength,which is usually expressed by bond dissociation energy (BDE) in literatures [16, 17]. There are many kinds of methods for evaluating the bond strength. Experimentally, there are reaction kinetics,mass spectrometry,photoionization, zero-electron kinetic energy spectrum,photoacoustic calorimetry, and photochemical methods. Theoretically,theab initiocalculation method,density functional method and ONIOM method have been used to calculate the bond strength. However,there are some obstacles and shortcomings in accurate measurement of BDE both from experiments and theory [18, 19]. Therefore,many methods have come forth to predict and measure the bond strength [12, 13, 14, 15, 16, 17, 18, 19]. Recently,Yanget al.have proposed a new quantity to measure and characterize bond strength,denoted by Dpb which is the minus of the potential acting on one electron in a molecule (PAEM) at the bond center (bc),a new concept [20, 21]. The larger the Dpb is,the stronger the chemical bond is.
In this letter,we calculated the Dpb of C-H and N-H bonds for 32 cyclic compounds as examples and show that the value of Dpb along a bond is closely related to the bond strength,and it can be used to rationalize the sites for the electrophilic substitution attack. This demonstrated that bond strength can be used to elucidate the regioselectivity of electrophilic substitution reactions as well 2. Theoretical method
If a molecule is in its ground state,the potential acting on one electron at positionrin the molecule (PAEM) is expressed:
where the first term is the attractive potential offered by all nuclei, the second term is the potential provided by all other electrons,the summation involving index A runs over all nuclei of the molecule considered,ZA is the charge on nucleus A,RA is the position vector of nucleus A,rand r' are the positions of the electrons,p(r) stands for the one-electron density,and p(r,r' ) represents two-electron density function that describes one electron at positionr,and another electron at r' at the same time.
Denoting the depth of the PAEM at the bond center,Dpb characterizes how easily the electron interflows from one atomic region to another through the bond region [20, 21]. In the bond region,the PAEM has a maximum point along the bond,and Dpb is the absolute value of the PAEM at this point. The Dpb was calculated by theab initioMELD program and our own program atab initio SDCI level [20, 21, 22, 23, 24, 25]. 3. Results and discussion 3.1. The Dpb of the PAEM at the bond center
In this section,all molecular geometries for 32 cyclic compounds used were optimized at MP2/6-311++G (3df,3pd) level of theory,and these PAEMs were calculated by using the MELDab initiomethod at SDCI/6-31++G(d,p) level and our own program .
Taking benzene for instance,we had calculated the PAEM of C-H chemical bond at bond center. The PAEMV(r) along the C-H bond was calculated at various electron coordinates with an interval of being 0.005 a.u.,as shown in Fig. 1 (bold line). We can obtain a maximum point in the curve of PAEM. Therefore,we can know the electron coordinate corresponding to the maximum. Then,along a line that is through this point and perpendicular to the C-H bond,the PAEM was calculated at various electron coordinates,as depicted in Fig. 1 (line) where it is a minimum at the point. This electron coordinate corresponding to a saddle point of the PAEM is called the bond center. As a result,the PAEM curve lines along and perpendicular to the C-H bond in benzene are displayed around C-H bond in benzene in Fig. 1.
|Fig. 1. The curves of the PAEM along and perpendicular to the C-H bond in benzene.|
In Fig. 1,the bold line and the slender line are the PAEMs along and perpendicular to the C-H bond in benzene,respectively. The crossing point of the two lines which are along the C-H bond (black line) and perpendicular to the C-H bond (slender line) is a special point. The PAEM gap between this point and bond center is the Dpb value. Fig. 1 describes the value and meaning of Dpb in space. The electron coordinate of the PAEM at the saddle point is marked by a solid circle on the C-H chemical bond,which is called the bond center (bc) of the C-H bond. The solid balls denote the C and H. The distance between the saddle point and bond center is the Dpb value as exhibited in Fig. 1. The Dpb value for the C-H bond in benzene is 1.8934 hartree. The values of Dpb along the C-H and N-H bonds for all model compounds have been figured out in a similar way. 3.2. Regioselectrivity of electrophilic substitution indicated by the
values of Dpb for benzoid compounds In order to ascertain the weaker bonds in aromatic compounds which are most easily broken,the values of Dpb using the above method along C-H bonds in the rings are calculated,and averaged in the orthoandmetapositions,then collected in Table 1. It was found that the smaller the Dpb is,the weaker the bond is, and the easier the substitution reaction is at that site. The weaker bonds,as ascertained by means of the Dpb values,are more likely to be broken during electrophilic substitution of these aromatic compounds.
For instance,the order of Dpb values ismeta>para>orthofor aniline that has an electron-donating group,indicating that the electrophilic substitution reaction has priority to take place at the orthoandparapositions. The study of molecular diagrams has shown that in aniline theorthoandparapositions are rich inpelectrons . For phenol,the sequence of bond strength ismeta>ortho>para based on the Dpb values,predicting that the sites for electrophilic substitution reaction are at paraandorthopositions. The same results which direct the electrophilic substitution reaction atortho andparapositions have been obtained for anisole,toluene,and biphenyl. Indeed,these results are in agreement with those which were obtained by means of the methods considering their electronic properties,and they are also in accord with the empirical rules for orientation in electrophilic aromatic substitution [6, 7, 8].
As for halogenated benzene,the sequence of Dpb values are ortho>meta>parafor fluorobenzene and chlorobenzene,indicating that the preferable sites are theparaposition which are in agreement with those previously reported [6, 7, 8],while the order of Dpb values isortho>para>meta,which indicates the sites for electrophilic attack being atmetapositions for bromobenzene.
The Dpb order isortho>para>metafor nitrobenzene,which has an electron-withdrawing group,which suggests the electrophilic substitution reaction mainly occurs atmetapositions and is fairly consistent with the sequence which is derived from the analysis of non-condensed Fukui function,MEP,HOMO as well as experimental data . However,the sequence according to the analysis of condensed Fukui function isortho≥meta>>parafor electrophilic substitution reaction,which is in disagreement with the experimental data [4, 5, 6, 7, 8, 9, 10]. As for benzoic acid,the bond strength sequence isortho>para>meta,which indicates preference at themetasites for electrophilic attack in terms of Dpb values. Indeed,Meneses et al. have demonstrated that the sites of electrophilic attack are at metapositions according to the condensed local hardnesshkvalues on atomk. For benzaldehyde and benzamide,the bond strength sequences are ortho>para>meta,indicating the metapositions for electrophilic substitution reaction,which is in accord with the experimental data [4, 5, 6, 7, 8, 9, 10]. Interestingly,the sites of eletrophilic substitution reaction which are predicted from the Dpb values are the same with those that are based on the electronic properties,including Fukui function,molecular electrostatic potential (MEP),the HOMOdensity,andpelectron density distribution. Indeed,the dominant factors which mainly control the regioselectivity of electrophilic substitution reaction are both electronic nature of the attacked site and the bond strength of the broken bond.
In the following,the sites for electrophilic attack are discussed in terms of both electronic nature and the bond strength indicated by Dpb values for naphthalene,anthracene and phenanthrene. The Dpb values along C-H bonds are shown in Fig. 2.
The Dpb values along C-H bonds in Fig. 2 show that the sites for electrophilic attack are atapositions rather thanbpositions for naphthalene. As for anthracene,the sequence of the sites for substitution reaction is 9>1>2 by using the Dpb values. With respect to phenanthrene,the sites for electrophilic attack are at 1 and 10 that are the carbon labels. All the results of the predicted sites for the electrophilic attacks are in fair agreement with those previously reported . This successfully demonstrates that the bond strength can be related to the regioselectivity of electrophilic substitution reaction.
|Fig. 2. he values of Dpb along C-H bonds for naphthalene,anthracene and phenanthrene (atomic units).|
In order to better illustrate and predict the regioselectivity of substitution reaction,the values of Dpb along C-H and N-H bonds for 16 heterocyclic compounds are shown in Fig. 3,respectively.
|Fig. 3. The values of Dpb along C-H and N-H bonds for 16 heterocyclic compounds (atomic units)|
According to the Dpb values as in Fig. 3,the preferred site of electrophilic substitution reaction is at carbon 4 for pyrazole, carbon 5 for imidazole,and ataposition for furaldehyde; these results are in accordance with those previously reported . However,the sites for substitution reaction are atbpositions rather thanapositions for pyrrole,furan,and thiphene based on the Dpb values,while theapositions were previously reported [27, 28]. As for five-membered heterocycles,the regioselectivity of electrophilic substitution reaction is mainly controlled by electronic properties,while the bond strength also plays a vital role in this process. As for indole,the site for substitution reaction is at carbon 3 as predicted both by means of Dpb values and experimental data . Theaposition substitutions have been predicted by previous methods for six-membered heterocycles . Notably,the preliminary results can be obtained in terms of Dpb values. Accordingly,the weaker bonds are predicted and determined in terms of Dpb values for these heterocyclic compounds. 4. Conclusion
The values of Dpb along C-H and N-H bonds for 32 cyclic aromatic compoundsin situwere calculated,and the weaker bonds are indicated by their Dpb values. The sites of electrophilic substitution reaction based on bond strength are in accordance with those which are indicated in terms of electronic properties. Indeed,the bond strength of the broken bond has a close relationship with the regioselectivity of the substitution reaction. The Dpb is a good indicator and predictor for rationalizing the regioselectivity of electrophilic substitution reaction for cyclic compounds. This method is straightforward and convenient,and may also provide insight into the regioselectivity of electrophilic substitution reactions. The Dpb values along chemical bonds of the broken bond may be applied to rationalize the sites for substitution reactions or predict the regioselectivity of electrophilic substitution reaction in other cases.Acknowledgments
The authors are very grateful to Prof. E.R. Davidson for providing us the MELD package and other kind helps. Thanks are also given to the support of the National Natural Science Foundation of China (Nos. 21133005 and 21473083),as well as program for Liaoning Excellent Talents in University LNET (No. LJQ2013111),and Natural Science Foundation of Liaoning Province (No. 2014020150).
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