Fukui函数和局域软度应用于亲电加成反应的区位选择性的研究
Fukui Function and Local Softness Related to the Regioselectivity of Electrophilic Addition Reactions
收稿日期: 20170830 接受日期: 2017109
基金资助: 

Corresponding authors:
Received: 20170830 Accepted: 2017109
Fund supported: 
theNationalNaturalScienceFoundationofChina. 
Fukui函数、局域软度、广义Fukui函数以及广义软度通常被称为反应描述符。使用它们研究和探讨了HCl与不对称烯烃以及溴苯硒与不对称苯乙烯的亲电加成反应的区位选择性。在MP2/6311++G(d, p)理论水平下，采用有限差分方法计算这些反应描述符，同时也使用ABEEMσπ方法进行了计算。ABEEMσπ模型下的局域软度和广义局域软度，分别结合局域硬软酸碱(HSAB)原理，得出亲电试剂氯化氢与溴苯硒，更容易进攻不对称乙烯和苯乙烯中的马氏碳原子，符合马氏规则。而有限差分方法不能完全地解释该系列反应的区位选择性。此外，主要产物所对应的马氏碳原子的广义局域软度值，就能够预测出此类反应的活性序列，所得结果与速率常数有很好的关联。
关键词：
Regioselectivities of electrophilic addition reactions of hydrogen chloride to asymmetric alkenes and benzeneselenenyl bromide to substituted styrenes have been investigated by using reactivity descriptors, including Fukui function f(r), local softness s(r), generalized Fukui function f^{G}(r), and generalized local softness s^{G}(r). All of them are obtained from the finite difference approximation method calculated by ab initio method at MP2/6311++G(d, p) level of theory and our ABEEMσπ model, respectively. According to the generalized version of the local hardsoft and acidbase (HSAB) principle, the forecasted regioselectivities of our investigated additions using the ABEEMσπ model are in fair agreement with the experimental values. In particular, we can also rationalize their reaction rate constants by the generalized local softness, i.e., the softest the site is, the easiest the reaction is. Hence, the generalized reactivity descriptors work quite well.
Keywords：
本文引用格式
朱尊伟, 杨巧凤, 徐珍珍, 赵东霞, 樊红军, 杨忠志.
ZHU Zunwei, YANG Qiaofeng, XU Zhenzhen, ZHAO Dongxia, FAN Hongjun, YANG Zhongzhi.
1 Introduction
Electrophilic addition of an electrophile to alkenes is one of the most widely studied electrophilic reactions ^{19}, as shown in Fig. 1. The analysis of this sort of reactions has attracted great concern of both experimental and theoretical studies. Regioselectivity for the electrophilic addition has been shown to follow the empirical Markovnikov's rules ^{10}, the addition of an acidic proton to a double bond of an alkene yields a product where the proton is bound to the carbon atom bearing the largest number of hydrogen atoms when the substituent of alkene is electrondonating group. And when the substituent is electronaccepting group, the proton of acid favors to attack the carbon atom bearing the smallest number of hydrogen atoms, which calls the antiMarkovnikov's rule. Many theoretical ^{14, 8} and experimental ^{57, 9} studies have focused on the regioselectivity of electrophilic addition to alkene all the while, such as, frontier molecular orbital (FMO) theory is sometimes used for explaining the regioselectivity of reaction ^{8}. Suresh and his coworkers have employed the molecular electrostatic potential to confirm the regioselectivity of Markovnikov reaction ^{2}. Recently, Yang, Ding and Zhao ^{1} have performed to use the frontier electron density of initialstate carbon atoms in molecular face theory (MFT) to estimate its regioselectivity: if the frontier electron density encoded on the Markovnikov carbon atom is larger than that of antiMarkovnikov, the reaction may be predicted to proceed on the Markovnikov route, and otherwise it may prefer the antiMarkovnikov route.
Fig 1
Fig 1
The regioselectivities of electrophilic additions of hydrogen chloride to the substituted ethenes (R_{3} = H) and benzeneselenenyl bromide to substituted styrenes (R_{1} = R_{2} = H), including Markovnikov and antiMarkovnikov products.
The local hardsoft and acidsbases (HSAB) principle is an efficient method in conceptual density functional theory (CDFT) to predict the regioand stereoselectivities of reactions, especially the corresponding softness matching in a local approach ^{1117} for two or four or much more reactive points between two reactants. LiEvans ^{18} proposed that for a hard reaction the site of minimal Fukui function (FF) is preferred and for a soft reaction the site of maximal Fukui function is preferred. Gazquez and Mendez ^{19} stated that the reaction between two chemical species will not necessarily occur through their softest atoms, but through those sites whose local softness are close to each other. In this respect, Geerlings, Proft and Langenacker ^{20} suggested that local softness should be used as an intermolecular reactivity descriptor, whereas the FF is as an intramolecular one. Thus, the comparisons of the FF or condensed FF values for different systems are meaningless because they represent only the relative reactivity among different sites within a molecule. Therefore, in order to rationalize the intermolecular reactivity, we have proposed a series of generalized reactivity descriptors ^{21}, including generalized Fukui function (GFF) and generalized local softness (GLS) ^{22}.
Recently, based on the generalized reactivity descriptors we have been successful to predict and to explain the regio/stereoselectivities of DielsAlder reactions ^{22} and the enzymatic catalyzed reactions of biological system ^{21} and to correlate their intermolecular reactivities of all reactions in terms of the atombond electronegativity equalization method (ABEEMσπ) model with the local HSAB principle at its generalized version. And we have obtained the results in good agreement with the experimentally observed outcomes.
In this paper, we will use the usual reactivity descriptors and the generalized one combined with the local HSAB principle to investigate the regioselectivities of the electrophilic additions of alkene including the hydrogen chloride and benzeneselenyl with unsymmetrical alkene and to rationalize their order of reaction rate constants by the ab initio method at the level of MP2/6311++G(d, p) with the finite difference approximation (FDA) method and the ABEEMσπ model. It should be noted that the FDA method involves the three systems of N, N + 1, and N  1 electrons, but ABEEMσπ model only involves one system of N electron.
2 Theory background
2.1 The reactivity descriptors
Fukui function (FF) is one of the important reactivity descriptors in predicting the intramolecular reactivity in CDFT ^{23, 24}. Parr and Yang defined the FF
where
2.2 The finite difference approximation (FDA)
In the FDA method, according to the Eq.(1), the condensed FF of nucleophilic attack for systems with electron gain can be written as
and the condensed FF of electrophilic attack for systems with electron donation can be expressed as
where q_{k}(N + 1), q_{k}(N), and q_{k}(N  1) stand for the partial charges on atom k in a molecule with N + 1, N, and N  1 electrons at the same geometry structure, respectively ^{27}.
A local softness descriptor
where, s_{k}^{+} and s_{k}^{} imply how global softness is redistributed among various atoms of the molecule by the condensed Fukui function. The global softness, S, can be given as ^{24} S = 1/I A where I and A are the ionization potential and electron affinity, respectively. The first ionization potential I can be obtained by I= E_{N1}  E_{N} and the electron affinity A by A = E_{N+1}  E_{N} with E_{N1}, E_{N}, and E_{N+1} denoting the total energies of the systems with N  1, N, and N + 1 electrons, respectively. The quantities involved can be calculated by an ab initio method at high level of theory.
2.3 ABEEMσπ model
Based on the DFT and electronegativity equalization method (EEM) ^{2834}, Yang and his coworkers have developed ABEEMσπ model ^{3545}, which explicitly partitions a molecule into atom, chemical bond, and lone pair (lp) regions. In this model, the single bond consists of one σ region, where the center of the charge for σ bond is located on the position of the ratio of the covalent atomic radii of two bonded atom; the double bond consists of one σ region and four π regions, where center of the σ bond charge is similar with the σ region of single bond and the π bond partial charges are placed above and below the doublebonded atoms at the covalent radii of the this doublebonded atoms perpendicular to the plane formed by the σ bond; and the center of charge and its orientation for the lp region is determined in terms of the chemical surrounding.
In terms of the definition of electronegativity based on DFT, the effective electronegativity of a region a, χ_{a}, can be expressed as:
where χ_{a}^{*} and 2η_{a}^{*} are valencestate electronegativity and hardness of the region a, respectively. a and b denote two regions, including the atom or single bond σ or double bond σ and π or lone pairs regions. q_{a} and q_{b} are the partial charges of regions a and b, R_{a, b} denotes the distance between regions a and b, and k, 0.57, is an overall correction coefficient in this formalism ^{22, 3547}. The electronegativity equalization principle demands that the effective electronegativity of every region is equal to the overall electronegativity of the molecule, χ_{mol}:
For an arbitrary molecule partitioned into m regions, solving the Eq.(8) with the constraint Eq.(9) on its net charge, q_{mol}, if the parameters χ_{a}^{*} and 2η_{a}^{*} are known, we can obtain the charge of every region.
On the basis of the definition of the FF, we can express the FF of region a in our ABEEMσπ model as:
So, the global hardness 2η_{mol} can be expressed as:
Hardness expressions for all the regions in a molecule like Eq.(11), altogether with the normalization condition of the FF,
2.4 The generalized reactivity descriptors
The generalized Fukui function (GFF)
where, the
3 Computational details
We investigated the electrophilic additions of hydrogen chloride to asymmetric alkenes and benzeneselenenyl bromide to substituted styrenes, as shown in Fig. 1. The geometries of all reactants were optimized and obtained by the B3LYP/6311+ G(d, p) level of theory in Gaussian03 ^{48}. All optimized reactants were stationary points of potential energy surface after checking the frequencies at the same level of theory.
3.1 Calibration of parameters χ^{*} and 2η^{*} for ABEEMσπ Model
According to Eq.(7) and Eq.(11), we have calibrated the parameters χ^{*} and 2η^{*}, through a regression and leastsquares optimization procedure by dealing with some model molecules ^{35}. For all model molecules, ab initio HartreeFock MO calculations were performed with STO3G basis sets in Gaussian 03 ^{48} and then the partial charges of all the model molecules were obtained by the Mulliken population analysis. Then the charge distributions obtained for the model molecules were brought into Eqs.(7–9) in order to determine the parameters χ^{*} and 2η^{*} through a regression and leastsquares optimization procedure ^{22, 3538, 46, 47}. The old types of parameters were obtained from our previous work ^{37}, and the new added types and parameters of χ^{*} and 2η^{*} are listed in Table 1.
Table 1 Parameters χ^{*} and 2η^{*} in ABEEMσπ Model.
Type of ABEEMσπ parameter  χ^{*}  2η^{*}  
Cl_{17}―Ph―C_{626}＝C_{62}  C_{66} in ―Ph  2.500  6.800 
π_{66}  3.850  94.150  
C_{626}  2.500  7.200  
π_{626}  3.790  94.150  
Cl_{17}  3.010  20.099  
C_{62}＝C_{64}―R  C_{62}  2.500  10.200 
π_{62}  3.500  80.319  
C_{64}  2.600  6.200  
π_{64}  3.580  88.150  
Se―  1.800  34.970  
Br―  2.880  70.019  
σ_{CSe}  4.900  35.000  
σ_{SeBr}  6.950  75.000  
lp_{Cl}  5.536  46.900  
lp_{Br}  5.965  70.000  
lp_{Be}  3.700  7.164 
For the calibration, the reason why we use the minimum STO3G basis set is not due to its timeconsuming but more importantly due to its physical significance. Ab initio calculation with a higher level of basis set can give more accurate prediction of energy and geometry, but can not give more suitable partial charges than lower level of basis set for practical use. This phenomenon comes from the fact that a diffuse basis function located on an atom may to some extent cover the regions of the other adjacent atoms leading to a somewhat overestimating population of this atom in the Mulliken population analysis. Derouane and coworkers ^{49} showed that the formal charges calculated with the 621 basis set are higher than those computed with the STO3G basis set, and thus suggested STO3G charges may be more reliable. Wilson and Ichikawa ^{50} and TorrentSucarrat and their coworkers ^{51} pointed out that the charge transfer between atoms in a molecule is overestimated when the polarization basis sets are used. Huzinaka et al. ^{52} and Jakalian et al. ^{53}, as well as our group^{47}, had experienced that the use of higher level of basis sets overestimates the overlapping between their respective basis functions belonging to two atoms in a molecule. For example, if the 631G^{*} basis set is used, the polarity of a molecule calculated by the partial charges is overestimated by 10%–15% than if the STO3G basis set is used ^{53}. Therefore, in the calibration process of the parameters, STO3G basis set has been used in the ab initio calculations for all the model molecules to obtain the partial charges from Mulliken population analysis.
3.2 Calculation of Fukui function and local softness
Geerlings, Proft and Langenacker ^{20} suggested that local softness should be used as an intermolecular reactivity descriptor, whereas the FF is as an intramolecular one. Under the FDA method, via S = 1/(I  A), the global softness were obtained, where the first ionization potential I and the electron affinity A were calculated by ab initio method at MP2/6311++G(d, p) level of theory. In terms of Eqs.(3) and (4), the condensed FFs of center atoms were calculated using the natural population analysis (NPA) at the MP2/6311++G(d, p) level of theory, then obtained their local softness via Eqs.(5) and (6).
In the ABEEMσπ model, the FFs of center atoms were calculated by Eq.(11), then their GFFs were calculated by Eq.(12). Their global softness was obtained by Eq.(11) because of it being the inverse of the hardness, hence the local softness and the GLS were calculated by Eqs.(2) and (13), respectively.
3.3 Expression of the local HSAB principle under the finite difference approach and ABEEMσπ model
The local HSAB principle claimed ^{19} that the interaction between two molecules will occur not necessarily through their the softest atoms but rather through those atoms of two systems, and their Fukui functions of which are close. Based on this principle, the softnessmatching criteria was proposed by Chandea, Nguyen, Geerlings and coworkers for understanding the regioselectivity of cycloaddition reactions ^{1113, 15, 16}. The softnessmatching criterion at a locallocal approach in the case of multiple sites of interaction has been cast in the form of the minimization of a quadratic form to articulate. In our investigated reactions, because there are two reaction center atoms in electrophilic additions, we will use the absolute values of differences between the local softness of the reaction center atoms of two reactants to express.
Hence, within the FDA method, the expression of the local HSAB principle is written as Eq.(14), where the i is the site of reactivity on molecule A, and the k is the site of reactivity on molecule B, as seen in Fig. 1, and the s_{Ai}^{+} is the condensed local softness of the ith atom in A, which represents that the electrophile H atom in HCl or [PhSe] group in PhSeBr acquires a electron sharing from the πbond of substituted ethene and the s_{Bk}^{} is the condensed local softness of the kth atom in B, which represents that the reactant B will be attacked by H atom or [PhSe] group to donate an electron to be shared. And then, based on the proposed generalized reactivity descriptor, the local HSAB principle can be expressed as the Eq.(15). In this kind of the reaction, the superscript + denotes the reactivity descriptor of the electrophilic H atom, while the superscript – represents the reactivity index of double bond C atom in alkene.
In terms of ABEEMσπ model, the local HSAB principle can be expressed to the Eqs.(16) and (17), where the s_{Ai}, s_{Bk}, and
According to the local HSAB principle, the smaller the ∆s or ∆s^{G} is, the easier the reaction is. In this paper, we only consider the state of single reactant, when ∆s_{MA} < ∆s_{AM} or ∆s_{MA}^{G} < ∆s_{AM}^{G}, the Markovnikov product should be the main; and when ∆s_{MA} > ∆s_{AM} or ∆s_{MA}^{G} > ∆s_{AM}^{G}, the antiMarkovnikov product should be favored. And the generalized reactivity descriptor can be further used to rationalize the reaction rate constants, i.e., the greater the s_{Bk}^{G} is, the greater the reactivity is, and the easier the reaction is.
4 Results and discussion
4.1 Regioselectivity of the addition of HCl to alkene
For the addition of HCl to unsymmetrical olefin CH_{2}＝CR_{1}R_{2}, when the substituent is electrondonating group, such as alkyl, the reactions comply with the Markovnikov's rules to occur. When the substituent is electronaccepting group, such as ―CHO, ―COOH, the reactions comply with the antiMarkovnikov's rules. As seen in Fig. 1, these substituents belong to the alkyls, so the regioselectivities of these reactions abide by the Markovnikov's rules to produce the Markovnikov's products.
According to Eqs.(14)–(17), the difference values,
Table 2 The difference values, ∆s_{MA}, ∆s_{AM}, ∆s_{MA}^{G} and ∆s_{AM}^{G}, for HCl with alkene in terms of MP2/6311++G(d, p) level under the finite difference approximation, and our ABEEMσπ model.
Finite difference approximation  ABEEMσπ model  
∆s_{MA}  ∆s_{AM}  ∆s_{AM}^{G}  ∆s_{MA}^{G}  10^{3}∆s_{MA}  10^{3}∆s_{AM}^{G}  10∆s_{MA}^{G}  10∆s_{MA}^{G}  
ethene  0.589  0.589  2.647  2.647  0.069  0.069  0.526  0.526  
propene  0.533  0.581  6.017  5.579  2.099  9.250  0.739  1.760  
1butene  0.549  0.556  8.863  8.779  2.867  5.727  0.981  2.012  
2methylpropene  0.604  0.627  8.195  7.924  3.008  6.643  0.964  2.122 
Table 3 The values of condensed f(r), f^{G}(r), s(r), and s^{G}(r) for the H atom of electrophile HCl and the C_{MA} and C_{AM} of unsymmetrical alkenes at the level of MP2/6311++G(d, p) and the ABEEMσπ model.
Finite difference approximation  ABEEMσπ model  
f^{+}  f^{G+}  s^{+}  s^{G+}  f  f^{G}  s  s^{G}  
HCl  H  0.7503  1.5007  1.5446  3.0893  0.2855  0.5709  0.0133  0.0265  
f^{}  f^{G}  s^{}  s^{G}  f  f^{G}  s  s^{G}  
ethene  C_{MA}  0.4242  2.5451  0.9560  5.736  0.1196  0.7176  0.0132  0.0791  
C_{AM}  0.4242  2.5451  0.9560  5.736  0.1196  0.7176  0.0132  0.0791  
propene  C_{MA}  0.4043  3.6388  1.0118  9.106  0.0796  0.7168  0.0112  0.1004  
C_{AM}  0.3849  3.4639  0.9632  8.668  0.1607  1.4464  0.0225  0.2025  
1butene  C_{MA}  0.3952  4.7424  0.9960  11.952  0.0623  0.7481  0.0104  0.1246  
C_{AM}  0.3924  4.7090  0.9890  11.868  0.1139  1.3672  0.0190  0.2277  
2methylpropene  C_{MA}  0.3842  4.6099  0.9404  11.285  0.0632  0.7580  0.0102  0.1229  
C_{AM}  0.3749  4.4989  0.9178  11.013  0.1227  1.4724  0.0199  0.2387 
As shown in Table 2, following the FDA method, the values of ∆s_{MA} (0.589), ∆s_{AM} (0.589) and ∆s_{MA}^{G} (2.647), ∆s_{AM}^{G} (2.647) for the reaction between HCl with ethene are equal to each other, respectively, which, of course, indicates that there is no regioselectivity in this reaction. When the olefin is propene, the value of ∆s_{MA} (0.533) is smaller than the relevant ∆s_{AM} (0.581). According to the local HSAB principle, the H atom of HCl favors to attack the Markovnikov's carbon atom, so this result is in line with the experimental regioselectivity. However, the value of ∆s_{MA}^{G} (6.017) is greater than the ∆s_{AM}^{G} (5.579) by using the generalized local softness, then the regioselectivity of this reaction would be anticipated the antiMarkovnikov's attacking. But, this result is not in agreement with the experimental result. By using the same way to deal with the rest two additions of HCl to 1butene and 2methylpropene, we also obtain ∆s_{MA} < ∆s_{AM} and ∆s_{MA}^{G} > ∆s_{AM}^{G}. Hence, according to the local HSAB principle, within the FDA method, the predicted results obtained from the usual local softness are better than those from the generalized local softness (GLS).
And then, how about are the results in terms of the ABEEMσπ model? It is clearly seen from Table 3 that the both values of ∆s_{MA} and ∆s_{AM} are 0.069 × 10^{3}, and both ∆s_{MA}^{G} and ∆s_{AM}^{G} are 5.26 when the olefin is ethene, which indicates that the two doublebonded carbon atoms are identical. When R_{1} is H and R_{2} is ―CH_{3},
It was reported that the rate constants for the addition of HI to ethene, propene, and 2methylpropene were in the ratio 1:90:700 ^{5, 6}, which indicated that with raising the substituents, the reaction rates gradually became greater and greater. Furthermore, experimental activation energies of the additions of HCl to ethene (166.105 kJ·mol^{1}), to propene (144.348 kJ·mol^{1}), and to 2methylpropene (119.244 kJ·mol^{1}) were reported ^{2, 9}, which implied when the substituents gradually become larger and larger, the additions of HCl to CH_{2}CR_{1}R_{2} are more and more easy to process. The generalized reactivity descriptors, GFF and GLS themselves, can rationalize the intermolecular reactivity, and especially forecast the order of reaction rate constants for a series of reactions. Hence, we applied the GLS, rather than
The investigated electrophilic additions of HCl to alkenes, we have only considered the reactivity descriptors of reactants, which means that the values of GLS for the H atom of HCl are fixed and just the values of GLS for the C_{MA} of alkenes are taken as variables, where the values of GLS for reaction centers by FDA method and ABEEMσπ model are listed in Table 3, i.e., we can disregard the GLS of H atom in HCl and only compare the GLS of C_{MA} in alkenes of the main product. It is clear from our calculations that the values of
In a word, both the usual reactivity descriptors and the generalized ones from ABEEMσπ model in combination with the local HSAB principle can successfully interpret and forecast the regioselectivities of the additions of HCl to alkenes, which results are in agreement with the Markovnikov rule, but the results of FDA method are not good. And then, the values of
4.2 The regioselectivity of addition for benzeneselenyl bromide with alkene
The additions of benzeneselenyl bromide to alkenes are usually considered to be the electrophilic addition reactions^{7}. We have chosen four reactions between benzeneselenyl bromide and substituted styrene (XPhCH＝CH_{2}), where the substituents PhX of alkenes are Ph, 3ClPh, 4ClPh and 4CH_{3}Ph, respectively. Here, [PhSe] group in electrophile is considered to be the H atom of HCl and it has the positive charge, which attacks one of the doublebonded carbon atoms of alkenes with enriched electron. The Br atomic charges obtained by HF/STO3G level of theory and ABEEMσπ model are 0.100 and 0.140 a.u., respectively. Table 4 lists the charges of C_{MA} and C_{AM}, q_{MA} and q_{AM}, calculated by HF/STO3G level of theory and ABEEMσπ model, respectively.
Table 4 The charges of C_{MA}, C_{AM} obtained from HF/STO3G and ABEEMσπ Model.
X―PhCH＝CH_{2}  HF/STO3G  ABEEMσπ  
q_{MA}  q_{AM}  q_{MA}  q_{AM}  
H  0.128  0.057  0.125  0.054  
3Cl  0.122  0.057  0.116  0.042  
4Cl  0.122  0.058  0.116  0.042  
4CH_{3}  0.129  0.057  0.123  0.051 
These C_{MA} possess much more negative charge and the C_{AM} possess a little charge compared with C_{MA}, hence, the electrophile [PhSe] group will favor to attack the C_{MA}. Here, we could consider the substituents X together with benzene (X―Ph―) as a whole to be the electrondonating groups, i.e. these four reactions should obey the Markovnikov's rules according to the greater attraction between [PhSe] group and C_{MA}, which are just in line with the experimental results^{7}. We also can see that the q_{MA} of 3Cl and 4Cl are less than that of the others, because the interaction between ―Cl, the electronwithdrawing group, and benzene, the electrondonating group, represents the character of the electrondonating group in nonpolar solution, so leading to that result, if the reactions react in polar solution, the result may be the opposite ^{7}, however, the all calculations about these reactions were calculated at the gas state in vacuum. The charges of ABEEMσπ and ab initio method are in agreement by and large.
Then, we make use of the usual local softness and the generalized one from FDA method and the ABEEMσπ model combination with local HSAB principle to estimate the regioselectivities of above four additions, the values of ∆s_{MA},
Table 5 The values of ∆s_{MA}, ∆s_{AM}, ∆s_{MA}^{G} and ∆s_{AM}^{G} for PhSeBr with substituted styrene (XPhCH=CH_{2}) at the level of MP2/6311++G(d, p) with the finite difference approach and ABEEMσπ model.
X―PhCH＝CH_{2}  finite difference approach  ABEEMσπ Model  ^{a}MA: AM  
∆s_{MA}  ∆s_{AM}  ∆s_{MA}^{G}  ∆s_{AM}^{G}  10^{4}∆s_{MA}  10^{4}∆s_{AM}  10^{2}∆s_{MA}^{G}  10^{2}∆s_{AM}^{G}  
H  0.841  1.457  8.915  18.780  1.666  1.680  4.683  4.711  78:22  
3Cl  0.854  1.413  9.133  18.066  1.636  1.649  4.600  4.629  59:41  
4Cl  0.857  1.442  9.183  18.534  1.644  1.658  4.625  4.652  76:24  
4CH_{3}  0.853  1.517  7.128  19.754  1.579  1.593  6.689  6.721  86:14 
^{a} Those reactions are reacting in benzene at 25 ℃.
It can be seen from that Table 5 the four
We can obtain two sequences:
Fig 2
Fig 2
The line charts of the reaction rates (upper), the s^{G} (middle) and s^{G} (lower) of C_{MA} atoms in the four additions of benzeneselenyl bromide to the substituted styrenes.
Fig. 2 (middle) displays the line chart of the s^{G} obtained from the ABEEMσπ model. And Fig. 2 (lower) represents the line charts of the s^{G} of the C_{MA} atoms calculated by FDA method. It can be found from the Fig. 2 that the order of s_{MA}^{G} is s_{MA}^{G}(4Cl) < s_{MA}^{G}(3Cl) < s_{MA}^{G}(H) < s_{MA}^{G}(4CH_{3}) (FDA method) and that of s_{MA}^{G} is s_{MA}^{G}(3Cl) < s_{MA}^{G}(4Cl) < s_{MA}^{G}(H) < s_{MA}^{G}(4CH_{3}) (ABEEMσπ model). The sequence via ABEEMσπ model is just in accord with that of the experimental reaction rates, but that of FDA method is not for the ―Cl substituted additions.
Therefore, the applications of the generalized reactivity descriptor combined with the local HSAB principle on this series of electrophilic additions demonstrate that both the values of
5 Conclusions
For the addition reactions of HCl to the substituted ethenes and benzeneselenyl bromide to the substituted styrenes, according to the local HSAB principle, the values of the softness differences,
As the performance of the generalized reactivity descriptor, it is shown that the C_{MA} atoms of all reactions prefer to be attacked in terms of ABEEMσπ model, which is in agreement with the experimental results. But, the results of FDA method can not obtain such good indication. However, it is shown that there are two inverse orders, compared with the orders of experimental rate constants for these two series of electrophilic additions by using the Δs^{G} from FDA and ABEEMσπ model. In fact, only generalized local softness (GLS) of center atoms can be related to the orders of the experimental reaction rate constants by both the FDA method and the ABEEMσπ model except the results of the FDA method for 3Cl substituted addition with a little flaw.
Up to now, we have applied the generalized reactivity descriptors to study on several kinds of reactions, such as to predict the regioand stereoselectivity of DielsAlder reactions and to correlate their reaction rate constants, to rationalize the intermolecular reactivities and regioselectivities of enzymatic catalyzed nucleophilic reactions, etc. Moreover, we will continue to apply the generalized Fukui function and the generalized local softness to investigate other systems and to further check their rationality and validity.
参考文献
/
〈  〉 