自然轨道福井函数和成键活性描述符应用于解释苯硫醌和1,3-二烯的[2 + 4] 和[4 + 2]环加成反应中的成键机理

闫超咸，杨帆，吴睿智，周大刚，杨兴，周盼盼

兰州大学化学化工学院，甘肃省有色金属化学与资源利用重点实验室，功能有机分子化学国家重点实验室，兰州 730000

1 In troduction

Mono-ortho-thioquinones1–4w ith the general formula 1 can serve as electron-poor heterodienes to react w ith many alkenes w ith the general formula 2 which act as electron-rich dienophiles via either a [2 + 4]5or a [4 + 2]6–13cycloaddition,leading to the formation of the spiro derivative (3) or the benzoxathiin cycloadduct (4) as the main product, as depicted in Scheme 1. Theoretical and experimental investigations of the[2 + 4] and [4 + 2] reaction mechanisms were also carried out by Menichetti and coworkers, and they suggested that the reactions of o-thioquinones w ith acyclic dienes undergo the[2 + 4] path and are kinetically favored while the reactions of o-thioquinones w ith cyclic dienes go through the [4 + 2] path and are thermodynam ically favored14,15. These reactions stimulate our great interest in exploring the mechanisms of their different bonding processes.

Chemical reaction involves the bond breakage and formation, so using the chem ical reactivity descriptor of a bond or an orbital to reveal the bonding process would be helpful for understanding the bonding process of the reaction. Recently, a new type of condensed Fukui function based on the natural bond orbital theory (NBO16) for describing the chemical reactivity of a bond or an orbital, the so-called natural orbital Fukui function (NOFF) was proposed17, which can effectively interpret the bond formation mechanism17,18. On the other hand, more recently, the bonding reactivity descriptor based on the condensed-to-atom Fukui function19,20was proposed, and it is capable of evaluating the bonding trend between two atoms.Accordingly, in this work, we w ill apply NOFF and bonding reactivity descriptor to the [2 + 4] and [4 + 2] cycloadditions of o-thioquinones w ith 1,3-dienes to elucidate and assess the different bonding processes.

2 Theo retical fram ew o rks

For NOFF, theorfunction indicates the electronic response of a natural bond orbital upon electron addition or removal (N is the total number of electrons), respectively17.The positiveorsuggests that the orbital can accept or donate electrons, respectively. While the negativeormay not necessarily imply the electron philicity of an orbital,meaning that the orbital does not accept or donate electrons,respectively.

Scheme 1 Reactions of mono-ortho-thioquinones and alkenes via either [2 + 4] or [4 + 2] cycloaddition.

The Fukui functions can be represented by the change in the chemical potential μ due to perturbations in the external potential ν(r)21,22,

For chemical reaction, favorable reactions are closely related to the stabilization of the frontier molecular orbitals23,24, which can be referred to the “|dμ| big is good” rule25. Favorable electron-transfer interactions between reactants are related to the overlap between the Fukui functions of the reactive sites26–28.In a chemical reaction, to stabilize the frontier electrons, the chem ical potential μ should have the maximum change, so the reaction should occur between the charge-accepting site w ith the biggest(or) and the charge-donating site w ith the biggest(or), meaning that:

For the reaction between two reactants (M 1 and M 2), their reaction sites (α and β) conform to the follow ing energy expression26–28:

The reaction sites (α and β) are the bonding sites which occurs between M 1 and M 2, so the bonding between α and β termed as fbondingcan be w ritten as the sum of their Fukui functions. The large value of fbondingis favorable because the arithmetic/geometric mean inequality indicates that(fbonding)2is an upper bound to the product of the Fukui functions.Therefore, the maximum change in chem ical potential associated w ith electron transfer from site α (or β) to site β (or α) has the follow ing relationship:

where qkis the electronic charge of atom k and N is the number of electrons. These two condensed Fukui functions characterize the reactivity preferences for nucleophilic and electrophilic attacks on atom k, respectively.

In terms of the theoretical basis of f bonding mentioned above, it can be supposed that the bonding formation process can be represented using condensed-to-atom Fukui functions. The bonding would occur between the atom k1of M 1 and the atom k2of M 2 when the atoms k1and k2possess large values of Fukui functions(or) and(or f). Thereby, the sum of their Fukui functions should be as large as possible.Consequently, the descriptor fbondingwhich reveals the bonding trend for nucleophilic/electrophilic reaction can be w ritten as:

It is termed as the bonding reactivity descriptor29.Accordingly, the bonding formation would take place when the value of the f+bondingquantity is as large as possible.

3 Com pu tational m ethods

All calculations in this work were performed using the Gaussian 09 package30. The molecular geometries of the studied systems were fully optimized using the B3LYP functional31,32w ith 6-31+G(d,p) basis set. NBO16,33,34analysis was implemented at the same computational level, which can provide the natural orbital occupancy and natural atom ic charge.

Fig.1 The optim ized geometries for o-thioquinone (R1) and 1,3-dienes (R2, R2′) w ith some atom s numbered.

Tab le 1 NOFFs (unit in electrons) of the C1＝S1 and C2＝O 2 doub le bonds in R1 and of the C1＝C2 and C3＝C4 double bonds in R2 and R2’, and the reactivities of their natural bond orbitals based on the NOFF values a.

4 Resu lts and d iscussion

The representative [2 + 4] and [4 + 2] cycloadditions of o-thioquinone (R1) w ith 1,3-dienes (R2, R2’) investigated previously15were selected for this study, as shown in Fig.1.Different from the previous study, in this work, we analyzed the bonding formation mechanisms from the viewpoints of NOFF and bonding reactivity descriptor.

4.1 Perspective from NOFFs

For [2 + 4] cycloaddition of R1 w ith R2, one C＝S double bond in R1 and two C＝C double bonds in R2 directly participate in the reaction, they reorganize each other toform a six-membered ring containing one C＝C double bond and two new sigma bonds (i.e., C―C and C―S bonds). With regard to[4 + 2] cycloaddition of R1 w ith R2’, the C＝S and C＝O double bonds in R1 react w ith one C=C double bond in R2’ to give a six-membered ring containing one C＝C double bond and two new sigma bonds (i.e., C―S and C―O bonds). The nucleophilic or electrophilic nature of the double bond or its natural bond orbital involved in [2 + 4] and [4 + 2]cycloadditions determines the reaction process. Thereby, the reactivities of these double bonds w ill be assessed using the two NOFFs oand.

The f+nboand f−nbovalues for the C＝S and C＝O double bonds in R1 and for the C=C double bonds in R2 and R2’ are summarized in Table 1. For the C＝S double bond in R1, its BD(1)C1―S1o= 0.00004) is able to accept electrons while the BD(2)C1―S1= 0.92991) is able to donate electrons,the BD*(1)C1–S1 is inactive and the BD*(2)C1―S1=0.02222) seems to be electron-donating. With respect to the C=O double bond in R1, both its BD(1)C2―O2 (=0.00008) and BD(2)C2―O2= 0.01660) are able to donate electrons, the BD*(1)C2―O2 is inactive and the BD*(2)C2―O2 (= 0.01291) seems to be electron-donating. A bonding orbital has the ability to accept electrons which w ill strengthen the bond, but it is energetically unfavorable for an antibonding orbital in donating electrons, so the electron-donating character of an antibonding orbital w ill be disregarded herein. For the C1＝C2 double bond in R2, the BD(1)C1―C2 is inactive and BD(2)C1―C2 (= 0.96019)has the ability of donating electrons, but its BD*(1)C1―C2 is amphiphilic (= 0.00046,= 0.00196) and the BD*(2)C1–C2 (= 0.03795) seems to be electron-donating.The C3＝C4 double bond in R2 has the similar reactivity features to the C1＝C2 double bond (Table 1). The C3＝C4 double bond is located at the end of the R2, so it is more susceptible to being attacked by R1 than the C1＝C2 double bond. According to these values, in the [2 + 4] cycloaddition of R1 w ith R2 (Fig.2), the BD(2)C3―C4 bonding orbital of R2 donates electrons to the BD(1)C1―S1 bonding orbital of R1,and the BD*(1)C1―C2 antibonding orbital of R2 accepts electrons from the BD(2)C1―S1 bonding orbital of R1. As a result, a circular loop forms and leads to the six-membered ring accompanied by the formations of two new covalent bonds(i.e., C―S and C―C bonds).

With regard to the C1＝C2 double bond in R2’, the BD(1)C1―C2 is inactive and BD(2)C1―C2= 0.95200)can donate electrons, the BD*(1)C1―C2= 0.00052,= 0.00206) is amphiphilic and the BD*(2)C1―C2 (=0.05365) seems to be electron-donating. The C3＝C4 double bond has the similar reactivity features. Noticeably, different from the C1＝C2 double bond, the C3＝C4 double bond is located at the end of the R2’, so it is more easily to be attacked by R1. Therefore, in the [4 + 2] cycloaddition of R1 w ith R2’(Fig.3), the BD(2)C3―C4 bonding orbital of R2’ donates electrons to the BD(1)C1–S1 bonding orbital of R1, and the BD*(1)C3―C4 antibonding orbital of R2’ accepts electrons from the C2―O2 bonding orbital (e.g., BD(1)C2―O2 and BD(2)C2―O2) of R1. Consequently, the circular loop in leading to the six-membered ring forms which accomplishes the formations of two new covalent bonds (i.e., C―S and C―O bonds).

Fig.2 Proposed mechanism of [2 + 4] cycloaddition of R1 w ith R2.

Fig.3 Proposed mechanism of [4+2]cycloaddition of R1 w ith R2’.

Table 2 Fukui functions for atom s in the molecules R1, R2 and R2’.

4.2 Perspec tive from bond ing reac tivity desc rip tor

In this section, the negative Fukui function w ill not be considered because a negative Fukui function usually comes from the inability of a molecule to accommodate orbital relaxation caused by the changed number of electrons and/or improper charge partitioning techniques35–37or distorted molecular structures38,39. As summarized in Table 2, the C1 atom of R1 has the largestvalue (0.111) compared to other C atoms, indicating it is more susceptible to nucleophilic attack.The S1 and O2 atoms of R1 possessing largevalues (i.e.,0.123 and 0.311, respectively) mean their abilities to be susceptible to nucleophilic attack, while the O2 atom possessing the largestvalue (0.543) suggests that it is more susceptible to electrophilic attack. For R2 or R2’, the largestandvalues are observed for its C4 atom, followed by the C1 atom possessing the largerandvalues. Their C3 atoms also have largevalues. For the reaction between R1 and R2,according to the Fukui function values, it can be seen that the S1 atom of R1 and C4 atom of R2 readily forms C―S bond due to the largevalue (i.e.=+), while the C1 atom of R1 and C1 atom of R2 forms C―C bond=1 +). Although the O2 atom of R1 has the largestandvalues, the C2 atom bonded w ith O2 has lower reactivity due to the smallerand fvalues. Both the C1 and S1 atoms of R1 w ith good reactivity render them to react w ith R2 via [2 + 4] cycloaddition. The C1＝C2 and C3＝C4 double bonds of R2’ are different from those of R2, the steric effect makes the [4 + 2] cycloaddition more favorable, so only one C＝C double bond interacts with R1. The C4 atom of R2’ has largerandvalues than the C1 atom, and the C3 atom has largervalue than the C2 atom, so the C3＝C4 double bond located at the end of R2’ is more susceptible to being attacked by R1. Therefore, the bonding processes occur between S1 atom of R1 and C4 atom of R2’ (=+, and between O2 atom of R1 and C3 of R2’ (=+).The possible bonding mechanisms for [2 + 4] and [4 + 2]cycloadditions are shown in Figs.4 and 5, respectively.

Fig.4 Possible bonding mechanism s for [2 + 4] cycloaddition of R1 w ith R2.

Fig.5 Possible bonding mechanisms for [4 + 2] cycloaddition of R1 w ith R2’.

5 Conc lusions

In this work, natural orbital Fukui function (NOFF) which characterizes the electronic philicity of a bond or an orbital in a molecular system and bonding reactivity descriptor derived from Fukui functions which characterizes the bonding trend have been employed to explain the mechanisms of reactions between o-thioquinones and acyclic dienes via either [2 + 4] or[4 + 2] cycloaddition. NOFFs show that a bonding orbital w ith the electron-donating ability of one reactant interacts w ith an antibonding or bonding orbital w ith the electron-accepting ability of the other one, and vice versa. The electron transfer from an electron-donating bonding orbital to an electronaccepting antibonding/bonding orbital leads to the formation of a circular loop which is accompanied by the formations of two covalent bonds and thus the cyclic product. From bonding reactivity descriptor, the atom k1of one molecule w ith a large value in f+k1can readily form a covalent bond w ith atom k2of another molecule w ith a large value in f−k2, and the mechanism of [2 + 4] as well as [4 + 2] cycloaddition between o-thioquinone and acyclic diene is well interpreted. These results further suggest that NOFF and bonding reactivity descriptor are efficient Fukui functions w ithin the framework of conceptual density functional theory (CDFT)20,40,41or density functional reactivity theory (DFRT)25,42-44in explaining the bonding process of chemical reaction.

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