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Application of Natural Orbital Fukui Functions and Bonding Reactivity Descriptor in Understanding Bond Formation Mechanisms Underlying [2+4] and [4+2] Cycloadditions of o-Thioquinones with 1, 3-Dienes

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 基金资助: 国家自然科学基金.  21403097中央高校基本科研业务费专项资金.  lzujbky-2016-45

Corresponding authors: ZHOU Panpan, Email: zhoupp@lzu.edu.cn; Tel.: +86-931-8912862

 Fund supported: theNationalNaturalScienceFoundationofChina.  21403097the Fundamental Research Funds for the Central Universities, China.  lzujbky-2016-45

Abstract

o-Thioquinones can undergo either [2+4] or [4+2] cycloaddition reactions with acyclic dienes. To illustrate the bonding processes in these cycloadditions, the natural orbital Fukui function (NOFF) and bonding reactivity descriptor have been employed. The electrophilicity of a bond or an orbital in the o-thioquinone as well as in the acyclic diene has been found using the NOFF, which suggests that electron transfer takes place from an electron-donating bonding orbital to an electron-accepting antibonding/bonding orbital, leading to the cyclic product via the formation of a circular loop and two covalent bonds. The bonding reactivity descriptor shows that covalent bonds readily form between atom k1 of one molecule with a large fk1+ value and atom k2 of another molecule with a large fk2- value. Both the NOFF and the bonding reactivity descriptor are efficient tools for interpreting the mechanism underlying the [2+4] and [4+2] cycloaddition between o-thioquinones and acyclic dienes.

Keywords： Fukui function ; Natural orbital Fukui function (NOFF) ; Bonding reactivity descriptor ; Cycloaddition ; Nucleophilic/electrophilic attack

YAN Chaoxian, YANG Fan, WU Ruizhi, ZHOU Dagang, YANG Xing, ZHOU Panpan. Application of Natural Orbital Fukui Functions and Bonding Reactivity Descriptor in Understanding Bond Formation Mechanisms Underlying [2+4] and [4+2] Cycloadditions of o-Thioquinones with 1, 3-Dienes. Acta Physico-Chimica Sinica[J], 2018, 34(5): 497-502 doi:10.3866/PKU.WHXB201709222

1 Introduction

Mono-ortho-thioquinones 1-4 with the general formula 1 can serve as electron-poor heterodienes to react with many alkenes with the general formula 2 which act as electron-rich dienophiles via either a [2+4] 5 or a [4+2] 6-13 cycloaddition, 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 with acyclic dienes undergo the [2+4] path and are kinetically favored while the reactions of o-thioquinones with cyclic dienes go through the [4+2] path and are thermodynamically favored 14, 15. These reactions stimulate our great interest in exploring the mechanisms of their different bonding processes.

Scheme 1

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

Chemical reaction involves the bond breakage and formation, so using the chemical 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 (NBO 16) for describing the chemical reactivity of a bond or an orbital, the so-called natural orbital Fukui function (NOFF) was proposed 17, which can effectively interpret the bond formation mechanism 17, 18. On the other hand, more recently, the bonding reactivity descriptor based on the condensed-to-atom Fukui function 19, 20 was proposed, and it is capable of evaluating the bonding trend between two atoms. Accordingly, in this work, we will apply NOFF and bonding reactivity descriptor to the [2+4] and [4+2] cycloadditions of o-thioquinones with 1, 3-dienes to elucidate and assess the different bonding processes.

2 Theoretical frameworks

For NOFF, the fnbo+ or fnbo- function indicates the electronic response of a natural bond orbital upon electron addition or removal (N is the total number of electrons), respectively 17. The positive fnbo+ or fnbo- suggests that the orbital can accept or donate electrons, respectively. While the negative fnbo+ or fnbo- may not necessarily imply the electron philicity of an orbital, meaning that the orbital does not accept or donate electrons, respectively.

$f_{{\rm{nbo}}}^ + = \left( {\frac{{\partial {n_{{\rm{nbo}}}}}}{{\partial N}}} \right)_{v{\rm{(r)}}}^ + = n_{{\rm{nbo}}}^{N + 1}-n_{{\rm{nbo}}}^N$

$f_{{\rm{nbo}}}^-= \left( {\frac{{\partial {n_{{\rm{nbo}}}}}}{{\partial N}}} \right)_{v{\rm{(r)}}}^-= n_{{\rm{nbo}}}^N-n_{{\rm{nbo}}}^{N - 1}$

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,

$f(r) = {\left( {\frac{{\delta \mu }}{{\delta \nu (r)}}} \right)_N}$

For chemical reaction, favorable reactions are closely related to the stabilization of the frontier molecular orbitals 23, 24, which can be referred to the "|dμ| big is good" rule 25. Favorable electron-transfer interactions between reactants are related to the overlap between the Fukui functions of the reactive sites 26-28. In a chemical reaction, to stabilize the frontier electrons, the chemical potential μ should have the maximum change, so the reaction should occur between the charge-accepting site with the biggest fα+ (or fβ+) and the charge-donating site with the biggest fβ- (or fα-), meaning that:

$\Delta \mu \propto \max f_{\rm{ \mathsf{ α} }}^ + + \max f_{\rm{ \mathsf{ β} }}^{\rm{ - }}$

${\rm{or}}\;\Delta \mu \propto \max f_{\rm{ \mathsf{ β} }}^ + + \max f_{\rm{ \mathsf{ α} }}^ -$

For the reaction between two reactants (M1 and M2), their reaction sites (α and β) conform to the following energy expression 26-28:

$\int {\frac{{f_{{\rm{M}}1}^ + ({r_1})f_{{\rm{M}}2}^ - ({r_2})}}{{\left| {{r_1} - {r_2}} \right|}}{\rm{d}}{r_1}{\rm{d}}{r_2} \approx \sum\limits_{{\rm{ \mathsf{ α} }} \in {{\rm{M}}2}} {\sum\limits_{{\rm{ \mathsf{ β} }} \in {{\rm{M}}2}} {\frac{{f_\alpha ^ + f_\beta ^ - }}{{\left| {{r_{1;{\rm{ \mathsf{ α} }}}} - {r_{2;{\rm{ \mathsf{ β} }}}}} \right|}}} } } \le \frac{1}{4}\sum\limits_{{\rm{ \mathsf{ α} }} \in {{\rm{M}}2}} {\sum\limits_{{\rm{ \mathsf{ β} }} \in {{\rm{M}}2}} {\frac{{{{(f_{\rm{ \mathsf{ α} }}^ + + f_{\rm{ \mathsf{ β} }}^ - )}^2}}}{{\left| {{r_{1;{\rm{ \mathsf{ α} }}}} - {r_{2;{\rm{ \mathsf{ β} }}}}} \right|}}} }$

or

$\int {\frac{{f_{{\rm{M}}1}^ + ({r_1})f_{{\rm{M}}2}^ - ({r_2})}}{{\left| {{r_1} - {r_2}} \right|}}{\rm{d}}{r_1}{\rm{d}}{r_2} \approx \sum\limits_{{\rm{ \mathsf{ α} }} \in {{\rm{M}}2}} {\sum\limits_{{\rm{ \mathsf{ β} }} \in {{\rm{M}}2}} {\frac{{f_{\rm{ \mathsf{ α} }}^ + f_{\rm{ \mathsf{ β} }}^ - }}{{\left| {{r_{1;{\rm{ \mathsf{ α} }}}} - {r_{2;{\rm{ \mathsf{ β} }}}}} \right|}}} } } \le \frac{1}{4}\sum\limits_{{\rm{ \mathsf{ α} }} \in {{\rm{M}}2}} {\sum\limits_{{\rm{ \mathsf{ β} }} \in {{\rm{M}}2}} {\frac{{{{(f_{\rm{ \mathsf{ α} }}^ + + f_{\rm{ \mathsf{ β} }}^ - )}^2}}}{{\left| {{r_{1;{\rm{ \mathsf{ α} }}}} - {r_{2;{\rm{ \mathsf{ β} }}}}} \right|}}} }$

The reaction sites (α and β) are the bonding sites which occurs between M1 and M2, so the bonding between α and βtermed as fbonding can be written as the sum of their Fukui functions. The large value of fbonding is favorable because the arithmetic/geometric mean inequality indicates that ¼(fbonding)2 is an upper bound to the product of the Fukui functions. Therefore, the maximum change in chemical potential associated with electron transfer from site α (or β) to site β (or α) has the following relationship:

$f_{{\rm{bonding}}}^ \pm = {\rm{max}}f_{\rm{ \mathsf{ α} }}^ + + {\rm{max}}f_{\rm{ \mathsf{ β} }}^ - \sim \Delta \mu$

${\rm{or}}\;f_{{\rm{bonding}}}^ \pm = {\rm{max}}f_{\rm{ \mathsf{ β} }}^ - + {\rm{max}}f_{\rm{ \mathsf{ α} }}^ + \sim \Delta \mu$

The condensed-to-atom Fukui function for an atom k in a molecule can be derived from the difference in atomic charges 19, 20:

$f_k^ + = {q_k}(N)-{q_k}(N + 1), {\rm{governing}}\;{\rm{nucleophilic}}\;{\rm{attack}}$

$f_k^-= {q_k}(N-1)-{q_k}(N), {\rm{governing}}\;{\rm{electrophilic}}\;{\rm{attack}}$

where qk is 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 fbonding 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 M1 and the atom k2of M2 when the atoms k1and k2 possess large values of Fukui functions fk1+ (or fk1) and fk-2 (or fk2+). Thereby, the sum of their Fukui functions should be as large as possible. Consequently, the descriptor fbonding which reveals the bonding trend for nucleophilic/electrophilic reaction can be written as:

$f_{{\rm{bonding}}}^ \pm = f_{k1}^ + + f_{k2}^-$

It is termed as the bonding reactivity descriptor 29. Accordingly, the bonding formation would take place when the value of the fbonding+ quantity is as large as possible.

3 Computational methods

All calculations in this work were performed using the Gaussian 09 package 30. The molecular geometries of the studied systems were fully optimized using the B3LYP functional 31, 32 with 6-31+G(d, p) basis set. NBO 16, 33,