A Molecular Electron Density Theory Study and Mechanistic Aspect

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Article Participation of Phosphorylated Analogues of Nitroethene in Diels–Alder Reactions with Anthracene: A Molecular Electron Density Theory Study and Mechanistic Aspect

Agnieszka K ˛acka-Zych

Institute of Organic Chemistry and Technology, Cracow University of Technology, Warszawska 24, 31-155 Cracow, Poland; [email protected]

Received: 30 October 2020; Accepted: 20 November 2020; Published: 23 November 2020

Abstract: The structure and the contribution of the bis(2-chloroethyl) 2-nitro 1a and 2-bromo- 2-nitroethenylphosphonates 1b with anthracene 2 in the Diels–Alder (DA) reactions have been studied within the Molecular Electron Density Theory (MEDT) at the B3LYP functional together with 6-31G(d), 6-31+G(d) and 6-31+G(d,p) basic sets. Analysis of the Conceptual Density Functional Theory (CDFT) reactivity indices indicates that 1a and 1b can be classified as a strong electrophile and marginal nucleophile, while 2 is classified as a strong electrophile and strong nucleophile. The studied DA reactions take place through a one-step mechanism. A Bonding Evolution Theory (BET) of the one path associated with the DA reaction of 1a with 2 indicates that it is associated with non-concerted two-stage one-step mechanism. BET analysis shows that the first C2-C3 single bond is formed in Phase VI, while the second C1-C6 single bond is formed in the Phase VIII. The formation of both single bonds occurs through the merging of two C2 and C3, C1 and C6 pseudoradical centers, respectively.

Keywords: Diels–Alder reaction; anthracene; molecular mechanism; bonding evolution theory; molecular electron density theory

1. Introduction The Diels–Alder (DA) reaction is among the most formidable available protocols for the construction of optically active compounds, with extensive synthetic applications in natural products with a large range of biological activity [1–4]. Many studies concerning of the DA reactions put these reactions in a completely different light; a one-step mechanism has been replaced by a two-step mechanism undergoing through the intermediate. Korotayev and Sosnovsky [5] presented experimental studies of the reaction between (E)-1,1,1-trifluoro-3-nitrobut-2-ene and 3,3-dimethyl-2-morpholinbutene (Scheme1) in which, apart from the main product, the Authors confirmed the presence of an acyclic adduct. Recently theoretical studies [6] confirm the stepwise, zwitterionic mechanism formation of final, internal nitronate. In 2011, Korotaev and co-workers [7] studied the reactions of α-(trihaloethylidene)-nitroalkanes with push–pull enamines (Scheme2). It was found that the reaction of α-(trihaloethylidene)-nitroalkanes with push–pull enamines affords one to cycloadduct or linear enamines depending on the nature of the trihalomethyl group. In the case of the experimental [8] and theoretical [9] research of the reaction between 1-methylpyrrole and dimethyl acetylenedicarboxylate two alternative reaction pathways have also been considered. This reaction proceeds with a two-step formation of cycloadduct, and intramolecular proton transfer affords a Michael adduct (Scheme3).

Organics 2020, 1, 36–48; doi:10.3390/org1010004 www.mdpi.com/journal/organics Organics 2020, 1, FOR PEER REVIEW 2

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Scheme 1. Experimentally and theoretically observed course of reaction between (E)-1,1,1-trifluoro- 3-nitrobut-2-ene and 3,3-dimethyl-2-morpholinobutene [5,6].

In 2011, Korotaev and co-workers [7] studied the reactions of α-(trihaloethylidene)-nitroalka nes with push–pull enamines (Scheme 2). It was found that the reaction of α-(trihaloethylidene)- Scheme 1.1. Experimentally and theoretically observed course of reaction between (E) (E)-1,1,1-triﬂuoro--1,1,1-trifluoro- nitroalkanes with push–pull enamines affords one to cycloadduct or linear enamines depending on 3-nitrobut-2-ene3-nitrobut-2-ene and 3,3-dimethyl-2-morpholinobutene3,3-dimethyl-2-morpholinobutene [[55,6,6].]. the nature of the trihalomethyl group. In 2011, Korotaev and co-workers [7] studied the reactions of α-(trihaloethylidene)-nitroalkanes with push–pull enamines (Scheme 2). It was found that the reaction of α-(trihaloethylidene)- nitroalkanes with push–pull enamines affords one to cycloadduct or linear enamines depending on the nature of the trihalomethyl group.

Scheme 2. Experimentally observed course of reaction between α-(trihaloethylidene)-nitroalkanes with push–pull enamines [7].

In the case of the experimental [8] and theoretical [9] research of the reaction between 1- methylpyrrole and dimethyl acetylenedicarboxylate two alternative reaction pathways have also Scheme 2. Experimentally observed course of reaction between α-(trihaloethylidene)-nitroalkanes been considered. This reaction proceeds with a two-step formation of cycloadduct, and with push–pull enamines [7]. intramolecular proton transfer affords a Michael adduct (Scheme 3). In the case of the experimental [8] and theoretical [9] research of the reaction between 1- methylpyrrole and dimethyl acetylenedicarboxylate two alternative reaction pathways have also been considered. This reaction proceeds with a two-step formation of cycloadduct, and intramolecular proton transfer affords a Michael adduct (Scheme 3).

Scheme 3.3. ExperimentallyExperimentally and and theoretically theoretically observed observed course course of reactionof reaction between between 1-methylpyrrole 1-methylpyrrole with dimethylwith dimethyl acetylenedicarboxylate acetylenedicarboxylate [8,9]. [8,9].

Anisimova and co-workers [10], examined the reactions of the bis(2-chloroethyl) 2-nitro 1a and Anisimova and co-workers [10], examined the reactions of the bis(2-chloroethyl) 2 -nitro 1a and 2-bromo-2-nitroethenylphosphonates2-bromo-2-nitroethenylphosphonates 1b1b withwith anthracene 22 which lead to product 3a,b and trace Scheme 3. Experimentally and theoretically observed course of reaction between 1-methylpyrrole amounts of acyclic adduct 4a,b (Scheme(Scheme4 ).4). The The authors authors did did not not undertake undertake any any research research on on the the with dimethyl acetylenedicarboxylate [8,9]. mechanism of these reactions. Based on the presence of an acyclic product 4a-b in the post-reaction mixture, we can suspect the formation of 3a-b to come about by a two-step mechanism. In this case, Anisimova and co-workers [10], examined the reactions of the bis(2-chloroethyl) 2-nitro 1a and the possibility of creating a product 3a-b through a two-step mechanism is highly presumable. On this 2-bromo-2-nitroethenylphosphonates 1b with anthracene 2 which lead to product 3a,b and trace basis,Scheme the mechanism 3. Experimentally of the bis(2-chloroethyl) and theoretically observed 2-nitro 1a courseand of 2-bromo-2-nitroethenylphosphonates reaction between 1-methylpyrrole amounts of acyclic adduct 4a,b (Scheme 4). The authors did not undertake any research on the 1b withwith anthracene dimethyl acetylenedicarboxylate2 require a deeper exploration. [8,9]. To ﬁll the gap that has arisen, we seal to execute the Molecular Electron Density Theory (MEDT) [11] analysis, in which a connection of the analysis of Anisimova and co-workers [10], examined the reactions of the bis(2-chloroethyl) 2-nitro 1a and 2-bromo-2-nitroethenylphosphonates 1b with anthracene 2 which lead to product 3a,b and trace amounts of acyclic adduct 4a,b (Scheme 4). The authors did not undertake any research on the

Organics 2020, 1, FOR PEER REVIEW 3 mechanism of these reactions. Based on the presence of an acyclic product 4a-b in the post-reaction mixture, we can suspect the formation of 3a-b to come about by a two-step mechanism. In this case, the possibility of creating a product 3a-b through a two-step mechanism is highly presumable. On this basis, the mechanism of the bis(2-chloroethyl) 2-nitro 1a and 2-bromo-2- nitroethenylphosphonates 1b with anthracene 2 require a deeper exploration. To fill the gap that has Organics 2020, 1 38 arisen, we seal to execute the Molecular Electron Density Theory (MEDT) [11] analysis, in which a connection of the analysis of reaction profiles, key stationary structures and the Bonding Evolution Theoryreaction proﬁles, (BET) [ key12] stationary analysis structures of the molecular and the Bonding mechanism Evolution of Theory reaction (BET) bis(2 [12-]chloroethyl) analysis of the-2- nitroethenylphosphonatesmolecular mechanism of reaction 1a with bis(2-chloroethyl)-2-nitroethenylphosphonates anthracene 2. 1a with anthracene 2.

Scheme 4. 4. ExperimentallyExperimentally observed observed course course of the of reaction the reaction bis(2-chloroethyl) bis(2-chloroethyl) 2-nitro 1a 2-nitro and 2- 1abromo and- 22-bromo-2-nitroethenylphosphonates-nitroethenylphosphonates 1a,b with1a,b anthracenewith anthracene 2 [10]. 2 [10].

2. Computational Details 2. Computational Details All calculations associated with the DA reactions were performed using the GAUSSIAN All calculations associated with the DA reactions were performed using the GAUSSIAN 16 16 package [13] in the Prometheus computer cluster of the CYFRONET regional computer center package [13] in the Prometheus computer cluster of the CYFRONET regional computer center in in Cracow. The geometries of all reactants, transition state structures (TSs) and products of the reactions Cracow. The geometries of all reactants, transition state structures (TSs) and products of the reactions were fully optimized using the B3LYP [14] functional together with the 6-31G(d), 6-31+G(d) and were fully optimized using the B3LYP [14] functional together with the 6-31G(d), 6-31+G(d) and 6- 6-31+G(d,p) basis sets. This computational level has already been successfully used for the exploration 31+G(d,p) basis sets. This computational level has already been successfully used for the exploration of a reaction involving several different nitrocompounds and others [15–19]. Intrinsic reaction of a reaction involving several different nitrocompounds and others [15–19]. Intrinsic reaction coordinate (IRC) calculations [20] were achieved in all instances to verify that the located TSs are coordinate (IRC) calculations [20] were achieved in all instances to verify that the located TSs are connected to the corresponding minimum stationary points associated with reactants and products. connected to the corresponding minimum stationary points associated with reactants and products. The solvent effects of benzene were simulated using a relatively simple self-consistent reaction field The solvent effects of benzene were simulated using a relatively simple self-consistent reaction field (SCRF) [21–23] based on the polarizable continuum model (PCM) of Tomasi’s group [24,25]. The values (SCRF) [21–23] based on the polarizable continuum model (PCM) of Tomasi’s group [24,25]. The valuesof energies, of energies, enthalpies, enthalpies, entropies entropies and Gibbs and Gibbsfree energies free energies were calculatedwere calculated for temperature for temperature 353K. The353K. global The global electron electron density density transfer transfer (GEDT) (GEDT) [26] values [26] werevalues calculated were calculated as the sum as the of sumthe natural of the atomic charges (q), obtained by a Natural Population Analysis (NPA) [27,28], by the equation: GEDT naturalP atomic charges (q), obtained by a Natural Population Analysis (NPA) [27,28], by the equation: (f) = q for all atoms belonging to each fragment (f) of the TSs at the B3LYP(PCM)/6-31G(d) level GEDTq (f)f = , for all atoms belonging to each fragment (f) of the TSs at the B3LYP(PCM)/6- ∈ 31G(d)of theory. level of theory. Indexes of σ-bonds-bonds development (l) were designed accordingaccording toto equationequation [[1515]:]:

TS P rTSXY rrPXY l XY  1  X Y X Y lX Y = 1 − P− − − − rPXY rX Y − where rTSX-Y is the distance between the reaction centers X and Y in the transition structure and rPX-Y where rTS is the distance between the reaction centers X and Y in the transition structure and rP is the sameX-Y distance in the corresponding product. X-Y is the same distance in the corresponding product. Global electronic properties of the reactants were estimated according to the equations Global electronic properties of the reactants were estimated according to the equations recommended in references [29,30]. The electronic chemical potentials (μ), chemical hardness (η) and recommended in references [29,30]. The electronic chemical potentials (µ), chemical hardness (η) global nucleophilicity (N) have been calculated according to a well-known protocol [31,32]. and global nucleophilicity (N) have been calculated according to a well-known protocol [31,32]. Electrophilic 푃+ and nucleophilic 푃− Parr functions [33] were obtained from the changes of atomic Electrophilic P+푘 and nucleophilic P 푘. Parr functions [33] were obtained from the changes of atomic spin density (ASD)k of the reagents. k− spin density (ASD) of the reagents. Electron Localization Function (ELF) [34] research was accomplished with the TopMod package Electron Localization Function (ELF) [34] research was accomplished with the TopModpackage [35]. [35]. The bonding modifications through the analyzed reaction were studied, according to the BET The bonding modifications through the analyzed reaction were studied, according to the BET [12], by executing the topological analysis of the ELF for 173 nuclear configurations along the IRC path. The ELF molecular geometries and basin attractor positions were depicted using the GaussView program [36]. ELF localization domains were represented by using the Paraview software at an Organics 2020, 1 39 isovalue of 0.75 a.u [37,38]. A similar approach has been successfully used to explain the mechanism of different types of reactions [16–19,39].

3. Results and Discussion The present theoretical study has been divided into three parts: (i) ﬁrst, the analysis of the conceptual density functional theory (CDFT) reactivity indices and ELF characterization of the reactants was carried out (ii) second, the DA reaction proﬁles of the bis(2-chloroethyl) 2-nitro- 1a and bis(2-chloroethyl) 2-bromo-2-nitroethenylphosphonates 1b with anthracene 2 including full diagnostic of all critical structures are explored and characterized (iii) and next, a BET study of the reaction between bis(2-chloroethyl) 2-nitro-ethenylphosphonate 1a and anthracene 2, in order to characterize the molecular mechanism was performed.

3.1. Analysis of the CDFT Reactivity Indices and ELF Characterization of the Reactants In order to understand the contribution of reagents in the DA reactions, the analysis of the global indices was achieved at the B3LYP/6-31G(d) level of theory, within the context of the CDFT [29,30]. The electronic chemical potential µ, chemical hardness η, global electrophilicity ω and global nucleophilicity N are collected in Table1.

Table 1. B3LYP/6-31G(d) electronic chemical potential µ, chemical hardness η, global electrophilicity ω, and global nucleophilicity N, in eV, for the studied reagents.

µ η ω N 1a 5.59 5.19 3.01 0.94 − 1b 5.62 4.74 3.33 1.13 − 2 3.43 3.59 1.64 3.89 −

The electronic chemical potential [40] µ of 2, 3.34 eV, is higher than that of 1a and 1b, − 5.59 eV and 5.62 eV, respectively. On the basic of the calculated values of the electronic chemical − − potential, it can be concluded that the GEDT [27,28] in these DA reactions will proceed from anthracene 2 towards to bis(2-chloroethyl) 2-nitro nitroethenylphosphonate 1a and bis(2-chloroethyl) 2-bromo-2-nitroethenylphosphonates 1b. The electrophilicity [31] ω and global nucleophilicity [32]N indices of 1a are 3.01 eV and 0.94 eV and for 1b are 3.33 eV and 1.13 eV. Based on the electrophilicity [41] and nucleophilicity [42] scale, 1a and 1b can be classiﬁed as a strong electrophile and marginal nucleophile. In turn, the electrophilicity ω and global nucleophilicity N indices of 2 are 1.64 eV and 3.89 eV, respectively. According to that, 2 can be classiﬁed as a strong electrophile but remaining a strong nucleophile. The electron density changes on the electrophile and nucleophile can be sensed by the nucleophilic + Pk−. and electrophilic Pk Parr functions [33], which are good predictors for local reactivity in polar + processes. The electrophilic Pk and the nucleophilic Pk−. and Parr functions for the GS of the reagents are gathered in Figure1. + + + An analysis of the electrophilic Pk Parr functions of 1a, Pk = 0.33 and 1b, Pk = 0.31, indicates + that C2 atoms in both are the most electrophilic their center. In turn, the C1 atoms in 1a, Pk = 0.15 and + 1b, Pk = 0.16, indicate the lower electrophilic character. In the case of 2, an analysis of the nucleophilic Pk− Parr functions, indicate that C3, Pk− = 0.29, and C6, Pk− = 0.29, are the most nucleophilic center in the molecule while C4, C5, C7 and C8 centers show negligible nucleophilic characters. In order to characterize the ELF structures of bis(2-chloroethyl) 2-nitro- 1a and bis(2-chloroethyl) 2-bromo-2-nitroethenylphosphonates 1b with anthracene 2 a quantum chemical analysis of Becke and Edgecombe’s ELF [34] was conducted. Figure2 shows the most important valence basin populations and ELF localization domains. Organics 2020, 1, FOR PEER REVIEW 5

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1a·- 1b·-

2·+ 1a·- 1b·- Figure 1. 3D representations of the ASD of the radical anion 1a·- and 1b·- and the radical cation 2a·+, together + − with the electrophilic 푃푘 Parr functions of 1a-b and the nucleophilic 푃푘 Parr functions of 2.

+ + + An analysis of the electrophilic 푃푘 Parr functions of 1a, 푃푘 = 0.33 and 1b, 푃푘 = 0.31, indicates that + C2 atoms in both are the most electrophilic their center. In turn, the C1 atoms in 1a, 푃푘 = 0.15 and + 1b, 푃푘 = 0.16, indicate the lower electrophilic character. In the case of 2, an analysis of the − − − nucleophilic 푃푘 Parr functions, indicate that C3, 푃푘 = 0.29, and C6, 푃푘 = 0.29, are the most nucleophilic center in the molecule while C4, C5, C7 and C8 centers show negligible nucleophilic characters. In order to characterize the ELF structures of 2·bis(2+ -chloroethyl) 2-nitro- 1a and bis(2-chloroethyl) 2-bromo-2-nitroethenylphosphonates 1b with anthracene 2 a quantum chemical analysis of Becke Figure 1.1. 3D3D representations representations of of the the ASD ASD of the of theradical radical anion anion 1a·- and1a - 1b·and- and1b the- and radical the radicalcation 2a· cation+, together2a +, · · · and Edgecombe’s ELF [3+4] was + conducted. Figure 2 shows the− most important valence basin togetherwith the electrophilic with the electrophilic 푃 Parr functionsP Parr functionsof 1a-b and of the1a-b nucleophilicand the nucleophilic 푃푘 Parr functionsP− Parr of functions 2. of 2. populations and ELF localization푘 kdomains. k + + + An analysis of the electrophilic 푃푘 Parr functions of 1a, 푃푘 = 0.33 and 1b, 푃푘 = 0.31, indicates that + C2 atoms in both are the most electrophilic their center. In turn, the C1 atoms in 1a, 푃푘 = 0.15 and + 1b, 푃푘 = 0.16, indicate the lower electrophilic character. In the case of 2, an analysis of the − − − nucleophilic 푃푘 Parr functions, indicate that C3, 푃푘 = 0.29, and C6, 푃푘 = 0.29, are the most nucleophilic center in the molecule while C4, C5, C7 and C8 centers show negligible nucleophilic characters. In order to characterize the ELF structures of bis(2-chloroethyl) 2-nitro- 1a and bis(2-chloroethyl) 2-bromo-2-nitroethenylphosphonates 1b with anthracene 2 a quantum chemical analysis of Becke and Edgecombe’s ELF [34] was conducted. Figure 2 shows the most important valence basin populations and ELF localization domains.

Organics 2020, 1, FOR PEER REVIEW 6 1a 1b

2 Figure 2. B3LYP/6-31G(d) basin attractor positions together with the most signiﬁcant valence Figure 2. B3LYP/6-31G(d)1a basin attractor positions together with the1b most significant valence basin basinpopulations populations of bis(2 of-chloroethyl) bis(2-chloroethyl) 2-nitronitroethenyl 2-nitronitroethenyl-phosphonate-phosphonate 1a and bis(21a and-chloroethyl) bis(2-chloroethyl) 2-bromo- 2-bromo-2-nitroethenyl-phosphonate2-nitroethenyl-phosphonate 1b with anthracene1b with anthracene 2. 2.

ELF topological analysis of bis(2-chloroethyl) 2-nitroethenylphosphonate 1a, in the most important region, shows the presence of two V(C1,C2) and V’(C1,C2) disynaptic basins integrating the same value of 1.74 e. In the bis(2-chloroethyl) 2-bromo-2-nitroethenylphosphonate 1b, we also find, in the most important region, V(C1,C2) and V’(C1,C2) disynaptic basins integrating 1.85 e and 1.84 e, respectively. These disynaptic basins are associated with C1-C2 double bonds in 1a and 1b molecules. In turn, an ELF topological analysis of anthracene 2 of the C-C bonding regions belonging to the aromatic rings are characterized by the presence of six V(C3,C4), V(C4,C5), V(C5,C6), V(C6,C7), V(C7,C8) and V(C8,C3) disynaptic basins integrating in all cases 2.47 e–2.93 e (Figure 2). These disynaptic basins are connected with partial double bonds in the most important region in anthracene 2.

3.2. DA Reaction Profiles of the bis(2-chloroethyl) 2-nitro- 1a and bis(2-chloroethyl) 2-bromo-2- Nitroethenylphosphonates 1b with Anthracene 2 Second, the DA reactions between bis(2-chloroethyl) 2-nitro- 1a and bis(2-chloroethyl) 2-bromo- 2-nitroethenylphosphonates 1b with anthracene 2 were studied. The relative electronic energies of the stationary points involved in the DA reactions between 1a-b and 2 are presented in Scheme 5. A one-step mechanism is determined for these DA reactions after to perform a carefully of the corresponding stationary points (Scheme 5).

Scheme 5. DA reaction of the bis(2-chloroethyl) 2-nitro-ethenylphosphonate 1a and bis(2-chloroethyl) 2-bromo-2-nitroethenylphosphonates 1b with anthracene 2. B3LYP(PCM)/6-31G(d) relative energies are given in kcal·mol−1.

The quantum-chemical calculations show that the reactions 1a-b with 2 in the benzene solution at the initial stage lead to molecular complexes (MCs). The energy is reduced until the formation of MCs located 1.6 (MC1) and 3.0 (MC2) kcal/mol bellow the separated reagents takes place. The activation energy associated with the reactions 1a-b with 2, via TS1 and TS2, presents a high value,

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Figure 2. B3LYP/6-31G(d) basin attractor positions together with the most significant valence basin populations of bis(2-chloroethyl) 2-nitronitroethenyl-phosphonate 1a and bis(2-chloroethyl) 2-bromo- Organics 2020, 1 41 2-nitroethenyl-phosphonate 1b with anthracene 2.

ELF topological topological analysis analysis of bis(2-chloroethyl) of bis(2-chloroethyl) 2-nitroethenylphosphonate 2-nitroethenylphosphonate1a, in the 1a most, in important the most region,important shows region, the presence shows the of twopresence V(C1,C2) of two and V(C1,C2) V’(C1,C2) and disynaptic V’(C1,C2) basins disynaptic integrating basins the integrating same value ofthe 1.74 same e. Invalue the bis(2-chloroethyl)of 1.74 e. In the bis(2 2-bromo-2-nitroethenylphosphonate-chloroethyl) 2-bromo-2-nitroethenylphosphonate1b, we also ﬁnd, 1b in, the we most also importantfind, in the region, most important V(C1,C2) andregion, V’(C1,C2) V(C1,C2) disynaptic and V’(C1,C2) basins integratingdisynaptic 1.85basins e and integrating 1.84 e, respectively. 1.85 e and These1.84 e, disynapticrespectively. basins These are disynaptic associated basins with C1-C2are associated double bondswith C1 in-C21a doubleand 1b bondsmolecules. in 1a Inand turn, 1b anmolecules. ELF topological In turn, an analysis ELF topological of anthracene analysis2 ofof theanthracene C-C bonding 2 of the regions C-C bonding belonging regions to thebelonging aromatic to ringsthe aromatic are characterized rings are charby theacterized presence by of the six presence V(C3,C4), of V(C4,C5), six V(C3,C4), V(C5,C6), V(C4,C5), V(C6,C7), V(C5,C6), V(C7,C8) V(C6,C7), and V(C8,C3)V(C7,C8) and disynaptic V(C8,C3) basins disynaptic integrating basins in integrating all cases 2.47 in all e–2.93 cases e 2.47 (Figure e–2.932). e These (Figure disynaptic 2). These basinsdisynaptic are connectedbasins are connected with partial with double partial bonds double in bonds the most in the important most important region in region anthracene in anthracene2. 2.

3.2. DA Reaction Profiles Proﬁles of the bis(2-chloroethyl)bis(2-chloroethyl) 2-nitro-2-nitro- 1a1a andand bis(2-chloroethyl)bis(2-chloroethyl) 2-bromo-2- 2-bromo-2-NitroethenylphosphonatesNitroethenylphosphonates 1b with Anthracene 1b with Anthracene 2 2 Second,Second, the the DA DA reactions reactions between between bis(2- bis(2-chloroethyl)chloroethyl) 2-nitro 2-nitro-- 1a and b1ais(2and-chloroethyl) bis(2-chloroethyl) 2-bromo- 2-bromo-2-nitroethenylphosphonates2-nitroethenylphosphonates 1b with anthracene1b with anthracene 2 were studied.2 were The studied. relative The electronic relative energies electronic of energiesthe stationary of the points stationary involved points in involvedthe DA reactions in the DA between reactions 1a-b between and 2 are1a-b presentedand 2 are in presentedScheme 5. inA Schemeone-step5 . mec A one-stephanism mechanism is determined is determined for these forDA these reactions DA reactions after to after perform to perform a carefully a carefully of the of thecorresponding corresponding stationary stationary points points (Scheme (Scheme 5). 5).

Scheme 5.5. DADA reaction reaction of of the the bis(2 bis(2-chloroethyl)-chloroethyl) 2 2-nitro-ethenylphosphonate-nitro-ethenylphosphonate 1a andand bis(2 bis(2-chloroethyl)-chloroethyl) 2-bromo-2-nitroethenylphosphonates2-bromo-2-nitroethenylphosphonates 1b with anthracene 2. B3LYP(PCM)/6 B3LYP(PCM)/6-31G(d)-31G(d) relative energies 1 are given in kcal mol −1 . are given in kcal·mol· − .

The quantum-chemicalquantum-chemical calculationscalculations show show that that the the reactions reactions1a-b 1a-bwith with2 in2 in the the benzene benzene solution solution at theat the initial initial stage stage lead lead to molecularto molecular complexes complexes (MCs). (MCs The). The energy energy is reduced is reduced until until the formation the formation of MCs of locatedMCs located 1.6 (MC1 1.6 ) ( andMC1 3.0) and (MC2 3.0) kcal (MC2/mol) kcal/mol bellow the bellow separated the separated reagents takes reagents place. takes The place. activation The 1 energyactivation associated energy withassociated the reactions with the1a-b reactionswith 2, via1a-TS1b withand 2,TS2 via, TS1 presents and aTS2 high, presents value, 22.4 a high kcal value,mol− 1 · and 19.3 kcal mol− , respectively. Then, formation of the ﬁnal products 3a-b are exothermic by ·1 1 13.0 kcal mol− and 14.4 kcal mol− , respectively. The relative enthalpies, Gibbs free energy and · · entropies of the stationary points involved in the DA reactions between 2-nitro-ethenylphosphonate 1a, bis(2-chloroethyl) 2-bromo-2-nitroethenylphosphonates 1b and anthracene 2 are given in Table2. B3LYP(PCM)/6-31G(d) the activation Gibbs free energy associated with DA reactions 1a-b and 2, via TS1 and TS2 is 36.8 kcal mol 1 and 35.2 kcal mol 1, respectively. The calculations carried out using · − · − 6-31+G(d) and 6-31+G(d,p) basic sets (see Table S1 in Supplementary Information) show increase of Gibbs free energy in the case of reaction between bis(2-chloroethyl) 2-nitro-ethenylphosphonate 1a and anthracene 2, for TS1 38.5 kcal mol 1 and 38.8 kcal mol 1, respectively. In turn, in the case of the reaction · − · − between bis(2-chloroethyl) 2-bromo-2-nitroethenylphosphonates 1b and anthracene 2, we observed the reduction of Gibbs free energy for TS2, 30.3 kcal mol 1 and 31.2 kcal mol 1, respectively. · − · − Organics 2020, 1, FOR PEER REVIEW 7

22.4 kcal·mol−1 and 19.3 kcal·mol−1, respectively. Then, formation of the final products 3a-b are exothermic by 13.0 kcal·mol−1 and 14.4 kcal·mol−1, respectively. The relative enthalpies, Gibbs free energy and entropies of the stationary points involved in the DA reactions between 2-nitro- ethenylphosphonate 1a, bis(2-chloroethyl) 2-bromo-2-nitroethenylphosphonates 1b and anthracene 2 are given in Table 2. B3LYP(PCM)/6-31G(d) the activation Gibbs free energy associated with DA reactions 1a-b and 2, via TS1 and TS2 is 36.8 kcal·mol−1 and 35.2 kcal·mol−1, respectively. The calculations carried out using 6-31+G(d) and 6-31+G(d,p) basic sets (see Table S1 in Supplementary OrganicsInformation2020, 1 ) show increase of Gibbs free energy in the case of reaction between bis(2-chloroethyl) 2- 42 nitro-ethenylphosphonate 1a and anthracene 2, for TS1 38.5 kcal·mol−1 and 38.8 kcal·mol−1, respectively. In turn, in the case of the reaction between bis(2-chloroethyl) 2-bromo-2- 1 Tablenitroethenylphosphonates 2. B3LYP(PCM)/6-31G(d) 1b and The anthracene relative enthalpies, 2, we observe Gibbsd freethe reduction energy (∆ Hof andGibbs∆G, free in kcalenergymol for− ) 1 1 · andTS2, entropies 30.3 kcal·mol (∆S,−1 in and cal 31.2mol −kcal·molK− ), computed−1, respectively. in benzene, for the stationary points involved in the · · reactions of the bis(2-chloroethyl) 2-nitro 1a and bis(2-chloroethyl) 2-bromo-2-nitroethenylphosphonates 1b withTable anthracene 2. B3LYP(PCM)/62. -31G(d) The relative enthalpies, Gibbs free energy (ΔH and ΔG, in kcal·mol−1) and entropies (ΔS, in cal·mol−1·K −1), computed in benzene, for the stationary points involved in the reactions of the bis(2-chloroethyl)Transition 2-nitro 1a and bis(2∆-Hchloroethyl)353 2-bromo∆G353-2-nitroethenylphosphonates∆S353 1b with anthracene 2. 1+2 MC1 2.1 7.9 33.7 → − − 1+2 TS1 21.8 36.8 50.4 → Transition ΔH353 ΔG353 ΔS353 − 1+2 3a 13.6 1.5 50.7 → 1+2→MC1 − −2.1 7.9 −33.7 − 1+2 MC21+2→TS1 3.621.8 36.8 4.8 −50.4 28.0 → − − 1+2 TS2 1+2→3a 18.7−13.6 1.5 35.2 −50.7 55.3 → − 1+2 3b 1+2→MC2 15.0−3.6 4.8 3.8 −28.0 63.0 → 1+2→TS2 − 18.7 35.2 −55.3 − 1+2→3b −15.0 3.8 −63.0 Optimized critical structures for the DA reactions between 1a-b and 2, including some selected distancesOptimized and keyparameters, critical structures are givenfor the inDA Figure reactions3 and between Table 31a.- Atb andTS1 2, including, the distance some betweenselected the C1 anddistances C6, and and the key C2 parameters, and C3 interacting are given in atoms Figure are 3 and 2.106 Table Å, 3 and. At TS1 2.430, the Å, distance respectively. between These the C1 values suggestand an C6, asynchronous and the C2 and bond C3 formationinteracting process.atoms are We 2.106 also Å observe, and 2.430 the Å same , respectively. relationship These in values the case of suggest an asynchronous bond formation process. We also observe the same relationship in the case TS2 in DA reaction of the bis(2-chloroethyl) 2-bromo-2-nitroethenylphosphonate 1b with anthracene of TS2 in DA reaction of the bis(2-chloroethyl) 2-bromo-2-nitroethenylphosphonate 1b with 2 (Figure3, Table3). The DA reactions of 1a-b and 2 were analyzed by computing the GEDT [26] anthracene 2 (Figure 3, Table 3). The DA reactions of 1a-b and 2 were analyzed by computing the (TableGEDT3). The [26 GEDT,] (Table for 3). theThe transitionGEDT, for statesthe transition of the reaction states of the1a-b reactionwith 2 1a, are-b with for TS1 2, are0.30 for eTS1 and 0.30 for TS2 0.36 e.e and Based for TS2 on the 0.36 calculated e. Based on GEDT the calculated values, GEDT we can values, conclude we can that conclude these reactionsthat these reactions show strong show polar characterstrong of polar DA reactionscharacter of between DA reactions1a-b andbetween anthracene 1a-b and2 anthracene. 2.

Organics 2020, 1, FOR PEER REVIEW 8 MC1 TS1 3a

MC2 TS2 3b

FigureFigure 3. Views 3. Views of criticalof critical structures structures for for DADA reaction of of bis(2 bis(2-chloroethyl)-chloroethyl) 2-nitro 2-nitro-ethenylphosphonate-ethenylphosphonate 1a and1a bis(2-chloroethyl)and bis(2-chloroethyl) 2-bromo-2-nitroethenylphosphonates 2-bromo-2-nitroethenylphosphonates 1b1b withwith anthracene anthracene 2 in 2thein light the lightof of B3LYP(PCM)B3LYP(PCM)/6/6-31G(d)-31G(d) calculations. calculations.

Table 3. Key parameters of critical structures for DA reactions of bis(2-chloroethyl) 2-nitro and 2- bromo-2-nitroethenylphosphonates 1a,b and anthracene 2 according to B3LYP(PCM)/6-31G(d) calculations.

C2-C3 C1-C6 Structure Δl GEDT [e] Imaginary Frequency [cm−1] r [Å] l r [Å] l MC1 6.816 3.925 TS1 2.106 0.664 2.430 0.448 0.22 0.30 −399.48 3a 1.576 1.566 MC2 7.256 5.187 TS2 1.958 0.762 2.805 0.203 0.56 0.36 −332.75 3b 1.581 1.561

3.3. BET Study of the DA Reaction between bis(2-chloroethyl) 2-nitro-ethenylphosphonate 1a and Anthracene 2 A BET study of the analyzed reaction of the bis(2-chloroethyl) 2-nitro-ethenylphosphonate 1a and anthracene 2 was carried out, in order to understand the bonding changes in this reaction. Scheme 6 contains the molecular mechanism depicted by Lewis-like structures resulted from the ELF topology. In turn, the populations of the most important valence basins are assembled in Table 4.

Organics 2020, 1, FOR PEER REVIEW 8

Organics 2020, 1 43

Table 3. Key parameters of critical structures for DA reactions of bis(2-chloroethyl) 2-nitro and 2-bromo-2-nitroethenylphosphonates 1a,b and anthracene 2 according to B3LYP(PCM)/6-31G(d) calculations.

C2-C3 C1-C6 GEDT Imaginary Structure ∆l 1 r [Å] l r [Å] l [e] Frequency [cm− ]

MC1 6.816 3.925 TS1 MC22.106 0.664 2.430 0.448TS2 0.22 0.30 3b 399.48 − 3a 1.576 1.566 Figure 3. Views of critical structures for DA reaction of bis(2-chloroethyl) 2-nitro-ethenylphosphonate MC2 7.256 5.187 1a and bis(2-chloroethyl) 2-bromo-2-nitroethenylphosphonates 1b with anthracene 2 in the light of TS2 1.958 0.762 2.805 0.203 0.56 0.36 332.75 − B3LYP(PCM)/63b 1.581-31G(d) calculations. 1.561

Table 3. Key parameters of critical structures for DA reactions of bis(2-chloroethyl) 2-nitro and 2- 3.3. BET Study of the DA Reaction between bis(2-chloroethyl) 2-nitro-ethenylphosphonate 1a and Anthracene 2 bromo-2-nitroethenylphosphonates 1a,b and anthracene 2 according to B3LYP(PCM)/6-31G(d) Acalculations. BET study of the analyzed reaction of the bis(2-chloroethyl) 2-nitro-ethenylphosphonate 1a and anthracene 2 was carried out, in order to understand the bonding changes in this reaction. Scheme6 C2-C3 C1-C6 Structure Δl GEDT [e] Imaginary Frequency [cm−1] contains the molecularr mechanism[Å] l r depicted [Å] l by Lewis-like structures resulted from the ELF topology. In turn, the populationsMC1 6.816 of themost 3.925 important valence basins are assembled in Table4. The DA reactionTS1 2. of106 bis(2-chloroethyl) 0.664 2.430 0.448 2-nitro-ethenylphosphonate 0.22 0.30 −1a399.48with anthracene 2 takes place along eight3a different1.576 phases. 1.566Phase I, 3.49 Å d(C2-C3) > 2.66 Å and3.64 Å d(C1-C6) > 2.43 ≥ ≥ Å, begins at molecularMC2 7.256 complex (MC15.187), which corresponds with the first structure of the IRC path. The ELF pictureTS2 of MC11.958is practically0.762 2.805 the 0.203 same 0.56 as the ELF0.36 picture of the separated−332.75 reagents (Table4). Phase II begins3b at1.P1581, 2.66 Å 1.561d(C2-C3) > 2.50 Å and 2.43 Å d(C1-C6) > 2.21 Å. At this point, ≥ ≥ we observed the merger of the two V(C1,C2) and V’(C1,C2) disynaptic basins, present in the previous point,3.3. BET into Study one newof the V(C1,C2) DA Reaction disynaptic between basin, bis(2-chloroethyl) integrating 2 3.32-nitro e.- Thisethenylphosphonate topological change 1a and is connected withAnthracene a rupture 2 of the double C1-C2 in bis(2-chloroethyl) 2-nitro-ethenylphosphonate 1a. Phase III, 2.50 Å d(C2-C3) > 2.45 Å and 2.21 Å d(C1-C6) > 2.13 Å, starts at P2, with energy cost A BET study of≥ the analyzed reaction of the bis(2≥ -chloroethyl) 2-nitro-ethenylphosphonate 1a of 17.1 kcal mol 1. The ELF picture of P2, shows the presence of a new V(C3) monosynaptic basin, and anthracene· −2 was carried out, in order to understand the bonding changes in this reaction. integratingScheme 6 contains 0.13 e (Figure the molecular4). This topologicalmechanism changedepicted is by related Lewis to-like the formationstructures ofresulted a new frompseudoradical the ELF centertopology. at C3 In carbonturn, the in populations effect of depopulation of the most V(C8,C3) important and valence V(C3,C4) basins disynaptic are assembled basins. in Table 4.

Scheme 6. Simpliﬁed representation of the molecular mechanism of the DA reaction between bis(2-chloroethyl) 2-nitro-ethenylphosphonate 1a and anthracene 2 by Lewis-like structures ensuing from the Electron Localization Function (ELF) analysis lengthwise the reaction path. Organics 2020, 1 44

Table 4. ELF valence basin populations, distances of the forming bonds, B3LYP(PCM)/6-31G(d) relative electronic energies a, MC1–3a, deﬁning the eight phases characterizing the molecular mechanism of the DA reaction between bis(2-chloroethyl) 2-nitro-ethenylphosphonate 1a and anthracene 2. MC1, TS1 and the cycloadduct 3a are also caught. Distances are given in angstroms, Å, electron populations in average number of electrons, e, relative energies in kcal mol 1. · − Points 1a 2 MC1 P1 P2 P3 P4 P5 P6 P7 3a TS1 Phases I II III IV V VI VII VIII d(C2-C3) 3.489 2.659 2.502 2.449 2.412 2.356 2.316 2.184 1.566 2.430 d(C1-C6) 3.643 2.429 2.208 2.132 2.081 2.005 1.956 1.821 1.576 2.106 ∆E 0.0 8.5 17.1 22.0 21.8 15.8 5.5 2.7 11.5 24.0 − − V(C1,C2) 1.74 1.75 3.32 3.19 2.95 2.69 2.55 2.45 2.22 1.99 2.87 V’(C1,C2)1.74 1.69 V(C3,C4) 2.71 2.81 2.65 2.58 2.55 2.53 2.49 2.45 2.33 2.05 2.54 V(C4,C5) 2.47 2.45 2.59 2.60 2.61 2.62 2.65 2.66 2.70 2.75 2.61 V(C5,C6) 2.71 2.79 2.65 2.50 2.40 2.35 2.29 2.23 2.16 2.05 2.37 V(C6,C7) 2.93 2.83 2.69 2.53 2.46 2.41 2.34 2.31 2.22 2.07 2.44 V(C7,C8) 2.47 2.48 2.54 2.60 2.61 2.62 2.64 2.65 2.69 2.77 2.61 V(C8,C3) 2.93 2.81 2.76 2.69 2.64 2.61 2.61 2.47 2.33 2.06 2.61 V(C3) 0.13 0.23 0.32 0.28 V(C2) 0.34 0.45 0.40 V(C1) 0.38 0.50 0.57 V(C2,C3) 0.96 1.07 1.38 1.76 V(C6) 0.15 V(C1,C6) 1.02 1.79 a Relative to the ﬁrst point of the IRC, MC1.

Phase IV, 2.45 Å d(C2-C3) > 2.41 Å and 2.13 Å d(C1-C6) > 2.08 Å, begins at P3. In this phase, ≥ ≥ we notice the emergence of a new V(C2) monosynaptic basin integrating 0.34 e. This topological change is connected with formation a second new pseudoradical center at C2 carbon atom (Figure4). Together with this change, the V(C1,C2) disynaptic basin experiences a depopulation to 2.95 e at P3. The transition state TS1 of the HDA reaction is found in this phase, d(C2-C3) = 2.43 Å and d(C2-C6) = 2.10 Å (Table4). Phase V, 2.41 Å d(C2-C3) > 2.36 Å and 2.08 Å d(C1-C6) > 2.01 Å, starts at P4 and is characterized ≥ ≥ by the creation of a new V(C1) monosynaptic basin, integrating 0.38 e. This topological change is related to the formation of a pseudoradical center at the C1 carbon. The electron density for formation of pseudoradical center at C1 comes from the C1-C2 bonding region which experiences depopulation from 2.95 e at P3 to 2.69 e at P4. Phase VI, 2.36 Å d(C2-C3) > 2.32 Å and 2.01 Å d(C1-C6) > 1.96 Å, begins at P5. At the ≥ ≥ beginning of this phase, the first most relevant change along the IRC path takes place. The two V(C2) and V(C3) current at P4 are missing, a new V(C2,C3) disynaptic basin, integrating 0.96 e, is established. These topological changes are connected with formation of the first C2-C3 single bond. A C2-C3 bond begins to form at a C-C distance of 2.356 Å (Figure4). Phase VII, 2.32 Å d(C2-C3) > 2.18 Å and 1.96 Å d(C1-C6) > 1.82 Å, starts at P6, which is ≥ ≥ characterized by formation of a new V(C6) monosynaptic basin, integrating 0.15 e. This topological change is related to formation the next pseudoradical center at C6 carbon. The last Phase VIII, 2.18 Å d(C2-C3) > 1.57 Å and 1.82 Å d(C1-C6) > 1.58 Å, is located between ≥ ≥ points P7 and final product 3a. The ELF picture of P7 feature the formation of a new V(C2,C6) disynaptic basin, integrating 1.02 e, as a result of the merger of the two V(C2) and V(C6) monosynaptic basins. These topological changes are related with formation of a second C2-C6 single bond in 3a molecule. Organics 2020, 1 45 Organics 2020, 1, FOR PEER REVIEW 10

P2 P3 P4

P5 P6 P7

FigureFigure 4. TheThe most most important important ELF ELF valence valence basins basins of the of thestructure structure P2–P7 P2–P7 aligned aligned in the in two the C two-C single C-C singlebond bond formation formation in the in the reaction reaction between between bis(2 bis(2-chloroethyl)-chloroethyl) 2 2-nitro-ethenylphosphonate-nitro-ethenylphosphonate 1a1a andand anthraceneanthracene 22.. TheThe electronelectron populations,populations, inin averageaverage numbernumber ofof electrons,electrons, areare givengiven inin e.e.

BasedPhase IV on, the2.45 BET Å ≥analysis, d(C2-C3 some) > 2.41 appealing Å and 2.13 conclusions Å ≥ d(C1 concerning-C6) > 2.08 theÅ , begins mechanism at P3 of. In DA this reaction phase, ofwe the notice bis(2-chloroethyl) the emergence 2-nitro-ethenylphosphonate of a new V(C2) monosynaptic1a and basin anthracene integrating2 0.34can e. be This drawn: topological (i) the mechanismchange is connected of analyzed with DA formation reaction a cansecond be topologicallynew pseudoradica characterizedl center at C2 by carbon eight diatomﬀerent (Figure phases 4). (seeTogether Table with4); (ii) this at change, the beginning the V(C1,C2) of the disynaptic reaction, webasin observed experiences the rupturea depopulation of the C1-C2 to 2.95 double e at P3. bondThe transition in bis(2-chloroethyl) state TS1 of 2-nitro-ethenylphosphonatethe HDA reaction is found in1a this; (iii) phase, next, wed(C2 observed-C3) = 2.43 formation Å and d(C2 of three-C6) pseudoradical= 2.10 Å (Table centers 4). at C3, C2 and C1 carbon atoms; (iv) the formation of the ﬁrst C2-C3 single bond occursPhase at point V, 2.41P5 (see Å ≥ Figure d(C2-4C3 and) > Scheme 2.36 Å 6 and); (v) 2.08 in the Å next ≥ d( phaseC1-C6) we > observed2.01 Å , starts the formation at P4 and of is pseudoradicalcharacterized by center the creation at C6 carbon of a new and V(C1) next creation monosynaptic of the second basin, C1-C6integrating single 0.38 bond. e. This The topological formation ofchange both is single related bonds to the occurs formation through of a pseudoradi the mergingcal center of two at C2 the and C1 carbon. C3, C1 The and electron C6 pseudoradical density for centers,formation respectively. of pseudoradical center at C1 comes from the C1-C2 bonding region which experiences depopulation from 2.95 e at P3 to 2.69 e at P4. 4. Conclusions Phase VI, 2.36 Å ≥ d(C2-C3) > 2.32 Å and 2.01 Å ≥ d(C1-C6) > 1.96 Å , begins at P5. At the beginning of thisThe phase, reactions the first of most the bis(2-chloroethyl) relevant change along 2-nitro-ethenylphosphonate the IRC path takes place.1a Theand two bis(2-chloroethyl) V(C2) and V(C3) 2-bromo-2-nitroethenylphosphonatecurrent at P4 are missing, a new V(C2,C3)1b with disynaptic anthracene basin,2 have integrating been analyzed 0.96 withine, is established. the MEDT These study attopological the B3LYP(PCM) changes/6-31G(d) are connected calculations. with formation The received of the results first are C2 supported-C3 single by bond. the combination A C2-C3 bond of begins to form at a C-C distance of 2.356 Å (Figure 4).

Organics 2020, 1 46 the analysis of the CDFT reactivity indices at the ground state of the reagents, analyzed of the reaction profiles and BET study of the one exemplary reaction path. Analysis of reactivity indices chances are that the strong electrophilic character of the bis(2-chloroethyl) 2-nitro-ethenylphosphonate 1a and bis(2-chloroethyl) 2-bromo-2-nitroethenylphosphonate 1b. The aforementioned analysis showed that anthracene 2 can be classified as a strong electrophile while remaining a strong nucleophile. ELF analysis of electronic structures of 1a and 1b shows that they have in the most important region, two V(C1,C2) and V’(C1,C2) disynaptic basins. These disynaptic basins are associated with C1-C2 double bonds. An ELF topological analysis of anthracene 2 of the C-C bonding regions belonging to the aromatic rings are characterized by the presence of six disynaptic basins which are connected with partial double bonds. The present MEDT study established DA reactions between phosphorylated analogues of nitroethene and anthracene. DA reactions of the 1a-b with 2 should be regarded as a two-stage one-step process. BET analysis of the molecular mechanism associated with the DA reaction of bis(2-chloroethyl) 2-nitro-ethenylphosphonate 1a with anthracene 2 indicates that it is initialized by the rupture of the C1-C2 double bond in 1a molecule and formation of three pseudoradical centers at C1, C2 and C3 carbon. In the next stage we observed the formation of first C2-C3 single bond, a new pseudoradical center at C6 carbon and in the last stage of the reaction and the formation of a second C1-C6 single bond.

Supplementary Materials: The following are available online at http://www.mdpi.com/2673-401X/1/1/4/s1. Funding: This research received no external funding. Acknowledgments: Partial support of this research by PL-Grid Infrastructure are gratefully acknowledged. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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