Insights into the reaction mechanism between phosphacyclopropenylidene and methyleneimine: A theoretical study

Abstract

The reaction mechanism between phosphacyclopropenylidene and methyleneimine has been systematically investigated at the M06–2X/6–311++G(d,p) level of theory in order to better understand the reactivity of unsaturated cyclic phosphorus-bearing carbene. Geometry optimizations and vibrational analyses have been conducted for the stationary points on the potential energy surface of the system. Calculations show that the spiro bicyclic intermediate could be produced through the cycloaddition process between phosphacyclopropenylidene and methyleneimine initially. The reaction mechanism is illustrated with frontier molecular orbital theory. Introduction of electron-withdrawing group in phosphacyclopropenylidene will better facilitate the addition process. Through subsequent ring-expanding and hydrogen-migrating process, fuse-ring and allene compounds could be produced, respectively. Furthermore, it’s easy for spiro bicyclic intermediate and another methyleneimine to form a spiro tricyclic compound. This study is helpful to understand the reactivity of phosphacyclopropenylidene, the evolution of phosphorus-bearing molecules in space, and to offer an alternative approach to the formation of phosphorus-bearing heterocyclic compound.

Keywords

Phosphacyclopropenylidene methyleneimine reaction mechanism molecular orbital

1 Introduction

Approximate 180 molecules have been detected in the interstellar medium (ISM) or in circumstellar envelopes (CSEs) of late-type stars [1], including six phosphorus-bearing molecules, PN [2, 3], CP [4], HCP [5], PO [6], CCP [7] and PH₃ [8, 9]. As a carbon-phosphorus-bearing molecule, HC₂P might exist in the hot core of star-forming regions [10]. Additionally, HC₂P is one of the products of the reaction between interstellar molecules CP and CH₂CO theoretically [11].

There are three isomers of HC₂P based on the theoretical investigation: triplet linear HCCP (HCCP^t, phosphapropynylidene), singlet circular HC₂P (HC₂P^s, phosphacyclopropenylidene), and singlet bent CCPH (CCPH^s, phosphapropadienylidene) [12]. Saito et al. detected microwave spectrum of the HC₂P in the mixture of phosphine and acetylene for the first time using a source-modulated microwave spectrometer. The results show that the structure of HC₂P is a linear phospho-allenic form, which is somewhat modified by a phosphorene [13]. Detailed and precise measure of line frequencies of HC₂P is available for its astronomical search in the circumstellar envelopes or dark molecular clouds. Műller and Woon calculated dipole moments of compounds containing silicon and phosphorus, including HC₂P, for assessing the column density, denoting abundances and predicting reactivity [14].

The order of stability of three HC₂P isomers is HCCP^t > HC₂P^s>CCPH^s [15]. For example, based on Boo’s results, the relative electronic energy of HCCP^t, HC₂P^s, CCPH^s is 0, 4.2, and 17.5 kcal/mol at the MP2/cc–pVDZ level of theory, respectively [12]. Ding et al. investigated the structures and isomerization pathways of HC₂P isomers in both singlet and triplet states at various levels and drew parallel conclusions with aforementioned study [16].

Over the years, it has attracted scientists’ interests in the reaction mechanism and theoretical study [17 –19]. The reaction of azacyclopropenylidene (c–C₂HN) has been studied, which enriched the azacyclopropenylidene chemistry and provided alternative approaches for synthesizing relevant nitrogen-bearing compounds [20]. Phosphacyclopropenylidene (HC₂P^s) is an analogue of azacyclopropenylidene. We believe that further investigation for the reaction mechanism between phosphacyclopropenylidene and unsaturated compounds can stimulate relevant experimental and theoretical studies of HC₂P. In the present study, we have performed comprehensive theoretical investigation of the reaction mechanism between phosphacyclopropenylidene and methyleneimine by employing the M06–2X method with 6–311++G(d,p) basis set. The research results indicate that three products, fuse-ring, allene, and spiro tricyclic compound, are formed. The present results will enrich the available data for the relevant phosphacyclopropenylidene chemistry and discuss the possibility of formation of phosphorus-bearing molecules by means of phosphacyclopropenylidene.

2 Calculation method

The potential energy, gradients and Hessians obtained from M06–2X method with 6–311++G(d,p) base set level are usually more reliable and hence is used to locate all the stationary points along the reaction pathway without imposing any symmetry constraints [21, 22]. Frequency analyses have been conducted to confirm the nature of the minima and transition states. Moreover, intrinsic reaction coordinate (IRC) calculations have also been made to further validate the calculated transition states connecting reactants and products. Additionally, the relevant energy quantities, such as the reaction energies and barrier heights, have been corrected with zero-point vibrational energy (ZPVE) corrections.

All the calculations have been performed using Gaussian 09 program [23].

3 Results and discussion

As displayed in Scheme 1, three possible pathways for the title reaction have been proposed. The geometric parameters for the reactants (R1-phosphacyclopropenylidene and R2-methyleneimine), transition states (TS), intermediates (IM), and products (P) involved in the pathway (1), (2), and (3) are displayed in Figure 1. The corresponding reaction profile is illustrated in Fig. 2.

Scheme 1

The proposed three pathways for the reaction between phosphacyclopropenylidene and methyleneimine.

Fig.1

Optimized structures of the reactants (phosphacyclopropenylidene and methyleneimine), transition states (TS), intermediates (IM), and products (P) in the reaction pathways (1), (2), and (3) at the M06–2X/6–311++G(d,p) level of theory, where the bond length and bond angle (in red) are in angstrom and degree, respectively.

Fig.2

Reaction profiles for the pathways (1), (2), and (3) between R1 (phosphacyclopropenylidene) and R2 (methyleneimine) at the M06–2X/6–311++G(d,p) level of theory.

3.1 Step (a): cycloaddition reaction process to form a spiro bicyclic intermediate IMa

For the pathway (1) and (2), the common intermediate IMa is formed via a cycloaddition reaction process with an energy barrier of 51.0 kJ/mol. The unique imaginary frequency calculated for the corresponding transition state (TSa) in the step (a) is 446i cm^–1 at the M06–2X/6–311++G(d,p) level of theory.

As shown in Fig. 1, the distance of C¹–C³ and C¹–N¹ in TSa is 1.844 and 2.415 Å, respectively. Thus, in the transition state TSa, two new bonds of C¹C³ and C¹N¹ are to be formed. At the same time, the distance of C³–N¹ in R2 fragment of TSa is reached to 1.324 Å, which elongated 0.061 Å than that in methyleneimine. Therefore, based on the bond length data, the double bond C³N¹ in methyleneimine is to be transformed into single bond in IMa via TSa. The formation of new σ bond of C¹C³ and C¹N¹ and the cleavage of π bond of C³N¹ happened simultaneously. Therefore, step (a) is a concerted cycloaddition reaction process. As shown in Fig. 3, those changes can be further validated by the IRC calculations on the basis of TSa.

Fig.3

The relatively energy and selected bond lengths change along the reaction coordinates of the step (a).

Qualitatively, the cycloaddition reaction process of step (a) can be understood from the frontier molecular orbital theory. As displayed in Fig. 4, the frontier orbitals for LUMO+1 of R1 (phosphacyclopropenylidene) and HOMO of R2 (methyleneimine) are symmetrical matching. As R1 initially interacts with R2, the 2p unoccupied orbital of C¹ in R1 inserts into the π orbital of R2 to form a π–p donor-acceptor bond, resulting in the formation of the spiro bicyclic intermediate IMa. The less the electron densities on C¹ atom in R1, the easier will be the insertion process of the formation of a π–p donor-acceptor bond.

Fig.4

The calculated MO orbitals for R1 (phosphacyclopropenylidene), R2 (methyleneimine), and IM2.

There are two π electrons of the R1 (C¹ offers an empty p-orbital, C² and P offers a π electron, respectively), conforming to the Hückel rule (π electrons are 4n + 2, n = 0). Therefore, R1 is an aromatic molecule. By the conjugation effect, introduction of electron-withdrawing group at C² in R1 will decrease the electron density on C¹, which will better facilitate in the reaction between R1 and R2. Introduction of electron-donating group will lead to the opposite effect. As summarized in Table 1, introduction of electron-withdrawing group, F, CF₃ and CN, decreases the electron density at C¹ atom in R1, by which it can decrease the barrier of step (a). On the contrary, electron-donating group, CH₃, OH, OCH₃ and N(CH₃)₂, increase the barrier of step (a).

Table 1

The barrier (in kJ/mol) in step (a) of the cycloaddition reaction process between XC₂P^s and methyleneimine at the M06–2X/6–311++G(d,p) level of theory^a

X (electron-withdrawing group)	Barrier (kJ/mol)	X (electron-donating group)	Barrier (kJ/mol)
F	49.4	CH₃	52.2
CF₃	48.5	OH	53.2
CN	48.7	OCH₃	53.0
		N(CH₃)₂	53.1

^aWhen X = H, the barrier is 51.0 kJ/mol.

IMa is a spiro bicyclic compound. Two three-membered rings, C¹C²P and C¹C³N¹, share C¹ atom. IMa can transfer to P1 through ring expansion process (step (1)) and to IM2 through H migration process (step (2)).

3.2 Step (1): ring-expanding process to form a fuse-ring compound P1

For the pathway (1), the product P1 is formed via a ring-expanding process of IMa. The unique imaginary frequency calculated for the corresponding transition state TS1 in the step (1) is 609i cm^–1.

In TS1, the cleavage of π bond of C²P forms single electron on C² and P, the cleavage of σ bond of C¹N¹ forms single electron on C¹ and N¹, respectively. In the meanwhile, two single electrons on C² and N¹ form a new σ bond, the other two single electrons on C¹ and P form a new π bond. The distance of C²–N¹ in TS1 is 2.153 Å, denoting the formation of a new σ bond between C² and N¹. The distance of C¹–P in TS1 is 1.732 Å, which is between the length of single bond (C¹P in IMa, 1.855 Å) and double bond (C¹P in P1, 1.680 Å), denoting the transformation of C¹P bond from single bond to double bond. P1 is a fuse-ring compound, which is exothermic with the value of 45.6 kJ/mol compared with that of the reactants. As shown in Fig. 5, those changes of bond length can be further validated by the IRC calculations on the basis of TS1.

Fig.5

The relatively energy and selected bond lengths change along the reaction coordinates of the step (1).

3.3 Step (2a): H-migrating process to form a spiro intermediate IM2

The step (2a) in pathway (2) is the hydrogen (H¹) migration from C² to the adjacent P, resulting in the isomerization of IMa into IM2 via TS2a. Here, the calculated energy is 88.7 kJ/mol, the imaginary frequency of TS2a is 794i cm^–1. In details, as shown in Fig. 1, the distance of C²–H¹ in TS2a has been elongated to 1.588 Å, and the distance of P–H¹ reached to 1.488 Å, indicating that the H¹ atom can migrate from C² to P. In the meantime, the bond length of C²P in TS2a increases to 1.843 Å (the bond length of C²P in IMa is 1.655 Å), suggesting the double bond of C²P in IMa will be transferred into the single bond of C²P in IM2.

Similar as IMa, IM2 is also a spiro intermediate. The difference between IM2 and IMa is that the former has a pair of lone electrons on C² atom. That is, IM2 is characterized by unstable carbene structure. Along the reaction profile, IM2 is endothermic with the value of 61.0 kJ/mol compared with that of the reactants. In general, carbene will isomerize to the stable species by bonding its lone electrons. Therefore, IM2 can isomerize to P2 through a ring-opening process of C¹C²P, or react with methyleneimine to form P3.

3.4 Step (2b): ring-opening process to form an allene product P2

As mentioned above, IM2 can isomerize to P2 through a ring-opening process of C¹C²P via TS2b, which is named as step (2b). Here, the calculated energy of TS2b is 86.3 kJ/mol and the imaginary frequency of TS2b is 159i cm^–1. As shown in Fig. 1, the distance of C¹–P in TS2b has been elongated to 1.948 Å, indicating the break-up of the C¹P bond and the open-up of C¹C²P ring. In P2, the bond length of C¹C² is 1.291 Å, which fall in the range of the intermediate between C = C double bond and C≡C triple bond length. Analogously, the bond length of C²P (1.639 Å) in P2 is similar with CP double bond (C²P double bond is 1.679 Å in R1), and is great shorter than CP single bond (C²P single bond is 1.887 Å in IM2). The three atoms, C¹, C², and P, are approaching to the same line (∠C¹C²P is 172.7°). Therefore, P2 is the allenes structure. Along the reaction profile, P2 is exothermic with the value of 131.4 kJ/mol comparison with that of the reactants.

3.5 Pathway (3): addition reaction process to form a spiro tricyclic compound P3

IM2 is similar to R1, both of them have carbene characteristic. IM2 can react with methyleneimine to form P3 via TS3. The reaction of IM2 and methyleneimine is similar to the reaction of R1 and methyleneimine. As displayed in Fig. 4, the frontier orbitals for LUMO of IM2 and HOMO of R2 are symmetrical matching. As IM2 initially interacts with methyleneimine, the 2p unoccupied orbital of C² in IM2 inserts into the π orbital of methyleneimine to form a π–p donor-acceptor bond, resulting in the formation of the spiro tricyclic compound P3. Unlike the R1, IM2 has no aromatic characteristic. Therefore, it is easier for the reaction of IM2 and methyleneimine than that of R1 and methyleneimine, which can be demonstrated through the barrier in step (3) (20.8 kJ/mol) and step (a) (51.0 kJ/mol).

4 Conclusions

In this study, the reaction mechanism between phosphacyclopropenylidene and methyleneimine has been systematically investigated employing the M06–2X/6–311++G(d,p) level of theory. The reaction involves three pathways: pathway (1), (2), and (3). The spiro bicyclic compound is the common intermediate for three pathways through cycloaddition process. Introduction of electron-withdrawing group in phosphacyclopropenylidene will better facilitate the cycloaddition process. Introduction of electron-donating group will lead to the opposite effect. Pathway (1) is the process of formation of phosphorus-bearing fuse-ring compound via a ring expansion. Pathway (2) is the process of formation of phosphorus-bearing allene compound through hydrogen migration and ring-opening. Pathway (3) is to form a phosphorus-bearing spiro tricyclic compound. This study is helpful to understand the reactivity of phosphacyclopropenylidene, the evolution of phosphorus-bearing molecules in space, and to offer an alternative approach to the formation of phosphorus-bearing heterocyclic compound.

Footnotes

Acknowledgments

This work was supported by National Nature Science Foundation of China (31370090), project of 20 items for promoting collaborative innovation of Jinan (2019GXRC058), and project of Iceland research centre of University of Jinan (18GB04).

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