Insight into structural and π–magnesium bonding characteristics of the X₂Mg⋯Y (X = H, F; Y = C₂H₂, C₂H₄ and C₆H₆) complexes

Abstract

Quantum chemical calculations have been performed to study the nature of interaction of complexes formed by MgX₂ (X = H, F) molecules with acetylene, ethylene, and benzene, respectively. Results indicate that nonbonded interactions, namely π–magnesium bonds, contribute to the stability of the resulting dimers. An intriguing structural evolution has been found for the complexes with different π electron donors. Upon complexation, both the Mg–X and C–C bonds lengthened, accompanied by redshifted X–Mg–X and C–C stretching vibrations. NBO analysis reveals that the main charge-transfer from the conjugated molecules to MgX₂ is from the π_CC bonding orbital to the empty lone pair orbital of Mg. Energy decomposition analysis indicates that the stability of the topic complexes mainly comes from the attractive electrostatic interaction and polarization, similar to the case of π–beryllium bonds. When compared with other nonbonded interactions, it is found that π–magnesium bonds are stronger than π–lithium and π–sodium bonds. Especially, they are comparable in strength to π–beryllium bonds with MgF₂ playing the role of Lewis acid.

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Introduction

Noncovalent interactions play a key role in chemistry and biochemistry research,^1–4 especially as far as molecular recognition^5,6 and molecular medicine^7,8 are concerned. In recent years, numerous experimental and theoretical endeavors have been devoted to understanding the origin and strength of such interactions. Hydrogen bond is one of the most crucial and common noncovalent interactions. The formation of hydrogen bond can be depicted as X–H⋯Y where X–H represents the hydrogen bond donor and the hydrogen acceptor Y may be an atom or an anion, or a fragment, or a molecule. In 1971, Morokuma⁹ reported the first theoretical evidence of a π–hydrogen bonding complex H₂CO⋯2H₂O in which the C=O group acts as the proton acceptor. As an analog of hydrogen bonds, the existence of lithium bond was theoretically predicted in 1970¹⁰ and experimentally confirmed by Ault and Pimentel¹¹ in 1975. During the past decades, lithium bond has been identified in a variety of systems, and many non-traditional lithium bonding interactions have been put forward, such as π–lithium bond.¹² In the same vein, the concept of π–sodium bond has been proposed lately.¹³ Note that a similar interaction in the X₃M⋯π (M = B, Al; X = H, Cl, Br) complexes was also elaborated by Grabowski.¹⁴

Most recently, Yañez et al.¹⁵ have demonstrated that there is an interaction between BeX₂ (X = H, F, Cl, OH) and different Lewis bases, namely NH₃, H₂O, FH, PH₃, SH₂, ClH and BrH. They examined this special kind of weak interactions and defined it as “beryllium bonds” in a similar way as the definition of hydrogen bonds and lithium bonds. Subsequently, the concept of beryllium bond attracted much attention and research interest. Eskandari explored the nature of beryllium bonds by a QTAIM study.¹⁶ The investigation of interaction between squaric acid and BeH₂ by Montero-Campillo and coworkers¹⁷ has revealed significant cooperative effects between the beryllium bond and the BeH⋯HO dihydrogen bond. Yañez's group¹⁸ focused on the ternary BeR₂:C₆X₆:Y⁻ complexes (R = H, F and Cl, X = H and F, and Y = Cl and Br) and provided clear evidence for favorable cooperativity in beryllium bond and aromatic ring:anion interaction. They also proposed the existence of π–beryllium bonds between ethylene and acetylene and BeX₂ (X = H, F, and Cl) derivatives, and found that the π–beryllium bonds are about four times stronger than π–hydrogen bonds.¹⁹ In a very recent paper, Yu et al. theoretically characterized a kind of beryllium bonding complexes with radicals playing the role of Lewis base.²⁰

The extensive studies of beryllium bonds, as well as the similarity between beryllium and magnesium elements, naturally lead to a question: does magnesium bond, as a congener of beryllium bond, exist? The answer is already known. In a very recent work, Yang and co-workers have demonstrated that there is another weak interaction other than lithium bond between LiNH₂ and MgH₂ molecules, and consequently proposed the existence of magnesium bond.²¹ Compared with the well-studied beryllium bonds, the systematic study of magnesium bonds is of additional significance. On the one hand, magnesium-containing complexes are nontoxic, which facilitates the experimental analysis. On the other hand, the element of magnesium widely exists in organisms and plays an essential role in a variety of biochemical processes. For instance, magnesium ions are important in the formation of DNA origami structures²² and affect their conductivity as well.²³ Hence, the interactions between magnesium derivatives and conjugated systems are of great research value.

Here, we focused on the formation of π–magnesium bond and systematically studied the interaction between conjugated molecules (C₂H₂, C₂H₄ and C₆H₆) and MgX₂ (X = H, F) molecule by using quantum chemical methods. Herein, ethylene, acetylene and benzene have played the role of π electron donors in the previous investigations of π–hydrogen,²⁴ π–lithium,¹² and π–halogen bonds.²⁵ The main objectives of this paper are (1) to understand how the MgX₂ and conjugated molecules respond to each other and explore the origin of π–magnesium bond, (2) to reveal different geometrical features of the X₂Mg⋯C₂H₂, X₂Mg⋯C₂H₄ and X₂Mg⋯C₆H₆ complexes, (3) to compare the strength of π–magnesium bond with other nonbonding interactions concerned, including conventional magnesium bonds, π–beryllium bonds, π–lithium bonds and π–sodium bonds, and (4) to analyze the relationship between π–magnesium bonding strength and different π electron donors. We hope that the results from this work not only provide reference to the researches in the field of biochemistry and physiology in view of the important role that magnesium element plays therein, but also help to understand the interaction between conjugated π–systems and other metal atoms, for example the behavior of transition metal atoms adsorbed on graphene or graphene oxide sheets, etc.^26–28

Computational details

The optimized structures of the X₂Mg⋯C₂H₂, X₂Mg⋯C₂H₄ and X₂Mg⋯C₆H₆ (X = H, F) complexes were obtained at the MP2/aug-cc-pVTZ level by using the counterpoise procedure.^29,30 Then the vibrational frequency calculations were performed to ascertain that these geometries are true minima on the potential energy surface. Intermolecular interaction energies (E_int) of the complexes were calculated using the coupled cluster theory with single and double excitations and perturbative contribution of connected triple excitations [CCSD(T)] method with the aug-cc-pVTZ basis set. The E_int values have been calculated as the difference between the energy of the complex (E_AB) and the sum of the energy of the monomer subunits (E_A, E_B), by the following formula,

E_int = E_AB(M_AB) − E_A(M_AB) − E_B(M_AB) (1)

To eliminate the basis set superposition error (BSSE) effect in the interaction energy given by eqn (1), we use the same basis set, M_AB, for the monomers calculation as for the complex calculation. Besides, the total interaction energy can be decomposed into four components using the LMOEDA method,³¹ as shown in eqn (2)

ΔE_int = ΔE_elstat + ΔE_ex+rep + ΔE_pol + ΔE_disp (2)

where ΔE_elstat, ΔE_ex+rep, ΔE_pol and ΔE_disp correspond to electrostatic, exchange-repulsion, polarization, and correlation terms, respectively. These components were computed at the SCF/aug-cc-pVTZ level except that the ΔE_disp term was obtained at the MP2 level, by using the GAMESS program.³²

The bonding in the complexes was investigated based on two different but complementary methods, namely the quantum theory of atoms in molecules (QTAIM)^33,34 and natural bond orbital (NBO) analysis.³⁵ Using the AIM2000 and AIMALL program,^34,36–38 we have obtained the molecular graphs for these complexes and the electron densities of π–magnesium bond critical points (BCPs).

Unless otherwise specified, all the calculations were performed with the Gaussian 09 program package.³⁹

Results and discussion

Geometrical structures and π–magnesium bond

Using the counterpoise procedure, the optimized geometries of the X₂Mg⋯C₂H₂, X₂Mg⋯C₂H₄ and X₂Mg⋯C₆H₆ (X = H, F) complexes with all real frequencies have been obtained at the MP2/aug-cc-pVTZ level, which are presented in Fig. 1. The important geometrical parameters are listed in Table 1. For comparisons, the optimized structures of corresponding monomers are given in Fig. S1 in the (ESI†). The NBO charges of these complexes at the MP2 level are listed in Table 2. Note that we also obtained the hydrogen bonding structures of the X₂Mg⋯C₂H₂ and X₂Mg⋯C₂H₄ dimers (see Fig. S2, ESI†), which are 4.45–9.50 kcal mol⁻¹ higher in energy than π–magnesium bonding structures, so the latter are considered to be global minima on the interaction potential energy surface.

Fig. 1 Optimized structures of the (I) H₂Mg⋯C₂H₂, (II) H₂Mg⋯C₂H₄, (III) H₂Mg⋯C₆H₆, (IV) F₂Mg⋯C₂H₂, (V) F₂Mg⋯C₂H₄, and (VI) F₂Mg⋯C₆H₆ complexes at the MP2/aug-cc-pVTZ level (P and O denote the centers of C1–C2 bond and the C₆H₆ ring, respectively).

Table 1 Main geometrical parameters of the X₂Mg⋯C₂H₂, X₂Mg⋯C₂H₄ and X₂Mg⋯C₆H₆ (X = H, F) complexes. Bond lengths in Å and bond angles in degrees. P and O denote the centers of the C1–C2 bond and the C₆H₆ ring, respectively

Complex	Symmetry	dMg–P	dMg–C1	RC1–C2	RMg–X	∠X1MgX2	∠X1MgP	∠MgPO	∠X–MgP–C	θ^a
a See Fig. 1 for definition.
H2Mg⋯C2H2	C2v	2.617	2.687	1.216	1.721	162.2	98.9		0.0	0.0
F2Mg⋯C2H2	C2v	2.460	2.534	1.216	1.785	159.5	100.3		0.0	0.9
H2Mg⋯C2H4	C2v	2.702	2.784	1.340	1.719	161.3	99.3		0.0	−0.4
F2Mg⋯C2H4	C2	2.523	2.611	1.341	1.783	157.1	101.5		61.8	−1.3
H2Mg⋯C6H6	Cs	2.683	2.773	1.401	1.725	159.4	105.9	90.6	90.0	−0.5
F2Mg⋯C6H6	Cs	2.504	2.601	1.404	1.789	151.5	115.9	86.0	90.0	0.5
H2Mg	D∞h				1.707	180.0
F2Mg	D∞h				1.768	180.0
C2H2	D∞h			1.212						0.0
C2H4	D2h			1.333						0.0
C6H6	D6h			1.394						0.0

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Table 2 The NBO charges (in |e|) of selected atoms in the six X₂Mg⋯C₂H₂, X₂Mg⋯C₂H₄ and X₂Mg⋯C₆H₆ (X = H, F) complexes. Δq = q_complex − q_monomer

	Mg			X1/X2	C1–C2			Q^CT^a
	qcomplex	qmonomer	Δq	qcomplex	qcomplex	qmonomer	Δq
a Q^CT denotes the electron transfer from the conjugated molecule to the MgX2 molecule.
H2Mg⋯C2H2	1.199	1.253	−0.054	−0.621	−0.478	−0.450	−0.028	0.043
H2Mg⋯C2H4	1.184	1.253	−0.069	−0.619	−0.716	−0.682	−0.034	0.054
H2Mg⋯C6H6	1.188	1.253	−0.065	−0.620/−0.629	−0.488	−0.382	−0.106	0.061
F2Mg⋯C2H2	1.771	1.829	−0.058	−0.902	−0.510	−0.450	−0.060	0.033
F2Mg⋯C2H4	1.754	1.829	−0.075	−0.904	−0.756	−0.682	−0.074	0.054
F2Mg⋯C6H6	1.757	1.829	−0.072	−0.902/−0.903	−0.536	−0.382	−0.154	0.048

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From Fig. 1 and Table 1, these dimers show intriguing structural features. The X₂Mg and the acetylene molecules are coplanar in the X₂Mg⋯C₂H₂ (X = H, F) complexes, which have C_2v symmetry. The binding distance (d_Mg–P) of two monomers, defined as the distance between Mg atom and the center of C1–C2 bond, are 2.617 and 2.460 Å for the H₂Mg⋯C₂H₂ and F₂Mg⋯C₂H₂ complexes, respectively. As to the X₂Mg⋯C₂H₄ species, H₂Mg⋯C₂H₄ shows a similar structure to that of X₂Mg⋯C₂H₂, that is, the H₂Mg molecule is coplanar with the C=C bond. Whereas, the situation is different for the F₂Mg⋯C₂H₄ complex. A deflection of the F₂Mg molecule is found when it interacts with the ethylene molecule. From Table 1, the dihedral angle ∠F–MgP–C is 61.8°. As a result, the F₂Mg⋯C₂H₄ complex is of C₂ symmetry. The repulsive interaction between negatively charged F and C atoms is considered to be the reason for the unusual deflection of the F₂Mg molecule.

From Table 2, the C atom carries much more negative charge in ethylene than in acetylene and benzene molecules. Consequently, the F₂Mg molecule deviates from the frontal plane to reduce the F⋯C repulsion interaction. The d_Mg–P distances of the X₂Mg⋯C₂H₂ dimers are shorter than those of corresponding C₂H₄-based species, implying that acetylene is a stronger π electron donor than ethylene and has a stronger interaction with the X₂Mg molecules. According to previous report, the LiF molecule favours the face center geometry while HF prefers the bond center geometry with benzene.²⁴ Similar to the case of HF, the X₂Mg molecule interacts with one of the C–C bond (partial double) instead of interacting with the center of the benzene ring (see Fig. 1). Besides, the C1–C2 bond is perpendicular to the X₂Mg molecular plane and leads to C_s-symmetric structure of X₂Mg⋯C₆H₆. From Table 1, the d_Mg–P distances are 2.683 and 2.504 Å for the H₂Mg⋯C₆H₆ and F₂Mg⋯C₆H₆ dimers, respectively, which are slightly shorter than those of corresponding X₂Mg⋯C₂H₄ ones.

From Table 1, all the d_Mg–P distances vary in the range of 2.460–2.702 Å, which are longer than the conventional magnesium bond distances of 2.07–2.10 Å (ref. 21) in the LiNH₂⋯HMgX (X = H, F, Cl, Br, CH₃, OH, and NH₂) dimers. Nevertheless, the Mg⋯C1 distances of 2.534–2.784 Å are much shorter than the sum of van der Waals radii of Mg and C atoms (3.7 Å),⁴⁰ reflecting a strong interaction between X₂Mg and the conjugated molecules, in the present six complexes. As shown in Table 2, the C1–C2 charges in the free C₂H₂, C₂H₄, and C₆H₆ molecules are negative (−0.382 to −0.682 |e|), and the Mg atom carries positive charges of 1.253 |e| and 1.829 |e|, in the MgH₂ and MgF₂ monomers, respectively. Thus, the nature of the interaction between X₂Mg and conjugated molecules, namely π–magnesium bond, may mainly derive from the electrostatic attraction interaction. During the π–magnesium bond formation, the Mg atom becomes less positive, whereas the negative charge on the C1–C2 bond increases. Note that similar situation occurred for the interaction between FH and C₆H₆ molecules.⁴¹ From the table, 0.033–0.061 |e| electron transfer occurs from the conjugated molecules to the MgX₂ molecule. It is noted that the charge transfer is ca. 0.02 |e| in the BeX₂ (X = H, F) complexes of benzene,¹⁹ indicating a smaller charge transfer interaction in the π–beryllium bonding complexes.

Table 3 lists the main orbitals involved in charge transfer and corresponding second order stabilization energies of these π–magnesium bonding complexes, which are obtained on the basis of SCF electron densities. From the table, the main charge-transfer from the conjugated molecules to MgF₂ is from the π_CC bonding orbital to the empty 3s and 3p orbitals of Mg. As for the H₂Mg-based series, the situation is a bit complex. From Table 3, there are two main orbital interactions for the H₂Mg⋯C₆H₆ complex, namely π_CC → p(Mg) and π_CC → s(Mg), just like the case of F₂Mg⋯π dimers. By contrast, the largest second order stabilization energy only involved electron donation from the π_CC bonding orbital to the empty 3p orbital of Mg for the H₂Mg⋯C₂H₄ and H₂Mg⋯C₂H₂ complexes. No π_CC → s(Mg) charge transfer has been found because the 3s orbital is mixed with a 3p orbital of Mg to form two sp hybrids involved in the H–Mg–H bond for these two complexes. Instead, there are some secondary donor–acceptor interactions, including the electron donation from π_CC bonding orbital to the antibonding orbital, from σ_CC and σ_CH bonding orbitals to the empty 3p orbitals of Mg.

Table 3 Second order stabilization energies (kcal mol⁻¹) of the orbital interactions in the X₂Mg⋯C₂H₂ X₂Mg⋯C₂H₄ and X₂Mg⋯C₆H₆ (X = H, F) complexes

complex	πCC → p(Mg)	πCC → s(Mg)		σCC → p(Mg)	σCC → s(Mg)	σCH → p(Mg)
F2Mg⋯C6H6	10.88	8.62		2.39
F2Mg⋯C2H4	5.58	20.63
F2Mg⋯C2H2	9.10	10.98
H2Mg⋯C6H6	12.52	10.94		5.22	1.33	3.48
H2Mg⋯C2H4	18.39		5.76	1.55		7.44
H2Mg⋯C2H2	19.81		4.74	2.24		6.50

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Table 1 shows that the binding distance d_Mg–P increases in the order 2.460 Å (F₂Mg⋯C₂H₂) < 2.504 Å (F₂Mg⋯C₆H₆) < 2.523 Å (F₂Mg⋯C₂H₄) and 2.617 Å (H₂Mg⋯C₂H₂) < 2.683 Å (H₂Mg⋯C₆H₆) < 2.702 Å (H₂Mg⋯C₂H₄). The data suggest that C₂H₂ is the best π electron donor among the three conjugated molecules and may form the strongest π–magnesium bond with the X₂Mg molecules. On the other hand, the d_Mg–P distances of the F₂Mg-based complexes are obviously shorter than those of H₂Mg-based ones, reflecting that the π–magnesium bonds are stronger in the former species. This is reasonable because MgF₂ is a better Lewis acid than MgH₂.

Due to the π–magnesium bond formation, the Mg–X bonds of the MgX₂ molecules elongate 0.012–0.021 Å. For instance, the Mg–H bond lengths are 1.721, 1.719 and 1.725 Å in the H₂Mg⋯C₂H₂, H₂Mg⋯C₂H₄ and H₂Mg⋯C₆H₆ complexes, respectively, while it is 1.707 Å in the free MgH₂ molecule. Meanwhile, both Mg–X bonds are seen to bend in a direction opposite to the conjugated molecules, leading to a bending angle ∠X1MgX₂ of 151.5–162.2°.

For the unsaturated moiety, the structural distortion is not obvious when compared with the corresponding monomer. From Table 1 and Fig. S1 (ESI†), the C1–C2 bond slightly lengthens upon the complex formation. For instance, the R_C1–C2 length of 1.261 Å for X₂Mg⋯C₂H₂ is 0.05 Å longer than that of the isolated C₂H₂ molecule. In contrast, the length of R_C1–C2 only elongates 0.01 Å due to the interaction between X₂Mg and the benzene ring. Such bond lengthenings indicate slightly weaker C1–C2 bonds in the complexes, which is confirmed by their lesser Wiberg bond index than those in corresponding monomers (see Table S1, ESI†). Besides, as can be seen from Table 1, the angle θ (the deflection of C–H bond from the horizontal plane that contains C–C bond) is 0.9° in the F₂Mg⋯C₂H₂ complex, showing that the C₂H₂ subunit is not linear herein. Similarly, the C₂H₄ and C₆H₆ subunits are not strictly planar in the studied complexes with θ ranging from −1.3° to 0.5°.

Interaction energies

Interaction energy is one of the most important measurement of the intermolecular interaction. Table 4 collects the BSSE-corrected interaction energies of the X₂Mg⋯C₂H₂, X₂Mg⋯C₂H₄ and X₂Mg⋯C₆H₆ (X = H, F) complexes. The CCSD(T) interaction energies of these complexes range from −7.22 to −15.80 kcal mol⁻¹. The BSSE of 0.31–1.61 kcal mol⁻¹ is less than 10.2% of the total interaction energy. The MP2 results agree very well with those from the CCSD(T) method, and the difference between the both does not exceed 7.1%. So the MP2 method is also a good choice to characterize the strength of π–magnesium bond. From the table, electron correlation is important for interaction energy calculations of the H₂Mg-based species, which amounts to 18.7–47.6% of the CCSD(T) interaction energy. In contrast, it contributes much less to the interaction energy of the F₂Mg-based complexes.

Table 4 Interaction energies (kcal mol⁻¹) of the six complexes at different levels with the aug-cc-pVTZ basis set. Electron correlation contribution has been computed by the formula EC = |CCSD(T) − SCF|/CCSD(T) × 100%

Complex	SCF	MP2	CCSD(T)	BSSE	EC	dMg–P
F2Mg⋯C6H6	−13.74	−15.52	−15.80	1.61	13.0%	2.504
F2Mg⋯C2H4	−13.08	−13.16	−13.47	0.90	2.9%	2.523
F2Mg⋯C2H2	−15.71	−15.00	−15.66	0.81	0.3%	2.460
H2Mg⋯C6H6	−4.45	−9.09	−8.49	0.70	47.6%	2.683
H2Mg⋯C2H4	−5.11	−7.48	−7.22	0.34	29.2%	2.702
H2Mg⋯C2H2	−7.24	−8.97	−8.91	0.31	18.7%	2.617

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It has been reported that the interaction energies of π–lithium¹² and π–beryllium¹⁹ bonding complexes usually increase in a linear manner with the decreasing binding distances between two monomers. So the binding distances (d_Mg–P) of the π–magnesium bonding dimers are also shown in Table 4 to facilitate comparison. From the table, the absolute interaction energy increases in the order H₂Mg⋯C₂H₄ (−7.22 kcal mol⁻¹) < H₂Mg⋯C₆H₆ (−8.49 kcal mol⁻¹) < H₂Mg⋯C₂H₂ (−8.91 kcal mol⁻¹), which accords with the decreasing Mg⋯P distance from H₂Mg⋯C₂H₄ to H₂Mg⋯C₂H₂.

However, there is an exception in the MgF₂-based complexes. As shown in Table 4, the interaction energy increases in the order F₂Mg⋯C₂H₄ (−13.47 kcal mol⁻¹) < F₂Mg⋯C₂H₂ (−15.66 kcal mol⁻¹) < F₂Mg⋯C₆H₆ (−15.80 kcal mol⁻¹), that is, the F₂Mg⋯C₆H₆ complex exhibits larger interaction energy than that of F₂Mg⋯C₂H₂ though the latter has a shorter binding distance. As discussed later, this inconsistency can be interpreted on the basis of AIM analysis. Besides, the interaction energies of F₂Mg-based complexes are nearly twice of those of the H₂Mg-based ones, indicating that the former species are much more stable than the latter. This is consistent with the shorter binding distances in the F₂Mg-based species.

In order to gain more insight into the origin and nature of π–magnesium bonds, the LMOEDA analysis has been performed. The results indicate significant electrostatic and polarization energies in the complexation between MgX₂ and π electron donors. The former is at least half and the latter accounts for ca. 28–45%, of the total attractive interaction energy (see Table 5). Similarly, the Yañez's group¹⁹ also reported that the electrostatic term constituted the largest stabilizing contribution to the formation of π–beryllium bonding complexes. It is worth mentioning that the dispersion energy also makes a non-negligible contribution (17.6%) to the stabilization of the H₂Mg⋯C₆H₆ complex. Obviously, the MgF₂-based complexes exhibit larger attractive interaction energies but smaller exchange-repulsion energies than the MgH₂-based ones.

Table 5 LMO–EDA partition terms (kcal mol⁻¹) for the X₂Mg⋯C₂H₂, X₂Mg⋯C₂H₄ and X₂Mg⋯C₆H₆ (X = H, F) complexes

	Eelst	Epol	Edisp	Eex+rep
F2Mg⋯C6H6	−15.35	−13.83	−1.82	15.45
F2Mg⋯C2H4	−18.53	−9.91	−0.11	15.38
F2Mg⋯C2H2	−23.14	−10.47	0.68	17.90
H2Mg⋯C6H6	−13.06	−8.68	−4.64	17.26
H2Mg⋯C2H4	−15.82	−7.50	−2.37	18.18
H2Mg⋯C2H2	−19.16	−8.11	−1.74	20.00

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As reported in previous works, the interaction energies of the FLi⋯Y and HNa⋯Y (Y = C₂H₂, C₂H₄ and C₆H₆) complexes vary in the ranges of −8.35 to −10.83 kcal mol⁻¹ (calculated at the B3LYP/6-311++G(d, p) level)¹² and −4.32 to −6.90 kcal mol⁻¹ (at the MP2/6-311++G(d, p) level),¹³ respectively. Obviously, the interaction energies of the topic complexes are much larger than those of corresponding π–lithium and π–sodium bonding species. The F₂Mg⋯C₂H₂ and F₂Mg⋯C₂H₄ complexes possess comparable interaction energies to those of π–beryllium bonding X₂Be⋯C₂H₂/C₂H₄ (X = H, F, Cl) species, whose interaction energies vary in the range of −11.90 to −14.76 kcal mol⁻¹ at the CCSD(T)/aug-cc-pVTZ level.¹⁹ In contrast, the H₂Mg⋯C₂H₂ and H₂Mg⋯C₂H₄ complexes exhibit much smaller interaction energies. In addition, the interaction energies are −10.00 and −7.10 kcal mol⁻¹ for the F₂Be⋯C₆H₆ and H₂Be⋯C₆H₆ complexes at the PBE/TZ2P level,⁴² as reported by Feng's group. Hence, the X₂Mg⋯C₆H₆ complex has larger interaction energy than X₂Be⋯C₆H₆, whether X represents F or H atom. As far as conventional magnesium bonding complexes are concerned, Yang and co-workers reported considerable binding energies of 63.2–66.5 kcal mol⁻¹ for the LiNH₂⋯HMgX (X = H, F, Cl, Br, CH₃, OH, and NH₂) complexes.²¹ This is not surprising in view of the fact that these complexes are stabilized not only by magnesium bonds but also by concomitant lithium bonds.

Harmonic vibrational frequencies and Raman activity

The calculated harmonic vibrational frequencies for typical intermolecular vibrational modes of the X₂Mg⋯C₂H₂, X₂Mg⋯C₂H₄ and X₂Mg⋯C₆H₆ (X = H, F) complexes are shown in Table 6, the corresponding data of monomers are collected in Table S2 in ESI.† In view of the fact that the C–C and X–Mg–X symmetric stretching vibrations do not have infrared intensity, the Raman intensities of the representative vibrations are shown in the tables. From Table 6, the frequencies of the stretching mode of the π–magnesium bonds π⋯Mg are in the range of 141.2–240.7 cm⁻¹. The symmetric stretching frequency of the MgH₂ molecule decreases as much as 42.8 cm⁻¹, 38.7 cm⁻¹, and 51.7 cm⁻¹ when interacting with acetylene, ethylene and benzene molecules, respectively, accompanied by a decrease in Raman intensity. In comparison, the MgF₂ symmetric stretching vibration is much less red-shifted in the complexes. Meanwhile, all the X–Mg–X antisymmetric stretching vibrations undergo substantial redshift of 44.1–61.1 cm⁻¹ along with the π–magnesium bond formation. The C–C stretching vibrations of C₂H₂ and C₂H₄ molecules are also red-shifted when complexed with the MgX₂ molecule, and the decreased vibrational frequencies are 14.7–20.0 cm⁻¹. Effect of the complexation with MgX₂ molecule on the C1–C2 stretching vibration of C₆H₆ is relatively small. From Table 6, the C–C stretching vibration frequency of C₆H₆ only decreases 7.6 and 7.0 cm⁻¹ in the H₂Mg⋯C₆H₆ and F₂Mg⋯C₆H₆ dimers, respectively. Note that the redshifts of C–C and Mg–X stretching vibration modes accord well with the bond lengthening, both indicating the weakened C–C and Mg–X bonds upon π–magnesium bond formation.

Table 6 Main harmonic vibrational frequencies (v, cm⁻¹) and corresponding Raman intensities (RI, au) of the X₂Mg⋯C₂H₂, X₂Mg⋯C₂H₄, and X₂Mg⋯C₆H₆ (X = H, F) complexes

	X–Mg–X sym. stretch			X–Mg–X antisym. stretch			C–C stretch			π··· Mg stretch
	v	Δv	ΔRI	v	Δv	ΔRI	v	Δv	ΔRI	v
H2Mg⋯C2H2	1591.3	−42.8	−90.6	1606.3	−50.6	16.6	1952.0	−15.7	16.6	168.2
F2Mg⋯C2H2	540.8	−10.7	−1.4	815.2	−46.0	0.2	1953.1	−14.7	0.2	240.7
H2Mg⋯C2H4	1595.5	−38.7	−70.7	1610.7	−46.2	24.4	1661.1	−16.9	24.4	145.0
F2Mg⋯C2H4	546.2	−5.2	−1.4	817.0	−44.1	0.2	1658.0	−20.0	0.2	222.7
H2Mg⋯C6H6	1582.5	−51.7	−151.9	1603.3	−53.6	55.6	1007.4	−7.6	55.6	141.2
F2Mg⋯C6H6	545.3	−6.1	−2.0	800.0	−61.1	0.3	1005.2	−7.0	0.3	208.0

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AIM analysis

Bader's quantum theory of atoms in molecules (QTAIM)^33,34 is useful in providing significant insight into the nature and strength of intermolecular interactions. This theory is based on the topological analysis of electron density and its Laplacian at the bond critical point (BCP). The Laplacian is the sum of λ₁, λ₂, and λ₃, the three eigenvalues of the Hessian matrix of electron density.

In order to gain more information about the weak interactions in π–magnesium bonding dimers, the calculated topological parameters at the π⋯Mg BCPs for the six complexes are exhibited in Table 7, where the electron densities ρ(r)_BCP and their Laplacians ∇²ρ(r) are also given. From Table 7, the ρ(r) values increase in the order 0.0116 au for H₂Mg⋯C₆H₆ < 0.0125 au for H₂Mg⋯C₂H₄ < 0.0138 au for H₂Mg⋯C₂H₂ and 0.0160 au for F₂Mg⋯C₆H₆ < 0.0175 au for F₂Mg⋯C₂H₄ < 0.0190 au for F₂Mg⋯C₂H₂, demonstrating that acetylene is the best Lewis base and can form the strongest π–magnesium bond herein. By contrast, the C₆H₆ molecule is a weaker π electron donor in view of the relatively smaller ρ(r) values of the π⋯Mg BCPs.

Table 7 The topological properties at the π⋯Mg bond critical point (all units are atomic units)

Complex	ρ(r)	λ1	λ2	λ3	∇^2ρ(r)
H2Mg⋯C2H2	0.0138	−0.0132	−0.0073	0.0828	0.0624
F2Mg⋯C2H2	0.0190	−0.0208	−0.0155	0.1333	0.0971
H2Mg⋯C2H4	0.0125	−0.0117	−0.0055	0.0644	0.0471
F2Mg⋯C2H4	0.0175	−0.0189	−0.0133	0.1096	0.0774
H2Mg⋯C6H6	0.0116	−0.0077	−0.0051	0.0568	0.0440
F2Mg⋯C6H6	0.0160	−0.0162	−0.0076	0.0989	0.0750

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The molecular graphs of the X₂Mg⋯C₂H₂, X₂Mg⋯C₂H₄ and X₂Mg⋯C₆H₆ complexes are presented in Fig. 2. The figure shows that there only exists one bond path (BP) linking the magnesium atom with C=C or C≡C bond by a bond critical point (BCP) for the H₂Mg⋯C₂H₂, H₂Mg⋯C₂H₄, F₂Mg⋯C₂H₂ and F₂Mg⋯C₂H₄ complexes. For the X₂Mg⋯C₂H₂ complexes, the bond path actually connects the Mg atom and the non-nuclear attractor (NNA) situated between two BCPs of the CC bond (Fig. 2). The similar case occurred in the interaction between AlF₃ and C₂H₂ molecules.¹⁴ Whereas, the situation is more complex for the F₂Mg⋯C₆H₆ complex, where exists four kinds of interactions between the F₂Mg and C₆H₆ molecules. The first one is the magnesium bond formed between Mg and the center of C1–C2 bond via a BCP (ρ(r) = 0.0160 au). The second interaction is cage path (CP) linking Mg, F and π electron of benzene containing a cage critical point (CCP) with ρ(r)_CCP of 0.0052 au. The third one is two ring paths (RP) linking Mg, F and some C atoms by ring critical point (RCP) with ρ(r)_RCP of 0.0059 au. Besides, we can also see another bond path linking F1 atom and one of the C–C bond, indicating an interaction between F atom and the benzene ring and the corresponding ρ(r)_BCP value is 0.0063 au. These additional interactions between MgF₂ and C₆H₆ molecules may well explain why the F₂Mg⋯C₆H₆ complex exhibits a larger interaction energy than that of F₂Mg⋯C₂H₂ although it has a longer binding distance and a smaller Mg⋯π ρ(r)_BCP value. Similarly, there are one RCP and one CCP between the H₂Mg molecule and benzene ring in addition to the Mg⋯π BCP (ρ(r) = 0.0116 au), and the corresponding ρ(r)_RCP and ρ(r)_CCP values are both equal to 0.0050 au. As a result, the H₂Mg⋯C₆H₆ complex is more stable than H₂Mg⋯C₂H₄ even though the π–magnesium bonding interaction is stronger in the latter. As far as the π–beryllium bonding species is concerned, there is only one bond path was found linking the Be atom to one carbon atom of benzene, and the ρ(r)_BCP values are 0.0190 and 0.0223 au for the H₂Be⋯C₆H₆ and F₂Be⋯C₆H₆ complexes, respectively.⁴² By contrast, the Mg⋯π ρ(r)_BCP values are slightly smaller (see Table 7). Nevertheless, the X₂Mg⋯C₆H₆ complexes show larger interaction energies than corresponding X₂Be⋯C₆H₆ ones due to the combined effect of multiple interactions between X₂Mg and benzene molecules.

Fig. 2 The molecular graphs of the X₂Mg⋯C₂H₂, X₂Mg⋯C₂H₄ and X₂Mg⋯C₆H₆ (X = H, F) complexes (red, green and blue dots denote BCP, CCP and RCPs, respectively).

Conclusion

The structural characteristics and interaction nature of complexes formed between MgX₂ (X = H, F) and conjugated molecules have been investigated in detail. The stability of the topic species originates from the formation of π–magnesium bonds, where 0.033–0.061 |e| electron transfer occurs and the conjugated molecules play the role of electron donor. NBO analysis reveals that the main charge-transfer involves the π_CC bonding orbital and the empty lone pair orbitals of Mg. Interesting geometrical features have been found for these complexes. The angles between the MgF₂ molecular plane and C1–C2 bond are 0°, 61.8° and 90° with Lewis bases being C₂H₂, C₂H₄ and C₆H₆, respectively. During the π–magnesium bond formation, all the Mg–X bonds lengthened. Accordingly, the X–Mg–X stretching vibrations are red-shifted. The same holds for the C–C stretching modes. According to the computed interaction energies, the MgF₂-based complexes are more stable than the MgH₂-based ones, which may be attributed to the less positive Mg charge of the MgH₂ molecule. AIM analysis indicates that MgX₂ forms stronger π–magnesium bond with acetylene compared to ethylene and benzene. Meanwhile, several additional interactions have been found between the MgX₂ and C₆H₆ molecules, explaining why the F₂Mg⋯C₆H₆ complex shows the largest interaction energy value.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 21173095, 21303066, 21573089) and State Key Development Program for Basic Research of China (Grant No. 2013CB834801).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra23368f

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