Behavior of interactions between hydrogen chalcogenides and an anthracene π-system elucidated by QTAIM dual functional analysis with QC calculations

Abstract

The nature of EH₂-*-π(C₁₄H₁₀) interactions (E = O, S, Se and Te) of an anthracene system was elucidated by applying QTAIM dual functional analysis (QTAIM-DFA) after clarification of the structural features with quantum chemical (QC) calculations. π-HB (hydrogen bond) interactions were detected for E = O, S, Se and Te, whereas π-EB (chalcogen bond) interactions were observed for E = O in (EH₂)-*-π(C₁₄H₁₀), where the bond paths connected H in EH₂ to C₁₄H₁₀ in π-HB, and they connected E in EH₂ to C₁₀H₈ in π-EB. The QTAIM-DFA parameters of (R, θ) and (θ_p, κ_p) were evaluated for the interactions via analysing the plots of H_b(r_c) versus H_b(r_c) − V_b(r_c)/2 for the interactions at the bond critical points. Data obtained from the perturbed structures around the fully optimized structures were employed for the plots, in addition to the fully optimized structures. Data obtained from the fully optimized structures were analysed using (R, θ), which corresponded to the static nature, and those obtained from the perturbed structures were analysed using (θ_p, κ_p), which represented the dynamic nature of the interactions, where θ_p corresponds to the tangent line of the plot and κ_p is the curvature. The θ and θ_p values are less than 90° for all the interactions examined, except for the ⁱH-*-¹¹C(π) interaction in TeH₂-*-C₁₄H₁₀ (C₁: IIB_Atc), where ⁱH is located closer to the centre of C₁₄H₁₀. Therefore, the interactions examined were predicted to have vdW nature, appeared in the pure-CS (closed shell) interaction region, although ⁱH-*-¹¹C(π) was predicted to have the pure-CS/typical-HB nature without covalency. Additionally, the π-HB interaction seems to be slightly stronger than π-EB in (OH₂)-*-π(C₁₄H₁₀).

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Introduction

Significant attention has been paid to the interactions between hydrogen chalcogenides (EH₂: E = O, S, Se and Te) and aromatic π-systems, and some structures have been reported for benzene adducts formed through π-interactions.^1–8 The interactions in benzene π-systems are mainly characterized by the hydrogen bonds formed between EH₂ and the benzene π-system, which act as a proton donor and proton acceptor, respectively, and have been called hydrogen bonds of the π-type (π-HBs) herein.^1–8 The π-HB (hydrogen bond) interactions were also investigated for 1 : 1 and 2 : 1 adducts between EH₂ (E = O and S) and the naphthalene π-system.^9–20 Indeed, there have been many investigations on π-adducts, which are mainly based on a theoretical background; however, these investigations seem to be rather limited to structural features. The nature of the π-HB interactions has seldom been reported, especially for the anthracene π-system, π(C₁₄H₁₀), to the best of our knowledge.

Very recently, we reported the nature of the EH₂⋯π interactions for benzene and naphthalene π-systems, together with their structural features.^1,2,10,11 The H atom(s) in EH₂ is (are) connected to the benzene π-system, EH₂⋯π(C₆H₆), via bond paths (BPs). Through careful examination of the BPs in the adducts, another type of interaction was also detected in H₂E⋯π(C₆H₆), where E in EH₂ is joined to the benzene π-system via a BP. Such interaction was called a chalcogen π-type (π-EB) bond. EH₂ is connected to the C atoms or BCPs (bond critical points: r_c: *)²¹ on the C=C bonds of C₆H₆ by BPs. In the case of the benzene π-system, π-EBs seem more important relative to π-HBs, although the predicted importance may change depending on the calculation system.²

What happens if EH₂ (E = O, S, Se and Te) interacts with the anthracene π-system? The anthracene π-system contains two types of (three) benzene π-systems and one type of (two) naphthalene π-system, in addition to the original anthracene π-system. What are the differences and similarities in the EH₂⋯π interactions between the anthracene π-system and the π-systems of naphthalene and benzene? The nature of the interactions in (EH₂)⋯π(C₁₄H₁₀) (E = O, S, Se and Te) is elucidated together with its structural feature. Scheme 1 illustrates some of the structures expected for (EH₂)-*-π(C₁₄H₁₀) of the 1 : 1 adducts, which are inferred from the structures of (EH₂)-*-π(C₁₀H₈) and (EH₂)-*-π(C₆H₆). Type IIA_Atc and type IIC_Atc in (EH₂)⋯π(C₁₄H₁₀) are defined for the adduct, where EH₂ locates on the central and outer benzene rings of anthracene, respectively, whereas it is above the ¹¹C–¹²C (or ¹³C–¹⁴C) bond in type IIB_Atc. The structures for the 1 : 1 adduct of (EH₂)-*-π(C₆H₆) and (EH₂)-*-π(C₁₀H₈) are also shown in Scheme 1 for convenience of discussion. The optimized structures are called type Ia_Bzn, Ib_Bzn and type II_Bzn for (EH₂)-*-π(C₆H₆) and type I_Nap and type II_Nap for (EH₂)-*-π(C₁₀H₈).

Scheme 1 Structures expected for (EH₂)⋯π(C₁₄H₁₀) (E = O, S, Se and Te), based on that optimized for (EH₂)⋯π(C₆H₆) and (EH₂)⋯π(C₁₀H₈).

The QTAIM (quantum theory of atoms-in-molecules) approach, introduced by Bader^22,23 enables the analysis of the nature of chemical bonds and interactions.^24–30 Interactions seem to be defined by the corresponding BPs, but we must be careful to use the correct terminology with the concept.³¹ BCP is an important concept in QTAIM, which is a point along the BP at the interatomic surface, where charge density, ρ(r), reaches a minimum.³² It is denoted by ρ_b(r_c), in addition to other QTAIM functions at BCPs, such as Laplacians of ρ(r) (∇²ρ_b(r_c)), total electron energy densities H_b(r_c), potential energy densities V_b(r_c) and kinetic energy densities G_b(r_c), together with k_b(r_c) (= V_b(r_c)/G_b(r_c)).

Recently, we proposed QTAIM dual functional analysis (QTAIM-DFA),^33–36 according to QTAIM.^22–30,37 QTAIM-DFA enables experimental chemists to analyse their own results concerning chemical bonds and interactions with their own image.³⁸ QTAIM-DFA provides an excellent possibility for evaluating, classifying and understanding weak to strong interactions in a unified form.^33–36 To elucidate the nature of the interactions in question with QTAIM-DFA, H_b(r_c) is plotted versus H_b(r_c) − V_b(r_c)/2 [= (ħ²/8m)∇²ρ_b(r_c)], where both the x and y axes are given units of energy. In our treatment, data for perturbed structures around fully optimized structures are employed for the plots, in addition to the fully optimized structures.^33–36 We propose the concept of “the dynamic nature of interactions” which originated from the data containing the perturbed structures.^{33a,34–36,39}

Data from the fully optimized structures correspond to the static nature of interactions. QTAIM-DFA is applied to typical chemical bonds and interactions and rough criteria are established. The rough criteria can distinguish the chemical bonds and interactions in question from others. QTAIM-DFA and the criteria are explained in the ESI with Schemes S1 and S2, Fig. S1 and eqn (S1)–(S7).‡ The basic concept of the QTAIM approach is also surveyed.

QTAIM-DFA is applied to elucidate the dynamic and static nature of the interactions in (EH₂)-*-π(C₁₄H₁₀) (E = O, S, Se and Te). The discussion is limited to the 1 : 1 adducts of (EH₂)-*-π(C₁₄H₁₀) for simplicity. Herein, we present the results of the investigations on the nature of the interactions in question. The interactions are classified and characterized as a reference by employing the criteria.

Methodological details in calculations

Structures were optimized using the Gaussian 09 programs.⁴⁰ The 6-311+G(3df) basis set⁴¹ was employed for O, S and Se and the basis set of the (7433111/743111/7411/2 + 1s1p1d1f) type from Sapporo Basis Set Factory⁴² was used for Te with the 6-311++G(d, p) basis set⁴¹ for C and H. The basis set system (BSS) is called BSS-F according to examinations of the BSSs in a previous study. The Møller–Plesset second order energy correlation (MP2) level⁴³ was applied to the calculations. Optimized structures were confirmed by the frequency analysis.

QTAIM functions were calculated by employing the wfn files using the Gaussian 09 program package⁴⁰ with the same method for optimizations, and the data were analysed with the AIM2000 program.⁴⁴ The normal coordinates of internal vibrations (NIV) obtained by the frequency analysis were employed to generate the perturbed structures,^35,36 which is explained in eqn (1). The k-th perturbed structure in question (S_kw) was generated by the addition of the normal coordinates of the k-th internal vibration (N_k) to the standard orientation of a fully optimized structure (S₀) in the matrix representation.³⁵ The coefficient f_kw in eqn (1) controls the difference in the structures between S_kw and S₀: f_kw is determined to satisfy eqn (2) for the interaction in question, where, r and r₀ stand for the distances in question in the perturbed and fully optimized structures, respectively, with a₀ of Bohr radius (0.52918 Å). The perturbed structures with NIV correspond to that with r being elongated or shortened by 0.05a₀ or 0.1a₀, relative to r₀, as shown in eqn (2). N_k of five digits are used to predict S_kw. The selected vibration must contain the motion of the interaction in question most effectively among all the zero-point internal vibrations.

S_kw = S₀ + f_kwN_k (1)

r = r₀ + wa₀ (w = (0), ±0.05 and ±0.1; a₀ = 0.52918 Å) (2)

y = c_o + c₁x + c₂x² + c₃x³ (3)

(R_c²: square of correlation coefficient).

In the QTAIM-DFA treatment, H_b(r_c) is plotted versus H_b(r_c) − V_b(r_c)/2 for data of five points of w = 0, ±0.05 and ±0.1, as shown in eqn (2). Each plot is analysed using a regression curve of the cubic function, as shown in eqn (3), where (x, y) = (H_b(r_c) − V_b(r_c)/2, H_b(r_c)) (R_c² > 0.99999 usually).⁴⁵

Results and discussion

Structural feature of (EH₂)⋯π(C₁₄H₁₀) (E = O, S, Se and Te)

Before the final structural optimizations for (EH₂)-*-π(C₁₄H₁₀) (E = O, S, Se and Te), the minima were searched for systematically with MP2/BSS-F. The search was started assuming typically type IIA_Atc, type IIB_Atc and type IIC_Atc structures of the C₁ symmetry. The type IIA_Atc and type IIB_Atc structures of (EH₂)-*-π(C₁₄H₁₀) were optimized for E = O and S, whereas only type IIB_Atc was optimized for E = Se and Te. The processes of the convergence are summarized in Table S1 of the ESI.‡

The type IIA_Atc structure optimized for (OH₂)-*-π(C₁₄H₁₀) with MP2/BSS-F was apparently different from type IIB_Atc, as confirmed by the r₁ values. In the case of (SH₂)⋯π(C₁₄H₁₀), one structure was optimized, which was close to the type IIA_Atc structure if initially assuming a typical type IIA_Atc structure. The type IIA_Atc structure optimized for (SH₂)⋯π(C₁₄H₁₀) [SH₂⋯π(C₁₄H₁₀) (C₁: IIA_Atc)] seems somewhat distorted from the C_s symmetry.⁴⁶ The search converged to another one, if started assuming typical type IIB_Atc and type IIC_Atc structures, which are close to type IIA_Atc. Indeed, their r₁ values are very close to each other, but the ϕ₂ and ϕ₃ values seem meaningfully different for the two types (Fig. 1c and d, respectively). Therefore, the second structure is (tentatively) called type IIB_Atc, herein. No type I_Atc structures were detected after similar treatment, even if optimizations started from those very close to type IA_Atc.

Fig. 1 Molecular graphs for OH₂-*-π(C₁₄H₁₀) (C₁: type IIA_Atc) (a), H₂O-*-π(C₁₄H₁₀) (C₁: type IIB_Atc) (b), SH₂-*-π(C₁₄H₁₀) (C₁: type IIA_Atc) (c), SH₂-*-π(C₁₄H₁₀) (C₁: type IIB_Atc) (d), SeH₂-*-π(C₁₄H₁₀) (C₁: type IIB_Atc) (e) and TeH₂-*-π(C₁₄H₁₀) (C₁: type IIB_Atc) (f), calculated with MP2/BSS-F. The bond critical points (BCPs) are denoted by red dots, ring critical points (RCPs) by yellow dots and cage critical points (CCPs) by green dots, together with bond paths by pink lines. Carbon atoms are in black and hydrogen atoms are in grey, with oxygen, sulphur, selenium and tellurium atoms in red, yellow, pink and purple, respectively.

Table 1 collects the structural parameters selected for the optimized structures of (EH₂)-*-π(C₁₄H₁₀) (E = O, S, Se and Te), r₁, r₂, r₃, θ₁, θ₂, θ₃, ϕ₁, ϕ₂ and ϕ₃, which are defined in Scheme 2. The optimized structures are not shown in the figures, but they can be found in molecular graphs, which are drawn on the optimized structures (see Fig. 1). What factors appear to control the optimized structures? We compared the H⋯H distance in EH₂, r(H, H: EH₂), with the ¹¹C⋯¹³C distance in C₁₄H₁₀, r(¹¹C, ¹³C: C₁₄H₁₀). Indeed, r(H, H: EH₂) for E = O (1.522 Å), S (1.931 Å), Se (2.088 Å) and Te (2.361 Å) is shorter than r(¹¹C, ¹³C: C₁₄H₁₀) (2.452 Å for the central benzene ring), but the differences in r (Δr = r(C, C: C₁₄H₁₀) − r(H, H: EH₂)) are larger than 0.5 Å for O (Δr = 0.9303 Å) and S (0.5215 Å), whereas they are smaller than 0.4 Å for Se (0.3644 Å) and Te (0.0913 Å) (see Table S2 of the ESI‡). The type IIB_Atc structures of (EH₂)-*-π(C₁₄H₁₀) (E = O, S, Se and Te) would form with no limitations of Δr, whereas it may be necessary for Δr larger than around 0.5 Å to give the type IIA_Atc structures (E = O and S). In the case of type IIB_Atc, one H in EH₂ seems to be slightly above the ¹¹C⋯¹³C bond for E = S, Se and Te, but OH₂ seems to exist almost right above the ¹¹C⋯¹³C bond, which may also be controlled by Δr. Indeed, the difference in Δr between E = S and Se seems small, at a first glance, but the small difference would play an important role in the appearance of the type IIA_Atc structure.

Table 1 Structural parameters for (EH₂)⋯π(C₁₄H₁₀) (E = O, S, Se and Te) optimized at the MP2 level with BSS-F^abc

Species (X–Y) (symmetry: type)	r1 (Å)	r2 (Å)	r3 (Å)	θ1 (°)	θ2 (°)	θ3 (°)	ϕ1 (°)	ϕ2 (°)	ϕ3 (°)	ΔEES^d (kJ mol^−1)	ΔEEnt^e (kJ mol^−1)
a BSS-F: the 6-311+G(3df) basis set was employed for O, S and Se and the basis set of the (7433111/743111/7411/2 + 1s1p1d1f) type for Te with the 6-311++G(d,p) basis set for C and H.b See Scheme 2 for the structural parameters.c Optimized structures are not given in the figures but can be found in the molecular graphs drawn on the optimized structures (see Fig. 1).d ΔEES = EES((EH2)-*-π(C14H10)) − (EES(EH2) + EES(C14H10)) on the energy surface.e ΔEEnt = EEnt((EH2)-*-π(C14H10)) − (EEnt(EH2) + EEnt(C14H10)) with the thermal corrections to enthalpies.f Very close to Cs.g The structures are very close to each other; however, they are analysed as two different structures here since the differences in ϕ2 and ϕ3 seem meaningful. They are called IIAAtc and IIBAtc.
OH2⋯π(C14H10) (C1:^f IIAAtc)	3.2865	0.9629	0.9629	89.9	51.8	103.5	−92.5	−1.7	2.8	−22.7	−18.1
H2O⋯π(C14H10) (C1: IIBAtc)	3.6682	0.9631	0.9624	63.4	69.6	103.6	−93.8	−14.3	3.5	−21.9	−17.6
SH2⋯π(C14H10) (C1: IIAAtc)^g	3.6162	1.3389	1.3400	80.5	60.6	92.2	−92.1	−6.4	−3.3	−28.7	−25.0
SH2⋯π(C14H10) (C1: IIBAtc)^g	3.6165	1.3389	1.3400	80.5	60.6	92.2	−91.8	−2.1	−1.9	−28.7	−25.0
SeH2⋯π(C14H10) (C1: IIBAtc)	3.6959	1.4597	1.4603	78.9	61.5	91.3	−91.5	3.0	−0.2	−31.7	−28.3
TeH2⋯π(C14H10) (C1: IIBAtc)	3.7703	1.6576	1.6578	78.1	64.2	91.5	−89.9	−11.4	−17.5	−40.5	−36.8

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Scheme 2 Structural Parameters Illustrated for Type II_Atc of (EH₂)-*-π(C₁₄H₁₀) (E = O, S, Se and Te).

What are the stabilization energies in the formation of the adducts? Table 1 contains the ΔE (ΔE_ES and ΔE_Ent) values for (EH₂)⋯π(C₁₄H₁₀), where, ΔE_ES and ΔE_Ent are the ΔE values on the energy surfaces and those with the thermal corrections to enthalpies, respectively [ΔE = (E((EH₂)⋯π(C₁₄H₁₀)) − (E(EH₂) + E(C₁₄H₁₀))]. An excellent correlation was obtained in the plot of ΔE_Ent versus ΔE_ES (y = 5.262 + 1.047x; R_c² = 0.998 (n = 6: number of data points)), although is not shown in the figure. Therefore, the ΔE_ES values will be employed for the discussion of ΔE. A good correlation was also obtained in the plot of ΔE_ES versus r₁, if the data for H₂O⋯π(C₁₄H₁₀) (C₁: IIB_Atc) are neglected (y = −1410.42 + 820.87x – 121.30x²; R_c² = 0.975 (n = 5)), where the structure of H₂O⋯π(C₁₄H₁₀) (C₁: IIB_Atc) seems different from the others.

What are the relations between ΔE_Atc, ΔE_Nap and ΔE_Bzn? The ΔE_Nap values are linearly proportional to ΔE_Bzn in type II. The ratio of ΔE_Nap/ΔE_Bzn becomes larger in the order of E = O (ΔE_Nap/ΔE_Bzn = 1.34) < S (1.60) < Se (1.68) < Te (1.75), which shows a substantial chalcogen dependence. On the other hand, the ΔE_Atc/ΔE_Nap ratio seems almost constant for E = O (ΔE_Atc/ΔE_Nap = 1.01) < S (1.07) < Se (1.09) < Te (1.11). The different basis sets for Te may somewhat affect the evaluated values for E = Te, which are from the Sapporo Basis Set Factory, whereas the others are from the Gaussian09 program. What mechanisms operate to control the ratios? It is difficult to clarify this, however, we examined the ratios of r_1 : Bzn/r_1 : Nap and r_1 : Atc/r_1 : Nap. The r_1 : Bzn/r_1 : Nap ratios become larger in the order of 1.01 (E = O) < 1.13 (S) < 1.15 (Se) < 1.19 (Te) and the r_1 : Atc/r_1 : Nap ratios increase similarly in the order of 1.00 (E = O) < 1.09 (S) < 1.11 (Se) < 1.13 (Te). However, the chalcogen dependence of the ratios seems somewhat smaller for r_1 : Atc/r_1 : Nap, relative to the case for r_1 : Bzn/r_1 : Nap. These results would be responsible for the observed ΔE/ΔE ratios, although the vdW and/or covalent radii of chalcogens must also be carefully examined for the discussion.

Before the application of QTAIM-DFA to (EH₂)⋯π(C₁₄H₁₀), the molecular graphs and contour plots are examined next.

Molecular graphs and contour plots of ρ(r) for (EH₂)⋯π(C₁₄H₁₀)

Fig. 1 illustrates the molecular graphs for (EH₂)-*-π(C₁₄H₁₀) (E = O, S, Se and Te), which were calculated with MP2/BSS-F. The BCPs are clearly detected, which contain that expected between EH₂ and C₁₄H₁₀. Each BP with a BCP connects each H in EH₂ and the carbon atom of ¹¹C or ¹³C in C₁₄H₁₀ for all optimized structures in Table 2, except for the type IIB_Atc of H₂O-*-π(C₁₄H₁₀). The BP with BCP joins O in OH₂ and a carbon atom of ¹¹C or ¹³C in C₁₄H₁₀ of OH₂-*-π(C₁₄H₁₀). Therefore, the interactions between EH₂ and C₁₄H₁₀ are classified by π-HBs for all the adducts in Table 2, except for the type IIB_Atc of H₂O-*-π(C₁₄H₁₀), the interaction of which should be classified by the π-EB type. Ring critical points (RCPs) and cage critical points (CCPs) are also detected in Fig. 1. Fig. 2 shows the contour plots of ρ(r) for (EH₂)⋯π(C₁₄H₁₀) (E = O, S, Se and Te) calculated with MP2/BSS-F. The contour plots of ρ(r) are drawn on a plane containing E, BCP (*) of the (EH₂)-*-π type and an atom or BCP suitable for the contour plots of (EH₂)-*-π(C₁₄H₁₀). The BCPs are well located at the (three dimensional) saddle points of ρ(r) in the species. Negative Laplacians and trajectory plots are drawn in Fig. S2 and S3 of the ESI.‡ It is well visualized how the BCPs are classified through ∇²ρ(r) and the space around the species is well divided by the atoms in it.

Table 2 QTAIM functions and QTAIM-DFA parameters for the interactions in (EH₂)-*-π(C₁₄H₁₀) (E = O, S, Se and Te) evaluated with MP2/BSS-F^a

Interaction (X-*-Y)^e	Type^b	ρb(rc) (eao^−3)	c∇^2ρb(rc)^c (au)	Hb(rc) (au)	kb(rc)^d	R (au)	θ (°)	Freq (cm^−1)	kf (unit^f)	θp (°)	κp (au^−1)	Classification characterization
a BSS-F: the 6-311+G(3df) basis set employed for O, S and Se and the basis set of the (7433111/743111/7411/2 + 1s1p1d1f) type for Te with the 6-311++G(d, p) basis set for C and H.b See Scheme 1 and Fig. 1.c c∇^2ρb(rc) = Hb(rc) − Vb(rc)/2, where c = ħ^2/8m.d kb(rc) = Vb(rc)/Gb(rc).e The optimized structure has C1 symmetry and atoms taking part in the interaction are shown in bold with BCP denoted by *.f mDyne Å^−1.g Very close to Cs symmetry.h ^iH and ^oH in EH2 stand for the atoms taking part in the interactions, which are placed more inside and more outside, respectively, in relation to the centre of C14H10.i Vary large value of 1259 au^−1.
OHH-*-^11(13)C(π)	IIAAtc^g	0.0060	0.0024	0.0007	−0.814	0.0025	72.6	108.7	0.0411	74.5	8.0	p-CS/vdW
H2O-*-^13C(π)	IIBAtc	0.0069	0.0029	0.0009	−0.831	0.0031	73.9	104.5	0.0346	79.3	18.1	p-CS/vdW
S^oH^iH-*-^11C(π)^h	IIAAtc	0.0072	0.0027	0.0009	−0.807	0.0029	72.1	65.9	0.0151	72.2	1.1	p-CS/vdW
S^iH^oH-*-^13C(π)^h	IIAAtc	0.0065	0.0024	0.0007	−0.835	0.0025	74.2	65.9	0.0151	74.3	145.7	p-CS/vdW
S^oH^iH-*-^11C(π)^h	IIBAtc	0.0070	0.0027	0.0009	−0.799	0.0029	71.5	65.8	0.0161	73.6	37.3	p-CS/vdW
S^iH^oH-*-^13C(π)^h	IIBAtc	0.0065	0.0024	0.0007	−0.836	0.0025	74.2	65.8	0.0161	73.4	61.8	p-CS/vdW
Se^oH^iH-*-^11C(π)^h	IIBAtc	0.0072	0.0028	0.0010	−0.789	0.0029	70.8	54.6	0.0158	72.7	30.4	p-CS/vdW
Se^iH^oH-*-^13C(π)^h	IIBAtc	0.0070	0.0025	0.0007	−0.846	0.0026	75.0	54.6	0.0158	74.2	37.1	p-CS/vdW
Te^oH^iH-*-^11C(π)^h	IIBAtc	0.0077	0.0028	0.0008	−0.829	0.0029	73.7	50.5	0.0086	93.8	^i	p-CS/t-HBnc
Te^iH^oH-*-^13C(π)^h	IIBAtc	0.0088	0.0031	0.0008	−0.849	0.0032	75.3	23.9	0.0028	82.9	299.8	p-CS/vdW

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Fig. 2 Contour plots of ρ(r) for OH₂-*-(C₁₄H₁₀) (C₁: type IIA_Atc) (a), H₂O-*-(C₁₄H₁₀) (C₁: type IIB_Atc) (b), SH₂-*-(C₁₄H₁₀) (C₁: type IIA_Atc) (c), SH₂-*-(C₁₄H₁₀) (C₁: type IIB_Atc) (d), SeH₂-*-(C₁₄H₁₀) (C₁: type IIB_Atc) (e) and TeH₂-*-(C₁₄H₁₀) (C₁: type IIB_Atc) (f), calculated with MP2/BSS-F. The BCPs on the plane are denoted by red dots, those outside of the plane in dark pink dots, RCPs by blue squares, CCPs by green dots and bond paths on the plane by black line and those outside of the plane are by grey lines. Carbon atoms are in black and hydrogen atoms are in grey, with the other atoms in black. The contours (ea₀⁻³) are at 2^l (l = ±8, ±7, …, 0) with 0.0047 (heavy line).

Survey of the interactions in (EH₂)-*-π(C₁₄H₁₀) (E = O, S, Se and Te)

As shown in Fig. 1 and 2, some BPs are apparently curved. Therefore, the lengths of the BPs (r_BP) will be substantially different from the straight-line distances (R_SL) in some cases. The r_BP and R_SL values are collected in Table S2 of the ESI‡ for (EH₂)-*-π(C₁₄H₁₀) (E = O, S, Se and Te), which were evaluated with MP2/BSS-F, together with the differences between r_BP and R_SL (Δr_BP = r_BP − R_SL). There are two types of BPs in each adduct since each adduct has C₁ symmetry. Therefore, it is necessary to define the BPs to distinguish the two. Letting ⁱH and ^oH in EH₂ connect to π(C₁₄H₁₀) through BPs, which are placed more inside and more outside, respectively, in relation to the centre of C₁₄H₁₀, then ⁱBP and ^oBP can be defined as ⁱBP (ⁱH-*-π) and ^oBP (^oH-*-π), respectively.

The Δr_BP values are small (ca. 0.03 Å) for ⁱBP (S^oHⁱH-*-¹¹C(π)) and ⁱBP (Se^oHⁱH-*-¹¹C(π)) in (EH₂-*-π(C₁₄H₁₀)) (C₁: IIB_Atc). Thus, the ⁱBPs can be approximated as straight lines. However, the Δr_BP value is large (0.41 Å) for ^oBP (SeⁱH^oH-*-¹¹C(π)), which seems difficult to be approximated by a straight line. The values seem moderate (0.09–0.17 Å) for most of the π-HB and π-EB interactions in EH₂-*-π(C₁₄H₁₀) for E = O, S, Se and Te, other than three cases. The BPs could be approximated as almost straight lines to gentle curves. The r_BP values are plotted versus R_SL in Fig. 3. A very good correlation was obtained for the case of 0.09 ≤ Δr_BP ≤ 0.17 Å, which is shown in the figure. The data for three BPs deviate from the correlation, although two of them can be approximated as straight lines, as mentioned above.

Fig. 3 Plots of r_BP versus R_SL for (EH₂)-*-π(C₁₄H₁₀) (E = O, S, Se and Te), evaluated with BSS-F at the MP2 level.

QTAIM-DFA was applied to the interactions between EH₂ and C₁₄H₁₀ in EH₂-*-π(C₁₄H₁₀) (E = O, S, Se and Te) and the QTAIM functions were calculated for the interactions at BCP. The results are given in Table 2. Fig. 4 shows the plot of H_b(r_c) versus H_b(r_c) − V_b(r_c)/2 for EH₂-*-π(C₁₄H₁₀) (E = O, S, Se and Te), which contains the data for the perturbed structures evaluated with MP2/BSS-F. All the data in Fig. 4 appear in the area of H_b(r_c) − V_b(r_c)/2 > 0 and H_b(r_c) > 0, which belongs to the pure-CS (closed shell: p-CS) region. The plots were analysed according to eqn (S3)–(S6) of the ESI‡ by applying QTAIM-DFA. These results are discussed next.

Fig. 4 Plots of H_b(r_c) versus H_b(r_c) − V_b(r_c)/2 for (EH₂)-*-π(C₁₄H₁₀), evaluated with MP2/BSS-F. Compounds with marks are shown in the figure.

Nature of π-HBs and π-EBs in EH₂-*-π(C₁₄H₁₀) (E = O, S, Se and Te)

Table 2 collects the QTAIM-DFA parameters of (R, θ) and (θ_p, κ_p) for the π-HB and π-EB interactions, together with the frequencies and the force constants (k_f) correlated to NIV, which are employed to generate the perturbed structures. The nature of π-HBs and π-EBs in EH₂-*-π(C₁₄H₁₀) is discussed based on the (R, θ, θ_p) values employing the standard values as a reference (see Scheme S2 of the ESI‡). It should be instructive to survey the criteria related to that herein before a detailed discussion. The criteria tell us that 45° < θ < 90° for pure-CS interactions. The θ_p value predicts the character of the interactions. In the p-CS region, the character of the interactions will be the vdW type for 45° < θ_p < 90°, whereas it will be the t-HB (typical hydrogen bonds) type with no covalency (t-HB_nc) for 90° < θ_p ≤ 125°, where θ_p = 125° tentatively corresponds to θ = 90°.

The θ and θ_p values are less than 90° for all the π-HBs and π-EB in EH₂-*-π(C₁₄H₁₀) examined herein, except for the TeⁱH^oH-*-¹¹C(π) interaction in TeH₂-*-π(C₁₄H₁₀). Therefore, the π-HBs and π-EB interactions in EH₂-*-π(C₁₄H₁₀) in Table 2 are all classified by the pure-CS interactions and characterized as the vdW type (p-CS/vdW), except for TeⁱH^oH-*-¹¹C(π) in TeH₂-*-π(C₁₄H₁₀). Although ^oBP (TeⁱH^oH-*-¹³C(π)) is predicted to have the nature of (p-CS/vdW), ⁱBP (TeⁱH^oH-*-¹¹C(π)) is predicted to have the nature of (p-CS/t-HB_nc). The π-EB interaction in the H₂O-*-¹¹C(π) type [(θ, θ_p) = (73.9°, 79.3°)] is predicted to be somewhat stronger than the π–HB interaction of the OHH-*-¹¹C(π) type [(θ, θ_p) = (72.6°, 74.5°)] for OH₂-*-π(C₁₄H₁₀). The π-HB interactions in the anthracene system are predicted to be very similar to that in the naphthalene system, which seem slightly stronger than that in the benzene system. The results are in accordance with that derived from the energies for the formation of the adducts.

The delocalization indexes and ellipticity are the important parameters to clarify and understand the nature of the (EH₂)⋯π interactions.⁴⁷ The nature of the (EH₂)⋯π interactions will be discussed elsewhere based on these parameters for the series of (EH₂)⋯π(C₆H₆), (EH₂)⋯π(C₁₀H₈), and (EH₂)⋯π(C₁₄H₁₀) (E = O, S, Se and Te).

Conclusions

The behaviour of the interactions for EH₂ adducts with the anthracene π-system (E = O, S, Se and Te) in a 1 : 1 ratio is elucidated by applying QTAIM-DFA. The structures were optimized with MP2/BSS-F. Two types of structures were optimized for E = O and S, whereas one was optimized for E = Se and Te. The BCPs are clearly detected in the molecular graphs. The interactions are the π-HB type for EH₂-*-π(C₁₄H₁₀) (C₁: IIA_Atc) (E = O and S) and EH₂-*-π(C₁₄H₁₀) (C₁: IIB_Atc) (E = S, Se and Te), whereas they are the π-EB type for H₂O-*-π(C₁₄H₁₀) (C₁: IIB_Atc). The QTAIM-DFA parameters of (R, θ) and (θ_p, κ_p) are calculated for the species, according to eqn (S3)–(S6).‡ The θ values are less than 90° for all interactions examined in this work. The θ_p values are also less than 90° for all the interactions in question, except for ⁱH-*-¹¹C(π) in TeH₂-*-C₁₄H₁₀ (C₁: IIB_Atc). Therefore, all the π-HB and π-EB interactions examined in this work are classified by pure-CS interactions and characterized as vdW in nature (p-CS/vdW), although ⁱH-*-¹¹C(π) in TeH₂-*-C₁₄H₁₀ (C₁: IIB_Atc) is predicted to have the p-CS/t-HB nature without covalency. The π-EB interaction is predicted to be somewhat stronger than π-HB in (OH₂)-*-π(C₁₄H₁₀). It is demonstrated that the predicted nature of EH₂-*-π(C₁₄H₁₀) is closer to that of EH₂-*-π(C₁₀H₈) rather than that of EH₂-*-π(C₆H₆). The π-HB and π-EB interactions in the anthracene π-system are well elucidated by applying QTAIM-DFA.

Acknowledgements

This work was partially supported by a Grant-in-Aid for Scientific Research (No. 26410050) from the Ministry of Education, Culture, Sports, Science and Technology, Japan. The support of the Wakayama University Original Research Support Project Grant and the Wakayama University Graduate School Project Research Grant is also acknowledged.

Notes and references

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Footnotes

† Dedicated to Professor Marian Mikołajczyk (Professor at the Centre of Molecular and Macromolecular Studies, Polish Academy of Sciences in Lodz, Poland) on the occasion of his 80th birthday.

‡ Electronic supplementary information (ESI) available: QTAIM-DFA approach, Cartesian coordinates for optimized structures of (EH₂)⋯π(C₁₄H₁₀) (E = O, S, Se and Te). See DOI: 10.1039/c7ra04224h

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