Quantum chemical calculations with the AIM approach applied to the π-interactions between hydrogen chalcogenides and naphthalene

Abstract

The nature of the π–interactions in the 1 : 1 and 2 : 1 adducts of EH₂ with the naphthalene π-system (E = O, S, Se and/or Te) is elucidated by applying QTAIM-DFA (QTAIM dual functional analysis). The H–*–π interactions are detected in EH₂–*–π(C₁₀H₈) and (EH₂)₂–*–π(C₁₀H₈) for E = S, Se and Te, whereas E–*–π interactions are in OH₂–*–π(C₁₀H₈), (OH₂)₂–*–π(C₁₀H₈) and HE–H–*–π(C₁₀H₈) (denoted by HHE–*–C₁₀H₈) (E = S, Se and Te). Asterisks * emphasize the existence of bond critical points (BCPs) on the interactions in question. H_b(r_c) are plotted versus H_b(r_c) − V_b(r_c)/2 at the BCPs in QTAIM-DFA. Plots for the fully optimized structures are analyzed using the polar coordinate (R, θ) representation. Those containing the perturbed structures are by (θ_p, κ_p): θ_p corresponds to the tangent line of the plot and κ_p is the curvature. While (R, θ) describe the static nature, (θ_p, κ_p) represent the dynamic nature of interactions. The θ and θ_p values are less than 90° for all interactions in question, examined in this work, except for θ_p = 90.6° for HHTe–*–π(C₁₀H₈). Therefore, all interactions examined are classified by the pure-CS (closed shell) interactions and predicted to have vdW-nature, except for HHTe–*–π(C₁₀H₈), which should have the character of the typical HB-nature without covalency. The π–EB interaction in HHS–*–C₁₀H₈ is predicted to have the border character between the vdW-nature and the typical HB-nature without covalency, since θ_p = 89.8°. The nature of four interactions appeared between 2H in TeH₂ and C₁₀H₈ in TeH₂–*–π(C₁₀H₈) is also clarified well using QTAIM-DFA.

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Introduction

Hydrogen chalcogenides (EH₂: E = O, S, Se and Te) will form hydrogen bonds (HBs) through each of two polarized E–H bonds with electron donors, such as lone pair orbitals and π-orbitals.^1–6 The polarized E–H bonds of the E^δ−–H^δ+ type act as acceptors at the positively charged H atoms. Conventional HBs of the shared proton interaction type (c-HBs) are formed when lone pair orbitals are supplied from atoms of main groups. Lone pair orbitals of the s- and p-types are contained in EH₂, which also act as donors in the formation of c-HBs. Another type of HBs, containing the H⋯π interactions, will form if π-orbitals are provided from benzene, naphthalene and the derivatives to the proton donors. Such HBs will be called π–HBs, here. Energies in the formation of c-HBs are typically 10–40 kJ mol⁻¹ for the neutral form.^6,7 The H⋯π interactions between EH₂ and π-orbitals seem weaker than c-HBs. Weak proton accepting ability of π-orbitals, relative to that of the lone pair orbitals, must be mainly responsible for the difference.

We reported the behavior of the H–*–π and E–*–π interactions in EH₂ adducts with benzene, (EH₂)–*–π(C₆H₆) (E = O, S, Se and Te) (see Scheme 1),⁶ after clarification of the behavior of c-HBs.⁸ The asterisks (*) emphasize the presence of bond critical points (BCPs) on the bond paths (BPs) in question.⁹ The E–*–π interactions will also be called π–EBs, in this paper. The π–EBs are suggested to be stronger than π–HBs in the same (EH₂)–*–π(C₆H₆), although they are reconfirmed to be weaker than c-HBs.⁶

Scheme 1 Structures for (EH₂)⋯π(C₁₀H₈) and (EH₂)₂⋯π(C₁₀H₈) (E = O, S, Se and Te), together with those for (EH₂)⋯π(C₆H₆).

It must be challenging to elucidate the nature of π–HBs and π–EBs in the EH₂ adducts with various π-systems, in a unified form. We paid attention to the EH₂ adducts with naphthalene π-system (E = O, S, Se and Te), as the next extension. What are the similarities and differences in the behavior of the interactions in the EH₂ adducts with naphthalene and benzene π-systems? The behavior of the interactions in the EH₂ adducts with naphthalene π-system is to be clarified, together with the structural feature. Scheme 1 illustrates the structures of (EH₂)–*–π(C₁₀H₈) and (EH₂)₂–*–π(C₁₀H₈) with the notation, employed in this paper. While (EH₂)⋯π(C₆H₆) was mainly used to discuss the structural feature, whereas (EH₂)–*–π(C₆H₆) was for the discussion of the interactions, although tentative.⁶ Similar notation is employed for the naphthalene π-system. Structures of HE–H–*–π(C₁₀H₈), EH₂–*–π(C₁₀H₈) and (EH₂)₂–*–π(C₁₀H₈) are called type I_Nap, type II_Nap and type III_Nap, respectively. While (EH₂)–*–π(C₁₀H₈) stand for all plausible structures of the 1 : 1 adducts between EH₂ and naphthalene π-system, (EH₂)₂–*–π(C₁₀H₈) describes the 2 : 1 adducts. Therefore, (EH₂)–*–π(C₁₀H₈) contains HE–H–*–π(C₁₀H₈) and EH₂–*–π(C₁₀H₈).

Lots of investigations on the π interactions have been accumulated, mainly based on the theoretical background. A few structures were reported for the benzene adducts formed through the π interactions. The π–HB interactions in EH₂–*–π(C₁₀H₈) and (EH₂)₂–*–π(C₁₀H₈) were investigated for E = O and S.^4,10–17 However, the structures of the naphthalene adducts seem much seldom reported, to the best of our knowledge. Consequently, the results for the benzene adducts explained well the observed structures, together with the observed behavior of the H–*–π and E–*–π interactions. The nature of the H–*–π and E–*–π interactions in the naphthalene adducts will be elucidated and explained well with QTAIM-DFA, although the results are not directly compared with the observed ones.

QTAIM (the quantum theory of atoms-in-molecules) approach, introduced by Bader,^18,19 enables us to analyze the nature of chemical bonds and interactions.^20–26 Interactions are unambiguously defined by BPs. BCP is an important concept in QTAIM. BCP is a point along the BP at the interatomic surface, where charge density ρ(r) reaches a minimum. It is denoted by ρ_b(r_c).²⁷ Recently, we proposed QTAIM-DFA (QTAIM dual functional analysis),^28–30 which concerns chemical bonds and interactions by their own image, for experimental chemists to analyze their own results. QTAIM-DFA provides an excellent possibility for evaluating, classifying and understanding weak to strong interactions in a unified form.^28–31 H_b(r_c) are plotted versus H_b(r_c) − V_b(r_c)/2 in QTAIM-DFA, where H_b(r_c) and V_b(r_c) are the total electron energy densities and potential energy densities at BCPs, respectively. In our treatment, data for perturbed structures around fully optimized ones are employed for the plots, in addition to the fully optimized structures.^28–32 We proposed the concept of “the dynamic nature of interactions” originated from the data containing the perturbed structures.^28a,29–31 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 have been 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,† employing Schemes S1 and S2, Fig. S1 and eqn (S1)–(S7).† The basic concept of the QTAIM approach is also surveyed.

The behavior of the π–HB and π–EB interactions in (EH₂)–*–π(C₆H₆) was elucidated by applying QTAIM-DFA.⁶ In this process, the methodology has been established, to clarify the behavior of the interactions with QTAIM-DFA. QTAIM-DFA is now applied to elucidate the dynamic and static behavior of the interactions in the EH₂ adducts with a naphthalene π-system (E = O, S, Se and Te). 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. The nature of the H–*–π and E–*–π interactions, established in this work, for the EH₂ adducts with naphthalene, as well as those with benzene, will serve as the standard for the interactions with various types of π-systems.

Methodological details in calculations

Structures were optimized using the Gaussian 09 programs.³³ The 6-311+G(3df) basis set³⁴ was employed for O, S and Se and the basis set of the (7433111/743111/7411/2 + 1s1p1d1f) type from Sapporo Basis Set Factory³⁵ was for Te with the 6-311++G(d, p) basis set³⁴ for C and H. The basis set system (BSS) is called BSS-F after examinations of the BSSs in a previous study. The Møller–Plesset second order energy correlation (MP2) level³⁶ was applied to the calculations. Optimized structures were confirmed by the frequency analysis.

QTAIM functions were calculated using the Gaussian 09 program package³³ with the same method for optimizations, and the data were analyzed with the AIM2000 program.³⁷ Normal coordinates of internal vibrations (NIV) obtained by the frequency analysis were employed to generate the perturbed structures.^30,31 The method is explained in eqn (1). A kth perturbed structure in question (S_kw) was generated by the addition of the normal coordinates of the kth internal vibration (N_k) to the standard orientation of a fully optimized structure (S₀) in the matrix representation.³⁰ 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 an 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 those with r being elongated or shortened by 0.05a₀ or 0.1a₀, relative to r₀, as shown in eqn (2). Or the perturbed structures with NIV correspond to the amplification of the selected motion in the zero-point internal vibrations to the extent where r satisfies eqn (2). N_k of five digits are used to predict S_kw. We use this method to generate the NIV of the perturbed structures. 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 = c₀ + c₁x + c₂x² + c₃x³ (3)

(R_c²: square of correlation coefficient).

In the AIM-DFA treatment, H_b(r_c) are 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 analyzed 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 in usual).^28–31,38

Results and discussion

Structural optimization of (EH₂)_n⋯π(C₁₀H₈) (n = 1 and 2: E = O, S, Se and Te)

Structures were optimized for (EH₂)⋯π(C₁₀H₈) and (EH₂)₂⋯π(C₁₀H₈) (E = O, S, Se and Te), with BSS-F at the MP2 level (MP2/BSS-F). Three types of structures were optimized (cf. Scheme 1). Optimized structures of HE–H⋯π(C₁₀H₈) have the C₁ symmetry of type I_Nap, which are denoted by HE–H⋯π(C₁₀H₈) (C₁: type I_Nap), so are by EH₂⋯π(C₁₀H₈) (C₁: type II_Nap) and (EH₂)₂⋯π(C₁₀H₈) (C_i/C₁ (C_i or C₁): type III_Nap) for EH₂⋯π(C₁₀H₈) and (EH₂)₂⋯π(C₁₀H₈), respectively. HE–H⋯π(C₁₀H₈) (C₁: type I_Nap) and EH₂⋯π(C₁₀H₈) (C₁: type II_Nap) belong to (EH₂)⋯π(C₁₀H₈), as mentioned above, whereas (EH₂)₂⋯π(C₁₀H₈) (C_i/C₁: III_Nap) contains one type of the structure for each E. Table 1 collects the structural parameters, r₁, r₂, r₃, θ₁, θ₂, θ₃, ϕ₁, ϕ₂ and ϕ₃, defined in Scheme 2. The optimized structures are not shown in figures but some can be found in Fig. 2, where the molecular graphs are drawn on the optimized structures.

Table 1 Structural parameters for (H₂E)_n⋯π(C₁₀H₈) (n = 1 and 2: E = O, S, Se and Te), optimized at the MP2 level with BSS-F^a,b

Species (X⋯Y) (symmetry)	r1 (Å)	r2 (Å)	r3 (Å)	θ1 (°)	θ2 (°)	θ3 (°)	ϕ1 (°)	ϕ2 (°)	ϕ3 (°)	ΔEES^c (kJ mol^−1)	ΔEZP^d (kJ mol^−1)	Type
a See text for BSS-F.b The structural parameters being defined in Scheme 2.c ΔEES = EES((EH2)n–*–π(C10H8)) − (nEES(EH2) + EES(C10H8)) (n = 1 and 2) on the energy surface.d ΔEZP = EZP((EH2)n–*–π(C10H8)) − (nEZP(EH2) + EZP(C10H8)) (n = 1 and 2) with the zero-point energy corrections.
HS–H⋯π(C10H8) (C1)	3.3060	1.3392	1.3390	88.2	60.7	92.8	−86.6	−10.2	−173.3	−24.9	−22.1	INap
HSe–H⋯π(C10H8) (C1)	3.3167	1.4597	1.4606	90.6	63.0	91.8	−90.3	0.4	178.8	−28.0	−26.0	INap
HTe–H⋯π(C10H8) (C1)	3.3236	1.6579	1.6607	92.6	66.4	90.9	−92.3	7.1	176.4	−41.2	−39.6	INap
OH2⋯π(C10H8) (C1)	3.2937	0.9631	0.9624	82.6	51.8	103.5	−91.3	−14.7	0.3	−21.7	−19.5	IINap
SH2⋯π(C10H8) (C1)	3.5572	1.3391	1.3391	89.1	46.1	92.2	−89.8	−2.2	−3.1	−26.7	−25.3	IINap
SeH2⋯π(C10H8) (C1)	3.6310	1.4596	1.4596	89.0	45.7	91.2	−90.1	2.3	4.2	−29.0	−27.4	IINap
TeH2⋯π(C10H8) (C1)	3.7063	1.6572	1.6572	89.2	47.2	91.5	−88.7	−12.5	−18.1	−36.4	−34.1	IINap
(OH2)2⋯π(C10H8) (C1)	3.2833	0.9625	0.9625	89.9	51.9	103.6	−90.7	0.4	−2.4	−41.7	−38.1	IIINap
(SH2)2⋯π(C10H8) (Ci)	3.5514	1.3390	1.3390	90.0	46.6	92.2	−90.1	7.2	10.7	−51.8	−48.2	IIINap
(SeH2)2⋯π(C10H8) (Ci)	3.6297	1.4596	1.4596	90.0	45.8	91.2	−90.6	5.0	7.2	−56.1	−53.4	IIINap
(TeH2)2⋯π(C10H8) (C1)	3.7123	1.6573	1.6573	90.0	47.2	91.4	−91.6	12.5	18.1	−73.4	−68.5	IIINap

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Scheme 2 Structural parameters for (EH₂)_n–*–π(C₁₀H₈) (n = 1 and 2: E = O, S, Se and Te).

The structure of HO–H⋯π(C₁₀H₈) (C₁: type I_Nap) converges to OH₂⋯π(C₁₀H₈) (C₁: type II_Nap), as shown in eqn (4). All attempts to search HO–H⋯π(C₁₀H₈) (type I_Nap) are unsuccessful. HO–H⋯π(C₁₀H₈) (type I_Nap) must not be an energy minimum. On the other hand, the HE–H⋯π(C₁₀H₈) (C₁: type I_Nap) structures are optimized for E = S, Se and Te, even if the optimizations are started from the structures expected for type I_Nap′, as shown in eqn (5).

How are the stabilization energies in the formation of the adducts? Table 1 contains the ΔE (ΔE_ES and ΔE_ZP) values for (EH₂)_n–*–π(C₁₀H₈), where ΔE_ES and ΔE_ZP are the ΔE values on the energy surfaces and those corrected by the zero-point energies, respectively: ΔE = E((EH₂)_n–*–π(C₁₀H₈)) − (nE(EH₂) + E(C₁₀H₈)) (n = 1 and 2). An excellent correlation was obtained in the plot of ΔE_ZP versus ΔE_ES (y = 0.597 + 0.948x; R_c² = 0.998), although not shown in the figure. Therefore, the ΔE_ES values will be employed for the discussion of ΔE.

While the magnitudes of ΔE_ES for HE–H–*–π(C₁₀H₈) (C₁: type I_Nap) are almost equal to those for EH₂–*–π(C₁₀H₈) (C₁: type II_Bzn) (0.93–1.13 time), the values for (EH₂)₂–*–π(C₁₀H₈) (C_i/C₁: type III_Nap) are almost two times larger than those for EH₂–*–π(C₁₀H₈) (C₁: type II_Nap) (1.86–2.02 times), if ΔE_ES of the same E are compared. The magnitudes of ΔE_ES for EH₂–*–π(C₁₀H₈) (C₁: type II_Nap) are 1.3–1.7 times larger than those for EH₂–*–π(C₆H₆) (C₂: type II_Bzn), if those of the same E are compared, although one imaginary frequency is predicted for each of EH₂–*–π(C₆H₆) (C₂: type II_Bzn). To visualize the relationships clearer, the ΔE_ES values of HE–H–*–π(C₁₀H₈) (C₁: type I_Nap) and (EH₂)₂–*–π(C₁₀H₈) (C_i/C₁: type III_Nap) are plotted versus those of EH₂–*–π(C₁₀H₈) (C₁: type II_Nap). Fig. 1 shows the plots, together with ΔE_ES of EH₂–*–π(C₁₀H₈) (C₂: type II_Bzn) versus those of EH₂–*–π(C₆H₆) (C₂: type II_Bzn). Very good correlations are obtained for the plots, which are given in the figure, although data for (OH₂)₂–*–π(C₁₀H₈) deviate from the correlation for ΔE_ES of (EH₂)₂–*–π(C₁₀H₈) versus those of EH₂–*–π(C₁₀H₈).

Fig. 1 Plots of ΔE_ES for HE–H–*–π(C₁₀H₈) (C₁: type I_Nap) () and (EH₂)₂–*–π(C₁₀H₈) (C_i/C₁: type III_Nap) () versus those of EH₂–*–π(C₁₀H₈) (C₁: type II_Nap) with the deviated data for (OH₂)₂–*–π(C₁₀H₈) (). Plot of ΔE_ES for EH₂–*–π(C₆H₆) (C₂: type II_Bzn) () versus those for EH₂–*–π(C₁₀H₈) (C₁: type II_Nap) is also shown, together with EH₂–*–π(C₁₀H₈) (C₁: type II_Nap) () as a reference.

The results may show that factors to contribute to ΔE_ES would be proportional in these species. However, the E dependence in ΔE_ES for HE–H–*–π(C₁₀H₈) and (EH₂)₂–*–π(C₁₀H₈) seem 0.58 and 1.32 times more sensitive, respectively, if that for EH₂–*–π(C₁₀H₈) is taken as 1.0 (Fig. 1). Similarly, the E dependence in ΔE_ES for EH₂–*–π(C₁₀H₈) seems 5.5 times more sensitive, relative to the case of EH₂–*–π(C₆H₆) (1.32/0.24 = 5.5), although the magnitudes are 1.3–1.7 times larger for the former.

QTAIM-DFA is applied to the π–HB and π–EB interactions in (EH₂)_n–*–π(C₁₀H₈) (n = 1 and 2: E = O, S, Se and Te) to clarify the nature of the interactions in the adducts. Molecular graphs, contour plots, negative Laplacians, and trajectory plots are examined, before the detail discussion.

Molecular graphs, contour plots of ρ(r), negative Laplacians and trajectory plots for (EH₂)_n–∗–π(C₁₀H₈) (n = 1 and 2: E = O, S, Se and Te)

Fig. 2 illustrates some molecular graphs for (EH₂)_n–*–π(C₁₀H₈) (n = 1 and 2: E = O, S, Se and Te), evaluated with MP2/BSS-F. BCPs are clearly detected, containing the interactions in question, together with RCPs (ring critical points) and CCPs (cage critical points). BPs with BCPs are not detected between H in EH₂ and C₁₀H₈ (π–HBs) in HE–H–*–π(C₁₀H₈) (C₁: type I_Nap) for E = S, Se and Te, instead, BPs with BCPs are detected between E in EH₂ and ⁹C in C₁₀H₈ (π–EBs) (see Scheme 1 and Fig. 2). We reported similar type of π–EB between Te in TeH₂ and BCP (C=C) of C₆H₆ in HTe–H–*–π(C₆H₆), evaluated with MP2/BSS-F (see Fig. S2 of the ESI†). Only one π–EB interaction is detected in each of HHE–*–π(C₁₀H₈) (C₁: type I_Nap), which is taken as synonymous with HE–H–*–π(C₁₀H₈) (C₁: type I_Nap) for E = S, Se and Te, whereas π–EB appears accompanied by π–HB in HTe–H–*–π(C₆H₆) (C_s: type Ib_Bzn). Similarly, one π–EB interaction is detected for OH₂–*–π(C₁₀H₈) (C₁: type II_Nap) (eqn (4)).

Fig. 2 Molecular graphs for HS–H–*–π(C₁₀H₈) (C₁: type I_Nap) (a), HSe–H–*–π(C₁₀H₈) (C₁: type I_Nap) (b), HTe–H–*–π(C₁₀H₈) (C₁: type I_Nap) (c), OH₂–*–π(C₁₀H₈) (C₁: type II_Nap) (d), SH₂–*–π(C₁₀H₈) (C₁: type II_Nap) (e), TeH₂–*–π(C₁₀H₈) (C₁: type II_Nap) (f), (OH₂)₂–*–π(C₁₀H₈) (C₁: type III_Nap) (g), (SeH₂)₂–*–π(C₁₀H₈) (C_i: type III_Nap) (h) and (TeH₂)₂–*–π(C₁₀H₈) (C₁: type III_Nap) (i), evaluated 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 BPs by pink lines (). Carbon atoms are in black () and hydrogen atoms are in gray (), with oxygen, sulfur, selenium and tellurium atoms being in red (), yellow (), pink () and purple (), respectively.

However, double π–HBs are confirmed between two H atoms in EH₂ and ⁹C in EH₂–*–π(C₁₀H₈) (type II_Nap) for E = S, Se and Te, which do not contain π–EBs. Moreover, double π–HBs are between TeH₂ and ⁴C and ⁵C for TeH₂–*–π(C₁₀H₈) (C₁: type II_Nap), in addition to double π–HBs between two H atoms in EH₂ and ⁹C. The smaller dihedral angle between the TeH₂ and C₁₀H₈ planes in TeH₂–*–π(C₁₀H₈) would be responsible for the appearance of the double π–HBs between EH₂ and ⁴C and ⁵C. In the case of (EH₂)₂–*–π(C₁₀H₈) (C_i/C₁: III_Nap), quartet of π–HBs are detected between four H atoms in (EH₂)₂ and ⁹C and ¹⁰C atoms for E = S, Se and Te, whereas only two π–EBs are observed between two O atoms in (OH₂)₂ and ⁹C or ¹⁰C atoms. As a whole, π–HBs are detected in EH₂–*–π(C₁₀H₈) (C₁: type II_Nap) and (EH₂)₂–*–π(C₁₀H₈) (C_i/C₁: type III_Nap) for E = S, Se and Te, whereas π–EBs are observed for HHE–*–π(C₁₀H₈) (C₁: type I_Nap) for E = S, Se and Te, OH₂–*–π(C₁₀H₈) (C₁: type II_Nap) and (OH₂)₂–*–π(C₁₀H₈) (C₁: type III_Nap). π–EBs will be discussed separately from π–HBs.

Fig. 3 shows the contour plots of ρ(r) for selected (EH₂)_n–*–π(C₁₀H₈) (n = 1 and 2: E = O, S, Se and Te), calculated with MP2/BSS-F, which are drawn on a plane containing E, BCP of (EH₂)–*–π(C₁₀H₈) and an atom or BCP suitable for the contour plots. BCPs are well located at the saddle points of ρ(r) in the species (Fig. 3). Fig. 4 draws the negative Laplacians of ρ(r) for the selected species. It is well visualized how BCPs are classified through ∇²ρ(r) (Fig. 4). The trajectory plots of ρ(r) are drawn similarly in Fig. S3 of the ESI.† The space around the species is well divided into atoms in it.

Fig. 3 Contour plots of ρ_b(r_c) for HS–H–*–π(C₁₀H₈) (C₁: type I_Nap) (a), HSe–H–*–π(C₁₀H₈) (C₁: type I_Nap) (b), HSe–H–*–π(C₁₀H₈) (C₁: type I_Nap) (c), OH₂–*–π(C₁₀H₈) (C₁: type II_Nap) (d), SH₂–*–π(C₁₀H₈) (C₁: type II_Nap) (e), TeH₂–*–π(C₁₀H₈) (C₁: type II_Nap) (f), (OH₂)₂–*–π(C₁₀H₈) (C₁: type III_Nap) (g), (SeH₂)₂–*–π(C₁₀H₈) (C_i: type III_Nap) (h), and (TeH₂)₂–*–π(C₁₀H₈) (C₁: type III_Nap) (i), evaluated with MP2/BSS-F. Bond critical points (BCPs) on the plane are denoted by red dots (), those outside of the plane in dark pink dots (), ring critical points (RCPs) by blue squares (), cage critical points (CCPs) by green dots () and BPs on the plane by black lines and those outside of the plane are by gray lines. Atoms on and outside the plane are in black () and gray (), respectively.

Fig. 4 Negative Laplacians for HS-H–*–π(C₁₀H₈) (C₁: type I_Nap) (a), HSe–H–*–π(C₁₀H₈) (C₁: type I_Nap) (b), HTe–H–*–π(C₁₀H₈) (C₁: type I_Nap) (c), OH₂–*–π(C₁₀H₈) (C₁: type II_Nap) (d), SH₂–*–π(C₁₀H₈) (C₁: type II_Nap) (e), TeH₂–*–π(C₁₀H₈) (C₁: type II_Nap) (f), (OH₂)₂–*–π(C₁₀H₈) (C₁: type III_Nap) (g), (SeH₂)₂–*–π(C₁₀H₈) (C_i: type III_Nap) (h) and (TeH₂)₂–*–π(C₁₀H₈) (C₁: type III_Nap) (i), evaluated with MP2/BSS-F. Positive and negative areas are shown by blue and red lines, respectively.

Survey of interactions in (EH₂)_n–*–π(C₁₀H₈) (n = 1 and 2: E = O, S, Se and Te)

Some BPs in (EH₂)_n–*–π(C₁₀H₈) (n = 1 and 2) apparently curve, as shown in Fig. 2. Therefore, the lengths of BPs (r_BP) are substantially longer than the straight-line distances (R_SL) in such cases. The r_BP values and the components (r_BP1 and r_BP2: r_BP = r_BP1 + r_BP2) in question are collected in Table S2 of the ESI,† together with the R_SL values, where r_BP1 and r_BP2 correspond to those between H or E in EH₂ (E = O, S, Se and Te) and BCP in question and between BCP in question and a C atom in C₁₀H₈, respectively.

Fig. 5 shows the plot of r_BP versus R_SL for (EH₂)_n–*–π(C₁₀H₈) (n = 1 and 2: E = O, S, Se and Te), evaluated with MP2/BSS-F. It is visualized that the differences between r_BP and R_SL (Δr_BP = r_BP − R_SL) seem large (0.31–0.52 Å) for π–HBs in (EH₂)_n–*–π(C₁₀H₈) (n = 1 and 2) for E = S, Se and Te, moderately large (0.13–0.25 Å) for π–EBs in OH₂–*–π(C₁₀H₈) and (OH₂)₂–*–π(C₁₀H₈), whereas Δr_BP are small (0.03–0.06 Å) for π–EBs in HHE–*–π(C₁₀H₈) (E = S, Se and Te) and additional π–HBs in TeH₂–*–π(C₁₀H₈). The plot of r_BP versus R_SL gives very good correlation for the case of 0.03 < Δr_BP < 0.06 Å, where the correlation is given in the figure. Contours of ρ_b(r_c) seem very complex, when they are very close to H in EH₂ and C in C₁₀H₈. This must be the reason for the (highly) curved BPs (see Fig. 3). The (highly) curved BPs result in the large Δr_BP values in π–HBs of (EH₂)_n–*–π(C₁₀H₈) (n = 1 and 2) for E = S, Se, and Te.

Fig. 5 Plot of r_BP versus R_SL for (EH₂)_n–*–π(C₁₀H₈) (n = 1 and 2: E = O, S, Se and Te), evaluated with MP2/BSS-F.

The R_SL and r_BP values in EH₂–*–π(C₁₀H₈) are larger than the corresponding values in (EH₂)₂–*–π(C₁₀H₈) for E = O, S and Te, although the values of the former seem smaller than (or close to) those corresponding values of the latter for E = Se. The R_SL values in HHE–*–π(C₁₀H₈) become larger in the order of E = S < Se ≤ Te. The R_SL values seem to be controlled mainly by the van der Waals radii of the atoms of which order should be E = O < S ≤ Se < Te. However, the R_SL values seem shortened as the interactions become stronger, where the strength of the interactions would be larger in the order of E = O < S < Se < Te. Consequently, the observed order in R_SL must also be affected on the strength of the interactions, so is the order for r_BP in π–HBs of HE–H–*–π(C₁₀H₈) for E = S, Se and Te.

QTAIM functions are calculated for (EH₂)_n–*–π(C₁₀H₈) (n = 1 and 2: E = O, S, Se and Te) at BCPs with MP2/BSS-F. Tables 2 and 3 collect the values for π–HBs and π–EBs, respectively. Fig. 6 shows the plot of H_b(r_c) versus H_b(r_c) − V_b(r_c)/2 for the data in Tables 2 and 3, together with those for the perturbed structures around the fully optimized ones, generated with NIV. All data in Fig. 6 appear in the area of H_b(r_c) − V_b(r_c)/2 > 0 and H_b(r_c) > 0, which belong to the pure-CS (closed shell) region. The plots are analyzed according to eqn (S3)–(S6)† by applying QTAIM-DFA. The results for π–EBs are discussed separately from those of π–HBs, later.

Table 2 QTAIM functions and QTAIM-DFA parameters for the π–HB interactions in (EH₂)_n–*–π(C₁₀H₈) (n = 1 and 2: E = O, S, Se and Te), optimized with MP2/BSS-F^a

Species (X–*–Y)^b (symmetry: type)	ρb(rc) (ea0^−3)	c∇^2ρb(rc)^c (au)	Hb(rc) (au)	kb(rc)^d	R (au)	θ (°)	Freq (cm^−1)	kf^e (unit)	θp (°)	κp (au^−1)
a See text for BSS-F.b Data are given at BCPs of π–HBs, which are shown by *. BP connects H in EH2 and C in C10H8 (see Fig. 2).c Hb(rc) – Vb(rc)/2, where c = ħ^2/8m.d kb(rc) = Vb(rc)/Gb(rc).e mDyn Å^−1.f NIV of the symmetric internal vibration being employed to generate the perturbed structures.
SH2–*–π(C10H8) (C1: type IINap)	0.0070	0.0029	0.0011	−0.772	0.0031	69.6	82.5	0.021	70.0	62.3
SeH2–*–π(C10H8) (C1: type IINap)	0.0070	0.0028	0.0010	−0.777	0.0030	70.0	64.5	0.026	71.1	39.6
TeH2–*–π(C10H8) (C1: type IINap)	0.0073	0.0027	0.0009	−0.807	0.0029	72.1	174.1	0.075	74.8	41.6
(Additional TeH2–*–^4C and ^5C)	0.0072	0.0026	0.0007	−0.834	0.0027	74.1	62.5	0.014	79.5	474
(SH2)2–*–π(C10H8) (Ci: type IIINap)	0.0072	0.0029	0.0011	−0.783	0.0031	70.3	82.3	0.016	82.4	230
(SeH2)2–*–π(C10H8) (Ci: type IIINap)^f	0.0071	0.0028	0.0010	−0.774	0.0030	69.8	58.5	0.011	76.2	16.8
(TeH2)2–*–π(C10H8) (C1: type IIINap)	0.0073	0.0027	0.0009	−0.807	0.0028	72.0	187.4	0.089	74.4	89.5

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Table 3 QTAIM functions and QTAIM-DFA parameters for the π–EB interactions in HHE–*–π(C₁₀H₈) (E = S, Se and Te) and (OH₂)_n–*–π(C₁₀H₈) (n = 1 and 2), optimized with MP2/BSS-F^a

Species (X–*–Y)^b (symmetry: type)	ρb(rc) (ea0^−3)	c∇^2ρb(rc)^c (au)	Hb(rc) (au)	kb(rc)^d	R (au)	θ (°)	Freq (cm^−1)	kf^e (unit)	θp (°)	κp (au^−1)
a See text for BSS-F.b Data are given at BCPs of π–EBs, which are shown by *. BP connects E in EH2 and C in C10H8 (see Fig. 2).c Hb(rc) – Vb(rc)/2, where c = ħ^2/8m.d kb(rc) = Vb(rc)/Gb(rc).e mDyn Å^−1.f NIV of the symmetric internal vibration being employed to generate the perturbed structures.
HHS–*–π(C10H8) (C1: type INap)	0.0077	0.0033	0.0011	−0.800	0.0035	71.6	74.0	0.028	89.8	52.5
HHSe–*–π(C10H8) (C1: type INap)	0.0081	0.0033	0.0011	−0.796	0.0035	71.2	58.6	0.024	83.6	4.7
HHTe–*–π(C10H8) (C1: type INap)	0.0102	0.0036	0.0009	−0.860	0.0037	76.2	66.3	0.028	90.6	152
OH2–*–π(C10H8) (C1: type IINap)	0.0069	0.0029	0.0009	−0.812	0.0031	72.4	94.6	0.028	76.0	8.0
(OH2)2–*–π(C10H8) (C1: type IIINap)^f	0.0071	0.0030	0.0009	−0.818	0.0031	72.8	93.6	0.031	78.9	25.6

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Fig. 6 Plots of H_b(r_c) versus H_b(r_c) − V_b(r_c)/2 for the data of (EH₂)_n–*–π(C₁₀H₈) (n = 1 and 2: E = O, S, Se and Te), evaluated with MP2/BSS-F. Species with colors and marks are shown in the figure.

Application of QTAIM-DFA to π–HBs in EH₂ adducts of naphthalene π-system

Table 2 collects the QTAIM-DFA parameters of (R, θ) and (θ_p, κ_p) for the π–HB interactions at BCPs in (EH₂)_n–*–π(C₁₀H₈) (n = 1 and 2: E = O, S, Se and Te), evaluated with MP2/BSS-F. The QTAIM functions, the frequencies and the force constants (k_f), related to NIV employed to generate the perturbed structures are also collected in Table 2. The θ and θ_p values are less than 90° for all π–HBs in (EH₂)_n–*–π(C₁₀H₈), examined in this work. Consequently, all π–HBs in Table 2 are classified by the pure-CS interactions and characterized as the vdW nature. In the case of TeH₂–*–π(C₁₀H₈) (C₁: II_Nap), (θ, θ_p) = (74.1, 79.5°) for the additional HBs between two H atoms in TeH₂ and the ⁴C and ⁵C atoms in C₁₀H₈, which are larger than (θ, θ_p) = (72.1, 74.8°) for HBs between two H atoms in TeH₂ and the ⁹C atom in C₁₀H₈. The former is predicted to be somewhat stronger than the latter.

Nature of π–EBs in EH₂ adducts of naphthalene π-system, elucidated with QTAIM-DFA

The π–EB interactions are detected in HHE–*–π(C₁₀H₈) (C₁: type I_Nap) for E = S, Se and Te, OH₂–*–π(C₁₀H₈) (C₁: type II_Nap) and (OH₂)₂–*–π(C₁₀H₈) (C₁: type III_Nap). Table 3 collects the QTAIM-DFA parameters of (R, θ) and (θ_p, κ_p) for the π–EB interactions at BCPs in the species, evaluated with MP2/BSS-F. QTAIM functions, the frequencies and the force constants (k_f), related to NIV employed to generate the perturbed structures are also collected in Table 3. The θ and θ_p values are less than 90° for the all π–EBs in (EH₂)_n–*–π(C₁₀H₈), except for HHTe–*–π(C₁₀H₈) (C₁: I_Nap). Consequently, all π–HBs in Table 3 are classified by the pure-CS interactions and characterized as the vdW nature except for HHTe–*–π(C₁₀H₈) (C₁: I_Nap). The π–EB interaction in HHTe–*–π(C₁₀H₈) (C₁: I_Nap) with θ_p = 90.6° is classified by the pure-CS interaction and characterized as the typical-HB without covalency.

It is of very interest since the θ_p value of 89.8° is predicted for the π–EB interaction in HHS–*–π(C₁₀H₈) (C₁: type I_Nap), whereas θ_p = 83.6° is for HHSe–*–π(C₁₀H₈) (C₁: type I_Nap), which is substantially less than 90°. The π–EB interaction in HHS–*–π(C₁₀H₈) is characterized to have the border nature between the vdW nature and the typical-HB nature without covalency, whereas that in HHSe–*–π(C₁₀H₈) is substantially characterized as the vdW nature, irrespective of the expectation. The θ values are almost equal with each other (71.2–71.6°). The difference in the dynamic behavior shown by θ_p seems to originate from the difference in the linearity of the three ⁹CEH′ atoms in HHE–*–π(C₁₀H₈). The value of∠⁹CEH′ becomes larger in the order of E = Se (∠⁹CEH′ = 152.8°) < S (155.5°) < Te (157.4°), where the larger value is given for each among the two. It is shown that ∠⁹CEH′ for E = S is larger than that for E = Se by 2.7°, under our calculation conditions.

While the π–HB interactions are detected in EH₂–*–π(C₁₀H₈) (C₁: type II_Nap) and (EH₂)₂–*–π(C₁₀H₈) (C_i/C₁: type III_Nap) for E = S, Se and Te, π–EBs are observed in HHE–*–π(C₁₀H₈) (C₁: type I_Nap) for E = S, Se and Te, OH₂–*–π(C₁₀H₈) (C₁: type II_Nap), and (OH₂)₂–*–π(C₁₀H₈) (C₁: type III_Nap). The π-orbitals of the second benzene ring in naphthalene seems to accelerate to the appearance of π–EBs in HHE–*–π(C₁₀H₈) (C₁: type I_Nap) for E = S, Se and Te.

We are also much interested in the EH₂ adducts of anthracene π-system. Such investigation is in progress.

Conclusions

Behavior of the interactions is elucidated for the EH₂ adducts with naphthalene π-system (E = O, S, Se and Te) of the 1 : 1 and 2 : 1 ratios, by applying QTAIM-DFA. Structures were optimized with MP2/BSS-F. Three types of structures were optimized. They are HE–H⋯π(C₁₀H₈) (type I_Nap) (E = S, Se and Te), EH₂⋯π(C₁₀H₈) (type II_nap) and (EH₂)₂⋯π(C₁₀H₈) (type III_Nap) for E = O, S, Se and Te (Table 1). The type I_nap structure of HO–H⋯π(C₁₀H₈) was not detected. The ΔE (ΔE_ES and ΔE_ZP) values [= E((EH₂)_n–*–π(C₁₀H₈)) − nE(EH₂) − E(C₁₀H₈): n = 1 and 2] are evaluated for the species. Excellent correlation was obtained in the plot of ΔE_ZP versus ΔE_ES (y = 0.597 + 0.948x; R_c² = 0.998). The magnitudes of ΔE for type II_Nap are about 1.5 times larger than those for the corresponding adducts of type II_Bzn, if the adducts of the same E are compared. The magnitudes for type II_Nap are almost the same as those for type I_Nap and the magnitudes for type III_Nap are almost 2 times larger than those for type II_Nap, if the adducts of the same E are compared.

BCPs are clearly detected in the molecular graphs, containing those for the interactions in question. However, π–HBs between H in EH₂ and C₁₀H₈ are not detected, instead, π–EBs between E in EH₂ and ⁹C in C₁₀H₈ are detected for HE–H–*–π(C₁₀H₈) (C₁: type I_Nap) (E = S, Se and Te). All data in (EH₂)_n–*–π(C₁₀H₈) (n = 1 and 2: E = O, S, Se and/or Te) investigated in this work appear in the pure-CS region of H_b(r_c) − V_b(r_c)/2 > 0 and H_b(r_c) > 0. QTAIM-DFA parameters of (R, θ) and (θ_p, κ_p) are calculated for the species, according to eqn (S3)–(S6).† The values are compared with those of the standard values to discuss the nature of the interactions. The θ values are less than 90° for all interactions in question in (EH₂)_n–*–π(C₁₀H₈) examined in this work, which correspond to the pure-CS interactions. The θ_p values are also less than 90° for all interactions in question, except for HHTe–*–C₁₀H₈ (C₁: type I_Nap) (θ_p = 90.6°). Therefore, the π–HB and π–EB interactions in all species in naphthalene π-system, examined in this work, are classified as the pure-CS interactions and characterized to have the vdW-nature, except for HHTe–*–C₁₀H₈ (I_Nap: C₁). The π–EB interaction is predicted to have the character of typical HB-nature without covalency. Similarly, the θ_p value of HHS–*–C₁₀H₈ (C₁: type I_Nap) is evaluated to be 89.8°, which is very close to 90°, therefore, the π–EB interaction should have the border character between the vdW-nature and the typical HB-nature without covalency. The π–HB and π–EB interactions in the EH₂ adducts of naphthalene π-system are well classified and characterized by applying QTAIM-DFA.

Acknowledgements

This work was partially supported by a Grant-in-Aid for Scientific Research (No. 23350019 and 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.

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37. The AIM2000 program (Version 2.04) is employed to analyze and visualize atoms-in-molecules: F. Biegler-König, J. Comput. Chem., 2000, 21, 1040–1048 , see also ref. 20g.
38. W. Nakanishi and S. Hayashi, J. Phys. Chem. A, 2013, 117, 1795–1803.

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Footnote

† Electronic supplementary information (ESI) available: QTAIM-DFA approach, cartesian coordinates for optimized structures of EH₂⋯π(C₁₀H₆) (E = O, S, Se and Te). See DOI: 10.1039/c6ra04738f

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