Extremely stable system of 1-haloselanyl-anthraquinones: experimental and theoretical investigations

Abstract

Highly stable selanyl halides, 1-ATQSeX (X = I (1), Br (2) and Cl (3)), were prepared. The structures of 1, 2, 6 (1-ATQSeX: X = Me) and 7 (1-ATQBr) were determined. QC calculations were performed on 1–3, 4 (X = F), 5 (X = H), 6, 7 and 8 (X = SeATQ-1). The O⋯Se distances in 1–4 from the sum of the vdW radii of the atoms (Δr(Se, O₁)) were less than −1 Å, in magnitude, which must be the driving force for the high stability. The O-*-Se interactions seem stronger in the order of 1 < 2 < 3 < 4. The intrinsic dynamic and static natures of O⋯Se and/or Se⋯X in 1–8 are elucidated by QTAIM dual functional analysis (QTAIM-DFA). The Se-*-I, Se-*-Br, Se-*-Cl and Se-*-F interactions in 1–4 are predicted to have the natures of covalent, TBP with CT, TBP with CT, and typical HB with covalency, respectively, whereas O-*-Ses in 1–4 are all predicted to have the nature of MC with CT. The Se-*-H, Se-*-C_Me and Se-*-Se interactions in 5, 6 and 8 are all predicted to have the covalent nature, while O-*-Ses in 5, 6 and 8 are all predicted to have the nature of typical HB with no covalency. The E(2) values of 1–6 and 8 are calculated with NBO analysis, and correlate excellently with Δr(Se, O₁), except for Se-*-F, for which E(2) is evaluated to be much larger. The E(2) values also correlate very well with C_ii⁻¹ for all Se-*-X in 1–4, although data from 5, 6 and 8 deviated from the correlation, where C_ii is the diagonal element of the compliance (force) constant for the internal vibrations. The behaviour of the interactions is further examined based on the QTAIM-DFA parameters of θ and θ_p. The stabilizing effect is further confirmed by the calculations with the ν(C=O) values analyzed carefully.

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Introduction

Selanyl halides (ArSe-X: X = I, Br, Cl and F) are of current and continuous interest.^1–8 The Se–X bonds in selanyl halides are usually (very) unstable, especially for ArSe-I, while selanyl bromides and chlorides are relatively stable. The small enthalpy for the formation of RSe-X from RSeSeR and X₂ must be responsible for the instability, especially for X = I. ArSeI will be in equilibrium with (ArSeSeAr + I₂)/2 and/or (ArSe(⋯I₂)SeAr)/2 in solutions, as shown in eqn (1).⁹ The highly polar nature of the Se^δ+–X^δ− bonds makes them very reactive. The large differences in electronegativity (χ)^10,11 between Se and X would be responsible for the large bond polarity. Indeed, the bond polarity is easily accepted for X = F (χ_F = 4.10), Cl (χ_Cl = 2.83), and Br (χ_Br = 2.74) with χ_Se = 2.48, but the direction could be inverse (Se^δ−–X^δ+) for X = H and I, since χ_I = 2.21 and χ_H = 2.1.

It is vitally important to clarify the factors controlling the fine details of structures, to understand the stability of selanyl halides, where the factors will create high functionalities of materials. Hypervalent n(G)⋯σ*(Y–X) 3c-4e (three centre-four electron) interactions of the σ type (GYX σ(3c-4e)) should be a typical example of such factors. GYX σ(3c-4e) operates to align the three GYX atoms linearly.¹ Such interactions have been skilfully utilized as tools for materials development,^1,12 such as supramolecular chemistry and donor–acceptor complexes for electronic materials. The interactions also operate typically in biological activity, regulation of enzymatic functions, and stabilization of folded protein structures. They often appear in the unsymmetric form.^1,7,12Fig. 1 illustrates the typical cases of GYX σ(3c-4e) (Y = Se), with the approximate MO model for σ(3c-4e). The bonding scheme of σ(3c-4e) is mainly explained based on ψ₂, where the central atom is highly positively charged while the outside two are highly negatively charged. Namely, σ(3c-4e) will form and is stabilized by the highly electropositive atoms at the central position with the highly electronegative ones at the outside positions.

Fig. 1 (a) GSeX σ(3c-4e) interaction in the benzene system, (b) approximate MO model for σ(3c-4e), (c)–(e) effort for the stabilization of Se–X by GSeX σ(3c-4e) and (f) the Se–I bond stabilized sterically by the cavity-shaped Bpq.

Much effort has been made to stabilize and isolate ArSe-I, together with ArSe-Br and ArSe-Cl, through the coordination by G at the back side of Se in σ*(Se–X). The coordination usually yields the T-shaped GSeX σ(3c-4e),^1,7,12 which is often highly unsymmetric. Tomoda and co-workers stabilized and isolated the ArSe-X (X = Cl and Br) species through coordination by X⁻ (I) and the carbonyl oxygen (II).^2–5 The Se–X bonds are also stabilized with G = RR'N, RO and halogens bonded to the benzyl carbon. Singh and co-workers investigated the unsymmetric N⋯Se–X interactions in 2-[2′-(4′,4′-dimethyl)oxazolinyl]phenylselanyl halides (III).^12,13 The N⋯Se distances are shorter than the sum of the van der Waals radii¹⁴ of N and Se by 0.32 Å for X = Cl and Br and 0.28 Å for X = I.¹³ (see Fig. 1 for the structures of I–III). On the other hand, the Se–I bond is stabilised not by the donating group but by the cavity-shaped steric protection group (Bpq).¹⁵ The Se–I bond distance in BpqSe-I is 2.5203(11) Å. This will be discussed again later.

We encountered the formation of 1-(iodoselanyl)anthraquinone (1-ATQSeI: 1) as only one product, in the reaction of 1-(benzylselanyl)anthraquinone (1-ATQSeBzl) with I₂ in CHCl₃. Eqn (2) explains the reaction. The selanyl iodide 1 was extremely stable; it is stable for over one year in air, for example. Chart 1 shows the structures of 1-ATQSeX (X = I (1), Br (2), Cl (3), F (4), H (5) and Me (6)), together with 1-bromoanthraquinone (7) and anthraquinone-1,1′-diselenide (X = SeATQ-1 (8)), although there is no sign for the formation of 8 in the reaction of eqn (2).

Chart 1 Structures of 1-substituted anthraquinones (1–7) and (1-ATQSe)₂ (8).

Why is the Se–I bond in 1 so stable toward air and moisture? Are the Se–X bonds in 2–4 similarly stable? What are the factors that stabilise the Se–X bonds in 1–4? The selanyl halides, 2 and 3, were prepared under similar conditions with good to excellent yields, whereas preparation of 4 was not tried (cf: eqn (2)). The nature of OSeX σ(3c-4e) in 1–4 is elucidated to understand the stability, together with that in 5 and 6, and OSeSeO σ(4c-6e) in 8. The OSeX σ(3c-4e) interactions must operate to stabilise the Se–X bonds in 1–4. The behaviour of the interactions and the structural features in 1–6 are clarified based on the experimentally determined structures and/or the theoretical investigations, together with the OSeSeO σ(4c-6e) in 8, referring to the O⋯Br interaction in 7.

How can the natures of the interactions in question be elucidated? The quantum theory of atoms-in-molecules dual functional analysis (QTAIM-DFA)^16–19 was applied to the interactions for this purpose. In the QTAIM approach, H_b(r_c) is plotted versus H_b(r_c) − V_b(r_c)/2 at the bond critical points (BCPs) on the interactions in question, where H_b(r_c) and V_b(r_c) are the total electron energy densities and the potential energy densities at the BCPs, respectively. (ρ_b(r_c) and G_b(r_c) stand for the electron densities and the kinetic energy densities at the BCPs, respectively.) Data from the fully optimized structures and the perturbed structures around fully optimized ones are plotted in QTAIM-DFA in our treatment, which is called QTAIM-DFA plots.^17,19 The perturbed structures are generated, employing the coordinates C_i derived from the diagonal element of the compliance (force) constants C_ii for the internal vibrations.^20–22 The method is called CIV and is highly reliable.^23,24

Each plot for an interaction is analysed by the polar coordinate (R, θ) parameters with the (θ_p, κ_p) parameters. The R and θ parameters are calculated for the data point of the interaction in the fully optimized structure at the origin. While R corresponds to the energy for the interaction in question in the plot, θ, measured from the y axis, classifies the interaction. The (θ_p, κ_p) parameters are measured based on the plot at the data point for the interaction in the fully optimized structure. θ_p is measured from the y-direction, which corresponds to the tangent line of the plot, and κ_p is the curvature.^17,19,24 While θ_p characterizes the interaction, κ_p does not play an important role in the analysis of an interaction, although it contains deep meaning. The (R, θ) parameters are calculated based on the data of the fully optimized structures; therefore, they correspond to the static nature of interactions. The dynamic nature of interactions is proposed based on (θ_p, κ_p), which are derived from the data of the perturbed structures around fully optimized ones. The dynamic nature is described as the intrinsic dynamic nature, if the perturbed structures with CIV are employed. QTAIM-DFA is applied to standard interactions, and rough criteria that distinguish the interaction in question from others are obtained.^17,19,24 The criteria and QTAIM-DFA are explained in Schemes SA1–SA3, Fig. SA1 and SA2, Table SA1 and eqn (SA1)–(SA7) of the Appendix in the ESI,† together with the basic concept of the QTAIM approach.

The structures were determined for 1, 2, 6 and 7 by X-ray crystallographic analysis. The intrinsic dynamic and static natures of OSeX σ(3c-4e) were elucidated for 1–6 and OSeSeO σ(4c-6e) for 8, together with OBr σ(2c-4e) for 7. QTAIM-DFA was applied for the analysis, employing the perturbed structures generated with CIV. NBO analyses with the NBO6 program²⁵ were also employed to evaluate the CT terms of the OSeX σ(3c-4e) and OSeSeO σ(4c-6e) interactions. Herein, we present the results of the investigations, which supply useful insights into the natures of the interactions and the reason for the stability of the species. The relations between the E(2) values obtained by NBO and the O⋯Se distances and the C_ii values are also discussed.

Experimental

1-(Iodoselanyl)anthraquinone (1)

To a CHCl₃ solution of 1-(benzylselanyl)anthraquinone (1-ATQSeBzl: 9) (0.100 g, 0.27 mmol), was added I₂ (0.072 g, 0.28 mmol). The solution was stirred at room temperature for 24 hours under argon atmosphere. CHCl₃ was removed under vacuum. The residue was recrystallized in CHCl₃. 1 was obtained as dark purple prisms in 94% yield; mp. 205.2–205.8 °C (dec.); ¹H NMR (400 MHz, CDCl₃/TMS): δ 7.76 (t, J = 7.9 Hz, 1H), 7.81–7.91 (m, 2H), 8.29–8.42 (m, 4H); ¹³C NMR (100 MHz, CDCl₃/TMS): δ 126.7, 127.7, 127.8, 130.6, 131.2, 132.9, 134.6, 134.8, 135.2, 139.0, 141.3, 181.8, 184.1; ⁷⁷Se NMR (76 MHz, CDCl₃/Me₂Se): δ 798.6; i.r. ν_max(PTFE IR card)/cm⁻¹: 1635, 1680 (ν_C=O). Anal. Calcd for C₁₄H₇IO₂Se: C, 40.71; H, 1.71. Found: C, 40.69; H, 1.69.

1-(Bromoselanyl)anthraquinone (2)

To a CHCl₃ solution of 1-ATQSeBzl (0.100 g, 0.27 mmol), was added Br₂ (0.052 g, 0.30 mmol). The solution was stirred at room temperature for 1 hour under argon atmosphere. CHCl₃ was removed under vacuum. The residue was recrystallized in CHCl₃. 2 was obtained as brown prisms in 89% yield; mp. 222.8–223.3 °C (dec.); ¹H NMR (400 MHz, CDCl₃/TMS): δ 7.84–7.93 (m, 3H), 8.31 (dd, J = 0.9 and 7.1 Hz, 1H), 8.33–8.38 (m, 2H), 8.56 (dd, J = 0.9 and 8.1 Hz, 1H); ¹³C NMR (100 MHz, CDCl₃/TMS): δ 122.5, 126.8, 127.5, 127.6, 130.7, 132.4, 133.7, 133.9, 134.3, 134.6, 136.2, 141.3, 181.8, 182.0; ⁷⁷Se NMR (76 MHz, CDCl₃/Me₂Se): δ 1029.4. Anal. Calcd for C₁₄H₇BrO₂Se: C, 45.93; H, 1.93. Found: C, 45.91; H, 1.92.

1-(Chloroselanyl)anthraquinone (3)

To a CHCl₃ solution of 1-ATQSeBzl (0.100 g, 0.27 mmol), was added SO₂Cl₂ (0.040 g, 0.30 mmol). The solution was stirred at room temperature for 1 hour under argon atmosphere. The reaction solution was transferred to a separatory funnel, and using 50 mL of CHCl₃, the reaction solution in the vessel was washed into a separatory funnel. 30 mL of saturated NaHCO₃ solution was added and shaken well. After separation from the aqueous layer, the CHCl₃ solution was shaken well with saturated brine. After separation from the aqueous layer, the solution was dried on Na₂SO₄. CHCl₃ was removed under vacuum. The residue was recrystallized in CHCl₃. 3 was obtained as brown needles in 98% yield; mp. 204.6–205.1 °C (dec.); ¹H NMR (400 MHz, CDCl₃/TMS): δ 7.86 (dt, J = 1.3 and 7.3 Hz, 1H), 7.88 (dt, J = 1.3 and 7.4 Hz, 1H), 7.94 (dt, J = 1.3 and 7.4 Hz, 1H), 8.26 (d, J = 7.3 Hz, 1H), 8.33 (dd, J = 1.8 and 7.3 Hz, 1H), 8.36 (dd, J = 1.8 and 7.3 Hz, 1H), 8.56 (d, J = 8.2 Hz, 1H); ⁷⁷Se NMR (76 MHz, CDCl₃/Me₂Se): δ 1101.4. Anal. Calcd for C₁₄H₇ClO₂Se: C, 52.28; H, 2.19. Found: C, 52.27; H, 2.18.

1-(Methylselanyl)anthraquinone (6)

Following the method used for the preparation of 1,8-bis(methylselanyl)anthraquinone,²⁶ a suspension of dimethyl diselenide (0.700 g, 3.71 mmol) and sodium hydride (0.30 g, 12.36 mmol) in dry DMF (50 mL) was heated at 110 °C for 1 h. Then 1-chloroanthraquinone (1.50 g, 6.18 mmol) and CuI (1.41 g, 7.42 mmol) were added to the solution at 110 °C. After stirring for 3 h at 160 °C, the solution was subjected to dry chromatography on silica gel (dichloromethane as eluent) and concentrated under vacuum. The product was purified by using chromatography on silica gel (benzene as eluent) and recrystallized from benzene/ethanol. 6 was obtained as orange prisms (0.37 g, 20% yield). M.p. 224.8–225.1 °C; ¹H NMR (400 MHz, CDCl₃/TMS): δ 2.33 (s, 3H), 7.66 (t, J = 7.8 Hz, 1H), 7.76 (d, J = 8.2 Hz, 1H), 7.78 (td, J = 1.7 and 7.4 Hz, 1H), 7.81 (td, J = 1.7 and 7.4 Hz, 1H), 8.17 (dd, J = 1.1 and 7.4 Hz, 1H), 8.27 (dd, J = 1.8 and 7.3 Hz, 1H), 8.34 (dd, J = 1.7 and 7.4 Hz, 1H); ¹³C NMR (100 MHz, CDCl₃/TMS): δ 6.9 (¹J_Se–C = 69.9 Hz), 124.3, 127.0, 127.5, 130.3, 132.4, 132.7, 132.9, 133.7, 133.8, 134.3, 135.7, 141.8, 183.0, 183.7; ⁷⁷Se NMR (76 MHz, CDCl₃/Me₂Se): δ 319.7; i.r. ν_max(PTFE IR card)/cm⁻¹: 1667 (ν_C=O). Anal. Calcd for C₁₅H₁₀O₂Se: C, 59.81; H, 3.35. Found: C, 59.71; H, 3.42.

1-Bromoanthraquinone (7) (CAS RN: 632-83-7)²⁷

7 was obtained as yellow prisms in 57% yield; mp. 190.1–190.7 °C; ¹H NMR (400 MHz, CDCl₃/TMS): δ 8.37–8.23 (m, 3H), 8.04 (d, J = 7.8, 1H), 7.84–7.76 (m, 2H), 7.58 (td, J = 7.8, 4.9 Hz, 1H); ¹³C NMR (100 MHz, CDCl₃/TMS): δ 122.5, 126.8, 127.5, 127.6, 130.7, 132.4, 133.7, 133.9, 134.2, 134.6, 136.2, 141.3, 181.8, 182.0; i.r. ν_max(PTFE IR card)/cm⁻¹: 1681 (ν_C=O).

1-(Benzylselenyl)anthraquinone (9)

Following a similar method to that for 6, compound 9 was obtained as orange needles in 34% yield. M.p. 234.5–234.7 °C; ¹H NMR (400 MHz, CDCl₃/TMS): δ 4.22 (s, 2H), 7.27 (t, J = 7.3 Hz, 1H), 7.34 (t, J = 7.3 Hz, 2H), 7.46 (d, J = 7.7 Hz, 2H), 7.66 (t, J = 7.8 Hz, 1H), 7.78–7.83 (m, 2H), 7.89 (dd, J = 1.1 and 8.1 Hz, 1H), 8.20 (dd, J = 1.0 and 7.6 Hz, 1H), 8.26–8.35 (m, 2H); ¹³C NMR (100 MHz, CDCl₃/TMS): δ 30.5, 124.5, 127.0, 127.1, 127.5, 128.8, 129.3, 130.2, 132.6, 133.0, 133.1, 133.6, 133.9, 134.4, 135.7, 136.2, 142.5, 183.0, 183.8; ⁷⁷Se NMR (76 MHz, CDCl₃/Me₂Se): δ 429.9. Anal. Calcd for C₁₄H₁₄Se₂: C, 49.43; H, 4.15. Found: C, 49.42; H, 4.14.

X-ray structural determination of 1, 2, 6 and 7

The crystals of 1, 2, 6 and 7 were grown by slow evaporation of chloroform-hexane solutions at room temperature. The intensity data were collected on a CCD diffractometer equipped with graphite-monochromed Mo Kα radiation (λ = 0.71070 Å) at 120(2) K for 1 and at 102(2) K for 2, 6 and 7. The structures were solved by direct methods SHELXS97²⁸ and SHELXS2014/7²⁹ refined by full-matrix least-square techniques. All the non-hydrogen atoms were refined anisotropically. Crystallographic details are given in the ESI.† CCDC 2339576 for 1, 2339577 for 2, 2339579 for 6 and 2339580 for 7 contain the supplementary crystallographic data for this paper.†

Methodological details of calculations

Calculations were performed employing the Gaussian 09 program package.³⁰ The basis set of the Sapporo-TZP with diffuse functions of the 1s1p type (Sapporo-TZP + 1s1p) was employed for all atoms, implemented from Sapporo Basis Set Factory.³¹ The basis set system is called BSS-A. In BSS-B, Sapporo-TZP + 1s1p was for O and Se with Sapporo-DZP for C and H. The Møller–Plesset second-order energy correlation (MP2) level³² was applied to the calculations. Optimized structures were confirmed by frequency analysis. The results of the frequency analysis were used to obtain the compliance constants (C_ii) and the coordinates (C_i) correspond to C_ii.

The method to generate the perturbed structures with CIV is explained in eqn (3). The i-th perturbed structure in question (S_iw) is generated by the addition of the i-th coordinates derived from C_ii (C_i) to the standard orientation of a fully optimized structure (S_o), in the matrix representation. The coefficient g_iw in eqn (3) controls the structural difference between S_iw and S_o: g_iw is determined to satisfy eqn (4) for r, where r and r_o stand for the interaction distances in question in the perturbed and fully optimized structures, respectively, with a_o = 0.52918 Å (Bohr radius). The C_i values of five digits are used to predict S_iw.

S_iw = S_o + g_iw·C_i (3)

r = r_o + wa_o (w = (0), ±0.025 and ±0.05; a_o = 0.52918 Å) (4)

y = c_o + c₁x + c₂x² + c₃x³ (5)

R_c²: square of the correlation coefficient.

The values of QTAIM functions were calculated using the same basis set system as in the optimizations, unless otherwise noted. They were analysed with the AIM2000³³ and AIMAll³⁴ program. In QTAIM-DFA plot of H_b(r_c) versus H_b(r_c) − V_b(r_c)/2, five data points of w = 0, ±0.025 and ±0.05 in eqn (4) were applied. Each plot was analysed using a regression curve of the cubic function, shown in eqn (5), where (x, y) = (H_b(r_c) − V_b(r_c)/2, H_b(r_c)) (R_c² > 0.99999 in usual).¹⁹

Results and discussion

Structures of 1 and 2, in relation to those of 6 and 7

The X-ray crystallographic analyses were carried out for a suitable crystal of each of 1, 2, 6 and 7. Fig. 2 shows the structures of 1, 2 and 6, while that of 7 is illustrated in Fig. S1 of the ESI.†Table 1 collects the observed structural parameters necessary for the discussion. The values are given for the O⋯Se distances (r(Se, O₁)), the Se–X distances (r(Se, X)) and the Se–C₁ distances (r₃(Se, C₁)) in 1, 2 and 6 with the C₁–Br distance (r₃(C₁, Br)) in 7. The r(Se, O₁) values from the sum of the van der Waals radii of O and Se (Δr(Se, O₁) = r_obsd(Se, O₁) − [r_vdW(Se) + r_vdW(O)]) are also given. Table 1 collects the angles of ∠O₁SeX, ∠C₁SeX, ∠SeC₁C₂, ∠SeC₁C₁₄, ∠O₁C₁₃C₁₂ and ∠O₁C₁₃C₁₄ and the differences in the angles around C₁ (Δ∠SeC₁C₂ = ∠SeC₁C₂ − ∠SeC₁C₁₄) and C₁₃ (Δ∠O₁C₁₃C₁₄ = ∠O₁C₁₃C₁₄ − ∠O₁C₁₃C₁₂). The torsional angles of ∠SeC₁C₁₃O₁ and ∠XSeC₁C₁₃ are also given for 1, 2 and 6, together with the corresponding value of ∠BrC₁C₁₃O₁ for 7.

Fig. 2 Structures of 1 (a), 2 (b) and 6 (c), determined by X-ray analysis.

Table 1 Structural parameters observed for 1, 2, 6 and 7

Parameter	1 obsd	2 obsd	6 obsd	7 obsd
a Se should be read Br and X being ignored for 7obsd. b Δr(Se, O1) = robsd(Se, ^1O) − [rvdW(Se) + rvdW(O)]. c Δ∠SeC1C2 = ∠SeC1C2 − ∠SeC1C14. d Δ∠O1C13C14 = ∠O1C13C14 − ∠O1C13C12.
r(Se, O1)/Å	2.382(2)	2.284(2)	2.661(2)	2.919(4)
Δr(Se, O1)^b/Å	−1.04	−1.14	−0.76	−0.45
r(Se, X)/Å	2.586(1)	2.3947(9)	1.953(2)	—
r(Se, C1)/Å	1.918(5)	1.902(3)	1.910(2)	1.903(5)
∠O1SeX/°	178.28(8)	177.55(6)	173.96(7)	—
∠C1SeX/°	100.3(1)	98.16(9)	99.65(9)	—
∠SeC1C2/°	124.3(3)	124.8(2)	120.7(2)	114.0(4)
∠SeC1C14/°	116.9(3)	115.9(2)	121.0(2)	124.7(3)
Δ∠SeC1C2^c/°	7.4	8.9	−0.3	−10.7
∠O1C13C12/°	121.7(4)	122.0(3)	120.4(2)	119.4(4)
∠O1C13C14/°	118.5(4)	117.8(3)	120.8(2)	122.3(4)
Δ∠O1C13C14^d/°	−3.4	−4.2	0.4	2.9
∠SeC1C13O1/°	−0.2(4)	2.1(2)	0.7(1)	−0.4(3)
∠XSeC1C13/°	179.0(2)	178.66(8)	177.77(9)	—

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The observed Δr(Se, O₁) values of 1, 2 and 6 are −1.04, −1.14 and −0.76 Å, respectively. The Δr(Se, O₁) values for 1 and 2 are much larger in magnitude than those of Δr(Se, N) in N⋯Se–I (−0.28 Å) and N⋯Se–Br (−0.32 Å) in III. The much shorter Δr(Se, O₁) values in 1 and 2 must be the strong driving force for the extremely stable nature of the species. The strongly attractive n(O₁)⋯σ*(Se–X) σ(3c-4e) interactions must be the reason for the highly negative values of Δr(Se, O₁). The excellent accepting ability of σ*(Se–X: X = I and Br) and the very good donating ability of n_p(O) are responsible for the attractive interactions. However, it is necessary to consider the steric compressive effect around O and Se for the highly negative Δr(Se, O₁) values in 1 and 2, relative to Δr(Se, N) in III, since Δr(Br, O₁) of 7 (−0.45 Å) is also highly negative.

The Δ∠SeC₁C₂ and Δ∠O₁C₁₃C₁₄ values must also correlate strongly to the Δr(Se, O₁) values. The observed values are 7.4° and −3.4°, respectively, for 1, and 8.9° and −4.2°, respectively, for 2, while they are −0.3° and 0.4°, respectively, for 6, and −10.7° and 2.9°, respectively, for 7. Why are the Δ∠SeC₁C₂ and Δ∠O₁C₁₃C₁₄ values so highly negative in 1 and 2? We paid much attention to the cyclic O₁SeC₁C₁₄C₁₃ five-membered rings formed in the species. The ring contains 6π electrons, therefore, it will be stabilized more if the ring becomes closer to a regular pentagon, although the AO sizes of C, O and Se need to be considered. This must be the reason for Δ∠SeC₁C₂ and Δ∠O₁C₁₃C₁₄ and Δr(Se, O₁) being highly negative. The three factors operate together to stabilize the compounds.

The ¹O and Se atoms placed at the anthracene-1,9-positions seem advantageous for keeping the five-membered rings planar. The Δ∠SeC₁C₂ and Δ∠O₁C₁₃C₁₄ values in 6 are almost null in magnitude, which would arise from the much smaller attractive nature of n(O₁)⋯σ*(Se–X) σ(3c-4e), relative to the case of 1 and 2. The values of Δ∠SeC₁C₂ and Δ∠O₁C₁₃C₁₄ in 7 are highly positive. The very large repulsive O⋯Br σ(2c-4e) interaction must be responsible for the results, irrespective of the cyclic O₁BrC₁C₁₄C₁₃ 6π five-membered ring formation. The contribution from the repulsive O⋯Br σ(2c-4e) interaction seems stronger than that of the cyclic O₁SeC₁C₁₄C₁₃ 6π five-membered ring formation in this case.

After clarification of the structural features of 1, 2, 6 and 7, based on the observed results, the next extension is to draw the whole picture of the interactions, together with the structural features, based on the calculated results for 1–8.

QC calculations

The factors that control the fine details of the structures, based on the QC calculations, must operate also in crystals. However, other factors in crystals, such as the crystal packing effect, would be stronger than those predicted by the QC calculations, in some cases. The observed structures in the crystals will be preferentially stabilised also in the gas phase, if the structures in the two states are (very) close to each other, since common factors must operate in both states, irrespective of the crystal packing effect. Indeed, it is instructive to examine the structures optimized with the QC calculations, but we must be careful when the observed structures are discussed based on the optimized results, since the calculation conditions are often substantially different from the experimental conditions, containing calculation errors. The basis sets and the levels employed for the calculations must be carefully examined to achieve the purpose. A conformer seems rationalized by the calculations when the conformer is predicted to be more stable than the competitive one by over 10 kJ mol⁻¹, in our cases. Differences between the calculated and observed distances less than 0.013 Å are desirable, and less than 0.03 Å is well accepted, if the nature of an interaction in question is discussed in relation to the observed structure.

QC calculations on 1–7 and 8

QC calculations were performed on 1–7 with MP2/BSS-A and 8 with MP2/BSS-B, where the cost performance for the calculations of 8 is considered under our calculation conditions. Table 2 summarizes the results of the calculations. The differences between the calculated and observed values of r(¹O, Se) [Δr_co(¹O, Se) = r_calcd(¹O, Se) − r_obsd(¹O, Se)] for 1, 2 and 6 are 0.002 Å (=2.380–2.378 Å), 0.025 Å and 0.034 Å, respectively, and the Δr_co(Se, X) values for 1, 2 and 6 are −0.025 Å (=2.5825–2.5574 Å), −0.023 Å and −0.014 Å, respectively. Similarly, the Δ∠_coO₁SeX (= ∠_calcdO₁SeX − ∠_obsdO₁SeX) values for 1, 2 and 6 are 0.5° (= 178.4–177.9°), −1.1° and −0.5°, respectively. The results show that the optimized structures reproduce very well the observed structures. The calculated values for Δr(Se, O₁) of 1, 2 and 6 are −1.04, −1.11 and −0.79 Å, respectively, which are very close to the observed values of −1.04, −1.14 and −0.76 Å, respectively. The MP2/BSS-A method seems excellent for the purpose of this work. Fig. 3 summarizes the structural features around O⋯Se–X in 1, 2, 3, 6 and 8, with that around O⋯Br in 7.

Fig. 3 Structural features around OSeX σ(3c-4e) in 1, 2, 3, 6 and 8 and around OBr σ(2c-4e) in 7. The observed values are shown with the calculated ones in parentheses.

Table 2 Structural parameters for 1–7 optimized with MP2/BSS-A and 8 with MP2/BSS-B^a

Species	1 (Cs)	2 (Cs)	3 (Cs)	4 (Cs)	5 (Cs)	6 (Cs)	7 (C1)	8 (C2)
a BSS-A stands for (S-TZP + 1s1p) and BSS-B does for (S-TZP + 1s1p) applied to O, Se and X with S-DZP to C and H. b Δr(Se, O1) = rcalcd(Se, O1) − [rvdW(Se) + rvdW(O)]. c Δ∠SeC1C2 = ∠SeC1C2 − ∠SeC1C14. d Δ∠O1C13C14 = ∠O1C13C14 − ∠O1C13C12. e Δrco(Se, O1) = rcalcd(Se, O1) − robsd(Se, O1). f Δrco(Se, X) = rcalcd(Se, X) − robsd(Se, X). g Δ∠coO1SeX = ∠calcdO1SeX − ∠obsdO1SeX. h Δ∠coSeC1C14 = ∠calcdSeC1C14 − ∠obsdSeC1C14. i Δ∠coO1C13C14 = ∠calcd O1C13C14 − ∠obsdO1C13C14.
r(Se, O1)/Å	2.3803	2.3089	2.2784	2.1863	2.6359	2.6275	2.9168	2.6013
Δr(Se, O1)^b/Å	−1.0397	−1.1111	−1.1416	−1.2337	−0.7841	−0.7925	−0.4532	−0.8187
r(Se, X)/Å	2.5574	2.3717	2.2275	1.8101	1.4623	1.9393	—	2.3391
r(Se, C1)/Å	1.8970	1.8890	1.8851	1.8624	1.8915	1.8911	1.8776	1.9234
∠O1SeX/°	177.91	176.41	175.49	171.67	165.43	173.45	—	173.75
∠C1SeX/°	99.52	97.37	96.22	91.77	90.80	98.38	—	101.23
∠SeC1C2/°	124.67	124.99	125.06	124.56	119.80	120.92	115.24	121.41
∠SeC1C14/°	117.10	116.69	116.59	116.76	121.62	120.97	124.09	119.80
Δ∠SeC1C2^c/°	7.57	8.30	8.47	7.80	−1.82	−0.05	−8.85	1.61
∠O1C13C12/°	121.52	121.97	122.21	123.06	120.76	120.54	119.87	120.74
∠O1C13C14/°	119.08	118.45	118.14	117.22	120.71	120.74	122.53	120.30
Δ∠O1C13C14^d/°	−2.44	−3.52	−4.07	−5.84	−0.05	0.20	2.66	−0.44
∠SeC1C13O1/°	0.00	0.00	0.00	0.00	0.00	0.00	0.00	1.49
∠XSeC1C13/°	180.00	180.00	180.00	180.00	180.00	180.00	180.00	173.80
Δrco(Se, O1)^e/Å	0.0023	0.0249	—	—	—	−0.0335	−0.0022	—
Δrco(Se, X)^f/Å	−0.0251	−0.0230	—	—	—	−0.0137	—	—
Δ∠coO1SeX^g/°	0.49	−1.14	—	—	—	−0.51	—
Δ∠coSeC1C14 ^h/°	0.10	0.79	—	—	—	−0.03	−0.61	—
Δ∠coO1C13C14 ^i/°	1.18	0.65	—	—	—	−0.06	0.23	—

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The Se–Se bond distance in 8 is expected to be close to the Se–Br distance in 2, of which the calculated values are 2.339 Å and 2.372 Å, respectively. The difference between the two is 0.03 Å in magnitude, which satisfies the expectation. However, the Se⋯O₁ distances in 8 and 2 are predicted to be 2.601 Å and 2.309 Å, of which the difference is 0.29 Å in magnitude. The difference (0.29 Å) in magnitude in the latter is much larger than that in the former (0.03 Å).

What factors operate to control the Se⋯O₁ distances in 2 and 8? The factors can be explained by extending the aforementioned factors, the contributions from the attractive O⋯Se–X σ(3c-4e) interactions and the cyclic O₁SeC₁C₁₄C₁₃ 6π five-membered rings formed in the species. The ring is commonly formed both in 8 and 2. Therefore, the main difference arises from the stability of OSeX σ(3c-4e), namely the difference in the accepting ability of σ*(Se–X), where the donating O atom is common for both. The accepting ability of σ*(Se–Br) in 2 is much higher than σ*(Se–Se) in 8, which is the main reason for the observed results.

It is instructive to examine the calculated Δr(Se, O₁), Δ∠SeC₁C₂ and/or Δ∠O₁C₁₃C₁₄ values in 1–6 and 8, together with Δr(Br, O₁), Δ∠BrC₁C₁₄ and/or Δ∠O₁C₁₃C₁₄ values in 7 shown in Table 2, for better understanding of the stability. Fig. 4 shows the plot of the Δr(Se, O₁), Δ∠SeC₁C₂ and/or Δ∠O₁ C₁₃C₁₄ values calculated for 1–6 and 8, with the corresponding values for 7. The expected order of the stability is shown by eqn (6), judging from the Δr(Se, O₁) values. The order is supported by Δ∠SeC₁C₂ and Δ∠O₁C₁₃C₁₄. The order can be explained similarly by extending the stabilising ability of OSeX σ(3c-4e)/OBr σ(2c-4e) and cyclic 6π five-membered rings. The O₁⋯Se–X interactions can be understood easily by dividing the species into three groups of G(A), G(B) and G(C). The n(O)⋯σ*(Se–X) interactions in 1–4 are very strong, which form G(A). The very high accepting ability of σ*(Se–X: X = I, Br, Cl and F) is responsible for the results. G(B) contains 8, 5 and 6, of which n(O)⋯σ*(Se–X: X = Se, H and C_Me) interactions have the σ*(Se–X) of moderate to weak accepting ability. On the other hand, 7 consists of G(C), of which O₁⋯Br interaction is strongly repulsive.

4 > 3 > 2 > 1 ≫ 8 > 6 ≥ 5 ≫ 7 (6)

Fig. 4 Plots of Δr(Se, O₁), Δ∠(SeC₁C₂) and Δ∠(O₁C₁₃C₁₄), shown by the black, red and blue lines, respectively, for 1–8. The ΔΔ∠ values (= Δ∠O₁C₁₃C₁₄ − Δ∠SeC₁C₂) are given in red and blue for the negative and positive values, respectively, with the arrows.

After clarifying the structural features of 1–4, the next extension is to elucidate the natures of the interactions.

Molecular graphs with contour plots for 1–4

Molecular graphs are drawn on the optimized structures of 1–7 with MP2/BSS-A and 8 with MP2/BSS-B. The contour plot is also drawn on a plane containing the O₁⋯Se–X interaction in the molecular graph. All BCPs expected for O₁-*-Se, Se-*-X, Se-*-Se, and/or O₁-*-Br are clearly detected in the corresponding species, together with all RCPs (ring critical points). All BCPs are well located at the (three-dimensional) saddle points on the bonds and interactions. Fig. 5 illustrates the molecular graphs with the contour plots, exemplified by 1–4. The molecular graphs with the contour plots for 5–8 are drawn in Fig. S2 of the ESI.† BPs in question seem straight for 1–8. To examine the linearity of the BPs, further, the lengths of the BPs (r_BP) in question are calculated, together with the corresponding straight-line distances (R_SL). The values are collected in Table S1 of the ESI,† which contains the differences between them (Δr_BP = r_BP − R_SL). The Δr_BP values are less than 0.01 Å. Consequently, the BPs for all interactions in question can be described by the straight lines (see also Fig. S3 of the ESI†).

Fig. 5 Molecular graphs with contour plots for 1–4 calculated with MP2/BSS-A (shown by (a)–(d), respectively). The BCPs are denoted by red dots, RCPs are indicated by yellow dots and BPs by pink lines. The carbon, hydrogen, oxygen, selenium, iodine, bromine, chlorine and fluorine atoms are shown in black, grey, red, magenta, purple, brown, light green and light blue, respectively. Contour plots are drawn on the planes containing the O⋯Se–X interaction for each.

QTAIM functions for O-*-Se, O-*-Br and/or Se-*-X in 1–8

QTAIM functions were calculated at the BCPs of O-*-Se and Se-*-X in 1–6 and Se-*-Br in 7, evaluated with MP2/BSS-A, and at the BCPs of O-*-Se and Se-*-Se in 8, evaluated with MP2/BSS-B. Table 3 collects the ρ_b(r_c), H_b(r_c) − V_b(r_c)/2 [= (ħ²/8m)∇²ρ_b(r_c)] and H_b(r_c) values. The H_b(r_c) values are plotted versus H_b(r_c) − V_b(r_c)/2 for the data shown in Table 3, together with those from the perturbed structures generated with CIV. Fig. 6 shows the plots. QTAIM-DFA parameters of (R, θ) and (θ_p, κ_p) are obtained by analysing the plots in Fig. 6, according to eqn (SA3)–(SA6) of the ESI.†Table 3 also collects the QTAIM-DFA parameters for 1–8. Table 3 contains the compliance constants C_ii, correlated to CIV employed to generate the perturbed structures.

Fig. 6 Plots of H_b(r_c) versus H_b(r_c) − V_b(r_c)/2 at BCPs of O-*-Se and Se-*-X in 1–6 and O-*-Br in 7, calculated with MP2/BSS-A, and those of O-*-Se and Se-*-Se in 8 calculated with MP2/BSS-B. The perturbed structures are generated with CIV.

Table 3 QTAIM functions and QTAIM-DFA parameters for O-*-Se-*-X in 1–6 and O-*-Br in 7, calculated with MP2/BSS-A, and those for O-*-Se-*-Se-*-O in 8, calculated with MP2/BSS-B, together with the C_ii values and the predicted natures for the interactions^a,b

Species (symmetry)	Interaction (O-*-Se-*-X)	ρ b(rc) (eao^−3)	c∇^2ρb(rc)^c (au)	H b(rc) (au)	R (au)	θ (°)	C ii (unit)^ii	θ p:CIV (°)	κ p:CIV (au^−1)	Predicted nature
a Fig. 5 for molecular graphs with contour plots drawn on the optimized structures of 1–4. b Fig. S2† for molecular graphs with contour plots drawn on the optimized structures of 5–8. c ∇^2ρb(rc) = Hb(rc) − Vb(rc)/2, where c = ħ^2/8m. d R = (x^2 + y^2)^1/2, where (x, y) = (Hb(rc) − Vb(rc)/2, Hb(rc)). e θ = 90° − tan^−1(y/x). f C ij = ∂^2E/∂fi∂fj, where i and j refer to internal coordinates, and fi and fj, corresponding to i and j, respectively, are the external force components acting on the system. g θ p = 90° − tan^−1(dy/dx). h κ p = |d^2y/dx|/[1 + (dy/dx)^2]^3/2. i The regular CS interaction of the CT-MC nature. j The SS interaction of Cov-w. k The regular CS interaction of the CT-TBP nature. l The regular CS interaction of the HB nature with covalency. m The pure CS interaction of the HB nature with no covalency. n The SS interaction of Cov-s. o The pure CS interaction of the vdW interactions.
1 (Cs)^j	O-*-Se	0.048	0.016	−0.005	0.0170	108.7	2.48	159.6	52.9	r-CS/CT-MC^i
	Se-*-I	0.084	−0.001	−0.032	0.0325	181.7	0.68	191.9	1.3	SS/Cov-w^j
2 (Cs)^j	O-*-Se	0.055	0.017	−0.009	0.0192	119.1	2.43	168.7	27.4	r-CS/CT-MC
	Se-*-Br	0.094	0.001	−0.039	0.0390	178.6	0.64	190.8	1.2	r-CS/CT-TBP^k
3 (Cs)^j	O-*-Se	0.058	0.017	−0.011	0.0205	123.6	2.39	171.2	19.1	r-CS/CT-MC
	Se-*- Cl	0.107	0.001	−0.052	0.0525	178.6	0.59	186.6	3.0	r-CS/CT-TBP
4 (Cs)^j	O-*-Se	0.069	0.018	−0.020	0.0265	138.1	1.96	174.7	2.8	r-CS/CT-MC
	Se-*-F	0.140	0.039	−0.085	0.0932	155.1	0.36	144.6	4.6	r-CS/t-HBwc^l
5 (Cs)	O-*-Se	0.028	0.012	0.001	0.0121	84.5	2.28	109.2	102.8	p-CS/t-HBnc^m
	Se-*-H	0.180	−0.032	−0.150	0.1532	192.0	0.28	178.3	4.3	SS/Cov-s^n
6 (Cs)	O-*-Se	0.028	0.012	0.001	0.0123	85.2	2.22	110.2	100.9	p-CS/t-HBnc
	Se-*-CMe	1.516	−0.020	−0.098	0.0995	191.4	0.37	189.1	4.0	SS/Cov-w
7 (C1)	O-*-Br	0.018	0.008	0.002	0.0086	77.0	2.86	84.9	34.4	p-CS/vdW^o
8 (C2)^j	O-*-Se	0.030	0.012	0.001	0.0125	87.6	2.46	115.5	152.3	p-CS/t-HBnc
	Se-*-Se	0.105	−0.005	−0.048	0.0483	185.5	0.57	194.0	1.9	SS/Cov-w

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Nature of O-*-Se and Se-*-X in 1–7 and 8

The nature of the interactions in question is discussed based on the (R, θ, θ_p) values, employing the standard values as a reference (see Scheme SA3 of the ESI†). While θ classifies the interaction, θ_p characterizes it. It is instructive to survey the criteria before detailed discussion. The criteria tell us that 45° < θ < 90° for the pure closed shell (p-CS) interactions (H_b(r_c) − V_b(r_c)/2 > 0; H_b(r_c) > 0), 90° < θ < 180° for regular CS (r-CS) interactions (H_b(r_c) − V_b(r_c)/2 > 0; H_b(r_c) < 0), and 180° < θ for the shard shell (SS) interactions (H_b(r_c) − V_b(r_c)/2 < 0). The p-CS interactions contain the vdW interactions and typical hydrogen bonds (t-HB) with no covalency (t-HB_nc), while the t-HB with covalency (t-HB_wc), the molecular complex formation through CT (CT-MC) and the TBP adduct formation through CT (CT-TBP) appear in the r-CS interaction region. The classical covalent bonds (Cov) appear in the SS region, and are subdivided into the strong (Cov-s: R > 0.15 au) and weak ones (Cov-w: R < 0.15 au). The borderlines between the interactions for vdW/t-HB_nc, t-HB_nc/t-HB_wc, t-HB_wc/CT-MC, CT-MC/CT-TBP and CT-TBP/Cov-w are mainly determined based on the criteria. The (θ, θ_p) values of (75°, 90°), (90°, 125°), (115°, 150°), (150°, 180°) and (180°, 190°) correspond to the borderlines, respectively. The basic parameters, described in bold, are superior to the tentatively given parameters, described by the plain font in the classification and characterization of interactions.

The intrinsic dynamic and static natures of the interactions in question are easily understood, if they are discussed separately as those of G(A), G(B) and G(C). The natures of O-*-Se and Se-*-X (X = I (1), Br (2), Cl (3) and F (4)) in G(A) are discussed first. The (R, θ, θ_p) values of Se-*-X in 1–4 are (0.033 au, 181.7°, 191.9°), (0.039 au, 178.6°, 190.8°), (0.053 au, 178.6°, 186.6°) and (0.093 au, 155.1°, 144.6°), respectively. Therefore, the Se-*-I, Se-*-Br, Se-*-Cl and Se-*-F interactions in 1–4 are predicted to have the SS/Cov-w, r-CS/CT-TBP, r-CS/CT-TBP and r-CS/t-HB_wc natures, respectively. However, the natures of Se-*-Br and Se-*-Cl interactions seem close to the border area between SS/Cov-w and r-CS/CT-TBP, judging from the θ values. The (R, θ, θ_p) values of O-*-Se in 1–4 are (0.017 au, 108.7°, 159.6°), (0.019 au, 119.1°, 168.7°), (0.021 au, 123.6°, 171.2°) and (0.027 au, 138.1°, 174.7°), respectively. Therefore, the O-*-Se interactions in 1–4 are all predicted to have the r-CS/CT-MC nature. The O-*-Se interactions become stronger in the order of 1 < 2 < 3 < 4.

The (R, θ, θ_p) values of Se-*-H in 5, Se-*-C_Me in 6 and Se-*-Se in 8 of G(B) are (0.153 au, 192.0°, 178.3°), (0.100 au, 191.4°, 189.1°) and (0.048 au, 185.5°, 194.0°), respectively. Therefore, the interactions are predicted to have the SS/Cov-s, SS/Cov-w and SS/Cov-w natures, respectively. The (R, θ, θ_p) values of O-*-Se in 5, 6 and 8 are (0.012–0.013 au, 84.5–87.6°, 109.2–115.5°), therefore, the interactions are all predicted to have the p-CS/t-HB_nc natures. The natures are very close to each other. The (R, θ, θ_p) values for O-*-Br in 7 of G(C) are (0.009 au, 77.0°, 84.9°). As a result, it is predicted to have the negligibly weak p-CS/vdW nature.

The strengths of n(O)⋯σ*(Se–X) σ(3c-4e) in 1–6 are further examined by comparing their O-*-Se interactions with those in 2-C₆H₄(CHO)SeX (II: X = I, Br, Cl, F, H and Me) and 2-C₆H₄(CH₂OMe)SeX (IV: X = I, Br, Cl, F, H and Me), where IV corresponds to the structure shown in Fig. 1a, of which G is replaced by MeO. The QTAIM-DFA plot of H_b(r_c) versus H_b(r_c) − V_b(r_c)/2 for O-*-Se of 1–6, II (X) and IV (X) is shown in Fig. S4 of ESI,† where the perturbed structures are generated with CIV (see Table S2 of ESI† for the data of II (X) and IV (X), Fig. S5 and S6† for molecular graphs with contour plots drawn on the optimized structures of II (X) and IV (X), respectively). The rough order of the strengths is shown in eqn (7). Two types of basic orders are derived from eqn (7). One is O-*-Se (X = I) < O-*-Se (Br) < O-*-Se (Cl) < O-*-Se (F), if the members of a common structure are compared, and another is O-*-Se (IV) < O-*-Se (II) < O-*-Se (1–6), if the interactions of the same X are compared.

Behaviour of the O-*-Se and Se-*-X interactions

We proposed very recently that the interaction shows the normal behaviour, if θ_p > θ (Δθ_p = θ_p − θ > 0), whereas it shows the inverse behaviour, if θ_p < θ (Δθ_p < 0). It is noted that the inverse behaviour of interactions will arise from the abnormal behaviour of G_b(r_c) (therefore, that of H_b(r_c) − V_b(r_c)/2) at BCP of an interaction in question. This method is applied to the O-*-Se and Se-*-X interactions in 1–6, 8, II (X) and IV (X) to examine the behaviour of the interactions further.

The Δθ_p values are plotted versus θ for the O-*-Se and Se-*-X interactions in 1–6, II and IV in Fig. 7. Three dotted lines are drawn in black, blue and red, which show the typical areas or borders of the normal, weak normal and inverse behaviour of interactions, respectively.³⁵ As shown in Fig. 7, all interactions in 1–6, 8, II (X) and IV (X) show the normal behaviour, except for Se-*-F in (4, II (F) and IV (F)), Se-*-H in (5, II (H) and IV (H)) and Se-*-C_Me in (6, II (Me) and IV (Me)), although Se-*-Cl in (3, II (Cl) and IV (Cl)) and Se-*-O in (II (H), II (Me), IV (H) and IV (Me)) show the weak normal behaviour.

Fig. 7 Plots of Δθ_p (=θ_p − θ) versus θ for O-*-Se and Se-*-X in 1–6, II (X) and/or IV (X), calculated with MP2/BSS-A and O-*-Se and Se-*-Se in 8 with MP2/BSS-B (θ_β = 207.7°).

The inverse behaviour can be recognized in the plot in Fig. 6, if the plot is carefully observed. The plots in Fig. 6 show a right-handed smooth stream, as a whole, which is a typical sign for θ_p > θ after the analysis of the plots. However, the plot for Se-*-F of 4 shows a direction perpendicular to the whole stream, which is a typical sign for θ_p < θ after the analysis. The plots for Se-*-H of 5 and Se-*-C_Me of 6 seem to show a similar trend to that of Se-*-F in 4, although the trends are weak. The analysed (θ, θ_p) values are (155.1°, 144.6°) for Se-*-F in 4, (192.0°, 178.3°) for Se-*-H in 5 and (191.4°, 189.1°) for Se-*-C_Me in 6, of which θ_p are all smaller than θ. The inverse behaviour tends to appear in the interactions in which the atomic numbers and natures between the connected atoms are largely different.³⁵

The contributions of the CT terms are evaluated for the n(O)⋯σ*(Se–X) σ(3c-4e) interactions in 1–6 and 8 with the NBO analysis. The strength of the interactions is discussed based on E(2), next.

NBO analysis for 3c-4e interactions in 1–6 and 8

How do the CT terms of the OSeX σ(3c-4e) interactions contribute to stabilize 1–6 and 8? The second-order perturbation of the NBO analysis²⁴ is applied to n(O)⋯σ*(Se–X) σ(3c-4e) in 1–6 and 8. The E(2) stabilization energy associated with delocalization of the NBO (i: donor) → NBO (j: acceptor) type is calculated according to eqn (8), where q_i is the donor orbital occupancy, ε_i and ε_j are the orbital energies of diagonal elements, and F(i,j) is the off-diagonal NBO Fock matrix element. Table 4 collects the contributions separately by the intramolecular n_s(O)⋯σ*(Se–X) and n_p(O)⋯σ*(Se–X) interactions for 1–6 and 8. The total contributions of the n_s+p(O)⋯σ*(Se–X) type are obtained by the simple addition of the two terms for an X.

E(2) = q_iF(i,j)²/(E_j − E_i) (8)

Table 4 Contributions from the CT terms of the donor–acceptor type to the n(O)⋯σ*(Se–X) interactions in 1–6, calculated with the NBO analysis under MP2/BSS-A and to the n(O)⋯σ*(Se–Se)⋯n(O) interactions in 8, calculated with the NBO analysis under MP2/BSS-B^a

Species (symmetry)	NBO(i) → NBO(j)	E(2)^b (kcal mol^−1)	ΔE^c (au)	F(i,j)^d	NBO(i) → NBO(j)	E(2)^b (kcal mol^−1)	ΔE^c (au)	F(i,j)^d
a BSS-A stands for (S-TZP + 1s1p) and BSS-B does for (S-TZP + 1s1p) applied to O, Se and X with S-DZP to C and H. b Second order perturbation energy given by eqn (8). c The diagonal elements (orbital energies). d The off-diagonal NBO Fock matrix element.
1 (Cs)	ns(O) → σ*(Se–I)	4.93	0.79	0.056	np(O) → σ*(Se–I)	25.68	0.42	0.093
2 (Cs)	ns(O) → σ*(Se–Br)	5.58	0.80	0.060	np(O) → σ*(Se–Br)	33.17	0.46	0.110
3 (Cs)	ns(O) → σ*(Se–Cl)	5.89	0.82	0.062	np(O) → σ*(Se–Cl)	35.66	0.49	0.118
4 (Cs)	ns(O) → σ*(Se^+ F^−)	8.93	0.68	0.070	np(O) → σ*(Se^+ F^−)	75.24	0.40	0.154
5 (Cs)	ns(O) → σ*(Se–H)	2.02	1.01	0.040	np(O) → σ*(Se–H)	5.31	0.57	0.049
6 (Cs)	ns(O) → σ*(Se–CMe)	1.88	0.99	0.039	np(O) → σ*(Se–CMe)	5.78	0.54	0.050
8 (C2)	ns(O) → σ*(Se–Se)	2.30	0.85	0.039	np(O) → σ*(Se–Se)	7.93	0.43	0.052

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The contributions from the n_s(O)⋯σ*(Se–X) and n_p(O)⋯σ*(Se–X) interactions are 4.9 ≤ E(2) ≤ 8.9 kcal mol⁻¹ and 25.7 ≤ E(2) ≤ 75.2 kcal mol⁻¹, respectively, for G(A) of 1–4, while the contributions are 1.9 ≤ E(2) ≤ 2.3 kcal mol⁻¹ and 5.3 ≤ E(2) ≤ 7.9 kcal mol⁻¹, respectively, for G(B) of 5, 6 and 8. The contributions for G(A) of 1–4 are much larger than the corresponding ones for G(B) of 5, 6 and 8. The much larger contributions from σ*(Se–X: X = I, Br, Cl and F) in G(A), relative to the case of σ*(Se–X: X = Se, H, and C_Me) in G(B) are confirmed again, based on E(2). The order in E(2) for n_p(O)⋯σ*(Se–X) can be described by eqn (9) and the order for n_s(O)⋯σ*(Se–X) seems similar, although the values are (very) small, relative to the former.

4 ≫ 3 > 2 > 1 ≫ 8 > 6 ≥ 5 (9)

What are the relations between E(2) and Δr(Se, O₁) and C_ii⁻¹? The E(2) values for n_s(O)⋯σ*(Se–X), n_p(O)⋯σ*(Se–X) and n_s+p(O)⋯σ*(Se–X) are plotted versus Δr(Se, O₁) for 1–6 and 8. Fig. 8 shows the plot. The E(2) values for n_s(O)⋯σ*(Se–X), n_p(O)⋯σ*(Se–X) and n_s+p(O)⋯σ*(Se–X) increase proportionally as Δr(Se, O₁) becomes more negative. The plot of E(2) for n_s(O)⋯σ*(Se–X) versus Δr(Se, O₁) for 1–6 and 8 gave a (very) good correlation (y = –13.54x − 8.89: R_c² = 0.946), and excellent correlation for n_p(O)⋯σ*(Se–X) (y = –84.70x − 61.37: R_c² = 0.999) was also obtained, so was the plot for n_s+p(O)⋯σ*(Se–X) (y = –95.99x − 68.30: R_c² = 0.999), where the data for 4 was omitted from the correlation(s). The E(2) value for 4 is evaluated as much larger than that expected from the correlation. The zwitterionic nature of Se⁺⋯X⁻, resulting from the very high polar nature of Se^δ+–X^δ−, must be responsible for the deviation(s).

Fig. 8 Plots of E(2) versus Δr(Se, O₁) in the n_k(O) → σ*(Se–X) interactions (k = s, p and s + p) for 1–6 calculated with MP2/BSS-A and 8 with MP2/BSS-B.

The E(2) values for n_s(O)⋯σ*(Se–X), n_p(O)⋯σ*(Se–X) and n_s+p(O)⋯σ*(Se–X) for 1–6 and 8 are similarly plotted versus C_ii⁻¹. Fig. 9 shows the plot. The E(2) values for n_s(O)⋯σ*(Se–X), n_p(O)⋯σ*(Se–X) and n_s+p(O)⋯σ*(Se–X) increase proportionally as C_ii⁻¹ increases for 1–4, but the similar relation seems difficult to find for 5, 6 and 8. Therefore, the correlations can be discussed only for the data from 1–4. The correlations of E(2) versus C_ii⁻¹ in 1–4 were (very) good for n_s(O)⋯σ*(Se–X) (y = 34.98x − 8.88: R_c² = 0.994), n_p(O)⋯σ*(Se–X) (y = 438.97x − 148.51: R_c² = 0.997) and n_s+p(O)⋯σ*(Se–X) (y = 473.95x − 157.40: R_c² = 0.997). The very large E(2) value of 4 is well correlated to the corresponding C_ii⁻¹ value. In the case of 5, 6 and 8, the E(2) values do not correlate well to the C_ii⁻¹ values, where the E(2) values are much smaller than expected for those C_ii⁻¹ values.³⁶

Fig. 9 Plots of E(2) versus C_ii⁻¹ in the n_k(O) → σ*(Se–X) interactions (k = s, p and s + p) for 1–6 calculated with MP2/BSS-A and 8 with MP2/BSS-B.

Stability of the selanyl halides, examined by QC calculations

The stability of 1-(haloselanyl)anthraquinones (1–4) was further examined, mainly employing the energy of the formation (EF) based on the QC calculations, together with 1-ATQSeH (5) and 1-ATQSeMe (6). EF_ES, EF_ZP and EF_FE stand for EF on the potential energy surface and considering the zero-point energies and the Gibbs free energies, respectively. The QC calculations were similarly performed on PhSeX (X = I, Br, Cl, F, H and Me), the results of which were employed as the standard for the corresponding values of 1-ATQSeX (X = I, Br, Cl, F, H and Me, respectively), where Se–X in PhSeX has no substantial mechanisms to stabilize it, such as in O⋯Se–X of 1–4. The calculations on (1-ATQSe)₂ (8), necessary to evaluate the EF values, were not successfully performed with MP2/BSS-1. Therefore, the species are calculated or recalculated with MP2/BSS-2.

Judging from the EF values, 1-ATQSeX becomes more stable in the order of X = I < Br < Cl < F. The order seems just the inverse of the experimental impressions. The actual inverse order of the reactivity would be responsible for the experimental impressions. The overall trends in the EF values of PhSeX seem very similar to those of 1-ATQSeX. However, examining the individual values, the differences become clear. Based on EF_ES and EF_ZP, 1-ATQSeI is predicted to be more stable than the components by 5–6 kJ mol⁻¹, whereas PhSeI is less stable than the components by 6 kJ mol⁻¹. The results show that ArSeI would be less stable than the components; however, it could be more stable than the components if the Se–I bond is suitably stabilized, as in 1-ATQSeI. Nevertheless, the stability of ArSeI seems almost the same as that of the components, if discussed with EF_FE. ArSeI would be stabilized about 10 kJ mol⁻¹, if the Se–I bond is suitably stabilized. The stabilizing effect seems much larger for Se–X in the order of X = I < Br < Cl < F, although the reactivity of the bonds is contained in the experimental impressions.

The Se–X bonds in 1-ATQSeX (X = I, Br, Cl and F) are predicted to be longer than the corresponding values in PhSeX (X = I, Br, Cl and F, respectively), by 0.04–0.06 Å (Table 5), which demonstrates well the expectations that the Se–X bonds will be longer if stabilized as in O⋯Se–X. The observed Se–I bond length in 1-ATQSe-I (2.5825(7) Å) is longer than that reported for BpqSe-I (2.5203(11) Å, see Fig. 1) by 0.062 Å. The results show very good concurrence between the calculated and observed results. The effect from O on Se–X seems very small for 5 and 6, based on the Δr(Se,X) values, for example.

Table 5 Energies for 1–6 and 8, optimized with MP2/BSS-B, together with PhSeX, PhSeSePh and X₂ (X = I, Br, Cl and F)^a

Species/no (symmetry)	E ES (au)	EFES^c (ΔEFES) (kJ mol^−1)	EFZP (ΔEFZP)^d^,^e (kJ mol^−1)	EFFE (ΔEFFE)^f (kJ mol^−1)	ΔEFFE^f (kJ mol^−1)	Δr(Se,X)^g (Å)
a BSS-B stands for (S-TZP + 1s1p) applied to O, Se and X with S-DZP to C and H. b Calculated energy on the potential surface. EES(8: C2) = −6172.78111 au, EES(PhSeSePh: C2) = −5261.96523 au, EES(I2: D∞h) = −13 836.15437 au, EES(Br2: D∞h) = −5145.24800 au, EES(Cl2: D∞h) = −919.29079 au, EES(F2: D∞h) = −199.25805 au; EES(H2: D∞h) = −1.15628 au and EES(MeMe: D3d) = −79.53834 au. c Energy for the formation of ArSeX from (ArSeSeAr + X2)/2: EF(ArSeX) = E(ArSeX) − [E(ArSeSeAr)/2 + E(X2)/2]. d EF considering the zero-point energies and the contribution from the zero-point energies to EF. e EF considering the Gibbs free energies and the contribution from the thermal part of the Gibbs free energies to EF. f Differences in EF considering the Gibbs free energies for 1–6 from those of the corresponding PhSeX for each. g Differences in the Se–X distances for 1–6 from those of the corresponding PhSeX for each, and the contribution from the thermal part of the Gibbs free energies to EF.
1 (Cs)	−10 004.46991	−5.7 (as 0.0)	−5.4 (0.3)	−9.3 (−3.6)	−7.7	0.046
2 (Cs)	−5659.02673	−32.0 (as 0.0)	−31.0 (1.0)	−34.2 (−2.2)	−17.5	0.053
3 (Cs)	−3546.06692	−52.4 (as 0.0)	−50.9 (1.5)	−54.2 (−1.8)	−22.7	0.055
4 (Cs)	−3186.09508	−198.2 (as 0.0)	−195.1 (3.1)	−197.8 (0.4)	−42.5	0.043
5 (Cs)	−3086.96085	43.4 (as 0.0)	43.0 (−0.4)	37.7 (−5.7)	25.8	−0.001
6 (Cs)	−3126.14319	20.6 (as 0.0)	28.0 (7.4)	15.1 (−5.5)	−16.0	0.009
PhSeI (C1)	−9549.05745	6.2 (as 0.0)	6.2 (0.0)	−1.6 (−7.8)	As 0.0	As 0.0
PhSeBr (C1)	−5203.61009	−9.1 (as 0.0)	−8.9 (0.2)	−16.7 (−7.6)	As 0.0	As 0.0
PhSeCl (C1)	−3090.63715	−24.0 (as 0.0)	−23.5 (0.5)	−31.5 (−7.5)	As 0.0	As 0.0
PhSeF (C1)	−2730.55830	−148.8 (as 0.0)	−147.4 (1.4)	−155.3 (−6.5)	As 0.0	As 0.0
PhSeH (C1)	−2631.55217	22.5 (as 0.0)	27.5 (5.0)	11.9 (−10.6)	As 0.0	As 0.0
PhSeMe (Cs)	−2670.73597	41.5 (as 0.0)	39.9 (−1.6)	31.1 (−10.4)	As 0.0	As 0.0

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Effect of n(O)⋯σ*(Se–X) on the carbonyl stretching frequencies

The carbonyl stretching frequencies (ν(C=O)) would be somewhat affected from the n(O)⋯σ*(Se–X) σ(3c-4e) interactions, which is to be clarified. The carbonyl stretching frequencies (ν(C=O)) in 1–8 exist originally as higher and lower ones (ν_org:H(C=O) and ν_org:L(C=O), respectively), due to the substituent at the 1-position. The levels are described as α and α − γ, respectively. Two of ν_org:H(C=O) and ν_org:L(C=O) interact mutually and then destabilise ν_org:H(C=O) and stabilise ν_org:L(C=O) by the factors of β and β′, respectively, where β = β′ is often assumed. The interaction forms ν_L(C=O) and ν_H(C=O), which would have the symmetry close to ν_s(C=O) and ν_as(C=O), respectively. The signals close to ν_s(C=O) would be (very) small, if a substantial change in the dipole moment dose not arise. Based on the above discussion, two signals (suitably) assigned to ν(C=O) are considered to behave as ν_s(C=O) and ν_as(C=O) in the discussion, although they contain some aryl stretching modes. Scheme 1 shows the outline of the diagram for ν(C=O) in 1–8, which explains ν_av(C=O) and Δν(C=O), also Δν_av(C=O) and ΔΔν(C=O), the differences in ν_av(C=O) and Δν(C=O) between the species, A and B.

Scheme 1 Overview of the ν(C=O) interactions in 1–8.

Table 6 summarizes the calculated ν(C=O) values (ν_calcd(C=O)) for 1–8 under MP2/BSS-B. Each ν_calcd(C=O) consists of two signals.

Table 6 The carbonyl stretching frequencies calculated and/or observed for 1–8, calculated under MP2/BSS-B

No	ν calcd(C=O) (cm^−1)	ν calcd:av(C=O) (cm^−1)	Δνcalcd(C=O)^a (cm^−1)	Δνobsd(C=O) (cm^−1)
a Δνcalcd(C=O) = νcalcd:H(C=O) − νcalcd:L(C=O). b Not obtained.
1	1633.9; 1684.2	1659.1	50.3	1635; 1680
2	1631.3; 1683.7	1657.5	52.4
3	1630.9; 1683.5	1657.2	52.6
4	1630.6; 1682.2	1656.4	51.6
5	1664.6; 1685.9	1675.3	21.3
6	1661.6; 1685.0	1673.3	23.4	1667
7	1682.4; 1691.4	1686.9	9.0	1681
8	1656.5; 1685.3	1670.9	28.8

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Table 6 contains the average values (ν_calcd:av(C=O)) and the differences between the two (Δν_calcd(C=O)). The ν_calcd(C=O) values of 1–7, obtained under MP2/BSS-A, are collected in Table S3 of the ESI.† The ν_calcd:av(C=O) values are 1656–1659 cm⁻¹ for 1–4 and 1671–1675 cm⁻¹ for 5, 6 and 8 with 1687 cm⁻¹ for 7, while the Δν_calcd(C=O) values are 50–53 cm⁻¹ for 1–4 and 21–29 cm⁻¹ for 5, 6 and 8 with 9 cm⁻¹ for 7. The orders of ν_calcd:av(C=O) and Δν_calcd(C=O) are shown in eqn (10) and (11), respectively. The orders are (just) the inverse with each other. The contributions from n(O)⋯σ*(Se–X) σ(3c-4e) to ν_calcd:av(C=O) and Δν_calcd(C=O) are not clear, but the order shown in eqn (11) is well correlated to those in eqn (6) and (9). The results remind us of the relationship between the order in Δν_calcd(C=O) and that of the stability based on Δr(Se, O₁) and that in E(2) calculated for n_p(O)⋯σ*(Se–X) with NBO. The results could be rationalized by considering that the order in Δν_calcd(C=O) is closely related to ΔΔν(C=O), which will be γ_B − γ_A, if β_B = β_A and β′_B = β′_A.

4 < 3 ≤ 2 < 1 ≪ 8 < 6 < 5 ≪ 7 (10)

3 ≥ 2 > 4 > 1 ≫ 8 ≫ 6 > 5 ≫ 7 (11)

Table 6 also contains the observed values (ν_obsd(C=O)) for 1, 6 and 7, where only ν_L(C=O) are detected for 6 and 7. To clarify the behaviour of ν(C=O) in 1–8, more, the observed values and the calculated values under MP2/BSS-A and MP2/BSS-B are plotted versus those calculated with MP2/BSS-B, where the latter plot is for the standard. Fig. 10 shows the plot. The correlation for the plot of ν(C=O) with MP2/BSS-A for 1–7 is excellent (y = 1.124x − 204.1: R_c² = 0.998). The data points of ν_obsd(C=O) of 1, 6 and 7 appear very close to the plot for those calculated with MP2/BSS-B and the points correlate well with the values calculated under MP2/BSS-B (y = 0.904x + 159.8: R_c² = 0.975). The ν(C=O) values for 1–8 are better understood through the plot in Fig. 10, together with eqn (10) and (11).

Fig. 10 Plots of ν_obsd(C=O) () and ν_calcd(C=O) () with MP2/BSS-A versus ν_calcd(C=O) with MP2/BSS-B, with the plot of ν_calcd(C=O) with MP2/BSS-B versus the same values ().

Conclusions

Selanyl halides are usually very unstable, due to the small enthalpy for the formation. Selanyl iodides are, therefore, in equilibrium with the components and/or the molecular complex type adducts. We encountered the formation of unexpectedly stable 1-ATQSeI (1) in the reaction of 1-ATQSeBzl with I₂ in CHCl₃. Then, 1-ATQSeBr (2) and 1-ATQSeCl (3) were prepared and the structures of 1, 2, 1-ATQSeMe (6) and 1-ATQBr (7) were determined. The behaviour and the natures of O⋯Se and Se⋯X were elucidated by the combination of the experimental results on 1, 2, 6 and 7 with those from the QC calculations on 1, 2, 3, 6, 7 and 1-ATQSeX (X = F (4) and H (5)) and (1-ATQSe)₂ (8). The observed and/or calculated O⋯Se distances in 1–4 from the sum of the vdW radii of the bonding atoms (Δr(Se, O₁)) are negative and the magnitudes amount to over 1 Å, which must be the main driving force for their high stability. The attractive n(O)⋯σ*(Se–X) interactions operate to strongly stabilize 1–4. The formation of the stable cyclic O₁SeC₁C₁₄C₁₃ 6π five-membered rings formed in 1–4, together with 8, supports shortening of the O⋯Se distances. They work together to stabilize the species.

While the Se-*-I, Se-*-Br, Se-*-Cl and Se-*-F interactions in 1–4 are predicted to have the SS/Cov-w, r-CS/CT-TBP, r-CS/CT-TBP and r-CS/t-HB_wc natures, respectively, the O-*-Se interactions in 1–4 are all predicted to have the r-CS/CT-MC natures, where the O-*-Se interactions seem stronger in the order of 1 < 2 < 3 < 4. The E(2) values of 1–6 and 8, calculated with the NBO analysis, correlated excellently with Δr(Se, O₁), except for Se-*-F, for which E(2) is evaluated to be much larger, perhaps due to the contribution as the twitter-ionic Se⁺–F⁻ form. The correlation between E(2) and C_ii⁻¹ was also examined. The correlation was very good for all Se-*-X in 1–4, although data for 5, 6 and 8 deviated from the correlation.

The results will help in the design of stable selanyl halides, and in sulfenyl halides and tellanyl halides.

Conflicts of interest

The authors declare no conflict of interest.

Acknowledgements

The computations were partially performed at the Research Centre for Computational Science, Okazaki, Japan. The author acknowledges the financial support from JSPS KAKENHI Grant Number JP24K08394.

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Footnote

† Electronic supplementary information (ESI) available: Computational data, and the fully optimized structures given by Cartesian coordinates for 1–8, II, and IV. CCDC 2339576, 2339577, 2339579 and 2339580. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d4dt00760c

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