Atoms‐in‐Molecules Analysis of Extended Hypervalent Five‐Center, Six‐Electron (5c–6e) C₂Z₂O Interactions at the 1,8,9‐Positions of Anthraquinone and 9‐Methoxyanthracene Systems

Abstract

To clarify the nature of five‐center, six‐electron (5c–6e) C₂Z₂O interactions, atoms‐in‐molecules (AIM) analysis has been applied to an anthraquinone, 1,8‐(MeZ)₂ATQ (1 (Z=Se), 2 (Z=S), and 3 (Z=O)), and a 9‐methoxyanthracene system, 9‐MeO‐1,8‐(MeZ)₂ATC (4 (Z=Se), 5 (Z=S), and 6 (Z=O)), as well as 1‐(MeZ)ATQ (7 (Z=Se), 8 (Z=S), and 9 (Z=O)) and 9‐MeO‐1‐(MeZ)ATC (10 (Z=Se), 11 (Z=S), and 12 (Z=O)). The total electronic energy density (H_b(r_c)) at the bond critical points (BCPs), an appropriate index for weak interactions, has been examined for 5c–6e C₂Z₂O and 3c–4e CZO interactions of the n_p(O)⋅⋅⋅σ*(ZC) type in 1–12. Some hydrogen‐bonded adducts were also re‐examined for convenience of comparison. The total electronic energy densities varied in the following order: O⋅⋅⋅O (3: H_b(r_c)=0.0028 au)=O⋅⋅⋅O (6: 0.0028 au)>O⋅⋅⋅O (9: 0.0025 au)≥NN⋅⋅⋅HF (0.0024 au)≥O⋅⋅⋅O (12: 0.0023 au)≫H₂O⋅⋅⋅HOH (0.0015 au)>S⋅⋅⋅O (8: 0.0013 au)=S⋅⋅⋅O (2: 0.0013 au)≥S⋅⋅⋅O (11: 0.0012 au)=S⋅⋅⋅O (5: 0.0012 au)>HF⋅⋅⋅HF (0.0008 au)=Se⋅⋅⋅O (10: 0.0008 au)=Se⋅⋅⋅O (4: 0.0008 au)≥Se⋅⋅⋅O (1: 0.0007 au)≥Se⋅⋅⋅O (7: 0.0006 au)≫HCN⋅⋅⋅HF (−0.0013 au). H_b(r_c) values for S⋅⋅⋅O were predicted to be smaller than the hydrogen bond of H₂O⋅⋅⋅HOH and H_b(r_c) values for Se⋅⋅⋅O are very close to or slightly smaller than that for HF⋅⋅⋅HF in both the ATQ and 9‐MeOATC systems. In the case of Z=Se and S, H_b(r_c) values for 5c–6e C₂Z₂O interactions are essentially equal to those for 3c–4e CZO if Z is the same. The results demonstrate that two n_p(O)⋅⋅⋅σ*(ZC) 3c–4e interactions effectively connect through the central n_p(O) orbital to form the extended hypervalent 5c–6e system of the σ*(CZ)⋅⋅⋅n_p(O)⋅⋅⋅σ*(ZC) type for Z=Se and S in both systems. Natural bond orbital (NBO) analysis revealed that n_s(O) also contributes to some extent. The electron charge densities at the BCPs, NBO analysis, and the total energies calculated for 1–12, together with the structural changes in the PhSe derivatives, support the above discussion.

Introduction

Extended hypervalent bonds, mc–ne (m≥4),1–4, which are σ‐type linear bonds that are greater than three‐center, four‐electron bonds (3c–4e), are of current interest.1d, 5–8 Our strategy to construct mc–ne (m≥4) bonds is to employ nonbonded interactions containing lone‐pair orbitals.2–4 We have previously reported the formation of extended hypervalent 4c–6e Z₄ (Z=Se, S, and Br),2, 4 5c–6e C₂Z₂O (Z=Se and S),3 6c–8e Se₂Br₄, and 7c–10e Se₂Br₅ bonds,4 as well as their nature. Linear alignments of four atoms have also been reported by others, although they are not recognized as extended hypervalent bonds.9 Weak interactions control the fine structures of compounds and create highly functionalized materials. Information on the weak interactions will also be supplied through the elucidation of the nature of extended hypervalent mc–ne (m≥4) bonds.

The formation of 5c–6e C₂Z₂O systems was established on the basis of the linear alignment of five CZ⋅⋅⋅O⋅⋅⋅ZC atoms (Z=Se and S) in 1,8‐bis(phenylselanyl)anthraquinone (I), 9‐methoxy‐1,8‐bis(phenylselanyl)anthracene (II), and their derivatives. The quantum chemical (QC) calculations, incorporating the energy‐lowering effect of linear alignment, the direction of the charge transfer (CT), and the orbital interaction maps, support the formation of 5c–6e C₂Z₂O in I and II. The linear alignment of the 5c–6e C₂Z₂O entity is a typical example of an extended hypervalent bond.3 Scheme 1 shows the molecular orbital approximation of 5c–6e Z₅. Indeed, the simple bonding scheme enables us to visualize how molecular orbitals are constructed from the atomic orbitals in 5c–6e Z₅, but it never provides information on the nature of the bonding. We were very interested in the real nature of the bonding in 5c–6e C₂Z₂O. However, the nature of the bonding between the oxygen and chalcogen atoms in 5c–6e CZ⋅⋅⋅O⋅⋅⋅ZC (Z=Se and S) has not been clarified yet.

Scheme 1

Molecular orbital approximation of 5c–6e Z₅.

Bader proposed a method to analyze chemical bonds, as well as their nature, that is known as the AIM (atoms‐in‐molecules) method.10 The method can be applied to weak bonds as well as classical chemical bonds.11–16 Some criteria have been proposed to enable weak interactions to be recognized, separate from the classical bonds, based on the nature of the bond critical points (BCPs).10

We applied the AIM method to the extended hypervalent 5c–6e C₂Z₂O (Z=Se, S, and O) unit in the anthraquinone (ATQ) system, 1,8‐bis(methylchalcogeno)anthraquinones (1,8‐(MeZ)₂ATQ: 1 (Z=Se), 2 (Z=S), and 3 (Z=O)) after determination of the structures by means of X‐ray crystallographic analysis. Of plausible structures such as AA and BB, compounds 1–3 adopt the BB structure, according to our definition, with both ZC_Me bonds lying in the ATQ plane, similar to the cases of I and II (Scheme 2). p–π conjugation of the n_p(Z)–π(ATQ)–n_p(Z) type must play an important role in stabilizing 5c–6e C₂Z₂O (BB). No such p–π conjugation is present in the 9‐methoxyanthracene (9‐MeOATC) system, 9‐methoxy‐1,8‐bis(methylchalcogeno)anthracenes (9‐MeO‐1,8‐(MeZ)₂ATC: 4 (Z=Se), 5 (Z=S), and 6 (Z=O)), owing to the lack of a suitable n_p(O) orbital. Therefore, the purer 5c–6e C₂Z₂O nature will be clarified by examining the bonding nature in 4–6. AIM analysis was also applied to 4–6. Scheme 3 shows how extended hypervalent 5c–6e C₂Z₂O interactions of the σ*(CZ)⋅⋅⋅n_p(O)⋅⋅⋅σ*(ZC) type can be formed starting from two hypervalent 3c–4e interactions of the n_p(O)⋅⋅⋅σ*(ZC) type, connecting effectively through the central n_p(O) orbital. AIM analysis was also carried out for the 3c–4e O⋅⋅⋅ZC interactions in 1‐(MeZ)ATQ (7 (Z=Se), 8 (Z=S), and 9 (Z=O)) and 9‐MeO‐1‐(MeZ)ATC (10 (Z=Se), 11 (Z=S), and 12 (Z=O)) for convenience of comparison.

Scheme 2

AA and BB structures in 1 and 4.

Scheme 3

Formation of 5c–6e X₂Z₂Y through the connection of two 3c–4e XZY entities through the central n_p(Y) orbital.

Herein, we report the results of the AIM analysis of 5c–6e C₂Z₂O in 1–6, as well as 3c–4e CZO in 7–12, which clarifies the nature of the bonds. To the best of our knowledge this is the first AIM treatment of extended hypervalent bonds. The contribution of CT to 5c–6e C₂Z₂O in 1–6 and 3c–4e CZO interactions in 7–12 has also been evaluated by using natural bond orbital (NBO) analysis. The results demonstrate that the CT in 5c–6e C₂Z₂O in 1–6 and 3c–4e CZO in 7–12 controls the total energies. The results confirm that the energy‐lowering effect is responsible for the formation of extended hypervalent bonds.

Results and Discussion

Structures of 1,8‐(MeZ)₂ATQ (Z=Se, S, and O: 1–3): The X‐ray crystallographic analysis was carried out on suitable single crystals of 1–3, which were obtained by slow evaporation of solutions of the compounds in benzene containing 10–30 % v/v ethanol. Crystals of 1 and 3 contain only one type of structure, whereas crystals of 2 contain two types of structures (2 (S‐A) and 2 (S‐B)). The crystallographic data is collected in Table 1 and selected interatomic distances, angles, and torsional angles are reported in Table 2. Figures 1, 2, and 3 show the structures of 1, 2 (S‐A), and 3, respectively. The structure of 2 (S‐B) is given in the Supporting Information.

Table 1. Crystallographic data for 1–3.

	1	2	3
formula	C16H12O2Se2	C16H12O2S2	C16H12O4
Mr	394.18	300.38	268.26
T [K]	103(2)	103(2)	103(2)
crystal system	monoclinic	monoclinic	monoclinic
space group	P21/c (no. 14)	P121/n1 (no. 14)	P21/a (no. 14)
a [Å]	9.332(2)	14.171(3)	12.6272(12)
b [Å]	15.862(4)	12.058(2)	6.6216(4)
c [Å]	9.451(2)	16.221(3)	15.6593(14)
β [°]	107.483(3)	111.3621(19)	112.844(4)
V [Å^3]	1334.3(6)	2581.3(9)	1206.61(17)
Z	4	8	4
ρcalcd [g cm^−3]	1.962	1.546	1.477
F(000)	768	1248	560
no. of reflections collected	8865	22 316	8103
no. of independent reflections	2479 (Rint=0.0199)	5021 (Rint=0.0141)	2352 (Rint=0.0193)
no. of data/restraints/params	2479/0/229	5021/0/457	2352/0/229
goodness of fit, F2	1.081	1.118	1.113
R1, wR2	0.0177, 0.0422	0.0300, 0.0853	0.0403, 0.0990
	[I>2.0σ(I)]	[I>2.0σ(I)]	[I>2.0σ(I)]
largest diff. peak [e Å^−3]	0.371 to −0.422	0.420 to −0.229	0.420 to −0.279

Table 2. Selected interatomic distances [Å], angles [°], and torsional angles [°] in 1–3.

	1	2 (S‐A)	2 (S‐B)	3^[a]
interatomic distances
Z(1)O(1)	2.6356(13)	2.6364(11)	2.6495(11)	2.6169(15)
Z(2)O(1)	2.6344(13)	2.6485(11)	2.6392(11)	2.6129(15)
Z(1)C(1)	1.9100(19)	1.7631(14)	1.7610(14)	1.3590(16)
Z(1)C(15)	1.950(2)	1.8055(15)	1.8063(15)	1.4357(17)
Z(2)C(11)	1.9176(19)	1.7642(14)	1.7655(14)	1.3565(16)
Z(2)C(16)	1.955(2)	1.8085(15)	1.8119(15)	1.4334(17)
O(1)C(13)	1.233(2)	1.2266(17)	1.2296(17)	1.2209(17)
angles
Z(1)‐O(1)‐Z(2)	150.72(6)	158.21(4)	157.97(4)	150.15(6)
C(1)‐Z(1)‐C(15)	100.19(8)	102.43(7)	102.67(7)	117.90(11)
C(11)‐Z(2)‐C(16)	99.68(9)	102.83(7)	102.71(7)	118.19(11)
O(1)‐Z(1)‐C(15)	174.68(7)	179.75(7)	178.49(5)	155.05(9)
O(1)‐Z(2)‐C(16)	174.33(7)	176.08(6)	171.98(6)	151.15(9)
C(12)‐C(13)‐O(1)	120.25(16)	120.07(12)	120.24(12)	121.39(13)
C(14)‐C(13)‐O(1)	119.70(16)	120.10(12)	119.99(12)	120.44(12)
C(14)‐C(1)‐Z(1)	120.80(13)	120.95(10)	121.06(10)	117.57(12)
C(12)‐C(11)‐Z(2)	120.43(13)	121.36(10)	120.97(10)	117.83(12)
C(2)‐C(1)‐Z(1)	120.70(14)	120.47(11)	120.51(11)	122.57(12)
C(10)‐C(11)‐Z(2)	120.79(14)	120.86(11)	120.91(11)	122.26(12)
torsional angles
C(15)‐Z(1)‐C(1)‐C(14)	175.74(15)	178.72(11)	177.66(11)	168.01(12)
C(16)‐Z(2)‐C(11)‐C(12)	−178.42(15)	−173.14(11)	170.27(11)	177.92(12)
O(1)‐C(13)‐C(14)‐C(5)	−177.73(17)	−177.62(12)	175.31(12)	−159.35(14)
O(1)‐C(13)‐C(12)‐C(7)	−176.95(17)	177.52(12)	176.10(12)	−161.48(14)
C(6)‐C(5)‐C(14)‐C(1)	−179.53(16)	179.32(12)	179.32(12)	172.96(11)
C(6)‐C(7)‐C(12)‐C(11)	−179.33(16)	−179.10(12)	−179.54(12)	−177.95(11)
C(6)‐C(5)‐C(14)‐C(13)	1.7(3)	−0.50(19)	0.69(19)	−10.82(19)
C(6)‐C(7)‐C(12)‐C(13)	−0.1(3)	0.70(18)	0.87(19)	6.44(19)

• [a] Z(1) and Z(2) are O(3) and O(4), respectively.

Figure 1

Structure of 1: a) side view and b) top view (thermal ellipsoids are shown at the 50 % probability level).

Figure 2

Structure of 2 (S‐A): a) side view and b) top view (thermal ellipsoids are shown at the 50 % probability level).

Figure 3

Structure of 3: a) side view and b) top view (thermal ellipsoids are shown at the 50 % probability level).

The structures of 1, 2 (S‐A), and 2 (S‐B) are very close to C_2v symmetry, although the oxygen atom at the 9‐position flips slightly from the ATQ plane in each molecule. The structure of 3 is rather close to C_s symmetry, with the oxygen atom at the 9‐position flipping from the ATQ plane and the MeO groups moving in the opposite directions from the plane, although the magnitudes are not the same. The structures around the Z atoms in 1–3 are all BB by our definition, with the ZC_Me bonds in the ATQ plane (Figures 1, 2, and 3; see also Scheme 2).3, 17 The planarity of the anthraquinonyl group, containing the ZC_Me bonds, is very good for 1 and 2, but the structure is slightly bent in 3, as shown in Figures 1, 2, and 3 and by the data in Table 2.

The nonbonded O(1)⋅⋅⋅Se(1) and O(1)⋅⋅⋅Se(2) distances in 1 are 2.6356(13) and 2.6344(13) Å, respectively, which are 0.78–0.79 Å shorter than the sum of the van der Waals radii of the atoms (3.42 Å).18 The O(1)‐Se(1)‐C(15) and O(1)‐Se(2)‐C(16) angles are 174.68(7) and 174.33(7)°, respectively, which are close to 180° and desirable for the formation of a linear bond. The Se(1)‐O(1)‐Se(2) angle is 150.72(6)°, which is a deviation of about 30° from 180°. The angle is mainly determined by the O(1)C(13), Se(1)C(1), and Se(2)C(11) distances, as well as the angles around the atoms. If nonbonded 3c–4e n_p(O)⋅⋅⋅σ*(SeC)‐type interactions occur on both sides of the central n_p(O) orbital and the two interactions are connected effectively through the common n_p(O) orbital, the resulting nonbonded σ*(CSe)⋅⋅⋅n_p(O)⋅⋅⋅σ*(SeC) interaction leads to the formation of the 5c–6e C₂Se₂O system. Indeed, a 30° deviation of ∢Se(1)O(1)Se(2) would be borderline for the formation of the linear bond, but the central p_x orbital at the O(1) atom will work to form a 5c–6e system because the deviation is around 15° on each side of the p_x orbital if the Se⋅⋅⋅Se direction is set to the x axis.

The nonbonded O⋅⋅⋅S distances in 2 (S‐A) are 2.6364(11) and 2.6485(11) Å,19 which are 0.67–0.68 Å shorter than the sum of the van der Waals radii of the atoms (3.32 Å).18 The O(1A)‐S(1A)‐C(15A) and O(1A)‐S(2A)‐C(16A) angles for 2 (S‐A) are 179.75(7) and 176.08(6)°, respectively,19 which are close to 180° and desirable for the formation of a linear bond. The S(1A)‐O(1A)‐S(2A) angle for 2 (S‐A) is 158.21(4)°,19 which is more suitable for the central p_x orbital at the O(1) atom to form a linear 5c–6e C₂S₂O system than is the case of 1.

In the case of 3, the O(1)⋅⋅⋅O(3) and O(1)⋅⋅⋅O(4) nonbonded distances are 2.6169(15) and 2.6129(15) Å, which are 0.42–0.43 Å shorter than the sum of the van der Waals radii of the atoms (3.04 Å).18 The O(1)‐O(3)‐C(15), O(1)‐O(4)‐C(16), and O(3)‐O(1)‐O(4) angles are 155.05(9), 151.15(9), and 150.15(6)°, respectively, which deviate from 180° by about 30°. The deviations of all three angles are borderline for the formation of the 5c–6e C₂O₂O system in 3. Similarly, the O⋅⋅⋅O nonbonded distances of 2.613–2.617 Å would also be borderline for the interaction. Therefore, the 5c–6e C₂O₂O interaction would be weak in 3, even if it forms.

AIM analysis: The BB forms observed for 1–33, 17 must be more stable than the AA forms; the ZC_Me bonds are in the ATQ plane in BB and are almost perpendicular to the plane in AA (Scheme 2). The structures of 1–3 were optimized by employing the Gaussian 03 program20 with the 6‐311+G(2df) basis set for the oxygen and Z (Z=Se, S, and O) atoms and the 6‐311+G(2d,p) basis set for the carbon and hydrogen atoms. Calculations were performed at the density functional theory (DFT) level of the Becke three‐parameter hybrid functionals with the Lee–Yang–Parr correlation functional (B3LYP). The BB forms of 1–3 were optimized as the global minima, which reproduce well the observed structures of 1–3. The AA forms are local ones. The structures of AA and BB in 4–6 and A and B in 7–12 were also optimized by using the method applied to 1–3.

AIM analysis was performed by applying the AIM2000 program21 to the optimized BB structures of 1–6 and B structures of 7–12 using the Gaussian 03 program. Table 3 shows the results of the AIM analysis, giving the electron charge density and the total electronic energy density at the BCP between the Z and oxygen atoms (ρ_b(r_c) and H_b(r_c), respectively). Table 3 also gives the natural charges at the Z and oxygen atoms (Qn(Z) and Qn(O), respectively), calculated by the natural population analysis.22 Figures 4 and 5 exhibit BCPs, bond paths, and the contour maps of ρ_b(r_c) drawn on the optimized structures of 1 and 4, respectively. Table 4 summarizes some of the data relating to the BCPs of the weak interactions reported in this work.10a, 11, 13a Table 4 also gives data recalculated by a method similar to that used in this work, using the 6‐311++G(2df,2p) basis set at the B3LYP and/or MP2 levels, for convenience of comparison.23 The values recalculated with the B3LYP/6‐311++G(2df,2p) method were employed to gain a better understanding of the nature of the interactions.

Table 3. Results of the AIM analysis of the nonbonded Z⋅⋅⋅O interactions in 1–12.^[a]

Compound	BCP in (A, B)	Distance [Å]			ρb(rc) [e ao^−3]	∇^2ρb(rc) [e ao^−5]	Hessian eigenvalue					Hb(rc) [au]	Qn(A)	Qn(B)
		r(A, B)	r(A, BCP)	r(B, BCP)			λ1	λ2	λ3	λ1/λ2−1	|λ1|/λ3
1	(Se, O)	2.6493	1.3901	1.2611	0.0268	0.0846	−0.0228	−0.0210	0.1284	0.0857	0.178	0.0007	0.4837	−0.6232
	(Se, C)	1.9198	0.9827	0.9372	0.1565	−0.1336	−0.2206	−0.1796	0.2666	0.2283	0.827	−0.0965	0.4837	−0.2404
	(C, O)	1.2312	0.4193	0.8120	0.4012	−0.3659	−1.0633	−0.9931	1.6906	0.0707	0.629	−0.7034	0.6560	−0.6232
2	(S, O)	2.6258	1.3660	1.2685	0.0255	0.0856	−0.0216	−0.0202	0.1275	0.0693	0.169	0.0013	0.3822	−0.6050
	(S, C)	1.7724	0.9136	0.8589	0.1935	−0.2942	−0.3102	−0.2524	0.2685	0.2290	1.155	−0.1311	0.3822	−0.1404
	(C, O)	1.2267	0.4180	0.8087	0.4062	−0.3623	−1.0856	−1.0077	1.7310	0.0773	0.627	−0.7159	0.6721	−0.6050
3	(O, O)	2.5775	1.2668	1.3145	0.0181	0.0803	−0.0165	−0.0158	0.1125	0.0443	0.147	0.0028	−0.5095	−0.5567
	(O, C)	1.3454	0.8859	0.4606	0.3039	−0.5446	−0.6831	−0.6535	0.7920	0.0453	0.863	−0.4675	−0.5095	0.3878
	(C, O)	1.2145	0.4145	0.8000	0.4184	−0.3357	−1.1371	−1.0376	1.8390	0.0959	0.618	−0.7472	0.6538	−0.5567
4	(Se, O)	2.7651	1.4590	1.3095	0.0216	0.0690	−0.0174	−0.0164	0.1027	0.0610	0.169	0.0008	0.4120	−0.5901
	(Se, C)	1.9350	0.9989	0.9361	0.1524	−0.1312	−0.2127	−0.1760	0.2575	0.2085	0.826	−0.0906	0.4120	−0.1742
	(C, O)	1.3757	0.4776	0.8988	0.2869	−0.6090	−0.6091	−0.6003	0.6003	0.0147	1.015	−0.4238	0.3816	−0.5901
5	(S, O)	2.7137	1.4210	1.3047	0.0216	0.0724	−0.0178	−0.0167	0.1069	0.0659	0.167	0.0012	0.3207	−0.5889
	(S, C)	1.7847	0.9291	0.8558	0.1889	−0.2757	−0.3004	−0.2482	0.2728	0.2103	1.101	−0.1236	0.3207	−0.1376
	(C, O)	1.3713	0.4761	0.8959	0.2904	−0.6227	−0.6226	−0.6133	0.6132	0.0152	1.015	−0.4316	0.3841	−0.5889
6	(O, O)	2.5783	1.2715	1.3110	0.0182	0.0805	−0.0165	−0.0162	0.1132	0.0185	0.146	0.0028	−0.5357	−0.5958
	(O, C)	1.3572	0.8928	0.4653	0.2947	−0.5330	−0.6486	−0.6175	0.7332	0.0504	0.885	−0.4465	−0.5357	0.3777
	(C, O)	1.3638	0.4759	0.8889	0.2971	−0.6772	−0.6509	−0.6412	0.6149	0.0151	1.059	−0.4452	0.5276	−0.5958
7	(Se, O)	2.6518	1.3904	1.2633	0.0269	0.0843	−0.0229	−0.0211	0.1283	0.0853	0.178	0.0006	0.4928	−0.5645
	(Se, C)	1.9189	0.9821	0.9369	0.1568	−0.1341	−0.2210	−0.1800	0.2669	0.2278	0.828	−0.0969	0.4928	−0.1737
	(C, O)	1.2250	0.4174	0.8076	0.4073	−0.3485	−1.0870	−1.0144	1.7529	0.0716	0.620	−0.7187	0.5517	−0.5645
8	(S, O)	2.6398	1.3733	1.2753	0.0249	0.0834	−0.0211	−0.0197	0.1242	0.0711	0.170	0.0013	0.3854	−0.5582
	(S, C)	1.7713	0.9128	0.8586	0.1938	−0.2953	−0.3108	−0.2529	0.2684	0.2289	1.158	−0.1317	0.3854	−0.1318
	(C, O)	1.2226	0.4167	0.8059	0.4099	−0.3460	−1.0982	−1.0218	1.7740	0.0748	0.619	−0.7253	0.5507	−0.5582
9	(O, O)	2.6119	1.2849	1.3310	0.0168	0.0733	−0.0150	−0.0140	0.1023	0.0714	0.147	0.0025	−0.5086	−0.5400
	(O, C)	1.3440	0.8851	0.4599	0.3049	−0.5434	−0.6862	−0.6577	0.8005	0.0433	0.857	−0.4698	−0.5086	0.3945
	(C, O)	1.2169	0.4151	0.8018	0.4156	−0.3332	−1.1221	−1.0356	1.8245	0.0835	0.615	−0.7400	0.5511	−0.5400
10	(Se, O)	2.7545	1.4522	1.3061	0.0222	0.0700	−0.0182	−0.0168	0.1050	0.0833	0.173	0.0008	0.4112	−0.5882
	(Se, C)	1.9345	0.9989	0.9357	0.1526	−0.1319	−0.2129	−0.1765	0.2575	0.2062	0.827	−0.0806	0.4112	−0.1670
	(C, O)	1.3758	0.4779	0.8989	0.2864	−0.6084	−0.6092	−0.5978	0.5987	0.0191	1.018	−0.4226	0.3791	−0.5882
11	(S, O)	2.7204	1.4243	1.3086	0.0214	0.0711	−0.0178	−0.0166	0.1054	0.0723	0.169	0.0012	0.3187	−0.5884
	(S, C)	1.7844	0.9297	0.8548	0.1891	−0.2758	−0.3004	−0.2488	0.2735	0.2074	1.098	−0.1236	0.3187	−0.1323
	(C, O)	1.3739	0.4774	0.8974	0.2881	−0.6177	−0.6157	−0.6042	0.6022	0.0190	1.022	−0.4262	0.3805	−0.5884
12	(O, O)	2.6304	1.2996	1.3353	0.0164	0.0703	−0.0142	−0.0136	0.0982	0.0441	0.145	0.0023	−0.5383	−0.5811
	(O, C)	1.3576	0.8935	0.4650	0.2943	−0.5259	−0.6465	−0.6157	0.7363	0.0500	0.878	−0.4452	−0.5383	0.3826
	(C, O)	1.3713	0.4782	0.8942	0.2908	−0.6469	−0.6271	−0.6157	0.5959	0.0185	1.052	−0.4310	0.3853	−0.5811

• [a] Optimized with 6‐311+G(2df) basis set for the oxygen and Z (Se, S, and O) atoms and with the 6‐311+G(2d,p) basis set for the carbon and hydrogen atoms at the DFT (B3LYP) level of the Gaussian 03 program.

Figure 4

Contour map of ρ_b(r_c) of 1 in the anthraquinone plane, together with BCPs (•), ring critical points (▪), and bond paths. The contours [e a_o⁻³] are at 2^l (l=±8, ±7, …︁0), 0.3028, 0.0269 (dotted line), and 0.0047 (heavy line).

Figure 5

a) BCPs (•), ring critical points (▪), and bond paths of 4 and b) the partial contour map of ρ_b(r_c) of 4 in the O₁‐Se₂‐C₉ and O₁‐Se₁‐C₉ planes. The contours [e a_o⁻³] are at 2^l (l=±8, ±7, …︁0), 0.3028, 0.0216 (dotted line), and 0.0047 (heavy line).

Table 4. Results of the AIM analysis of weak interactions.

Adducts	BCP	Distance [Å]	ρb(rc) [e ao^−3]	∇^2ρb(rc) [e ao^−5]	Hessian eigenvalue	Hb(rc) [au]	Qn(A)	Qn(B)
	(A, B)	r(A, B)			|λ1|/λ3
van der Waals
NeHF^[a,b]	(Ne, H)	2.110	0.0099	0.0484	0.180
NeHF^[c,d]	(Ne, H)	2.3211	0.0058	0.0295	0.161	0.0014	0.0009	0.5513
ArHF^[a,b]	(Ar, H)	2.562	0.0077	0.0311	0.170
ArHF^[c,d]	(Ar, H)	2.5573	0.0079	0.0302	0.174	0.0016	0.0031	0.5508
hydrogen bonds
NNHF^[a,b]	(N, H)	2.076	0.0169	0.0647	0.200
NNHF^[c,d]	(N, H)	2.0639	0.0175	0.0636	0.209	0.0024	−0.0468	0.5567
(H2O)2^[b,e]	(O, H)	2.039	0.0198	0.0623	0.223
(H2O)2^[c,f]	(O, H)	1.9521	0.0233	0.0832	0.214	0.0012	−0.9365	0.4854
(H2O)2^[c,d]	(O, H)	1.9576	0.0236	0.0801	0.222	0.0015	−0.9334	0.4831
(HF)2^[b,e]	(H, F)	1.778	0.0262	0.1198	0.204
(HF)2^[c,f]	(H, F)	1.8440	0.0233	0.0936	0.213	0.0007	0.5541	−0.5487
(HF)2^[c,d]	(H, F)	1.8291	0.0250	0.0939	0.224	0.0008	0.5604	−0.5550
HCNHF^[a,b]	(N, H)	1.881	0.0284	0.0920	0.236
HCNHF^[c,d]	(N, H)	1.8200	0.0338	0.0944	0.266	−0.0013	−0.3801	0.5649
trihalide linear anions
[Br3]^−[c,d,g]	(Br, Br)	2.6212	0.0579	0.0668	0.295	−0.0107	−0.1010	−0.4495
[Cl3]^−[g–i]	(Cl, Cl)		0.063	0.117	0.259
[Cl3]^−[c,d,g]	(Cl, Cl)	2.3459	0.0762	0.0951	0.311	−0.0180	−0.1086	−0.4457
[F3]^−[g–i]	(F, F)		0.100	0.539	0.199
[F3]^−[c,d,g]	(F, F)	1.7275	0.1099	0.5404	0.217	−0.0060	−0.1018	−0.4491
13 (C2v)^[j,k]	(B, O)	2.431	0.022	0.058	0.266

• [a] With the MP2/6‐311G(2d,2p) method of the Gaussian 98 program.^[37] [b] See ref. [10 a]. [c] Recalculated in this work. [d] With the B3LYP/6‐311++G(2df,2p) method of the Gaussian 03 program. [e] With the 6‐31G** method of the Gaussian 98 program. [f] With the MP2/6‐311++G(2df,2p) method of the Gaussian 03 program. [g] The central atom being called A and the outside ones B. [h] With the 6‐311++G** method. [i] See ref. [11]. [j] With the 6‐31G(d) method at the DFT (B3PW91) level of the Gaussian 98 program. [k] See ref. [13 a].

Before discussing the results for the 5c–6e C₂Z₂O interactions in 1–6, it may be instructive to start with a discussion of the 3c–4e CZO interactions in 7–12.

AIM analysis of 3c–4e CZO in 7–12 with ρ_b(r_c): The charge densities at the BCP (ρ_b(r_c)) between the nonbonded Z⋅⋅⋅O atoms in 7 (Z=Se) and 8 (Z=S) of the ATQ system were evaluated to be 0.027 and 0.025 e a_o⁻³ (a_o=0.52177 Å), respectively (Table 3). While the ρ_b(r_c) values for 7 and 8 are smaller than that for HCN⋅⋅⋅HF (0.034 e a_o⁻³), they are larger than those for H₂O⋅⋅⋅HOH (0.024 e a_o⁻³) and HF⋅⋅⋅HF (0.025 e a_o⁻³), although the ρ_b(r_c) value for 8 is essentially equal to the latter (Table 4).10a The results suggest that the Z⋅⋅⋅O interactions in 7 (Z=Se) and 8 (Z=S) are stronger than the hydrogen bond in H₂O⋅⋅⋅HOH (and HF⋅⋅⋅HF), but weaker than the bond in HCN⋅⋅⋅HF.10a The values for 10 (Z=Se) and 11 (Z=S) of the 9‐MeOATC system are 0.022 and 0.021 e a_o⁻³, respectively (Table 3), which are smaller than that for H₂O⋅⋅⋅HOH, but larger than that for NN⋅⋅⋅HF (0.018 e a_o⁻³) (Table 4).10a The Z⋅⋅⋅O interactions in 10 (Z=Se) and 11 (Z=S) are substantially stronger than the hydrogen bond in NN⋅⋅⋅HF, but weaker than the hydrogen bond in H₂O⋅⋅⋅HOH.10a In the case of Z=O, the ρ_b(r_c) values for 9 and 12 are 0.017 and 0.018 e a_o⁻³, respectively. These values are slightly smaller than that for NN⋅⋅⋅HF, but are apparently larger than those corresponding to the van der Waals interactions in Ne⋅⋅⋅HF and Ar⋅⋅⋅HF (ρ_b(r_c)=0.006 and 0.008 e a_o⁻³, respectively) (Table 4).10a The results are summarized in Equation (1).

((1))

The ∇²ρ_b(r_c) values for 7–12 are 0.070–0.084 e a_o⁻⁵ (Table 3). The values lie in the range of hydrogen‐bonded adducts (0.064–0.094 e a_o⁻⁵). In general, negative values of ∇²ρ_b(r_c) appear at the BCPs of covalent bonds, whereas positive values correspond to ionic bonds.10 The positive values of ∇²ρ_b(r_c) in 7–12 are well understood based on this generalization. The ionic nature of the nonbonded Z⋅⋅⋅O interactions for Z=Se and S are well understood based on the CT of hypervalent n_p(O)→σ*(ZC) 3c–4e interactions. The (Qn(Se), Qn(O)) values are (0.493, −0.565) for 7 and (0.411, −0.588) for 10 and (Qn(S), Qn(O)) are (0.385, −0.558) for 8 and (0.319, −0.588) for 11.22 The positive and negative values developed at the chalcogen (Z=Se and S) and oxygen atoms support the ionic nature of the interactions.

The contributions of π character to the C₁Z bonds of 7–12 were examined. The ellipticities of the p–π conjugation of p(Z)π(ATQ) type in 7 (Z=Se: λ₁/λ₂−1=ε=0.23) and 8 (Z=S: 0.23) of the ATQ system are larger than those of 10 (Z=Se: ε=0.21) and 11 (Z=S: 0.21) of the 9‐MeOATC system. The values are also much larger than those for H₂CSe (ε=0.13) and H₂CS (ε=0.05),12 although the basis sets used for the calculations were not the same. The results show that p–π conjugation is significant in the C₁Z bonds of 7, 8, 10, and 11. The values for 9 (Z=O: ε=0.04) and 12 (Z=O: 0.05) are similar to the value of the ellipticity of H₂CO (0.04).12, 24 The values of the ellipticity in the Z⋅⋅⋅O interactions in 7 (Z=Se: ε=0.09) and 8 (Z=S: 0.07) are similar to those in 10 (Z=Se: ε=0.08) and 11 (Z=S: 0.07). The magnitude of the π character of the Z⋅⋅⋅O bonds in 7 and 8 is comparable to that in 10 and 11, although 10 and 11 seem to have no suitable p orbitals with which to construct the π(Z⋅⋅⋅O) interactions. The values for the Z⋅⋅⋅O interactions in 7, 8, 10, and 11 are larger than that for H₂CS and smaller than that for H₂CSe.12 While the ellipticity of the O⋅⋅⋅O interactions in 9 (ε=0.07) is very close to the values for 8 and 11, that for 12 (0.04) is smaller.

After elucidation of the nature of the BCPs in 7–12, we extended this study to the BCPs of the 5c–6e C₂Z₂O interactions in 1–6.

AIM analysis of 5c–6e C₂Z₂O in 1–6 with ρ_b(r_c): The optimized structures of 1–3 are of C_2v symmetry and those of 4–6 are of C_s symmetry.25 Therefore, the nature of the two BCPs in the nonbonded CZ⋅⋅⋅O⋅⋅⋅ZC interactions in 1–6 is the same. One of them is listed in Table 3.

The ρ_b(r_c) values for the nonbonded CZ⋅⋅⋅O⋅⋅⋅ZC interactions in 1 (Z=Se) and 2 (Z=S) are 0.027 and 0.026 e a_o⁻³, respectively, and those for 4 (Z=Se) and 5 (Z=S) are both 0.022 e a_o⁻³. The values of the CO⋅⋅⋅O⋅⋅⋅OC interactions in 3 and 6 are both 0.018 e a_o⁻³. The results for the 5c–6e C₂Z₂O interactions of 1–6 are summarized in Equation (2), along with the data for some hydrogen‐bonded adducts.

((2))

The results show that the values of ρ_b(r_c) for 1 and 2 of the ATQ system are larger than those for H₂O⋅⋅⋅HOH and HF⋅⋅⋅HF, whereas those for the 9‐MeOATC system with Z=Se and S are smaller than that for H₂O⋅⋅⋅HOH. The values for the O⋅⋅⋅O interactions are essentially equal to that for NN⋅⋅⋅HF.

Equations (1) and (2) were combined to give Equation (3). The characteristics of the 5c–6e C₂Z₂O and 3c–4e CZO interactions of 1–12, predicted on the basis of the values of ρ_b(r_c), are as follows: ρ_b(r_c) values for 5c–6e Z₂C₂O for Z=Se and S are essentially equal to those for 3c–4e ZCO, respectively, if the system is the same, whereas the former is slightly larger than the latter for Z=O. The results are in accord with the expectation that the Z⋅⋅⋅O interactions in 5c–6e C₂Z₂O (Z=Se, S, and O) are very similar to those in 3c–4e CZO. No saturation effect was detected in 5c–6e C₂Z₂O, relative to 3c–4e CZO, on the basis of the ρ_b(r_c) values. These results demonstrate that the extended hypervalent 5c–6e interactions in 1–6 of the σ*(CZ)⋅⋅⋅n_p(O)⋅⋅⋅σ*(ZC) type are formed by connecting two 3c–4e n_p(O)⋅⋅⋅σ*(ZC) elements effectively through the central n_p(O) orbital.

((3))

The π character of the nonbonded Z⋅⋅⋅O interactions in 5c–6e C₂Z₂O is essentially the same as that in 3c–4e CZO, and so are the C₁Z and CO bonds (Table 3).

Yamamoto and co‐workers reported the AIM analysis of the O⋅⋅⋅B⋅⋅⋅O 3c–4e interactions at the 1,8,9‐positions of 9‐(1,2‐C₆H₄O₂B)‐1,8‐(MeO)₂C₁₄H₇ (13). 13 The ρ_b(r_c) value is 0.022 e a_o⁻³ for the C_2v symmetric structure. While the ρ_b(r_c) value for 13 is larger than those for the O⋅⋅⋅O interactions in 3 and 6, it is smaller than those for the O⋅⋅⋅Z (Z=Se and S) interactions in 1, 4, 2, and 5, although the method of calculation was not the same. Because the conformation around the MeO groups in 13 is BB, the n_s(O) orbitals must act as donors in 13. The conformations around MeZ (Z=Se, S, and O) in 1–6 are all BB, therefore, the n_p(O) orbital of the central oxygen atom will play an important role in 1–6 as the donor. The direction of CT in 1–6 is completely different from that in 13: CT in 1–6 is of the σ*(CZ)←n_p(O)→σ*(ZC) type, whereas that in 13 must be of the n_s(O)→n_p(B)←n_s(O) type.26, 27

Linear trihalide ions, X₃⁻, are typical examples of 3c–4e interactions. The ρ_b(r_c) values for F₃⁻, Cl₃⁻, and Br₃⁻ are 0.110, 0.076, and 0.058 e a_o⁻³, respectively (Table 4). These values are about four, three, and two times larger than that of 1, respectively. The values decrease in the order F₃⁻>Cl₃⁻>Br₃⁻. The stability of X₃⁻ relative to X₂ and X⁻, (ΔE(X₃⁻)=E(X₃⁻)−E(X₂)−E(X⁻)) were evaluated to be −142.0, −124.1, and −137.7 kJ mol⁻¹, for X=F, Cl, and Br, respectively. The stabilization energies do not correlate well with ρ_b(r_c), which shows that ρ_b(r_c) does not reflect the stability in some cases.

After examination of the nature of the 5c–6e C₂Z₂O and 3c–4e CZO interactions based mainly on ρ_b(r_c) values, the next step was to employ the total electronic energy density at the BCP (H_b(r_c)), which will be a more appropriate index for the weak interactions.

AIM analysis on 5c–6e C₂Z₂O and 3c–4e CZO with H_b(r_c): The total electronic energy density at the BCP (H_b(r_c)) is the sum of the electronic potential (V) and kinetic energy (G) densities at the BCP (H_b(r_c)=G_b(r_c)+V_b(r_c)).28 The values of H_b(r_c) for 5c–6e C₂Z₂O and 3c–4e CZO interactions in 1–12 are also collected in Table 3. G_b(r_c) and V_b(r_c) are positive and negative, respectively, although not shown in Table 3. Because the magnitudes of G_b(r_c) are slightly larger than the corresponding V_b(r_c) values, H_b(r_c) values for 1–12 show a slightly positive nature. As also recognized in Table 3, H_b(r_c) values are negative for classical chemical bonds in 1–12. The values for X₃⁻ (X=F, Cl, and Br) and HCN⋅⋅⋅HF are also negative. However, those for the van der Waals and hydrogen‐bonded adducts in Table 4 are positive, except in the case of HCN⋅⋅⋅HF: the positive values of H_b(r_c) correspond to the ionic interactions.11, 12 The H_b(r_c) values for the nonbonded O⋅⋅⋅ZC interactions in 1–12 are all positive (Table 3). The H_b(r_c) values will clarify the nature of the interactions.

The values of H_b(r_c) for the nonbonded O⋅⋅⋅ZC interactions of 1–12 are summarized in Equation (4), together with those for hydrogen‐bonded adducts. The nonbonded O⋅⋅⋅Z interactions are classified into three groups by their H_b(r_c) values. 0.0028≥H_b(r_c: Z=O)≥0.0023, 0.0013≥H_b(r_c: Z=S)≥0.0012, and 0.0008≥H_b(r_c: Z=Se)≥0.0006. Therefore, H_b(r_c: Z=O)≈H_b(r_c: NN⋅⋅⋅HF), H_b(r_c: H₂O⋅⋅⋅HOH)≥H_b(r_c: Z=S)≥H_b(r_c: HF⋅⋅⋅HF), and H_b(r_c: HF⋅⋅⋅HF)≥H_b(r_c: Z=S). H_b(r_c) values for the O⋅⋅⋅Z interactions decrease in the order Z=O≫S>Se. It has been demonstrated that the σ*(CZ)⋅⋅⋅n_p(O)⋅⋅⋅σ*(ZC) 5c–6e interactions are effectively formed by the connection of two n_p(O)⋅⋅⋅σ*(ZC) 3c–4e entities through the central n_p(O) orbital, again based on values of H_b(r_c).

((4))

To clarify the relation between H_b(r_c) and ρ_b(r_c) in 1–12, H_b(r_c) was plotted versus ρ_b(r_c) for the compounds given in Equation (3). Figure 6 shows the results. The plots for the hydrogen‐bonded and van der Waals adducts are represented by an upward convex curve, shown by the dotted line. The point for NN⋅⋅⋅HF is very near to the top. While the points for the hydrogen‐bonded adducts are on the right‐side down slope, those for the van der Waals adducts are on the left‐side down slope.29

Figure 6

Plots of H_b(r_c) versus ρ_b(r_c) for 1–12 as well as hydrogen‐bonded (HCN⋅⋅⋅HF (i), HF⋅⋅⋅HF (ii), H₂O⋅⋅⋅HOH (iii), and NN⋅⋅⋅HF (iv)) and van der Waals adducts (Ar⋅⋅⋅HF (v) and Ne⋅⋅⋅HF (vi)). The plot for i–vi is connected by a smooth dotted line. The slope for 1–12 and i–iv is shown by a solid line (correlation: y=−0.21x+0.0060; r=0.91). The ATQ system with Z=Se and S construct g(a) and the 9‐MeOATC system with Z=Se and S form g(b). Groups g(a) and g(b) have been reclassified into g(Se) and g(S). Points for Z=O in both systems belong to g(c) (=g(O)).

The points for 1–12 appear along with the dotted line in Figure 6. They form three groups: g(a), g(b), and g(c). Groups g(a) and g(b) consist of the ATQ system with Z=Se and S (1, 7, 2, and 8) and the 9‐MeOATC system with Z=Se and S (4, 5, 10, and 11), respectively. On the other hand, the ATQ and 9‐MeOATC systems with Z=O (3, 6, 9, and 12) belong to g(c) (=g(O)). The points for H₂O⋅⋅⋅HOH and HF⋅⋅⋅HF appear very near those in g(a). Therefore, the nature of the 5c–6e C₂Z₂O and 3c–4e CZO interactions in g(a) must be similar to hydrogen bonds. This expectation is also supported by the fact that the slope of the points in g(a) is almost parallel to that of the dotted line. The nature of 5c–6e C₂Z₂O and 3c–4e CZO interactions in g(b) was analyzed similarly. However, the points for g(c) are near that of NN⋅⋅⋅HF, the top of the dotted line, and seem to be on the down slope leading to Ar⋅⋅⋅HF and Ne⋅⋅⋅HF. Consequently, it would be difficult to analyze the linear C₂Z₂O and CZO (Z=O) interactions in g(c) similarly to the cases of g(a) and g(b) (Z=Se and S) on the basis of the values of H_b(r_c). Groups g(a) and g(b) can be reclassified as g(Se) and g(S), as shown in Figure 6.

Why is the saturation effect not observed in the formation of 5c–6e C₂Z₂O interactions from a pair of 3c–4e CZO interactions? We noted the bond distances of the compounds predicted by the QC calculations. Shorter Z⋅⋅⋅O distances were predicted for 1 (2.649 Å) versus 7 (2.652 Å) (Z=Se), 2 (2.626 Å) versus 8 (2.640 Å) (Z=S), and 3 (2.578 Å) versus 9 (2.612 Å) (Z=O) in the ATQ system. The differences increase in the order: Δr(1, 7: −0.003 Å)<Δr(2, 8: −0.014 Å)<Δr(3, 9: −0.034 Å). The smaller distances in 5c–6e C₂Z₂O relative to 3c–4e CZO must operate to prevent saturation. On the other hand, the Z⋅⋅⋅O distances in the 9‐MeOATC system were predicted to be longer in 4 (2.765 Å) versus 10 (2.755 Å) (Z=Se) and in 5 (2.714 Å) versus 11 (2.720 Å) (Z=S). The flexible MeO group at the 9‐position must be responsible for the elongation of the bonds.

Figure 7 shows the optimized structures of 4 (BB) and 10 (B). The larger flip angle for the MeO group at the 9‐position of 4 (BB), relative to that of 10 (B), results in the longer Se⋅⋅⋅O distance for 4 (BB) relative to 10 (B). The torsional angle of the OC_Me bond with respect to the ATC plane in 4 (BB) is φ(C₁C₉OC_Me)=94.3°, which is closer to a right angle than in the case of 10 (B) (101.7°). The observed structural features in 4 (BB) and 10 (B) must be controlled by the weak interactions, such as the steric repulsions and attractive interactions in the molecules, which are closely related to the stabilities.

Figure 7

Optimized structures of a) 4 (BB) and b) 10 (B). The optimized torsional angles (φ(C₁C₉OC_Me)) for 4 (BB) and 10 (B) are 94.3 and 101.7°, respectively.

NBO analysis of 5c–6e C₂Z₂O and 3c–4e CZO: How are the 5c–6e C₂Z₂O and 3c–4e CZO interactions stabilized? The second‐order perturbation of the NBO analysis22 was examined for the σ*(CZ)⋅⋅⋅n(O)⋅⋅⋅σ*(ZC) 5c–6e and n(O)⋅⋅⋅σ*(ZC) 3c–4e interactions in the ATQ system of 1, 2, 7, and 8. The stabilization energy, E(2), associated with the delocalization of the NBO (i)→NBO (j) type, is estimated by Equation (5), in which 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 5 shows the results, with the values for 5c–6e C₂Z₂O corresponding to half of the 5c–6e interactions.

((5))

Table 5. Contributions of donor–acceptor interactions of the n(O)⋅⋅⋅σ*(ZC) type in 5c–6e C₂Z₂O and 3c–4e CZO (Z=Se and S) systems.

NBO (i)	NBO (j)	E(2) [kJ mol^−1]^[a]	ΔE [au]^[b]	F(i,j) [au]^[c]	Character
1 (BB)^[d]
np(O)	σ*(SeCMe)	18.5	0.40	0.039	5c–6e
ns(O)	σ*(SeCMe)	10.6	0.81	0.041	ns→σ*
2 (BB)^[e]
np(O)	σ*(SCMe)	13.4	0.45	0.035	5c–6e
ns(O)	σ*(SCMe)	8.0	0.86	0.031	ns→σ*
7 (B)^[f]
np(O)	σ*(SeCMe)	24.6	0.40	0.044	3c–4e
ns(O)	σ*(SeCMe)	8.0	0.80	0.035	ns→σ*
8 (B)^[g]
np(O)	σ*(SCMe)	15.4	0.45	0.037	3c–4e
ns(O)	σ*(SCMe)	4.4	0.86	0.027	ns→σ*

• [a] Second‐order perturbation energy in the NBO analysis. [b] ΔE=E(j)−E(i). [c] F(i,j) is the off‐diagonal NBO Fock matrix element. See Equation (5). [d] ∢C₉OSe=104.26°, ∢OSeC_Me=173.73°, ∢SeOSe=151.48°. [e] ∢C₉OS=101.07°, ∢OSC_Me=179.79°, ∢SOS=157.85°. [f] ∢C₉OSe=103.57°, ∢OSeC_Me=173.95°. [g] ∢C₉OS=99.95°, ∢OSC_Me=179.96°.

Contributions of CT from both n_p(O) and n_s(O) to σ*(ZC) in 1, 2, 7, and 8 are 58.2, 42.8, 32.6, and 19.8 kJ mol⁻¹, respectively. The values are close to the evaluated energy differences between BB and AA (or B and A) for these compounds, which are −49.9, −38.9, −25.5, and −19.7 kJ mol⁻¹, respectively (see Table 6). CT is mainly responsible for ΔE, although the magnitudes of ΔE are smaller than the CT contributions.

Table 6. Energies, together with the selected bond lengths, angles, and torsional angles, optimized for AA and BB in 1–6 and A and B in 7, 8, and 10.^[a]

Compound	E [au]	ΔE [kJ mol^−1]	r(C1Z) [Å]	r(ZCMe) [Å]	r(O⋅⋅⋅Z) [Å]	Δr(O⋅⋅⋅Z) [Å]	∢C1ZCMe	∢OZCMe	∢ZOZ	ϕ(C9C1ZCMe)
1 (BB)	−5570.7164	−49.9	1.9198	1.9716	2.6493	−0.3361	99.71	173.73	151.48	180.00
1 (AA)	−5570.6974	0.0	1.9358	1.9622	2.9854	0.0000	103.80	68.66	157.50	58.39
2 (BB)	−1564.0561	−38.9	1.7724	1.8232	2.6258	−0.3081	102.69	179.79	157.85	180.00
2 (AA)	−1564.0413	0.0	1.7847	1.8211	2.9339	0.0000	105.75	70.49	163.19	60.01
3 (BB)	−918.0790	−13.7	1.3454	1.4187	2.5775	−0.1307	119.84	151.62	179.46	180.00
3 (AA)	−918.0738	0.0	1.3618	1.4300	2.7082	0.0000	117.12	84.13	179.24	80.29
4 (BB)	−5535.9609	−33.1	1.9350	1.9623	2.7651	−0.2699	100.23	172.38	143.74	−176.25
4 (AA)	−5535.9483	0.0	1.9451	1.9639	3.0350	0.0000	100.45	76.70	154.52	65.76
5 (BB)	−1529.3040	−25.2	1.7847	1.8163	2.7137	−0.2389	103.07	175.12	150.10	−177.82
5 (AA)	−1529.2944	0.0	1.7948	1.8228	2.9526	0.0000	102.78	77.93	159.03	67.82
6 (BB)	−883.3365	−17.3	1.3572	1.4161	2.5783	−0.1043	119.06	151.01	176.60	−177.68
6 (AA)	−883.3299	0.0	1.3748	1.4266	2.6826	0.0000	115.32	88.81	177.72	86.75
7 (B)	−3129.8466	−25.5	1.9189	1.9716	2.6518	−0.3660	99.64	173.95	–	180.00
7 (A)	−3129.8369	0.0	1.9377	1.9630	3.0178	0.0000	103.32	68.87	–	62.19
8 (B)	−1126.5164	−19.7	1.7713	1.8229	2.6398	−0.3460	102.67	179.96	–	180.00
8 (A)	−1126.5089	0.0	1.7832	1.8208	2.9858	0.0000	105.99	69.20	–	57.66
10 (B)	−3095.0962	−10.8	1.9345	1.9629	2.7545	−0.3001	100.16	173.40	–	178.81
10 (A)	−3095.0921	0.0	1.9436	1.9663	3.0546	0.0000	100.50	73.74	–	63.69

• [a] Optimized with the 6‐311+G(2df) basis set for oxygen and Z (Z=Se, S, and O) atoms and the 6‐311+G(2d,p) basis set for carbon and hydrogen atoms at the DFT (B3LYP) level of the Gaussian 03 program.

Note that n_s(O), as well as n_p(O), contribute much to the σ*(CZ)⋅⋅⋅n(O)⋅⋅⋅σ*(ZC) 5c–6e and n(O)⋅⋅⋅σ*(ZC) 3c–4e interactions. The contributions of n_s(O), relative to n_p(O), are 57, 60, 33, and 29 % for 1 (BB), 2 (BB), 7 (B), and 8 (B), respectively (Table 5). These ratios must essentially be controlled by ∢ZOC₉ and ∢OZC_Me, as well as ∢ZOZ. The ratios for 5c–6e C₂Z₂O (Z=Se and S) are about twice as large as those for 3c–4e CZO (Z=Se and S), respectively. The results show that there is a greater chance of n_s(O) taking part in the σ*(CZ)⋅⋅⋅n(O)⋅⋅⋅σ*(ZC) interactions with ∢ZOZ=151–158° than expected based on the 3c–4e CZO interactions.

Energy‐lowering effect by 5c–6e C₂Z₂O and 3c–4e CZO: Table 6 collects the energies and selected bond distances and angles optimized for AA and BB in 1–6 and A and B in 7, 8, and 10.30

The energy differences between BB and AA (ΔE(n)=E(n: BB)−E(n: AA), where n=1–6) were examined. The values of ΔE(1), ΔE(2), ΔE(4), and ΔE(5) are −49.9, −38.9, −33.1, and −25.2 kJ mol⁻¹, respectively. The differences must be a reflection of the stabilization in 5c–6e C₂S₂O relative to 5c–6e C₂Se₂O and the p–π conjugation of n_p(Se)–π(ATQ) type versus that of n_p(Se)–π(ATC) type. The ratios of ΔE(2)/ΔE(1) and ΔE(5)/ΔE(4) are 0.76–0.78, which shows that the energy‐lowering effect of the 5c–6e C₂S₂O interaction is about three quarters that of 5c–6e C₂Se₂O if the system is the same. The ratios of ΔE(4)/ΔE(1) and ΔE(5)/ΔE(2) are 0.65–0.66. The effect on the 9‐MeOATC system is about two thirds of that on the ATQ system if Z is the same.31

The nonbonded Z⋅⋅⋅O distances in BB are shorter than those in AA (Δr(n)=r(n: BB)−r(n: AA)<0, for n=1–6). The values of Δr(1), Δr(2), Δr(4), and Δr(5) are −0.336, −0.308, −0.270, and −0.239 Å, respectively. The large steric repulsion in AA must be reduced by the longer r(AA). On the other hand, the enlarged steric repulsion caused by the shorter r(BB) would be compensated by the energy‐lowering effect through the formation of a 5c–6e C₂Z₂O interaction, together with p–π conjugation.

The energy differences between B and A (ΔE(n)=E(n: B)−E(n: A), where n=7, 8, and 10) were also examined. The ΔE(7), ΔE(8), and ΔE(10) values are −25.5, −19.7, and −10.8 kJ mol⁻¹, respectively. Whereas the ΔE(1) and ΔE(2) values are nearly twice as large as ΔE(7) and ΔE(8), respectively, ΔE(4) is about three times as large as ΔE(10). The flexibility around the MeO group must be responsible for these predictions (see Figure 7). The σ*(CZ)←n_p(O)→σ*(ZC) 5c–6e interaction is demonstrated to operate effectively by the connection of two n_p(O)→σ*(ZC) 3c–4e interactions through the central n_p(O) orbital in the ATQ and 9‐MeOATC systems with Z=Se and S, although n_s(O) also contributes to the interactions.

Scheme for the formation of 5c–6e C₂Z₂O interactions: Extended hypervalent 5c–6e C₂Z₂O interactions of the σ*(CZ)⋅⋅⋅n_p(O)⋅⋅⋅σ*(ZC) type will form when two hypervalent 3c–4e CZO interactions are connected effectively through the central n_p(O) orbital, as shown in Scheme 3. Scheme 4 shows a scheme for the formation of 5c–6e C₂Se₂O interactions, as exemplified by the formation of I,3 starting from the n_p(Se) orbital (1c–2e) in 1‐(phenylselanyl)anthracene (III).32 Path a shows a process via 1‐(phenylselanyl)anthraquinone (IV)33 and path b a process via 1,8‐bis(phenylselanyl)anthracene (V).3

Scheme 4

Formation of 5c–6e C₂Se₂O starting from 1c–2e n_p(Se), exemplified by phenylselanyl derivatives.

When the two hydrogen atoms at the 9,10‐positions in III are replaced by carbonyl oxygen atoms in path a, III (A) changes to IV (B) with the formation of 3c–4e CSeO interactions.33 Anthraquinone I (BB) forms if the hydrogen atom at the 8‐position of IV (B) is then substituted by a PhSe group in path a. The 3c–4e CSeO interaction in IV (B) changes to a 5c–6e C₂Se₂O interaction in this substitution with two SeC_Ph bonds and an oxygen atom at the 1,8,9‐positions of I (BB). On the other hand, anthracene III (A) with a n_p(Se) orbital (1c–2e) is transformed to V (AA) with two independent n_p(Se) orbitals (a couple of 1c–2e) in path b when the hydrogen atom at the 8‐position in III (A) is substituted by another PhSe group. Anthracene V (AA) changes to I (BB) by replacement of the hydrogen atoms at the 9,10‐positions in V (AA) with carbonyl oxygen atoms. In this process, the two independent n_p(Se) orbitals (a pair of independent 1c–2e) in V (AA) are incorporated into the 5c–6e C₂Se₂O interaction in I (BB). A similar scheme can be drawn for II.

AIM analysis of 1–12 revealed the nature of CZ⋅⋅⋅O⋅⋅⋅ZC 5c–6e (Z=Se, S, and O) and CZ⋅⋅⋅O 3c–4e interactions. NBO analysis and the energies calculated for 1–12 support the discussion. The structural change from III (A) to I (BB) in Scheme 4 shows how 5c–6e C₂Se₂O interactions are constructed from a n_p(Se) orbital (1c–2e) through 3c–4e CSeO interactions or two independent n_p(Se) orbitals (a pair of independent 1c–2e).

Conclusion

The nature of BCPs in the n_p(O)⋅⋅⋅σ*(ZC) interactions (Z=Se, S, and O) in 1–12 has been examined by using the AIM method after determination of the structures of 1–3 by means of X‐ray crystallographic analysis. The ρ_b(r_c) values of the n_p(O)⋅⋅⋅σ*(ZC) interactions (Z=Se, S, and O) in 1–12 are summarized in Equations (1)–(3). The ρ_b(r_c) and ∇²ρ_b(r_c) values of the BCPs in the nonbonded Z⋅⋅⋅O⋅⋅⋅Z interactions in 1–6 are, respectively, very close to those corresponding to the O⋅⋅⋅Z interactions in 7–12. Consequently, the two n_p(O)⋅⋅⋅σ*(ZC) interactions in 1–6 have been demonstrated to be connected effectively at the central n_p(O) orbital to form extended hypervalent 5c–6e interactions of the σ*(CZ)⋅⋅⋅n_p(O)⋅⋅⋅σ*(ZC) type. The direction of the CT is of σ*(CZ)←n_p(O)→σ*(ZC) type. The H_b(r_c) term was also applied to the 5c–6e C₂Z₂O and 3c–4e CZO systems in 1–12, which must be a more appropriate index of weak interactions. The results emphasize that the strength of the interactions increase in the order: O⋅⋅⋅O≪S⋅⋅⋅O<Se⋅⋅⋅O.

The contributions of CT to 5c–6e C₂Z₂O and 3c–4e CZO were evaluated by using NBO analysis. The results have been related to the energy differences between structures BB and AA, which were also calculated. The ΔE(1) value (=E(1: BB)−E(1: AA)) is −49.9 kJ mol⁻¹, ΔE(2)=−38.9 kJ mol⁻¹, ΔE(4)=−33.1 kJ mol⁻¹, and ΔE(5)=−25.2 kJ mol⁻¹. The differences must reflect the stabilization of 5c–6e C₂S₂O relative to 5c–6e C₂Se₂O and the p–π conjugation of the n_p(Se)–π(ATQ) type versus that of the n_p(Se)–π(ATC) type. The ratios of ΔE(2)/ΔE(1) and ΔE(5)/ΔE(4) are 0.76–0.78, which shows that the energy‐lowering effect of 5c–6e C₂S₂O is about three quarters that of 5c–6e C₂Se₂O, if the system is the same. The ratios of ΔE(4)/ΔE(1) and ΔE(5)/ΔE(2) are 0.65–0.66, which shows that the effect in the 9‐MeOATC system is about two thirds that in the ATQ group, if Z is the same. Nonbonded Z⋅⋅⋅O distances were also examined: r(AA) is longer than the corresponding r(BB) distance in 1–6. The large steric repulsion must be reduced in AA by the longer r(AA) and the increased steric repulsion caused by the shorter r(BB) would be compensated by the energy‐lowering effect through the formation of 5c–6e C₂Z₂O as well as the p–π conjugation.

The structures of the phenylselanyl derivatives of ATQ provide a scheme detailing the formation of the 5c–6e C₂Se₂O system, starting from n_p(Se) (1c–2e), by two pathways. One is by way of the 3c–4e CSeO system and the other is through two independent n_p(Se) orbitals (a pair of independent 1c–2e). The scheme clarifies how weak interactions such as 5c–6e C₂Se₂O determine the fine structures of compounds.

Experimental Section

General: Manipulations were performed under nitrogen or argon using standard vacuum‐line techniques. Glassware was dried at 130 °C overnight. Solvents and reagents were purified by standard procedures as necessary. Melting points were measured with a Yanako MP‐S3 and uncorrected. NMR spectra were recorded at 25 °C with a JEOL JNM‐AL 300 spectrometer (¹H, 300 MHz; ¹³C, 75.45 MHz; ⁷⁷Se, 57.25 MHz). The ¹H, ¹³C, and ⁷⁷Se chemical shifts are given in parts per million relative to those of Me₄Si, internal CDCl₃, and external MeSeMe, respectively. Column chromatography was performed on silica gel (Fuji Silysia BW‐300) and acidic and basic alumina (E. Merk). Flash column chromatography was performed with 300—400 mesh silica gel and acidic and basic alumina. Analytical thin‐layer chromatography was performed on precoated silica gel plates (60F‐254) using the systems (v/v) indicated. Elemental analyses were performed by using a J‐Science Lab Co., Ltd., JM10 Micro Corder.

1,8‐Bis(methylselanyl)anthraquinone (1): A suspension of dimethyl diselenide (1.00 g, 5.32 mmol) and sodium hydride (0.49 g, 12.77 mmol) in dry DMF (60 mL) was heated at 110 °C for 1 h. Then 1,8‐dibromoanthraquinone (1.47 g, 5.32 mmol) and CuI (2.33 g, 12.23 mmol) were added to the solution at 110 °C. After stirring for 3 h at 140 °C, the solution was subjected to dry chromatography on silica gel (dichloromethane as eluent) and concentrated under vacuo. The product was purified by using chromatography on silica gel (benzene as eluent) and recrystallized from benzene/ethanol. Compound 1 was obtained as a red solid (0.12 g, 5.7 % yield). M.p. 267.5–268.9 °C; ¹H NMR (300.40 MHz, CDCl₃/TMS): δ=2.53 (s, 6 H; CH₃Se), 7.62–7.71 (m, 4 H), 8.08 ppm (dd, ³J(H,H)=6.8 Hz, ⁴J(H,H)=1.7 Hz, 2 H); ¹³C NMR (74.45 MHz, CDCl₃/TMS): δ=65.7 (CH₃Se), 124.0, 130.7, 132.6, 132.6, 134.8, 141.8, 183.1 (CO), 184.2 ppm (CO); ⁷⁷Se NMR (57.25 MHz, CDCl₃/MeSeMe): δ=315.7 ppm; elemental analysis calcd (%) for C₁₆H₁₂O₂Se₂: C 48.75, H 3.07; found: C 48.75, H 3.17.

1,8‐Bis(methylthio)anthraquinone (2): Following a method similar to that for 1, compound 2 was obtained as orange needles (0.28 g, 23 % yield). M.p. 234.5–235.8 °C; ¹H NMR (300.40 MHz, CDCl₃/TMS): δ=2.32 (s, 6 H; CH₃S), 7.65 (t, ³J(H,H)=7.7 Hz, 2 H), 7.77 (d, ³J(H,H)=7.9 Hz, 2 H), 8.15 ppm (dd, ³J(H,H)=7.4 Hz, ⁴J(H,H)=1.2 Hz, 2 H); ¹³C NMR (74.45 MHz, CDCl₃/TMS): δ=65.6 (CH₃S), 122.8, 129.2, 129.5, 132.6, 134.2, 145.9, 183.2 (CO), 184.1 ppm (CO); elemental analysis calcd (%) for C₁₆H₁₂O₂S₂: C 63.97, H 4.03; found: C 63.85, H 4.13.

1,8‐Bis(methoxy)anthraquinone (3):34 Sodium hydride (0.83 g, 21.68 mmol) was added to a solution of chrysazin (2.00 g, 8.33 mmol) in a mixture of dry THF (40 mL) and dry DMF (20 mL). The solution was stirred for 30 min and then left at reflux for 30 min. Methyl iodide (1.56 mL, 24.98 mmol) was added to the solution cooled to room temperature. Then the solution was stirred for 2 h at this temperature. As the reaction was initiated by heating, methyl iodide (1.56 mL, 24.98 mmol) was added to the solution at 60 °C. After cooling to 25 °C, sodium hydride (0.45 g, 11.62 mmol) was added. The reaction mixture was left at reflux for 30 min, stirred at room temperature overnight, and then concentrated. The crude product was purified by using chromatography on silica gel (dichloromethane as eluent) and recrystallized from benzene/ethanol. Compound 3 was obtained as yellow needles (1.79 g, 78 % yield). M.p. 225.8–226.8 °C; ¹H NMR (300.40 MHz, CDCl₃/TMS): δ=4.01 (s, 6 H; CH₃O), 7.30 (d, ³J(H,H)=8.3 Hz, 2 H), 7.63 (t, ³J(H,H)=8.1 Hz, 2 H), 7.83 ppm (d, ³J(H,H)=7.5 Hz, 2 H); ¹³C NMR (74.45 MHz, CDCl₃/TMS): δ=56.5 (CH₃O), 118.0, 118.8, 123.9, 133.8, 134.7, 159.4, 182.8 (CO), 184.0 ppm (CO); elemental analysis calcd (%) for C₁₆H₁₂O₄: C 71.64, H 4.51; found: C 71.62, H 4.54.

X‐ray structure determination: Single crystals of red prisms of 1, orange needles of 2, and yellow needles of 3 were obtained by slow evaporation of solutions of the compounds dissolved in benzene containing ethanol. X‐ray diffraction data for 1–3 were collected on a Rigaku/MSC Mercury CCD diffractometer equipped with a graphite‐monochromated Mo_Kα radiation source (λ=0.71070 Å) at 103(2) K. The structures of 1–3 were solved by direct methods (SIR97),35 and refined by the full‐matrix least‐squares method on F² for all reflections (SHELXL‐97).36 All non‐hydrogen atoms were refined anisotropically; hydrogen atoms were refined isotropically.

CCDC‐603371 (1), CCDC‐603372 (2), and CCDC‐603373 (3) contain the supplementary crystallographic data for this paper. These data can be obtained free of charge from the Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.

MO calculations: Ab initio molecular orbital calculations were performed on a Silent‐SCC T2 (Itanium2) computer by employing the Gaussian 03 program20 with the 6‐311+G(2df) basis set for oxygen, sulfur, and selenium atoms and the 6‐311+G(2d,p) basis set for carbon and hydrogen atoms. Calculations were performed on structures BB and AA of 1–6, structure B of 7–12, and structure A of 7, 8, and 10 at the density functional theory (DFT) level of the Becke three‐parameter hybrid functional combined with the Lee–Yang–Parr correlation functional (B3LYP). AIM analysis was performed with the AIM2000 program20 after optimization of the structures.

Acknowledgements

This work was partially supported by a Grant‐in‐Aid for Scientific Research (No. 16550038) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan.