Analysis of One-Bond Se-Se Nuclear Couplings in Diselenides and 1,2-Diselenoles on the Basis of Molecular Orbital Theory: Torsional Angular Dependence, Electron Density Influence, and Origin in ¹𝐽(Se,Se)

Abstract

Nuclear couplings for the Se-Se bonds, ¹𝐽(Se,Se), are analyzed on the basis of the molecular orbital (MO) theory. The values are calculated by employing the triple 𝜁 basis sets of the Slater type at the DFT level. ¹𝐽(Se,Se) are calculated modeled by MeSeSeMe (1a), which shows the typical torsional angular dependence on 𝜙(C_MeSeSeC_Me). The dependence explains well the observed ¹𝐽_obsd(Se,Se) of small values (≤64 Hz) for RSeSeR^′ (1) (simple derivatives of 1a) and large values (330–380 Hz) observed for 4-substituted naphto[1,8-𝑐,𝑑]-1,2-diselenoles (2) which correspond to symperiplanar diselenides. ¹𝐽 (Se, Se : 2) becomes larger as the electron density on Se increases. The paramagnetic spin-orbit terms contribute predominantly. The contributions are evaluated separately from each MO (𝜓_𝑖) and each 𝜓_𝑖→𝜓_𝑎 transition, where 𝜓_𝑖 and 𝜓_𝑎 are occupied and unoccupied MO's, respectively. The separate evaluation enables us to recognize and visualize the origin and the mechanism of the couplings.

1. Introduction

Indirect nuclear spin-spin coupling constants (𝐽) provide highly important information around coupled nuclei, containing strongly bonded and weakly interacting states, since the values depend on the electron distribution between the nuclei [1–10]. One–bond (¹𝐽), two-bond (geminal) (²𝐽), three-bond (vicinal) (³𝐽), and even longer coupling constants (^𝑛𝐽(𝑛≥4)) are observed between selenium atoms, which will give important information around the coupled nuclei. The mechanism for ¹𝐽 must be of the through-bond type; however, that for ^𝑛𝐽(𝑛≥2) would contain through-space interactions, especially for ^𝑛𝐽(𝑛≥4). Quantum chemical (QC) calculations are necessary for the analysis and the interpretation of the J values with physical meanings. Important properties of molecules will be clarified by elucidating the mechanism of spin-spin couplings on the basis of the molecular orbital (MO) theory.

Various ¹𝐽_obsd (Se, Se) values are reported for alkyl and/or aryl derivatives of dimethyl diselenide (1a) (RSeSeR^′: 1). They are usually small (¹𝐽_obsd(Se, Se:  1) ≤ 64 Hz ; see Table 1). We examined ¹𝐽(Se, Se) of naphto[1,8-c,d]-1,2-diselenole (4-Y-1,8-Se₂C₁₀H₅ (2): Y=H (a) [11–15], OMe (b), Me (c), Cl (d), COOMe (e), CN (f), and NO₂ (g), which correspond to the symperiplanar diselenides (Figure 1). The ¹𝐽(Se, Se) values are measured for 2c, 2d, and 2g, and large ¹𝐽_obsd(Se, Se) values of 330–380 Hz are detected. Table 1 summarizes the ¹𝐽_obsd(Se, Se) values.

Table 1 

Observed ¹𝐽_obsd(Se, Se) values of some selenium compounds.

Figure 1 

Why are ¹𝐽_obsd(Se, Se: 2) much larger than ¹𝐽_obsd(Se, Se: 1)? How do ¹𝐽_obsd(Se, Se: 2) depend on the substituent Y in 2? ¹𝐽(Se, Se) are analyzed on the basis of the MO theory, as the first step to investigate the nature of the bonded and nonbonded interactions between selenium atoms through ^𝑛𝐽(Se, Se) [18]. ¹𝐽(Se, Se) are calculated for 1a and 2a–g.

According to the nonrelativistic theory, there are several mechanisms contributing to the spin-spin coupling constants. As expressed in (1), the total value (^𝑛𝐽_TL) is composed of the contributions from the diamagnetic spin-orbit (DSO) term (^𝑛𝐽_DSO), the paramagnetic spin-orbit (PSO) term (^𝑛𝐽_PSO), the spin-dipolar (SD) term (^𝑛𝐽_SD), and the Fermi contact (FC) term (^𝑛𝐽_FC),

^𝑛𝐽_TL=^𝑛𝐽_DSO+^𝑛𝐽_PSO+^𝑛𝐽_SD+^𝑛𝐽_FC. (1)

Scheme 1 summarizes the mechanism of the indirect nuclear spin-spin couplings. The origin of the terms, ^𝑛𝐽_DSO, ^𝑛𝐽_PSO, ^𝑛𝐽_SD, and ^𝑛𝐽_FC, is also illustrated, contributing to ^𝑛𝐽_TL. The ground state of a molecule (M) is the singlet state (𝑆₀) if the nuclei (N) in M have no magnetic moments. However, the ground state cannot be the pure 𝑆₀ if N possesses magnetic moments, 𝜇_𝑁. The ground state perturbed by 𝜇_𝑁 is expressed as follows: DSO arise by the reorganization of 𝑆₀; therefore, they are usually very small. PSO appears by the mixing of upper singlet states (𝑆₁,𝑆₂,𝑆₃,…). FC and SD originate if admixtures occur from upper triplet states (𝑇₁,𝑇₂,𝑇₃,…), where only s-type atomic orbitals contribute to FC.

Scheme 1 

How do the indirect nuclear spin-spin couplings originate? Mechanisms for 𝑛𝐽DSO, 𝑛𝐽PSO, 𝑛𝐽SD, and 𝑛𝐽FC terms, contributing to 𝑛𝐽TL.

Calculated ¹𝐽_TL values are evaluated separately by the four components as shown in (1). The ¹𝐽(Se, Se) values are evaluated using the Slater-type atomic orbitals, which are equipped in the ADF 2008 program [19–23]. Evaluations of the values are performed employing the ADF program, after structural optimizations with the Gaussian 03 program [24]. Contributions from each 𝜓_𝑖 and each 𝜓_𝑖→𝜓_𝑎 transition are evaluated separately, where 𝜓_𝑖 and 𝜓_𝑎 denote occupied and unoccupied MOs, respectively. The treatment enables us to recognize and visualize clearly the origin of the indirect nuclear spin-spin couplings.

2. Experimental

2.1. Materials and Measurements

Manipulations were performed under an argon atmosphere with 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 Yanaco-MP apparatus of uncorrected. Flash column chromatography was performed on silica gel (Fuji Silysia PSQ-100B), acidic and basic alumina (E. Merck).

NMR spectra were recorded at 297 K in CDCl₃ and DMSO-𝑑₆ solutions. ¹H, ¹³C, and ⁷⁷Se NMR spectra were measured at 300, 75.5, and 76.2 MHz, respectively. Chemical shifts are given in ppm relative to those of TMS for ¹H and ¹³C NMR spectra and relative to reference compound Me₂Se for ⁷⁷Se NMR spectra.

2.2. Preparation of 4-methylnaphtho[1,8-c,d]-1,2-diselenole (𝟐𝐛)

According to a method similar to that previously reported for 2a [11–17] from 1,8-dichloro-4-methylnaphthalene, 2b was obtained as purple needles in 68% yield, m.p. 127.0–128.0^∘C. ¹H NMR (CDCl₃, 300 MHz, TMS): 𝛿 2.50 (s, 3H), 7.09 (dd, 1H, 𝐽=0.9 and 7.6 Hz), 7.25 (d, 1H, 𝐽=7.3 Hz), 7.36 (dd, 1H, 𝐽=0.6 and 6.9 Hz), 7.55 (dd, 1H, 𝐽=0.7 and 8.4 Hz); ¹³C NMR (CDCl₃, 75.5 MHz, TMS): 𝛿 18.6, 120.4, 120.7, 121.0, 127.4, 128.2, 130.4, 137.0, 137.3, 138.0, 141.1; ⁷⁷Se NMR (CDCl₃, 76.2 MHz, Me₂Se): 𝛿 411.8, 420.6. Anal. Calc. for C₁₁H₈Se₂: C, 44.32; H, 2.70%; found: C, 44.21; H, 2.63%.

2.3. Preparation of 4-chloronaphtho[1,8-c,d]-1,2-diselenole (𝟐𝐜)

According to a method similar to that previously reported for 2a [11–17] from 1,4,8-trichloronaphthalene, 2c was obtained as brown needles in 58% yield, m.p. 155.0–156.0^∘C. ¹H NMR (CDCl₃, 300 MHz, TMS): 𝛿 7.24 (d, 1H, 𝐽=8.1 Hz), 7.30 (d, 1H, 𝐽=7.9 Hz), 7.34 (t, 1H, 𝐽=7.7 Hz), 7.39 (dd, 1H, 𝐽=1.2 and 7.4 Hz), 7.81 (dd, 1H, 𝐽=1.3 and 7.9 Hz); ¹³C NMR (CDCl₃, 75.5 MHz, TMS): 𝛿 120.5, 120.6, 121.9, 127.3, 127.4, 128.6, 135.0, 138.5, 140.0, 141.2; ⁷⁷Se NMR (CDCl₃, 76.2 MHz, Me₂Se): 𝛿 422.6, 444.6. Anal. Calc. for C₁₀H₅Se₂Cl: C, 37.71; H, 1.58%; found: C, 37.83; H, 1.60%.

2.4. Preparation of 4-nitronaphtho[1,8-c,d]-1,2-diselenole (𝟐𝐝)

According to a method similar to that previously reported for 2a [11–17] from 1,8-dibromo-4-nitronaphthalene, 2d was obtained as dark purple needles in 28% yield, m.p. 196.0–197.0^∘C. ¹H NMR (CDCl₃, 300 MHz, TMS): 𝛿 7.40 (d, 1H, 𝐽=8.3 Hz), 7.52 (dd, 1H, 𝐽=4.1 and 7.6 Hz), 7.53 (s, 1H), 8.18 (d, 1H, 𝐽=8.3 Hz), 8.51 (dd, 1H, 𝐽=2.7 and 4.1 Hz); ¹H NMR (DMSO-d₆, 300 MHz, TMS): 𝛿 7.57 (dd, 1H, 𝐽=7.5 and 8.5 Hz), 7.77 (d, 1H, 𝐽=8.5 Hz), 7.84 (dd, 1H, 𝐽=0.7 and 7.5 Hz), 8.20 (d, 1H, 𝐽=8.5 Hz), 8.29 (dd, 1H, 𝐽=0.7 and 8.5 Hz); ¹³C NMR (DMSO-d₆, 75.5 MHz, TMS): 𝛿 118.2, 120.0, 123.4, 127.1, 129.4, 131.1, 139.0, 140.8, 144.2, 155.5; ⁷⁷Se NMR (CDCl₃, 76.2 MHz, Me₂Se): 𝛿 448.8, 474.4. Anal. Calc. for C₁₀H₅Se₂NO₂: C, 36.50; H, 1.53; N, 4.26%; found: C, 36.41; H, 1.40; N, 4.19%.

2.5. Measurements of ¹𝐽(Se, Se)

During the measurement of ⁷⁷Se NMR spectra for 2g (Y=NO₂) in chloroform-d solutions (0.050 M) at 297 K, a typical AB quartet pattern of the spectra was observed. After careful analysis of the spectrum for 2g, ¹𝐽(Se, Se) of 330.8 Hz was obtained. The ¹𝐽(Se, Se) values are obtained similarly by the careful analysis of the spectra for 2c and 2d.

2.6. Calculation Method

Structures of 1a are optimized employing the 6-311++G(3df,2pd) basis sets of the Gaussian 03 program [24–28] at the DFT (B3LYP) level [29–32]. The torsional angle C_MeSeSeC_Me (𝜙) is 88.38 in the full-optimized structure of 1a. Calculations that are further performed on 1a: 1a are fully optimized except for 𝜙, which are fixed by every 15^∘ or 30^∘. Optimizations are also performed on 2a–g using the 6-311+G(3df) basis sets [25–28] for Se and the 6-311+G(3d,2p) basis sets for other nuclei at the DFT (B3LYP) level [29–32]. The 𝐶_2𝑣 symmetry is assumed for 2a, 𝐶_𝑠 for 2b–d and 2f, and the 𝐶₁ symmetry for 2e and 2g.

The 𝐽(Se, Se) values are calculated with the triple 𝜉 basis sets of the Slater type with two sets of polarization functions (2×1s, 2×2s, 2×2p, 2×3s, 2×3p, 3×3d, 3×4s, 3×4p, 1×4d, and 1×4f for Se) at the DFT (BLYP) level of the ADF 2008 program [19–23], applying on the optimized structures with the Gaussian 03 program [24]. Calculations are performed at the nonrelativistic level. The scalar ZORA relativistic formulation [33–35] is also applied to 2a, for convenience of comparison. The ^𝑛𝐽_TL values are evaluated separately by ^𝑛𝐽_DSO, ^𝑛𝐽_PSO, ^𝑛𝐽_SD, and ^𝑛𝐽_FC, as shown in (1). Mechanisms of the nuclear couplings are revealed by decomposing the contributions to each 𝜓_𝑖 and each 𝜓_𝑖→𝜓_𝑎 transition [36, 37].

3. Results and Discussion

3.1. Observed ¹𝐽_obsd(Se, Se)

Table 1 collects ¹𝐽_{𝑜𝑏𝑠𝑑}(Se, Se), necessary for discussion. The magnitudes of the ¹𝐽_obsd(Se, Se) values are usually small (< 64 Hz) for the simple derivatives of MeSeSeMe (1a) (RSeSeR^′: 1) [9, 16, 17]. On the other hand, large ¹𝐽_obsd(Se, Se) are recorded for 2 (4-Y-1,8-Se₂C₁₀H₅), which correspond to symperiplanar diselenides, although not detected in 2a (Y=H) [11–15]. The values are 379.4 Hz for 2b (Y=Me), 375.9 Hz for 2c (Y=Cl), and 330.8 Hz for 2d (Y=NO₂). ¹𝐽(Se, Se: 2) becomes smaller as the electron accepting ability of Y increases.

3.2. Mechanism of ¹𝐽(Se, Se) in 𝟏𝐚

Table 2 shows the calculated ¹𝐽_TL and the components, ¹𝐽_DSO, ¹𝐽_PSO, ¹𝐽_SD, and ¹𝐽_FC, in ¹𝐽(Se, Se: 1a). ¹𝐽_TL(Se, Se: 1a) is predicted to be less than 44 Hz for 𝜙=90^∘±15^∘. Therefore, ¹𝐽_obsd(Se, Se: 1) is explained substantially and modeled by 1a with 𝜙≈90^∘, although R and R^′ in 1 must also affect on the values. ¹𝐽(Se, Se: 1a) is predicted to be very large at 𝜙=0^∘ (684 Hz) and 180^∘ (628 Hz). Consequently, ¹𝐽_obsd(Se, Se: 2) of 331–379 Hz are essentially explained by ¹𝐽(Se, Se: 1a) with 𝜙=0^∘. Figure 2 draws the plots of ¹𝐽_DSO, ¹𝐽_PSO, ¹𝐽_SD, ¹𝐽_FC, ¹𝐽_SD+FC, and ¹𝐽_TL versus 𝜙 in 1a. It is well demonstrated that ¹𝐽_TL changes depending on 𝜙, similarly to the case of ³𝐽(H, H), three-bond (vicinal) couplings in ¹H NMR spectra [1, 2]. ¹𝐽_DSO are negligible (< 0.03 Hz).

Table 2 

¹𝐽(Se, Se) values calculated for 𝟏𝐚^{(a), (b)}.

Figure 2 

Plots of 1𝐽DSO (■),1𝐽PSO (□),1𝐽SD (▲),1𝐽FC (♦),1𝐽SD+FC (△), and 1𝐽TL (○) versus 𝜙(CSeSeC) in 1𝐽(Se, Se: 1a).

How do ¹𝐽_PSO(Se, Se: 1a) and ¹𝐽_SD+FC(Se, Se: 1a) [=¹𝐽_SD(Se, Se: 1a) + ¹𝐽_FC(Se, Se: 1a)] contribute to ¹𝐽_TL(Se, Se: 1a)? ¹𝐽_PSO(Se, Se: 1a) and ¹𝐽_SD+FC(Se, Se: 1a) are plotted versus ¹𝐽_TL(Se, Se: 1a), although not shown. The correlations are given in (2) and (3), respectively. The results exhibit that ¹𝐽_PSO(Se, Se: 1a) and ¹𝐽_SD+FC(Se, Se: 1a) contribute 65% and 35% to ¹𝐽_TL(Se, Se: 1a), respectively, irrespective of the𝜙(CSeSeC) values:

¹𝐽_PSO(Se,Se:𝟏𝐚)=0.651×¹𝐽_TL(Se,Se:𝟏𝐚)−4.1(𝑟²=0.999),₁𝐽_SD+FC(Se,Se:𝟏𝐚)=0.349×¹𝐽_TL(Se,Se:𝟏𝐚)+4.2(𝑟²=0.998). (2)(3)

Why does ¹𝐽(Se, Se: 1a) show the torsional angular dependence? What orbitals and transitions contribute to the dependence? ¹𝐽_PSO(Se, Se: 1a) is analyzed next.

3.2.1. Analysis of ¹𝐽_PSO(Se, Se) in 𝟏𝐚

The mechanism of ¹𝐽_PSO(Se, Se: 1a) is discussed by analyzing the contributions separately from each 𝜓_𝑖 and each 𝜓_𝑖→𝜓_𝑎 transition. Table 3 lists the 𝜙 dependence of ¹𝐽_PSO(Se, Se: 1a) contributed from 𝜓₁– 𝜓₄₃, 𝜓₁– 𝜓₃₈, 𝜓₃₉– 𝜓₄₃, 𝜓₃₉, 𝜓₄₀, 𝜓₄₁, 𝜓₄₂, and𝜓₄₃. The contribution from 𝜓₃₉– 𝜓₄₃ to ¹𝐽_PSO(Se, Se: 1a) is large, whereas that from 𝜓₁– 𝜓₃₈ is small, although not shown. The plot of the contributions from 𝜓₃₉– 𝜓₄₃ (y) versus those from 𝜓₁– 𝜓₄₃ (x) provides an excellent correlation (𝑦=0.976𝑥+37.3∶𝑟²=0.9999). Figure 3(a) shows those from 𝜓₃₉, 𝜓₄₀, 𝜓₄₁, 𝜓₄₂, and 𝜓₄₃ and Figure 3(b)exhibits those from 𝜓₃₉– 𝜓₄₁, 𝜓₄₂– 𝜓₄₃, and 𝜓₃₉– 𝜓₄₃. Contributions from 𝜓₄₂ and 𝜓₄₃ exchange with each other at 𝜙≈90. Those of 𝜓₃₉ and 𝜓₄₀ do at 𝜙≈135 (Figure 3(a)). The contributions from 𝜓₄₂- 𝜓₄₃ and 𝜓₃₉-𝜓₄₁ almost cancel out at 𝜙≈90 (Figure 3(b)).

Table 3 

Contributions to the torsional angular dependence in ¹𝐽_PSO(Se, Se: 𝟏𝐚) from 𝜓_𝑖 (a),(b).

(a)

(b)

Figure 3 

Origin of the torsional angular dependence in 1𝐽PSO (Se, Se: 1a): (a) contributions from each of 𝜓39, 𝜓40, 𝜓41, 𝜓42, and 𝜓43 and (b) those from 𝜓39– 𝜓41, 𝜓42-𝜓43, and 𝜓39-𝜓43.

Magnitudes of the contributions from 𝜓₄₂ and 𝜓₄₃ to ¹𝐽_PSO(Se, Se: 1a) are very large at 0 and 180 (Table 3), although those from 𝜓₄₂ and 𝜓₄₃ are negative and positive directions, respectively. The values amount to −353 to −360 Hz and 753–793 Hz, respectively. The contributions from 𝜓₄₂-𝜓₄₃ are 433, 218, and 400 Hz at 0, 90, and 180, respectively, and those from 𝜓₃₉-𝜓₄₁ are 17, −198, and 10 Hz at 0, 90, and 180, respectively. Therefore, the mechanism of ¹𝐽_PSO(Se, Se: 1a) will be clarified by analyzing the contributions from 𝜓₄₂ and 𝜓₄₃ at 0 and 180. The mechanism would be complex at 90, since the small magnitude is the results of the total contributions from 𝜓₃₉-𝜓₄₃.

Figure 4 shows the 𝜓₄₂→𝜓₄₄ and 𝜓₄₃→𝜓₄₄ transitions at both 𝜙=0 and 180 which are shown in Table 3. Characters of 𝜓₄₂(HOMO-1), 𝜓₄₃(HOMO), and 𝜓₄₄(LUMO) are 𝜋(Se–Se), 𝜋^∗(Se–Se), and 𝜎^∗(Se–Se), respectively, at 𝜙=0 and 180. 𝜓₄₂(HOMO-1) is essentially the same as 𝜓₄₃(HOMO) at 𝜙=90. 𝜓₄₂and 𝜓₄₃ at 𝜙=90 are also drawn in Figure 4, to show how 𝜓₄₂ and 𝜓₄₃ interconvert with each other. Contrary to the case of 𝜙≈0 and 180, all of 𝜓₃₉– 𝜓₄₃ contribute to ¹𝐽_PSO(Se, Se: 1a) at 𝜙≈90. Contributions from the 𝜓₄₂→𝜓₄₄ and 𝜓₄₃→𝜓₄₄ transitions to ¹𝐽_PSO(Se, Se: 1a) at 90 are almost cancelled by those from the 𝜓₃₉→𝜓₄₄, 𝜓₄₀→𝜓₄₄, and 𝜓₄₁→𝜓₄₄ transitions. In addition, both ¹𝐽_SD(Se, Se: 1a) and ¹𝐽_FC(Se, Se: 1a) substantially contribute at 𝜙≈90. Consequently, it is difficult to specify a few orbitals, together with the transitions, which control ¹𝐽(Se, Se: 1a) at 𝜙≈90. The character of 𝜓₄₄ [LUMO: 𝜎^∗(Se–Se)] does not change so much depending on 𝜙. Therefore, the behavior of 𝜓₃₉-𝜓₄₃ must be mainly responsible for the 𝜙 dependence in ¹𝐽(Se, Se: 1a) (see Figures 3 and 4). The MO description in Figure 4 visualizes the origin of ¹𝐽_PSO(Se, Se: 1a) and helps us to understand the mechanism, especially at 𝜙=0 and 180.

Figure 4 

Contributions to 1𝐽PSO(Se, Se: 1a) from the 𝜓42→𝜓44 and 𝜓43→𝜓44 transitions at 𝜙=0, 90, and 180. The interconversion between 𝜓42 and 𝜓43 at 𝜙≈90 is also depicted.

After elucidation of the mechanism for ¹𝐽_PSO(Se, Se: 1a), next extension is to clarify ¹𝐽(Se, Se: 2) on the basis of the MO theory.

3.2.2. Evaluation of ¹𝐽(Se, Se) for 𝟐

Table 4 collects the calculated ¹𝐽_TL(Se, Se: 2) values, together with 𝐽_PSO(Se, Se: 2), ¹𝐽_SD(Se, Se: 2), ¹𝐽_FC(Se, Se: 2), and ¹𝐽_SD+FC(Se, Se: 2). Table 4 also contains the nuclear changes calculated with the natural bond orbital analysis (NBO) method (Qn(Se) [38–40] for 2 having Y of H (a), OMe (b), Me (c), Cl (d), COOMe (e), CN (f), and NO₂ (g). The Y dependence of ¹𝐽_obsd(Se, Se: 2) is well reproduced by the calculations. ¹𝐽_TL(Se, Se: 2) are predicted to be larger than the observed values by about 100 Hz. The DFT method overestimates the reciprocal energy differences (𝜀_𝑎−𝜀_𝑖)⁻¹, which would partly be responsible for the larger evaluation. The ¹𝐽(Se, Se) values are calculated at both nonrelativistic and scalar ZORA relativistic levels for 2a. The former is smaller than the latter. The value calculated at the nonrelativistic level seems to be closer to the observed value than that obtained with the scalar ZORA relativistic formulation in our calculation system. Therefore, it would be reasonable to discuss the ^𝑛𝐽(Se, Se) value calculated at the nonrelativistic level in this case.

Table 4 

¹𝐽(Se, Se) and Qn(Se) calculated on the full-optimized structure of 𝟐^{(a), (b), (c)}.

Before discussion of ¹𝐽(Se, Se: 2), it would be instructive to clarify the behavior of Qn(Se: 2), which changes depending on Y. Figure 5 shows the plot of Qn(²Se: 2) versus Qn(¹Se: 2). The correlations of the linear type (𝑦=𝑎𝑥+𝑏 with r (correlation coefficient) are given in the figure. The results show that Qn(²Se: 2) grows larger as the accepting ability of Y increases for Y=H, OMe, Me, Cl, and COOMe then it becomes almost constant for Y=CN and NO₂ while Qn(¹Se: 2) grows larger as the accepting ability of Y increases for all Y in Table 4. Qn(²Se: 2) seems saturated for Y of very strong acceptors such as CN and NO₂ while Qn(¹Se: 2) will not for all Y.

Figure 5 

Plot of Qn(2Se) versus Qn(1Se) in 2.

How do ¹𝐽_𝑇𝐿(Se, Se: 2) being controlled? ¹𝐽_𝑇𝐿(Se, Se: 2) are plotted versus Qn(¹Se), Qn(²Se), and Qn(¹Se)+Qn(²Se). Figure 6 shows the plot of ¹𝐽_𝑇𝐿(Se, Se: 2) versus Qn(¹Se), which gives best correlation among the three. The correlation is given in the figure. ¹𝐽_𝑇𝐿(Se, Se: 2) are confirmed to be controlled by Qn(¹Se). One might imagine that ¹𝐽_TL (Se, Se: 2) should be controlled by Qn(¹Se)+Qn(²Se). The saturation in Qn(²Se) shown in Figure 5 would perturb to give good correlations for ¹𝐽_TL(Se, Se: 2) versus 𝑄𝑛(¹Se)+𝑄𝑛(²Se). It is demonstrated that ¹𝐽_TL(Se, Se: 2) becomes smaller when Qn(Se) increases, experimentally and theoretically.

Figure 6 

Plot of 1J(Se, Se: 2) versus Qn(1Se) in 2.

After clarification of the Y dependence in ¹𝐽_TL(Se, Se: 2), next extension is to elucidate the mechanism for ¹𝐽(Se, Se: 2) on the basis of the MO theory.

3.3. Mechanism of ¹𝐽(Se, Se) in 𝟐𝐚

How do ¹𝐽_PSO(Se, Se: 2) and ¹𝐽_SD+FC(Se, Se: 2) contribute to ¹𝐽_TL(Se, Se: 2) in the change of Y? ¹𝐽_PSO(Se, Se: 2) and ¹𝐽_SD+FC(Se, Se: 2) are plotted versus ¹𝐽_TL(Se, Se: 2) for various Y in Table 4. The results for ¹𝐽_PSO(Se, Se: 2) and ¹𝐽_SD+FC(Se, Se: 2) are given in (4) and (5), respectively. The correlations are very good, which shows that ¹𝐽_PSO(Se, Se: 2) contributes predominantly to ¹𝐽_TL(Se, Se: 2) (70%), irrespective of Y: ¹𝐽_PSO(Se,Se∶𝟐)=0.704×¹𝐽_TL(Se,Se∶𝟐)+8.3(𝑟²=0.999),₁𝐽_SD+FC(Se,Se∶𝟐)=0.295×¹𝐽_TL(Se,Se∶𝟐)−8.0(𝑟²=0.994) (4)(5)

The origin of ¹𝐽(Se, Se: 2) is elucidated by analyzing ¹𝐽_PSO(Se, Se: 2a) on the basis of the MO theory, since ¹𝐽_PSO(Se, Se) contributes predominantly to ¹𝐽_TL(Se, Se) irrespective of Y. Figure 7 depicts the contributions of ¹𝐽_PSO(Se, Se: 2a) separately from each 𝜓_𝑖 and each 𝜓_𝑖→𝜓_𝑎 transition. (a)–(c) in Figure 7 plot the contributions to ¹𝐽_PSO(Se, Se: 2a) from each 𝜓_𝑖 and each transition of the 𝜓₆₇→𝜓_𝑎 and 𝜓₆₆→𝜓_𝑎 types, respectively. In Figure 7(a), contributions around 𝜓₅-𝜓₁₀, 𝜓₂₃-𝜓₂₈, and 𝜓₅₃-𝜓₆₇ originate mainly from atomic 2p(Se), 3p(Se), and 4p(Se) orbitals, respectively. Those caused by 2p(Se) and 3p(Se) are almost cancelled by summarizing over the corresponding orbitals. Therefore, 4p(Se) substantially contribute to ¹𝐽_PSO(Se, Se: 2a). Especially, 𝜓₆₇ (HOMO) and 𝜓₆₆ (HOMO-1) control ¹𝐽_PSO(Se, Se: 2a). 𝜓_𝑎 of 𝜓₆₈ determines ¹𝐽_PSO(Se, Se: 2a), among a lot of 𝜓_𝑖→𝜓_𝑎 transitions in 𝜓_𝑖 of 𝜓₆₇ and 𝜓₆₆, as shown in Figures 7(b) and 7(c).

(a)

(b)

(c)

Figure 7 

MO analysis of 1𝐽PSO(Se, Se: 2a): (a) contributions from each 𝜓𝑖, (b) from each 𝜓67→𝜓𝑎 transition, and (c) from each 𝜓66→𝜓𝑎 transition.

Figure 8 shows the 𝜓₆₇→𝜓₆₈ and 𝜓₆₆→𝜓₆₈ transitions in ¹𝐽_PSO(Se, Se: 2a). The large ¹𝐽_PSO(Se, Se: 2a) value arises from the mixing of 𝜓₆₈ [LUMO: 𝜎^∗(Se–Se)] into 𝜓₆₇ [HOMO: 𝜋^∗(Se–Se)] and 𝜓₆₆ [HOMO-1: 𝜋(Se–Se)] at the singlet state. The MO presentation in Figure 8 is essentially the same as the 𝜓₄₂→𝜓₄₄ and 𝜓₄₃→𝜓₄₄ transitions in ¹𝐽_PSO(Se, Se: 1a) at 𝜙=0 in Figure 4, although 𝜓₆₇ (2a) and 𝜓₆₆ (2a) contain the 𝜋(Nap) character. Large ¹𝐽_PSO(Se, Se: 2) and small ¹𝐽_obsd(Se, Se: 1) are well understood by the 𝜙 dependence in the calculated ¹𝐽(Se, Se: 1a) values.

Figure 8 

MO analysis of 1𝐽PSO(Se, Se: 2a): main contributions from the 𝜓67 (HOMO)→𝜓68 (LUMO) and 𝜓66→𝜓68 transitions are depicted.

4. Conclusion

Nuclear spin-spin coupling constants (𝐽) provide highly important information around coupled nuclei, containing strongly bonded and weakly interacting states. The ¹𝐽(Se, Se) values are analyzed as the first step to investigate the nature of the bonded and nonbonded interactions between the Se atoms through ^𝑛𝐽(Se, Se). QC calculations are necessary for the analysis and the interpretation of the 𝐽 values with physical meanings. Calculated ^𝑛𝐽_TL are composed of the contributions from ^𝑛𝐽_DSO, ^𝑛𝐽_PSO, ^𝑛𝐽_SD, and ^𝑛𝐽_FC. The decomposition helps us to consider the mechanisms of the spin-spin couplings, which are closely related to the electronic structures of compounds. Main contributions are evaluated separately from each 𝜓_𝑖 and each 𝜓_𝑖→𝜓_𝑎 transition, where 𝜓_𝑖 and 𝜓_𝑎 are occupied and unoccupied MO's, respectively.

¹𝐽(Se, Se) is calculated modeled by MeSeSeMe (1a), which shows the typical torsional angular dependence of 𝜙(C_MeSeSeC_Me). The dependence explains well ¹𝐽_obsd(Se, Se) of small values for RSeSeR^′ (1) and large values for 4-Y-1,8-Se₂C₁₀H₅ (2) which correspond to symperiplanar diselenides. ¹𝐽_TL(Se, Se: 2) are confirmed to be controlled by Qn(Se). ¹𝐽_TL(Se, Se: 2) are demonstrated to be smaller when Qn(Se) becomes larger, experimentally and theoretically. The PSO terms contribute predominantly to ¹𝐽(Se, Se). The contributions are analyzed separately from each 𝜓_𝑖 and each 𝜓_𝑖→𝜓_𝑎 transition. The MO description of each transition enables us to recognize and visualize clearly the origin and the mechanisms of the indirect nuclear spin-spin couplings. Important properties of molecules, such as electronic structures, will be clarified by elucidating the mechanisms of the spin-spin couplings on the basis of the MO theory.

Acknowledgments

This work was partially supported by a Grant-in-Aid for Scientific Research (nos. 16550038, 19550041, and 20550042) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan.