# 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 inJ1(Se, Se)

Authors: Akito Tanioku; Satoko Hayashi; Waro Nakanishi
Journal: Bioinorganic Chemistry and Applications
 (2009)

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## Abstract

Nuclear couplings for the Se-Se bonds,J1(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. J1(Se, Se) are calculated modeled by MeSeSeMe (1a), which shows the typical torsional angular dependence on ϕ(CMeSeSeCMe). The dependence explains well the observed J1(Se, Se)obsd 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. J1 (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 (ψi) and each ψi→ψa transition, where ψi and ψa are occupied and unoccupied MO's, respectively. The separate evaluation enables us to recognize and visualize the origin and the mechanism of the couplings.


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## Body

## 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 (J1), two-bond (geminal) (J2), three-bond (vicinal) (J3), and even longer coupling constants (Jn(n≥4)) are observed between selenium atoms, which will give important information around the coupled nuclei. The mechanism for J1 must be of the through-bond type; however, that for Jn(n≥2) would contain through-space interactions, especially for Jn(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.VariousJ1obsd (Se, Se) values are reported for alkyl and/or aryl derivatives of dimethyl diselenide (1a) (RSeSeR′: 1). They are usually small (J1obsd(Se, Se:  1) ≤ 64 Hz ; see Table 1). We examined J1(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 J1(Se, Se) values are measured for 2c, 2d, and 2g, and large J1obsd(Se, Se) values of 330–380 Hz are detected. Table 1 summarizes the J1obsd(Se, Se) values.Table 1
ObservedJ1obsd(Se, Se) values of some selenium compounds.
CompoundJ1obsd(Se, Se) [Hz]CommenttBuSeSeMe2.7(a)nBuSeSeMe36.3(a)MeSeSePh22(a)o-O2NC6H4SeSeCN64(b)2 (Y = Me)379.4This work2 (Y = Cl)375.9This work2 (Y = NO2)330.8This work(a) References [9, 16]. (b) References [9, 17].Figure 1Why areJ1obsd(Se, Se: 2) much larger than J1obsd(Se, Se: 1)? How do J1obsd(Se, Se: 2) depend on the substituent Y in 2? J1(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 Jn(Se, Se) [18]. J1(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 (JTLn) is composed of the contributions from the diamagnetic spin-orbit (DSO) term (JDSOn), the paramagnetic spin-orbit (PSO) term (JPSOn), the spin-dipolar (SD) term (JSDn), and the Fermi contact (FC) term (JFCn),(1)JTLn=JDSOn+JPSOn+JSDn+JFCn.Scheme1 summarizes the mechanism of the indirect nuclear spin-spin couplings. The origin of the terms, JDSOn, JPSOn, JSDn, and JFCn, is also illustrated, contributing to JTLn. 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, μN. The ground state perturbed by μN 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 forJDSOn, JPSOn, JSDn, and JFCn terms, contributing to JTLn.CalculatedJTL1 values are evaluated separately by the four components as shown in (1). The J1(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 ψi and each ψi→ψa transition are evaluated separately, where ψi and ψa 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 at130°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 inCDCl3 and DMSO-d6 solutions. H1, C13, and Se77 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 H1 and C13 NMR spectra and relative to reference compound Me2Se for Se77 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 for2a [11–17] from 1,8-dichloro-4-methylnaphthalene, 2b was obtained as purple needles in 68% yield, m.p. 127.0–128.0°C. H1 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); C13 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; Se77 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 for2a [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); C13 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; Se77 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 for2a [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. H1 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); H1 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); C13 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; Se77 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 ofJ1(Se, Se)

During the measurement ofSe77 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, J1(Se, Se) of 330.8 Hz was obtained. The J1(Se, Se) values are obtained similarly by the careful analysis of the spectra for 2c and 2d.


### 2.6. Calculation Method

Structures of1a 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 CMeSeSeCMe (ϕ) is 88.38º 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 C2v symmetry is assumed for 2a, Cs for 2b–d and 2f, and the C1 symmetry for 2e and 2g.TheJ(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 JnTL values are evaluated separately by JnDSO, JnPSO, JnSD, and JnFC, as shown in (1). Mechanisms of the nuclear couplings are revealed by decomposing the contributions to each ψi and each ψi→ψa transition [36, 37].


## 2.1. Materials and Measurements

Manipulations were performed under an argon atmosphere with standard vacuum-line techniques. Glassware was dried at130°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 inCDCl3 and DMSO-d6 solutions. H1, C13, and Se77 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 H1 and C13 NMR spectra and relative to reference compound Me2Se for Se77 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 for2a [11–17] from 1,8-dichloro-4-methylnaphthalene, 2b was obtained as purple needles in 68% yield, m.p. 127.0–128.0°C. H1 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); C13 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; Se77 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 for2a [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); C13 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; Se77 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 for2a [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. H1 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); H1 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); C13 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; Se77 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 ofJ1(Se, Se)

During the measurement ofSe77 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, J1(Se, Se) of 330.8 Hz was obtained. The J1(Se, Se) values are obtained similarly by the careful analysis of the spectra for 2c and 2d.


## 2.6. Calculation Method

Structures of1a 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 CMeSeSeCMe (ϕ) is 88.38º 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 C2v symmetry is assumed for 2a, Cs for 2b–d and 2f, and the C1 symmetry for 2e and 2g.TheJ(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 JnTL values are evaluated separately by JnDSO, JnPSO, JnSD, and JnFC, as shown in (1). Mechanisms of the nuclear couplings are revealed by decomposing the contributions to each ψi and each ψi→ψa transition [36, 37].


## 3. Results and Discussion

### 3.1. ObservedJ1obsd(Se, Se)

Table1 collects Jobsd1(Se, Se), necessary for discussion. The magnitudes of the Jobsd1(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 Jobsd1(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). J1(Se, Se: 2) becomes smaller as the electron accepting ability of Y increases.


### 3.2. Mechanism ofJ1(Se, Se) in 1a

Table2 shows the calculated JTL1 and the components, JDSO1, JPSO1, JSD1, and JFC1, in J1(Se, Se: 1a). JTL1(Se, Se: 1a) is predicted to be less than 44 Hz for ϕ=90°±15°. Therefore, Jobsd1(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. J1(Se, Se: 1a) is predicted to be very large at ϕ=0° (684 Hz) and 180° (628 Hz). Consequently, Jobsd1(Se, Se: 2) of 331–379 Hz are essentially explained by J1(Se, Se: 1a) with ϕ=0°. Figure 2 draws the plots of JDSO1, JPSO1, JSD1, JFC1, JSD+FC1, and JTL1 versus ϕ in 1a. It is well demonstrated that JTL1 changes depending on ϕ, similarly to the case of J3(H, H), three-bond (vicinal) couplings in H1 NMR spectra [1, 2]. JDSO1 are negligible (< 0.03 Hz).Table 2
J1(Se, Se) values calculated for 1a(a), (b).
ϕErel(c)JPSO1JSD1JFC1JSD+FC1JTL1[°][kJ mol-1][Hz][Hz][Hz][Hz][Hz]0.036.9447.2217.818.6236.4683.715.033.0399.2200.615.2215.8615.030.025.3288.5163.12.7165.8454.360.06.176.1101.4−43.358.1134.275.00.920.087.8−64.723.143.188.40.04.184.5−76.77.811.990.00.04.284.6−77.96.710.9105.02.329.991.5−77.414.144.0120.07.494.7109.3−60.548.8143.5150.017.6291.5171.7−8.2163.5455.0165.021.5370.6201.19.0210.1580.7180.022.8400.7213.414.3227.7628.4For(a) the abbreviation, see text. J(b)1DSO being less than 0.03 Hz.Relative(c) to optimized value (−5267.7384 au) at ϕ = 88.38º in kJ mol-1.Figure 2
Plots ofJDSO1 (■),JPSO1 (□),JSD1 (▲),JFC1 (♦),JSD+FC1 (△), and JTL1 (○) versus ϕ(CSeSeC) in J1(Se, Se: 1a).How doJPSO1(Se, Se: 1a) and JSD+FC1(Se, Se: 1a) [=JSD1(Se, Se: 1a) + JFC1(Se, Se: 1a)] contribute to JTL1(Se, Se: 1a)? JPSO1(Se, Se: 1a) and JSD+FC1(Se, Se: 1a) are plotted versus JTL1(Se, Se: 1a), although not shown. The correlations are given in (2) and (3), respectively. The results exhibit that JPSO1(Se, Se: 1a) and JSD+FC1(Se, Se: 1a) contribute 65% and 35% to JTL1(Se, Se: 1a), respectively, irrespective of theϕ(CSeSeC) values:(2)J1PSO(Se,Se:1a)=0.651×J1TL(Se,Se:1a)-4.1(r2=0.999),(3)J1SD+FC(Se,Se:1a)=0.349×J1TL(Se,Se:1a)+4.2(r2=0.998).Why doesJ1(Se, Se: 1a) show the torsional angular dependence? What orbitals and transitions contribute to the dependence? JPSO1(Se, Se: 1a) is analyzed next.


#### 3.2.1. Analysis ofJ1PSO(Se, Se) in 1a

The mechanism ofJPSO1(Se, Se: 1a) is discussed by analyzing the contributions separately from each ψi and each ψi→ψa transition. Table 3 lists the ϕ dependence of JPSO1(Se, Se: 1a) contributed from ψ1–ψ43, ψ1–ψ38, ψ39–ψ43, ψ39, ψ40, ψ41, ψ42, andψ43. The contribution from ψ39–ψ43 to JPSO1(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≈90º. Those of ψ39 and ψ40 do at ϕ≈135º (Figure 3(a)). The contributions from ψ42-ψ43 and ψ39–ψ41 almost cancel out at ϕ≈90º (Figure 3(b)).Table 3
Contributions to the torsional angular dependence inJ1PSO(Se, Se: 1a) from ψi (a),(b).
ϕ [°]0.015.030.060.075.088.490.0105.0120.0150.0165.0180.0ψ1–ψ43447.2399.2288.576.119.94.14.329.994.7291.4370.5400.7ψ39–ψ43449.9403.1294.984.435.220.420.645.9109.1302.2380.3410.4ψ39−121.2−117.6−108.9−80.9−63.0−44.9−42.6−18.98.7−146.9−155.1−157.7ψ40181.2163.4118.713.7−28.6−59.4−62.8−90.8−114.365.385.493.0ψ41−43.3−48.3−60.8−87.9−94.3−93.1−92.4−79.9−54.028.762.475.0ψ42−359.7−333.7−266.1−84.09.695.6111.921.2−71.9−261.5−328.1−352.7ψ43792.9739.4612.0323.7211.5122.2106.5214.3340.7616.6715.7752.8ψ42→ψ44(c)−333.3−307.1−240.9−69.415.693.3116.533.2−54.4−235.6−298.1−321.0ψ43→ψ44(c)747.2695.7574.7312.4206.8125.9103.2202.0320.7581.5673.8708.6In(a) Hz.For(b) the abbreviation, see text. Contribution(c) from the transition.Origin of the torsional angular dependence inJ1PSO (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.
(a)(b)Magnitudes of the contributions fromψ42 and ψ43 to JPSO1(Se, Se: 1a) are very large at 0º and 180º (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 0º, 90º, and 180º, respectively, and those from ψ39–ψ41 are 17, −198, and 10 Hz at 0º, 90º, and 180º, respectively. Therefore, the mechanism of J1PSO(Se, Se: 1a) will be clarified by analyzing the contributions from ψ42 and ψ43 at 0º and 180º. The mechanism would be complex at 90º, since the small magnitude is the results of the total contributions from ψ39–ψ43.Figure4 shows the ψ42→ψ44 and ψ43→ψ44 transitions at both ϕ=0º and 180º 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=0º and 180º. ψ42(HOMO-1) is essentially the same as ψ43(HOMO) at ϕ=90º. ψ42and ψ43 at ϕ=90º are also drawn in Figure 4, to show how ψ42 and ψ43 interconvert with each other. Contrary to the case of ϕ≈0 and 180º, all of ψ39–ψ43 contribute to J1PSO(Se, Se: 1a) at ϕ≈90º. Contributions from the ψ42→ψ44 and ψ43→ψ44 transitions to J1PSO(Se, Se: 1a) at 90º are almost cancelled by those from the ψ39→ψ44, ψ40→ψ44, and ψ41→ψ44 transitions. In addition, both J1SD(Se, Se: 1a) and J1FC(Se, Se: 1a) substantially contribute at ϕ≈90º. Consequently, it is difficult to specify a few orbitals, together with the transitions, which control J1(Se, Se: 1a) at ϕ≈90º. 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 J1(Se, Se: 1a) (see Figures 3 and 4). The MO description in Figure 4 visualizes the origin of J1PSO(Se, Se: 1a) and helps us to understand the mechanism, especially at ϕ=0º and 180º.Figure 4
Contributions toJ1PSO(Se, Se: 1a) from the ψ42→ψ44 and ψ43→ψ44 transitions at ϕ=0, 90, and 180º. The interconversion between ψ42 and ψ43 at ϕ≈90º is also depicted.After elucidation of the mechanism forJ1PSO(Se, Se: 1a), next extension is to clarify J1(Se, Se: 2) on the basis of the MO theory.


#### 3.2.2. Evaluation ofJ1(Se, Se) for 2

Table4 collects the calculated JTL1(Se, Se: 2) values, together with JPSO(Se, Se: 2), JSD1(Se, Se: 2), JFC1(Se, Se: 2), and JSD+FC1(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 Jobsd1(Se, Se: 2) is well reproduced by the calculations. JTL1(Se, Se: 2) are predicted to be larger than the observed values by about 100 Hz. The DFT method overestimates the reciprocal energy differences (εa-εi)-1, which would partly be responsible for the larger evaluation. The J1(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 Jn(Se, Se) value calculated at the nonrelativistic level in this case.Table 4
J1(Se, Se) and Qn(Se) calculated on the full-optimized structure of 2(a), (b), (c).
CompoundJ1PSO[Hz]J1SD[Hz]J1FC[Hz]J1SD+FC[Hz]J1TL[Hz]Qn(Se1)Qn(Se2)Symmetry2a(Y=H)362.2195.2−54.1141.1503.30.23670.2367C2v2b(Y=OMe)394.3207.5−54.2153.3547.70.22560.2264Cs2c(Y=Me)363.6195.1−55.3139.8503.50.23340.2296Cs2d(Y=Cl)360.1193.4−53.1140.3500.40.24480.2443Cs2e(Y=COOMe)324.1178.2−55.7122.5446.60.25930.2556C12f(Y=CN)326.6180.6−52.6128.0454.60.26770.2564Cs2g(Y=NO2)299.7167.6−53.9113.7413.40.28240.2576C12a(Y=H)(d)390.7206.42.6209.0599.70.23670.2367C2vFor(a) the abbreviation, see text. JDSO(b)1 being less than 0.03 Hz. Se(c)1 and Se2 being attached to C1 and C8 in 4-Y-1,8-Se2C10H5 (2), respectively. On(d) the basis of scalar ZORA.Before discussion ofJ1(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(Se2: 2) versus Qn(Se1: 2). The correlations of the linear type (y=ax+b with r (correlation coefficient) are given in the figure. The results show that Qn(Se2: 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(Se1: 2) grows larger as the accepting ability of Y increases for all Y in Table 4. Qn(Se2: 2) seems saturated for Y of very strong acceptors such as CN and NO2 while Qn(Se1: 2) will not for all Y.Figure 5
Plot ofQn(2Se) versus Qn(1Se) in 2.How doJTL1(Se, Se: 2) being controlled? JTL1(Se, Se: 2) are plotted versus Qn(Se1), Qn(Se2), and Qn(Se1)+Qn(Se2). Figure 6 shows the plot of JTL1(Se, Se: 2) versus Qn(Se1), which gives best correlation among the three. The correlation is given in the figure. JTL1(Se, Se: 2) are confirmed to be controlled by Qn(Se1). One might imagine that JTL1 (Se, Se: 2) should be controlled by Qn(Se1)+Qn(Se2). The saturation in Qn(Se2) shown in Figure 5 would perturb to give good correlations for JTL1(Se, Se: 2) versus Qn(Se1)+Qn(Se2). It is demonstrated that JTL1(Se, Se: 2) becomes smaller when Qn(Se) increases, experimentally and theoretically.Figure 6
Plot of1J(Se, Se: 2) versus Qn(1Se) in 2.After clarification of the Y dependence inJTL1(Se, Se: 2), next extension is to elucidate the mechanism for J1(Se, Se: 2) on the basis of the MO theory.


### 3.3. Mechanism ofJ1(Se, Se) in 2a

How doJPSO1(Se, Se: 2) and JSD+FC1(Se, Se: 2) contribute to JTL1(Se, Se: 2) in the change of Y? JPSO1(Se, Se: 2) and JSD+FC1(Se, Se: 2) are plotted versus JTL1(Se, Se: 2) for various Y in Table 4. The results for JPSO1(Se, Se: 2) and JSD+FC1(Se, Se: 2) are given in (4) and (5), respectively. The correlations are very good, which shows that JPSO1(Se, Se: 2) contributes predominantly to JTL1(Se, Se: 2) (70%), irrespective of Y:
(4)JPSO1(Se,Se:2)=0.704×J1TL(Se,Se:2)+8.3(r2=0.999),(5)JSD+FC1(Se,Se:2)=0.295×J1TL(Se,Se:2)-8.0(r2=0.994)The origin ofJ1(Se, Se: 2) is elucidated by analyzing JPSO1(Se, Se: 2a) on the basis of the MO theory, since JPSO1(Se, Se) contributes predominantly to JTL1(Se, Se) irrespective of Y. Figure 7 depicts the contributions of JPSO1(Se, Se: 2a) separately from each ψi and each ψi→ψa transition. (a)–(c) in Figure 7 plot the contributions to JPSO1(Se, Se: 2a) from each ψi and each transition of the ψ67→ψa and ψ66→ψa 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 JPSO1(Se, Se: 2a). Especially, ψ67 (HOMO) and ψ66 (HOMO-1) control JPSO1(Se, Se: 2a). ψa of ψ68 determines JPSO1(Se, Se: 2a), among a lot of ψi→ψa transitions in ψi of ψ67 and ψ66, as shown in Figures 7(b) and 7(c).MO analysis ofJPSO1(Se, Se: 2a): (a) contributions from each ψi, (b) from each ψ67→ψa transition, and (c) from each ψ66→ψa transition.
(a)(b)(c)Figure8 shows the ψ67→ψ68 and ψ66→ψ68 transitions in JPSO1(Se, Se: 2a). The large JPSO1(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 JPSO1(Se, Se: 1a) at ϕ=0º in Figure 4, although ψ67 (2a) and ψ66 (2a) contain the π(Nap) character. Large JPSO1(Se, Se: 2) and small Jobsd1(Se, Se: 1) are well understood by the ϕ dependence in the calculated J1(Se, Se: 1a) values.Figure 8
MO analysis ofJPSO1(Se, Se: 2a): main contributions from the ψ67 (HOMO)→ψ68 (LUMO) and ψ66→ψ68 transitions are depicted.


## 3.1. ObservedJ1obsd(Se, Se)

Table1 collects Jobsd1(Se, Se), necessary for discussion. The magnitudes of the Jobsd1(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 Jobsd1(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). J1(Se, Se: 2) becomes smaller as the electron accepting ability of Y increases.


## 3.2. Mechanism ofJ1(Se, Se) in 1a

Table2 shows the calculated JTL1 and the components, JDSO1, JPSO1, JSD1, and JFC1, in J1(Se, Se: 1a). JTL1(Se, Se: 1a) is predicted to be less than 44 Hz for ϕ=90°±15°. Therefore, Jobsd1(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. J1(Se, Se: 1a) is predicted to be very large at ϕ=0° (684 Hz) and 180° (628 Hz). Consequently, Jobsd1(Se, Se: 2) of 331–379 Hz are essentially explained by J1(Se, Se: 1a) with ϕ=0°. Figure 2 draws the plots of JDSO1, JPSO1, JSD1, JFC1, JSD+FC1, and JTL1 versus ϕ in 1a. It is well demonstrated that JTL1 changes depending on ϕ, similarly to the case of J3(H, H), three-bond (vicinal) couplings in H1 NMR spectra [1, 2]. JDSO1 are negligible (< 0.03 Hz).Table 2
J1(Se, Se) values calculated for 1a(a), (b).
ϕErel(c)JPSO1JSD1JFC1JSD+FC1JTL1[°][kJ mol-1][Hz][Hz][Hz][Hz][Hz]0.036.9447.2217.818.6236.4683.715.033.0399.2200.615.2215.8615.030.025.3288.5163.12.7165.8454.360.06.176.1101.4−43.358.1134.275.00.920.087.8−64.723.143.188.40.04.184.5−76.77.811.990.00.04.284.6−77.96.710.9105.02.329.991.5−77.414.144.0120.07.494.7109.3−60.548.8143.5150.017.6291.5171.7−8.2163.5455.0165.021.5370.6201.19.0210.1580.7180.022.8400.7213.414.3227.7628.4For(a) the abbreviation, see text. J(b)1DSO being less than 0.03 Hz.Relative(c) to optimized value (−5267.7384 au) at ϕ = 88.38º in kJ mol-1.Figure 2
Plots ofJDSO1 (■),JPSO1 (□),JSD1 (▲),JFC1 (♦),JSD+FC1 (△), and JTL1 (○) versus ϕ(CSeSeC) in J1(Se, Se: 1a).How doJPSO1(Se, Se: 1a) and JSD+FC1(Se, Se: 1a) [=JSD1(Se, Se: 1a) + JFC1(Se, Se: 1a)] contribute to JTL1(Se, Se: 1a)? JPSO1(Se, Se: 1a) and JSD+FC1(Se, Se: 1a) are plotted versus JTL1(Se, Se: 1a), although not shown. The correlations are given in (2) and (3), respectively. The results exhibit that JPSO1(Se, Se: 1a) and JSD+FC1(Se, Se: 1a) contribute 65% and 35% to JTL1(Se, Se: 1a), respectively, irrespective of theϕ(CSeSeC) values:(2)J1PSO(Se,Se:1a)=0.651×J1TL(Se,Se:1a)-4.1(r2=0.999),(3)J1SD+FC(Se,Se:1a)=0.349×J1TL(Se,Se:1a)+4.2(r2=0.998).Why doesJ1(Se, Se: 1a) show the torsional angular dependence? What orbitals and transitions contribute to the dependence? JPSO1(Se, Se: 1a) is analyzed next.


### 3.2.1. Analysis ofJ1PSO(Se, Se) in 1a

The mechanism ofJPSO1(Se, Se: 1a) is discussed by analyzing the contributions separately from each ψi and each ψi→ψa transition. Table 3 lists the ϕ dependence of JPSO1(Se, Se: 1a) contributed from ψ1–ψ43, ψ1–ψ38, ψ39–ψ43, ψ39, ψ40, ψ41, ψ42, andψ43. The contribution from ψ39–ψ43 to JPSO1(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≈90º. Those of ψ39 and ψ40 do at ϕ≈135º (Figure 3(a)). The contributions from ψ42-ψ43 and ψ39–ψ41 almost cancel out at ϕ≈90º (Figure 3(b)).Table 3
Contributions to the torsional angular dependence inJ1PSO(Se, Se: 1a) from ψi (a),(b).
ϕ [°]0.015.030.060.075.088.490.0105.0120.0150.0165.0180.0ψ1–ψ43447.2399.2288.576.119.94.14.329.994.7291.4370.5400.7ψ39–ψ43449.9403.1294.984.435.220.420.645.9109.1302.2380.3410.4ψ39−121.2−117.6−108.9−80.9−63.0−44.9−42.6−18.98.7−146.9−155.1−157.7ψ40181.2163.4118.713.7−28.6−59.4−62.8−90.8−114.365.385.493.0ψ41−43.3−48.3−60.8−87.9−94.3−93.1−92.4−79.9−54.028.762.475.0ψ42−359.7−333.7−266.1−84.09.695.6111.921.2−71.9−261.5−328.1−352.7ψ43792.9739.4612.0323.7211.5122.2106.5214.3340.7616.6715.7752.8ψ42→ψ44(c)−333.3−307.1−240.9−69.415.693.3116.533.2−54.4−235.6−298.1−321.0ψ43→ψ44(c)747.2695.7574.7312.4206.8125.9103.2202.0320.7581.5673.8708.6In(a) Hz.For(b) the abbreviation, see text. Contribution(c) from the transition.Origin of the torsional angular dependence inJ1PSO (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.
(a)(b)Magnitudes of the contributions fromψ42 and ψ43 to JPSO1(Se, Se: 1a) are very large at 0º and 180º (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 0º, 90º, and 180º, respectively, and those from ψ39–ψ41 are 17, −198, and 10 Hz at 0º, 90º, and 180º, respectively. Therefore, the mechanism of J1PSO(Se, Se: 1a) will be clarified by analyzing the contributions from ψ42 and ψ43 at 0º and 180º. The mechanism would be complex at 90º, since the small magnitude is the results of the total contributions from ψ39–ψ43.Figure4 shows the ψ42→ψ44 and ψ43→ψ44 transitions at both ϕ=0º and 180º 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=0º and 180º. ψ42(HOMO-1) is essentially the same as ψ43(HOMO) at ϕ=90º. ψ42and ψ43 at ϕ=90º are also drawn in Figure 4, to show how ψ42 and ψ43 interconvert with each other. Contrary to the case of ϕ≈0 and 180º, all of ψ39–ψ43 contribute to J1PSO(Se, Se: 1a) at ϕ≈90º. Contributions from the ψ42→ψ44 and ψ43→ψ44 transitions to J1PSO(Se, Se: 1a) at 90º are almost cancelled by those from the ψ39→ψ44, ψ40→ψ44, and ψ41→ψ44 transitions. In addition, both J1SD(Se, Se: 1a) and J1FC(Se, Se: 1a) substantially contribute at ϕ≈90º. Consequently, it is difficult to specify a few orbitals, together with the transitions, which control J1(Se, Se: 1a) at ϕ≈90º. 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 J1(Se, Se: 1a) (see Figures 3 and 4). The MO description in Figure 4 visualizes the origin of J1PSO(Se, Se: 1a) and helps us to understand the mechanism, especially at ϕ=0º and 180º.Figure 4
Contributions toJ1PSO(Se, Se: 1a) from the ψ42→ψ44 and ψ43→ψ44 transitions at ϕ=0, 90, and 180º. The interconversion between ψ42 and ψ43 at ϕ≈90º is also depicted.After elucidation of the mechanism forJ1PSO(Se, Se: 1a), next extension is to clarify J1(Se, Se: 2) on the basis of the MO theory.


### 3.2.2. Evaluation ofJ1(Se, Se) for 2

Table4 collects the calculated JTL1(Se, Se: 2) values, together with JPSO(Se, Se: 2), JSD1(Se, Se: 2), JFC1(Se, Se: 2), and JSD+FC1(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 Jobsd1(Se, Se: 2) is well reproduced by the calculations. JTL1(Se, Se: 2) are predicted to be larger than the observed values by about 100 Hz. The DFT method overestimates the reciprocal energy differences (εa-εi)-1, which would partly be responsible for the larger evaluation. The J1(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 Jn(Se, Se) value calculated at the nonrelativistic level in this case.Table 4
J1(Se, Se) and Qn(Se) calculated on the full-optimized structure of 2(a), (b), (c).
CompoundJ1PSO[Hz]J1SD[Hz]J1FC[Hz]J1SD+FC[Hz]J1TL[Hz]Qn(Se1)Qn(Se2)Symmetry2a(Y=H)362.2195.2−54.1141.1503.30.23670.2367C2v2b(Y=OMe)394.3207.5−54.2153.3547.70.22560.2264Cs2c(Y=Me)363.6195.1−55.3139.8503.50.23340.2296Cs2d(Y=Cl)360.1193.4−53.1140.3500.40.24480.2443Cs2e(Y=COOMe)324.1178.2−55.7122.5446.60.25930.2556C12f(Y=CN)326.6180.6−52.6128.0454.60.26770.2564Cs2g(Y=NO2)299.7167.6−53.9113.7413.40.28240.2576C12a(Y=H)(d)390.7206.42.6209.0599.70.23670.2367C2vFor(a) the abbreviation, see text. JDSO(b)1 being less than 0.03 Hz. Se(c)1 and Se2 being attached to C1 and C8 in 4-Y-1,8-Se2C10H5 (2), respectively. On(d) the basis of scalar ZORA.Before discussion ofJ1(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(Se2: 2) versus Qn(Se1: 2). The correlations of the linear type (y=ax+b with r (correlation coefficient) are given in the figure. The results show that Qn(Se2: 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(Se1: 2) grows larger as the accepting ability of Y increases for all Y in Table 4. Qn(Se2: 2) seems saturated for Y of very strong acceptors such as CN and NO2 while Qn(Se1: 2) will not for all Y.Figure 5
Plot ofQn(2Se) versus Qn(1Se) in 2.How doJTL1(Se, Se: 2) being controlled? JTL1(Se, Se: 2) are plotted versus Qn(Se1), Qn(Se2), and Qn(Se1)+Qn(Se2). Figure 6 shows the plot of JTL1(Se, Se: 2) versus Qn(Se1), which gives best correlation among the three. The correlation is given in the figure. JTL1(Se, Se: 2) are confirmed to be controlled by Qn(Se1). One might imagine that JTL1 (Se, Se: 2) should be controlled by Qn(Se1)+Qn(Se2). The saturation in Qn(Se2) shown in Figure 5 would perturb to give good correlations for JTL1(Se, Se: 2) versus Qn(Se1)+Qn(Se2). It is demonstrated that JTL1(Se, Se: 2) becomes smaller when Qn(Se) increases, experimentally and theoretically.Figure 6
Plot of1J(Se, Se: 2) versus Qn(1Se) in 2.After clarification of the Y dependence inJTL1(Se, Se: 2), next extension is to elucidate the mechanism for J1(Se, Se: 2) on the basis of the MO theory.


## 3.2.1. Analysis ofJ1PSO(Se, Se) in 1a

The mechanism ofJPSO1(Se, Se: 1a) is discussed by analyzing the contributions separately from each ψi and each ψi→ψa transition. Table 3 lists the ϕ dependence of JPSO1(Se, Se: 1a) contributed from ψ1–ψ43, ψ1–ψ38, ψ39–ψ43, ψ39, ψ40, ψ41, ψ42, andψ43. The contribution from ψ39–ψ43 to JPSO1(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≈90º. Those of ψ39 and ψ40 do at ϕ≈135º (Figure 3(a)). The contributions from ψ42-ψ43 and ψ39–ψ41 almost cancel out at ϕ≈90º (Figure 3(b)).Table 3
Contributions to the torsional angular dependence inJ1PSO(Se, Se: 1a) from ψi (a),(b).
ϕ [°]0.015.030.060.075.088.490.0105.0120.0150.0165.0180.0ψ1–ψ43447.2399.2288.576.119.94.14.329.994.7291.4370.5400.7ψ39–ψ43449.9403.1294.984.435.220.420.645.9109.1302.2380.3410.4ψ39−121.2−117.6−108.9−80.9−63.0−44.9−42.6−18.98.7−146.9−155.1−157.7ψ40181.2163.4118.713.7−28.6−59.4−62.8−90.8−114.365.385.493.0ψ41−43.3−48.3−60.8−87.9−94.3−93.1−92.4−79.9−54.028.762.475.0ψ42−359.7−333.7−266.1−84.09.695.6111.921.2−71.9−261.5−328.1−352.7ψ43792.9739.4612.0323.7211.5122.2106.5214.3340.7616.6715.7752.8ψ42→ψ44(c)−333.3−307.1−240.9−69.415.693.3116.533.2−54.4−235.6−298.1−321.0ψ43→ψ44(c)747.2695.7574.7312.4206.8125.9103.2202.0320.7581.5673.8708.6In(a) Hz.For(b) the abbreviation, see text. Contribution(c) from the transition.Origin of the torsional angular dependence inJ1PSO (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.
(a)(b)Magnitudes of the contributions fromψ42 and ψ43 to JPSO1(Se, Se: 1a) are very large at 0º and 180º (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 0º, 90º, and 180º, respectively, and those from ψ39–ψ41 are 17, −198, and 10 Hz at 0º, 90º, and 180º, respectively. Therefore, the mechanism of J1PSO(Se, Se: 1a) will be clarified by analyzing the contributions from ψ42 and ψ43 at 0º and 180º. The mechanism would be complex at 90º, since the small magnitude is the results of the total contributions from ψ39–ψ43.Figure4 shows the ψ42→ψ44 and ψ43→ψ44 transitions at both ϕ=0º and 180º 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=0º and 180º. ψ42(HOMO-1) is essentially the same as ψ43(HOMO) at ϕ=90º. ψ42and ψ43 at ϕ=90º are also drawn in Figure 4, to show how ψ42 and ψ43 interconvert with each other. Contrary to the case of ϕ≈0 and 180º, all of ψ39–ψ43 contribute to J1PSO(Se, Se: 1a) at ϕ≈90º. Contributions from the ψ42→ψ44 and ψ43→ψ44 transitions to J1PSO(Se, Se: 1a) at 90º are almost cancelled by those from the ψ39→ψ44, ψ40→ψ44, and ψ41→ψ44 transitions. In addition, both J1SD(Se, Se: 1a) and J1FC(Se, Se: 1a) substantially contribute at ϕ≈90º. Consequently, it is difficult to specify a few orbitals, together with the transitions, which control J1(Se, Se: 1a) at ϕ≈90º. 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 J1(Se, Se: 1a) (see Figures 3 and 4). The MO description in Figure 4 visualizes the origin of J1PSO(Se, Se: 1a) and helps us to understand the mechanism, especially at ϕ=0º and 180º.Figure 4
Contributions toJ1PSO(Se, Se: 1a) from the ψ42→ψ44 and ψ43→ψ44 transitions at ϕ=0, 90, and 180º. The interconversion between ψ42 and ψ43 at ϕ≈90º is also depicted.After elucidation of the mechanism forJ1PSO(Se, Se: 1a), next extension is to clarify J1(Se, Se: 2) on the basis of the MO theory.


## 3.2.2. Evaluation ofJ1(Se, Se) for 2

Table4 collects the calculated JTL1(Se, Se: 2) values, together with JPSO(Se, Se: 2), JSD1(Se, Se: 2), JFC1(Se, Se: 2), and JSD+FC1(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 Jobsd1(Se, Se: 2) is well reproduced by the calculations. JTL1(Se, Se: 2) are predicted to be larger than the observed values by about 100 Hz. The DFT method overestimates the reciprocal energy differences (εa-εi)-1, which would partly be responsible for the larger evaluation. The J1(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 Jn(Se, Se) value calculated at the nonrelativistic level in this case.Table 4
J1(Se, Se) and Qn(Se) calculated on the full-optimized structure of 2(a), (b), (c).
CompoundJ1PSO[Hz]J1SD[Hz]J1FC[Hz]J1SD+FC[Hz]J1TL[Hz]Qn(Se1)Qn(Se2)Symmetry2a(Y=H)362.2195.2−54.1141.1503.30.23670.2367C2v2b(Y=OMe)394.3207.5−54.2153.3547.70.22560.2264Cs2c(Y=Me)363.6195.1−55.3139.8503.50.23340.2296Cs2d(Y=Cl)360.1193.4−53.1140.3500.40.24480.2443Cs2e(Y=COOMe)324.1178.2−55.7122.5446.60.25930.2556C12f(Y=CN)326.6180.6−52.6128.0454.60.26770.2564Cs2g(Y=NO2)299.7167.6−53.9113.7413.40.28240.2576C12a(Y=H)(d)390.7206.42.6209.0599.70.23670.2367C2vFor(a) the abbreviation, see text. JDSO(b)1 being less than 0.03 Hz. Se(c)1 and Se2 being attached to C1 and C8 in 4-Y-1,8-Se2C10H5 (2), respectively. On(d) the basis of scalar ZORA.Before discussion ofJ1(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(Se2: 2) versus Qn(Se1: 2). The correlations of the linear type (y=ax+b with r (correlation coefficient) are given in the figure. The results show that Qn(Se2: 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(Se1: 2) grows larger as the accepting ability of Y increases for all Y in Table 4. Qn(Se2: 2) seems saturated for Y of very strong acceptors such as CN and NO2 while Qn(Se1: 2) will not for all Y.Figure 5
Plot ofQn(2Se) versus Qn(1Se) in 2.How doJTL1(Se, Se: 2) being controlled? JTL1(Se, Se: 2) are plotted versus Qn(Se1), Qn(Se2), and Qn(Se1)+Qn(Se2). Figure 6 shows the plot of JTL1(Se, Se: 2) versus Qn(Se1), which gives best correlation among the three. The correlation is given in the figure. JTL1(Se, Se: 2) are confirmed to be controlled by Qn(Se1). One might imagine that JTL1 (Se, Se: 2) should be controlled by Qn(Se1)+Qn(Se2). The saturation in Qn(Se2) shown in Figure 5 would perturb to give good correlations for JTL1(Se, Se: 2) versus Qn(Se1)+Qn(Se2). It is demonstrated that JTL1(Se, Se: 2) becomes smaller when Qn(Se) increases, experimentally and theoretically.Figure 6
Plot of1J(Se, Se: 2) versus Qn(1Se) in 2.After clarification of the Y dependence inJTL1(Se, Se: 2), next extension is to elucidate the mechanism for J1(Se, Se: 2) on the basis of the MO theory.


## 3.3. Mechanism ofJ1(Se, Se) in 2a

How doJPSO1(Se, Se: 2) and JSD+FC1(Se, Se: 2) contribute to JTL1(Se, Se: 2) in the change of Y? JPSO1(Se, Se: 2) and JSD+FC1(Se, Se: 2) are plotted versus JTL1(Se, Se: 2) for various Y in Table 4. The results for JPSO1(Se, Se: 2) and JSD+FC1(Se, Se: 2) are given in (4) and (5), respectively. The correlations are very good, which shows that JPSO1(Se, Se: 2) contributes predominantly to JTL1(Se, Se: 2) (70%), irrespective of Y:
(4)JPSO1(Se,Se:2)=0.704×J1TL(Se,Se:2)+8.3(r2=0.999),(5)JSD+FC1(Se,Se:2)=0.295×J1TL(Se,Se:2)-8.0(r2=0.994)The origin ofJ1(Se, Se: 2) is elucidated by analyzing JPSO1(Se, Se: 2a) on the basis of the MO theory, since JPSO1(Se, Se) contributes predominantly to JTL1(Se, Se) irrespective of Y. Figure 7 depicts the contributions of JPSO1(Se, Se: 2a) separately from each ψi and each ψi→ψa transition. (a)–(c) in Figure 7 plot the contributions to JPSO1(Se, Se: 2a) from each ψi and each transition of the ψ67→ψa and ψ66→ψa 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 JPSO1(Se, Se: 2a). Especially, ψ67 (HOMO) and ψ66 (HOMO-1) control JPSO1(Se, Se: 2a). ψa of ψ68 determines JPSO1(Se, Se: 2a), among a lot of ψi→ψa transitions in ψi of ψ67 and ψ66, as shown in Figures 7(b) and 7(c).MO analysis ofJPSO1(Se, Se: 2a): (a) contributions from each ψi, (b) from each ψ67→ψa transition, and (c) from each ψ66→ψa transition.
(a)(b)(c)Figure8 shows the ψ67→ψ68 and ψ66→ψ68 transitions in JPSO1(Se, Se: 2a). The large JPSO1(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 JPSO1(Se, Se: 1a) at ϕ=0º in Figure 4, although ψ67 (2a) and ψ66 (2a) contain the π(Nap) character. Large JPSO1(Se, Se: 2) and small Jobsd1(Se, Se: 1) are well understood by the ϕ dependence in the calculated J1(Se, Se: 1a) values.Figure 8
MO analysis ofJPSO1(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 J1(Se, Se) values are analyzed as the first step to investigate the nature of the bonded and nonbonded interactions between the Se atoms through Jn(Se, Se). QC calculations are necessary for the analysis and the interpretation of the J values with physical meanings. Calculated JTLn are composed of the contributions from JDSOn, JPSOn, JSDn, and JFCn. 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 ψi and each ψi→ψa transition, where ψi and ψa are occupied and unoccupied MO's, respectively.J1(Se, Se) is calculated modeled by MeSeSeMe (1a), which shows the typical torsional angular dependence of ϕ(CMeSeSeCMe). The dependence explains well Jobsd1(Se, Se) of small values for RSeSeR′ (1) and large values for 4-Y-1,8-Se2C10H5 (2) which correspond to symperiplanar diselenides. JTL1(Se, Se: 2) are confirmed to be controlled by Qn(Se). JTL1(Se, Se: 2) are demonstrated to be smaller when Qn(Se) becomes larger, experimentally and theoretically. The PSO terms contribute predominantly to J1(Se, Se). The contributions are analyzed separately from each ψi and each ψi→ψa 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.



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*Source: 381925-2009-08-06.xml*