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 1 J(Se, Se)

Nuclear couplings for the Se-Se bonds, 1 J(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. 1 J(Se, Se) are calculated modeled by MeSeSeMe (1a), which shows the typical torsional angular dependence on ϕ(CMeSeSeCMe). The dependence explains well the observed 1 J 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. 1 J (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.

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][2][3][4][5][6][7][8][9][10]. One-bond ( 1 J ), two-bond (geminal) ( 2 J ), three-bond (vicinal) ( 3 J ), and even longer coupling constants ( n J (n ≥ 4)) are observed between selenium atoms, which will give important information around the coupled nuclei. The mechanism for 1 J must be of the through-bond type; however, that for n J (n ≥ 2) would contain through-space interactions, especially for n J (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.
Why are 1 J obsd (Se, Se: 2) much larger than 1 J obsd (Se, Se: 1)? How do 1 J obsd (Se, Se: 2) depend on the substituent Y in 2? 1 J (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 n J (Se, Se) [18]. 1 J (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 ( n J TL ) is composed  Figure 1 of the contributions from the diamagnetic spin-orbit (DSO) term ( n J DSO ), the paramagnetic spin-orbit (PSO) term ( n J PSO ), the spin-dipolar (SD) term ( n J SD ), and the Fermi contact (FC) term ( n J FC ), n J TL = n J DSO + n J PSO + n J SD + n J FC .
Scheme 1 summarizes the mechanism of the indirect nuclear spin-spin couplings. The origin of the terms, n J DSO , n J PSO , n J SD , and n J FC , is also illustrated, contributing to n J TL . The ground state of a molecule (M) is the singlet state (S 0 ) if the nuclei (N) in M have no magnetic moments. However, the ground state cannot be the pure S 0 if N possesses magnetic moments, μ N . The ground state perturbed by μ N is expressed as follows: DSO arise by the reorganization of S 0 ; therefore, they are usually very small. PSO appears by the mixing of upper singlet states (S 1 , S 2 , S 3 , . . .). FC and SD originate if admixtures occur from upper triplet states (T 1 , T 2 , T 3 , . . .), where only s-type atomic orbitals contribute to FC. Calculated 1 J TL values are evaluated separately by the four components as shown in (1). The 1 J (Se, Se) values are evaluated using the Slater-type atomic orbitals, which are equipped in the ADF 2008 program [19][20][21][22][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.

Materials and Measurements.
Manipulations were performed under an argon atmosphere with standard vacuumline 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 CDCl 3 and DMSO-d 6 solutions. 1 H , 13 C , and 77 Se 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 1 H and 13 C NMR spectra and relative to reference compound Me 2 Se for 77 Se NMR spectra.
Magnitudes of the contributions from ψ 42 and ψ 43 to 1 J PSO (Se, Se: 1a) are very large at 0 o and 180 o (Table 3)   does not change so much depending on φ. Therefore, the behavior of ψ 39 -ψ 43 must be mainly responsible for the φ dependence in 1 J (Se, Se: 1a) (see Figures 3 and 4). The MO description in Figure 4 visualizes the origin of 1 J PSO (Se, Se: 1a) and helps us to understand the mechanism, especially at φ = 0 o and 180 o . After elucidation of the mechanism for 1 J PSO (Se, Se: 1a), next extension is to clarify 1 J (Se, Se: 2) on the basis of the MO theory.  Table 4 also contains the nuclear changes calculated with the natural bond orbital analysis (NBO) method (Qn(Se)) [38][39][40] for 2 having Y of H (a), OMe (b), Me (c), Cl (d), COOMe (e), CN (f), and NO 2 (g). The Y dependence of 1 J obsd (Se, Se: 2) is well reproduced by the calculations. 1 J 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 1 J (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 n J (Se, Se) value calculated at the nonrelativistic level in this case.   Before discussion of 1 J (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( 2 Se : 2) versus Qn( 1 Se : 2). The correlations of the linear type (y = ax + b with r (correlation coefficient)) are given in the figure. The results show that Qn( 2 Se : 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 NO 2 while Qn( 1 Se : 2) grows larger as the accepting ability of Y increases for all Y in Table 4. Qn( 2 Se : 2) seems saturated for Y of very strong acceptors such as CN and NO 2 while Qn( 1 Se : 2) will not for all Y.
After clarification of the Y dependence in 1 J TL (Se, Se: 2), next extension is to elucidate the mechanism for 1 J (Se, Se: 2) on the basis of the MO theory.  Table 4. The results for 1 J PSO (Se, Se: 2) and 1 J SD+FC (Se, Se: 2) are given in (4) and (5), respectively. The correlations are very good, which shows that 1 J PSO (Se, Se: 2) contributes predominantly to 1 J TL (Se, Se: 2) (70%), irrespective of Y:

Conclusion
Nuclear spin-spin coupling constants (J) provide highly important information around coupled nuclei, containing strongly bonded and weakly interacting states. The 1 J (Se, Se) values are analyzed as the first step to investigate the nature of the bonded and nonbonded interactions between the Se atoms through n J (Se, Se). QC calculations are necessary for the analysis and the interpretation of the J values with physical meanings. Calculated n J TL are composed of the contributions from n J DSO , n J PSO , n J SD , and n J 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. 1 J (Se, Se) is calculated modeled by MeSeSeMe (1a), which shows the typical torsional angular dependence of φ(C Me SeSeC Me ). The dependence explains well 1 J obsd (Se, Se) of small values for RSeSeR (1) and large values for 4-Y-1,8-Se 2 C 10 H 5 (2) which correspond to symperiplanar diselenides. 1 J TL (Se, Se: 2) are confirmed to be controlled by Qn(Se). 1 J TL (Se, Se: 2) are demonstrated to be smaller when Qn(Se) becomes larger, experimentally and theoretically. The PSO terms contribute predominantly to 1 J (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 spinspin 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.