Table of Contents Author Guidelines Submit a Manuscript
Bioinorganic Chemistry and Applications
Volume 2009, Article ID 381925, 9 pages
http://dx.doi.org/10.1155/2009/381925
Research Article

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

Department of Material Science and Chemistry, Faculty of Systems Engineering, Wakayama University, 930 Sakaedani, Wakayama 640-8510, Japan

Received 19 January 2009; Revised 15 April 2009; Accepted 8 May 2009

Academic Editor: Vito Lippolis

Copyright © 2009 Akito Tanioku et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Nuclear couplings for the Se-Se bonds, , are analyzed on the basis of the molecular orbital (MO) theory. The values are calculated by employing the triple basis sets of the Slater type at the DFT level. are calculated modeled by MeSeSeMe (1a), which shows the typical torsional angular dependence on . The dependence explains well the observed of small values ( Hz) for (1) (simple derivatives of 1a) and large values (330–380 Hz) observed for 4-substituted naphto[1,8-]-1,2-diselenoles (2) which correspond to symperiplanar diselenides. (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 and each transition, where and 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 () 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 [110]. One–bond (), two-bond (geminal) (), three-bond (vicinal) (), and even longer coupling constants are observed between selenium atoms, which will give important information around the coupled nuclei. The mechanism for must be of the through-bond type; however, that for would contain through-space interactions, especially for . 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 (Se, Se) values are reported for alkyl and/or aryl derivatives of dimethyl diselenide (1a) (: 1). They are usually small ((Se, Se:  1) 64 Hz ; see Table 1). We examined (Se, Se) of naphto[1,8-c,d]-1,2-diselenole (4-Y-1,8- (2): (a) [1115], OMe (b), Me (c), Cl (d), COOMe (e), CN (f), and (g), which correspond to the symperiplanar diselenides (Figure 1). The (Se, Se) values are measured for 2c, 2d, and 2g, and large (Se, Se) values of 330–380 Hz are detected. Table 1 summarizes the (Se, Se) values.

tab1
Table 1: Observed (Se, Se) values of some selenium compounds.
381925.fig.001
Figure 1

Why are (Se, Se: 2) much larger than (Se, Se: 1)? How do (Se, Se: 2) depend on the substituent Y in 2? (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 (Se, Se) [18]. (Se, Se) are calculated for 1a and 2ag.

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

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

381925.scheme.001
Scheme 1: How do the indirect nuclear spin-spin couplings originate? Mechanisms for , , , and terms, contributing to .

Calculated values are evaluated separately by the four components as shown in (1). The (Se, Se) values are evaluated using the Slater-type atomic orbitals, which are equipped in the ADF 2008 program [1923]. Evaluations of the values are performed employing the ADF program, after structural optimizations with the Gaussian 03 program [24]. Contributions from each and each transition are evaluated separately, where and 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 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 and DMSO- solutions. , , and 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 and NMR spectra and relative to reference compound for NMR spectra.

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

According to a method similar to that previously reported for 2a [1117] from 1,8-dichloro-4-methylnaphthalene, 2b was obtained as purple needles in 68 yield, m.p. 127.0–C. NMR (, 300 MHz, TMS): 2.50 (s, 3H), 7.09 (dd, 1H, and 7.6 Hz), 7.25 (d, 1H,  Hz), 7.36 (dd, 1H, and 6.9 Hz), 7.55 (dd, 1H, and 8.4 Hz); NMR (, 75.5 MHz, TMS): 18.6, 120.4, 120.7, 121.0, 127.4, 128.2, 130.4, 137.0, 137.3, 138.0, 141.1; NMR (, 76.2 MHz, ): 411.8, 420.6. Anal. Calc. for : 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 ()

According to a method similar to that previously reported for 2a [1117] from 1,4,8-trichloronaphthalene, 2c was obtained as brown needles in 58 yield, m.p. 155.0–C. 1H NMR (, 300 MHz, TMS): 7.24 (d, 1H,  Hz), 7.30 (d, 1H,  Hz), 7.34 (t, 1H,  Hz), 7.39 (dd, 1H, and 7.4 Hz), 7.81 (dd, 1H, and 7.9 Hz); NMR (, 75.5 MHz, TMS): 120.5, 120.6, 121.9, 127.3, 127.4, 128.6, 135.0, 138.5, 140.0, 141.2; NMR (, 76.2 MHz, ): 422.6, 444.6. Anal. Calc. for : 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 ()

According to a method similar to that previously reported for 2a [1117] from 1,8-dibromo-4-nitronaphthalene, 2d was obtained as dark purple needles in 28 yield, m.p. 196.0–C. NMR (, 300 MHz, TMS): 7.40 (d, 1H,  Hz), 7.52 (dd, 1H, and 7.6 Hz), 7.53 (s, 1H), 8.18 (d, 1H,  Hz), 8.51 (dd, 1H, and 4.1 Hz); NMR (DMSO-, 300 MHz, TMS): 7.57 (dd, 1H, and 8.5 Hz), 7.77 (d, 1H,  Hz), 7.84 (dd, 1H, and 7.5 Hz), 8.20 (d, 1H,  Hz), 8.29 (dd, 1H, and 8.5 Hz); NMR (DMSO-, 75.5 MHz, TMS): 118.2, 120.0, 123.4, 127.1, 129.4, 131.1, 139.0, 140.8, 144.2, 155.5; NMR (, 76.2 MHz, ): 448.8, 474.4. Anal. Calc. for : C, 36.50; H, 1.53; N, 4.26; found: C, 36.41; H, 1.40; N, 4.19.

2.5. Measurements of (Se, Se)

During the measurement of NMR spectra for 2g () 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, (Se, Se) of 330.8 Hz was obtained. The (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 [2428] at the DFT (B3LYP) level [2932]. The torsional angle () is 88.38 in the full-optimized structure of 1a. Calculations that are further performed on 1a: 1a are fully optimized except for , which are fixed by every or . Optimizations are also performed on 2a–g using the 6-311+G(3df) basis sets [2528] for Se and the 6-311+G(3d,2p) basis sets for other nuclei at the DFT (B3LYP) level [2932]. The symmetry is assumed for 2a, for 2bd and 2f, and the symmetry for 2e and 2g.

The (Se, Se) values are calculated with the triple basis sets of the Slater type with two sets of polarization functions (21s, 22s, 22p, 23s, 23p, 33d, 34s, 34p, 14d, and 14f for Se) at the DFT (BLYP) level of the ADF 2008 program [1923], applying on the optimized structures with the Gaussian 03 program [24]. Calculations are performed at the nonrelativistic level. The scalar ZORA relativistic formulation [3335] is also applied to 2a, for convenience of comparison. The values are evaluated separately by , , , and , as shown in (1). Mechanisms of the nuclear couplings are revealed by decomposing the contributions to each and each transition [36, 37].

3. Results and Discussion

3.1. Observed (Se, Se)

Table 1 collects (Se, Se), necessary for discussion. The magnitudes of the (Se, Se) values are usually small (< 64 Hz) for the simple derivatives of MeSeSeMe (1a) (: 1) [9, 16, 17]. On the other hand, large (Se, Se) are recorded for 2 (4-Y-1,8-), which correspond to symperiplanar diselenides, although not detected in 2a () [1115]. The values are 379.4 Hz for 2b (), 375.9 Hz for 2c (), and 330.8 Hz for 2d (). (Se, Se: 2) becomes smaller as the electron accepting ability of Y increases.

3.2. Mechanism of (Se, Se) in

Table 2 shows the calculated and the components, , , , and , in (Se, Se: 1a). (Se, Se: 1a) is predicted to be less than 44 Hz for . Therefore, (Se, Se: 1) is explained substantially and modeled by 1a with , although R and in 1 must also affect on the values. (Se, Se: 1a) is predicted to be very large at (684 Hz) and (628 Hz). Consequently, (Se, Se: 2) of 331–379 Hz are essentially explained by (Se, Se: 1a) with . Figure 2 draws the plots of , , , , , and versus in 1a. It is well demonstrated that changes depending on , similarly to the case of (H, H), three-bond (vicinal) couplings in NMR spectra [1, 2]. are negligible (< 0.03 Hz).

tab2
Table 2: (Se, Se) values calculated for (a), (b).
381925.fig.002
Figure 2: Plots of (), (), (), (), (), and () versus (CSeSeC) in (Se, Se: 1a).

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

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

3.2.1. Analysis of (Se, Se) in

The mechanism of (Se, Se: 1a) is discussed by analyzing the contributions separately from each and each transition. Table 3 lists the dependence of (Se, Se: 1a) contributed from , , , , , , , and. The contribution from to (Se, Se: 1a) is large, whereas that from is small, although not shown. The plot of the contributions from (y) versus those from (x) provides an excellent correlation (). Figure 3(a) shows those from , , , , and and Figure 3(b)exhibits those from , , and . Contributions from and exchange with each other at . Those of and do at (Figure 3(a)). The contributions from - and almost cancel out at (Figure 3(b)).

tab3
Table 3: Contributions to the torsional angular dependence in (Se, Se: ) from .
fig3
Figure 3: Origin of the torsional angular dependence in (Se, Se: 1a): (a) contributions from each of , , , , and and (b) those from ,, and .

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

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

381925.fig.004
Figure 4: Contributions to (Se, Se: 1a) from the and transitions at , 90, and . The interconversion between and at is also depicted.

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

3.2.2. Evaluation of (Se, Se) for

Table 4 collects the calculated (Se, Se: 2) values, together with (Se, Se: 2), (Se, Se: 2), (Se, Se: 2), and (Se, Se: 2). Table 4 also contains the nuclear changes calculated with the natural bond orbital analysis (NBO) method (Qn(Se) [3840] for 2 having Y of H (a), OMe (b), Me (c), Cl (d), COOMe (e), CN (f), and (g). The Y dependence of (Se, Se: 2) is well reproduced by the calculations. (Se, Se: 2) are predicted to be larger than the observed values by about 100 Hz. The DFT method overestimates the reciprocal energy differences , which would partly be responsible for the larger evaluation. The (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 (Se, Se) value calculated at the nonrelativistic level in this case.

tab4
Table 4: (Se, Se) and Qn(Se) calculated on the full-optimized structure of (a), (b), (c).

Before discussion of (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) versus Qn(: 2). The correlations of the linear type ( with r (correlation coefficient) are given in the figure. The results show that Qn(: 2) grows larger as the accepting ability of Y increases for , OMe, Me, Cl, and COOMe then it becomes almost constant for and while Qn(: 2) grows larger as the accepting ability of Y increases for all Y in Table 4. Qn(: 2) seems saturated for Y of very strong acceptors such as CN and while Qn(: 2) will not for all Y.

381925.fig.005
Figure 5: Plot of Qn(2Se) versus Qn(1Se) in 2.

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

381925.fig.006
Figure 6: Plot of 1J(Se, Se: 2) versus Qn(1Se) in 2.

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

3.3. Mechanism of (Se, Se) in

How do (Se, Se: 2) and (Se, Se: 2) contribute to (Se, Se: 2) in the change of Y? (Se, Se: 2) and (Se, Se: 2) are plotted versus (Se, Se: 2) for various Y in Table 4. The results for (Se, Se: 2) and (Se, Se: 2) are given in (4) and (5), respectively. The correlations are very good, which shows that (Se, Se: 2) contributes predominantly to (Se, Se: 2) (70), irrespective of Y:

The origin of (Se, Se: 2) is elucidated by analyzing (Se, Se: 2a) on the basis of the MO theory, since (Se, Se) contributes predominantly to (Se, Se) irrespective of Y. Figure 7 depicts the contributions of (Se, Se: 2a) separately from each and each transition. (a)–(c) in Figure 7 plot the contributions to (Se, Se: 2a) from each and each transition of the and types, respectively. In Figure 7(a), contributions around , , and 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 (Se, Se: 2a). Especially, (HOMO) and (HOMO-1) control (Se, Se: 2a). of determines (Se, Se: 2a), among a lot of transitions in of and , as shown in Figures 7(b) and 7(c).

fig7
Figure 7: MO analysis of (Se, Se: 2a): (a) contributions from each , (b) from each transition, and (c) from each transition.

Figure 8 shows the and transitions in (Se, Se: 2a). The large (Se, Se: 2a) value arises from the mixing of [LUMO: (Se–Se)] into [HOMO: (Se–Se)] and [HOMO-1: (Se–Se)] at the singlet state. The MO presentation in Figure 8 is essentially the same as the and transitions in (Se, Se: 1a) at in Figure 4, although (2a) and (2a) contain the (Nap) character. Large (Se, Se: 2) and small (Se, Se: 1) are well understood by the dependence in the calculated (Se, Se: 1a) values.

381925.fig.008
Figure 8: MO analysis of (Se, Se: 2a): main contributions from the (HOMO)→ (LUMO) and transitions are depicted.

4. Conclusion

Nuclear spin-spin coupling constants () provide highly important information around coupled nuclei, containing strongly bonded and weakly interacting states. The (Se, Se) values are analyzed as the first step to investigate the nature of the bonded and nonbonded interactions between the Se atoms through (Se, Se). QC calculations are necessary for the analysis and the interpretation of the values with physical meanings. Calculated are composed of the contributions from , , , and . 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 and each transition, where and are occupied and unoccupied MO's, respectively.

(Se, Se) is calculated modeled by MeSeSeMe (1a), which shows the typical torsional angular dependence of (SeSe). The dependence explains well (Se, Se) of small values for (1) and large values for 4-Y-1,8- (2) which correspond to symperiplanar diselenides. (Se, Se: 2) are confirmed to be controlled by Qn(Se). (Se, Se: 2) are demonstrated to be smaller when Qn(Se) becomes larger, experimentally and theoretically. The PSO terms contribute predominantly to (Se, Se). The contributions are analyzed separately from each and each 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.

References

  1. M. Karplus, “Contact electron-spin coupling of nuclear magnetic moments,” The Journal of Chemical Physics, vol. 30, no. 1, pp. 11–15, 1959. View at Publisher · View at Google Scholar
  2. M. Karplus, “Vicinal proton coupling in nuclear magnetic resonance,” Journal of the American Chemical Society, vol. 85, no. 18, pp. 2870–2871, 1963. View at Publisher · View at Google Scholar
  3. M. Barfield and W. B. Smith, “Internal H-C-C angle dependence of vicinal 1H-1H coupling constants,” Journal of the American Chemical Society, vol. 114, no. 5, pp. 1574–1581, 1992. View at Publisher · View at Google Scholar
  4. F. B. Mallory, C. W. Mallory, K. E. Butler et al., “Nuclear spin-spin coupling via nonbonded interactions. 8. The distance dependence of through-space fluorine-fluorine coupling,” Journal of the American Chemical Society, vol. 122, no. 17, pp. 4108–4116, 2000. View at Publisher · View at Google Scholar
  5. T. Helgaker, M. Jaszuński, and K. Ruud, “Ab initio methods for the calculation of NMR shielding and indirect spin-spin coupling constants,” Chemical Reviews, vol. 99, no. 1, pp. 293–352, 1999. View at Publisher · View at Google Scholar
  6. H. Fukui, “Theory and calculation of nuclear spin-spin coupling constants,” Progress in Nuclear Magnetic Resonance Spectroscopy, vol. 35, no. 3, pp. 267–294, 1999. View at Publisher · View at Google Scholar
  7. M. Bienati, C. Adamo, and V. Barone, “Performance of a new hybrid Hartree—Fock/Kohn—Sham model (B98) in predicting vibrational frequencies, polarisabilities and NMR chemical shifts,” Chemical Physics Letters, vol. 311, no. 1-2, pp. 69–76, 1999. View at Publisher · View at Google Scholar
  8. R. H. Contreras, J. E. Peralta, C. G. Giribet, M. C. Ruiz de Azua, and J. C. Facelli, “Advances in theoretical and physical aspects of spin-spin coupling constants,” in Annual Reports on NMR Spectroscopy, G. A. Webb, Ed., vol. 41, pp. 55–184, Academic Press, New Yrok, NY, USA, 2000. View at Google Scholar
  9. T. M. Klapötke and M. Broschag, Eds., Compilation of Reported 77Se NMR Chemical Shifts, John Wiley-VCH, New York, NY, USA, 1996.
  10. T. Helgaker and M. Pecul, “Spin-spin coupling constants with HF and DFT method,” in Calculations of NMR and EPR Parameters: Theory and Applications, M. Kaupp, M. Bühl, and V. G. Malkin, Eds., chapter 7, Wiley-VCH, Weinheim, Germany, 2004. View at Google Scholar
  11. J. Meinwald, D. Dauplaise, F. Wudl, and J. J. Hauser, “Peri-bridged naphthalenes from 1,8-dilithionaphthalene,” Journal of the American Chemical Society, vol. 99, no. 1, pp. 255–257, 1977. View at Publisher · View at Google Scholar
  12. J. Meinwald, D. Dauplaise, and J. Clardy, “Peri-bridged naphthalenes. 2. Unsymmetrical diatomic chalcogen bridges,” Journal of the American Chemical Society, vol. 99, no. 23, pp. 7743–7744, 1977. View at Publisher · View at Google Scholar
  13. D. Dauplaise, J. Meinwald, J. C. Scott, H. Temkin, and J. Clardy, “Synthesis and properties of chalcogen-bridged naphthalenes: a new series of electron donors,” Annals of the New York Academy of Sciences, vol. 313, no. 1, pp. 382–394, 1978. View at Publisher · View at Google Scholar
  14. K. Yui, Y. Aso, and T. Otsubo, “Syntheses and properties of binaphtho[1,8-del-1,3-dithiin-2-ylidene and its selenium analogue,” Chemistry Letters, vol. 15, no. 4, pp. 551–554, 1986. View at Publisher · View at Google Scholar
  15. Y. Aso, K. Yui, T. Miyoshi, T. Otsubo, F. Ogura, and J. Tanaka, “Dichalcogen-bridged acenaphthenes as new electron donors,” Bulletin of the Chemical Society of Japan, vol. 61, no. 6, pp. 2013–2018, 1988. View at Publisher · View at Google Scholar
  16. J. A. Anderson, J. D. Odom, and A. J. Zozulin, “Preparation of unsymmetrical alkyl methyl and alkyl phenyl diselenides and determination of their selenium-77 chemical shifts and 77Se-77Se spin-spin coupling constants,” Organometallics, vol. 3, no. 10, pp. 1458–1465, 1984. View at Publisher · View at Google Scholar
  17. G. Llabres, M. Baiwir, J.-L. Piette, and L. Christiaens, “77Se, 13C and 1H NMR investigations on ortho-carbonyl benzeneselenenyl derivatives,” Organic Magnetic Resonance, vol. 15, no. 2, pp. 152–154, 1981. View at Publisher · View at Google Scholar
  18. W. Nakanishi and S. Hayashi, “Torsional angular dependence of J1(Se, Se) and fermi contact control of J4(Se, Se): analysis of Jn(Se, Se)(n=14) based on molecular orbital theory,” Chemistry: A European Journal, vol. 14, no. 18, pp. 5645–5655, 2008. View at Publisher · View at Google Scholar
  19. G. te Velde, F. M. Bickelhaupt, E. J. Baerends et al., “Chemistry with ADF,” Journal of Computational Chemistry, vol. 22, no. 9, pp. 931–967, 2001. View at Publisher · View at Google Scholar
  20. C. Fonseca Guerra, J. G. Snijders, G. Te Velde, and E. J. Baerends, “Towards an order-N DFT method,” Theoretical Chemistry Accounts, vol. 99, no. 6, pp. 391–403, 1998. View at Publisher · View at Google Scholar
  21. E. J. Baerends, J. Autschbach, A. Bérces et al., “ADF 2008.01, SCM, Theoretical Chemistry,” Vrije Universiteit, Amsterdam, The Netherlands, http://www.scm.com/.
  22. E. van Lenthe and E. J. Baerends, “Optimized Slater-type basis sets for the elements 1-118,” Journal of Computational Chemistry, vol. 24, no. 9, pp. 1142–1156, 2003. View at Publisher · View at Google Scholar
  23. D. P. Chong, E. van Lenthe, S. Van Gisbergen, and E. J. Baerends, “Even-tempered slater-type orbitals revisited: from hydrogen to krypton,” Journal of Computational Chemistry, vol. 25, no. 8, pp. 1030–1036, 2004. View at Publisher · View at Google Scholar
  24. M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., GAUSSIAN 03 (Revision D.05), Gaussian, Inc., Pittsburgh, Pa, USA, 2004.
  25. R. C. Binning Jr. and L. A. Curtiss, “Compact contracted basis sets for third-row atoms: Ga-Kr,” Journal of Computational Chemistry, vol. 11, no. 10, pp. 1206–1216, 1990. View at Publisher · View at Google Scholar
  26. L. A. Curtiss, M. P. McGrath, J.-P. Blaudeau, N. E. Davis, R. C. Binning Jr., and L. Radom, “Extension of Gaussian-2 theory to molecules containing third-row atoms Ga-Kr,” The Journal of Chemical Physics, vol. 103, no. 14, pp. 6104–6113, 1995. View at Publisher · View at Google Scholar
  27. M. P. McGrath and L. Radom, “Extension of Gaussian-1 (G1) theory to bromine-containing molecules,” The Journal of Chemical Physics, vol. 94, no. 1, pp. 511–516, 1991. View at Publisher · View at Google Scholar
  28. T. Clark, J. Chandrasekhar, G. W. Spitznagel, and P. Von Ragué Schleyer, “Efficient diffuse function-augmented basis sets for anion calculations—III: the 3-21+G basis set for first-row elements, Li-F,” Journal of Computational Chemistry, vol. 4, no. 3, pp. 294–301, 1983. View at Publisher · View at Google Scholar
  29. A. D. Becke, “Density-functional exchange-energy approximation with correct asymptotic behavior,” Physical Review A, vol. 38, no. 6, pp. 3098–3100, 1988. View at Publisher · View at Google Scholar
  30. A. D. Becke, “Density-functional thermochemistry—III: the role of exact exchange,” The Journal of Chemical Physics, vol. 98, no. 7, pp. 5648–5652, 1993. View at Publisher · View at Google Scholar
  31. C. Lee, W. Yang, and R. G. Parr, “Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density,” Physical Review B, vol. 37, no. 2, pp. 785–789, 1988. View at Publisher · View at Google Scholar
  32. B. Miehlich, A. Savin, H. Stoll, and H. Preuss, “Results obtained with the correlation energy density functionals of becke and Lee, Yang and Parr,” Chemical Physics Letters, vol. 157, no. 3, pp. 200–206, 1989. View at Publisher · View at Google Scholar
  33. E. van Lenthe, E. J. Baerends, and J. G. Snijders, “Relativistic regular two-component Hamiltonians,” The Journal of Chemical Physics, vol. 99, no. 6, pp. 4597–4610, 1993. View at Publisher · View at Google Scholar
  34. E. van Lenthe, E. J. Baerends, and J. G. Snijders, “Relativistic total energy using regular approximations,” The Journal of Chemical Physics, vol. 101, no. 11, pp. 9783–9792, 1994. View at Publisher · View at Google Scholar
  35. E. van Lenthe, A. Ehlers, and E. J. Baerends, “Geometry optimizations in the zero order regular approximation for relativistic effects,” The Journal of Chemical Physics, vol. 110, no. 18, pp. 8943–8953, 1999. View at Publisher · View at Google Scholar
  36. J. Autschbach and T. Ziegler, “Nuclear spin-spin coupling constants from regular approximate relativistic density functional calculations—I: formalism and scalar relativistic results for heavy metal compounds,” The Journal of Chemical Physics, vol. 113, no. 3, pp. 936–947, 2000. View at Publisher · View at Google Scholar
  37. J. Autschbach and T. Ziegler, “Nuclear spin-spin coupling constants from regular approximate relativistic density functional calculations—II: spin-orbit coupling effects and anisotropies,” The Journal of Chemical Physics, vol. 113, no. 21, pp. 9410–9418, 2000. View at Publisher · View at Google Scholar
  38. A. E. Reed, R. B. Weinstock, and F. Weinhold, “Natural population analysis,” The Journal of Chemical Physics, vol. 83, no. 2, pp. 735–746, 1985. View at Publisher · View at Google Scholar
  39. J. E. Carpenter and F. Weinhold, “Analysis of the geometry of the hydroxymethyl radical by the “different hybrids for different spins” natural bond orbital procedure,” Journal of Molecular Structure: THEOCHEM, vol. 169, pp. 41–62, 1988. View at Publisher · View at Google Scholar
  40. E. D. Glendening, A. E. Reed, J. E. Carpenter, and F. Weinhold, “NBO Ver. 3.1”.