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Published in final edited form as: J Mol Struct. 2015 Feb 5;1081:530–535. doi: 10.1016/j.molstruc.2014.10.023

Influence of Benzannulation on Metal Coordination Geometries: Synthesis and Structural Characterization of Tris(2-mercapto-1-methylbenzimidazolyl)hydroborato Cadmium Bromide, {[TmMeBenz]Cd(μ-Br)}2

Joshua H Palmer 1, Gerard Parkin 1,
PMCID: PMC4296741  NIHMSID: NIHMS638647  PMID: 25601793

Abstract

The tris(2-mercapto-1-methylbenzimidazolyl)hydroborato cadmium complex, {[TmMeBenz]Cd(μ–Br)}2, may be synthesized via the reaction of [TmMeBenz]K with CdBr2. X-ray diffraction demonstrates that {[TmMeBenz]Cd(μ–Br)}2 exists as a dimer, which is in marked contrast to the monomeric structure of the non-benzannulated counterpart, [TmMe]CdBr, and thereby demonstrates that benzannulation of tris(2-mercapto-1-methylbenzimidazolyl)hydroborato ligands can have a distinct impact on the molecular structure of their metal complexes. In accord with this observation, density functional theory calculations indicate that the benzannulated dimers, {[TmMeBenz]Cd(μ–X)}2 (X = Cl, Br, I), are more stable with respect to dissociation than are their non-benzannulated counterparts, {[TmMe]Cd(μ–X)}2. Furthermore, the calculations also indicate that the stability of the dimer depends on the nature of X, such that the dimer becomes more stable in the sequence I < Br < Cl.

Keywords: Cadmium, tris(2-mercaptoimidazolyl)hydroborato, halide, benzannulation, benzannulation, trigonal-bipyramidal

INTRODUCTION

The tris(mercaptoimidazolyl)hydroborato class of ligands, [TmR], as introduced by Reglinski and Spicer,1,2,3 has proven to be of much use in coordination chemistry by virtue of its ability to provide a well-defined [S3] donor platform, which provides a valuable complement to Trofiomenko’s [N3] donor tris(pyrazolyl)hydroborato class of ligands.4,5,6 For example, we have used [TmR] ligands both to (i) model aspects of metalloenzymes that feature sulfur-rich active sites and (ii) mimic the interactions of toxic metals such as mercury, cadmium and lead with cysteine thiolate groups.712 One reason for the widespread use of [TmR] ligands is the fact that the properties of the ligand can be readily tailored by variation of the R substituents, in a manner akin to that of the tris(pyrazolyl)hydroborato [N3] donor ligand system.4,5 In this regard, while the most common variation pertains to the nature of the 1-R substituent,13 we recently introduced tris(mercaptoimidazolyl)hydroborato ligands, namely [TmMeBenz] and [TmButBenz], in which the imidazolyl groups are benzannulated.14 Here, we describe the impact of benzannulation in cadmium chemistry.

RESULTS AND DISCUSSION

Treatment of the tris(2-mercapto-1-methylbenzimidazolyl)hydroborato potassium complex, [TmMeBenz]K,14b with CdBr2 results in the formation of {[TmMeBenz]Cd(μ–Br)}2, as illustrated in Scheme 1.

Scheme 1.

Scheme 1

The molecular structure of {[TmMeBenz]Cd(μ–Br)}2 has been determined by single crystal X-ray diffraction (Figure 1), thereby demonstrating that the [TmMeBenz] ligand exhibits κ3-coordination, as is most commonly observed for [TmR] ligands.13 Most interesting, however, is the observation that the compound is dimeric, in contrast to the monomeric structure observed for the analogous non-benzannulated derivative, [TmMe]CdBr.15 The significance of this result is underscored by the fact that there are no structurally characterized compounds listed in the Cambridge Structural Database (CSD)16 that feature cadmium in a [S3Br2] coordination environment. Furthermore, there are only six structurally characterized complexes listed in the CSD that feature any metal in a [S3Br2] environment,17 while there are only nine examples of dimeric cadmium complexes that feature 5-coordinate cadmium with two μ–Br bridges.18 The direct comparison of the molecular structures of {[TmMeBenz]Cd(μ–Br)}2 and [TmMe]CdBr, therefore, makes it evident that benzannulation of a tris(2-mercaptoimidazolyl)hydroborato ligand can have a notable impact on the coordination chemistry of cadmium.

Figure 1.

Figure 1

Molecular structure of {[TmMeBenz]Cd(μ–Br)}2.

Selected bond lengths and angles for {[TmMeBenz]Cd(μ–Br)}2 are presented in Table 1, from which it is evident that the coordination geometry of cadmium is approximately trigonal bipyramidal, with a τ5 five-coordinate geometry index19 of 0.72; this value is much closer to that for an idealized trigonal bipyramidal (1.00) than for a square pyramidal geometry (0.00). The axial sites in {[TmMeBenz]Cd(μ–Br)}2 are occupied by one bromine and one sulfur atom, while the equatorial sites are occupied by one bromine and two sulfur atoms. For example, the S(1)–Cd–Br’ bond angle of {[TmMeBenz]Cd(μ–Br)}2 is close to 180° [171.15(2) °], while the Br-Cd-Br’ bond angle is close to 90° [84.80(2)°]. The Cd–Br bonds within {[TmMeBenz]Cd(μ–Br)}2 are asymmetric, such that the axial bond on each cadmium center [d(Cd–Brax) = 2.8977(6) Å] is longer than the equatorial bond [d(Cd–Breq) = 2.6336(7) Å].* Correspondingly, the axial Cd–S bond length [2.6473(9) Å] is longer than the equatorial Cd–S bonds [2.5724(8) Å and 2.5812(8) Å], albeit that this difference is less than that for the Cd–Br bond lengths.

Table 1.

Selected bond lengths (Å) and angles (°) for {[TmMeBenz]Cd(µ–Br)}2.

Cd–Br 2.6336(7) S(1)–Cd–Br 88.91(2)
Cd-Br′ 2.8977(6) S(2)–Cd–Br 125.78(2)
Cd–S(1) 2.6473(9) S(3)–Cd–Br 128.24(2)
Cd–S(2) 2.5724(8) S(1)–Cd–S(2) 96.97(3)
Cd–S(3) 2.5812(8) S(1)–Cd–S(3) 98.05(3)
S(2)–Cd–S(3) 104.29(3)
S(1)–Cd–Br′ 171.150(17)
S(2)–Cd–Br′ 81.78(2)
S(3)–Cd–Br′ 90.74(2)
Br-Cd–Br′ 84.797(16)

Density functional theory (DFT) calculations performed on the molecule in the gas phase are in accord with the experimental structure and reproduce both the trigonal bipyramidal geometry of {[TmMeBenz]Cd(μ–Br)}2 (Figure 2) and also the difference in axial (2.963 Å) and equatorial (2.761 Å) Cd–Br bond lengths. Furthermore, the calculations indicate that formation of the dimer is enthalpically favored over that of the monomer, [TmMeBenz]CdBr (Figure 3), by 7.2 kcal mol−1 (Scheme 2). Monomeric [TmMeBenz]CdBr exhibits a well-defined pseudotetrahedral geometry, with a four-coordinate τ4 geometry index of 0.86 (for which an ideal tetrahedron has a value of 1.00),20 in which the bromine is coincident with the B•••Cd vector, i.e. the B•••Cd–Br angle is 179.8°. Also of note, the Cd–Br bond of [TmMeBenz]CdBr (2.605 Å) is shorter than both the axial and equatorial bonds of {[TmMeBenz]Cd(μ–Br)}2 (2.761 Å and 2.963 Å).

Figure 2.

Figure 2

Geometry optimized structure of {[TmMeBenz]Cd(μ–Br)}2.

Figure 3.

Figure 3

Geometry optimized structure of [TmMeBenz]CdBr.

Scheme 2.

Scheme 2

Corresponding density functional theory calculations have also been performed on the non-benzannulated counterparts, {[TmMe]Cd(μ–Br)}2 (Figure 4) and [TmMe]CdBr (Figure 5), which exhibit similar structural differences to those of the [TmMeBenz] derivatives. For example, as observed for the [TmMeBenz] system, the calculated Cd–Br bond in the monomer (2.613 Å) is shorter than those in the dimer (2.750 Å and 3.006 Å). However, an important difference with the benzannulated system is that the formation of the dimer is less strongly favored enthalpically, with ΔE = −3.9 kcal mol−1, i.e. Kdimer[TmMeBenz] > Kdimer[TmMe] (Scheme 2). As such, the calculations are in accord with the experimental observation (Table 2) of a dimer in the solid state for the benzannulated complex, {[TmMeBenz]Cd(μ–Br)}2, but a monomer for the non-benzannulated compound, [TmMe]CdBr.

Figure 4.

Figure 4

Geometry optimized structure of {[TmMe]Cd(μ–Br)}2.

Figure 5.

Figure 5

Geometry optimized structure of [TmMe]CdBr.

Table 2.

Monomer versus dimer nature of experimentally determined structures of {[TmR]CdX}n.

{[TmR]CdX}n
X [TmMe] [TmMeBenz]
Cl a dimerc
Br monomerb dimerd
I a monomerc
(a)

data not available.

(b)

reference 15.

(c)

reference 12.

(d)

this work.

It is also pertinent to compare the dimerization energies of [TmMeBenz]CdBr and [TmMe]CdBr with those of the chloride and iodide counterparts (Table 3). In each case, the benzannulated derivatives show a greater tendency to form a dimeric structure. Furthermore, the tendency to form the dimeric structure increases in the sequence I < Br < Cl. The latter trend is in accord with the experimental observation that {[TmMeBenz]Cd(μ–Br)}2 and {[TmMeBenz]Cd(μ–Cl)}212 exist as dimers in the solid state, but [TmMeBenz]CdI12 is a monomer.

Table 3.

Energetics for dimerization of [TmR]CdX.

Compound ΔEdimerization (kcal mol−1)
[TmMe]CdCl −7.7
[TmMe]CdBr −3.9
[TmMe]CdI 1.2
[TmMeBenz]CdCla −10.7
[TmMeBenz]CdBr −7.2
[TmMeBenz]CdIa −0.7
(a)

data taken from reference 12.

The observation that the benzannulated dimers, {[TmMeBenz]Cd(μ–X)}2, are more stable with respect to dissociation than are their non-benzannulated counterparts, {[TmMe]Cd(μ–X)}2, provides an interesting illustration of how benzannulation can modify the nature of a system. In this regard, the example complements several other reports concerned with benzannulated [TmRBenz] ligands. For example, the benzannulated tris(mercaptoimidazolyl)borohydride ligand of {[TmMeBenz]Na}2(μ-THF)3 coordinates in a κ3-manner, which is in marked contrast to the κ2-, κ1- and κ0-modes that have been reported for various non-benzannulated [TmMe]Na derivatives.14a Furthermore, whereas [TmMe]K·4H2O possesses a polymeric structure in which each [TmMe] ligand bridges two potassium centers, benzannulated [TmMeBenz]K(OCMe2)3 exists as a discrete monomeric species in which the [TmMeBenz] ligand coordinates in a novel κ4S3H manner.14b Finally, whereas [TmR]Tl compounds exist as dinuclear molecules in which two of the sulfur donors coordinate to different thallium centers, all three sulfur donors of the [TmRBenz] ligands of both [TmMeBenz]Tl and [TmButBenz]Tl chelate to thallium.14b

CONCLUSIONS

In summary, treatment of the tris(2-mercapto-1-methylbenzimidazolyl)hydroborato potassium complex, [TmMeBenz]K, with CdBr2, results in the formation of the bromide bridged dimer, {[TmMeBenz]Cd(μ–Br)}2, which is the first example of a 5-coordinate cadmium compound that possesses a [S3Br2] coordination environment. In this regard, the structure of {[TmMeBenz]Cd(μ–Br)}2 is distinct from that of the non-benzannulated counterpart, [TmMe]CdBr, which exists as a tetrahedral monomer, thereby demonstrating that benzannulation can have a notable impact on cadmium chemistry. Density functional theory calculations indicate that the benzannulated dimers, {[TmMeBenz]Cd(μ–X)}2 (X = Cl, Br, I), are more stable with respect to dissociation than are their non-benzannulated counterparts, {[TmMe]Cd(μ–X)}2, a result that is in accord with the experimental observations. Furthermore, the calculations also indicate that the stability of the dimer depends on the nature of X, and becomes more stable in the sequence I < Br < Cl.

EXPERIMENTAL SECTION

General Considerations

NMR spectra were measured on a Bruker Avance 500 DMX spectrometer. 1H NMR spectra are reported in ppm relative to SiMe4 (δ = 0) and were referenced internally with respect to the protio solvent impurity (δ 7.26 for CDCl3).21 13C NMR spectra are reported in ppm relative to SiMe4 (δ = 0) and were referenced internally with respect to the solvent (δ 77.16 for CDCI3)21. Coupling constants are given in hertz. IR spectra were recorded as KBr pellets on a Nicolet iS10 FT-IR spectrometer (ThermoScientific), and the data are reported in reciprocal centimeters. All chemicals were purchased from Sigma-Aldrich. [TmMeBenz]K was prepared by the literature method.14b

X-ray structure determinations

Single crystal X-ray diffraction data were collected on a Bruker Apex II diffractometer and crystal data, data collection and refinement parameters are summarized in Table 4. The structures were solved using direct methods and standard difference map techniques, and were refined by full-matrix least-squares procedures on F2 with SHELXTL (Version 2013/4).22

Table 4.

Crystal, intensity collection and refinement data.

{[TmMeBenz]CdBr}2·C6H6
lattice Triclinic
formula C54H50B2Br2Cd2N12S6
formula weight 1465.66
space group
P1
a 11.226(3)
b 11.930(3)
c 12.139(3)
α/° 86.970(3)
β/° 80.445(3)
γ/° 63.629(3)
V3 1435.9(6)
Z 1
temperature (K) 130(2)
radiation (λ, Å) 0.71073
ρ(calcd.) g cm−3 1.695
μ(Mo Kα), mm−1 2.399
θmax, deg. 30.507
no. of data collected 49072
no. of data 8755
no. of parameters 359
R1 [I > 2σ(I)] 0.0389
wR2 [I > 2σ(I)] 0.0790
R1 [all data] 0.0597
wR2 [all data] 0.0841
Rint 0.0690
GOF 1.016

Computational Details

Calculations were carried out using DFT as implemented in the Jaguar 7.7 (release 107) suite of ab initio quantum chemistry programs.23 Geometry optimizations were performed with the B3LYP density functional24 using the 6–31G** (H, B, C, N, S, Cl) and LAV3P (Cd, Br, I) basis sets. The energies of the optimized structures were re-evaluated by additional single point calculations on each optimized geometry using the cc-pVTZ(-f) correlation consistent triple-ζ(H, B, C, N, S, Cl, Br) and LAV3P (Cd, I) basis sets.25 Basis set superposition errors were taken into account by using the Boys-Bernardi counterpoise correction.26

Synthesis of {[TmMeBenz]Cd(μ–Br)}2

A suspension of [TmMeBenz]K (15 mg, 0.028 mmol) in CDCl3 (0.7 mL) was treated with CdBr2 (23 mg, 0.084 mmol) in an NMR tube equipped with a J. Young valve, and the mixture was heated for 4 days at 100°C. The white suspension was filtered and the solvent was then removed from the filtrate in vacuo to give {[TmMeBenz]Cd(μ–Br)}2·CDCl3 as a white solid (6 mg, 29% yield). Colorless crystals of composition {[TmMeBenz]Cd(μ–Br)}2·C6H6, suitable for X-ray diffraction, were obtained via cooling of a hot, saturated solution in C6H6. Anal. calcd. for {[TmMeBenz]Cd(μ–Br)}2·CHCl3: C, 39.1; H, 3.0; N, 11.2. Found: C, 39.9; H, 3.0; N, 11.2. 1H NMR (CDCl3): δ3.84 [s, 18H of 6NCH3], 5.65 [br s, 2H of 2BH], 7.22 [m, 6H of 6C6H4], 7.34 [m, 18H of 6C6H4]. 13C NMR (CDCl3): δ31.7 [CH3 of NCH3], 110.0 [CH of C6H4], 113.6 [CH of C6H4], 124.1 [CH of C6H4], 124.2 [CH of C6H4], 133.7 [C of C6H4], 136.1 [C of C6H4], 165.2 [C=S]. IR (KBr pellet, cm−1): 3059 (vw), 2930 (w), 2850 (vw), 1481 (m), 1459 (m), 1439 (m), 1401 (m), 1363 (s), 1349 (s), 1296 (m), 1235 (w), 1191 (w), 1155 (m), 1140 (m), 1096 (w), 1014 (w), 998 (w), 855 (w), 811 (w), 743 (m).

Supplementary Material

Highlights.

  • The cadmium complex, {[TmMeBenz]Cd(μ–Br)}2 has been synthesized.

  • X-ray diffraction demonstrates that {[TmMeBenz]Cd(μ–Br)}2 exists as a dimer.

  • Benzannulation of [TmMe]CdX stabilizes the dimeric form {[TmMeBenz]Cd(μ–X)}2.

  • The dimeric form becomes more stable in the sequence I < Br < Cl.

Acknowledgment

Research reported in this publication was supported by the National Institute of General Medical Sciences of the National Institutes of Health under Award Number R01GM046502. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

Footnotes

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*

For comparison, the average Cd–Br bond length for compounds listed in the Cambridge Structural Database is 2.662 Å.

This value refers to the formation of one mole of dimer.

APPENDIX A. Supplementary Data

Crystallographic data in CIF format (CCDC # 1021454). These data can be obtained free of charge via http://www.ccdc.cam.ac.uk/conts/retrieving.html, or from the Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: (+44) 1223-336-033; or e-mail: deposit@ccdc.cam.ac.uk. Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.molstruct.xxxxxx.

References

  • 1.(a) Garner M, Reglinski J, Cassidy I, Spicer MD, Kennedy AR. J. Chem. Soc. Chem. Commun. 1996:1975–1976. [Google Scholar]; (b) Reglinski J, Garner M, Cassidy ID, Slavin PA, Spicer MD, Armstrong DR. J. Chem. Soc. Dalton Trans. 1999:2119–2126. [Google Scholar]
  • 2.(a) Spicer MD, Reglinski J. Eur. J. Inorg. Chem. 2009:1553–1574. [Google Scholar]; (b) Parkin G. New J. Chem. 2007;31:1996–2014. doi: 10.1039/b712012e. [DOI] [PMC free article] [PubMed] [Google Scholar]; (c) Smith JM. Comm. Inorg. Chem. 2008;29:189–233. [Google Scholar]; (d) Soares LF, Silva RM. Inorg. Synth. 2002;33:199–202. [Google Scholar]
  • 3.Kreider-Mueller A, Rong Y, Owen JS, Parkin G. Dalton Trans. 2014;43:10852–10865. doi: 10.1039/c4dt01271b. [DOI] [PubMed] [Google Scholar]
  • 4.(a) Scorpionates – The Coordination Chemistry of Polypyrazolylborate Ligands, S. London: Trofimenko, Imperial College Press; 1999. [Google Scholar]; (b) Scorpionates II: Chelating Borate Ligands C. London: Pettinari, Imperial College Press; 2008. [Google Scholar]
  • 5.Santini C, Pellei M, Lobbia GG, Papini G. Mini-Rev. Org. Chem. 2010;7:84–124. [Google Scholar]
  • 6.(a) Parkin G. Chem. Rev. 2004;104:699–767. doi: 10.1021/cr0206263. [DOI] [PubMed] [Google Scholar]; (b) Parkin G. Chem. Commun. 2000:1971–1985. [Google Scholar]; (c) Parkin G. In: Met. Ions Biol. Syst. Chapter 14. Sigel A, Sigel H, Dekker M, editors. Vol. 38. New York: 2001. pp. 411–460. [PubMed] [Google Scholar]; (d) Parkin G. Adv. Inorg. Chem. 1995;42:291–393. [Google Scholar]
  • 7.Bridgewater BM, Parkin G. Inorg. Chem. Commun. 2001;4:126–129. [Google Scholar]
  • 8.(a) Bridgewater BM, Parkin G. Inorg. Chem. Commun. 2000;3:534–536. [Google Scholar]; (b) Bridgewater BM, Parkin G. J. Am. Chem. Soc. 2000;122:7140–7141. [Google Scholar]; (c) Magyar JS, Weng TC, Stern CM, Dye DF, Rous BW, Payne JC, Bridgewater BM, Mijovilovich A, Parkin G, Zaleski JM, Penner-Hahn JE, Godwin HA. J. Am. Chem. Soc. 2005;127:9495–9505. doi: 10.1021/ja0424530. [DOI] [PubMed] [Google Scholar]
  • 9.(a) Bridgewater BM, Fillebeen T, Friesner RA, Parkin G. J. Chem. Soc. Dalton Trans. 2000:4494–4496. [Google Scholar]; (b) Melnick JG, Zhu G, Buccella D, Parkin G. J. Inorg. Biochem. 2006;100:1147–1154. doi: 10.1016/j.jinorgbio.2005.12.023. [DOI] [PubMed] [Google Scholar]
  • 10.Morlok MM, Janak KE, Zhu G, Quarless DA, Parkin G. J. Am. Chem. Soc. 2005;127:14039–14050. doi: 10.1021/ja0536670. [DOI] [PubMed] [Google Scholar]
  • 11.(a) Melnick JG, Parkin G. Science. 2007;317:225–227. doi: 10.1126/science.1144314. [DOI] [PubMed] [Google Scholar]; (b) Melnick JG, Yurkerwich K, Parkin G. Inorg. Chem. 2009;48:6763–6772. doi: 10.1021/ic900721g. [DOI] [PMC free article] [PubMed] [Google Scholar]; (c) Melnick JG, Yurkerwich K, Parkin G. J. Am. Chem. Soc. 2010;132:647–655. doi: 10.1021/ja907523x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 12.Palmer JH, Parkin G. Dalton Trans. 2014;43:13874–13882. doi: 10.1039/c4dt01820f. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 13.See, for example reference 2a and: Yurkerwich K, Yurkerwich M, Parkin G. Inorg. Chem. 2011;50:12284–12295. doi: 10.1021/ic201504d. Santini C, Lobbia GG, Pettinari C, Pellei M, Valle G, Calogero S. Inorg. Chem. 1998;37:890–900. Kimblin C, Bridgewater BM, Churchill DG, Parkin G. Chem. Commun. 1999:2301–2302. Tesmer M, Shu M, Vahrenkamp H. Inorg. Chem. 2001;40:4022–4029. doi: 10.1021/ic0101275. Bakbak S, Bhatia VK, Incarvito CD, Rheingold AL, Rabinovich D. Polyhedron. 2001;20:3343–3348. Bailey PJ, Dawson A, McCormack C, Moggach S, Oswald IDH, Parsons S, Rankin DWH, Turner A. Inorg. Chem. 2005;44:8884–8898. doi: 10.1021/ic0505293. Ibrahim MM, Shu M, Vahrenkamp H. Eur. J. Inorg. Chem. 2005:1388–1397. Mihalcik DJ, White JL, Tanski JM, Zakharov LN, Yap GPA, Incarvito CD, Rheingold AL, Rabinovich D. Dalton Trans. 2004:1626–1634. doi: 10.1039/b401056f.
  • 14.(a) Al-Harbi A, Rong Y, Parkin G. Dalton Trans. 2013;42:11117–11127. doi: 10.1039/c3dt51092a. [DOI] [PubMed] [Google Scholar]; (b) Rong Y, Palmer JH, Parkin G. Dalton Trans. 2014;43:1397–1407. doi: 10.1039/c3dt52418c. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 15.Cassidy I, Garner M, Kennedy AR, Potts GBS, Reglinski J, Slavin PA, Spicer MD. Eur. J. Inorg. Chem. 2002:1235–1239. [Google Scholar]
  • 16.Cambridge Structural Database (Version 5.35) 3D Search and Research Using the Cambridge Structural Database [Google Scholar]; Allen FH, Kennard O. Chemical Design Automation News. 1993;8(1):31–37. [Google Scholar]
  • 17.(a) Kolb U, Beuter M, Drager M. Inorg. Chem. 1994;33:4522–4530. [Google Scholar]; (b) Nishijo J, Miyazaki A, Enoki T. Bull. Chem. Soc. Jpn. 2004;77:715–727. [Google Scholar]; (c) Charmant JPH, Jahan AHMM, Norman NC, Orpen AG. Inorg. Chim. Acta. 2005;358:1358–1364. [Google Scholar]; (d) Senda S, Ohki Y, Hirayama T, Toda D, Chen J-L, Matsumoto T, Kawaguchi H, Tatsumi K. Inorg. Chem. 2006;45:9914–9925. doi: 10.1021/ic0610132. [DOI] [PubMed] [Google Scholar]; (e) Ohki Y, Yasumura K, Kuge K, Tanino S, Ando M, Li Z, Tatsumi K. Proc. Natl. Acad. Sci. 2008;105:7652–7657. doi: 10.1073/pnas.0800538105. [DOI] [PMC free article] [PubMed] [Google Scholar]; (f) Sommer H, Eichhöfer A, Drebov N, Ahlrichs R, Fenske D. Eur. J. Inorg. Chem. 2008;2008:5138–5145. [Google Scholar]
  • 18.(a) Nieuwenhuyzen M, Wilkins CJ. J. Chem. Soc. Dalton Trans. 1993:2673–2681. [Google Scholar]; (b) Rogers RD, Bond AH. Inorg. Chim. Acta. 1996;250:105–117. [Google Scholar]; (c) Matsunaga Y, Fujisawa K, Amir N, Miyashita Y, Okamoto K-i. Appl. Organomet. Chem. 2005;19:778–789. [Google Scholar]; (d) Döring M, Hahn G, Imhof W. Acta Crystallogr. Sect. E. 2006;E62:m429–m431. [Google Scholar]; (e) Park BK, Eom GH, Kim SH, Kwak H, Yoo SM, Lee YJ, Kim C, Kim S-J, Kim Y. Polyhedron. 2010;29:773–786. [Google Scholar]; (f) Wang Y-T, Yan S-C, Tang G-M, Zhao C, Li T-D, Cui Y-Z. Inorg. Chim. Acta. 2011;376:492–499. [Google Scholar]; (g) du Plessis M, Barbour L. J. Dalton Trans. 2012;41:3895–3898. doi: 10.1039/c1dt11564b. [DOI] [PubMed] [Google Scholar]; (h) Jia H-L, Jia M-J, Ding H, Yu J-H, Jin J, Zhao J-J, Xu J-Q. Cryst Eng Comm. 2012;14:8000–8009. [Google Scholar]; (i) Shirvan SA, Haydari Dezfuli S, Khazali F, Aghajeri M, Borsalani A. Acta Crystallogr. Sect. E. 2012;E68:m1471. doi: 10.1107/S1600536812045928. [DOI] [PMC free article] [PubMed] [Google Scholar]; (j) Pickhardt J, Staub B. Z. Naturforsch. 1999;54B:329–336. [Google Scholar]
  • 19.τ5 = (β–α)/ 60, where β– α is the difference between the two largest angles. See: Addison AW, Rao TN, Reedijk J, Vanrijn J, Verschoor GC. J. Chem. Soc. Dalton Trans. 1984:1349–1356.
  • 20.τ4 = [360 – (α+ β)]/141, where α+ β is the sum of the two largest angles. See: Yang L, Powell DR, Houser RP. Dalton Trans. 2007:955–964. doi: 10.1039/b617136b.
  • 21.Gottlieb HE, Kotlyar V, Nudelman A. J. Org. Chem. 1997;62:7512–7515. doi: 10.1021/jo971176v. [DOI] [PubMed] [Google Scholar]
  • 22.(a) Sheldrick GM. Federal Republic of Germany: University of Göttingen, Göttingen; 1981. SHELXTL, An Integrated System for Solving, Refining and Displaying Crystal Structures from Diffraction Data. [Google Scholar]; (b) Sheldrick GM. Acta Cryst. 2008;A64:112–122. [Google Scholar]
  • 23.Jaguar 7.7. New York, NY: Schrödinger, LLC; 2010. [Google Scholar]
  • 24.(a) Becke AD. J. Chem. Phys. 1993;98:5648–5652. [Google Scholar]; (b) Becke AD. Phys. Rev. A. 1988;38:3098–3100. doi: 10.1103/physreva.38.3098. [DOI] [PubMed] [Google Scholar]; (c) Lee CT, Yang WT, Parr RG. Phys. Rev. B. 1988;37:785–789. doi: 10.1103/physrevb.37.785. [DOI] [PubMed] [Google Scholar]; (d) Vosko SH, Wilk L, Nusair M. Can. J. Phys. 1980;58:1200–1211. [Google Scholar]; (e) Slater JC, editor. Quantum Theory of Molecules and Solids, Vol. 4: The Self-Consistent Field for Molecules and Solids. New York: McGraw-Hill; 1974. [Google Scholar]
  • 25.(a) Hay PJ, Wadt WR. J. Chem. Phys. 1985;82:270–283. [Google Scholar]; (b) Wadt WR, Hay PJ. J. Chem. Phys. 1985;82:284–298. [Google Scholar]; (c) Hay PJ, Wadt WR. J. Chem. Phys. 1985;82:299–310. [Google Scholar]
  • 26.(a) Boys SF, Bernardi F. Mol. Phys. 1970;19:553–566. [Google Scholar]; (b) van Duijneveldt FB, van Duijneveldt-van de Rijdt JGCM, van Lenthe JH. Chem. Rev. 1994;94:1873–1885. [Google Scholar]; (c) Davidson ER, Chakravorty S. J. Chem. Phys. Lett. 1994;217:48–54. [Google Scholar]; (d) Pyykkö P. Chem. Rev. 1997;97:597–636. doi: 10.1021/cr940396v. [DOI] [PubMed] [Google Scholar]

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