Short communication
Extraction and DFT Study on the Complexation of the Sodium Cation with Dibenzo-18-crown-6
Emanuel Makrllk,1'* Petr Toman2 and Petr Vanura3
1 Faculty of Applied Sciences, University of West Bohemia, Husova 11, 306 14 Pilsen, Czech Republic
2 Institute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic, Heyrovskeho sq. 2,
162 06 Prague 6, Czech Republic
3 Department of Analytical Chemistry, Institute of Chemical Technology, Prague, Technicka 5,
166 28 Prague 6, Czech Republic
* Corresponding author: E-mail: makrlik@centrum.cz
Received: 05-10-2010
Abstract
From extraction experiments and /-activity measurements, the extraction constant corresponding to the equilibrium Na+(aq) + A-(aq) + 1(nb) ^ 1-Na+(nb) + A-(nb) taking place in the two-phase water-nitrobenzene system (A- = picrate, 1 = dibenzo-18-crown-6; aq = aqueous phase, nb = nitrobenzene phase) was evaluated as was log Kex (1-Na+, A-) = 1.7 ± 0.1. Further, the stability constant of the complex 1-Na+ in nitrobenzene saturated with water calculated for a temperature of 25 °C: log Pnb (1-Na+) = 6.9 ± 0.1. Finally, by using quantum mechanical DFT calculations, the most probable structures of the resulting complex were solved.
Keywords: Sodium cation, dibenzo-18-crown-6, complexation, extraction and stability constants, water-nitrobenzene system, DFT, complex structures
1. Introduction
In 1967, Pedersen published his first papers1'2 dealing with cyclic polyether compounds with oxyethylene groups -CH2-CH2-O-, that are called crowns owing to their structure. These electroneutral compounds form relatively stable complexes in nonaqueous solvents, especially with alkali and alkaline-earth metal cations, the cations being placed in the ligand cavities. The ratio of the size of the crown ligand cavity to the ion radius of the central cation is a decisive or at least an important factor in the stability of the complex compounds formed.3 It is the complexing properties of the crowns that are due to the rapid development of the chemistry of these cyclic polyet-hers that we have witnessed in the recent decades. At this point it should be noted that several reviews have covered many aspects of their chemistry.3-6
The dicarbollylcobaltate anion7 and some of its halogen derivatives are very useful reagents for the extraction of various metal cations (especially Cs+, Sr2+, Ba2+, Eu3+ and Am3+) from aqueous solutions into a polar orga-
nic phase, both under laboratory conditions for purely theoretical or analytical purposes,8-29 and on the technological scale for the separation of some high-activity isotopes in the reprocessing of spent nuclear fuel and acidic radioactive waste.30,31
In the current work, the stability constant of the ca-tionic complex species 1-Na+, where 1 denotes dibenzo-18-crown-6 (see Scheme 1), in nitrobenzene saturated with water was determined. Moreover, applying quantum mechanical DFT calculations, the most probable structures of the mentioned complex species were predicted.
Scheme 1. Structural formula of dibenzo-18-crown-6 (abbrev. 1).
2. Experimental
Dibenzo-18-crown-6 (abbrev. 1; see Scheme 1) was purchased from Fluka. The other chemicals used (Lache-ma, Brno, Czech Republic) were of reagent grade purity. A solution of sodium picrate (NaA) in water was prepared by dissolving stoichiometric amount of picric acid in an aqueous solution of NaOH. The radionuclide 22Na+ (DuPont, Belgium) was of standard radiochemical purity.
The extraction experiments were carried out in 10 mL glass test-tubes with polyethylene stoppers: 2 mL of an aqueous solution of NaA of the concentration in the range from 5 x 10-4 to 1 x 10-3 mol/L and microamounts of 22Na+ were added to 2 mL of a nitrobenzene solution of 1, the concentration of which varied from 1 x 10-3 to 2 x 10-3 mol/L (in all experiments, the initial concentration of 1 in nitrobenzene, C™'nd, was always higher than the initial concentration of NaA in water, CiNn,aaAq). The test-tubes filled with the solutions were shaken for 2 h at 25 ± 1 °C, using a laboratory shaker. Then the phases were separated by centrifugation. Afterwards, 1 mL samples were taken from each phase and their y-activities were measured using a well-type NaI(Tl) scintillation detector connected to a y-analyzer NK 350 (Gamma, Budapest, Hungary).
The equilibrium distribution ratios of sodium, DNa, were determined as the ratios of the measured radioactivities of 22Na+ in the nitrobenzene and aqueous samples.
Na+(aq) + A(aq) + 1(nb) ^ 1-Na+(nb) + A(nb);
Kex (1-Na+, A-) with the equilibrium extraction constant K (1-Na+, A ):
(3)
[Na-yA-jJlL
(4)
It is necessary to emphasize that 1 is a considerably hydrophobic ligand, practically present in the nitrobenzene phase only, where this ligand forms - with the Na+ cation - the relatively stable complex 1-Na+.
Taking into account the conditions of electroneutra-lity in the organic and aqueous phases
[1'Na+lnb= [A-]nb
[Na+1 = [A-l
(5)
(6)
the mass balances of 1 and NaA at equal volumes of the nitrobenzene and aqueous phases
[1'Na+]nb + [1lnb = Cr" [Na+1 + [1-Na+lnb = CS
(7)
(8)
and the measured equilibrium distribution ratio of sodium
3. Results and Discussion
Regarding the results of previous papers,7,32 the two-phase water-NaA (A- = picrate)-nitrobenzene extraction system can be described by the following equilibrium
Na+(aq) + A-(aq) ^ Na+(nb) + A-(nb); Kex (Na+, A-) (1)
with the corresponding extraction constant Kex (Na+, A); aq and nb denote the presence of the species in the aqueous and nitrobenzene phases, respectively. For the constant K (Na+, A ) one can write32
Dns= [1-Na+]nh / [Na+1
(9)
kv.k (Vi .A 1	+,,:■ k
(2)
where KNa+ and KN- are the individual extraction constants for Na+ and A-, respectively, in the water-nitrobenzene system.32 Knowing the values log KiNa+ = -6.032 and log KiA- = -0.8 (A- = picrate),32 the extraction constant Kex (Na+, A ) was simply calculated from Eq. (2) as log Kex (Na+, A-)= -5.2.
Previous results33-37 indicated that the two-phase water- NaA (A- = picrate)-nitrobenzene-1 (1 = dibenzo-18-crown-6) extraction system, chosen for determination of the stability constant of the complex 1-Na+ (see Experimental), can be characterized by the main chemical equilibrium
then combination of relationships (4)-(9) gives the final expression for the extraction constant Kex (1-Na+, A):
Re* (1-Na , A

-t irunb
D
v C^ (10)
+ DNa
In this study, from the extraction experiments and /-activity measurements (see Experimental) by means of Eq. (10), the following value of the constant Kex (1-Na+, A) was determined: log Kex (1-Na+, A) = 1.7 ± 0.1.
Furthermore, with respect to previous results,33-37 for the extraction constants Kex (Na+, A) and Kex (1-Na+, A-) defined above, as well as for the stability constant of the complex 1-Na+ in nitrobenzene saturated with water, denoted by /¡nb (1-Na+), one gets
log ßnb (1-Na+) = log KeX (1'Na+, A-) -- log Kex (Na+, A-)
(11)
Using the constants log Kex (Na+, A ) and log Kex (1-Na+, A) given above, and applying Eq. (11), we obtain the stability constant of the 1-Na+ complex in water-saturated nitrobenzene at 25 °C as log /¡nb (1-Na+) = 6.9 ± 0.1, which is in relatively good agreement with the value log /¡nb (1-Na+) = 7.1 (1 = dibenzo-18-crown-6) determined previously.33
The quantum mechanical calculations were carried out at the density functional level of theory (DFT, B3LYP functional) using the Gaussian 03 suite of programs.38 The 6-31G(d) basis set was used and the optimizations were unconstrained. Although a possible influence of a polar solvent on the detailed structures of 1 and the complex species with Na+ could be imagined, our quantum mechanical calculations in similar cases, performed in an analogous way, showed very good agreement of experiment with theory.39-44
Iwachido et al.45 determined the hydration number of the dibenzo-18-crown-6-Na+ (i. e., 1*Na+) complex in the organic phase of the water-nitrobenzene extraction system as h (1-Na+) = 1.2. Thus, in our study, let us consider further both the "nonhydrated" state (1*Na+) and the "hydrated" state (1-Na+- H2O) of the mentioned complex species.
In the model calculations, we optimized the molecular geometries of the parent dibenzo-18-crown-6 ligand 1 and its cationic complex species with Na+. The optimized structure of a free ligand 1 with C2 symmetry is illustrated in Figure 1. In Figure 2, the most energetically favoured structure obtained by the DFT optimization of the 1*Na+ complex having also C2 symmetry is depicted, together with the lengths of the corresponding strong Na+ ••• O bonds (in A; 1 A = 0.1 nm). The calculated binding energy of this complex is 376.5 kJ/mol.
The structures A and B obtained by the full DFT optimizations of the cationic complex species 1-Na+- H2O are shown in Figures 3 and 4, respectively, including the lengths of the corresponding strong bonds. Besides, it should be noted that the structure B of the considered "hydrated" complex 1-Na+- H2O is stabilized by strong hydrogen bond OH • O (2.03 A) as well. The binding energies corresponding to the structures A and B were found to be very close: 450.4 and 449.7 kJ/mol, respecti-
Figure 2. Two projections of the DFT optimized structure of the 1-Na+ complex [B3LYP/6-31G(d)]. The Na+ ••• O distances: 2.60, 2.69, 2.56, 2.60, 2.69, and 2.56 Â.
vely. From these data it follows that the structures A and B of the resulting complex 1Na+ • H2O are apparently in a dynamic equilibrium.
a)
Figure 3. Two projections of the DFT optimized structure A of the 1.Na+. H2O complex [B3LYP/6-31G(d)]. The Na+ ••• O (of the parent ligand 1) distances: 2.74, 2.75, 2.65, 2.62, 2.62, and 2.64 Â; the Na+ • • • O (of the water molecule) distance: 2.28 Â.
Figure 1. Two projections of the DFT optimized structure of a free ligand 1 [B3LYP/6-31G(d)].
In conclusion, it is necessary to emphasize that the optimized structures A and B of the 1Na+^ H2O cationic complex species (see Figures 3 and 4) are evidently much more real than that of the complex 1^Na+ presented in Figure 2. This fact is confirmed especially by the respective binding energies given above.
Figure 4. Two projections of the DFT optimized structure B of the 1.Na+- H2O complex [B3LYP/6-31G(d)]. The Na+ ••• O (of the parent ligand 1) distances: 2.46, 2.50, 2.51, 2.84, 3.22, and 2.71 Â; the Na+ ••• O (of the water molecule) distance: 2.30 Â; the hydrogen bond OH ••• O length: 2.03 Â.
4. Acknowledgements
This work was supported by the Czech Ministry of Education, Youth and Sports (Projects MSM 4977751303 and MSM 6046137301) and by the Czech Science Foundation (Project P205/10/2280). The computer time at the MetaCentrum (Project MSM 6383917201), as well as at the Institute of Physics (computer Luna/Apollo), Academy of Sciences of the Czech Republic, is gratefully acknowledged.
5. References
1.	C. J. Pedersen, J. Am. Chem. Soc. 1967, 89, 2495-2496.
2.	C. J. Pedersen, J. Am. Chem. Soc. 1967, 89, 7017-7036.
3.	I. M. Kolthoff, Anal. Chem. 1979, 51, 1R-22R.
4.	J. J. Christensen, D. J. Eatough, R. M. Izatt, Chem. Rev. 1974, 74, 351-384.
5.	J. S. Bradshaw, R. M. Izatt, Acc. Chem. Res. 1997, 30, 338-345.
6.	R. M. Izatt, K. Pawlak, J. S. Bradshaw, Chem. Rev. 1991, 91, 1721-2085.
7.	E. Makrlik, P. Vanura, Talanta 1985, 32, 423-429.
8.	E. Makrlik, P. Vanura, P. Selucky, J. Solution Chem. 2009,
38,	1129-1138.
9.	E. Makrlik, P. Vannura, P. Selucky, J. Solution Chem. 2010,
39,	692-700.
10.	Z. Valentova, E. Makrlik, Acta Chim. Slov. 2007, 54, 175178.
11.	E. Makrlik, P. Vanura, P. Selucky, Acta Chim. Slov. 2008, 55, 430-433.
12.	E. Makrlik, P. Vanura, P. Selucky, Acta Chim. Slov. 2008, 55, 223-227.
13.	E. Makrlik, J. Budka, P. Vanura, Acta Chim. Slov. 2009, 56, 278-281.
14.	E. Makrlik, P. Vanura, P. Selucky, V. A. Babain, I. V. Smir-nov, Acta Chim. Slov. 2009, 56, 718-722.
15.	E. Makrlik, P. Vanura, P. Selucky, Acta Chim. Slov. 2009, 56, 475-479.
16.	E. Makrlik, P. Vanura, P. Selucky, Acta Chim. Slov. 2009, 56, 973-976.
17.	E. Makrlik, P. Vanura, P. Selucky, Acta Chim. Slov. 2010, 57, 470-474.
18.	E. Makrlik, P. Vanura, P. Selucky, Acta Chim. Slov. 2010, 57, 485-490.
19.	E. Makrlik, P. Vanura, P. Selucky, Acta Chim. Slov. 2010, 57, 922-926.
20.	E. Makrlik, P. Toman, P. Vanura, R. Rathore, Acta Chim. Slov. 2010, 57, 948-952.
21.	E. Makrlik, P. Vanura, Z. Phys. Chem. 2009, 225, 247-252.
22.	E. Makrlik, P. Vanura, P. Selucky, Z. Phys. Chem. 2009, 223, 253-261.
23.	E. Makrlik, P. Vanura, P. Selucky, Monatsh. Chem. 2008, 139, 597-600.
24.	E. Makrlik, J. Budka, P. Vanura, P. Selucky, Monatsh. Chem.
2009,	140, 157-160.
25.	E. Makrlik, P. Vanura, J. Budka, P. Selucky, Monatsh. Chem.
2010,	141, 31-33.
26.	E. Makrlik, P. Vanura, P. Selucky, J. Radioanal. Nucl. Chem.
2009,	279, 137-142.
27.	E. Makrlik, P. Vanura, Z. Sedläkovä, J. Radioanal. Nucl. Chem. 2009, 280, 607-611.
28.	E. Makrlik, P. Vannura, P. Selucky, J. Radioanal. Nucl. Chem.
2010,	283, 571-575.
29.	E. Makrlik, P. Vanura, P. Selucky, J. Radioanal. Nucl. Chem. 2010, 284, 137-142.
30.	V. N. Romanovskiy, I.V. Smirnov, V. A. Babain, T. A. Todd, R. S. Herbst, J. D. Law, K. N. Brewer, Solvent Extr. Ion Exch. 2001, 19, 1-21.
31.	J. D. Law, R. S. Herbst, T. A. Todd, V. N. Romanovskiy, V. A. Babain, V. M. Esimantovskiy, I. V. Smirnov, B. N. Zaitsev, Solvent Extr. Ion Exch. 2001, 19, 23-36.
32.	J. Rais, Collect. Czech. Chem. Commun. 1971, 36, 32533262.
33.	E. Makrlik, J. Hälovä, M. Kyrs, Collect. Czech. Chem. Commun.. 1984, 49, 39-44.
34.	E. Makrlik, P. Vanura, J. Radioanal. Nucl. Chem. 1996, 214, 339-346.
35.	M. Dankovä, E. Makrlik, P. Vanura, J. Radioanal. Nucl. Chem. 1997, 221, 251-253.
36.	E. Makrlik, P. Vanura, M. Dankovä, J. Radioanal. Nucl. Chem. 1999, 240, 579-583.
37.	E. Makrlik, P. Vanura, Monatsh. Chem. 2006, 137, 157- 161.
38.	M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, Jr., T. Vre-ven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N.
Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Moroku-ma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakr-zewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Fore-sman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cio-slowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-La-ham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, J. A. Pople, Gaussian 03, Revision C. 02, Gaussian, Inc., Wallingford, CT, 2004.
39.	J. Križ, J. Dybal, E. Makrlik, Biopolymers 2006, 82, 536548.
40.	J. Križ, J. Dybal, E. Makrlik, P. Vanura, J. Lang, Supramol. Chem. 2007, 19, 419-424.
41.	J. Križ, J. Dybal, E. Makrlik, P. Vanura, Supramol. Chem. 2008, 20, 387-395.
42.	J. Križ, J. Dybal, E. Makrlik, J. Budka, P. Vanura, Supramol. Chem. 2008, 20, 487-494.
43.	J. Križ, J. Dybal, E. Makrlik, J. Budka, J. Phys. Chem. A 2008, 112, 10236-10243.
44.	J. Križ, J. Dybal, E. Makrlik, J. Budka, P. Vanura, J. Phys. Chem. A 2009, 112, 5896-5905.
45.	T. Iwachido, M. Minami, M. Kimura, A. Sadakane, M. Kawasaki, K. Toei, Bull. Chem. Soc. Jap. 1980, 53, 703-708.
Povzetek
V dvofaznem sistemu voda-nitrobenzen smo proučevali ravnotežje Na+(aq) + A-(aq) + 1(nb) ^ 1-Na+(nb) + A-(nb), A-= pikrat, 1 = dibenzo-18-crown-6; aq = vodna faza, nb = nitrobenzen). Z meritvami množine porazdelitve posameznih snovi med obe fazi smo določili konstanto ekstrakcije, log Kex (1-Na+, A-) = 1.7 ± 0.1. Določili smo tudi konstanto stabilnosti kompleksa pri 15 °C 1-Na+ v nitrobenzenu, nasičenem z vodo, log j8nb (1-Na+) = 6.9 ± 0.1. S kvantno mehanskimi DFT računi smo predvideli tudi najbolj verjetno strukturo tega kompleksa.