Electric Field Gradient and Electronic Properties of Crown Thioether Compounds

Hyperfine Interact DOI 10.1007/s10751-010-0246-8 Electric field gradient and electronic properties of crown thioether compounds Filipe Camargo Dalmatti Alves Lima · Rafael Rodrigues do Nascimento · Marcos Brown Gonçalves · Stefaan Cottenier · Marília Junqueira Caldas · Helena Maria Petrilli © Springer Science+Business Media B.V. 2010 Abstract We compare published TDPAC experiments on 111Cd in the crown thioether C6H12S3AgCl with ab-initio electronic structure calculations performed within the framework of the Density Functional Theory using the Projector Aug- mented Wave method. We conclude from this comparison that the Cd atom at the very moment of the TDPAC experiment is positively charged, and we point out to a methodological difference between reproducing experimental electric-field gradients in molecules versus solid metals. Keywords Crown thioether · Electric field gradient at the nucleus · Cd · Charge state · CP-PAW · Electronic structure · DFT 1 Introduction Crown ethers are heterocyclic molecules, consisting of a ring which has several ether groups. They easily make coordinative bonds with other atoms and can act as a carrier of ions and small molecules. The mechanism behind this is described as a lock and key model, involving high binding affinities and selectivity for the entities that are to be carried. The size of the cavity available in each crown ether molecule varies and determines the type of cation which is bound most efficiently. The primary F. C. Dalmatti Alves Lima (B) · R. Rodrigues do Nascimento · M. B. Gonçalves · M. J. Caldas · H. M. Petrilli Instituto de Física, Universidade de São Paulo, CP 66318, 05315-970, São Paulo, SP, Brazil e-mail: [email protected] S. Cottenier Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052, Zwijnaarde, Belgium F.C. Dalmatti Alves Lima et al. uses of crown ethers are the solubilization of inorganic compounds, the separation of inorganic salts, liquid-membrane separation, liquid–liquid extraction, ion-sensitive electrodes, and organic synthesis as phase transfer reagents. Crown ethers have a potential to be used for handling radioactive isotopes in medical applications as well [1]: a radioisotope is bound due to the high affinity of the crown ether to either the radioisotope itself or to the transport molecule, and is subsequently delivered to the affected tissue. A family of crown thioethers was generated experimentally [2, 3] and the quadrupole interaction on a 111Cd nucleus in these molecules was measured by the Time Dependent Perturbed Angular Correlation (TDPAC) technique. Heinrich et al. [3] compared these measured quadrupole interaction frequencies with electric field gradients (EFG) calculated using an ab-initio Density Functional Theory (DFT) approach (“ADF” computer code and Slater type orbitals). The aim was to estab- lish a “fingerprint system”, by which measured quadrupole interactions could be uniquely assigned to specific sites in the molecule, based on their agreement with calculated EFGs. Although satisfying agreement was achieved between calculated and measured EFGs, it is somewhat worrying that the calculated EFG was not obtained at the Cd nucleus which appears in the experiment, but at the parent Ag nucleus which decays to Cd nanoseconds before the experimental event takes place. In the present study, we will examine to which extent the calculated EFGs are influenced by using Cd rather than Ag. It will be shown that charge state effects must be taken into account. 2 Methodology The theoretical method employed in this paper combines a reciprocal space self- consistent quantum mechanical method and the Car-Parrinello scheme [4]asem- bodied in the CP-PAW [5] computational code, an ab-initio all-electron method in the Kohn–Sham scheme [6] of the DFT. These calculations are performed in reciprocal space exploiting the Bloch’s theorem. In order to treat a molecule with this methodology, it is necessary to generate a unit cell large enough to guarantee that the periodic images do not interact with each other. Here we used a unit cell with dimensions 12 × 12 × 15 Å. We used the generalized gradient approximation (GGA) developed by Perdew, Burke and Ernzerhof (GGA-PBE) [7] to evaluate the EFG and performed geometry optimizations using 40 and 160 Ry as cutoff energies for the corresponding planes waves and charge density expansions. These choices were based on previous results of EFG calculations [8–13]. 3 Results and discussion 3.1 Geometrical structure We focus on the C6H12S3XCl crown ether, for which the EFG at the X = Cd site was measured using the 111Ag→111Cd TDPAC probe [2]. In our theoretical calculations, we considered for X either Ag, Cd or [Cd]+1,where the symbol [Cd]+1 refers to +1 the Cd site in the charged, [C6H12S3CdCl] , compound. As a starting point, the Electric field gradient and electronic properties of crown thioether compounds Fig. 1 The C6H12S3AgCl structure [11]. The θ angle is measured from a point in the middle of the plane connecting the S atoms, the metal and the Cl positions Table 1 Theoretical structural parameters determined in the present work = = = +1 +1 X-ray X Ag Ag X Cd Cd X [Cd] [Cd] S1-X (Å) 2.618 2.759 0.141 3.284 0.666 2.789 0.171 S2-X (Å) 2.6 2.796 0.196 3.203 0.603 2.765 0.165 S3-X (Å) 2.598 2.724 0.126 3.217 0.619 2.754 0.156 X-Cl (Å) 2.39 2.419 0.029 2.579 0.189 2.399 0.009 θ (◦) 3.3 2.7 0.6 12.3 9 2.8 0.5 Bond distances (S1-X, S2-X, S3-X, X-Cl) and angles (θ), where X = Ag,Cdand[Cd]+1; the symbol +1 +1 [Cd] refers to Cd in the [C6H12S3CdCl] compound. The experimental X-ray results available in the literature [11] are also shown. For easy reference we show the differences (X) between the experimental and theoretical results in each case. The angle θ is shown in Fig. 1 experimental [14] molecular structure, shown at Fig. 1, was used and a full structural optimization was subsequently performed. The results of these optimizations are shown in Table 1, together with experimental data for C6H12S3AgCl [14]. Figure 2 illustrates the geometries of these compounds after the structural relaxation. From the differences x (Table 1), between the calculated and experimental bond lengths and angles, we conclude that for X = Ag the experimental result is reasonably described, that replacement of Ag by Cd gives quite a different geometry, and that charging Cd by one positive elementary charge leads to a structure that is very comparable with the structure for X = Ag. The fact that the calculated bond lengths are slightly larger than the experimental value is a known artifact of DFT at the GGA level. 3.2 Electric field gradient results Experimental data for the principal component of the EFG tensor and its asymmetry parameter η are known at 77 and 295 K are at the Table 2. Their values are for F.C. Dalmatti Alves Lima et al. Fig. 2 Theoretical optimized structures obtained using the CP-PAW code for b C6H12S3AgCl; +1 c C6H12S3CdCl and d [C6H12S3CdCl] . For easy reference we repeat a the X-ray structure (Fig. 1) but in the same scale of the theoretical results Table 2 Theoretical EFGs and asymmetry parameters (η) obtained at the metal sites in the crown thioether compounds studied here Methodology Compound EFG (1021V/m2)(%) η Experimental C6H12S3CdCl (T = 295 K) 14.63 – 0.03 Experimental C6H12S3CdCl (T = 77 K) 14.59 – 0.06 Ab initio C6H12S3AgCl 13.94 4.5% 0.09 +1 Ab initio [C6H12S3CdCl] 17.25 17.9% 0.01 Ab initio C6H12S3CdCl 8.20 43.9% 0.60 +1 Ab initio [C6H12S3CdCl] (using Ag positions) 16.52 12.9% 0.04 The experimental results are from Reference [11]. For easy reference we also give the percentage deviation () between the theoretical and experimental results at T = 77 K practical purposes nearly identical. The calculated EFG at the Ag nucleus is in good agreement with the experimental value, which confirms the calculations by Heinrich et al. [3]. However, the experiment is not performed at an Ag nucleus, but at a Cd nucleus [15]. Therefore, we should compare the experimental value with a calculation for X = Cd. Here the agreement is not at all satisfying. This can be traced back to the geometry: for the experimental atomic positions (with Cd at the experimental Ag position), the calculated EFG at Cd is close to the experimental value. After the strong structural relaxation as shown in Table 1 and Fig. 2, the final EFG at Cd turns out to have a very different value. This situation can be resolved by realizing that a neutral Cd atom has one electron more than a neutral Ag atom. Upon the Ag→Cd decay, the nucleus becomes more positive by one elementary charge. Would this happen in a metal, then an electron from the conduction band would be readily supplied to neutralize the atom. This would happen before the excited Cd nucleus decays to its ground state, and therefore before the TDPAC event is registered. For a molecule in a solvent, however, the supply of electrons is much slower. Therefore, the TDPAC measurement is effectively done on a molecule with a Cd atom that lacks one electron. Indeed, the calculated EFG at [Cd]+1 is in much better agreement with the experimental value. The agreement is not perfect yet, and the dominant reason for this is most likely the fact that we neglected solvent effects (which were taken into account in [3].) Electric field gradient and electronic properties of crown thioether compounds 4 Conclusions We conclude from a comparison between experimental quadrupole interaction frequencies and ab initio calculated EFGs that a Cd atom in C6H12S3CdCl immediately after its decay from Ag in C6H12S3AgCl is positively charged.

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