DFT calculation of NMR δ(113Cd) in cadmium complexes

Polyhedron 117 (2016) 48–56

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DFT calculation of NMR d(113Cd) in cadmium complexes Girolamo Casella a,b,⇑, Francesco Ferrante c, Giacomo Saielli d,e a

Dipartimento di Scienze della Terra e del Mare (DiSTeM) dell’Università degli Studi di Palermo, Via Archirafi, 20, 90123 Palermo, Italy Consorzio Interuniversitario di Ricerca in Chimica dei Metalli nei Sistemi Biologici (C.I.R.C.M.S.B.), Piazza Umberto I, 70121 Bari, Italy c Dipartimento di Fisica e Chimica dell’Università degli Studi di Palermo, Parco d’ Orleans II, Viale delle Scienze, Ed. 17, 90128 Palermo, Italy d Istituto per la Tecnologia delle Membrane del CNR, Unità di Padova, Via Marzolo, 1, 35131 Padova, Italy e Dipartimento di Scienze Chimiche dell’Università, Via Marzolo, 1, 35131 Padova, Italy b

a r t i c l e

i n f o

Article history: Received 4 April 2016 Accepted 15 May 2016 Available online 24 May 2016 Keywords: 113 Cd NMR DFT Relativistic ZORA

a b s t r a c t We have tested several DFT protocols, at the non-relativistic and relativistic ZORA (scalar and spin–orbit) levels, for the calculation of the 113Cd chemical shifts, d(113Cd), for a number of cadmium complexes accounting for both different local coordination environments on the metal center, involving N, O and S ligands, and different geometrical arrangements. Moreover, suitable models as reference compounds for d(113Cd) evaluation have been set up in order to propose a complete computational approach to calculate d(113Cd) for cadmium complexes. Inclusion of relativistic corrections did not lead to any sensible improvement in the quality of results and, in this context, non-relativistic method, namely: B3LYP/Sadlej (Cd); 6-31g(d,p) (light atoms), showed to be the best approach to calculate d(113Cd) for the classes of compounds investigated. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Cadmium possesses two NMR active isotopes with spin 1/2, Cd and 113Cd, with very similar nuclear properties. 113Cd is the most used isotope due to its slightly higher NMR sensitivity. 113 Cd NMR chemical shift, d(113Cd), encompasses a relatively large spectral width of almost 1000 ppm. This spectral window, together with the high sensitivity of the d(113Cd) toward the coordination environment, allows accurate structural assignments necessary to recognize the coordination number and the type of ligand bonded to the metal center [8]. DFT methods have proved to be quite effective at predicting the NMR properties of diamagnetic systems containing heavy nuclei [9–16] and recently applications have been reported for some paramagnetic systems as well [17–20]. Concerning 113Cd, some non-relativistic DFT calculations of r(113Cd) and d(113Cd) has been already published. Ramamoorthy and co-workers focused on a small set of inorganic cadmium compounds, and cadmium complexes with ligand of biological interest, in solid state [21–23]. Hemmingsen and co-workers studied the performance of non-relativistic DFT methods for a set of small models mimicking typical coordination environments in metallo-proteins, also evaluating the effects of ligand types, coordination environments and structural changes [24]. In this respect they also studied, theoretically, the effect of water on the active site of phosphotriesterase models by NMR d(113Cd) [25]. Though the substantial good performance of the protocols proposed in literature (with Corrected Mean Absolute Errors ranging from about 20 to 50 ppm) [23,24], some 111

The coordination chemistry of cadmium has attracted increasing interest due to its toxicological properties which promotes several diseases in organisms. In particular, in humans Cd(II) starts carcinogenesis as well as the teratogen processes which lead to Itai–Itai, proteinuria and aminoaciduria and it is responsible for kidney and liver diseases as well [1]. Most of these toxicological effects arise from the affinity of Cd(II) toward target molecules bearing thiolic groups, e.g. metallothioneins and glutathione, even if Cd(II) can also interact with some residues exhibiting oxygen and nitrogen sites [1,2]. However, the search for cadmium detoxicant agents, acting by uptake mechanisms, is mainly focused on ligand bearing sulfur residues [3]. As a counterpart of this affinity toward biological targets, Cd(II) is often used as surrogate NMR probe to study the coordination environment of metal sites in several molecules of biological interest, usually metalloproteins, in place of some nuclei which cannot easily detected by NMR spectroscopy, mainly due to quadrupolar relaxation or paramagnetic behavior, such as: 67Zn, 63Cu, 55Mn, 43 Ca and 25Mg [4–7]. ⇑ Corresponding author at: Dipartimento di Scienze della Terra e del Mare (DiSTeM) dell’Università degli Studi di Palermo, Via Archirafi, 20, 90123 Palermo, Italy. E-mail addresses: [email protected] (G. Casella), francesco.ferrante@ unipa.it (F. Ferrante), [email protected] (G. Saielli). http://dx.doi.org/10.1016/j.poly.2016.05.038 0277-5387/Ó 2016 Elsevier Ltd. All rights reserved.

G. Casella et al. / Polyhedron 117 (2016) 48–56

sensible discrepancies between calculated and experimental d(113Cd) were sometimes observed. The effect of relativistic corrections in the perturbative BreitPauli Perturbation Theory (BPPT) framework, both at HF and DFT levels, were studied for the calculation of the r(113Cd) of Cd2+, Me2Cd, and [Cd(H2O)6]2+ and compared with fully relativistic four-component calculations [26]. Results showed that relativistic effects are important in the determination of the cadmium’s shielding constant, being the paramagnetic component of the shielding very sensitive to these effects. This was also observed for the calculation of r(113Cd) of solvated cadmium ion in aqueous solution, by molecular dynamic simulation and DFT [27]. Nevertheless the relevant d(113Cd) calculated, defined as d = rreference rcompound, for Me2Cd and [Cd(H2O)6]2+, wrt Cd2+, resulted almost unaffected by relativistic contributions, mainly due to the mutual cancelation with respect to the reference [27]. These results agree with the behavior of other heavy nuclei of the same row of Cadmium, e.g., Ru, Rh, Sn, where the calculated chemical shift often results almost unaffected due to the partial compensation of relativistic contributions [13–16], provided that no other heavy nuclei are bonded to the metal center. Nevertheless, relativistic effects can affect the geometry of the molecules, and their inclusion in the computational approaches could be important in geometry optimizations due to the sensible dependence of the bond distances, plane e dihedral angles involving the cadmium atom [24]. The set up of the computational reference for the evaluation of d(113Cd) has always been an important issue. The usual experimental references for 113Cd NMR are neat Me2Cd or aqueous solutions (1.0 or 0.1 M) of Cd(ClO4)2; sometimes also aqueous solutions of CdSO4 0.1 or 1 M are employed. Concerning neat Me2Cd, the occurrence of self-association processes sensibly affects the d(113Cd) value with respect to gas phase while in solution phase, the d(113Cd) of Me2Cd is also sensitive to concentration and to the nature of the solvent [28]. Moreover, for Cd(ClO4)2 1.0 M, in order to get reliable results, a suitable picture of the cadmium hexa-aquoion must be set up accounting for the necessary amount of solvent molecules, by using molecular dynamics (MD) approaches [27]. To bridge over these difficulties, in early DFT studies concerning the calculation of d(113Cd) the rationale for the choice of the computational reference was the experimental absolute 113Cd shielding, or the calculated r(113Cd) of a sample model for homologous classes of compounds, [21–23] or the least square fitting of calculated vs experimental shieldings [24]. To summarize, DFT seems to be a good approach in calculating d(113Cd) for cadmium complexes and, in particular, satisfactory agreement with the experimental values can be already obtained at non-relativistic DFT levels, which gives results comparable to full-relativistic approaches [26], while relativistic methods, based on perturbation formalism, does not seem to introduce appreciable improvements. However, the latter results has been figured out for a very small set of cadmium compounds. In this context, to the best of our knowledge, a systematic study on the performance of several computational methods for a larger set of cadmium complexes has not been reported to date.

2. Computational methods 2.1. Geometry optimization Two non-relativistic and one relativistic protocols have been used as implemented in the Gaussian 09 [29] and ADF (v. 2013.01) [30] packages, respectively. Optimization Protocol 1 (OP1) has been performed by using the B3LYP functional in the density functional theory framework with the following

49

gaussian-type basis sets: the correlation consistent polarized valence triple zeta (cc-pvtz) basis set [31] for light atoms and the cc-pvtz-PP basis set [32,33] for cadmium atom, which to a 28 electron small core relativistic pseudopotential joins a triple zeta quality valence basis set with the (37s33p22d2f1g)/[5s5p4d2f1g] contraction scheme. For optimization Protocol 2 (OP2), the B3LYP functional was employed with the correlation consistent polarized valence double zeta (cc-pvdz) basis set [31] for light atoms and the cc-pvdz-PP basis set [32,33]. For the cadmium atom, composed by a 28 electron small core relativistic pseudopotential and a double zeta quality valence basis set with the (22s19p11d1f)/[4s4p3d1f] contraction scheme. ZORA scalar relativistic geometry optimizations, Optimization Protocol 3 (OP3), have been performed by using the BLYP functional in conjunction with the TZ2P Slater-type basis set. Optimized cartesian coordinates for all the model systems studied are given as Supporting Information. A comparison with experimental data (where available, see Scheme 1 for references), showed that, for OP2 geometries, averaged calculated Cd-N distances and XCdY angles (X,Y = N,O,S) differ for a maximum of 0.07 Å and 1°, respectively. A unique exception has been observed for the axial Cd-OHEt distances (models 25 and 26) for which the maximum difference is 0.12 Å. For OP3 geometries, additional discrepancies with respect to OP2 geometries, of 0.02–0.03 Å in the Cd–N distances, and of 0.06 Å for the axial Cd-OHEt distances, were obtained. (A selection of averaged bond distances, and plane and dihedral angles are given as Supporting Information). 2.2. Shielding tensor calculation GIAO shielding tensor calculations of 113Cd, r(113Cd), were run with the Gaussian09, ADF, and DIRAC [34] packages with various combinations of functionals and basis sets, that will be indicated by the label [F/B], where F is the DFT exchange–correlation functional and B the basis sets. 2.2.1. Non-relativistic calculations NR-1[F/B] protocols have been set up by using Gaussian09 with several functionals (see Fig. 1). The gaussian type double zeta valence plus polarization all-electron basis sets named DZVP [35] and Sadlej [36], with contraction scheme (18s12p9d)/[6s5p3d] and (55s33p15d4f)/[11s9p5d2f], respectively, for the cadmium atom, and the gaussian type 6-31G(d), 6-31G(d,p), 6-31+G(d,p) and cc-pvdz basis sets, for light atoms, were chosen. NR-2[F/B] set of protocols consists of the BLYP and B3LYP functionals together with Slater-type double-f (DZP), triple-f (TZ2P) and quadruple-f (QZ4P) basis sets, witn nP (n = 1,2,4) polarization functions, respectively. Those calculations were performed by using ADF. 2.2.2. Relativistic scalar calculations RS[F/B] protocols have been run using ADF according to the relativistic ZORA scalar method with the BLYP and B3LYP functionals together with Slater-type DZP, TZ2P and QZ4P basis sets. 2.2.3. Relativistic spin–orbit and four-component calculations SO[F/B] protocols, in the relativistic ZORA spin–orbit approximation as implemented in the ADF pacakge, have been set up by using the BLYP and B3LYP exchange–correlation functionals together with Slater-type DZP, TZ2P and QZ4P basis sets. DC[F/B] protocol, in the four component DFT framework as implemented in the DIRAC program, is based on the Dirac–Coulomb Hamiltonian; also in this case the BLYP and B3LYP functionals have been chosen, joined with the uncontracted relativistic cV3Z basis set proposed by Dyall [37,38] for Cd (28s20p13d6f3g) and

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G. Casella et al. / Polyhedron 117 (2016) 48–56

Fig. 1. Absolute errors between calculated and experimental d(113Cd) for Et2Cd, wrt Me2Cd. (values in ppm). Calculated data are given in Table S1 (See Supporting Information).

the uncontracted cc-pvtz basis set for H and C. In these calculations, the contribution of S–S integrals was included by means of the interatomic SS correction scheme [39] and, according to relativistic prescriptions, the nuclei have been simulated by gaussian charge distributions [40]. The shielding tensors were calculated by using the simple magnetic balance approach in conjunction with London orbitals, as suggested by Olejniczak et al. [41]. This latter protocol have been used only to estimate the full relativistic effects on the shielding tensor of cadmium in dimethyl- and diethyl-cadmium in gas phase. 2.3. Shielding tensor calculation of 1 M aqueous solution of Cd(ClO4)2 In order to investigate the properties of the 1 M Cd(ClO4)2 aqueous solution, DFT-based Born–Oppenheimer molecular dynamics (MD) simulations have been performed by using the SIESTA method as implemented in the program with the same name, version 4.2 [42]. MD simulations have been done on a system formed by the Cd(ClO4)2
6H2O species and 50 H2O molecules, with periodic boundary conditions, mimicking a 1 M cadmium perchlorate water solution. The NpT ensemble has been employed, maintaining the temperature at T = 298 K by means of a Nóse thermostat [43,44] and the pressure at p = 1 bar by means of a Parrinello-Rahman barostat [45]. A timestep of 0.2 fs has been chosen and the simulation, which started from an optimized structure of the whole system, ran for a total of 10 ps. With regards to the computational method, the following settings has been used both for the optimization and the MD simulation: the Perdew–Becke–Ernzerhof GGA functional [46] has been joined to Troullier–Martins pseudopotentials [47], as supplied by the ABINIT [48] database and translated to the SIESTA format; a double zeta plus polarization quality basis set was generated, according to the SIESTA method [49], with an energy shift of 0.005 Ry. A 350 Ry has been applied for the sampling of the real space grid relevant to the calculation of energy terms in the SIESTA approach. Statistical data were accumulated after 5 ps of equilibration period; the simulated averaged value of the cell volume was 1784 ± 31 Å [3], which resulted in a density of the system estimated as 1.23 ± 0.02 g cm 3. This value is congruent with the measured density values of other cadmium salt solutions, such as 1.197 g cm 3 and 1.153 g cm 3 reported for CdSO4 1.033 M and CdCl2 1.006 M at 20 °C, respectively [50]. Shielding tensor calculations have been performed by using NR-1[F/B] protocols, as given in Table 3, on 20 snapshots extracted

from the last 5 ps of the MD simulations at an interval of 250 fs. Before the calculation, the simulation cell was replicated in all directions and all H2O molecules whose distance from the cadmium central atom was smaller than 9 Å were kept. Averaged isotropic r(113Cd) values and corresponding averaged eigenvalues of the shielding tensors from the 20 snapshots are given in Table 6. Cartesian coordinates of the selected snapshots are given as Supporting Information. For all the compounds studied, experimental d(113Cd) were acquired in the 292–300 K range. For cadmium-metallothionenine complexes it has been observed a maximum differential chemical shift of 0.1 ppm/K [51]. Temperature induced shifts were not accounted for being very small with respect to the scattering of the statistical data obtained. Chemical shifts have been obtained as [d = rref r, ppm], where rref is the shielding constant of the reference. Calculated r(113Cd) of Me2Cd(g) and of 1 M aqueous solution of Cd(ClO4)2 have been used as computational references. The results were evaluated through the statistical accuracy of the linear fit of dcalc vs. dexp (dcalc = adexp + b), the coefficient of determination R2, the Mean P Absolute Error, MAE = n|dcalc dexp|/n, and the Corrected Mean P Absolute Error, CMAE = n|dscaled dexp|/n, where dscaled = (dcalc b)/a measures the distance between the experimental value and the value predicted by the linear fitting.

3. Results and discussion 3.1. Reference models Measured d(113Cd)s of Me2Cd and Et2Cd in gas phase resulted ca. 62 ppm and 19 ppm, respectively, more deshielded with respect to the corresponding neat phases data, using the neat Me2Cd as reference [52]. Comparison between calculated 113Cd chemical shift of Et2Cd in gas phase with the corresponding experimental value has been previously reported and used as benchmark of the protocol rather than as computational reference [21]. Because of the high toxicity of Me2Cd, the experimental reference is often calibrated on the resonance frequency of the esa-aquo-cadmium ion, in 1.0 or 0.1 M aqueous solutions of Cd(ClO4)2. The d(113Cd) value in Cd(ClO4)2 1 M is more shielded of 644.06 ppm with respect to neat Me2Cd and of 706.15 ppm referred to the corresponding gas phase Me2Cd [28].

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3.1.1. Calculation of r(113Cd)s for Me2Cd(g) We start our discussion from the calculation in gas phase of r(113Cd) of Me2Cd(g) by evaluating the performance of the protocol according to the experimental d(113Cd) value for Et2Cd(g) referenced to Me2Cd(g). In Table 1 are given some relevant experimental and calculated bond distances for Me2Cd(g) and Et2Cd(g), obtained by using OP1, OP2 and OP3. OP1 and OP2 give better results concerning the Cd–C bond distances, which instead are slightly overestimated by the relativistic scalar OP3. We made a preliminary test by using several NR-1[F/B] approaches to calculate d(113Cd) for Et2Cd on OP1 geometries wrt to Me2Cd(g). Results are given as absolute errors and are summarized in Fig. 1, while calculated data are given as Supporting Information (Table S1). All calculated d(113Cd)s for Et2Cd(g) obtained with the DZVP basis set on Cd, both using 6-31G(d,p) and cc-pvdz basis set on light atoms, show a fair performance with all protocols but M06-L for which the chemical shift values resulted quite underestimated. From Fig. 1, also accounting for the functionals available for NR[F/B], SR[F/B], SO[F/B] and DC[F/B] protocols, we then selected the BLYP and the B3LYP functionals together with several basis sets, in order to make a comparison with non-relativistic and relativistic approaches in calculating the d(113Cd)s of Et2Cd(g), wrt to Me2Cd(g), on geometries optimized with OP1, OP2 and OP3. Results are given in Table 2. We consider DC[F/B] protocol as a benchmark, being the highest level of theory. In general, the calculated gas phase d(113Cd)s for Et2Cd indicate a substantial good performance of all methods used, even if the lacking of a straight trend can be noticed both in going from non-relativistic to full relativistic methods and in changing the quality of the basis set. The geometry optimization protocol seems to affect for few ppm the d(113Cd) value, while basis sets, being functional and geometry the same, impinge up to 20 ppm. The effect of the basis set seems more sensible when relativistic contributions are considered as in the case of RS[F/B] and SO[F/B] protocols, and TZ2P basis sets seems to show the worse performance. Spin–orbit effects do not strongly affect the calculated d(113Cd) most likely due to their partial cancelation in the difference d = rreference rsample. In fact, calculated d(113Cd) obtained at SO[F/B] level do not display great discrepancies, if compared to NR-2[F/B] and RS[F/B] ones (with a maximum d(113Cd) difference around to 10 ppm), though spin–orbit contributions, ranging from 410 to 480 ppm, represent up to the 15% of the total calculated r(113Cd) value. (see Tables S2 Supporting Information for the calculated r(113Cd)s and relevant spin–orbit contributions). Moreover, calculated shielding at DC[F/B] level for Me2Cd is in substantial agreement with the four component value calculated by Lantto

Table 2 Calculated d(113Cd) for Et2Cd, wrt to Me2Cd, at several levels of theory and basis sets on OP1, OP2 and OP3 geometries. Experimental d(113Cd) = 142.6 [28]. Values are given in ppm. (Relevant calculated r(113Cd) are given in Table S8). NR-1a BLYP OP1

NR-2b

RSb

SOb

NR-3

DC

155.4 120.6 153.0 123.6

147.5 145.8 146.0

143.3 138.7 145.2

151.6 145.2 156.5

144.9

155.3

OP2

155.6 120.9 153.6 124.1

148.3 146.4 146.7

143.9 139.7 146.0

152.4 146.4 157.4

145.5

157.6

OP3

150.4 114.4 147.9 119.6

143.7 141.6 142.2

140.4 135.4 140.6

148.9 142.1 152.8

141.2

152.3

145.2 113.3 142.6 115.6

137.8 135.3 136.6

134.0 128.5 135.6

141.8 134.6 145.8

134.7

145.8

OP2

145.7 113.7 142.3 116.1

138.5 136.0 137.2

134.6 129.6 136.3

142.2 135.9 146.5

135.3

148.0

OP3

140.1 109.4 137.5 111.6

134.1 131.2 132.9

131.2 125.3 131.7

138.3 131.7 141.8

130.8

142.9

B3LYP OP1

a In the entries are given the results obtained with, from top to bottom, DZVP (Cd); 6-31G(d,p) (H,C); Sadlej (Cd);6-31G(d,p) (H,C); DZVP (Cd);cc-pvdz (H,C) and Sadlej (Cd); cc-pvdz (H,C) gaussian type basis, respectively. b In the entries are given the results obtained with Slater type basis set of DZP, TZ2P and QZ4P quality, respectively.

et al. [26]. Finally, non-relativistic methods give very good results, comparable with the performance of the fully relativistic calculation in agreement with what already observed in Ref. [26] It is worth to note that, accounting for the corresponding r(113Cd) values, the small influences of the geometry on the d(113Cd) seems to be due mainly to a subtle balancing in the d = rreference rsample difference. As previously mentioned, it has been already studied, at non-relativistic level, how small variations of Cd–O bond lengths and relative plane, O–Cd–N, and dihedral, N–O–Cd–N, angles lead to variation of tenth of ppm in d(113Cd) [24]. In this respect, we observed that the trend of the Me2Cd(g) r(113Cd) as a function of the Cd–C distances, calculated at various theoretical levels, shows that even differences of 4–5 pm in the Cd–C bond length can lead to about 80 ppm of difference in the calculated r(113Cd). On the

Table 1 Structural data for the gas-phase optimized geometries of CdMe2 and CdEt2 obtained with OP1, OP2 and OP3. Distances (d) in pm, angles (h) in degrees (°).a

a

d(Cd–C)

d(C–C)

d(C–H)

h(Cd–C–H)

h(Cd–C–C)

h(C–C–H)

Me2Cd OP1 OP2 OP3 Ref. [21] Exp (g) Ref. [52]

213.2 212.9 216.1 203 211

– – – –

109.0 110.0 109.6 109 109

110.5 110.8 110.2 109.5 108.4

– – – –

– – – –

Et2Cd OP1 OP2 OP3 Ref. [21] Exp (g) [52]

215.5 215.2 218.5 206 213

153.4 153.7 154.6 150 150

109.4 110.5 109.8/109.9 110 110

107.0 107.2 106.8 107.9 108.8

115.4 115.7 115.1 117.8 116.2

111.7/112.0 110.2/112.2 111.5/112.0 111.9 114.4

Geometries are not symmetric: with OP2, methyl groups in CdMe2 are rotated by 19.9°, ethyl groups in CdEt2 are rotated by 15.4°.

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other hand, changing the C–Cd–C–H dihedral angle in its entire range lead to variations up to 5 ppm for each Cd–C distance considered. (related graphs and calculated r(113Cd) at NR-2, SC and SO levels are given in Supporting Information). Finally, accounting for the very similar results obtained, as regard the geometries optimized with the non-relativistic OP1 and OP2, we will use the less time demanding OP2 for the other molecules studied in this work. 3.1.2. r(113Cd) calculation of 1M water solution of Cd(ClO)4 In Table 3 are reported the averaged r(113Cd) values, obtained from the 20 snapshots selected from MD simulation, by using NR-1[F/B] with B3LYP and B3PW91 functionals together with

several combinations of basis set both for Cd and light atoms. (see Tables S3–S8 in Supporting Information for the complete set of calculated isotropic and eigenvalues data for all snapshots and the protocols with the Sadlej basis set for Cadmium). B3PW91 has been already used for r(113Cd) calculation [21–23]. Thus, for the sake of comparison with literature, we also calculated the r(113Cd) of this reference with this functional, in order to asses its performance on several cadmium complexes. The results have been compared with experiment [28,52] by calculating the d(113Cd)Cd(ClO4)2 = [rMe2Cd(g) rCd(ClO4)2], wrt the corresponding calculated gas phase r(113Cd) of Me2Cd(g), optimized OP2. Calculated d(113Cd)Cd(ClO4)2 with NR-1[B3LYP/Sadlej (Cd);6-31G(d,p)(H,C)] resulted in excellent agreement with the

Table 3 Averaged isotropic r(113Cd) of the 20 snapshots for the simulated aqueous solution of Cd(ClO4)2 1.0 M and calculated d(113Cd) wrt calculated gas phase r(113Cd) of Me2Cd. B3LYP (riso) Sadlej; 6-31G(d) Sadlej; 6-31G(d,p) Sadlej; 6-31 + G(d,p) DZVP; 6-31G(d,p) a

Experimental value:

3839.7 3837.1 3833.8 3834.1

d(113Cd)Cd(ClO4)2 [risoMe2Cd-risoCd(ClO4)2]a 716.0 709.5 687.2 856.7

B3PW91 (riso) 3848.0 3843.5 3838.4 3851.3

d(113Cd)Cd(ClO4)2 [risoMe2Cd-risoCd(ClO4)2] 695.3 687.0 667.7 847.9

706.13 ppm obtained from Refs. [28,52].

Scheme 1. Model systems investigated. (1)–(5) [53] (CDCl3); (6)–(13) [54] (CDCl3); (14)–(16) [55] (CD2Cl2); (17)–(24) [56] (CDCl3); (25)–(26) [57] (CDCl3). For models 14, 15, and 16, experimental d(113Cd)s were given wrt a solution 4.5 M of Cd(NO3)2 and then they were scaled by 31.87 ppm wrt 1.0 M Cd(ClO4)2 according to Refs. [28,58] Pz = Pyrazolyl.

G. Casella et al. / Polyhedron 117 (2016) 48–56

experimental value. Moreover, the calculated d(113Cd)Cd(ClO4)2 obtained with NR-1[B3LYP/Sadlej (Cd); 6-31G(d) (H,O,Cl)] is in quite good agreement with respect to the analogous one (d(113Cd)Cd(ClO4)2 = 3826 ppm), determined in a previous work with the same protocol, by least-squares fitting, using experimental data referenced to 0.1 M aqueous solution of Cd(ClO4)2 [24]. Concerning the calculated r(113Cd)s given in Table 3, we note a sensible improvement with respect to the 3755 ppm value calculated by Xin Li et al. [27] by means of a combined MD/DFT approach. The difference is likely due to the better description of the system time evolution obtained with our DFT-based molecular dynamics. At variance with the case of the ethylcadmium, we note that d (113Cd) for Cd(ClO4)2 is well reproduced using the Sadlej basis set on the metal center, accordingly with literature [21–24]. Taking into account the different performances of the protocols in calculating the d(113Cd) for Et2Cd and Cd(ClO4)2, wrt to Me2Cd(g), a final assessment in the choice of a suitable approach for the calculation of the isotropic d(113Cd) in cadmium complexes is needed.

3.2. Calibration of the protocols for cadmium complexes d(113Cd) is very sensitive to coordination number, type of ligand and geometry [8,21–24]. Thus, we have selected several molecules from literature (Scheme 1) aiming to cover as much as possible the different chemical environments and geometrical arrangements usually experienced by cadmium, also considering the most common ligands involved in cadmium coordination as nitrogen, oxygen and sulfur. The choice of the models considered also the presence of patterns of homologous series, displaying very close d(113Cd) values. All the experimental data are referred to non-coordinating solvents as CDCl3 and CD2Cl2. The occurrence of O, N or S in the cadmium coordination sphere spawns a trend of experimental d(113Cd), ranging from more shielded values, accounting for coordinated oxygen, to more deshielded values when sulfur is bonded to Cd, passing through nitrogen. These effects are roughly additive, then a mixed coordination on cadmium, involving O, N or S, gives d(113Cd) values accordingly.

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We have narrowed the choice of the protocols for the calculation of r(113Cd) to the non-relativistic protocols NR-1[F/B] [F = B3PW91, B3LYP; B = DZVP, Sadlej (Cd); 6-31G(d), 6-31G(d,p), 6-31+G(d,p) (light atoms)] and NR-2[B3LYP/B] [B = DZP; TZ2P], while relativistic calculations have been performed using the RS [B3LYP/B] [B = DZP; TZ2P] and SO[B3LYP/B] [B = DZP; TZ2P] protocols. For the calculations, both set of geometries, optimized with OP2 and OP3, were used. 3.2.1. Non-relativistic calculations We started by performing non-relativistic calculations of d (113Cd)s on geometries optimized with OP2 at NR-1[F/B] levels, [F = B3LYP; B3PW91/B = Sadlej, DZVP (Cd); 6-31G(d), 6-31G(d,p), 6-31+G(d,p) (light atoms)]. In Fig. 2 correlations of calculated vs experimental d(113Cd)s are given. Data obtained with the DZVP basis set on Cd are not reported due to their low performance and are given as Supporting Information (see Table S10). Fig. 2a and b, which correspond to the calculated d(113Cd)s wrt Cd(ClO4)2 1 M and Me2Cd(g), respectively, display different trends compared to the corresponding ideal correlations, mirroring the dependence of the r(113Cd)[Cd(ClO4)2] r(113Cd)[Me2Cd(g)] difference upon the protocol considered (See Table 3). Statistical data display very good correlations with a slight preference for those protocols with the B3LYP functional, while B3PW91 tends to underestimate calculated data. Moreover, for both functionals, the inclusion of diffusion functions in the basis sets for the light atoms tends to worsen the performance, while the 6-31G(d) and 6-31G(d,p) basis set perform better and quite similarly. In general, considering the spectral windows of cadmium, the CMAE values indicate a very good predictive power of the protocols used and, among them, the NR-1[B3LYP/Sadlej;6-31G(d,p)] appears more suitable also accounting for the good value of the r(113Cd)[Cd(ClO4)2] r(113Cd)[Me2Cd(g)] difference which then give results of almost the same accuracy with both references. Fig. 3 shows the correlations for the calculated d(113Cd) using geometries optimized with OP3. For this calculation, we only used the set of NR-1[B3LYP/B], [B = Sadlej (Cd), 6-31G(d),6-31G(d,p),631+G(d,p)] protocols due to its slightly better performance with respect to the B3PW91 functional and the results were referred only to Me2Cd(g). We did not use the calculated r(113Cd) of

Fig. 2. Correlations at NR-1[F/B] level of calculated d(113Cd) (ppm), wrt Cd(ClO4)2 and Me2Cd, respectively, for model systems of Scheme 1 on OP2 geometries Fit parameters: y = a + bx; R2 (a) wrt Cd(ClO4)2: (s) a = 15.06; b = 0.936; R2 = 0.9926; MAE = 8.53; CMAE = 6.31. (j) a = 12.75; b = 0.934; R2 = 0.9915, MAE = 8.52; CMAE = 6.67. (/) a = 20.22; b = 0.921; R2 = 0.9890; MAE = 10.37; CMAE = 8.05. (⁄) a = 16.40; b = 0.934; R2 = 0.9902; MAE = 9.73 CMAE = 7.30. (+) a = 11.33; b = 0.933; R2 = 0.9892; MAE = 8.45; CMAE = 7.96. (x) a = 13.26; b = 0.950; R2 = 0.9604; MAE = 13.26; CMAE = 13.45 (Solid line) ideal correlation: y = x. (b) wrt Me2Cd(g): (s) a = 40.15; b = 0.936; R2 = 0.9926; MAE = 9.43; CMAE = 6.31. (j) a = 37.44; b = 0.934; R2 = 0.9915; MAE = 8.51; CMAE = 6.67. (/) a = 13.40; b = 0.921; R2 = 0.9890; MAE = 27.85; CMAE = 8.05. (⁄) a = 19.65; b = 0.934; R2 = 0.9902; MAE = 16.69; CMAE = 7.30. (+) a = 16.97; b = 0.933; R2 = 0.9892; MAE = 19.36; CMAE = 7.96. (x) a = 16.725; b = 0.950; R2 = 0.9604; MAE = 43.32; CMAE = 13.45. (Solid line) ideal correlation: y = x.

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G. Casella et al. / Polyhedron 117 (2016) 48–56

both set of geometries, DZP basis sets perform slightly better than TZ2P, accounting for their CMAE and R2 values while the use of TZ2P basis set gives results closer to the experimental values. This is in agreement with the behavior observed for Et2Cd(g) as given in Table 2. In general, the performance of these protocols is similar with respect to the protocols in Figs. 2 and 3. In this case, the Dd(113Cd)max-geom and Dd(113Cd)max-geom values resulted about 52 and 14 ppm, irrespective of the basis set used.

Fig. 3. Correlations at NR-1[B3LYP/B] [B = Sadlej (Cd), 6-31G(d), 6-31G(d,p), 66-31 +G(d,p)] levels of calculated d(113Cd) (ppm), wrt Me2Cd, for model systems of Scheme 1 on OP3 geometries. Fit parameters: y = i + bx; R2 (s) a = 26.09; b = 0.959; R2 = 0.9823; MAE = 10.62; CMAE = 10.32. (j) a = 28.15; b = 0.947; R2 = 0.9831; MAE = 10.09; CMAE = 9.81. (/) a = 6.12; b = 0.930; R2 = 0.9832 MAE = 30.55; CMAE = 9.54. (Solid line) ideal correlation: y = x.

3.2.2. Relativistic scalar calculations Relativistic scalar calculations of d(113Cd) have been run at RS [B3LYP/B] [B = DZP,TZ2P] levels, always on OP2 and OP3 geometries. The results are given only referred wrt Me2Cd(g) (see Fig. 5). Considering both set of optimized structures, the protocols show no appreciable improvement with respect to the non-relativistic methods discussed. DZP basis set still perform better than TZ2P, and the effect of the basis set is more sensible in this case. Moreover, calculations on OP2 geometries give results comparable the non-relativistic methods, while calculations on OP3 geometries give slightly worse correlations. Dd(113Cd)max-geom resulted around 54 ppm for both basis set while for Dd(113Cd)avgavg-geom values of 43 ppm and 16 ppm, by using the DZP and TZ2P, respectively, have been found. This indicates a sensible basis set dependence with the inclusion of relativistic scalar corrections.

Cd(ClO4)2 as reference, considering the different level of theory used to perform the MD simulation. Concerning the effect of the geometry, the maximum, Dd(113Cd)max_geom, and averaged, Dd(113Cd)avg_geom, Dd(113Cd) differences for the same model calculate with OP2 and OP3 geometries, seem to be slightly affected by the optimization protocol used. In particular, for B3LYP, Dd(113Cd)max_geom of about 26 ppm and Dd(113Cd)avg_geom of about 12 ppm were observed. This differences account for the small variations in the final geometries (See Supporting Information). Finally, we performed non-relativistic r(113Cd) calculations at NR-2[B3LYP/B] [B = DZP, TZ2P] level for the molecules of Fig. 1, on OP2 and OP3 geometries, always wrt Me2Cd(g). Results are given in Fig. 4. The performance of the protocols is still good, even if results are systematically underestimated using Me2Cd(g) as reference. With

3.2.3. Relativistic spin–orbit calculations Relativistic ZORA spin–orbit calculations of d(113Cd) have been run at SO[B3LYP/B] [B = DZP;TZ2P] level, always on OP2 and OP3 geometries. The d(113Cd) were calculated only scaled wrt Me2Cd(g) and the relevant correlations are given in Fig. 6a. Considering both set of optimized structures, the protocols do not show any sensible improvement of the performance, behaving quite similarly to the other protocols discussed, accounting for slope, R2 and CMAE. Nevertheless, results are systematically shifted toward more shielded values with respect to the ideal correlation. In this respect, spin–orbit contributions seems to be quite overestimated as could be inferred from Fig. 6b where the correlations are given without their inclusion. For all the molecules, spin–orbit contributions, r (SO), resulted quite similar with values of 497 ± 14 ppm and

Fig. 4. Correlations at NR-2[B3LYP/B] [B = DZP; TZ2P] levels of calculated d(113Cd) (ppm), wrt Me2Cd, for model systems of Scheme 1 on OP2 and OP3 geometries. Fit parameters: y = a + bx; R.2 OP2 geometries: e a = 65.06; b = 1.009; R2 = 0.9815; MAE = 69.59; CMAE = 9.81. a = 33.59; b = 1.040; R2 = 0.9818; MAE = 55.05; CMAE = 10.29. OP3 geometries: s a = 118.45; b = 1.002; R2 = 0.9758; MAE = 62.10; CMAE = 12.80. d a = 29.56; b = 1.040; R2 = 0.9709; MAE = 49.23; CMAE = 13.56. (Solid line) ideal correlation: y = x.

Fig. 5. Correlations at RS-[B3LYP/B] [B = DZP;TZ2P] levels of calculated d(113Cd) (ppm), wrt Me2Cd, for model systems of Scheme 1 on OP2 and OP3 geometries. Fit parameters: y = a + bx; R2. e a = 16.02; b = 1.081; R2 = 0.9805; MAE = 26.21; CMAE = 10.86. a = 44.27; b = 1.160; R2 = 0.9734; MAE = 42.75; CMAE = 13.15. s a = 45.05; b = 1.072; R2 = 0.9318; MAE = 25.30; CMAE = 22.07. d a = 46.18; b = 1.148; R2 = 0.9482; MAE = 39.64; CMAE = 18.16. (Solid line) ideal correlation: y = x.

G. Casella et al. / Polyhedron 117 (2016) 48–56

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Fig. 6. Correlations at SO[B3LYP/TZ2P] (OP2 and OP3 optimization protocols) level of calculated d(113Cd) (ppm) with spin–orbit (a) and without spin–orbit (b) contributions, wrt Me2Cd(g). Fit parameters: y = a + bx; R2. (a) e a = 86.98; b = 0.967; R2 = 0.9747; MAE = 69.06; CMAE = 11.51. r a = 62.80; b = 1.060; R2 = 0.9846; MAE = 94.25; CMAE = 8.62. s a = 85.99; b = 0.955; R2 = 0.9697; MAE = 62.50; CMAE = 11.99. d a = 59.21; b = 1.049; R2 = 0.9576; MAE = 84.80; CMAE = 16.68. (Solid line) ideal correlation: y = x.

502 ± 19 ppm, for models optimized with OP2 and OP3 protocols, respectively. For Me2Cd(g), with both optimization protocols, the r(SO) contributions resulted ca. 50 ppm smaller than all the models, (445 ppm and 448 ppm for OP2 and OP3, respectively) due to the different chemical environment experienced by the cadmium in organocadmium compounds. As a matter of fact, r(SO) contributions for Et2Cd(g) was ca. only 6 ppm higher than the Me2Cd(g). As regard the effect of the optimization protocol, d(113Cd), Dd(113Cd)max-geom values of 47 ppm and 33 ppm have been obtained for DZP and TZ2P, respectively, while at variance with the case of relativistic scalar calculations, Dd(113Cd)avgavg-geom of about 15 ppm for both basis sets have been found. 4. Conclusions We have calculated isotropic d(113Cd) for some cadmium complexes, by using several DFT levels of theory, spanning from nonrelativistic to relativistic methods, the latter in the ZORA formalism at relativistic and spin–orbit levels, on structures optimized both at non-relativistic and relativistic scalar ZORA levels, by considering different functionals and basis sets. The effect of the direct inclusion of relativistic scalar contributions in optimization protocol lead to sensible different structures for the same models. This implies a differences of tenths of ppm, up to 50 ppm, in the calculated d(113Cd) with the same protocol. However, statistical data shows that the inclusion of these contributions do not appreciably improve the performance of the calculation. In general, for all the methods studied we obtained good results with CMAEs from ca. 7 up to 22 ppm, which are satisfactory accounting for the chemical shift range of 113Cd. However, calculated data showed that improving the level of theory in the r (113Cd) calculations, did not improve the performance of the results and for spin–orbit calculations, SO contributions seems to be not well pictured. Nevertheless, non-relativistic protocols showed a very high predictive power. Moreover, the computational references proposed, Me2Cd(g) and 1 M water solution of Cd(ClO4)2, chosen because they are the most used for experimental measures, gave very satisfactory results. In particular, the model of Cd(ClO4)2 1 M solution, has proved to be the more suitable computational reference, even if the size of the MD snapshots allowed us to use it only at non-relativistic level.

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