NMR J-Coupling Constants of TlâPt Bonded Metal Complexes in

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NMR J‑Coupling Constants of Tl−Pt Bonded Metal Complexes in Aqueous Solution: Ab Initio Molecular Dynamics and Localized Orbital Analysis Lucas C. Ducati,† Alex Marchenko,‡ and Jochen Autschbach*,‡ †

Department of Fundamental Chemistry Institute of Chemistry, University of São Paulo, Av. Prof. Lineu Prestes 748, São Paulo, SP 05508-000, Brazil ‡ Department of Chemistry University at Buffalo State, University of New York, Buffalo, New York 14260-3000, United States S Supporting Information *

ABSTRACT: The influence of solvent (water) coordination and dynamics on the electronic structure and nuclear magnetic resonance (NMR) indirect spin−spin coupling (J-coupling) constants in a series of Tl−Pt bonded complexes is investigated using Kohn−Sham (KS) Car−Parrinello molecular dynamics (CPMD) and relativistic hybrid KS NMR calculations with and without coordination to water. Coordination of the Tl center by water molecules has a dramatic impact on 1J(Tl−Pt) and other Jcoupling constants. It is shown that a previous computational study of the same complexes using static optimized structures and nonhybrid functionals was correct about the important role of the solvent but obtained reasonable agreement with experimental NMR data because of a cancellation of substantial errors. For example, the CPMD trajectories show that on average the inner coordination shell of Tl is not saturated, as previously assumed, which leads to poor agreement with experiment when the Jcoupling constants are averaged over the CPMD trajectories using NMR calculations with nonhybrid functionals. The combination of CPMD with hybrid KS NMR calculations provides a much more realistic computational model that reproduces the large magnitudes of 1J(Tl−Pt) and the correct trends for other coupling constants. An analysis of 1J(Tl−Pt) in terms of localized orbitals shows that the presence of coordinating water molecules increases the capacity for covalent interactions between Tl and Pt. There is pronounced multicenter bonding along the metal−metal axis of the complexes.

1. INTRODUCTION Heavy metal complexes play a role in many of nature’s processes, including, for example, photochemistry1 and catalysis.2 Many of these processes occur in solution, where the role of the solvent may have a dramatic impact on the properties and behavior of the complex. One of the primary tools used by chemists to determine structure and bonding of molecules and metal complexes in solution is nuclear magnetic resonance (NMR) spectroscopy. Accordingly, it is important to be able to rationalize and predict NMR parameters of metal complexes in solution using first-principles theory. The NMR parameters involving metals,3,4 including very heavy elements such as Pt, Hg, Tl, and Pb,5−13 (or even U14,15 and Pu16) are of significant experimental and theoretical interest. These NMR parameters of heavy metals can be correlated with (for instance) oxidation states and pronounced relativistic effects in the valence shell of the heavy atoms.8,17,18 It has been pointed out that relativistic effects may act as a “magnifying glass” to amplify subtle effects of metal−ligand (M−L) and metal−solvent coordination, in particular, on M−L and metal−metal (M−M) indirect spin−spin coupling (Jcoupling) constants.13,19,20 Theoretical modeling requires a © XXXX American Chemical Society

reliable treatment of relativistic effects as well as the influence of solvent and dynamics. The complexes [(NC)5Pt−Tl(CN)n]n−, where n = 0, 1, 2, 3, (1−4), and [(NC)5Pt−Tl−Pt(CN)5]3− (5), shown in Figure 1, belong to a fascinating and rare class of organometallic complexes that are stable in aqueous solution and afford direct, nonbridged bonds between Pt and Tl.21−25 The bonding in 1− 4 has been studied theoretically in refs 26 and 27. Further, it has been shown previously by Kohn−Sham (KS) density functional theory (DFT) calculations that the metal and ligand NMR chemical shifts28 and, in particular, the J-coupling constants29,30 are strongly impacted by coordination of water at the Tl center. In previous theoretical work, the inner coordination sphere of Tl was augmented with 5, 4, 2, 0, and 4 water molecules for complexes 1− 5, respectively, in geometry optimizations.20 It was shown, for example, that explicit coordination by water molecules causes the experimentally observed trend of decreasing 1J(Tl−Pt) from 71 to 25 kHz along the series 1−5. The trend was reversed when the Received: September 9, 2016

A

DOI: 10.1021/acs.inorgchem.6b02180 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 1. Complexes 1−5 studied in this work. Superscripts A−C are used to denote different ligand types, namely, axially coordinated to Pt (CA), directly coordinated to Tl (CB), and equatorially coordinated to Pt (CC).

nificant contributions.33 The most accurate computational model in the benchmark utilized a hybrid functional, included both scalar and spin−orbit (SO) relativistic effects, a continuum model for solvent effects, as well as a finite nuclear volume model, and delivered agreement with experimental data with a median relative deviation of 13%. Outliers in the benchmark were coordinatively unsaturated complexes measured in aqueous solution, including some thallium complexes. While there is little doubt that solvent effects are of paramount importance for the NMR spectra of 1−5, given the approximate nature of the calculations available in the literature it remains an open question what it really takes to model the NMR parameters with satisfactory accuracy and how the solvent alters the bonding in the systems and causes the large solvent effects on the J-couplings. In this work, all experimentally known J-coupling constants of the complexes are studied, with emphasis on 1J(Tl−Pt) because of its elusiveness, magnitude, and strong dependence on solvent effects. The purpose of this work is to shed light on the mechanism(s) by which the large, solvent-influenced, spin− spin coupling constants arise in complexes 1−5 and to obtain a faithful representation of their structure and coordination in aqueous solution. Car−Parrinello molecular dynamics34 (CPMD) is used to generate a set of snapshot geometries (molecular dynamics (MD) “frames” or “configurations”) over which spin−spin coupling constant data are averaged based on relativistic KS calculations for solute−solvent clusters. Spin− spin coupling results for selected frames are analyzed in detail to determine Tl−Pt coupling constant contributions35 from relativistic natural localized molecular orbitals (NLMOs), elucidating the manner in which the presence of explicit coordinating water molecules affect the bonding and spin−spin coupling constants. Unlike the previous model systems, with saturated or mostly saturated inner Tl coordination spheres, the average number of water molecules around Tl in the MD simulations is more consistent with transitions between fourcoordinate pseudotetrahedral and five-coordinate pseudopyramidal coordination environments. Using a hybrid KS functional is imperative to obtain reasonable MD-averaged Jcouplings.

calculations did not include solvation of the Tl center, and without solvent, the Tl−Pt coupling for 1 was predicted to be negative. The Tl−Pt coupling constants are among the largest (note the unit of kiloHz) known and driven by the strong relativistic effects in the valence shells of the two metals and metal-solvent interactions. The water coordination effects on the M−M J-coupling appear to be mainly electronic in nature, that is, not driven by solvent-induced geometry changes in the complex. Another remarkable feature of the NMR spectrum of 2 is the fact that the two-bond coupling 2J(Tl−CA) is much larger than the one-bond coupling 1J(Tl−CB). This has been attributed to an interplay of solvent effects and a strongly delocalized electronic structure along the CA−Pt−Tl−CB moiety.30 There is still much to learn about the fascinating NMR parameters of complexes 1−5. First, the dramatic solvent effects on the M−M J-couplings, in particular, has not been explained in detail. Second, the static solvent coordination motifs explored in previous theoretical work20,28−30dictated by computational limitations at the timeare unlikely to qualify as a faithful representation of the dynamic in situ structural space explored by the complexes. Third, past KS NMR calculations utilized nonhybrid functionals and generally did not reproduce the true magnitude of the observed J-couplings. Results for 1 J(Tl−Pt) close to experiment were obtained only with a shapecorrected KS potential31 for the ground-state calculations (the statistical average of orbital model exchange-correlation potential, or SAOP). The SAOP potential has the correct behavior far away from an isolated molecule and was originally designed for calculations of optical properties of molecules in gas phase. SAOP had shown some improvements over standard nonhybrid functionals in an NMR chemical shift benchmark32 via an increase of the gap between the highest occupied and lowest unoccupied orbitals, which tends to correct excessively large paramagnetic shielding contributions. However, SAOP was abandoned by us in subsequent NMR studies of metal complexes because of inconsistent performance. More recently, a benchmark study for J-couplings in heavy metal complexes has shown that hybrid functionals perform much better than nonhybrid functionals in relativistic KS calculations and that previously neglected finite-nucleus effects also provide sigB


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Amsterdam Density Functional (ADF, version 2014, revision 51267) molecular KS DFT package55 with a Slater-type orbital (STO) basis set for all atoms. Sixty-four (64) evenly spaced frames from the production trajectory, per complex, were initially used to determine the number of explicit water molecules required, with an additional 192 frames selected for statistical averaging of the calculated NMR parameters; that is, the final statistics were accumulated from 256 frames per trajectory, evenly spaced over the production run. No weighting of the configurations (e.g., according to their energy) was applied. The NMR calculations were performed following the prescription in refs 20 and 29 with the exceptions that the hybrid version of PBE, PBE0 (containing 25% exact exchange),56 and a Gaussian finite nuclear volume model57 were used. A subset of the calculations employed the Vosko−Wilk−Nusair58 (VWN) local density approximation functional, for comparison with the previous J-coupling calculations.29 SO effects were previously found to be small in comparison with solvent effects,29 and they were neglected except in a set of benchmark calculations detailed in the Supporting Information. All NMR calculations utilized the zero-order regular approximation (ZORA)59 to treat relativistic effects variationally. An augmented all-electron STO basis, developed for J-coupling calculations,33 was used for Tl and Pt. A polarized all-electron tripleζ valence TZP was used for all other atoms. The conductor-like screening model60 (COSMO) is a continuum solvent model and was employed to model bulk solvent effects in the finite cluster calculations, using the same parameters as those of ref 29 and compared against the default parameters implemented in ADF.61 The coupling constants were analyzed in terms of localized molecular orbitals (LMOs) using the relativistic J-coupling analysis described in ref 35, with natural LMOs (NLMOs) from the scalar ZORA STO-basis ground state calculations provided by a locally modified version of the Natural Bond Orbitals (NBO) program62 version 5.0. To maintain reasonable computational requirements in the NMR calculations, the MD frames were pruned to include the smallest number of nearest neighbor (NN) water molecules (to each complex) that affected the spin−spin coupling constants beyond the statistical errors. For this purpose, new open-source software was developed (version 0.2.1 was used to process, analyze, and visualize the data presented in this work).63 Selection of NNs was performed by creating a 3 by 3 by 3 supercell of the periodic simulation cell of each frame of interest. From this super cell, interatomic distances were compared to covalent radii plus a small additional factor (following typical conventions for semiempirical bond drawing)64 to determine molecular subunits. Nearest-neighbor water molecules were selected based on atom-to-atom distances, either between any atom of a complex and a solvent (nonbiased search) or between the Tl center and a solvent (biased search, favoring Tl solvation). Checks were performed to ensure that the number of NNs selected was always equal to the number requested and binned accordingly (i.e., 5, 10, 15, etc. NNs). For complex 1, the nonbiased and biased searches were compared in terms of the J-coupling data. For the number of explicit water molecules at which the calculations can be considered converged, the biased J-coupling constant results were nearly identical to the nonbiased results. Therefore, the nonbiased search was used for all subsequent calculations.

Section 2 provides the computational details for the dynamics and spin−spin coupling calculations, along with a description of the workflow used in moving between the MD trajectory and ab initio J-coupling constant calculations. Results are discussed in Section 3, where, first, a description of the solution structure and metal coordination by water is provided, followed by a description of bulk solvation model effects, and a spin−spin coupling constant analysis in terms of NLMOs. Section 4 summarizes the findings.

2. COMPUTATIONAL DETAILS CPMD simulations were performed with the plane-wave (PW) periodic-boundary DFT code Quantum ESPRESSO (QE), version 5.1.36 Geometries29 for complexes 1−5 were optimized using the PW module of QE. Cubic simulation cells were packed37 with one of the optimized complexes in the center and an appropriate number of hydronium ions to balance the corresponding charge of the complex. Water molecules were added such that the total number of solvent molecules (hydronium and water) equaled 64. Hydrogen atoms were replaced with deuterium. Each cell’s lattice parameter was selected such that the density of the cell was that of heavy water at 300 K. See the Supporting Information, Table S13, for unit cell dimensions. Geometry optimizations and CPMD simulations were performed using the Perdew, Burke, and Ernzerhof (PBE) generalized gradient approximation (GGA) exchange-correlation functional38 (see also Section 3 of the Supporting Information). A kinetic energy cutoff of 100 Ry was found suitable, providing an energy convergence of better than 2 meV per atom. Ultrasoft pseudopotentials, from the pslibrary 1.0.0,39 were used to represent the effective potential around each nucleus. Grimme’s semiempirical dispersion correction40 (D2) was employed for both geometry optimizations and CPMD simulations. For the CPMD simulations, a fictitious electron mass of 450 atomic units (au) and a time step of 5.0 au were chosen based on previous simulations in the literature.41,42 A three-chain Nosé−Hoover thermostat was employed with a target temperature of 330 K to mimic nuclear quantum effects of water43 and maintain the mobility of water molecules observed experimentally at ambient temperatures.43−46 After initial wave function optimization (using the CP module of QE), each trajectory was allowed to equilibrate for ∼3 ps in the canonical ensemble. Subsequently, microcanconical ensemble trajectories were simulated for a duration of 24.2 ps per trajectory. This portion of the simulation is referred to as the “production” trajectory based on which structural analyses and NMR calculations were performed. We assume that the dynamics is fast on the NMR time scale such that the experimentally detected NMR parameters would agree with the MD averages. Structural and coordination analyses were performed on 2001 evenly spaced (every 12.1 fs) frames from each production run. Bulk properties of solutions were assessed via calculated diffusion coefficients and pair correlation functions. Diffusion coefficients D were obtained using the Einstein relation and are 0.19, 0.23, 0.22, 0.09, and 0.13 Å2 ps−1, respectively, for the trajectories of complexes 1−5. For 1−3, the diffusion coefficients match well with experimentally available data for deuterated water 47,48 and recent CPMD simulations.43 Though the presence of an organometallic complex likely inhibits mobility in solution, the results are within the acceptable range for similar simulations46,49 of pure water. For complexes 4 and 5, the finite simulation times may also play a role in reducing the mobility of the water solvent. The use of an increased simulation temperaturecompared to experiment22partially compensates for an overstructuring of water that is typical in simulations with GGA functionals at ambient temperatures. Pair correlation functions for O− O and O−H are provided in Figures S1 and S2 (in the Supporting Information) and are in excellent agreement with comparable simulations for water that are available in the literature.43,50,51 The J-couplings are given for the isotopes 13C, 195Pt, and 205Tl. The J-coupling constants were calculated with the CPL module52−54 of the

3. RESULTS AND DISCUSSION 3.1. Choice of Functionals. Because of the coupled nature of the computational approach, the level of theory was chosen as a compromise between the suggestions in the literature for the dynamics of aqueous systems and the NMR parameter calculations. Prior to running dynamics, NMR benchmark calculations using three functionals and static optimized structures were performed (see Section 3 of the Supporting Information, specifically, Tables S7, S8, and S9). The VWN functional calculations reproduce the VWN J-coupling data from ref 29 for both water-coordinated and bare structures of C


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Inorganic Chemistry the complexes. However, VWN severely underestimates the Tl−Pt couplings in comparison with experiment and underperforms for the other coupling constants as well. Moving to a GGA functional, namely, PBE, improves the Tl−Pt and other Jcouplings slightly. In agreement with recommendations in the literature,33 the hybrid variant of PBE, PBE0, results in the best agreement with experimental J-coupling constants for the static structures (see Table S9 in the Supporting Information). Structural data for the different functionals and computational models are provided in the Supporting Information. Relevant interatomic distances between PBE and PBE0 differ by at most 3% and usually lesssee Tables S11 and S12. Because of the considerable computational requirements for CPMD, the PBE functional was selected for the dynamics. The following section compares aggregated structural results with experimentally available data, which justifies the chosen CPMD parameter set, and compares these findings with previous theoretical work in the literature, highlighting the differences in the in situ coordination around the Tl center. 3.2. Solution Structure and Coordination. Mean interatomic distances for the complexes, averaged over the production trajectories, are listed in Table 1. Experimentally

Table 2. Mean Interatomic Distances (in Å) and Standard Deviations (in Parentheses) for Tl−O Pairs Computed over Each Production Trajectorya complex

NN = 1

NN = 2

NN = 3

NN = 4

1 2 3 4 5

2.3(1) 2.4(1) 2.4(1) 4.5(5) 2.5(1)

2.4(1) 2.5(1) 3.6(6)

2.5(1) 3.1(5)

2.9(5)

2.6(1)

The NN identifier represents the distance of the first, second, etc. neighbor averaged of the trajectory. Distances are reported to the first significant figure in the standard deviation. Where data are ommitted, it is implied that subsequent NN molecules are never part of the first solvation shell around the Tl center (data for 4 are provided for comparison only). a

Table 1. Meana Interatomic Distances (in Å) for Each Complex complex

N(H2O)

Tl−Pt

Tl−CB

1 2 3 4 5

4 3 2 0 2

2.747 2.726 2.732 2.750 2.773

2.259 2.283 2.313

Tl−Oavg

Pt−CA

Pt−CC

2.509 2.659 3.008

2.031 2.037 2.060 2.074 2.082

2.028 2.026 2.022 2.021 2.022

2.535

Figure 2. Tl−O pair correlation functions for each production trajectory. Enumerated peak centroids and magnitudes can be found in Table 3.

a

Averaged over the course of the corresponding production trajectory. The Tl−O distance is averaged over the whole number of inner sphere water molecules listed, N(H2O). All standard errors are less than 3 × 10−3 Å

available EXAFS data (in situ) for these complexes can be found in Table S1 of the Supporting Information. Interatomic distances show agreement to within 0.08 and 0.02 Å for Tl−C and Pt−C pairs, respectively. The M-M distances are overestimated by less than (at most) 0.15 Å compared to solid state EXAFS data reported in the literature (see the Supporting Information of Reference 22). A survey of experimentally reported interatomic EXAFS distances for similarly sized bimetallic complexes characterized in aqueous media have M-M distances of 2.694−2.69665,66 Å for Pt−Pt bonded systems and 2.91467 Å for Tl−Tl (see also Reference 27). Given that the mean Tl−Pt distances observed in this work (for all trajectories) fall within the aforementioned ranges for Pt−Pt and Tl−Tl, and that GGA functionals are known to overestimate interatomic distances somewhat, the structures of complexes 1− 5 appear reasonable. Table 2 reports the average distance to the nth NN oxygen atom to Tl. The standard deviation of this distance gives a measure of the range of values explored by each coordinated water molecule. It is clear from the large standard deviation of the fourth NN for complex 1, for example, that this oxygen is part of the inner coordination sphere (of Tl) only part of the simulation time. This is also illustrated by the pair correlation function (Figure 2) and the pair count (Figure 3), that is, the integration of the pair correlation, between Tl and O for each simulation. The inner coordination sphere of Tl is indicated by

Figure 3. Tl−O pair counts; the normalized cumulative summation of Figure 2. The inner coordination sphere (of Tl) is described by the first plateau for all complexes except 4. Complex 4 has three cyano ligands, and no water coordination, directly to Tl, is observed.

a pronounced plateau in the pair count starting at ∼2.75 Å to ∼3.5 Å. A summary of the radial pair correlation function local maxima and minima as well as pair counts are collected in Table 3. The average inner-sphere coordination number Nisavg of Tl is also given in Table 3. For example, over the course of the simulation, the number of inner-shell water molecules for complex 1 is between three and four, implying that the Tl is D


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Inorganic Chemistry Table 3. Summarya of Tl−O Pair Correlation Function Peaks and (Fractional) Average Number of Inner Coordination Sphere Solvent Molecules around Tl

a

complex

rmax 1

gmax 1

rmax 2

gmax 2

Nisavg

1 2 3 4 5

2.35 2.48 2.42 3.00 2.56

6.83 4.82 2.45 0.01 4.41

3.99 3.99 3.98 4.00 3.00

0.87 0.48 0.47 0.13 0.13

3.6 2.8 1.5 0.0 2.0

Distances are given in angstroms.

coordinated by four waters slightly more than half of the time sampled, and by three waters otherwise (see Figure 12). It can be noted that the inner sphere of complex 4 is composed only of cyano ligands, even in the presence of water, and complex 5 is unique in that it maintains two inner-sphere solvent molecules around Tl consistently, with a bent Pt−Tl− Pt moiety. These two observations suggest a preferred structural motif for complexes 4 and 5 around the Tl center, namely, a four-coordinate pseudotetrahedral geometry when counting Pt, cyano carbon, and solvent oxygen atoms, which can be confirmed visually from the trajectories. For complexes 1−3, over the course of the simulations there is a comparatively rapid transition between four-coordinate pseudotetrahedral motifs and five-coordinate pseudopyramidal motifs. For example, in the trajectory for complex 1, this transition occurred more than seven times, resulting in an Nisavg value of 3.6. The skewness of the coordination distribution, that is, the asymmetry in the standard deviations presented in Table 2, is negligible and does not provide further insight into the coordination preferences. In the CPMD simulations, four-coordinate pseudotetrahedral and five-coordinate pseudopyramidal coordination around the Tl center by Pt, water molecules, andwhere applicable cyano ligands, predominate. This is in contrast with previous studies where a pseudo-octahedral (or pseudo-trigonal bipyramidal, for complex 3) coordination environment saturating the inner coordination sphere of Tl was assumed to be present.28−30 As shown in the following section, the structures obtained in this work provide a more reasonable description of the coordination environment of complexes 1−5 given the agreement with experimental J-coupling data when a more accurate electronic structure method is used for properties calculations than in the previous studies. 3.3. Spin−Spin Coupling Constants. NMR data were initially acquired from an evenly spaced coarse grid of 64 frames from each production trajectory to determine the required number of explicit water molecules needed in the J-coupling calculations. In increments of five explicit water molecules, the selection of solvent molecules was performed based on the nearest atom-to-atom distance between the given complex and water molecules. Figures 4−10 compare J-coupling constants computed at the scalar relativistic PBE0 level of theory. The asterisk “solvent count” in these figures corresponds to MD-averaged data, where all water molecules were removed and no implicit solvation (COSMO) was applied. All other data are also trajectory averages (as described above) but include COSMO to treat bulk solvent effects along with between 0 and 25 explicit nearest water molecules. Figure 4 shows the dependence of the Tl−Pt J-coupling on the explicit solvent count. For complex 1, in particular, the

Figure 4. Dependence of 1J(Tl−Pt) on explicit NN solvent count. All data are means corresponding to trajectory averages (64 frames). The asterisk corresponds to bare structures (no explicit or implicit solvation), while the remaining counts (0−25) correspond to structures including the given number of explicit nearest solvent molecules and implicit solvation via COSMO. Standard errors (in the means) are given by the solid black lines.

Figure 5. Dependence of 2J(Tl−CA) on NN solvent count. The two bond coupling from Tl to the axial carbon (see Figure 1) shows a dependence on solvent count for complex 5, requiring up to ∼20 NN water molecules. Note that for complex 5, J-coupling constants are averaged over both axial cyano ligands. See also the caption of Figure 4.

Figure 6. Dependence of 1J(Tl−CB) on NN solvent count. Tl cyano ligands are only present in complexes 2−4 (see Figure 1). Where open coordination sites exist (i.e., complex 2), water molecules have a large effect on the J-coupling constant, achieving convergence around 15 NN water molecules. Note that for complexes 3 and 4, averaged Jcoupling constant results are reported. See also the caption of Figure 4.

E


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Figure 7. Dependence of 2J(Tl−CC) on NN solvent count. Note that equivalent carbon atoms (CC, see Figure 1) are averaged. Only complex 4 shows little to no dependence on solvent count, likely because the electronic structure of Tl is dominated by its own cyano ligands; see Section 3.5). See also the caption of Figure 4.

Figure 10. Dependence of 1J(Pt−CC) on NN solvent count. Note that equivalent carbon atoms are averaged in the data displayed herein. Presence of explicit water molecules has a negligible influence on this spin−spin coupling. See also the caption of Figure 4.

Pt) is negative. For complex 2 the solvent effects are also extremely strong. Compared to the bare models, ∼10 explicit water molecules are required to produce the experimentally observed trend of decreasing 1J(Tl−Pt) along the series 1−4. Complexes 1 and 2 require up to ∼15 explicit water molecules for convergence. When fewer open coordination sites of Tl are available, due to the presence of cyano ligands or the second Pt(CN)5 moiety in complex 5, the dependence of 1J(Tl−Pt) on the explicit solvent count is less pronounced. Nonetheless, complex 5 requires up to 20 water molecules. Complexes 3 and 4 exhibit a weaker dependence on the solvent count. This trend is intuitive in the sense that 1 has the most bare Tl center in the absence of solvent. At the same time, the trend indicates that coordinated water and the cyano ligands of Tl play a very different role as far as the Tl−Pt J-coupling is concerned. Figures 5−10 show similar plots as Figure 4 for the other Jcouplings. On a relative scale, the impact of explicit solvation is also very pronounced. Because the computational requirements between 15 and 20 nearest water molecules do not vary considerably, 20 NN water molecules were selected in 192 additional frames to produce, combined with the 64 frames containing 20 water molecules that were calculated initially, a more closely spaced grid of 256 frames along the trajectories. These frames were used to generate the final J-coupling averages. The J-coupling constants averaged along the CPMD trajectories are collected in Table 4 and compared with experiment (in parentheses). Standard errors of the trajectory averages can be found in Table S18 in the Supporting Information. These are at most 1.8% relative to the calculated averages, and therefore 256 frames were deemed sufficient. Compared with experiment,22 the calculated 1J(Tl−Pt) are within just over 10% deviation. This is within the error bars of the computational model, previously estimated to be 13% at best for J-coupling constants involving heavy metals.33 Further systematic improvements toward experiment for the right reasons would require, among other aspects, a relativistic electronic structure model that reliably outperforms hybrid KS calculations. For all spin−spin couplings listed in Table 4, the decreasing magnitude of most of the experimental values along the series of complexes 1 to 5 is reproduced by the calculations. An exception to this trend is 2J(Tl−CC), where the magnitude of the coupling for 5 is between those of complexes 3 and 4 reproduced by the calculationsand 1J(Pt−CC), which

Figure 8. Dependence of 1 J(Pt−CA) on NN solvent count. Note that for complex 5, J-coupling constants are averaged over both sites (see Figure 1). Complex 1 again shows the strongest dependence on solvent count. Note that at 20 NNs included, some water molecules are coordinated directly to nitrogen atoms on cyano ligands. See also the caption of Figure 4.

Figure 9. Dependence of 2 J(Pt−CB) on NN solvent count. Note that complexes 1 and 5 do not contain cyano ligands bound directly to the Tl centers. Similarly to Figure 6, as the coordination sites of Tl become saturated with cyano ligands, the influence of NN water molecules stabilizes. See also the caption of Figure 4.

presence of explicit solvent has a truly dramatic effect especially when compared with the bare complex, where 1J(Tl− F


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Table 4. Calculated J-Coupling Constants (in Hz) Averaged over 256 Configurations of the CPMD Production Trajectory for Each Complexa complex

Tl−Pt

Tl−CA

1

63 356 (71 060) 56 189 (57 020) 50 232 (47 260) 44 412 (38 760) 17 863 (25 168)

16 718 (12 746) 13 258 (9743) 11 631 (8446) 10 532 (7270) 5285 (4600)

2 3 4 5

Tl−CB

Tl−CC

Pt−CA

−2559 (2446) −1656 (876) −952 (52)

−713 (592) −515 (452) −369 (338) −284 (255) −319 (308)

1089 (909) 970 (843) 868 (783) 822 (742) 721 (700)

Pt−CB

215 (200) 152 (128) 110

Pt−CC 867 (820) 867 (821) 882 (832) 895 (843) 908 (858)

a

Unsigned experimental data from ref 23 in parentheses. Standard errors for the MD averages are provided in Table S18 of the Supporting Information.

molecules. Many continuum solvent models, including COSMO, construct a solvent-accessible surface around the molecule, and surface charges are determined, based on the electrostatic potential around the molecule and the dielectric constant of the solvent, such as to mimic the presence of the solvent without treating it quantum mechanically. In the 2003 computational study of the NMR J-coupling parameters of the complexes,29 the atomic radius of Tl in the elemental solid (1.7 Å) was used to generate the solvent-accessible surface. COSMO was applied only to the explicitly solvated systems, and it was noted that when considering the overall very large solvent effects, the calculated J-couplings involving Tl were not very sensitive to the chosen thallium radius, because it was in close contact with the explicit water molecules andwhere applicablecyano ligads. The current default Tl radius in the ADF implementation of COSMO is 2.2 Å. During the course of this work a pronounced sensitivity of the Tl−Pt coupling on the Tl COSMO parameter was noted in the absence of explicit solvent. For instance, for complex 1, COSMO with the default Tl radius of 2.2 Å gives 1J(Tl−Pt) of ca. −10 kHz in the absence of explicit solvent, which is close to the bare model. This suggests that a Tl radius of 2.2 is too large to matter, as far as implicit solvation is concerned. Decreasing the Tl radius by 0.2 Å results only in a slight increase in this Jcoupling constant, to −9 kHz. However, reducing the Tl radius further, to 1.7 Å, gives a large increase of 1J(Tl−Pt) to ca. +40 kHz (variations in the radii of the other atoms cause negligible changes). This effect is also visible in Figure 4, comparing the asterisk (*the bare model) and “0” solvent counts. It appears that with a Tl radius close to that of the elemental solid (the covalent radius is even smaller, ca. 1.6 Å), COSMO starts to mimic the presence of the explicit solvent. However, with such a strong dependence of the Tl−Pt coupling on the Tl radius parameter, the continuum model is not reliable without additional explicit solvation. In the presence of explicit solvent, decreasing the Tl radius from 2.2 to 1.7 Å also has an effect of increasing 1J(Tl−Pt) but only by ∼3 kHz. Figure 11 shows one of the 256 snapshots used in computing the J-coupling values for complex 1 in Table 4. Overlaid in this image is the solvent-accessible surface generated from the COSMO radii, with the surface colored by the corresponding COSMO potential. Here, the Tl COSMO radius is 1.7 Å. The solvent-accessible surface does indeed come close to the Tl center, but because Tl is surrounded by explicit water molecules the impact in the NMR calculation is small

increases from 1 to 5also reproduced by the calculations. Note that the 1J(Tl−CB) and 2J(Tl−CC) are predicted to be negative; the experiments did not determine the signs. Overall, the trajectory averaged results are within expected33 deviations from experiment for the hybrid KS protocol employed. An outlier in terms of relative accuracy is the 1J(Tl−CB) constant of complex 4. As Table S9 in the Supporting Information shows, this coupling appears to be sensitive to SO effects, which are neglected in the trajectory averages in Table 4. This case appears to warrant further study. It is clear that previous calculations from ref 29, while being correct about the importance of the solvent effects on the NMR J-coupling constants, benefited from a compensation of substantial errors. An increase in the magnitude of the Tl−Pt coupling, in particular, with the number of water molecules coordinated to Tl beyond those predicted by the present MD simulations, was compensated for by lower coupling constant magnitudes produced by the then-available nonhybrid KS potentials. As pointed out in Section 3.1, the hybrid functional gives much larger Tl−Pt coupling constants, toward experiment, and improves the other J-couplings as well in most cases. A secondary error was present in the older calculations due to the lack of finite nuclear volume corrections. As shown in the Supporting Information, with the PBE functional and using the static solvated structures of ref 29, the Tl−Pt coupling is reduced by as much as 10 kHz when finite-nucleus effects are included in the calculations. Complex 2 has received attention in the past30 because, like for complexes 3 and 4, the two-bond coupling 2J(Tl−CA) is larger in magnitude than the one-bond coupling 1J(Tl−CB). The experimental unsigned 1J(Tl−CB) of 2 is 2.4 kHz. Given the good agreement with the magnitude of the calculated coupling, 2.6 kHz, we assign 1J(Tl−CB) to be negative. Our calculations agree with ref 30 in that for the bare complex 2, the two couplings are of approximately equal magnitude, due to a pronounced axial multicenter bonding (see Section 3.5), but opposite in sign. The solvent effects then render both couplings more positive, which increases the magnitude of the positive 2 J(Tl−CA) but decreases that of the negative 1J(Tl−CB). In ref 30, a static solvated structure of 1 with four water molecules appears to have led to an overestimation of the solvent effect on 1 J(Tl−CB) by pushing it to +3.1 kHz. 3.4. Implicit versus Explicit Solvation. As mentioned in the Computational Details section, a continuum solvent model, COSMO, was applied in the finite cluster NMR calculations to model bulk solvent effects beyond the shell of explicit water G


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Inorganic Chemistry

used to rationalize the solvent effect on 1J(Tl−Pt). For brevity, the discussion focuses on the most dramatic case, that is, complex 1. The analyses for complexes 2−4 revealed similar mechanisms in terms of solvent contributions. A complete listing of the J-coupling analysis for 2− 4 can be found in Tables S19−S21 in the Supporting Information. The LMOs used in this analysis are the “natural” LMOs (NLMOs) generated by the NBO algorithms.68 The NLMO basis has the advantage that the orbitals are further decomposed into idealized Lewis (L) structure core (CR), bond (BD), and lone-pair (LP) parent orbitals, along with non-Lewis (NL) delocalization tails. The latter are pronounced in the Tl−Pt complexes because of a significant multicenter bonding motif involving the metal centers and axial ligands. Note that we did not specifically request a search for three-center NBOs (this search is not default in the NBO program version used for the present study). The presence of multicenter bonding is readily apparent in the NLMO set, no matter if the generated NBO basis contains multicenter bond orbitals or not. The J-coupling analysis was performed on two different trajectory snapshots of complex 1 as shown in Figure 12, labeled T and P (taken ∼4 ps apart). In the presence of water molecules, snapshot T affords a pseudotetrahedral coordination motif around the Tl center, whereas snapshot P has Tl in a pseudosquare pyramidal motif. The interplay between these two coordination motifs can assist in the understanding of changes in the electronic structure around Tl, as they dominate the coordination space explored by complex 1. The J-coupling analysis for snapshots T and P is given in Table 5 and contains a comparison of the two structures computed without explicit or implicit solvation (bare), with explicit, but no implicit solvation (MD), and with both explicit and implicit solvation (MD+COSMO). Note that where explicit solvent is present, the 20 nearest water molecules are included. Two of the delocalized bonding orbitals for the CA− Pt−Tl moiety that feature prominently in the analysis are characterized in Table 6. As expected, when all solvent molecules are stripped off the T and P structures, as in the “bare” columns of Table 5, the analysis leads to similar results for the two snapshots. Differences appear because the metal complexes in the two snapshots have somewhat different structural parameters. The

Figure 11. Depiction of the solvent-accessible surface for the continuum solvent model COSMO, for a snapshot from the production trajectory of complex 1 with 20 explicit water molecules (snapshot Psee Section 3.5). The Tl atom is on the right, surrounded by water molecules. Red, gray, and blue regions on the surface correspond to negative, neutral, and positive potential, respectively.

compared to choosing a larger radius that, in the absence of explict water molecules, barely corresponds to solvation at all. Using COSMO in the calculations to represent bulk solvation in addition to the explicit first solvent shell is nonetheless very important, because it modifies the properties of the explicit water molecules, as shown in the next section. It is noted in passing that the addition of up to 128 explicit water molecules to complex 1, without COSMO, produced a similar 1 J(Tl−Pt) value as compared to using 20 explicit water molecule and COSMO. This means that the continuum model produces the desired effects of the bulk solvation of the explicit water cluster around the complex, at negligible computational cost. 3.5. J-Coupling Analysis. A scalar relativistic J-coupling analysis in terms of localized molecular orbitals (LMOs)35 was

Figure 12. Snapshots T (left, pseudotetrahedral coordination at the Tl center) and P (pseudosquare pyramidal coordination at the Tl center) for complex 1 considered in the J-coupling constant analysis. H


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Inorganic Chemistry Table 5. NLMO Analysis of 1J(Tl−Pt) for Snapshots T and P of Complex 1 (in Hz)a T bare CR Tl Tl−Pt CR Pt LP Pt NCA−Pt NCC−Pt LP O1 LP O2 LP O3 LP O4 all others total

2309 −8564 −97 −235 −5402 −2803

−22 −14 813

P

MD

MD+COSMO

7236 24 041 11 933 29 −9043 1657 387 310 611 481 −273 37 370

8855 74 201 17 309 −99 −29 614 1849 −2463 −1034 208 388 −618 68 981

bare 1776 −8899 −178 114 −4156 −2364

−23 −13 729

MD

MD+COSMO

5791 13 790 10 125 87 −11 644 −313 526 788 1069 316 −319 20 216

8360 41 878 19 277 24 −4695 4824 −192 88 241 28 −422 69 410

a

CR = core, LP = lone pair (nonbonding). Contributions from CR Pt, LP Pt, and water LP O represent sums over several LMOs. Contributions from CA−Pt and CC−Pt represent the Pt−C bonds and cyano ligand orbitals of the axial and equatorial (to Pt) cyano ligands, respectively. Comparison of bare (no explicit or implicit solvation), MD (20 explicit water molecules, no implicit solvation), and MD+COSMO (like MD, but with implicit solvation via COSMO) are provided. The “total” row checks to ensure that the summation (down the column) matches the full result from the KS calculation.

significantly. As shown in Section 3.4, the strong COSMO influence on 1J(Tl−Pt) in the explicitly solvated structures is not an artifact of a COSMO solvent-accessible surface being created around the metal centers. It is important to note that water oxygen orbitals show up explicitly in the analysis, indicating that the Tl−water orbital interactions directly influence 1J(Tl−Pt). There is an indication of a charge flow from water oxygen LPs to the complex, since the oxygen LP orbital parent NBO occupancies are 1.86, 1.92, and 1.93 (T, model MD, for O1 to O3, respectively), and 1.92, 1.93, 1.92, and 1.94 (P, model MD, for O1 to O4, respectively), instead of 2. Inclusion of bulk solvation via COSMO decreases these occupancies further due to polarization effects of the explicit water molecules, which also increases the mixing and scharacter of water oxygen LPs with the Tl center in the NLMOs. However, the LP O contributions are small compared to the total coupling constant. Instead, the orbital interactions between water and Tl take a profound influence on the bonding within the CA−Pt−Tl moiety, and these changes cause the variations in the 1J(Tl−Pt). For the T snapshot with MD+COSMO, the most profound solvent effect is the formation of a covalent Tl−Pt bond. The corresponding NLMO has a small amount (ca. 0.5%) of water oxygen LP character, highlighting the role of the water in the formation of the bond. The 74 kHz contribution to 1J(Tl−Pt) from the Tl−Pt bond is counter-balanced by a −30 kHz contribution from the Pt−CA bond. In the T snapshot, the Pt− CA orbital has pronounced three-center character with ∼15% of its density on Tl. The negative sign of this contribution can be rationalized by the fact that the Tl three-center bonding with CA takes some of the Tl 6s character away from the Tl−Pt bond and thereby reduces the magnitude of 1J(Tl−Pt). This loss is, to a large extent, compensated for by an increased involvement of the Pt 5s semicore orbital in the explicitly solvated structures (contributions from heavy atom outer-core orbitals to J-coupling have been noticed before in NLMO-based analyses, see ref 13 and citations therein). As the orbital overlap between Tl and Pt switches to the covalent bonding regime (upon solvation), an increased participation of both the Tl and Pt outer core orbitals in the Tl−Pt J-coupling is no unexpected.

Table 6. Characterization of Two Delocalized Bonding Orbitals for the CA−Pt−Tl Moiety of the Complex 1 Snapshots of Figure 12 in Terms of Weight from Different Atoms, and s/p/d/f Charactera bare Tl−Pt

CA−Pt

a

MD+COSMO

T

P

93 Tl s(100)

94 Tl s(100)

3 Pt s(25) p(3)d(71) 3 C s(53) p(47) 57 Pt s(13) d(87) 41 C s(47) p(53)

2 Pt s(29) p(3)d(68) 3 C s(55) p(45) 55 Pt s(16) d(84) 42 C s(47) p(53)

T 40 Tl s(90) p(10) 53 Pt s(18) p(1)d(81) 1 C s(53) p(47) 12 Pt s(16) p(3)d(81) 67 C s(52) p(48) 15 Tl s(93) p(7)

P 63 Tl s(93) p(7) 15 Pt s(18) p(3)d(79) 15 C s(61) p(39) 48 Pt s(15) d(85) 49 C s(51) p(49)

All numerical values are in percent.

calculated 1J(Tl−Pt) values are negative, suggesting that the orbital interactions between the metals is in a weak overlap “through space” regime.69 This is supported by the composition of the relevant NLMO leading to the −9 kHz contribution to 1 J(Tl−Pt), which is identified by the NBO algorithms as a delocalized Tl lone pair with a 3% contribution each at the Pt and CA centers. Additionally, there is a negative contribution to 1 J(Tl−Pt) from the bonding orbital between Pt and the axial carbon (Pt−CA) because the orbital has a slight three-center character (with ∼0.3% of its density at the Tl center) and likely also because of magnetic coupling of its unoccupied antibonding counterpart with the Tl lone pair. Other notable contributions, mainly canceling each other, come from the Tl outer core (dominantly from 5s) and equatorial NCC−Pt orbitals. The analysis of both snapshots with solvation (MD and MD +COSMO) highlight, again, the dramatic impact of solvent on the total 1J(Tl−Pt) and the contributions from different orbitals. Bulk solvation via COSMO modifies the properties of the water molecules in the explicit solvent shell, which in turn influences the NMR parameters in the complex very I


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Inorganic Chemistry For the P snapshot with MD+COSMO, the negative contribution from the Pt−CA orbital to 1J(Tl−Pt) is much smaller than for the T snapshot. Here, it is the Tl−Pt bond that has three-center character and is delocalized over CA, while the Pt−CA bond is more localized. In this snapshot, the combined contributions from the four Pt−CA bonds are of equal magnitude and opposite in sign to that of Pt−CC. The stronger three-center delocalization of the Tl−Pt bond in the solvated P snapshot reduces the contribution from the Tl−Pt orbital by over 30 kHz, but the lack of a strongly negative Pt−CA contribution leaves the value of 1J(Tl−Pt) very similar to that of the solvated snapshot T. The formal oxidation numbers of the metals in complex 1 are Pt(IV) and Tl(I). Of course, and, in particular, for Pt, the interplay of L−M electron donation and back-donation causes the calculated atomic charges to be smaller. The strong σdonation capability of the CN− ligands creates a system in which a positively charged Tl center is weakly attracted to the (NC)5Pt− moiety. The negative sign of the 1J(Tl−Pt) of the bare complex indicates that the M−M interaction is neither covalent nor purely ionic. The NBO analysis supports the assignment of the Tl−Pt interaction being in the weak overlap regime. The analysis further points to a pronounced capability of Tl to form a covalent bond with Pt in the solvated complex, enabled by Tl−O orbital interactions and some electron donation from water to Tl. For small numbers of water molecules, the M−M interaction appears not unlike a Tl→Pt donation bond. The electronic structure in the CA−Pt−Tl moiety of the fully solvated system is characterized by threecenter four-electron (3c-4e) bonding such that the dominant contributions to 1J(Tl−Pt) in the LMO picture are either coming from a three-center Tl−Pt bond (as in the analysis of snapshot P), or a two-center Tl−Pt bond accompanied by a three-center Pt−CA bond (as in the analysis of snapshot T). Further analysis shows that for complexes 2 and 3, inclusion of explicit and implicit solvent effects increases the covalent character between the metal centers as well as the contributions to 1J(Tl−Pt) from the outer core orbitals of both metals. For complex 4, where no direct solvent coordination of Tl occurs, a well-balanced covalent Tl−Pt bond is present even in the bare model, and inclusion of explicit and implicit solvent effects does not cause substantial changes. Addition of cyano ligands at the Tl center (CBN), starting with complex 2, increases the covalent character of the M−M interaction in the bare models. In the fully solvated systems, there is also considerable multicenter bonding along the primary axis of each complex. With an increasing number of cyano ligands coordinated to Tl, the increase of the extent of the axial delocalization due to the presence of water becomes less pronounced, as may be expected. Given that the presence of cyano ligands and water around Tl causes a similar trend as far as the capability of Tl to form a bond with Pt is concerned, it may appear unintuitive that in the solvated systems 1J(Tl−Pt) becomes smaller for increasing number of cyano ligands. To rationalize this finding, the 6s character in the Tl−Pt bonds must be considered. The s character of the Tl−Pt bond is a major driver for the magnitude of the J-coupling constant and contributes predominantly via the relativistic analogue of the Fermi contact mechanism. Moving along the series from 1 to 4, the density of the Tl−Pt bonding orbital decreases on Tl, while the density on Pt slightly increases. More importantly, the s-character decreases strongly at the Tl site, and to a lesser degree at the Pt site. In

combination, these effects cause a pronounced decrease of the 1 J(Tl−Pt) value along this series of complexes. Previous analyses of J-coupling in metal complexes (see ref 13 for an overview) in terms of the self-consistent field canonical MOs (CMOs), that is, the usual MOs, tended to produce many contributions with large magnitudes and opposite signs, which can render the analysis difficult compared to one in terms of localized MOs. However, some key contributions from the highest occupied (HOMO) and lowest unoccupied (LUMO) CMOs of complex 1 in the fully solvated system (MD + COSMO in Table 5) rationalize the solvent effects produced in the calculations. For instance, polarization effects from COSMO on the explicit water molecules shift much of the Tl 6s electron density from several lower-energy occupied CMOs to the HOMO. The HOMO of the fully solvated system also contains contributions from Pt 5p, 5d, and water oxygen 2p atomic orbitals. The LUMO remains rather unaffected. The increased Tl 6s character and the high energy of the HOMO compared to the CMOs in the model without implicit solvation causes an additional large Fermi contact contribution to the 1J(Tl−Pt) (analogous to the NLMO result above). This can be explained by a strong magnetic coupling of the HOMO−LUMO pair, aided by a relatively small energy gap between the two orbitals, which renders the Fermi-contact mechanism more efficient compared to a system where the Tl 6s contributions are “diluted” over several CMOs with lower energy and concomitant larger orbital energy gaps with lowlying unoccupied CMOs.

4. CONCLUSIONS The NMR J-coupling constants in the series of Tl−Pt bonded complexes of Figure 1in particular 1J(Tl−Pt)are shown to have a strong dependence on the coordination of water at the Tl site, in agreement with previous work. Contrary to the previous calculations, which were more approximate and utilized static structures with highly coordinated Tl sites, the MD simulations suggest a preference of Tl toward fourcoordinate pseudotetrahedral (4 and 5) and five-coordinate pseudopyramidal coordination motifs (1−3). In combination with relativistic hybrid KS NMR calculations, the trajectoryaveraged spin−spin couplings reproduce the large magnitudes and trends reported experimentally. The previous static calculations with nonhybrid functionals yielded acceptable agreement with experimental NMR data due to a compensation of errors caused by the approximations in the computational model. The dynamics-based computational model, in conjunction with hybrid functionals for the relativistic NMR calculations, is not perfect, but it gives reasonable agreement with the experimental data for good reasons. For example, the 1 J(Tl−Pt) values are within just over 10% deviation from experiment, which is within the expected error bars of the electronic structure method. Moreover, the experimental trends along the series of complexes 1 to 5 for all coupling constants are reliably reproduced. Finite nuclear volume effects on heavy metal−metal and metal−ligand J-coupling constants are important to include in the calculations. The next level of relativistic corrections, not included here, would be quantum electrodynamics effects.70 The computational model may be improved further, for instance, by performing the MD simulations with hybrid functionalsalbeit at a dramatic increase in computational cost. The sensitivity of the three-center−four-electron bonding J


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Inorganic Chemistry in the CA−Pt−Tl moiety to the presence of water may also require hybrid functionals that are parametrized to minimize the KS delocalization error,71 at least for the NMR calculations. A computational model with a large explicit solvation shell at a relativistic correlated wave function level of theory would be desirable, but it appears to be impractical for the time being. A decomposition of the electronic structures and Tl−Pt Jcouplings shows that both the presence of water and cyano ligands around Tl cause multicenter Tl−Pt bonding in the complexes, which facilitates large metal−metal J-coupling constants. The Tl−Pt interactions, in the absence of Tl-solvent coordination, are in a weak overlap regime for complex 1 and in an ionic bonding with weak to strong covalency regime for the other systems, depending on the presence of additional ligands at Tl. An increased number of cyano ligands at the Tl site strongly reduces the Tl s-character in the Tl−Pt bond. These main findings of the analysis rationalize both the dramatic increase of 1J(Tl−Pt) due to solvation, in particular, for complexes 1 and 2 (and the sign change for 1 when going from the bare complex to solution), and the pronounced decrease of 1 J(Tl−Pt) along the series 1−5 in solution. The surprisingly large increase of 1J(Tl−Pt) of complex 1 due to additional implicit solvation, via a continuum model, of a complex−water cluster can be rationalized by stronger interactions between the Tl ion with the more polar water molecules, a concomitant concentration of Tl 6s electron density in the HOMO, and a resulting strong HOMO−LUMO coupling by the Fermicontact J-coupling mechanism.

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(3) Bühl, M. NMR of Transition Metal Compounds. In Calculation of NMR and EPR Parameters. Theory and Applications; Kaupp, M., Bühl, M., Malkin, V. G., Eds.; Wiley-VCH: Weinheim, Germany, 2004; pp 421−431. (4) Bühl, M. DFT computations of transition-metal chemical shifts. Annu. Rep. NMR Spectrosc. 2008, 64, 77−125. (5) Hinton, J. F.; Metz, K. R. Thallium NMR Spectroscopy. In NMR of Newly Accessible Nuclei; Lazlo, P., Ed.; Academic: New York, 1983; pp 659−669. (6) Pregosin, P. S. Platinum NMR Spectroscopy. Annu. Rep. NMR Spectrosc. 1986, 17, 285−349. (7) Wrackmeyer, B.; Horchler, K. 207Pb NMR parameters. Annu. Rep. NMR Spectrosc. 1990, 22, 249−306. (8) Wrackmeyer, B.; Contreras, R. 199Hg NMR Parameters. Annu. Rep. NMR Spectrosc. 1992, 24, 267−329. (9) Granger, P. Groups 11 and 12: Copper to Mercury. In Transition Metal Nuclear Magnetic Resonance; Pregosin, P. S., Ed.; Elsevier: Amsterdam, 1991; pp 264−364. (10) Helgaker, T.; Jaszuński, M.; Ruud, K. Ab initio methods for the calculation of NMR shielding and indirect spin-spin coupling constants. Chem. Rev. 1999, 99, 293−352. (11) Autschbach, J. Calculation of Heavy-Nucleus Chemical Shifts: Relativistic All-Electron Methods. In Calculation of NMR and EPR Parameters. Theory and Applications; Kaupp, M., Bühl, M., Malkin, V. G., Eds.; Wiley-VCH: Weinheim, Germany, 2004, 227−247. (12) Autschbach, J.; Ziegler, T. Relativistic calculation of spin-spin coupling constants. In Calculation of NMR and EPR Parameters. Theory and Applications; Kaupp, M., Bühl, M., Malkin, V. G., Eds.;Wiley-VCH: Weinheim, Germany, 2004; pp 249−264. (13) Autschbach, J.; Zheng, S. Relativistic computations of NMR parameters from first principles: Theory and applications. Annu. Rep. NMR Spectrosc. 2009, 67, 1−95. (14) Le Bail, H. L.; Chachaty, C.; Rigny, P.; Bougon, R. Observation of the uranium 235 nuclear magnetic resonance signal. J. Phys., Lett. 1983, 44, 1017. (15) Schreckenbach, G. NMR shielding calculations across the periodic table: Diamagnetic uranium compounds. 2. Ligand and metal NMR. Inorg. Chem. 2002, 41, 6560−6572. (16) Yasuoka, H.; Koutroulakis, G.; Chudo, H.; Richmond, S.; Veirs, D. K.; Smith, A. I.; Bauer, E. D.; Thompson, J. D.; Jarvinen, G. D.; Clark, D. L. Observation of 239Pu Nuclear Magnetic Resonance. Science 2012, 336, 901−904. (17) Pyykkö, P.; Wiesenfeld, L. Relativistically parametrized extended Hückel calculations IV. Nuclear spin-spin coupling tensors for main group elements. Mol. Phys. 1981, 43, 557−580. (18) Jameson, C. K.; Jameson, A. K. Concurrent 19F and 77Se or 19F and 125Te NMR T1 measurements for determination of 77Se and125Te absolute shielding scales. Chem. Phys. Lett. 1987, 135, 254. (19) Zheng, S.; Autschbach, J. Modeling of heavy atom−ligand NMR spin-spin coupling in solution: Molecular dynamics study and natural bond orbital analysis of Hg−C J−coupling constants. Chem. - Eur. J. 2011, 17, 161−173. (20) Le Guennic, B.; Matsumoto, K.; Autschbach, J. On the NMR properties of platinum thallium bonded complexes: Analysis of relativistic density functional theory results. Magn. Reson. Chem. 2004, 42, S99−S116. (21) Berg, K. E.; Glaser, J.; Read, M. C.; Tóth, I. Nonbuttressed metal−metal−bonded complexes of Platinum and Thallium in aqueous solution: Characterization of [(NC)5Pt-Tl(CN)]− by multinuclear NMR. J. Am. Chem. Soc. 1995, 117, 7550−7751. (22) Maliarik, M.; Berg, K.; Glaser, J.; Sandström, M.; Tóth, I. New class of oligonuclear Platinum-Thallium compounds with a direct metal−metal bond. 2. Structural characterization of the complexes. Inorg. Chem. 1998, 37, 2910−2919. (23) Jalilehvand, F.; Maliarik, M.; Sandström, M.; Mink, J.; Persson, I.; Persson, P.; Tóth, I.; Glaser, J. New class of oligonuclear platinumthallium compounds with a direct metal-metal bond. 5. Structure determination of heterodimetallic cyano complexes in aqueous

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b02180. Theory benchmarks for the J-coupling constants, additional notes on the choice of the KS functional for this study, listing of technical parameters for dynamics, discussion of bulk solvent structures, tables with full statistical analysis of spin−spin coupling constant results (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: jochena@buffalo.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the Center for Computational Research (CCR) at the Univ. at Buffalo for providing computational resources and the National Science Foundation (Grant Nos. CHE-1265833 and CHE-1560881) for financial support. L.C.D. is grateful for fellowships from FAPESP (2014/219309) and CNPq (202068/2015-3).

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