Solvent effects on heavy atom nuclear spin-spin coupling constants: a theoretical study of Hg-C and Pt-P couplings

Coordination of Mercury(II) in Water Promoted over Hydrolysis in Solvated Clusters [Hg(H2O)1-6](aq)2+: Insights from Relativistic Effects and Free Energy Analysis

Understanding the nature of the interaction between mercury(II) ions, Hg2+, and water molecules is crucial to describe the stability and chemical behavior of structures formed during solvation, as well as the conditions that favor the Hg2+ coordination or inducing water hydrolysis. In our study, we explored exhaustively the potential energy surface of Hg2+ with up to six water molecules. We analyzed electronic and Gibbs free energies, binding, and nuclear magnetic resonance parameters. We used the zeroth-order regular approximation Hamiltonian, including scalar and spin-orbit relativistic corrections for free energy calculations and geometry optimizations to explore the interplay between electron correlation and relativistic effects. We analyzed intermolecular interactions with energy decomposition analysis, quantum theory of atoms in molecules, and natural bond orbital. Additionally, we used the four-component Dirac Hamiltonian to compute solvent effect on the magnetic shielding and J-coupling constants. Our results revealed that the water hydrolysis by Hg2+ requires a minimum of three water molecules. We found that the interaction between Hg2+ and water molecules is an orbital interaction due to relativistic effects and the most stable structures are opened-shape clusters, reducing the number of oxygen-mercury contacts and maximizing the formation of hydrogen bonds among water molecules. In these types of clusters, Hg2+ promotes the water hydrolysis over coordination with oxygen atoms. However, when we considered the change associated with the transfer of a cluster from the ideal gas to a solvated system, our solvation free energy analysis revealed that closed-shape clusters are more favorable, maximizing the number of oxygen-mercury contacts and reducing the formation of hydrogen bonds among water molecules. This finding suggests that, under room conditions, the coordination of Hg2+ is more favorable than hydrolysis. Our results have significant implications for understanding Hg2+ behavior in water, helping to develop targeted strategies for mercury remediation and management, and contributing to advancements in the broader field of environmental chemistry.

Computational 199 Hg NMR

Theoretical background and fundamental results dealing with the computation of mercury chemical shifts and spin-spin coupling constants are reviewed with a special emphasis on their stereochemical behavior and applications.

Enhancing NMR Quantum Computation by Exploring Heavy Metal Complexes as Multiqubit Systems: A Theoretical Investigation

Assembled together with the most common qubits used in nuclear resonance magnetic (NMR) quantum computation experiments, spin-1/2 nuclei, such as ¹¹³Cd, ¹⁹⁹Hg, ¹²⁵Te, and ⁷⁷Se, could leverage the prospective scalable quantum computer architectures, enabling many and heteronuclear qubits for NMR quantum information processing (QIP) implementations. A computational design strategy for prescreening recently synthesized complexes of cadmium, mercury, tellurium, selenium, and phosphorus (called MRE complexes) as suitable qubit molecules for NMR QIP is reported. Chemical shifts and spin-spin coupling constants (SSCCs) in five MRE complexes were examined using the spin-orbit zeroth order regular approximation (ZORA) at the density functional theory level and the four-component relativistic Dirac-Kohn-Sham approach. In particular, the influence of different conformers, basis sets, exchange-correlation functionals, and methods to treat the relativistic as well as solvent effects were studied. The differences in the chemical shifts and SSCCs between different low energy conformers of the studied complexes were found to be very small. The TZ2P basis set was found to be the optimum choice for the studied chemical shifts, while the TZ2P-J basis set was the best for the couplings studied in this work. The PBE0 exchange-correlation functional exhibited the best performance for the studied MRE complexes. The addition of solvent effects has not improved on the gas phase results in comparison to the experiment, with the exception of the phosphorus chemical shift. The use of MRE complexes as qubit molecules for NMR QIP could face the challenges in single qubit control and multiqubit operations. They exhibit chemical shifts appropriately dispersed, allowing qubit addressability and exceptionally large spin-spin couplings, which could reduce the time of quantum gate operations and likely preserve the coherence.

Four-component relativistic 31P NMR calculations for trans-platinum(ii) complexes: importance of the solvent and dynamics in spectral simulations

We report a combined experimental-theoretical study on the 31P NMR chemical shift for a number of trans-platinum(ii) complexes. Validity and reliability of the 31P NMR chemical shift calculations are examined by comparing with the experimental data. A successful computational protocol for the accurate prediction of the 31P NMR chemical shifts was established for trans-[PtCl2(dma)PPh3] (dma = dimethylamine) complexes. The reliability of the computed values is shown to be critically dependent on the level of relativistic effects (two-component vs. four component), choice of density functionals, dynamical averaging, and solvation effects. Snapshots obtained from ab initio molecular dynamics simulations were used to identify those solvent molecules which show the largest interactions with the platinum complex, through inspection by using the non-covalent interaction program. We observe satisfactory accuracy from the full four-component matrix Dirac-Kohn-Sham method (mDKS) based on the Dirac-Coulomb Hamiltonian, in conjunction with the KT2 density functional, and dynamical averaging with explicit solvent molecules.

Relativistic Effect on 1 J(M,C) in Me4 M, Me3 M- , Ph4 M, and Ph3 M- (M=Pb, Sn, Ge, Si, and/or C): Role of s-Type Lone Pair Orbitals in the Distinct Effect for the Anionic Species

Indirect one-bond nuclear spin-spin couplings between M and C [¹ J(M,C)] in Me₄ M, Me₃ M^- , Ph₄ M, and Ph₃ M^- (M=Pb, Sn, Ge, Si, C) are analyzed with consideration of the relativistic effect and by employing Slater-type basis sets. The evaluated total values ¹ J_TL (M,C) reproduced the observed values with some systematic calculation errors. Fermi contact terms ¹ J_FC (M,C) contribute predominantly to ¹ J_TL (M,C) (≈99 %). A distinct relativistic effect on ¹ J(Pb,C) is predicted for Me₃ Pb^- and Ph₃ Pb^- . The mechanisms for the distinct effect are elucidated by using the comparison between Me₃ Pb^- and Me₄ Pb as an example. The contributions to ¹ J_FC (M,C) [or ¹ J_SD+FC (M,C), where SD denotes the spin-dipolar term] are decomposed into those of occupied orbitals and occupied-to-unoccupied transitions. The s-type lone-pair orbitals are demonstrated to contribute to the distinct relativistic effect on ¹ J(Pb,C) of Me₃ Pb^- (and Ph₃ Pb^- ). The results are in sharp contrast to the cases of ¹ J(M,C) for M atoms lighter than Pb, such as Si, and are explained by the s character of the M-C bonds. This treatment enables visualization and clear recognition the origin of the nuclear couplings for the species exhibiting a relativistic effect.

What factors influence the metal-proton spin-spin coupling constants in mercury- and cadmium-substutited rubredoxin?

The indirect metal-proton spin-spin coupling constants between protons in cysteine groups and the mercury or cadmium nucleus have been calculated for a small model of Me-rubredoxin complex (Me = Cd, Hg) by means of density functional theory with zeroth-order regular approximation Hamiltonian (DFT-ZORA). The calculated spin-spin coupling constants, in spite of the moderate size of the model system, are in good agreement with the values measured in NMR experiment, which are in the 0.29-0.56 Hz range for the Cd complex and in the 0.57-2.20 Hz range for the Hg complex. The robustness of the chosen method has been verified by calculations with a number of different exchange-correlation functionals and basis sets. Additionally, it has been shown that the short- and long-distance metal-proton coupling constants are affected mainly by the values of the metal-proton distance and the H-N-C-C dihedral angle.

Computational study and molecular orbital analysis of NMR shielding, spin-spin coupling, and electric field gradients of azido platinum complexes

(195)Pt, (14)N, and (15)N NMR data for five azido (N(3)(-)) complexes are studied using relativistic density functional theory (DFT). Good agreement with experiment is obtained for Pt and N chemical shifts as well as Pt-N J-coupling constants. Calculated (14)N electric field gradients (EFGs) reflect experimentally observed trends for the line broadening of azido (14)N NMR signals. A localized molecular orbital analysis of the nitrogen EFGs and chemical shifts is performed to explain some interesting trends seen experimentally and in the first-principles calculations: (i) (14)N NMR signals for the Pt-coordinating (N(α)) nuclei in the azido ligands are much broader than for the central (N(β)) or terminal (N(γ)) atoms. The N(β) signals are particularly narrow; (ii) compared to N(γ), the N(α) nuclei are particularly strongly shielded; (iii) N(β) nuclei have much larger chemical shifts than N(α) and N(γ) ; and (iv) The Pt-N(α) J-coupling constants are small in magnitude when considering the formal sp hybridization of N(α). It is found that for N(α) a significant shielding reduction due to formation of the dative N(α)-Pt bond is counterbalanced by an increased shielding from spin-orbit (SO) coupling originating at Pt. Upon coordination, the strongly delocalized π system of free azide localizes somewhat on N(β) and N(γ). This effect, along with rehybridization at N(α) upon bond formation with Pt, is shown to cause a deshielding of N(γ) relative to N(α) and a strong increase of the EFG at N(α). The large 2p character of the azide σ bonds is responsible for the particularly high N(β) chemical shifts. The nitrogen s-character of the Pt-N(α) bond is low, which is the reason for the small J-coupling. Similar bonding situations are likely to be found in azide complexes with other transition metals.

NMR J-coupling constants in cisplatin derivatives studied by molecular dynamics and relativistic DFT

Solvent effects on J((195)Pt-(15)N) one-bond nuclear spin-spin coupling constants (J(PtN)) of cisplatin [cis-diamminedichloroplatinum(II)] and three cisplatin derivatives are investigated using a combination of density functional theory (DFT) based ab initio molecular dynamics (aiMD) and all-electron relativistic DFT NMR calculations employing the two-component relativistic zeroth-order regular approximation (ZORA). Good agreement with experiment is obtained when explicit solvent molecules are considered and when the computations are performed with a hybrid functional. Spin-orbit coupling causes only small effects on J(PtN) . Key factors contributing to the magnitude of coupling constants are elucidated, with the most significant being the presence of solvent as well as the quality of the density functional and basis set combination. The solvent effects are of the same magnitude as J(PtN) calculated for gas-phase geometries. However, the trends of J(PtN) among the complexes are already present in the gas phase. Results obtained with a continuum solvent model agree quite well with the aiMD results, provided that the Pt solvent-accessible radius is carefully chosen. The aiMD results support the existence of a partial hydrogen-bond-like inverse-hydration-type interaction affording a weak (1)J(Pt⋅⋅⋅H(w)) coupling between the complexes and the coordinating water molecule.

A computational investigation of J couplings involving ²⁷Al, ¹⁷O, and ³¹P

Indirect nuclear spin-spin (J) couplings between (31)P, (27)Al, and (17)O are computed for Cl(3)POAlCl(3), Ph(3)PO, Ph(3)PAlCl(3), Al(H(2)O)(6)(3+), an aluminophosphate model system, and grossite model systems, using the B3LYP hybrid functional and the pcJ-n and aug-pcJ-n basis sets. The results provide computational corroboration of the existence of J coupling constants between (31)P, (17)O, and (27)Al of suitable magnitude for INEPT-style experiments in which connectivity is established as a result of magnetization transfer using these couplings. Potentially useful correlations between structure (bond lengths, angles, dihedrals) and the coupling constants (1)J((27)Al, (17)O), (1)J((31)P, (17)O), and (2)J((31)P, (27)Al) are presented. Calculated values of near zero for both (1)J((27)Al, (17)O) and (2)J((31)P, (27)Al), depending on the molecule and the geometry, suggest that some structurally important correlations could be absent in NMR spectra which rely on magnetization transfers solely based on these isotropic coupling constants.

Modeling of heavy-atom-ligand NMR spin-spin coupling in solution: molecular dynamics study and natural bond orbital analysis of Hg-C coupling constants

Ab initio molecular dynamics (MD) and relativistic density functional NMR methods were applied to calculate the one-bond Hg-C NMR indirect nuclear spin-spin coupling constants (J) of [Hg(CN)(2) ] and [CH(3) HgCl] in solution. The MD averages were obtained as J((199) Hg-(13) C)=3200 and 1575 Hz, respectively. The experimental Hg-C spin-spin coupling constants of [Hg(CN)(2) ] in methanol and [CH(3) HgCl] in DMSO are 3143 and 1674 Hz, respectively. To deal with solvent effects in the calculations, finite "droplet" models of the two systems were set up. Solvent effects in both systems lead to a strong increase of the Hg-C coupling constant. From a relativistic natural localized molecular orbital (NLMO) analysis, it was found that the degree of delocalization of the Hg 5d(σ) nonbonding orbital and of the HgC bonding orbital between the two coupled atoms, the nature of the trans Hg-C/Cl bonding orbital, and the s character of these orbitals, exhibit trends upon solvation of the complexes that, when combined, lead to the strong increase of J(Hg-C).

Measurement of delta(1)J((199)Hg, (31)P) in [HgPCy3(OAc)2]2 and relativistic ZORA DFT investigations of mercury-phosphorus coupling tensors

Using 31P solid-state NMR spectroscopy, anisotropy in the indirect 199Hg-31P spin-spin coupling tensor (DeltaJ) for powdered [HgPCy3(OAc)2]2 (1) has been measured as 4700 +/- 300 Hz. Zeroth-order regular approximation (ZORA) density functional theory (DFT) calculations, including scalar and spin-orbit relativistic effects, performed on 1 and a series of other related compounds show that DeltaJ(199Hg, (31)P) arises entirely from the ZORA Fermi-contact-spin-dipolar cross term. The calculations validate assumptions made in the spectral analysis of 1 and in previous determinations of DeltaJ in powder samples, namely that J is axially symmetric and shares its principal axis system with the direct dipolar coupling tensor (D). Agreement between experiment and theory for various 199Hg, 31P spin-spin coupling anisotropies is reasonable; however, experimental values of 1J(199Hg, 31P)(iso) are significantly underestimated by the calculations. The most important improvements in the agreement were obtained as a result of including more of the crystal lattice in the model used for the calculations, e.g., a change of 43% was noted for 1J(199Hg, 31P)(iso) in [HgPPh3(NO3)2]2 depending on whether the two or three nearest nitrate ions are included in the model. Finally, we have written a computer program to simulate the effects of non-axial symmetry in J and of non-coincidence of the J and D on powder NMR spectra. Simulations clearly show that both of these effects have a pronounced impact on the 31P NMR spectrum of 199Hg-31P spin pairs, suggesting that the effects should be observable experimentally if a suitable compound can be identified.

Analyzing molecular properties calculated with two-component relativistic methods using spin-free natural bond orbitals: NMR spin-spin coupling constants

An analysis method for static linear response properties employing two-component (spin-orbit) relativistic density functional theory along with scalar relativistic "natural localized molecular orbitals" (NLMOs) and "natural bond orbitals" (NBOs) has been developed. The spin-orbit NLMO/NBO analysis has been applied to study the indirect spin-spin coupling (J-coupling) constants in Tl-I, PbH(4), and a dinuclear Pt-Tl bonded complex with a very large Pt-Tl coupling constant (expt.: 146.8 kHz). For Tl-I it is shown that the analysis scheme based on scalar relativistic NLMOs is applicable even if spin-orbit coupling is responsible for most of the coupling's magnitude. For PbH(4) it is shown that electron delocalization plays a much larger role for the Pb-H coupling than it is the case for the C-H coupling in methane. For the Pt-Tl complex the analysis clearly demonstrates the strong influence of the ligands on the Pt-Tl coupling constant and quantifies the effect of the delocalization of the Pt-Tl bond on the Pt-Tl coupling constant.

Density functional computations of 99Ru chemical shifts: relativistic effects, influence of the density functional, and study of solvent effects on fac-[Ru(CO)3I3]-

Solvent effects on the 99Ru NMR chemical shift of the complex fac-[Ru(CO)3I3]- are investigated computationally using density functional theory. Further, benchmark calculations of the 99Ru shift for a set of ten Ru complexes have been performed in order to calibrate the computational model and to determine the importance of relativistic effects on the 99Ru nuclear magnetic shielding and on the chemical shift. A computational model for fac-[Ru(CO)3I3]- that includes both explicit solvent molecules and a continuum model is shown to yield the best agreement with experiment. Relativistic corrections are shown to be of minor importance for determining 99Ru chemical shifts. On the other hand, the nature of the density functional is of importance. In agreement with literature data for ligand trends of 99Ru chemical shifts, the chemical shift range for different solvents is also best reproduced by a hybrid functional.

Spin–spin coupling constants in homonuclear polynitrogen species

Quantum chemical calculations provide new insights into the dependence of J(N,N) coupling tensors on bonding environment in a series of polynitrogen species including N(5)(+).

The solvation of the mercury(II) ion-a 199Hg NMR study

The solvation of the mercury(II) ion in solvents with different solvation properties, water, dimethylsulfoxide, N,N-dimethylthioformamide, and liquid ammonia, has been studied by means of (199)Hg NMR. The (199)Hg chemical shift shows a pronounced dependence on the coordination number of the mercury(II) ion in the solvates resulting in a difference of over 1200 ppm between basically tetrahedral and octahedral complexes. The chemical shifts can furthermore be associated with electron-pair donor properties of the solvents. The spin-lattice relaxation times of the (199)Hg nucleus in the solvates have been measured at different applied magnetic fields, concentrations, temperatures, and isotope substitutions. Possible mechanisms for the (199)Hg relaxation were proposed and the chemical shielding anisotropy in the solvates has been estimated. The (199)Hg relaxation rates and the anisotropy are correlated with the structure of the solvate complexes in solution obtained from recent LAXS and EXAFS studies.

The ?Invisible?13C NMR Chemical Shift of the Central Carbon Atom in [(Ph3PAu)6C]2+: A Theoretical Investigation

The experimental 13C NMR chemical shift of the central carbon atom in the octahedral [(Ph3PAu)6C]2+ cluster was investigated on the basis of relativistic density functional calculations. In order to arrive at independent model conclusions regarding the value of the chemical shift, a systematic study of the dependence of the cluster structure on the phosphine ligands, the chosen density functionals, and the basis set size was conducted. The best structures obtained were then used in the NMR calculations. Because of the cage-like cluster structure a pronounced deshielding of the central carbon nucleus could have been expected. However, upon comparison with the 13C NMR properties of the related complex [C{Au[P(C6H5)2(p-C6H4NMe2)]}6]2+, Schmidbaur et al. have assigned a signal at delta=135.2 ppm to the interstitial carbon atom. Our calculations confirm this value in the region of the aromatic carbon atoms of the triphenylphosphine ligands. The close-lying signals of the 108 phenyl carbon atoms can explain the difficulties of assigning them experimentally.

DFT analysis of NMR scalar interactions across the glycosidic bond in DNA

The relationship between the glycosidic torsion angle chi, the three-bond couplings (3)J(C2/4-H1') and (3)J(C6/8-H1'), and the one-bond coupling (1)J(C1'-H1') in deoxyribonucleosides and a number of uracil cyclo-nucleosides has been analyzed using density functional theory. The influence of the sugar pucker and the hydroxymethyl conformation has also been considered. The parameters of the Karplus relationships between the three-bond couplings and chi depend strongly on the aromatic base. (3)J(C2/4-H1') reveals different behavior for deoxyadenosine, deoxyguanosine, and deoxycytidine as compared to deoxythymidine and deoxyuridine. In the case of (3)J(C6/8-H1'), an opposite trans to cis ratio of couplings is obtained for pyrimidine nucleosides in contrast to purine nucleosides. The extremes of the Karplus curves are shifted by ca. 10 degrees with respect to syn and anti-periplanar orientations of the coupled nuclei. The change in the sugar pucker from S to N decreases (3)J(C2/4-H1') and (3)J(C6/8-H1'), while increasing (1)J(C1'-H1') for the syn rotamers, whereas all of the trends are reversed for the anti rotamers. The influence of the sugar pucker on (1)J(C1'-H1') is interpreted in terms of interactions between the n(O4'), sigma*(C1'-H1') orbitals. The (1)J(C1'-H1') are related to chi through a generalized Karplus relationship, which combines cos(chi) and cos(2)(chi) functions with mutually different phase shifts that implicitly accounts for a significant portion of the related sugar pucker effects. Most of theoretical (3)J(C2/4-H1') and (3)J(C6/8-H1') for uracil cyclo-nucleosides compare well with available experimental data. (3)J(C6/8-H1') couplings for all C2-bridged nucleosides are up to 3 Hz smaller than in the genuine nucleosides with the corresponding chi, revealing a nonlocal aspect of the spin-spin interactions across the glycosidic bond. Theoretical (1)J(C1'-H1') are underestimated with respect to the experiment by ca. 10% but reproduce the trends in (1)J(C1'-H1') vs chi.

A theoretical investigation of the remarkable nuclear spin-spin coupling pattern in [(NC)(5)Pt-Tl(CN)](-)

We address the problem of the interpretation of heavy nucleus spin-spin couplings for systems being studied in solution. Solvation can create counterintuitive features concerning the spin-spin couplings, which are enhanced by relativistic effects due to the presence of heavy nuclei. This should therefore be taken into consideration for the discussion of spectra obtained from solution. Evidence for such solvent effects is provided by a relativistic density functional study of [(NC)(5)Pt-Tl(CN)](-) (I). It is demonstrated that the remarkable experimentally observed spin-spin coupling pattern, e.g., (2)J(Tl-C) >> (1)J(Tl-C) and J(Pt-Tl) approximately 57 kHz, is semiquantitatively reproduced by our calculations if both relativistic effects and solvation are taken into account. Solvent effects are very substantial and shift the Pt-Tl coupling by more than 100%, e.g. Relativistic increase of s-orbital density at the heavy nuclei, charge donation by the solvent, and the specific features of the multicenter C-Pt-Tl-C bond are responsible for the observed coupling pattern.