Two-component relativistic hybrid density functional computations of nuclear spin-spin coupling tensors using Slater-type basis sets and density-fitting techniques

Dynamic and relativistic effects on Pt-Pt indirect spin-spin coupling in aqueous solution studied by ab initio molecular dynamics and two- vs four-component density functional NMR calculations

Treating 195Pt nuclear magnetic resonance parameters in solution remains a considerable challenge from a quantum chemistry point of view, requiring a high level of theory that simultaneously takes into account the relativistic effects, the dynamic treatment of the solvent-solute system, and the dynamic electron correlation. A combination of Car-Parrinello molecular dynamics (CPMD) and relativistic calculations based on two-component zeroth order regular approximation spin-orbit Kohn-Sham (2c-ZKS) and four-component Dirac-Kohn-Sham (4c-DKS) Hamiltonians is performed to address the solvent effect (water) on the conformational changes and JPtPt1 coupling. A series of bridged PtIII dinuclear complexes [L1-Pt2(NH3)4(Am)2-L2]n+ (Am = α-pyrrolidonate and pivalamidate; L = H2O, Cl-, and Br-) are studied. The computed Pt-Pt coupling is strongly dependent on the conformational dynamics of the complexes, which, in turn, is correlated with the trans influence among axial ligands and with the angle N-C-O from the bridging ligands. The J-coupling is decomposed in terms of dynamic contributions. The decomposition reveals that the vibrational and explicit solvation contributions reduce JPtPt1 of diaquo complexes (L1 = L2 = H2O) in comparison to the static gas-phase magnitude, whereas the implicit solvation and bulk contributions correspond to an increase in JPtPt1 in dihalo (L1 = L2 = X-) and aquahalo (L1 = H2O; L2 = X-) complexes. Relativistic treatment combined with CPMD shows that the 2c-ZKS Hamiltonian performs as well as 4c-DKS for the JPtPt1 coupling.

Lewis Acid Probe for Basicity of Sulfide Electrolytes Investigated by 11B Solid-State NMR

Sulfide-based solid-state lithium-ion batteries (SSLIB) have attracted a lot of interest globally in the past few years for their high safety and high energy density over the traditional lithium-ion batteries. However, sulfide electrolytes (SEs) are moisture-sensitive which pose significant challenges in the material preparation and cell manufacturing. To the best of our knowledge, there is no tool available to probe the types and the strength of the basic sites in sulfide electrolytes, which is crucial for understanding the moisture stability of sulfide electrolytes. Herein, we propose a new spectral probe with the Lewis base indicator BBr3 to probe the strength of Lewis basic sites on various sulfide electrolytes by 11B solid-state NMR spectroscopy (11B-NMR). The active sulfur sites and the corresponding strength of the sulfide electrolytes are successfully evaluated by the proposed Lewis base probe. The probed strength of the active sulfur sites of a sulfide electrolyte is consistent with the results of DFT (density functional theory) calculation and correlated with the H2S generation rate when the electrolyte was exposed in moisture atmosphere. This work paves a new way to investigate the basicity and moisture stability of the sulfide electrolytes.

Reducing Exact Two-Component Theory for NMR Couplings to a One-Component Approach: Efficiency and Accuracy

The self-consistent and complex spin-orbit exact two-component (X2C) formalism for NMR spin-spin coupling constants [ J. Chem. Theory Comput. 17, 2021, 3874-3994] is reduced to a scalar one-component ansatz. This way, the first-order response term can be partitioned into the Fermi-contact (FC) and spin-dipole (SD) interactions as well as the paramagnetic spin-orbit (PSO) contribution. The FC+SD terms are real and symmetric, while the PSO term is purely imaginary and antisymmetric. The relativistic one-component approach is combined with a modern density functional treatment up to local hybrid functionals including the response of the current density. Computational demands are reduced by factors of 8-24 as shown for a large tin compound consisting of 137 atoms. Limitations of the current ansatz are critically assessed for Sn, Pb, Pd, and Pt compounds, i.e. the one-component treatment is not sufficient for tin compounds featuring a few heavy halogen atoms.

Binding methane to a metal centre

The σ-alkane complexes of transition metals, which contain an essentially intact alkane molecule weakly bound to the metal, have been well established as crucial intermediates in the activation of the strong C-H σ-bonds found in alkanes. Methane, the simplest alkane, binds even more weakly than larger alkanes. Here we report an example of a long-lived methane complex formed by directly binding methane as an incoming ligand to a reactive organometallic complex. Photo-ejection of carbon monoxide from a cationic osmium-carbonyl complex dissolved in an inert hydrofluorocarbon solvent saturated with methane at -90 °C affords an osmium(II) complex, [η⁵-CpOs(CO)₂(CH₄)]⁺, containing methane bound to the metal centre. Nuclear magnetic resonance (NMR) spectroscopy confirms the identity of the σ-methane complex and shows that the four protons of the metal-bound methane are in rapid exchange with each other. The methane ligand has a characteristically shielded ¹H NMR resonance (δ -2.16), and the highly shielded carbon resonance (δ -56.3) shows coupling to the four attached protons (¹J_C-H = 127 Hz). The methane complex has an effective half-life of about 13 hours at -90 °C.

NMR Indirect Spin-Spin Coupling Constants in a Modern Quasi-Relativistic Density Functional Framework

A quasi-relativistic implementation of NMR indirect spin-spin coupling constants is presented. The exact two-component (X2C) Hamiltonian and its diagonal local approximation to the unitary decoupling transformation (DLU) are utilized together with the (modified) screened nuclear spin-orbit approach. In a restricted kinetic balance, the finite nucleus model is available for both the scalar and vector potentials. The implementation supports density functionals up to the fourth rung of Jacob's ladder, i.e., (range-separated) hybrid and local hybrid functionals based on a seminumerical ansatz. We assess the quality of our quasi-relativistic X2C approach by comparison with "fully" relativistic four-component results for small main-group molecules and alkynyl compounds. The mean absolute error introduced by the DLU scheme is less than 0.05 × 10¹⁹ T J^-2 of the reduced coupling constant for the small main-group molecules and 0.5 Hz for the alkynyl compounds. Thus, the error is significantly smaller than finite nucleus size effects for heavy elements. The basis set convergence and the impact of different density functional approximations are further studied. We propose a simple scheme to develop segmented-contracted relativistic all-electron basis sets for NMR spin-spin couplings. Our implementation allows us to perform calculations of extended molecules with reasonable computational effort, which is illustrated for the ¹J(¹¹⁹Sn, ³¹P) coupling constant of a low-valent tin phosphinidenide complex. The corresponding results are in good agreement with the experimental findings.

One-bond 1 J(15 N─19 F) spin-spin coupling constants of cationic fluorinating reagents: Insights from DFT calculations

We have investigated, by means of density functional theory protocols, the one-bond ¹ J(¹⁵ N─¹⁹ F) spin-spin coupling constants in a series of fluorinating reagents, containing the N─F bond, recently studied experimentally. The results of the calculations show a very good linear relationship with the experimental values, even though only the M06-2X(PCM)/pcJ-2//B3LYP/6-311G(d,p) level affords a very low mean absolute error. The calculations allow to analyze the various molecular orbitals contributions to the J coupling and to rationalize the observed positive sign, corresponding to a negative sign of the reduced spin-pin coupling constant K(N─F). Moreover, of the four Ramsey contributions, only the diamagnetic spin orbit is negligible, whereas the paramagnetic spin orbit and spin dipole terms decrease the magnitude of the Fermi contact (FC) term by an amount that goes from a minimum of 35% up to more than 60% of the FC term itself. Several effects have been investigated, namely, the contribution of the long-range solvent reaction field, relativistic corrections, and conformational and vibrational effects.

Relativistic DFT Calculations of 1JWH and 1JWC Provide Detailed Structural Insight of Cyclopentadienyl Binding in Cp2WH2

Experimental measurements of the one-bond scalar coupling of Cp₂WH₂ in tetrahydrofuran (¹J_WH = 73.4 Hz and ¹J_WC = 4.8 Hz) are compared to density functional theory calculations of the same based upon geometries minimized utilizing a variety of approximate functionals typically utilized to calculate organometallic geometries. One difference between the various functionals is the Cp-W distance, and d_CpW is linearly correlated to the calculated values for both ¹J_WH and ¹J_WC. Differences in the structures of the Cp₂WH₂ reported in the literature are compared to the calculated geometries, utilizing calculated values of ¹J_WH to provide insight into the differences. The distance between the tungsten and attached hydride as well as the angle of the cyclopentadienyl plane with respect to the tungsten cyclopentadienyl centroid vector also have a strong effect on ¹J_WH. A natural bond orbital (NBO) analysis of the orbital origins of ¹J_WH indicates that the W-H σ-bonding orbital is the primary contributor to the coupling constant.

Chalcogen Impact on Covalency within Molecular [Cu3(μ3-E)]3+ Clusters (E = O, S, Se): A Synthetic, Spectroscopic, and Computational Study

Reaction of the tricopper(I)-dinitrogen tris(β-diketiminate) cyclophane, Cu3(N2)L, with O-atom-transfer reagents or elemental Se affords the oxido-bridged tricopper complex Cu3(μ3-O)L (2) or the corresponding Cu3(μ3-Se)L (4), respectively. For 2 and 4, incorporation of the bridging chalcogen donor was supported by electrospray ionization mass spectrometry and K-edge X-ray absorption spectroscopy (XAS) data. Cu L2,3-edge X-ray absorption data quantify 49.5% Cu 3d character in the lowest unoccupied molecular orbital of 2, with Cu 3d participation decreasing to 33.0% in 4 and 40.8% in the related sulfide cluster Cu3(μ3-S)L (3). Multiedge XAS and UV/visible/near-IR spectra are employed to benchmark density functional theory calculations, which describe the copper-chalcogen interactions as highly covalent across the series of [Cu3(μ-E)]3+ clusters. This result highlights that the metal-ligand covalency is not reserved for more formally oxidized metal centers (i.e., CuIII + O2- vs CuII + O-) but rather is a significant contributor even at more typical ligand-field cases (i.e., Cu3II/II/I + E2-). This bonding is reminiscent of that observed in p-block elements rather than in early-transition-metal complexes.

Similar ligand-metal bonding for transition metals and actinides? 5f1 U(C7H7)2-versus 3d n metallocenes

U(C7H7)2- is a fascinating 5f1 complex whose metal-ligand bonding was assigned in the literature as being very similar to 3d7 cobaltocene, based on a crystal-field theoretical interpretation of the experimental magnetic resonance data. The present work provides an in-depth theoretical study of the electronic structure, bonding, and magnetic properties of the 5f1 U(C7H7)2-vs. 3d metallocenes with V, Co, and Ni, performed with relativistic wavefunction and density functional methods. The ligand to metal donation bonding in U(C7H7)2- is strong and in fact similar to that in vanadocene, in the sense that the highest occupied arene orbitals donate electron density into empty metal orbitals of the same symmetry with respect to the rotational axis (3dπ for V, 5fδ for U), but selectively with α spin (↑). For Co and Ni, the dative bonding from the ligands is β spin (↓) selective into partially filled 3dπ orbitals. In all systems, this spin delocalization triggers spin polarization in the arene σ bonding framework, causing proton spin densities opposite to those of the carbons. As a consequence, the proton spin densities and hyperfine coupling constants are negative for the Co and Ni complex, but positive for vanadocene. The of U(C7H7)2- is negative and similar to that of cobaltocene, but only because of the strong spin-orbit coupling in the actinocene, which causes to be opposite to the sign of the proton spin density. The study contributes to a better understanding of actinide 5f vs. transition metal 3d covalency, and highlights potential pitfalls when interpreting experimental magnetic resonance data in terms of covalent bonding for actinide complexes.

The Antagonist Effect of Nitrogen Lone Pair: 3 JHF versus 5 JHF

The long-range scalar coupling constant between proton and fluorine nuclei, ⁵ J_HF , is observed to be larger than ³ J_HF in the pyrimidinyl moiety of voriconazole. A set of smaller molecules is chosen (fluorobenzene, N-methyl-2-fluoropyridine, N-methyl-3-fluoropyridine, 3-fluoropyridine, 5-pyrimidine, and 2-fluoropyridine) to evaluate the influence of the nitrogen atom in the experimental J_HF values. Spectral aliased pure shift heteronuclear single quantum coherence spectroscopy (SAPS-HSQC) is applied to determine the relative sign between the J_CF and J_HF scalar couplings. Theoretical calculations show that the ³ J_HF and ⁵ J_HF coupling constants can be described mainly by a Fermi contact (FC) transmission mechanism. A decomposition analysis of J_HF in terms of localized molecular orbital (LMO) contributions allows us to determine that the interaction involving the nitrogen lone pair (LPN) is the main reason for the larger ⁵ J_HF compared to ³ J_HF . Our analysis indicates that delocalization of LPN has a positive contribution to the long-range coupling, while a negative one is observed for ³ J_HF .

Towards reliable references for electron paramagnetic resonance parameters based on quantum chemistry: the case of verdazyl radicals

We present an efficient and accurate computational procedure to calculate properties measurable by EPR spectroscopy. We simulate a molecular dynamics (MD) trajectory by employing the quantum mechanically derived force field (QMDFF) [S. Grimme, J. Chem. Theory Comput., 2014, 10, 4497] and sample the trajectory at different time steps. For each snapshot EPR properties are calculated with a hybrid density functional theory (DFT) method. EPR spectra are simulated based on the averaged results. We applied the strategy to a number of previously published and novel verdazyl radicals, for which we recorded EPR spectra. The resulting simulated spectra are compatible with experiment already before employing an additional fitting step, in contrast to those from single point electronic-structure calculations. After the refinement, the experimental data are excellently reproduced, and the fitted EPR parameters do not deviate much from the calculated ones. This provides confidence in ascribing a direct physical meaning to the refined data in terms of experimental EPR parameters rather than merely considering them as mathematical fit parameters. We also find that couplings to hydrogen nuclei have a significant influence on the spectra of verdazyl radicals.

NMR spin-spin coupling constants: bond angle dependence of the sign and magnitude of the vicinal (3)JHF coupling

The dependence of the magnitude and sign of (3)JHFF on the bond angle in fluoro-cycloalkene compounds is evaluated by electronic structure calculations using different levels of theory, viz. DFT, SOPPA(CCSD) and SOPPA(CC2). Localized molecular orbital contributions to (3)JHFF are analyzed to assess which orbitals are responsible for (3)JHFF and which are the most important coupling transmission mechanisms for each compound. Fluoro-ethylene is used as a model system to evaluate the dependence of the (3)JHFF coupling constant on the angle between the σCα-F and σCα'-HF vectors. Through-space and hyperconjugative transmission pathways and ring strain are identified as responsible for the opposite trend between (3)JHFF and bond angle, and for the negative signs obtained for the two molecules, respectively. One of the fluorine lone pairs, σCα'-HF, σCα-F, σCα'-Cβ' bonding orbitals and the σ*Cα-F antibonding orbital are involved in the J-coupling pathways, according to analyses of pairwise-steric and hyperconjugative energies.

The Relativistic Effects on the Carbon-Carbon Coupling Constants Mediated by a Heavy Atom

The (2)JCC, (3)JCC, and (4)JCC spin-spin coupling constants in the systems with a heavy atom (Cd, In, Sn, Sb, Te, Hg, Tl, Pb, Bi, and Po) in the coupling path have been calculated by means of density functional theory. The main goal was to estimate the relativistic effects on spin-spin coupling constants and to explore the factors which may influence them, including the nature of the heavy atom and carbon hybridization. The methods applied range, in order of reduced complexity, from the Dirac-Kohn-Sham (DKS) method (density functional theory with four-component Dirac-Coulomb Hamiltonian), through DFT with two- and one-component zeroth-order regular approximation (ZORA) Hamiltonians, to scalar effective core potentials (ECPs) with the nonrelativistic Hamiltonian. The use of DKS and ZORA methods leads to very similar results, and small-core ECPs of the MDF and MWB variety reproduce correctly the scalar relativistic effects. Scalar relativistic effects usually are larger than the spin-orbit coupling effects. The latter tend to influence the most the coupling constants of the sp(3)-hybridized carbon atoms and in compounds of the p-block heavy atoms. Large spin-orbit coupling contributions for the Po compounds are probably connected with the inverse of the lowest triplet excitation energy.

[P3Se4](+): A Binary Phosphorus-Selenium Cation

Although a fairly large number of binary group 15/16 element cations have been reported, no example involving phosphorus in combination with a group 16 element has been synthesized and characterized to date. In this contribution is reported the synthesis and structural characterization of the first example of such a cation, namely a nortricyclane-type [P3Se4](+). This cation has been independently discovered by three groups through three different synthetic routes, as described herein. The molecular and electronic structure of the [P3Se4](+) cage and its crystal properties in the solid state have been characterized comprehensively by using X-ray diffraction, Raman, and nuclear magnetic resonance spectroscopies, as well as quantum chemical calculations.

Interpretation of the longitudinal (13)C nuclear spin relaxation and chemical shift data for five bromoazaheterocycles supported by nonrelativistic and relativistic DFT calculations

The longitudinal relaxation times of (13)C nuclei and NOE enhancement factors for 2-bromopyridine (1), 6-bromo-9-methylpurine (2), 3,5-dibromopyridine (3), 2,4-dibromopyrimidine (4), and 2,4,6-tribromopyrimidine (5) have been measured at 25 °C and B0 = 11.7 T. The most important contributions to the overall relaxation rates of nonbrominated carbons, i.e., the relaxation rates due to the (13)C-(1)H dipolar interactions and the shielding anisotropy mechanism, have been separated out. For 3 and 5, additionally, the T2,Q((14)N) values have been established from (14)N NMR line widths. All of these data have been used to determine rotational diffusion tensors for the investigated molecules. The measured saturation recovery curves of brominated carbons have been decomposed into two components to yield relaxation times, which after proper corrections provided parameters characterizing the scalar relaxation of the second kind for (13)C nuclei of (79)Br- and (81)Br-bonded carbons. These parameters and theoretically calculated quadrupole coupling constants for bromine nuclei have allowed the values of one-bond (13)C-(79)Br spin-spin coupling constants to be calculated. Independently, the coupling constants and magnetic shielding constants of the carbon nuclei have been calculated theoretically using the nonrelativistic and relativistic DFT methods F/6-311++G(2d,p)/PCM and so-ZORA/F/TZ2P/COSMO (F = BHandH or B3LYP), respectively. The agreement between the experimental and theoretical values of these parameters is remarkably dependent on the theoretical method used.

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.

Relativistic calculations of magnetic resonance parameters: background and some recent developments

This article outlines some basic concepts of relativistic quantum chemistry and recent developments of relativistic methods for the calculation of the molecular properties that define the basic parameters of magnetic resonance spectroscopic techniques, i.e. nuclear magnetic resonance shielding, indirect nuclear spin-spin coupling and electric field gradients (nuclear quadrupole coupling), as well as with electron paramagnetic resonance g-factors and electron-nucleus hyperfine coupling. Density functional theory (DFT) has been very successful in molecular property calculations, despite a number of problems related to approximations in the functionals. In particular, for heavy-element systems, the large electron count and the need for a relativistic treatment often render the application of correlated wave function ab initio methods impracticable. Selected applications of DFT in relativistic calculation of magnetic resonance parameters are reviewed.

Perspective: relativistic effects

This perspective article discusses some broadly-known and some less broadly-known consequences of Einstein's special relativity in quantum chemistry, and provides a brief outline of the theoretical methods currently in use, along with a discussion of recent developments and selected applications. The treatment of the electron correlation problem in relativistic quantum chemistry methods, and expanding the reach of the available relativistic methods to calculate all kinds of energy derivative properties, in particular spectroscopic and magnetic properties, requires on-going efforts.

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.

Residual dipolar coupling between quadrupolar nuclei under magic-angle spinning and double-rotation conditions

Residual dipolar couplings between spin-1/2 and quadrupolar nuclei are often observed and exploited in the magic-angle spinning (MAS) NMR spectra of spin-1/2 nuclei. These orientation-dependent splittings contain information on the dipolar interaction, which can be translated into structural information. The same type of splittings may also be observed for pairs of quadrupolar nuclei, although information is often difficult to extract from the quadrupolar-broadened lineshapes. Here, the complete theory for describing the dipolar coupling between two quadrupolar nuclei in the frequency domain by Hamiltonian diagonalization is given. The theory is developed under MAS and double-rotation (DOR) conditions, and is valid for any spin quantum numbers, quadrupolar coupling constants, asymmetry parameters, and tensor orientations at both nuclei. All terms in the dipolar Hamiltonian become partially secular and contribute to the NMR spectrum. The theory is validated using experimental 11B and 35/37Cl NMR experiments carried out on powdered B-chlorocatecholborane, where both MAS and DOR are used to help separate effects of the quadrupolar interaction from those of the dipolar interaction. It is shown that the lineshapes are sensitive to the quadrupolar coupling constant of both nuclei and to the J coupling (including its sign). From these experiments, the dipolar coupling constant for a heteronuclear spin pair of quadrupolar nuclei may be obtained as well as the sign of the quadrupolar coupling constant of the perturbing nucleus; these are two parameters that are difficult to obtain experimentally otherwise.

[Pt@Pb12]2– — A challenging system for relativistic density functional theory calculations of 195Pt and 207Pb NMR parameters

We report computations of NMR chemical shifts and indirect spin-spin coupling constants (J couplings) for the [Pt@Pb12]2– “superatom”. The system is strongly influenced by relativistic effects. The Pt–Pb coupling constant is predicted to be negative, with its magnitude being in reasonable agreement with experiment. Pt and Pb chemical shifts also agree reasonably well with experiment. The Pb shielding tensor is strongly anisotropic, with a large deshielding principal component dominated by magnetic coupling between frontier orbitals of the cluster that resemble atomic g orbitals. The NMR parameters are sensitive to approximations made in the computations and require the inclusion of spin-orbit coupling in the theoretical model to achieve reliable results. Computing the NMR parameters of the compact [Pt@Pb12]2– system with its many electrons proves to be a challenging test case for relativistic density functional methods.

A ZORA-DFT and NLMO study of the one-bond fluorine–X indirect nuclear spin-spin coupling tensors for various VSEPR geometries

Zeroth-order regular approximation (ZORA) density functional theory (DFT) calculations of one-bond X–19F indirect nuclear spin-spin coupling (J) tensors were performed on a series of fluorine-containing compounds covering several valence shell electron pair repulsion (VSEPR) theory geometries for which J, by symmetry, is not required to be axially symmetric. The calculations show that the antisymmetric components of J are only of the same order of magnitude as the principal components of the symmetric J-coupling tensor for a few geometries, and that in cases of approximate axial symmetry along the bond, J remains nearly axially symmetric with its unique component along the bond. In general, different species having the same nominal geometry tend to have similar tensor orientations, magnitudes of anisotropy of J relative to the isotropic coupling constant, as well as the same dominant contributions from the different coupling mechanisms. Structures are also systematically modified to determine how the tensor components depend on geometrical parameters. The isotropic coupling constants are subsequently interpreted using a natural localized molecular orbital (NLMO) approach. Our results could prove to be useful for future experimental characterizations of J tensors in systems having symmetry properties that do not force J to be axially symmetric or coincident with the dipolar coupling tensor.

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.

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.