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

Relativistic Density Functional NMR Tensors Analyzed with Spin-free Localized Molecular Orbitals

The implementation of fast relativistic methods based on density functional theory, in conjunction with localized molecular orbital (LMO) based analysis, allows straightforward interpretations of NMR parameters in terms of contributions from core shells, lone pairs, and bonds, for compounds containing elements from across the periodic table. We present a conceptual review of a frequently used LMO analysis of NMR parameters calculated in the presence of spin-orbit interactions and other relativistic effects. An accompanying example focuses on the ¹⁵ N shielding in a heavy metal complex.

Experimental and Computational Study of a Tetraazamacrocycle Bis(aryloxide) Uranyl Complex and of the Analogues {E═U═NR}2+ (E = O and NR)

The reaction of [U(κ⁶-{(^t-Bu2ArO)₂Me₂-cyclam})I][I] (H₂{(^t-Bu2ArO)₂Me₂-cyclam} = 1,8-bis(2-hydroxy-3,5-di-tert-butyl)-4,11-dimethyl-1,4,8,11-tetraazacyclotetradecane) with 2 equiv of NaNO₂ in acetonitrile results in the isolation of the uranyl complex [UO₂{(^t-Bu2ArO)₂Me₂-cyclam}] (3) in 31% yield, which was fully characterized, including by single-crystal X-ray diffraction. Density functional theory (DFT) computations were performed to evaluate and compare the level of covalency within the U═E bonds in 3 and in the analogous trans-bis(imido) [U(κ⁴-{(^t-Bu2ArO)₂Me₂-cyclam})(NPh)₂] (1) and trans-oxido-imido [U(κ⁴-{(^t-Bu2ArO)₂Me₂-cyclam})(O)(NPh)] (2) complexes. Natural bond orbital (NBO) analysis allowed us to determine the mixing covalency parameter λ, showing that in 2, where both U-O_oxido and U-N_imido bonds are present, the U-N_imido bond registers more covalency with regard to 1, and the opposite is seen for U-O_oxido with respect to 3. However, the covalency driven by orbital overlap in the U-N_imido bond is slightly higher in 1 than in 2. The ¹⁵N-labeled complexes [U(κ⁴-{(^t-Bu2ArO)₂Me₂-cyclam})(¹⁵NPh)₂] (1-¹⁵N) and [U(κ⁴-{(^t-Bu2ArO)₂Me₂-cyclam})(O)(¹⁵NPh)] (2-¹⁵N) were prepared and analyzed by solution ¹⁵N NMR spectroscopy. The calculated and experimental ¹⁵N chemical shifts are in good agreement, displaying the same trend of δ_N (1-¹⁵N) > δ_N (2-¹⁵N) and reveal that the ¹⁵N chemical shift may serve as a probe for the covalency of the U═NR bond.

Covalency of Trivalent Actinide Ions with Different Donor Ligands: Do Density Functional and Multiconfigurational Wavefunction Calculations Corroborate the Observed "Breaks"?

A comprehensive ab initio study of periodic actinide-ligand bonding trends for trivalent actinides is performed. Relativistic density functional theory (DFT) and complete active-space (CAS) self-consistent field wavefunction calculations are used to dissect the chemical bonding in the [AnCl₆]^3-, [An(CN)₆]^3-, [An(NCS)₆]^3-, [An(S₂PMe₂)₃], [An(DPA)₃]^3-, and [An(HOPO)]^- series of actinide (An = U-Es) complexes. Except for some differences for the early actinide complexes with DPA, bond orders and excess 5f-shell populations from donation bonding show qualitatively similar trends in 5f ⁿ active-space CAS vs DFT calculations. The influence of spin-orbit coupling on donation bonding is small for the tested systems. Along the actinide series, chemically soft vs chemically harder ligands exhibit clear differences in bonding trends. There are pronounced changes in the 5f populations when moving from Pu to Am or Cm, which correlate with previously noted "breaks" in chemical trends. Bonding involving 5f becomes very weak beyond Cm/Bk. We propose that Cm(III) is a borderline case among the trivalent actinides that can be meaningfully considered to be involved in ground-state 5f covalent bonding.

Solvent effect on the 195Pt NMR properties in pyridonate-bridged PtIII dinuclear complex derivatives investigated by ab initio molecular dynamics and localized orbital analysis

An ab initio molecular dynamics investigation of the solvent effect (water) on the structural parameters, ¹⁹⁵Pt NMR spin-spin coupling constants (SSCCs) and chemical shifts of a series of pyridonate-bridged Pt^III dinuclear complexes is performed using Kohn-Sham (KS) Car-Parrinello molecular dynamics (CPMD) and relativistic hybrid KS NMR calculations. The indirect solvent effect (via structural changes) has a dramatic effect on the ¹J_PtPt SSCCs. The complexes exhibit a strong trans influence in solution, where the Pt-Pt bond lengthens with increasing axial ligand σ-donor strength. In the diaqua complex, where the solvent effect is more pronounced, the SSCCs averaged for CPMD configurations with explicit plus implicit solvation agree much better with the experimental data, while the calculations for static geometry and CPMD unsolvated configurations show large deviations with respect to experiment. The combination of CPMD with hybrid KS NMR calculations provides a much more realistic computational model that reproduces the large magnitudes of ¹J_PtPt and ¹⁹⁵Pt chemical shifts. An analysis of ¹J_PtPt in terms of localized and canonical orbitals shows that the SSCCs are driven by changes in the s-character of the natural atomic orbitals of Pt atoms, which affect the 'Fermi contact' mechanism.

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.

1 J CH Coupling in Benzaldehyde Derivatives: Ortho Substitution Effect

The natural J-coupling (NJC) method is applied to analyze the Fermi contact contribution of the NMR spin-spin coupling constant decomposing this contribution in terms of natural localized molecular orbitals. We investigated the influence of the basis set on the NJC analysis for the formyl group coupling constant (¹ J _CHf) of benzaldehyde derivatives. NJC and other NBO analyses, like steric and natural Coulombic energy, were chosen to explain the influence of electron-donating and electron-withdrawing groups on ¹ J _CHf for some substituted benzaldehydes (Me, OH, OMe, F, Cl, Br, I, and NO₂). For the ortho derivatives, electronegative substituents near the C-Hf bond increase the ¹ J _CHf coupling. This effect could be related to an increase in formyl carbon s character and changes in the carbon and hydrogen natural charges. This indicates that the substituents in ortho have a proximity effect on ¹ J _CHf coupling mainly of electrostatic origin instead of the expected hyperconjugative interactions.

"Through-Space" Relativistic Effects on NMR Chemical Shifts of Pyridinium Halide Ionic Liquids

We have investigated, using two-component relativistic density functional theory (DFT) at ZORA-SO-BP86 and ZORA-SO-PBE0 level, the occurrence of relativistic effects on the ¹ H, ¹³ C, and ¹⁵ N NMR chemical shifts of 1-methylpyridinium halides [MP][X] and 1-butyl-3-methylpyridinium trihalides [BMP][X₃ ] ionic liquids (ILs) (X=Cl, Br, I) as a result of a non-covalent interaction with the heavy anions. Our results indicate a sizeable deshielding effect in ion pairs when the anion is I^- and I₃ ^- . A smaller, though nonzero, effect is observed also with bromine while chlorine based anions do not produce an appreciable relativistic shift. The chemical shift of the carbon atoms of the aromatic ring shows an inverse halogen dependence that has been rationalized based on the little C-2s orbital contribution to the σ-type interaction between the cation and anion. This is the first detailed account and systematic theoretical investigation of a relativistic heavy atom effect on the NMR chemical shifts of light atoms in the absence of covalent bonds. Our work paves the way and suggests the direction for an experimental investigation of such elusive signatures of ion pairing in ILs.

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.

A Localized Molecular Orbital Study of the Halogen Substitution Effect on (103)Rh NMR Shielding in [Cp*RhX2]2, Where X = Cl, Br, or I

(103)Rh NMR parameters and the bonding structure of three complexes of [Cp*RhX2]2, where X = Cl, Br, or I, have been studied with the help of natural bond orbitals (NBOs) and natural localized molecular orbitals (NLMOs). The complexes of [Cp*RhX2]2, where X = Cl, Br, or I, have similar bonding structures, with the major difference being in the degree of covalency of the Rh-X bonds. The decomposition of (103)Rh NMR shielding into diamagnetic, paramagnetic, and spin-orbit terms shows that normal halogen dependence (NHD) of the (103)Rh NMR shift is defined mostly by the paramagnetic term, with the spin-orbit term being significantly smaller. The decomposition of (103)Rh shielding into spin-free NBO and NLMO contributions shows that (103)Rh shielding is dominated by Rh d-orbital deshielding contributions. We explain the NHD of the (103)Rh NMR shift with the increase in the energies of the virtual antibonding Rh-X orbitals along the X = Cl, Br, and I series.

On the truncation of the number of excited states in density functional theory sum-over-states calculations of indirect spin spin coupling constants

It is investigated, whether the number of excited (pseudo)states can be truncated in the sum-over-states expression for indirect spin-spin coupling constants (SSCCs), which is used in the Contributions from Localized Orbitals within the Polarization Propagator Approach and Inner Projections of the Polarization Propagator (IPPP-CLOPPA) approach to analyzing SSCCs in terms of localized orbitals. As a test set we have studied the nine simple compounds, CH4, NH3, H2O, SiH4, PH3, SH2, C2H2, C2H4, and C2H6. The excited (pseudo)states were obtained from time-dependent density functional theory (TD-DFT) calculations with the B3LYP exchange-correlation functional and the specialized core-property basis set, aug-cc-pVTZ-J. We investigated both how the calculated coupling constants depend on the number of (pseudo)states included in the summation and whether the summation can be truncated in a systematic way at a smaller number of states and extrapolated to the total number of (pseudo)states for the given one-electron basis set. We find that this is possible and that for some of the couplings it is sufficient to include only about 30% of the excited (pseudo)states.

Spying on the boron-boron triple bond using spin-spin coupling measured from 11B solid-state NMR spectroscopy

Boron–boron J coupling constants provide new insight into the nature of the boron–boron triple bond.

There is currently tremendous interest in the previously documented example of a stable species exhibiting a boron–boron triple bond (Science, 2012, 336, 1420). Notably, it has recently been stated using arguments based on force constants that this diboryne may not, in reality, feature a boron–boron triple bond. Here, we use advanced solid-state NMR and computational methodology in order to directly probe the orbitals involved in multiple boron–boron bonds experimentally via analysis of ¹¹B–¹¹B spin–spin (J) coupling constants. Computationally, the mechanism responsible for the boron–boron spin–spin coupling in these species is found to be analogous to that for the case of multiply-bonded carbon atoms. The trend in reduced J coupling constants for diborenes and a diboryne, measured experimentally, is in agreement with that known for alkenes and alkynes. This experimental probe of the electronic structure of the boron–boron multiple bond provides strong evidence supporting the originally proposed nature of the bonds in the diboryne and diborenes, and demonstrates that the orbitals involved in boron–boron bonding are equivalent to those well known to construct the multiple bonds between other second-row elements such as carbon and nitrogen.

Direct Characterization of Metal-Metal Bonds between Nuclei with Strong Quadrupolar Interactions via NMR Spectroscopy

Metal-metal bonds can be difficult to characterize directly. We demonstrate that J couplings between metal nuclei experiencing strong quadrupolar interactions can be easily measured from well-defined splittings in NMR spectra of powdered samples. Using (69/71)Ga NMR, it is shown that homonuclear J coupling, which is four orders of magnitude smaller than the quadrupolar coupling in a series of compounds featuring gallium-gallium bonds, can be extracted with a 2-D NMR experiment. The dependence of the multiplets on crystal symmetry reveals information on the structures of two Ga-Ga-bonded compounds for which diffraction data are unavailable. Interpretation of the data in a molecular orbital framework provides insight into the nature of the metal-metal bond.

Communication: Localized molecular orbital analysis of the effect of electron correlation on the anomalous isotope effect in the NMR spin-spin coupling constant in methane

We discuss the effect of electron correlation on the unexpected differential sensitivity (UDS) in the (1)J(C-H) coupling constant of CH4 using a decomposition into contributions from localized molecular orbitals and compare with the (1)J(N-H) coupling constant in NH3. In particular, we discuss the well known fact that uncorrelated coupled Hartree-Fock (CHF) calculations are not able to reproduce the UDS in methane. For this purpose we have implemented for the first time a localized molecular orbital analysis for the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes--SOPPA(CCSD) in the DALTON program. Comparing the changes in the localized orbital contributions at the correlated SOPPA and SOPPA(CCSD) levels and at the uncorrelated CHF level, we find that the latter overestimates the effect of stretching the bond between the coupled atoms on the contribution to the coupling from the localized bonding orbital between these atoms. This disturbs the subtle balance between the molecular orbital contributions, which lead to the UDS in methane.

Probing halogen bonds with solid-state NMR spectroscopy: observation and interpretation of J(77Se,31P) coupling in halogen-bonded PSe⋯I motifs

Intra-halogen bond J couplings measured via NMR spectroscopy and interpreted using natural localized molecular orbitals offer novel insights into this class of non-covalent interaction.

Boron–boron J coupling constants are unique probes of electronic structure: a solid-state NMR and molecular orbital study

J couplings measured between ¹¹B spin pairs in solid diboron compounds provide insight into electronic structure and crystallographic symmetry.

Symmetry-amplified J splittings for quadrupolar spin pairs: a solid-state NMR probe of homoatomic covalent bonds

Chemically informative J couplings between pairs of quadrupolar nuclei in dimetallic and dimetalloid coordination motifs are measured using J-resolved solid-state NMR experiments. It is shown that the application of a double-quantum filter is necessary to observe the J splittings and that, under these conditions, only a simple doublet is expected. Interestingly, the splitting is amplified if the spins are magnetically equivalent, making it possible to measure highly precise J couplings and unambiguously probe the symmetry of the molecule. This is demonstrated experimentally by chemically breaking the symmetry about a pair of boron spins by reaction with an N-heterocyclic carbene to form a β-borylation reagent. The results show that the J coupling is a sensitive probe of bonding in diboron compounds and that the J values quantify the weakening of the B-B bond which occurs when forming an sp(2)-sp(3) diboron compound, which is relevant to their reactivity. Due to the prevalence of quadrupolar nuclei among transition metals, this work also provides a new approach to probe metal-metal bonding; results for Mn2(CO)10 are provided as an example.

[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.

Molecular orbital analysis of the inverse halogen dependence of nuclear magnetic shielding in LaX₃, X = F, Cl, Br, I

The NMR nuclear shielding tensors for the series LaX(3), with X = F, Cl, Br and I, have been computed using two-component relativistic density functional theory based on the zeroth-order regular approximation (ZORA). A detailed analysis of the inverse halogen dependence (IHD) of the La shielding was performed via decomposition of the shielding tensor elements into contributions from localized and delocalized molecular orbitals. Both spin-orbit and paramagnetic shielding terms are important, with the paramagnetic terms being dominant. Major contributions to the IHD can be attributed to the La-X bonding orbitals, as well as to trends associated with the La core and halogen lone pair orbitals, the latter being related to X-La π donation. An 'orbital rotation' model for the in-plane π acceptor f orbital of La helps to rationalize the significant magnitude of deshielding associated with the in-plane π donation. The IHD goes along with a large increase in the shielding tensor anisotropy as X becomes heavier, which can be associated with trends for the covalency of the La-X bonds, with a particularly effective transfer of spin-orbit coupling induced spin density from iodine to La in LaI(3).

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).

Relativistic hybrid density functional calculations of indirect nuclear spin–spin coupling tensors — Comparison with experiment for diatomic alkali metal halides,

The accurate calculation of the isotropic (Jiso) and anisotropic (ΔJ) parts of indirect nuclear spin–spin coupling tensors is a stringent test for quantum chemistry, particularly for couplings involving heavy isotopes where relativistic effects and relativity – electron correlation cross terms are expected to play an important role. Experimental measurements on diatomic molecules in the gas phase offer ideal data for testing the success of computational approaches, since the data are essentially free from intermolecular effects, and precise coupling anisotropies may be reliably extracted in favourable cases. On the basis of available experimental molecular-beam coupling-tensor parameters for diatomic alkali metal halides, we tabulate known values of Jiso and, taking rotational–vibrational corrections to the direct dipolar coupling constant into account, precise values of ΔJ are determined for the ground rovibrational state. First-principles calculations of the coupling tensors were performed using a recently developed program based on hybrid density functional theory using the two-component relativistic zeroth-order regular approximation (ZORA). Experimental trends in Jiso and ΔJ are reproduced with correlation coefficients of 0.993 and 0.977, respectively. Periodic trends in the coupling constants and their dependence on the product of the atomic numbers of the coupled nuclei are discussed. Finally, the hybrid functional method is also successfully tested against experimental data for a series of polyatomic xenon fluorides and group-17 fluorides.

Analyzing Pt chemical shifts calculated from relativistic density functional theory using localized orbitals: the role of Pt 5d lone pairs

Pt chemical shifts were calculated from two-component relativistic density functional theory (DFT). The shielding tensors were analyzed by using a recently developed method to decompose the spin-orbit DFT results into contributions from spin-free localized orbitals (here: natural localized molecular orbitals (NLMOs) and natural bond orbitals (NBOs)). Seven chemical shifts in six Pt complexes with Pt oxidation states II, III, and IV; and halide, amino, and amidate ligands were analyzed, with particular focus on the role of nonbonding Pt 5d orbitals. A simple d-orbital 'rotation' model has been used to rationalize some of the observed trends such as the main difference between Pt(II) and Pt(IV) chemical shifts. The localized orbital analysis data showed that most of this difference as well as trends among different Pt complexes with similar coordination can be rationalized by comparing properties of the nonbonding Pt 5d orbitals. We have also analyzed the spin-orbit effects on the chemical shifts of [PtCl4](2-) compared to [PtBr4](2-).