On the relativistic theory of NMR chemical shifts

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.

Quantum Chemical Approaches to the Calculation of NMR Parameters: From Fundamentals to Recent Advances

Quantum chemical methods for the calculation of indirect NMR spin–spin coupling constants and chemical shifts are always in progress. They never stay the same due to permanently developing computational facilities, which open new perspectives and create new challenges every now and then. This review starts from the fundamentals of the nonrelativistic and relativistic theory of nuclear magnetic resonance parameters, and gradually moves towards the discussion of the most popular common and newly developed methodologies for quantum chemical modeling of NMR spectra.

Quantum chemical calculations of 77 Se and 125 Te nuclear magnetic resonance spectral parameters and their structural applications

An accurate quantum chemical (QC) modeling of ⁷⁷ Se and ¹²⁵ Te nuclear magnetic resonance (NMR) spectra is deeply involved in the NMR structural assignment for selenium and tellurium compounds that are of utmost importance both in organic and inorganic chemistry nowadays due to their huge application potential in many fields, like biology, medicine, and metallurgy. The main interest of this review is focused on the progress in QC computations of ⁷⁷ Se and ¹²⁵ Te NMR chemical shifts and indirect spin-spin coupling constants involving these nuclei. Different computational methodologies that have been used to simulate the NMR spectra of selenium and tellurium compounds since the middle of the 1990s are discussed with a strong emphasis on their accuracy. A special accent is placed on the calculations resorting to the relativistic methodologies, because taking into account the relativistic effects appreciably influences the precision of NMR calculations of selenium and, especially, tellurium compounds. Stereochemical applications of quantum chemical calculations of ⁷⁷ Se and ¹²⁵ Te NMR parameters are discussed so as to exemplify the importance of integrated approach of experimental and computational NMR techniques.

Relativistic Calculations of Nuclear Magnetic Resonance Parameters

Relativistic effects are important for the accurate evaluation of the observables of nuclear magnetic resonance (NMR) spectroscopy, the nuclear magnetic shielding and the indirect spin–spin coupling tensors. Some of the most notable relativistic effects, in particular for light elements in the vicinity of heavy nuclei, are due to spin–orbit effects, an effect difficult to evaluate when starting from a non-relativistic wavefunction. Two- and four-component relativistic methods include spin–orbit effects variationally, and the recent improvements in the computational efficiency of these methods open new opportunities for accurate calculations of NMR parameters also for molecules with heavy elements. We here present an overview of the different approximations that have been introduced for calculating relativistic effects with two- and four-component methods and how these methods can be used to calculate the NMR parameters. We will also give some examples of systems that have been studied computationally with two- and four-component relativistic methods and discuss the importance of relativistic effects on the shielding and indirect spin–spin coupling constants.

Chemical-shift tensors of heavy nuclei in network solids: a DFT/ZORA investigation of 207Pb chemical-shift tensors using the bond-valence method

Accurate computation of ²⁰⁷Pb magnetic shielding principal components is within the reach of quantum chemistry methods by employing relativistic ZORA/DFT and cluster models adapted from the bond valence model.

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.

Four-component relativistic theory for nuclear magnetic shielding: magnetically balanced gauge-including atomic orbitals

It is recognized only recently that the incorporation of the magnetic balance condition is absolutely essential for four-component relativistic theories of magnetic properties. Another important issue to be handled is the so-called gauge problem in calculations of, e.g., molecular magnetic shielding tensors with finite bases. It is shown here that the magnetic balance can be adapted to distributed gauge origins, leading to, e.g., magnetically balanced gauge-including atomic orbitals (MB-GIAOs) in which each magnetically balanced atomic orbital has its own local gauge origin placed on its center. Such a MB-GIAO scheme can be combined with any level of theory for electron correlation. The first implementation is done here at the coupled-perturbed Dirac-Kohn-Sham level. The calculated molecular magnetic shielding tensors are not only independent of the choice of gauge origin but also converge rapidly to the basis set limit. Close inspections reveal that (zeroth order) negative energy states are only important for the expansion of first order electronic core orbitals. Their contributions to the paramagnetism are therefore transferable from atoms to molecule and are essentially canceled out for chemical shifts. This allows for simplifications of the coupled-perturbed equations.

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-).

Decoupling of the Dirac equation correct to the third order for the magnetic perturbation

A two-component relativistic theory accurately decoupling the positive and negative states of the Dirac Hamiltonian that includes magnetic perturbations is derived. The derived theory eliminates all of the odd terms originating from the nuclear attraction potential V and the first-order odd terms originating from the magnetic vector potential A, which connect the positive states to the negative states. The electronic energy obtained by the decoupling is correct to the third order with respect to A due to the (2n+1) rule. The decoupling is exact for the magnetic shielding calculation. However, the calculation of the diamagnetic property requires both the positive and negative states of the unperturbed (A=0) Hamiltonian. The derived theory is applied to the relativistic calculation of nuclear magnetic shielding tensors of HX (X=F,Cl,Br,I) systems at the Hartree-Fock level. The results indicate that such a substantially exact decoupling calculation well reproduces the four-component Dirac-Hartree-Fock results.

Calculations of frequency-dependent molecular magnetizabilities with quasi-relativistic time-dependent generalized unrestricted Hartree–Fock method

The time-dependent generalized unrestricted Hartree-Fock (TDGUHF) method combined with a two-component quasi-relativistic Hamiltonian generated from the Douglas-Kroll-Hess (DKH) transformation was developed to calculate frequency-dependent molecular magnetizabilities, which are the linear response quantity of a molecule to an external magnetic field. By calculating the magnetizabilities of H(2)X (X = O, S, Se, and Te), the noble gases (He, Ne, Ar, Kr, and Xe) and small open shell molecules (CH(2), CH(3), and O(2)), we found that scalar relativistic terms affect mainly the diamagnetic magnetizability and spin-orbit (SO) interaction affects the paramagnetic magnetizability.

A Combined Experimental and Quantum Chemistry Study of Selenium Chemical Shift Tensors

A comprehensive investigation of selenium chemical shift tensors is presented. Experimentally determined chemical shift tensors were obtained from solid-state 77Se NMR spectra for several organic, organometallic, or inorganic selenium-containing compounds. The first reported indirect spin-spin coupling between selenium and chlorine is observed for Ph(2)SeCl(2) where 1J(77Se,35Cl)iso is 110 Hz. Selenium magnetic shielding tensors were calculated for all of the molecules investigated using zeroth-order regular approximation density functional theory, ZORA DFT. The computations provide the orientations of the chemical shift tensors, as well as a test of the theory for calculating the magnetic shielding interaction for heavier elements. The ZORA DFT calculations were performed with nonrelativistic, scalar relativistic, and scalar with spin-orbit relativistic levels of theory. Relativistic contributions to the magnetic shielding tensor were found to be significant for (NH4)2WSe4 and of less importance for organoselenium, organophosphine selenide, and inorganic selenium compounds containing lighter elements.

Theoretical investigation on H1 and C13 NMR chemical shifts of small alkanes and chloroalkanes

Using density functional theory (DFT) with the B3LYP, PBE, and PBE0 exchange-correlation functionals as well as the Moller-Plesset second-order perturbation theory (MP2) combined with a series of rather extended basis sets, 1H and 13C chemical shifts of small alkanes and chloroalkanes (with different numbers of chlorine atoms on specific positions) have been simulated and compared to experimental data. For the 1H chemical shifts, theory tends to reproduce experiment within the limits of the experimental errors. In the case of 13C chemical shift, the differences between theory and experiment increase monotonically with the number of chlorine atoms and exhibit a deviation from additivity. This behavior is related to the saturation of the experimental 13C chemical shifts with the number of chlorine atoms, whereas the evolution is mostly linear at both DFT and MP2 levels of approximation. This difference has been traced back to the relativistic spin-orbit coupling effects, which are exalted as a result of the enhancement of the s character of the C atom when increasing the number of linked Cl atoms. Thus, it was demonstrated that not only electron correlation but also relativistic effects have to be considered for estimating the 13C chemical shifts when several Cl atoms are directly attached to the C atom. Linear (theory/experiment) regressions have then been performed for the different types of C atoms, i.e., bearing one, two, and three Cl atoms, with excellent correlation coefficients. The linear correlation relationships so obtained can then serve to predict and facilitate the interpretation of the nuclear magnetic resonance spectra of more complex compounds. Furthermore, by investigating the basis set effects, the correlation between the chemical shifts calculated using the 6-311 + G(2d,p) basis set and the more extended 6-311 + G(2df,p) and aug-cc-pvtz basis sets is excellent, demonstrating that the choice of the 6-311 + G(2d,p) basis set for calculating the 1H and 13C chemical shifts is relevant.

Relativistic molecular orbital study of the optical and magnetic properties of hexachloro protactinate (IV): PaCl62−

Our ab initio all-electron Dirac-Fock and the corresponding nonrelativistic limit calculations performed at four Pa-Cl bond distances yield for octahedral PaCl(6) (2-) the optimized Pa-Cl bond distances of 2.758 and 2.771 Angstroms, respectively. Dirac scattered wave and its nonrelativistic limit calculations are performed at the optimized Pa-Cl bond distances using a first-order perturbation procedure to obtain the molecular g and hyperfine tensors for the octahedral anion PaCl(6) (2-). The calculated Zeeman and (231)Pa hyperfine interactions are in fairly good agreement with the electron paramagnetic resonance and electron nuclear double resonance values of the Pa(4+) impurity site in the octahedral Cs(2)ZrCl(6) lattice. The calculated relativistic transition energies of the 5f-->5f and 5f-->6d absorption bands are also in good agreement with the experimental results.

Quasirelativistic theory for the magnetic shielding constant. III. Quasirelativistic second-order Møller–Plesset perturbation theory and its application to tellurium compounds

The quasirelativistic (QR) generalized unrestricted Hartree-Fock method for the magnetic shielding constant [R. Fukuda, M. Hada, and H. Nakatsuji, J. Chem. Phys. 118, 1015 (2003); R. Fukuda, M. Hada, and H. Nakatsuji, J. Chem. Phys.118, 1027 (2003)] has been extended to include the electron correlation effect in the level of the second-order Møller-Plesset perturbation theory (MP2). We have implemented the energy gradient and finite-perturbation methods to calculate the magnetic shielding constant at the QR MP2 level and applied to the magnetic shielding constants and the NMR chemical shifts of 125Te nucleus in various tellurium compounds. The calculated magnetic shielding constants and NMR chemical shifts well reproduced the experimental values. The relations of the chemical shifts with the natures of ligands, and the tellurium oxidation states were investigated. The chemical shifts in different valence states were explained by the paramagnetic shielding and spin-orbit terms. The tellurium 5p electrons are the dominant origin of the chemical shifts in the Te I and Te II compounds and the chemical shifts were explained by the p-hole mechanism. The tellurium d electrons also play an important role in the chemical shifts of the hypervalent compounds.

Calculation of indirect nuclear spin–spin coupling constants within the regular approximation for relativistic effects

A new method for calculating the indirect nuclear spin-spin coupling constant within the regular approximation to the exact relativistic Hamiltonian is presented. The method is completely analytic in the sense that it does not employ numeric integration for the evaluation of relativistic corrections to the molecular Hamiltonian. It can be applied at the level of conventional wave function theory or density functional theory. In the latter case, both pure and hybrid density functionals can be used for the calculation of the quasirelativistic spin-spin coupling constants. The new method is used in connection with the infinite-order regular approximation with modified metric (IORAmm) to calculate the spin-spin coupling constants for molecules containing heavy elements. The importance of including exact exchange into the density functional calculations is demonstrated.