Magnetic shielding constants calculated by the infinite-order Douglas–Kroll–Hess method with electron-electron relativistic corrections

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.

QED Effect on the Nuclear Magnetic Shielding of ^{3}He

The leading quantum electrodynamic corrections to the nuclear magnetic shielding in one- and two-electron atomic systems are obtained in a complete form, and the shielding constants of ^{1}H, ^{3}He^{+}, and ^{3}He are calculated to be 17.735 436(3)×10^{-6}, 35.507 434(9)×10^{-6}, and 59.967 029(23)×10^{-6}, respectively. These results are orders of magnitude more accurate than previous ones, and, with the ongoing measurement of the nuclear magnetic moment of ^{3}He^{+} and planned ^{3}He^{2+}, they open the window for high-precision absolute magnetometry using ^{3}He NMR probes. The presented theoretical approach is applicable to all other light atomic and molecular systems, which facilitates the improved determination of magnetic moments of any light nuclei.

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.

Nuclear magnetic resonance parameters in Zn2, Cd2 and Hg2 dimers: relativistic calculations

The potential energy curves and the NMR properties: nuclear spin–spin coupling constants and nuclear shielding constants have been calculated for Zn2, Cd2 and Hg2 dimers using density functional theory. The calculations have been carried out using the relativistic four-component Dirac–Coulomb Hamiltonian, and, in the case of energy curves, also relativistic effective core potentials. In case of NMR parameters, the relativistic effects turned out to be critically important even for the lightest dimer, Zn2. The importance of the spin–orbit coupling depends on the internuclear distance: these effects tend to be significant for short internuclear distances.

Electron-Nucleus Hyperfine Coupling Calculated from Restricted Active Space Wavefunctions and an Exact Two-Component Hamiltonian

Exact two-component (X2C) relativistic nuclear hyperfine magnetic field operators were incorporated in X2C ab initio wavefunction calculations at the multireference restricted active space (RAS) level for calculations of nuclear hyperfine magnetic properties. Spin-orbit coupling was treated via RAS state interaction (SO-RASSI). The method was tested by calculations of electron-nucleus hyperfine coupling constants. The approach, implemented in the OpenMolcas program, overcomes a major limitation of a previous SO-RASSI implementation for hyperfine coupling that relied on nonrelativistic hyperfine operators [J. Chem. Theor. Comput. 2015, 11, 538-549] and therefore had limited applicability. Results from calculations on systems with light and heavy main group elements, transition metals, lanthanides, and one actinide complex demonstrate reasonably good agreement with experimental data, where available, as long as the active space can generate sufficient spin polarization.

Picture-change correction in relativistic density functional theory

Relativistic quantum chemical calculations are performed based on one of two physical pictures, namely the Dirac picture and the Schrödinger picture. With regard to the latter, the so-called picture-change effect (PCE) and picture-change correction (PCC) have been studied. The PCE, which is the change in the expectation value associated with the transformation, is not commonly a minor effect. The electron density, which is given by the expectation value of the density operator, is a fundamental variable in relativistic density functional theory (RDFT). Thus, performing the PCC in RDFT calculations is essential not only in terms of numerical agreement with the Dirac picture, but also from the viewpoint of fundamental theory. This paper explains theories and numerical studies of PCE and PCC in RDFT after overviewing those in properties, which involves the authors' works on the development of RDFT in the Schrödinger picture and relativistic exchange-correlation functionals based on picture-change-corrected variables.

RAQET: Large-scale two-component relativistic quantum chemistry program package

The Relativistic And Quantum Electronic Theory (RAQET) program is a new software package, which is designed for large-scale two-component relativistic quantum chemical (QC) calculations. The package includes several efficient schemes and algorithms for calculations involving large molecules which contain heavy elements in accurate relativistic formalisms. These calculations can be carried out in terms of the two-component relativistic Hamiltonian, wavefunction theory, density functional theory, core potential scheme, and evaluation of electron repulsion integrals. Furthermore, several techniques, which have frequently been used in non-relativistic QC calculations, have been customized for relativistic calculations. This article introduces the brief theories and capabilities of RAQET with several calculation examples. © 2018 Wiley Periodicals, Inc.

Relativistic and electron-correlation effects on the nuclear magnetic resonance shieldings of molecules containing tin and lead atoms

The reference values for NMR magnetic shieldings, σ(ref), are of the highest importance when theoretical analysis of chemical shifts are envisaged. The fact that the nonrelativistically valid relationship among spin-rotation constants and magnetic shieldings is not any longer valid for heavy atoms requires that the search for σ(ref) for such atoms needs new strategies to follow. We present here results of σ(ref) that were obtained by applying our own simple procedure which mixes accurate experimental chemical shifts (δ) and theoretical magnetic shieldings (σ). We calculated σ(Sn) and σ(Pb) in a family of heavy-halogen-containing molecules. We found out that σ(ref)[Sn;Sn(CH3)4] in gas phase should be close to 3864.11 ± 20.05 ppm (0.5%). For Pb atom, σ(ref)[Pb;Pb(CH3)4] should be close to 14475.1 ± 500.7 ppm. Such theoretical values correspond to calculations with the relativistic polarization propagator method, RelPPA, at the RPA level of approach. They are closer to experimental values as compared to those obtained applying few different functionals such as PBE0, B3LYP, BLYP, BP86, KT2, and KT3 of the density functional theory, DFT. We studied tin and lead shieldings of the XY(4-n)Z(n) (X = Sn, Pb; Y, Z = H, F, Cl, Br, I) and PbH(4-n)I(n) (n = 0, 1, 2, 3, 4) family of compounds with four-component functionals as implemented in the DIRAC code. For these systems results of calculations with RelPPA-RPA are more reliable than DFT ones. We argue about why those DFT functionals must be modified in order to obtain more accurate results of NMR magnetic shieldings within the relativistic regime: first, there is a dependence among both electron-correlation and relativistic effects that should be introduced in some way in the functionals; and second, the DIRAC code uses standard nonrelativistic functionals and the functionals B3LYP and PBE0 were parametrized only with data taken from light elements. It can explain why they are not able to properly introduce relativistic effects on nuclear magnetic shieldings. We finally show that in the analysis of magnetic shieldings for the family of compounds mentioned above, one must consider the newest and so-called heavy-atom effect on vicinal heavy atoms, HAVHA. Such effects are among the most important relativistic effects in these kind of compounds.

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.

Quantum-chemical analyses of aromaticity, UV spectra, and NMR chemical shifts in plumbacyclopentadienylidenes stabilized by Lewis bases

We carried out a series of zeroth-order regular approximation (ZORA)-density functional theory (DFT) and ZORA-time-dependent (TD)-DFT calculations for molecular geometries, NMR chemical shifts, nucleus-independent chemical shifts (NICS), and electronic transition energies of plumbacyclopentadienylidenes stabilized by several Lewis bases, (Ph)2 ((t) BuMe2 Si)2 C4 PbL1 L2 (L1, L2 = tetrahydrofuran, Pyridine, N-heterocyclic carbene), and their model molecules. We mainly discussed the Lewis-base effect on the aromaticity of these complexes. The NICS was used to examine the aromaticity. The NICS values showed that the aromaticity of these complexes increases when the donation from the Lewis bases to Pb becomes large. This trend seems to be reasonable when the 4n-Huckel rule is applied to the fractional π-electron number. The calculated (13)C- and (207)Pb-NMR chemical shifts and the calculated UV transition energies reasonably reproduced the experimental trends. We found a specific relationship between the (13)C-NMR chemical shifts and the transition energies. As we expected, the relativistic effect was essential to reproduce a trend not only in the (207)Pb-NMR chemical shifts and J[Pb-C] but also in the (13)C-NMR chemical shifts of carbons adjacent to the lead atom.

An efficient implementation of two-component relativistic exact-decoupling methods for large molecules

We present an efficient algorithm for one- and two-component relativistic exact-decoupling calculations. Spin-orbit coupling is thus taken into account for the evaluation of relativistically transformed (one-electron) Hamiltonian. As the relativistic decoupling transformation has to be evaluated with primitive functions, the construction of the relativistic one-electron Hamiltonian becomes the bottleneck of the whole calculation for large molecules. For the established exact-decoupling protocols, a minimal matrix operation count is established and discussed in detail. Furthermore, we apply our recently developed local DLU scheme [D. Peng and M. Reiher, J. Chem. Phys. 136, 244108 (2012)] to accelerate this step. With our new implementation two-component relativistic density functional calculations can be performed invoking the resolution-of-identity density-fitting approximation and (Abelian as well as non-Abelian) point group symmetry to accelerate both the exact-decoupling and the two-electron part. The capability of our implementation is illustrated at the example of silver clusters with up to 309 atoms, for which the cohesive energy is calculated and extrapolated to the bulk.