Olga L. Malkina

How Do Spin–Orbit-Induced Heavy-Atom Effects on NMR Chemical Shifts Function? Validation of a Simple Analogy to Spin–Spin Coupling by Density Functional Theory (DFT) Calculations on Some Iodo Compounds

Spin–orbit coupling is responsible for many heavy-atom effects on NMR chemical shifts, for example, normal halogen dependence. A simple but general model for spin–orbit-induced substituent effects has now been developed by analogy to the Fermi contact spin–spin coupling mechanism (see below). DFT calculations on some simple iodo compounds illustrate the scope and validity of the model.

The DFT route to NMR chemical shifts

An overview is given of the recent development and use of density functional methods in nuclear magnetic resonance (NMR) chemical‐shift calculations. The available density functional theory (DFT) methods are discussed, and examples for their validation and application are given. Relativistic effects are also considered, with an emphasis on spin–orbit coupling. The systems discussed range from transition‐metal complexes and clusters via biological systems and fullerenes to weakly bound van der Waals molecules. DFT results not published previously comprise spin–orbit effects on 31P chemical shifts in phosphorus halides, the orientation of the 31P‐shift tensor in Ru4(PPh)(CO)13, δ(95Mo) data, 13C and endohedral chemical shifts for fullerenes and for C60H36, as well as the shielding surface of the Ne2 molecule. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 91–105, 1999

A fully relativistic method for calculation of nuclear magnetic shielding tensors with a restricted magnetically balanced basis in the framework of the matrix Dirac-Kohn-Sham equation

A new relativistic four-component density functional approach for calculations of NMR shielding tensors has been developed and implemented. It is founded on the matrix formulation of the Dirac-Kohn-Sham (DKS) method. Initially, unperturbed equations are solved with the use of a restricted kinetically balanced basis set for the small component. The second-order coupled perturbed DKS method is then based on the use of restricted magnetically balanced basis sets for the small component. Benchmark relativistic calculations have been carried out for the (1)H and heavy-atom nuclear shielding tensors of the HX series (X=F,Cl,Br,I), where spin-orbit effects are known to be very pronounced. The restricted magnetically balanced basis set allows us to avoid additional approximations and/or strong basis set dependence which arises in some related approaches. The method provides an attractive alternative to existing approximate two-component methods with transformed Hamiltonians for relativistic calculations of chemical shifts and spin-spin coupling constants of heavy-atom systems. In particular, no picture-change effects arise in property calculations.

Calculation of spin—spin coupling constants using density functional theory

Abstract A density functional method for the calculation of spin—spin coupling constants has been developed and applied to a large set of molecules. The results for the Fermi contact contribution are strongly dependent on the exchange—correlation functional. The results for proton—proton, carbon—proton and carbon—carbon coupling constants are in good agreement with experiment but the agreement worsens from N to F. Improved results for the Fermi contact contribution will require new functionals. Nevertheless, even at the current stage, the new method represents a powerful tool for the calculation of coupling constants in large organic and biological molecules.

Calculation of electronic g-tensors for transition metal complexes using hybrid density functionals and atomic meanfield spin-orbit operators

We report the first implementation of the calculation of electronic g‐tensors by density functional methods with hybrid functionals. Spin‐orbit coupling is treated by the atomic meanfield approximation. g‐Tensors for a set of small main group radicals and for a series of ten 3d and two 4d transition metal complexes have been compared using the local density approximation (VWN functional), the generalized gradient approximation (BP86 functional), as well as B3‐type (B3PW91) and BH‐type (BHPW91) hybrid functionals. For main group radicals, the effect of exact‐exchange mixing is small. In contrast, significant differences between the various functionals arise for transition metal complexes. As has been shown previously, local and in particular gradient‐corrected functionals tend to underestimate the “paramagnetic” contributions to the g‐tensors in these cases and thereby recover only about 40–50% of the range of experimental g‐tensor components. This is improved to ca. 60% by the B3PW91 functional, which also gives slightly reduced standard deviations. The range increases to almost 100% using the half‐and‐half functional BHPW91. However, the quality of the correlation with experimental data worsens due to a significant overestimate of some intermediate g‐tensor values. The worse performance of the BHPW91 functional in these cases is accompanied by spin contamination. Although none of the functionals tested thus appears to be ideal for the treatment of electronic g‐tensors in transition metal complexes, the B3PW91 hybrid functional exhibited the overall most satisfactory performance. Apart from the validation of hybrid functionals, some aspects in the treatment of spin‐orbit contributions to the g‐tensor are discussed.

Calculations of NMR shielding constants by uncoupled density functional theory

Abstract Results are presented for NMR shielding constant calculations in the framework of uncoupled density functional theory with two different choices of the gauge origins for molecular orbitals. The calculations were carried out using a modified version of the program deMon. The approaches presented are much less time-consuming than analogous Hartree-Fock calculations. For the most part the results are in good agreement with those of the coupled Hartree-Fock IGLO (individual gauge for localized orbitals) method and with experimental data.

Spin-orbit correction to NMR shielding constants from density functional theory

A new method based on density functional theory for the calculation of spin-orbit corrections to NMR shielding constants is presented. This approach provides the opportunity of calculating the relativistic spin-orbit correction, based on a DFT method which incorporates correlation effects and with the use of a special choice of gauge origin. The inclusion of the one-electron spin-orbit operator brings the results for 1H chemical shifts in HF, HCl, HBr and HI and 13C chemical shifts in halogenomethanes into good agreement with experiment. The calculated one-electron spin-orbit corrections depend strongly on the basis set quality.

Fully relativistic calculations of NMR shielding tensors using restricted magnetically balanced basis and gauge including atomic orbitals

A recently developed relativistic four-component density functional method for calculation of nuclear magnetic resonance (NMR) shielding tensors using restricted magnetically balanced basis sets for the small component (mDKS-RMB) was extended to incorporate the gauge including atomic orbitals (GIAO) approach. The combined method eliminates a strong dependence of the results, calculated with a finite basis set, on the choice of the gauge origin for the magnetic potential of a uniform external magnetic field. Benchmark relativistic calculations have been carried out for xenon dimer and the HX series (X=F, Cl, Br, I), where spin-orbit effects are known to be very pronounced for hydrogen shieldings. Our results clearly demonstrate that shieldings calculated at the four-component level with a common gauge (i.e., without GIAO, IGLO, or similar methods to treat the gauge problem) depend dramatically on the choice of the common gauge. The GIAO approach solves the problem in fully relativistic calculations as it does in the nonrelativistic case.

Nuclear magnetic resonance spin-spin coupling constants from density functional theory: Problems and results

Our recently developed method for the calculation of indirect nuclear spin–spin coupling constants is studied in more detail. For the couplings between nuclei other than N, O, and F (which have lone pairs) the method yields very reliable results. The results for 1J(Si–H) couplings are presented and their dependence on the basis set quality is analyzed. Also, 2J(H–H) and 1J(X–H) couplings (X=C, Si, Ge, Sn) in XH4 molecules are presented and the relativistic effects on 1J(X–H) are discussed. The limitations of the method, which is based on density functional theory, are connected with the inability of the present LDA and GGA exchange‐correlation functionals to describe properly the spin‐perturbations (through the Fermi‐contact mechanism) on atoms to the right of the periodic table (containing lone pairs). However, the deviations from experiment of the calculated couplings for such nuclei are systematic, at least for one‐bond couplings, and therefore these calculated couplings should still be useful for NMR ...

THE HYPERFINE STRUCTURES OF SMALL RADICALS FROM DENSITY FUNCTIONAL CALCULATIONS

The isotropic and anisotropic hyperfine (hf) structures of a set of anionic, neutral and cationic radicals are investigated by means of local and nonlocal gradient‐corrected density functional theory (DFT). The molecules under study are formed by H, C, N, O, F, and Cl atoms, and the hf structures are computed at both the experimental (where present) and various DFT and CI optimized geometries. The agreement with experiment and with results from previous CI or MRCI calculations is generally very satisfactory. The anisotropic hf couplings are relatively insensitive to basis set effects and functional form, whereas the isotropic hf couplings are highly dependent on the form of the nonlocal corrections to the exchange functional, particularly for heteroatoms. Using the functional by Perdew and Wang (‘‘PW86’’), an excellent agreement with experiment is obtained for all neutral and cationic radicals, whereas for the halide containing anions somewhat elongated bond lengths, and thus less accurate hf structures, ...