Juha Vaara

Theory and computation of nuclear magnetic resonance parameters

The art of quantum chemical electronic structure calculation has over the last 15 years reached a point where systematic computational studies of magnetic response properties have become a routine procedure for molecular systems. One of their most prominent areas of application are the spectral parameters of nuclear magnetic resonance (NMR) spectroscopy, due to the immense importance of this experimental method in many scientific disciplines. This article attempts to give an overview on the theory and state-of-the-art of the practical computations in the field, in terms of the size of systems that can be treated, the accuracy that can be expected, and the various factors that would influence the agreement of even the most accurate imaginable electronic structure calculation with experiment. These factors include relativistic effects, thermal effects, as well as solvation/environmental influences, where my group has been active. The dependence of the NMR spectra on external magnetic and optical fields is also briefly touched on.

Perturbational ab initio calculations of relativistic contributions to nuclear magnetic resonance shielding tensors

We present perturbational ab initio calculations of the leading-order one-electron relativistic contributions to the nuclear magnetic resonance shielding tensor based on the Pauli Hamiltonian. The scalar relativistic and spin–orbit interaction effects, including both relativistic corrections to the wave function (“passive” relativistic effects) and relativistic magnetic perturbation operators (“active” effects), are considered for H2X (X=O, S, Se, Te, Po), HX (X=F, Cl, Br, I, At), and noble gas (Ne, Ar, Kr, Xe, Rn) systems. The perturbational corrections are calculated using linear and quadratic response theory applied to nonrelativistic reference states. We use the uncorrelated self-consistent field as well as correlated, multiconfigurational complete active space self-consistent field models. Results for the 1H and heavy-atom shielding constants and anisotropies are compared with Dirac–Hartree–Fock and quasirelativistic data.

Leading-order relativistic effects on nuclear magnetic resonance shielding tensors

We present perturbational ab initio calculations of the nuclear-spin-dependent relativistic corrections to the nuclear magnetic resonance shielding tensors that constitute, together with the other relativistic terms reported by us earlier, the full leading-order perturbational set of results for the one-electron relativistic contributions to this observable, based on the (Breit-)Pauli Hamiltonian. These contributions are considered for the H(2)X (X = O,S,Se,Te,Po) and HX (X = F,Cl,Br,I,At) molecules, as well as the noble gas (Ne, Ar, Kr, Xe, Rn) atoms. The corrections are evaluated using the relativistic and magnetic operators as perturbations on an equal footing, calculated using analytical linear and quadratic response theory applied on top of a nonrelativistic reference state provided by self-consistent field calculations. The (1)H and heavy-atom nuclear magnetic shielding tensors are compared with four component, nearly basis-set-limit Dirac-Hartree-Fock calculations that include positronic excitations, as well as available literature data. Besides the easy interpretability of the different contributions in terms of familiar nonrelativistic concepts, the accuracy of the present perturbational scheme is striking for the isotropic part of the shielding tensor, for systems including elements up to Xe.

Rovibrational effects, temperature dependence, and isotope effects on the nuclear shielding tensors of water: A new 17O absolute shielding scale

We calculate the rovibrational corrections, temperature dependence and isotope shifts of the isotropic and anisotropic nuclear shieldings of the water molecule. This is the first correlated study of rovibrational effects on the nuclear shieldings in the water molecule and the first study of these effects on the shielding anisotropies. The use of a large restricted active space self-consistent field wave function and a large basis set ensures that the results are of high accuracy. The rovibrational corrections are found to be substantial, 3.7% and 1.8% for the isotropic oxygen and hydrogen shieldings, respectively, in the 1H217O isotopomer at 300 K. For the shielding anisotropies and asymmetry parameters, the corresponding relative corrections are even larger. The changes in the shielding tensors due to molecular rotation and vibration are of the same order of magnitude as—and in some cases even exceed—the changes due to electron correlation. The accuracy of our calculated rovibrationally corrected oxygen ...

Relativistic, nearly basis-set-limit nuclear magnetic shielding constants of the rare gases He–Rn: A way to absolute nuclear magnetic resonance shielding scales

Relativistic four-component ab initio calculations using the Dirac–Coulomb Hamiltonian and converged, very large Gaussian one-particle basis sets are carried out for the nuclear magnetic shielding constants of rare gas atoms He–Rn in their ground state. A discrepancy between two earlier sets of theoretical results for He–Xe is attributed to the basis. Absolute nuclear magnetic resonance shielding scales for the investigated elements are established because electron correlation effects are negligible in this case. Future atomic-beam experiments are discussed.

Quadratic response calculations of the electronic spin-orbit contribution to nuclear shielding tensors

The electronic spin-orbit contribution to nuclear magnetic shielding tensors, which causes the heavy-atom chemical shift of the shielding of light nuclei in the vicinity of heavy elements, is calculated as a sum of analytical quadratic response functions. We include both the one- and two-electron parts of the spin-orbit Hamiltonian and consider the interaction with both the Fermi contact and the spin-dipolar mechanisms. Ab initio calculations at the SCF and MCSCF levels are presented for the 1H and 13C shielding tensors in the hydrogen and methyl halides. The applicability of different approximations to the full spin-orbit correction is discussed, and the calculated results are compared with experimental data, where available.

Second- and third-order spin-orbit contributions to nuclear shielding tensors

We present analytical calculations of the electronic spin–orbit interaction contribution to nuclear magnetic shielding tensors using linear and quadratic response theory. The effects of the Fermi contact and the spin-dipole interactions with both the one- and two-electron spin–orbit Hamiltonians, included as first-order perturbations, are studied for the H2X (X=O, S, Se, and Te), HX (X=F, Cl, Br, and I), and CH3X (X=F, Cl, Br, and I) systems using nonrelativistic multiconfiguration self-consistent field reference states. We also present the first correlated study of the spin–orbit-induced contributions to shielding tensors arising from the magnetic field dependence of the spin–orbit Hamiltonian. While the terms usually considered are formally calculated using third-order perturbation theory, the magnetic-field dependent spin-orbit Hamiltonian requires a second-order calculation only. For the hydrogen chalcogenides, we show that contributions often neglected in studies of spin–orbit effects on nuclear shie...

Relativistic spin-orbit effects on hyperfine coupling tensors by density-functional theory

A second-order perturbation theory treatment of spin-orbit corrections to hyperfine coupling tensors has been implemented within a density-functional framework. The method uses the all-electron atomic mean-field approximation and/or spin-orbit pseudopotentials in incorporating one- and two-electron spin-orbit interaction within a first-principles framework. Validation of the approach on a set of main-group radicals and transition metal complexes indicates good agreement between all-electron and pseudopotential results for hyperfine coupling constants of the lighter nuclei in the system, except for cases in which scalar relativistic effects become important. The nonrelativistic Fermi contact part of the isotropic hyperfine coupling constants is not always accurately reproduced by the exchange-correlation functionals employed, particularly for the triplet and pi-type doublet radicals in the present work. For this reason, ab initio coupled-cluster singles and doubles with perturbative triples results for the first-order contributions have been combined in the validation calculations with the density-functional results for the second-order spin-orbit contributions. In the cases where spin-orbit corrections are of significant magnitude relative to the nonrelativistic first-order terms, they improve the agreement with experiment. Antisymmetric contributions to the hyperfine tensor arise from the spin-orbit contributions and are discussed for the IO2 radical, whereas rovibrational effects have been evaluated for RhC, NBr, and NI.

Spin–spin coupling tensors by density-functional linear response theory

Density-functional theory (DFT) calculations of indirect nuclear magnetic resonance spin–spin coupling tensors J, with the anisotropic but symmetric parts being the particular concern, are carried out for a series of molecules with the linear response (LR) method. For the first time, the anisotropic components of J are reported for a hybrid functional. Spin–spin tensors calculated using the local density approximation (LDA), the gradient-corrected Becke–Lee–Yang–Parr (BLYP) functional, and the hybrid three-parameter BLYP (B3LYP) functional are compared with previous ab initio multiconfiguration self-consistent-field (MCSCF) LR results and experimental data. In general, the B3LYP functional provides reasonable accuracy not only for the isotropic coupling constants but also for the anisotropic components of J, with the results improving in the sequence LDA→BLYP→B3LYP. Error cancellation often improves the total DFT spin–spin coupling when the magnitude of the paramagnetic spin–orbit contribution is overesti...

Calculations of nuclear magnetic shielding in paramagnetic molecules

We propose and evaluate first principles methods for calculating the nuclear shielding tensor in open-shell, paramagnetic molecules, dealing with the case of small spin–orbit coupling that, in turn, implies the best applicability to light, organic compounds. The formalism is consistent up to second order in the fine structure constant, and includes orbital, fully anisotropic dipolar, and isotropic contact contributions to the tensor. The proposed method is implemented within the ab initio single- and multiconfiguration self-consistent field as well as density functional theory frameworks. The applications include small main-group radicals and larger nitroxide radicals. The analysis of the results and comparison with the experimental nuclear magnetic resonance data, which are available for the latter compounds, indicate promising accuracy and applicability of the density functional theory method to chemically interesting problems.