Nuclear Spin-rotation Tensors Research Articles

A relativistic relationship between parity-violating nuclear spin-rotation tensors and parity-violating NMR shielding tensors.

The nuclear-spin-dependent parity-violation contributions to the nuclear magnetic resonance shielding and nuclear spin-rotation tensors (σPV and MPV, respectively) are known to be formally related to one another in the non-relativistic regime. In this work, the polarization propagator formalism and the linear response within the elimination of small components model are used to show a new and more general relationship between them, which is valid within the relativistic framework. The full set of the zeroth- and first-order relativistic contributions to σPV and MPV are also given here for the first time, and these results are compared with previous findings. According to four-component relativistic calculations, the electronic spin-orbit effects are the most significant ones for the isotropic values of σPV and MPV in the H2X2 series of molecules (with X = O, S, Se, Te, and Po). When only scalar relativistic effects are taken into account, the non-relativistic relationship between σPV and MPV does hold. However, when the spin-orbit effects are taken into consideration, this old non-relativistic relationship breaks down, and therefore, the new one must be considered.

Relativistic study of parity-violating nuclear spin-rotation tensors.

We present a four-component relativistic approach to describe the effects of the nuclear spin-dependent parity-violating (PV) weak nuclear forces on nuclear spin-rotation (NSR) tensors. The formalism is derived within the four-component polarization propagator theory based on the Dirac-Coulomb Hamiltonian. Such calculations are important for planning and interpretation of possible future experiments aimed at stringent tests of the standard model through the observation of PV effects in NSR spectroscopy. An exploratory application of this theory to the chiral molecules H2X2 (X = 17O, 33S, 77Se, 125Te, and 209Po) illustrates the dramatic effect of relativity on these contributions. In particular, spin-free and spin-orbit effects are even of opposite signs for some dihedral angles, and the latter fully dominate for the heavier nuclei. Relativistic four-component calculations of isotropic nuclear spin-rotation constants, including parity-violating electroweak interactions, give frequency differences of up to 4.2 mHz between the H2Po2 enantiomers; on the nonrelativistic level of theory, this energy difference is 0.1 mHz only.

Relativistic theory of nuclear spin-rotation tensor with kinetically balanced rotational London orbitals.

Both kinetically balanced (KB) and kinetically unbalanced (KU) rotational London orbitals (RLO) are proposed to resolve the slow basis set convergence in relativistic calculations of nuclear spin-rotation (NSR) coupling tensors of molecules containing heavy elements [Y. Xiao and W. Liu, J. Chem. Phys. 138, 134104 (2013)]. While they perform rather similarly, the KB-RLO Ansatz is clearly preferred as it ensures the correct nonrelativistic limit even with a finite basis. Moreover, it gives rise to the same "direct relativistic mapping" between nuclear magnetic resonance shielding and NSR coupling tensors as that without using the London orbitals [Y. Xiao, Y. Zhang, and W. Liu, J. Chem. Theory Comput. 10, 600 (2014)].

Breit interaction effects in relativistic theory of the nuclear spin-rotation tensor

In this work, relativistic effects on the nuclear spin-rotation (SR) tensor originated in the electron-nucleus and electron-electron Breit interactions are analysed. To this end, four-component numerical calculations were carried out in model systems HX (X=H,F,Cl,Br,I). The electron-nucleus Breit interaction couples the electrons and nuclei dynamics giving rise to a purely relativistic contribution to the SR tensor. Its leading order in 1/c is of the same value as that of relativistic corrections on the usual second order expression of the SR tensor considered in previous work [I. A. Aucar, S. S. Gómez, J. I. Melo, C. G. Giribet, and M. C. Ruiz de Azúa, J. Chem. Phys. 138, 134107 (2013)], and therefore it is absolutely necessary to establish its relative importance. For the sake of completeness, the corresponding effect originating in the electron-electron Breit interaction is also considered. It is verified that in all cases these Breit interactions yield only very small corrections to the SR tensors of both the X and H nuclei in the present series of compounds. Results of the present work strongly suggest that in order to achieve experimental accuracy in the theoretical study of the SR tensor both electron-nucleus and electron-electron Breit effects can be safely neglected.

Body-fixed relativistic molecular Hamiltonian and its application to nuclear spin-rotation tensor: Linear molecules

The relativistic molecular Hamiltonian written in the body-fixed frame of reference is the basis for high-precision calculations of spectroscopic parameters involving nuclear vibrations and/or rotations. Such a Hamiltonian that describes electrons fully relativistically and nuclei quasi-relativistically is just developed for semi-rigid nonlinear molecules [Y. Xiao and W. Liu, J. Chem. Phys. 138, 134104 (2013)]. Yet, the formulation should somewhat be revised for linear molecules thanks to some unusual features arising from the redundancy of the rotation around the molecular axis. Nonetheless, the resulting isomorphic Hamiltonian is rather similar to that for nonlinear molecules. Consequently, the relativistic formulation of nuclear spin-rotation (NSR) tensor for linear molecules is very much the same as that for nonlinear molecules. So is the relativistic mapping between experimental NSR and NMR.

Body-fixed relativistic molecular Hamiltonian and its application to nuclear spin-rotation tensor

A relativistic molecular Hamiltonian that describes electrons fully relativistically and nuclei quasi-relativistically is proposed and transformed from the laboratory to the body-fixed frame of reference. As a first application of the resulting body-fixed relativistic molecular Hamiltonian, the long anticipated relativistic theory of nuclear spin-rotation (NSR) tensor is formulated rigorously. A "relativistic mapping" between experimental NSR and NMR is further proposed, which is of great value in establishing high-precision absolute NMR shielding scales.

Microwave Spectroscopy and Nuclear Magnetic Resonance Spectroscopy — What Is the Connection?

AbstractFor Abstract see ChemInform Abstract in Full Text.

Microwave spectroscopy and nuclear magnetic resonance spectroscopy--what is the connection?

The history and development of microwave spectroscopy and nuclear magnetic resonance (NMR) spectroscopy have much in common. In this Account, we discuss the less widely appreciated connections between the parameters measured using the two techniques. Selected examples from our laboratory and from the recent literature attest to the utility and importance of these connections. For example, how are nuclear spin-rotation tensors and NMR chemical shifts related? Why should chemists be interested in absolute magnetic shielding scales? What can chemists learn about trends in spin-spin coupling constants from the hyperfine parameters measured in microwave and molecular beam experiments? The increasingly important role of quantum-chemical calculations in the interpretation of the microwave and NMR data is also highlighted.

Ab Initio Calculations of NMR Parameters for Diatomic Molecules. An Exercise in Computational Chemistry

Many scientists seem to be unaware of the relatively simple relationship between nuclear spin-rotation tensors, C, and nuclear magnetic shielding tensors, σ, in linear molecules. The availability of accurate spin-rotation data from high-resolution microwave spectra or molecular beam experiments allows for meaningful comparison between nuclear magnetic shieldings derived from these experimental values and values determined from ab initio calculations, because both results are for isolated molecules. Presented here is an undergraduate-graduate-level exercise in the computational quantum chemistry of NMR parameters for a series of fluorine-containing diatomic molecules for which experimental spin-rotation data are available. Calculations carried out at the RHF/6-311++G(2d,2p) level demonstrate the relationship between Ramsey's paramagnetic term, σP, and C. In addition, electric field gradient calculations at this level of theory for Li, Na, K, and Cl in their fluorides qualitatively reproduce experimental ...

The microwave spectrum of an unstable molecule, HPO

The HPO molecule was identified by its microwave spectrum in the reaction of PH3 with microwave discharge products of an H2/O2 mixture; the a-type R branch transitions of J=1 ← 0 up to 4 ← 3 were observed in the frequency region of 40 to 162 GHz. High- K lines showed small splittings due to the phosphorus nuclear spin-rotation interaction. In addition to the rotational and centrifugal distortion constants, the observed spectrum yielded the nuclear spin-rotation tensor, the aa component which is −1.12 (37) MHz with 2.5 standard errors in parentheses. This large interaction is discussed in terms of second-order perturbation theory.