Related Experiment Video
Updated: Feb 12, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Gauge-origin independent formalism of two-component relativistic framework based on unitary transformation in nuclear
Masao Hayami1, Junji Seino2, Hiromi Nakai1
1Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo 169-8555, Japan.
Abstract:
This article proposes a gauge-origin independent formalism of the nuclear magnetic shielding constant in the two-component relativistic framework based on the unitary transformation. The proposed scheme introduces the gauge factor and the unitary transformation into the atomic orbitals. The two-component relativistic equation is formulated by block-diagonalizing the Dirac Hamiltonian together with gauge factors. This formulation is available for arbitrary relativistic unitary transformations. Then, the infinite-order Douglas-Kroll-Hess (IODKH) transformation is applied to the present formulation. Next, the analytical derivatives of the IODKH Hamiltonian for the evaluation of the nuclear magnetic shielding constant are derived. Results obtained from the numerical assessments demonstrate that the present formulation removes the gauge-origin dependence completely. Furthermore, the formulation with the IODKH transformation gives results that are close to those in four-component and other two-component relativistic schemes.
More Related Videos
Related Concept Videos
Formal Charges
Atomic Radii and Effective Nuclear Charge
Atomic Nuclei: Nuclear Magnetic Moment
Non-nuclear Inheritance
Nuclear Magnetic Resonance (NMR): Overview
NMR spectroscopy generates a spectrum where the characteristic absorption frequencies of the sample are...
Nuclear Power
Nuclear Fuels
Nuclear fuel consists of a fissile isotope, such as uranium-235, which must be present in sufficient quantity to provide a...

