Relativistic theory of nuclear magnetic resonance parameters in a Gaussian basis representation
Abstract
The calculation of NMR parameters from relativistic quantum theory in a Gaussian basis expansion requires some care. While in the absence of a magnetic field the expansion in a kinetically balanced basis converges for the wave function in the mean and for the energy with any desired accuracy, this is not necessarily the case for magnetic properties. The results for the magnetizability or the nuclear magnetic shielding are not even correct in the nonrelativistic limit (nrl) if one expands the original Dirac equation in a kinetically balanced Gaussian basis. This defect disappears if one starts from the unitary transformed Dirac equation as suggested by Kutzelnigg [Phys. Rev. A 67, 032109 (2003)]. However, a new difficulty can arise instead if one applies the transformation in the presence of the magnetic field of a point nucleus. If one decomposes certain contributions, the individual terms may diverge, although their sum is regular. A controlled cancellation may become difficult and numerical instabilities can arise. Various ways exist to avoid these singularities and at the same time get the correct nrl. There are essentially three approaches intermediate between the transformed and the untransformed formulation, namely, the bispinor decomposition, the decomposition of the lower component, andmore »
 Authors:
 Lehrstuhl fuer Theoretische Chemie, RuhrUniversitaet Bochum, D44780 Bochum (Germany)
 Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871 (China)
 Publication Date:
 OSTI Identifier:
 21559745
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 131; Journal Issue: 4; Other Information: DOI: 10.1063/1.3185400; (c) 2009 American Institute of Physics
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE; ACCURACY; DECOMPOSITION; DEFECTS; DIRAC EQUATION; EXPANSION; GAUSSIAN PROCESSES; MAGNETIC BALANCES; MAGNETIC FIELDS; MAGNETIC PROPERTIES; MAGNETIC SHIELDING; MAGNETIZATION; NUCLEAR MAGNETIC RESONANCE; NUCLEAR SCREENING; NUMERICAL ANALYSIS; QUANTUM MECHANICS; RELATIVISTIC RANGE; SINGULARITY; TRANSFORMATIONS; WAVE FUNCTIONS; CHEMICAL REACTIONS; DIFFERENTIAL EQUATIONS; ENERGY RANGE; EQUATIONS; FIELD EQUATIONS; FUNCTIONS; MAGNETIC RESONANCE; MATHEMATICS; MEASURING INSTRUMENTS; MECHANICS; PARTIAL DIFFERENTIAL EQUATIONS; PHYSICAL PROPERTIES; RESONANCE; SHIELDING; WAVE EQUATIONS
Citation Formats
Kutzelnigg, Werner, and Liu Wenjian. Relativistic theory of nuclear magnetic resonance parameters in a Gaussian basis representation. United States: N. p., 2009.
Web. doi:10.1063/1.3185400.
Kutzelnigg, Werner, & Liu Wenjian. Relativistic theory of nuclear magnetic resonance parameters in a Gaussian basis representation. United States. doi:10.1063/1.3185400.
Kutzelnigg, Werner, and Liu Wenjian. 2009.
"Relativistic theory of nuclear magnetic resonance parameters in a Gaussian basis representation". United States.
doi:10.1063/1.3185400.
@article{osti_21559745,
title = {Relativistic theory of nuclear magnetic resonance parameters in a Gaussian basis representation},
author = {Kutzelnigg, Werner and Liu Wenjian},
abstractNote = {The calculation of NMR parameters from relativistic quantum theory in a Gaussian basis expansion requires some care. While in the absence of a magnetic field the expansion in a kinetically balanced basis converges for the wave function in the mean and for the energy with any desired accuracy, this is not necessarily the case for magnetic properties. The results for the magnetizability or the nuclear magnetic shielding are not even correct in the nonrelativistic limit (nrl) if one expands the original Dirac equation in a kinetically balanced Gaussian basis. This defect disappears if one starts from the unitary transformed Dirac equation as suggested by Kutzelnigg [Phys. Rev. A 67, 032109 (2003)]. However, a new difficulty can arise instead if one applies the transformation in the presence of the magnetic field of a point nucleus. If one decomposes certain contributions, the individual terms may diverge, although their sum is regular. A controlled cancellation may become difficult and numerical instabilities can arise. Various ways exist to avoid these singularities and at the same time get the correct nrl. There are essentially three approaches intermediate between the transformed and the untransformed formulation, namely, the bispinor decomposition, the decomposition of the lower component, and the hybrid unitary transformation partially at operator and partially at matrix level. All three possibilities were first considered by Xiao et al. [J. Chem. Phys. 126, 214101 (2007)] in a different context and in a different nomenclature. Their analysis and classification in a more general context are given here for the first time. Use of an extended balanced basis has no advantages and has other drawbacks and is not competitive, while the use of a restricted magnetic balance basis can be justified.},
doi = {10.1063/1.3185400},
journal = {Journal of Chemical Physics},
number = 4,
volume = 131,
place = {United States},
year = 2009,
month = 7
}

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