Calculations of the magnetic shielding constants of heavy nuclei in polyatomic molecules

Abstract

AbstractsCoupled Hartree-Fock perturbation theory has been applied to compute the nuclear magnetic shielding tensors for "0, 14N, and 13C in the molecules of water, ammonia, and methane with four wave functions of increasing accuracy, expanded over basis sets of Gaussian functions. The agreement with the experimental data available for ammonia and methane is very good. Quantities necessary to evaluate the shielding for an arbitrary gauge are also given. The degree of gauge-invariance of the calculated properties is not satisfactory in the case of ammonia, while better results are found for water. Storungstheorie von gekoppeltem Hartree-Fock-Typ ist zur Berechnung der kernmagnetischen Abschirmungstensoren fur 1 7 0 , 14N, und I3C in den Wasser-, Ammoniak-und Methanmolekulen mittels vier in Gaussorbitalen ausgedriickten Wellenfunktionen mit wachsender Genauigkeit benutzt worden. Die Ubereinstimmung mit den zuganglichen Experimentaldaten fur Ammoniak und Methan ist sehr gut. Grossen die fur die Berechnungder Abschirmung fur einen willkiirlichen Eich notwendig sind, werden auch gegeben. Der Grad von Eichinvarianz der berechneten Eigenschaften ist im Ammoniakfall nicht befriedigend, wohingegen bessere Resultate fur Wasser erhalten werden. La theorie des perturbations de type

On the existence of a natural common gauge-origin for the calculation of magnetic properties of atoms and molecules via gaugeless basis sets

“…1 Their analysis is revised and completed hereafter, relying on the van Vleck 2 and Ramsey approaches 3-5 based on Rayleigh-Schrödinger perturbation theory (RSPT), and allowing for the results obtained by Arrighini, Maestro, and Moccia (AMM), 6-8 extended later on. [9][10][11][12][13][14][15] We confute the conclusions arrived at in Ref. 1 arguing that the point of view, shared by Kutzelnigg, Fleischer, and Schindler (KFS), 16 that the natural gauge origin coincides with the nucleus is correct, and that the criticism of Malkina et al 1 is partially inappropriate.…”

“…[9][10][11][12][13][14][15] For a molecule with n electrons and N nuclei, charge, mass, position with respect to an arbitrary origin, canonical, and angular momentum of the ith electron are indicated by −e, m e , r i ,p i , l i = r i ×p i , i = 1, 2. . .…”

“…Within the Ramsey formulation, 3-5 the diamagnetic contribution to nuclear shielding, for a closed-shell atom or molecule in the singlet electronic reference state | (0) a ≡ |a , is evaluated in a reference frame with origin r as the expectation value [7][8][9][10][11][12][13][14][15] …”

“…the paramagnetic contributions to nuclear magnetic shielding [3][4][5] can be denoted by [7][8][9][10][11][12][13][14][15] …”

“…(3) and (12), are invariant for exact [7][8][9][10][11][12][13][14][15] and optimal variational eigenfunctions. 17 Gauge invariance is related to charge-current conservation, 17, 20, 21 as can immediately be seen from relationship (12).…”