Abstract
Computational procedures, based on (i) the Ramsey common origin approach and (ii) the continuous transformation of the origin of the quantum mechanical current density-diamagnetic zero (CTOCD-DZ), were applied at the Hartree-Fock level to determine electric quadrupole polarizabilities of nuclear magnetic shielding for molecules in the presence of a nonuniform electric field with a uniform gradient. The quadrupole polarizabilities depend on the origin of the coordinate system, but values of the magnetic field induced at a reference nucleus, determined via the CTOCD-DZ approach, are origin independent for any calculations relying on the algebraic approximation, irrespective of size and quality of the (gaugeless) basis set employed. On the other hand, theoretical estimates of the induced magnetic field obtained by single-origin methods are translationally invariant only in the limit of complete basis sets. Calculations of electric quadrupole polarizabilities of nuclear magnetic shielding are reported for H(2), HF, H(2)O, NH(3), and CH(4) molecules.
Highlights
Contributions to nuclear magnetic shielding arising from molecular response to two perturbations, an external magnetic field and a nonuniform electric field, have been discussed in a few papers
Theoretical procedures have been developed to estimate chemical shifts caused by a uniform EFG on nuclear magnetic shielding,[38,39] allowing for the conventional common originCOapproach[40–42] and for a computational scheme formally based on a continuous transformation of the origin of the current density setting the diamagnetic contribution to zeroCTOCD-DZ.[43,44]
Some numerical tests have been made to investigate how the predictions for ␣I ,␥␦ depend on the quality of the gaugeless basis sets employed, i.e., the aug-cc-pCVDZ, aug-ccpCVTZ, and aug-cc-pCVQZ from Refs. 49 and 50 referred to as I–III, respectively, for NH3 and CH4
Summary
The effects of a time-independent, spatially uniform electric field on molecular magnetic properties described by second-rank tensors, e.g., magnetic susceptibility1 ␣ and magnetic shielding2 ␣I  of the Ith nucleus, can be studied in terms of third-rank tensors referred to as the correspondingelectric dipolepolarizabilities,[3] e.g., ␣,␥.4 Shielding dipole polarizabilities, or hypershieldings, have been widely investigated[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23] and review articles are available.[24–29]When a polar molecule is dissolved, it polarizes the surrounding medium, giving rise to an electric field—a “reaction field”—at the solute.[30,31] Buckingham proposed to calculate this field via the Onsager model.[3]. Contributions to nuclear magnetic shielding arising from molecular response to two perturbations, an external magnetic field and a nonuniform electric field, have been discussed in a few papers.
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