Abstract
Stagnation graphs provide a useful tool to analyze the main topological features of the often complicated vector field associated with magnetically induced currents. Previously, these graphs have been constructed using response quantities appropriate for modest applied magnetic fields. We present an implementation capable of producing these graphs in arbitrarily strong magnetic fields, using current-density-functional theory. This enables us to study how the topology of the current vector field changes with the strength and orientation of the applied magnetic field. Applications to CH4, C2H2 and C2H4 are presented. In each case, we consider molecular geometries optimized in the presence of the magnetic field. The stagnation graphs reveal subtle changes to this vector field where the symmetry of the molecule remains constant. However, when the electronic state and symmetry of the corresponding equilibrium geometry changes with increasing field strength, the changes to the stagnation graph are extensive. We expect that the approach presented here will be helpful in interpreting changes in molecular structure and bonding in the strong-field regime.
Highlights
An essential requirement is to ensure gauge–origin independence of the calculated currents; this has been achieved by a range of methods including: the individual gauge for localized orbitals (IGLO) method [24], the continuous set of gauge transformations (CSGT)
To test the efficiency of this new implementation and investigate how the current vector field topology and associated stagnation graph changes in the presence of strong magnetic fields, we study three small molecules: CH4, C2 H2 and C2 H4
The prefix u- indicates that the basis set is used in its uncontracted form; uncontracted basis sets are used to provide greater flexibility to describe the response of the wavefunction to the magnetic field
Summary
The topology and properties of magnetically induced currents have been widely studied using linear response techniques [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] and a number of programs have been developed to both calculate the induced currents and analyze their main features [18,20,21,22,23].An essential requirement is to ensure gauge–origin independence of the calculated currents; this has been achieved by a range of methods including: the individual gauge for localized orbitals (IGLO) method [24], the continuous set of gauge transformations (CSGT)approach [6,25,26], the continuous transformation of the gauge origin of the current density (CTOCD) method [8,10,14,15,27,28,29,30] and using London atomic orbitals (LAOs) [18,31] ( known as gauge-including atomic orbitals (GIAOs)). The physical current density is a rich source of chemical information [21,26,32,33,34,35,36,37]; its topology reflects the chemical structure of the molecule and its interaction with the applied magnetic field. The magnetically induced currents can be directly related to magnetic response properties via the induced current susceptibility, a tensor describing the derivative of the induced current with respect to the applied magnetic field. Evaluating this response quantity at a zero magnetic field and using the Biot-Savart law leads directly to magnetic susceptibilities and NMR shielding constants. Ring-current models have long been used to rationalize
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