Abstract
A suite of tools for the analysis of magnetically induced currents is introduced. These are applicable to both the weak-field regime, well described by linear response perturbation theory, and to the high-field regime, which is inaccessible to such methods. A disc-based quadrature scheme is proposed for the analysis of magnetically induced current susceptibilities, providing quadratures that are consistently defined between different molecular systems and applicable to both planar 2D and general 3D molecular systems in a black-box manner. The applicability of the approach is demonstrated for a range of planar ring systems, the ground and excited states of the benzene molecule and the ring, bowl and cage isomers of the C_20 molecule in the presence of a weak magnetic field. In the presence of a strong magnetic field, the para- to dia-magnetic transition of the BH molecule is studied, demonstrating that magnetically induced currents present a visual interpretation of this phenomenon, providing insight beyond that accessible using linear-response methods.
Highlights
The analysis of magnetically-induced current susceptibilities is a well-established approach that can provide a wealth of chemical information for understanding molecular magnetic properties and interactions.[1,2,3,4,5,6,7,8]. Such current susceptibilities have been determined via a range of gauge-origin independent electronic-structure approaches. These include the individual gauge for localized orbitals (IGLO) method,[9] the continuous set of gauge transformations (CSGT) approach,[8,10,11] the continuous transformation of the gauge origin of the current density (CTOCD) method[12,13,14,15,16,17,18,19] and the use of London atomic orbitals[20,21] (LAOs), known as gauge-including atomic orbitals (GIAOs)
The magnetically induced currents can be computed by finite differences from the physical current, evaluated for a small perturbative magnetic field applied along one Cartesian axis
We use a recently constructed family of current-dependent meta-generalized-gradient approximation functionals to determine magnetically induced current susceptibilities. The use of such a non-perturbative approach allows for the determination of current densities directly as a function of magnetic field strength; this aspect is explored for the BH molecule in this work
Summary
The analysis of magnetically-induced current susceptibilities is a well-established approach that can provide a wealth of chemical information for understanding molecular magnetic properties and interactions.[1,2,3,4,5,6,7,8] Such current susceptibilities have been determined via a range of gauge-origin independent electronic-structure approaches. We use a recently constructed family of current-dependent meta-generalized-gradient approximation (mGGA) functionals to determine magnetically induced current susceptibilities The use of such a non-perturbative approach allows for the determination of current densities directly as a function of magnetic field strength; this aspect is explored for the BH molecule in this work. There are two main approaches that may be used for the analysis of currents induced in molecular systems by external magnetic fields The first of these are integration techniques which, by constructing numerical quadratures over two-dimensional planes, allow the current density to be probed in specific parts of a molecule.[21,22] Secondly, topological techniques employing concepts from vector-field analysis such as separatrices and stagnation graphs are used to analyse the induced current fields.[8,38,39,40] Both approaches can provide quantitative information on the nature of the electron delocalisation in chemical species and their interactions with external fields. We use the same modification for non-perturbative calculations in the presence of external magnetic fields
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