Electronic orbital response to static magnetic fields. II. A general theoretical method

As a part of an ongoing project devoted to the development of theoretical foundations and computational methods for treating systems in external electro-magnetic fields, we present a new method here for dealing with magnetic fields of arbitrary strength and for arbitrary systems. The method is based on leaving the commonly used Coulomb gauge and instead introducing an operator gauge. We show that this method avoids the obstacles related with using the Coulomb gauge in combination with GIAOs (gauge-invariant atomic orbitals) as basis functions, i.e., complicated matrix elements and oscillatory behavior for non-magnetic terms. Moreover, our approach shares many features with the “Modern Theory of Magnetization,” which is based on the operator, ∇⃗k. However, our approach is not restricted to periodic systems and avoids many complications involved in the application of ∇⃗k. Our method is applicable for any system and field strength, and it readily provides an answer to the question of whether there is a surface/shape contribution to intensive magnetic responses for large systems. Test calculations on H2+ using a homemade ab initio program developed for small systems, and a simplified model for large systems, give mutually consistent and complementary results in support of our suggested approach, but not in complete agreement with results of GIAO calculations. We present a detailed analysis of this finding.