On the computation of frequency‐dependent molecular magnetizabilities via dynamical charge and current electron densities

Abstract

In the computation of molecular dynamic magnetizabilities and magnetic dipole moments, three different reference points are required: (i) origin of coordinate system, (ii) origin of vector potential A, and (iii) origin of multipole expansion. This study shows that methods relying on continuous translation of origin of the current density bold-italicIbold-italicBbold-italicrωt induced by optical magnetic fields provide an effective solution to the problem of choices (i) and (ii), in that they yield origin independent bold-italicIbold-italicB within the algebraic approximation, for any basis set. Frequency‐dependent magnetizabilities are also invariant with respect to (iii), as a consequence of symmetry, for a number of molecular point groups. In molecules of lower symmetries, computed magnetizabilities depend on origin of the multipole expansion. Large basis set computations carried out for water, ammonia, methane, ethane, ethylene, boranylborane, and hydroxilamine, at the DFT level, have been reported to document these statements. A comparison is made for results obtained within the conventional common origin approach for static magnetic field. Sum rules for invariance of computed properties are discussed. Representations of streamlines and stagnation graphs of dynamical current density vector field induced in the water molecule by monochromatic waves of four frequencies are displayed.

Origin-Independent Dynamic Polarizability Density from Coupled Cluster Response Theory

“…where α βα (R,P) (ω) is the frequency-dependent electric dipole polarizability in mixed dipole length-dipole velocity formalism. For a complete derivation of the expressions here reported, see ref 45 and the Supporting Information attached. α βα (R,P) (ω) is identical to eq 14 if the off-diagonal hypervirial relationship 46,47…”

“…The translationally invariant CDT defined via eq 18 can be interpreted as a polarizability density function, 32 alternative to—and, from the physical viewpoint, more meaningful than—the widely adopted expression in eq 13 , since where α βα ( R , P ) (ω) is the frequency-dependent electric dipole polarizability in mixed dipole length-dipole velocity formalism. For a complete derivation of the expressions here reported, see ref ( 45 ) and the Supporting Information attached. α βα ( R , P ) (ω) is identical to eq 14 if the off-diagonal hypervirial relationship 46 , 47 is satisfied.…”