Origin-Independent Densities of Static and Dynamic Molecular Polarizabilities

Abstract

The notion of the electric dipole polarizability density function of atoms and molecules has been considered. The current density induced by the time derivative of the electric field of monochromatic light allows for a new definition of the electric dipole polarizability density, which is translationally invariant. This translational invariance provides the physical meaning that was lacking in previous defined polarizability densities. The new polarizability density has been implemented at the TD-DFT level of theory. The origin independence has been proven in silico to hold regardless of the basis set size. Two emblematic molecules, i.e., CO and N 2 , which in many respects display similar electric response, have been studied in detail. The substantial differences, which have been highlighted in the topology of the parallel and perpendicular polarizability density tensor components of CO and N 2 , are grossly hidden by compensation, when integration is carried out to get the molecular properties.

Electronic current densities and origin-independent property densities induced by optical fields

“…In fact, the polarizability density is identical to the current density tensor (CDT) 27 and yields a practical recipe for computations, as recently shown. 28 Much in the same way, a translationally invariant density of optical rotatory power is obtained by the trace of the CDT associated with the current density vector induced by the magnetic field carried by the plane wave. 26,29 A few compounds, presenting interesting features from the chemical point of view, have been studied here.…”

“…51,52 Full implementation details can be found in ref. 28, 29 and 38, along with a number of preliminary examples, which were presented for a few molecules for both EDPD and SRPD. One of the main features of the implementation consists of transforming transition amplitudes from the time-dependent calculation into perturbed molecular orbitals, which permits orbital decomposition of the results, which are origin-independent for both densities.…”

“…Adopting the same notation as in previous papers, 28,29,38,39 for a molecule with n electrons and N clamped nuclei, i.e., within the Born-Oppenheimer (BO) approximation, 40 charge, mass, position, canonical and angular momentum of the k-th electron are indicated, in the configuration space, by Àe, m e , r k , p ˆk = Àih = k , l ˆk = r k  p ˆk, k = 1, 2. . .n.…”

“…So far, we have studied a series of atoms and simple molecules in terms of static and dynamic electric dipole polarizability density 28 and in terms of electric dipole polarization current density. 38 What emerged can be summarized as follows: (i) despite an always positive polarizability in the transparent region far from absorption, the dipole moment density ( 18) is found counter-oriented with respect to the induced electric field in regions close to the nuclei of a molecule, with the exception of He and H atoms, as for example, in H 2 , LiH, and BeH 2 ; (ii) in terms of current induced by time derivative of the electric field, these regions of counter-polarization correspond to the inner portion of toroidal currents, which are found ubiquitous in the proximity of all the nuclei in a molecule, except hydrogen, for any orientation of the inducing field; and (iii) quite obviously, the higher the electron density, the higher is the polarizability density.…”

“…In fact, the polarizability density is identical to the current density tensor (CDT) 27 and yields a practical recipe for computations, as recently shown. 28…”