Computation of Electromagnetic Properties of Molecular Ensembles

Abstract

We outline a methodology for efficiently computing the electromagnetic response of molecular ensembles. The methodology is based on the link that we establish between quantumchemical simulations and the transfer matrix (T-matrix) approach, a common tool in physics and engineering. We exemplify and analyze the accuracy of the methodology by using the time-dependent Hartree-Fock theory simulation data of a single chiral molecule to compute the T-matrix of a crosslike arrangement of four copies of the molecule, and then computing the circular dichroism of the cross. The results are in very good agreement with full quantum-mechanical calculations on the cross. Importantly, the choice of computing circular dichroism is arbitrary: Any kind of electromagnetic response of an object can be computed from its T-matrix. We also show, by means of another example, how the methodology can be used to predict experimental measurements on a molecular material of macroscopic dimensions. This is possible because, once the T-matrices of the individual components of an ensemble are known, the electromagnetic response of the ensemble can be efficiently computed. This holds for arbitrary arrangements of a large number of molecules, as well as for periodic or aperiodic molecular arrays. We identify areas of research for further improving the accuracy of the method, as well as new fundamental and technological research avenues based on the use of the T-matrices of molecules and molecular ensembles for quantifying their degrees of symmetry breaking. We provide T-matrix-based formulas for computing traditional chiro-optical properties like (oriented) circular dichroism, and also for quantifying electromagnetic duality and electromagnetic chirality. The formulas are valid for light-matter interactions of arbitrarily-high multipolar orders.

Modeling Optical Materials at the Single Scatterer Level: The Transition from Homogeneous to Heterogeneous Materials

“…In this paper, we have focused on random nanocomposites that contain nanospheres at volume fractions below because this range is experimentally accessible [ 43–49 ] and offers an unprecedented control of the magnitude and dispersion of the effective refractive index. [ 19 ] However, our approach can be readily generalized: First, to other types of scatterers, including atoms, molecules, [ 22 ] as well as nanoparticles with other shapes [ 8,29–31,65,66 ] and, second, also to other kinds of particle distributions. Specifically, both random packings [ 13,67–70 ] as well as the transition regime between ordered and disordered packings [ 71–74 ] exhibit a fascinating complexity.…”

“…This is because atoms or molecules can be treated on equal footing as nanoscopic scatterers, if their optical response is obtained from quantum mechanical simulations and captured in the notion of scattering theory. [ 22 ]…”

“…However, this does not limit the generality of our approach because both nanoparticles with other symmetries as well as atomic and molecular scatterers can be captured within the same framework. [ 8,22,29–35 ] For spherical nanoparticles with a radius of , the electric dipole polarizability can be determined using Mie theory [ 36 ] : where a 1 is the lowest order (electric dipole) Mie coefficient and is the size parameter. [ 2,37 ] By substituting this expression into Equation (1), the composite material's effective refractive index can be readily obtained from .…”

“…Finally, note that the particle sizes investigated here are only one order of magnitude larger than basic two‐atom molecules. [ 52 ] Since molecular scatterers can be modeled within the same framework, [ 22 ] this highlights that our approach will soon allow for modeling conventional optical bulk materials at the molecular level. Note that, as opposed to our approach of modeling materials in the bulk regime, the conventional method of numerically validating a homogenization procedure only involves comparing the extinction, scattering, and absorption cross sections of a scatterer distribution that is composed of a small number of scatterers with that of the homogenized medium.…”

Optical Chirality of Time-Harmonic Wavefields for Classification of Scatterers

“…In the following, we discuss the helicity of the incident light which is given by the VSH coefficients (p, q) in (1). The transformation [40,49,50]:…”