A Multi‐Scale Approach for Modeling the Optical Response of Molecular Materials Inside Cavities

Abstract

The recent fabrication advances in nanoscience and molecular materials point toward a new era where material properties are tailored in silico for target applications. To fully realize this potential, accurate and computationally efficient theoretical models are needed for: a) the computer‐aided design and optimization of new materials before their fabrication; and b) the accurate interpretation of experiments. The development of such theoretical models is a challenging multi‐disciplinary problem where physics, chemistry, and material science are intertwined across spatial scales ranging from the molecular to the device level, that is, from ångströms to millimeters. In photonic applications, molecular materials are often placed inside optical cavities. Together with the sought‐after enhancement of light‐molecule interactions, the cavities bring additional complexity to the modeling of such devices. Here, a multi‐scale approach that, starting from ab initio quantum mechanical molecular simulations, can compute the electromagnetic response of macroscopic devices such as cavities containing molecular materials is presented. Molecular time‐dependent density‐functional theory calculations are combined with the efficient transition matrix based solution of Maxwell's equations. Some of the capabilities of the approach are demonstrated by simulating surface metal‐organic frameworks ‐in‐cavity and J‐aggregates‐in‐cavity systems that have been recently investigated experimentally, and providing a refined understanding of the experimental results.

A T-matrix Based Approach to Homogenize Artificial Materials

“…We define the circular dichroism as CD = A + −A − 2 , where A + and A − are the absorption of lefthanded and right-handed circularly polarized plane waves, respectively. We observe in Figure 6(c) that the results obtained with the homogeneous model match perfectly those obtained with mpGMM, which explicitly considers the discrete SUR-MOF lattice [18].…”

“…The band diagrams in Figure S2 show that the molecular material is homogenizable in the considered frequency range. The T-matrix of the unit cell is computed using TD-DFT [18]. The lattice constants are in x-and y-direction a 1 = a 2 = 2.079 nm, and in z-direction a 3 = 1.922 nm.…”

“…We observe that the chirality is anisotropic. (c) Comparison of the absorption of an incident left-circularly polarized plane wave and the circular dichroism of a 77 nm thick slab computed with the effective material parameters, and directly with mpGMM which considers the discrete lattice explicitly[18]. The two results match perfectly.…”

“…The T-matrix and Ewald's method can be combined in numerical codes for computing the electromagnetic response of infinitely periodic systems [12][13][14], achieving efficiencies more than two orders of magnitude better than numerical solvers of Maxwell differential equations [15,16]. The calculations of the T-matrices of molecular unit cells by quantum-mechanical ab initio methods [17], in particular time-dependent density-functional theory (TD-DFT) [18,19], enable the consideration of systems including slabs of molecular materials such as optical planar cavities filled with SURMOFs [18]. Unfortunately, Ewald's method cannot be used for finite arrangements of scatterers, such as an object of finite shape made from a 3D lattice of unit cells.…”

A T‐Matrix Based Approach to Homogenize Artificial Materials

“…[11] The T-matrix and Ewald's method can be combined in numerical codes for computing the electromagnetic response of infinitely periodic systems, [12][13][14] achieving efficiencies more than two orders of magnitude better than numerical solvers of Maxwell differential equations. [15,16] The calculations of the T-matrices of molecular unit cells by quantummechanical ab initio methods, [17] in particular time-dependent density-functional theory (TD-DFT), [18,19] enable the consideration of systems including slabs of molecular materials such as optical planar cavities filled with SURMOFs. [18] Unfortunately, Ewald's method cannot be used for finite arrangements of scatterers, such as an object of finite shape made from a 3D lattice of unit cells.…”