Local-Field Effects in Linear Response Properties within a Polarizable Frozen Density Embedding Method

Abstract

In this work, we present a polarizable frozen density embedding (FDE) method for calculating polarizabilities of coupled subsystems. The method (FDE-pol) combines a FDE method with an explicit polarization model such that the expensive freeze/thaw cycles can be bypassed, and approximate nonadditive kinetic potentials are avoided by enforcing external orthogonality between the subsystems. To describe the polarization of the frozen environment, we introduce a Hirshfeld partition-based density-dependent method for calculating the atomic polarizabilities of atoms in molecules, which alleviates the need to fit the atomic parameters to a specific system of interest or to a larger general set of molecules. We show that the Hirshfeld partition-based method predicts molecular polarizabilities close to the basis set limit, and thus, a single basis set-dependent scaling parameter can be introduced to improve the agreement against the reference polarizability data. To test the model, we characterized the uncoupled and coupled response of small interacting molecular complexes. Here, the coupled response properties include the perturbation of the frozen system due to the external perturbation which is ignored in the uncoupled response. We show that FDE-pol can accurately reproduce both the exact uncoupled polarizability and the coupled polarizabilities of the supermolecular systems. Using damped response theory, we also demonstrate that the coupled frequency-dependent polarizability can be described by including local field effects. The results emphasize the necessity of including local-field effects for describing the response properties of coupled subsystems, as well as the importance of accurate atomic polarizability models.

Embedding Beyond Electrostatics: The Extended Polarizable Density Embedding Model

“…PDE (and PDE-X) instead rely on a classical description of environment polarization through an induced-dipole model, which is computationally more affordable. Recently, methods that combine classical polarization models to describe polarization in FDE have emerged, for example, with the three-layer QM/FDE/fluctuating charges model by Egidi et al and the polarizable FDE-EO by Pal et al , …”

Computational Model for Electrochemical Surface-Enhanced Raman Scattering: Key Role of the Surface Charges and Synergy between Electromagnetic and Charge-Transfer Enhancement Mechanisms

“…Notwithstanding the challenging nature of the SERS phenomenon, impressive theoretical advances have been carried out in just few decades after its discovery by Fleischmann, Hendra, and McQuillan . Among many achievements, it is worth to highlight the SERS selection rules derived by Lombardi and Birke by incorporating Herzberg–Teller vibronic coupling into Albrecht expression of the transition polarizability , and methodological advances led by the Jensen group. − …”

Theoretical and Numerical Comparison of Quantum- and Classical Embedding Models for Optical Spectra

“…We denote PE models with this effect included as PE . There is no corresponding term for FDE models, although extensions have been suggested that include differential polarization. ,,− Most of them are, however, rather computationally demanding or require embedded excited-state densities, which are somewhat tedious to obtain for TD-DFT methods …”

“…Also in the standard PE scheme, the local field effect is not incorporated. It’s effect on the oscillator strengths can, however, approximately be accounted for by adding an external effective field (EEF) term, ⟨ϕ a | V̂ loc |ϕ i ⟩, to M . , The required operator is defined as V̂ loc = prefix∑ italicts boldT t normala false( 1 false) boldR italicts bold-scriptE s uni = prefix∑ t boldT t normala false( 1 false) bold-italicμ ext , t ind where μ ext, t ind is the induced dipole to a unit field, bold-scriptE s uni . This approximate description has thereby an effect on the oscillator strengths only, but does not alter the excitation energies.…”