# A quantum-mechanical perspective on linear response theory within polarizable embedding

## TL;DR

This paper provides a rigorous quantum-mechanical foundation for linear response theory in polarizable embedding, analyzing subsystem decompositions, response function structures, and implications for molecular property calculations.

## Contribution

It introduces a quantum-mechanical derivation of linear response theory in polarizable embedding, clarifies subsystem response functions, and justifies classical approximations from quantum principles.

## Key findings

- Analysis of symmetric and nonsymmetric response function decompositions
- Derivation of conservation laws for absorption cross sections
- Identification of steps to connect quantum and classical descriptions

## Abstract

The derivation of linear response theory within polarizable embedding is carried out from a rigorous quantum-mechanical treatment of a composite system. Two different subsystem decompositions (symmetric and nonsymmetric) of the linear response function are presented, and the pole structures as well as residues of the individual terms are analyzed and discussed. This theoretical analysis clarifies which form of the response function to use in polarizable embedding, and we highlight complications in separating out subsystem contributions to molecular properties. For example, based on the nonsymmetric decomposition of the complex linear response function, we derive conservation laws for integrated absorption cross sections, providing a solid basis for proper calculations of the intersubsystem intensity borrowing inherent to coupled subsystems and how that can lead to negative subsystem intensities. We finally identify steps and approximations required to achieve the transition from a quantum-mechanical description of the composite system to polarizable embedding with a classical treatment of the environment, thus providing a thorough justification for the descriptions used in polarizable embedding models.