# Unified Framework for Molecular Response Functions of Different Electronic-Structure Models

## TL;DR

This paper introduces SymResponse, a flexible framework for calculating molecular response functions using various electronic-structure models.

## Contribution

The novelty is a unified symbolic framework that simplifies implementing and extending response theory across different models.

## Key findings

- SymResponse uses symbolic expressions to represent response functions for numerical evaluation.
- The framework is demonstrated with Hartree–Fock, DFT, and coupled-cluster methods.
- Elimination rules reduce computational effort in response calculations.

## Abstract

A unified framework—SymResponse—has been
developed
as a versatile tool to aid the implementation of response theory for
different electronic-structure models. The framework manipulates the
quasi-energy formulation of response theory at a symbolic level by
building on top of other well-developed symbolic libraries. Response
functions can therefore be nicely represented by “symbolic
expressions,” which can be further evaluated numerically by
users by developing their own evaluation routines with the assistance
of SymResponse. The design of SymResponse makes it extensible to different
electronic-structure models with only a moderate further amount of
development effort. Response theory at Hartree–Fock, density
functional theory, and coupled-cluster levels has been implemented
in the present work as a demonstration, where elimination rules [KristensenK.J. Chem. Phys.2008, 129, 214103]19063540
10.1063/1.3023123 can also be applied to offer the
possibility to reduce the size of computational tasks.