Excited-State Response Theory Within the Context of the Coupled-Cluster Formalism

TL;DR

This paper develops a second linear response theory within the coupled-cluster formalism to compute transition elements between excited states and extend to non-linear perturbations, enhancing excited-state quantum property calculations.

Contribution

It introduces a second linear response approach in coupled-cluster theory for excited states and extends it to non-linear propagations, offering new tools for excited-state analysis.

Findings

Consistent with quadratic response theory.

Enables calculation of transition elements between excited states.

Provides a framework for non-linear state propagation.

Abstract

Time-dependent response theories are foundational to the development of algorithms that determine quantum properties of electronic excited states of molecules and periodic systems. They are employed in wave-function, density-functional, and semiempirical methods, and are applied in an incremental order: linear, quadratic, cubic, etc. Linear response theory is known to produce electronic transitions from ground to excited state, and vice versa. In this work, a linear-response approach, within the context of the coupled cluster formalism, is developed to offer transition elements between different excited states (including permanent elements), and related properties. Our formalism, second linear response theory, is consistent with quadratic response theory, and can serve as an alternative to develop and study excited-state theoretical methods, including pathways for algorithmic acceleration. This work also formulates an extension of our theory for general propagations under non-linear external perturbations, where the observables are given by linked expressions which can predict their time-evolution under arbitrary initial states and could serve as a means of constructing general state propagators. A connection with the physics of wavefunction theory is developed as well, in which dynamical cluster operator amplitudes are related to wavefunction linear superposition coefficients.