Among the most highly productive methods to compute properties of electronic excited states, time-dependent (TD) response theories offer foundational approaches to study such systems, and these rely on wave function, density functional, and/or semi-empirical methods. The most common paradigm to study the properties of excited states with response theory requires analysis of the quadratic regime. We show a simple modification of linear response theory (called second linear response theory, SLR) that allows for the computation of excited state properties. The SLR theory in the context of TD coupled-cluster response theory is found to provide an alternative approach that is equivalent to its quadratic response formulation, and we present a state-to-state series of calculations that illustrate how this response theory improves the calculation of the excited-state density matrices. The way SLR theory treats the coupled-cluster reference of the system also leads, as an extension of it, to a new general TD coupled-cluster method that can assist in the extraction of excited-state information. This is discussed along with future applications.

Linear response approach to quadratic time-dependent coupled-cluster response theory

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ACS Fall 2022

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