The time-dependent bivariational principle: Theoretical foundation for real-time propagation methods of coupled-cluster type

TL;DR

This paper develops a differential geometric framework for the time-dependent bivariational principle, providing a foundation for real-time coupled-cluster propagation methods and introducing new equations of motion.

Contribution

It introduces a novel geometric perspective on TD-BIVP, deriving two classical Hamilton's equations from the real and imaginary parts of the action integral, and relates existing methods within this framework.

Findings

Derived two classical Hamilton's equations from the action integral.

Established conservation laws and Poisson brackets in the context of TD-BIVP.

Provided an overview connecting various real-time coupled-cluster methods.

Abstract

Real-time propagation methods for chemistry and physics are invariably formulated using variational techniques. The time-dependent bivariational principle (TD-BIVP) is known to be the proper framework for coupled-cluster type methods, and is here studied from a differential geometric point of view. It is demonstrated how two distinct classical Hamilton's equations of motion arise from considering the real and imaginary parts of the action integral. The latter is new, and can in principle be used to develop novel propagation methods. Conservation laws and Poisson brackets are introduced, completing the analogy with classical mechanics. An overview of established real-time propagation methods is given in the context of our formulation of the TD-BIVP, namely time-dependent traditional coupled-cluster theory, orbital-adaptive coupled-cluster theory, time-dependent orthogonal optimized coupled-cluster theory, and equation-of-motion coupled cluster theory.