Recent years have witnessed an increasing interest in time‐dependent coupled‐cluster (TDCC) theory for simulating laser‐driven electronic dynamics in atoms and molecules, and for simulating molecular vibrational dynamics. Starting from the time‐dependent bivariational principle, we review different flavors of single‐reference TDCC theory with either orthonormal static, orthonormal time‐dependent, or biorthonormal time‐dependent spin orbitals. The time‐dependent extension of equation‐of‐motion coupled‐cluster theory is also discussed, along with the applications of TDCC methods to the calculation of linear absorption spectra, linear and low‐order nonlinear response functions, highly nonlinear high harmonic generation spectra and ionization dynamics. In addition, the role of TDCC theory in finite‐temperature many‐body quantum mechanics is briefly described along with a few other application areas.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Theoretical and Physical Chemistry > Spectroscopy Software > Simulation Methods

We present a derivation of real-time (RT) time-dependent orbital-optimized Møller–Plesset (TDOMP2) theory and its biorthogonal companion, time-dependent non-orthogonal OMP2 theory, starting from the time-dependent bivariational principle and a parametrization based on the exponential orbital-rotation operator formulation commonly used in the time-independent molecular electronic structure theory. We apply the TDOMP2 method to extract absorption spectra and frequency-dependent polarizabilities and first hyperpolarizabilities from RT simulations, comparing the results with those obtained from conventional time-dependent coupled-cluster singles and doubles (TDCCSD) simulations and from its second-order approximation, TDCC2. We also compare our results with those from CCSD and CC2 linear and quadratic response theories. Our results indicate that while TDOMP2 absorption spectra are of the same quality as TDCC2 spectra, including core excitations where optimized orbitals might be particularly important, frequency-dependent polarizabilities and hyperpolarizabilities from TDOMP2 simulations are significantly closer to TDCCSD results than those from TDCC2 simulations.

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