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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