  We report the formulation of a new, cost-effective approximation method in
the time-dependent optimized coupled-cluster (TD-OCC) framework [T. Sato et
al., J. Chem. Phys. 148, 051101 (2018)] for first-principles simulations of
multielectron dynamics in an intense laser field. The method, designated as
TD-OCCD(T), is a time-dependent, orbital-optimized extension of the
"gold-standard" CCSD(T) method in the ground-state electronic structure theory.
The equations of motion for the orbital functions and the coupled-cluster
amplitudes are derived based on the real-valued time-dependent variational
principle using the fourth-order Lagrangian. The TD-OCCD(T) is size extensive
and gauge invariant, and scales as O(N^7) with respect to the number of active
orbitals N. The pilot application of the TD-OCCD(T) method to the strong-field
ionization and high-order harmonic generation from a Kr atom is reported in
comparison with the results of the previously developed methods, such as the
time-dependent complete-active-space self-consistent field (TD-CASSCF), TD-OCC
with double and triple excitations (TD-OCCDT), TD-OCC with double excitations
(TD-OCCD), and the time-dependent Hartree-Fock (TDHF) methods.
