Abstract
We demonstrate theoretically and numerically that laser-driven many-electron dynamics, as described by bivariational time-dependent coupled-cluster (CC) theory, may be analyzed in terms of stationary-state populations. Projectors heuristically defined from linear response theory and equation-of-motion CC theory are proposed for the calculation of stationary-state populations during interaction with laser pulses or other external forces, and conservation laws of the populations are discussed. Numerical tests of the proposed projectors, involving both linear and nonlinear optical processes for He and Be atoms and for LiH, CH+, and LiF molecules show that the laser-driven evolution of the stationary-state populations at the coupled-cluster singles-and-doubles (CCSD) level is very close to that obtained by full configuration interaction (FCI) theory, provided that all stationary states actively participating in the dynamics are sufficiently well approximated. When double-excited states are important for the dynamics, the quality of the CCSD results deteriorates. Observing that populations computed from the linear response projector may show spurious small-amplitude, high-frequency oscillations, the equation-of-motion projector emerges as the most promising approach to stationary-state populations.
Highlights
Providing unique time-resolved insights into electronic quantum dynamics and with the exciting prospect of detailed manipulation and control of chemical reactions,[1] increasing experimental and theoretical research efforts have been directed toward attosecond science in the past couple of decades see, for example, ref 2 for a recent perspective
Two conditions are used to define suitable projectors from CC linear response (CCLR) theory and from equationof-motion CC (EOMCC) theory: (i) the projector must reproduce the correct form of one-photon transition strengths and (ii) the projectors must yield populations that converge to the full configuration interaction (FCI) results in the limit of untruncated cluster operators
It is demonstrated that the populations provide valuable insight into the linear and nonlinear optical processes occurring during the interaction of the electrons with laser pulses
Summary
Providing unique time-resolved insights into electronic quantum dynamics and with the exciting prospect of detailed manipulation and control of chemical reactions,[1] increasing experimental and theoretical research efforts have been directed toward attosecond science in the past couple of decades see, for example, ref 2 for a recent perspective. Since energy is the physical quantity associated with time translations, textbook analyses of such interactions are naturally performed in terms of the population of the energy eigenstates the stationary states of the fieldfree particle system, see, for example, ref 42 Manybody theories such as TDFCI, MCTDHF, and TDCC theories do not express the wave function as a superposition of stationary states, making the analysis difficult to perform in simulations. The natural approach would be to define the stationary states from the zero-field Hamiltonian and zero-field wave function using, for example, linear response theory[47] or orthogonality-constrained imaginary time propagation.[48] The latter approach was investigated recently within the framework of MCTDHF theory by Lötstedt et al.,[49] who found that the stationary-state populations oscillate even after the pulse is turned off unless a sufficiently large number of active orbitals is included in the wave function expansion.
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