Interpretation of Coupled-Cluster Many-Electron Dynamics in Terms of Stationary States

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.

Conservation laws in coupled cluster dynamics at finite temperature

“…It has been shown that making the above action (Equation 10) stationary with respect to time-dependent orbitals leads to dynamics that satisfy Ehrenfest's theorem for all 1-electron operators 2,17,18,53,55 . This can be important because, as pointed out by Pedersen et al 55 , it leads to local conservation and gauge invariance in 1-electron properties.…”

“…In ab initio electron dynamics, a variety of methods have been applied to simulate various phenomena, such as multiple photon processes 1 , high harmonic generation 2 , and ultrafast laser dynamics 3 in atomic and molecular systems. Among them are time-dependent density functional theory 4 and wavefunction based methods such as time-dependent Hartree-Fock 5 , configuration interaction (CI) [6][7][8][9] , complete-active-space self-consistent field (CASSCF) 2 , multiconfigurational time-dependent Hartree-Fock [10][11][12] , density matrix embedding theory (DMET) 13 and coupled cluster (CC) methods [14][15][16][17][18] . Ab initio electron dynamics in materials has primarily been carried out at the time-dependent density functional theory level, although studies with low-order diagrammatic approximations have begun to appear 19 .…”

“…is satisfied for the 1-particle reduced density matrix (1RDM). At zero-temperature, this type of orbital dynamics has been used for time evolution with various ab initio methods, including time-dependent CI 53 , CASSCF 2 , DMET 13 , and CC 17,18,54,55 . Starting from this same idea, we can extend the Keldysh-CC method to include the variational orbital dynamics via a finitetemperature TDVP.…”

Accelerating Real-Time Coupled Cluster Methods with Single-Precision Arithmetic and Adaptive Numerical Integration

“…Real-time coupled cluster (RT-CC) methods, in particular, can achieve exceptionally high accuracy in many cases 17,18 and have been explored in the context of real-time simulations for some years. [9][10][11][19][20][21][22][23][24][25][26][27] However, RT-CC approaches also suffer from the same affliction as that of their time-independent counterparts, viz., high-degree polynomial scaling with the size of the molecular system. For ground-state coupled cluster theory, techniques such as local correlation, [28][29][30][31][32][33][34][35] fragmentation, [36][37][38][39] tensor decomposition, [40][41][42][43][44][45] and others have been developed to permit applications to larger molecular systems than conventional implementations allow.…”

Simulating weak-field attosecond processes with a Lanczos reduced basis approach to time-dependent equation of motion coupled cluster theory

“…Despite these early endeavours, real-time methods did not become practical at that time due to the lack of electron correlation effects at the Hartree-Fock level and the high computational cost associated with propagation of correlated wave functions. However, decades of steady advancements in computing power and numerical algorithms have led to a renewed interest in explicit time propagation in correlated methods like density functional theory [12,13], multiconfigurational selfconsistent-field [14][15][16], configuration interaction [17][18][19][20], algebraic diagrammatic construction [21,22] and coupledcluster [23][24][25][26][27][28][29][30][31][32][33].…”