arXiv subjects

Thomas Bondo Pedersen

Publications and source records attributed to Thomas Bondo Pedersen.

22 records · Page 2Linked to original sources

arXiv2022

Linear and nonlinear optical properties from TDOMP2 theory

In this work we present a derivation of the real-time time-dependent orbital-optimized Møller-Plesser TDOMP2 and its biorthogonal companion, time-dependent non-orthogonal OMP2 (TDNOMP2), theory starting from the time-dependent bivariational principle and a parametrization based on the exponential orbital-rotation operator formulation commonly used in time-independent molecular electronic-structure theory. We apply the TDOMP2 method to extract absorption spectra and frequency-dependent polarizabilities and first hyperpolarizabilities from real-time 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 with results from CCSD and CC2 linear and quadratic response theory. Our results indicate that while TDOMP2 absorption spectra are of the same quality as TDCC2 spectra, frequency-dependent polarizabilities and hyperpolarizabilties from TDOMP2 simulations are significantly closer to TDCCSD results than those from TDCC2 simulations.

physics.chem-ph↗

arXiv2020

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

We demonstrate theoretically and numerically that laser-driven many-electron dynamics, as described by bivariational time-dependent coupled-cluster theory, may be analyzed in terms of stationary-state populations. Projectors heuristically defined from linear response theory and equation-of-motion coupled-cluster 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 the He and Be atoms, and for the 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 theory provided 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 deteriorate. 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.

physics.chem-ph↗

arXiv2020

Numerical stability of time-dependent coupled-cluster methods for many-electron dynamics in intense laser pulses

We investigate the numerical stability of time-dependent coupled-cluster theory for many-electron dynamics in intense laser pulses, comparing two coupled-cluster formulations with full configuration interaction theory. Our numerical experiments show that orbital-adaptive time-dependent coupled-cluster doubles (OATDCCD) theory offers significantly improved stability compared with the conventional Hartree-Fock-based time-dependent coupled-cluster singles-and-doubles (TDCCSD) formulation. The improved stability stems from greatly reduced oscillations in the doubles amplitudes, which, in turn, can be traced to the dynamic biorthonormal reference determinants of OATDCCD theory. As long as these are good approximations to the Brueckner determinant, OATDCCD theory is numerically stable. We propose the reference weight as a diagnostic quantity to identify situations where the TDCCSD and OATDCCD theories become unstable.

physics.chem-ph↗

arXiv2019

Symplectic integration and physical interpretation of time-dependent coupled-cluster theory

The formulation of the time-dependent Schrodinger equation in terms of coupled-cluster theory is outlined, with emphasis on the bivariational framework and its classical Hamiltonian structure. An indefinite inner product is introduced, inducing physical interpretation of coupled-cluster states in the form of transition probabilities, autocorrelation functions, and explicitly real values for observables, solving interpretation issues which are present in time-dependent coupled-cluster theory and in ground-state calculations of molecular systems under influence of external magnetic fields. The problem of the numerical integration of the equations of motion is considered, and a critial evaluation of the standard fourth-order Runge--Kutta scheme and the symplectic Gauss integrator of variable order is given, including several illustrative numerical experiments. While the Gauss integrator is stable even for laser pulses well above the perturbation limit, our experiments indicate that a system-dependent upper limit exists for the external field strengths. Above this limit, time-dependent coupled-cluster calculations become very challenging numerically, even in the full configuration interaction limit. The source of these numerical instabilities is shown to be rapid increases of the amplitudes as ultrashort high-intensity laser pulses pump the system out of the ground state into states that are virtually orthogonal to the static Hartree-Fock reference determinant.

physics.chem-ph↗