Christoph Witzorky

Bio: Christoph Witzorky is an academic researcher from University of Potsdam. The author has contributed to research in topics: Wave function & High harmonic generation. The author has co-authored 1 publications.

Gaussian-Type Orbital Calculations for High Harmonic Generation in Vibrating Molecules: Benchmarks for H2.

Abstract: The response of the hydrogen molecular ion, H2+, to few-cycle laser pulses of different intensities is simulated. To treat the coupled electron-nuclear motion, we use adiabatic potentials computed with Gaussian-type basis sets together with a heuristic ionization model for the electron and a grid representation for the nuclei. Using this mixed-basis approach, the time-dependent Schrodinger equation is solved, either within the Born-Oppenheimer approximation or with nonadiabatic couplings included. The dipole response spectra are compared to all-grid-based solutions for the three-body problem, which we take as a reference to benchmark the Gaussian-type basis set approaches. Also, calculations employing the fixed-nuclei approximation are performed, to quantify effects due to nuclear motion. For low intensities and small ionization probabilities, we get excellent agreement of the dynamics using Gaussian-type basis sets with the all-grid solutions. Our investigations suggest that high harmonic generation (HHG) and high-frequency response, in general, can be reliably modeled using Gaussian-type basis sets for the electrons for not too high harmonics. Further, nuclear motion destroys electronic coherences in the response spectra even on the time scale of about 30 fs and affects HHG intensities, which reflect the electron dynamics occurring on the attosecond time scale. For the present system, non-Born-Oppenheimer effects are small. The Gaussian-based, nonadiabatically coupled, time-dependent multisurface approach to treat quantum electron-nuclear motion beyond the non-Born-Oppenheimer approximation can be easily extended to approximate wavefunction methods, such as time-dependent configuration interaction singles (TD-CIS), for systems where no benchmarks are available.

Approximation Schemes to Include Nuclear Motion in Laser-Driven Ab Initio Electron Dynamics: Application to High Harmonic Generation.

Abstract: The quantum mechanical description of many-electron dynamics in molecules driven by short laser pulses is at the heart of theoretical attochemistry. In addition to the formidable time-dependent electronic structure problem, the field faces the challenge that nuclear motion, ideally also treated quantum mechanically, may not be negligible, but scales enormously in effort. As a consequence, most first-principles calculations on ultrafast electron dynamics in molecules are done within the fixed-nuclear approximation. For laser-pulse excitation in H2+, where an "exact" treatment of the coupled nuclear-electron dynamics is possible, it has been shown that nuclear motion can have a nonnegligible impact on high harmonic generation (HHG) spectra (Witzorky et al., J. Chem. Theor. Comput. 2021, 17, 7353-7365). It is not so clear, however, how to include (quantum) nuclear motion also for more complicated molecules, with more electrons and/or nuclei, in particular when the electronic structure is described by correlated, multistate wavefunction methods such as the time-dependent configuration interaction (TD-CI). In this work, we suggest a scheme in which the Born-Oppenheimer potential energy surfaces of a molecule are approximated by model potentials (harmonic and asymptotic, as an expansion in 1/R), obtained from only a few ab initio calculations, with the prospect to treat complex molecular systems. The method is tested successfully for HHG by few-cycle laser pulses for the "exact" H2+ reference. It is then applied for diatomic molecules with more electrons and for a two-dimensional model of the water molecule using TD-CIS (S = single) for the electronic structure part.

High harmonic spectra computed using time-dependent Kohn-Sham theory with Gaussian orbitals and a complex absorbing potential.

Abstract: High harmonic spectra for H2 and H2 + are simulated by solving the time-dependent Kohn-Sham equation in the presence of a strong laser field using an atom-centered Gaussian representation of the density and a complex absorbing potential. The latter serves to mitigate artifacts associated with the finite extent of the basis functions, including spurious reflection of the outgoing electronic wave packet. Interference between the outgoing and reflected waves manifests as peak broadening in the spectrum as well as the appearance of spurious high-energy peaks after the harmonic progression has terminated. We demonstrate that well-resolved spectra can be obtained through the use of an atom-centered absorbing potential. As compared to grid-based algorithms, the present approach is more readily extensible to larger molecules.

Density-functional theory for electronic excited states

Abstract: This chapter provides a basic introduction to excited-state extensions of density functional theory (DFT), including time-dependent (TD-)DFT in both its linear-response and its explicitly time-dependent formulations. As applied to the Kohn-Sham DFT ground state, linear-response theory affords an eigenvalue-type problem for the excitation energies in a basis of singly-excited Slater determinants, and is widely known simply as "TDDFT" despite its frequency-domain formulation. This form of TDDFT is the mostly widely-used quantum-chemical method for excited states, due to a favorable combination of low cost and reasonable accuracy. The chapter surveys the accuracy of linear-response TDDFT, which is generally more sensitive to the details of the exchange-correlation functional as compared to ground-state DFT, and also describes some known systemic problems exhibited by this approach. Some of those problems can be corrected on a case-by-case basis using orbital-optimized, excited-state self-consistent field (SCF) calculations, in what is known as excited-state Kohn-Sham theory or a "Delta-SCF" procedure, a class of methods that includes restricted open-shell Kohn-Sham theory. Recent successes of these approaches are highlighted, including double excitations and core-level excitations. Finally, explicitly time-dependent (or "real-time") TDDFT involves propagation of the molecular orbitals in time following an external perturbation, according to the Kohn-Sham analogue of the time-dependent Schroedinger equation. The time-dependent approach has been used to model strong-field electron dynamics, and in the weak-field limit it provides a route to broadband spectra based on the time evolution of the dipole moment function. This is useful for describing high-energy excitations (as in x-ray spectroscopy) and in systems where the density of states is high, as demonstrated by a few examples.

Resonance Effect in Brunel Harmonic Generation in Thin Film Organic Semiconductors

Abstract: Organic semiconductors have attracted extensive attention due to their excellent optical and electronic properties. Here, we present an experimental and theoretical study of Brunel harmonic generation in two types of porphyrin thin films: tetraphenylporphyrin (TPP) and its organometallic complex derivative Zinc tetraphenylporphyrin (ZnTPP). Our results show that the $\pi$-$\pi^\ast$ excitation of the porphyrin ringsystem plays a major role in the harmonic generation process. We uncovered the contribution of an interband process to Brunel harmonic generation. In particular, the resonant ($S_0 \rightarrow S_2$ transition) enhanced multiphoton excitation is found to lead to an early onset of non-perturbative behavior for the 5th harmonic. Similar resonance effects are expected in Brunel harmonic generation with other organic materials.

Approximation Schemes to Include Nuclear Motion in Laser-Driven Ab Initio Electron Dynamics: Application to High Harmonic Generation.

Abstract: The quantum mechanical description of many-electron dynamics in molecules driven by short laser pulses is at the heart of theoretical attochemistry. In addition to the formidable time-dependent electronic structure problem, the field faces the challenge that nuclear motion, ideally also treated quantum mechanically, may not be negligible, but scales enormously in effort. As a consequence, most first-principles calculations on ultrafast electron dynamics in molecules are done within the fixed-nuclear approximation. For laser-pulse excitation in H2+, where an "exact" treatment of the coupled nuclear-electron dynamics is possible, it has been shown that nuclear motion can have a nonnegligible impact on high harmonic generation (HHG) spectra (Witzorky et al., J. Chem. Theor. Comput. 2021, 17, 7353-7365). It is not so clear, however, how to include (quantum) nuclear motion also for more complicated molecules, with more electrons and/or nuclei, in particular when the electronic structure is described by correlated, multistate wavefunction methods such as the time-dependent configuration interaction (TD-CI). In this work, we suggest a scheme in which the Born-Oppenheimer potential energy surfaces of a molecule are approximated by model potentials (harmonic and asymptotic, as an expansion in 1/R), obtained from only a few ab initio calculations, with the prospect to treat complex molecular systems. The method is tested successfully for HHG by few-cycle laser pulses for the "exact" H2+ reference. It is then applied for diatomic molecules with more electrons and for a two-dimensional model of the water molecule using TD-CIS (S = single) for the electronic structure part.