Strong-field time-dependent density-functional theory: Harmonic generation in molecular nitrogen

Michael R Mack, Purdue University

Abstract

Density-Functional Theory (DFT) is one of the most prominent ab initio quantum chemistry tools available to provide insight about atoms, molecules, biomolecules, and beyond. It was not until the late 1980's that advancements in approximations to the many-body effects as a density-functional made DFT an indispensible tool in theoretical and computational chemistry. The time-dependent extention, TDDFT, has been applied to excited state properties of atoms and molecules such as electronic excitations, excited state geometries, dipole moments and hyperpolarizabilities, etc. The use of ground-state approximations in the time-dependent formalism has resulted in rather surprising success, but also drastic failures. The application of TDDFT to strong-field phenomena has been fruitful, but again includes successes and failures. TDDFT is currently the only feasible electronic structure method to tap into the exciting field of strong-field molecular dynamics. Therefore, we use TDDFT to study High Harmonic Generation (HHG) in N2. HHG is an efficient source of coherent, attosecond pulses resulting from the interaction of an atomic or molecular medium with intense, low frequency light. The measurement of harmonic generation is the induced dipole moment of the system. The dipole moment is a time-dependent density-functional, therefore, TDDFT is an appropriate tool for this study. The effect of the asymptotic spatial behavior of the exchange-correlation (xc) potential of TDDFT is investigated for the calculation of high harmonic spectra. We compare the harmonic spectrum of N2 obtained via the adiabatic local density approximation (A-LDA) and the asymptotically corrected (adiabatic) van Leeuwen-Baerends (A-LB94) approximation. While the A-LB94 decays like −1/r, as the exact xc potential does, another known condition is violated, namely the zero force condition. We compare the harmonic spectrum of N2 using the related approximations to the time-dependent xc potential of Kohn-Sham TDDFT to understand their application to strong-field studies. The harmonic spectra predicted using the A-LDA and A-LB94 approximation to the time-dependent xc potential are similar, however, the multielectron dynamics are not. Strong-field orbital ionization and induced dipoles are improved when the approximation to the xc potential exhibits the −1/ r decay. On the other hand, the A-LB94 introduces a fictitious forces on the electron density that generates a spurious dipole. Although both approximations yield qualitatively similar harmonic spectra, the A-LDA does for the wrong reasons.

Degree

M.S.

Advisors

Wasserman, Purdue University.

Subject Area

Molecular chemistry

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