# Time-Dependent Multiconfiguration Self-Consistent-Field Study on Resonantly Enhanced High-Harmonic Generation from Transition Metal Elements

## TL;DR

This study uses advanced first-principles simulations to analyze high-harmonic generation in transition metals, revealing the crucial role of 3p electrons and giant resonances in resonant enhancement.

## Contribution

It demonstrates the application of TD-CASSCF and TD-ORMAS methods to open-shell atoms, identifying the origin of resonant harmonics in transition metals.

## Key findings

- Resonant peak at ~50 eV matches experimental observations
- 3p electrons are essential for resonant harmonic generation
- Constructively interfering 3p-3d giant resonances cause the enhancement

## Abstract

We theoretically study high-harmonic generation (HHG) from transition metal elements Mn and Mn$^+$, using full-dimensional, all-electron, first-principles simulations. The HHG spectra calculated with the time-dependent complete-active-space self-consistent-field (TD-CASSCF) and occupation-restricted multiple-active-space (TD-ORMAS) methods exhibit a prominent peak at $\sim 50$ eV, successfully reproducing resonant enhancement observed in previous experiments [R.A. Ganeev \textit{et al.}, Opt. Express \textbf{20}, 25239 (2012)]. Artificially freezing $3p$ orbitals in simulations results in its disappearance, which shows the essential role played by $3p$ electrons in the resonant harmonics (RH). Further transition-resolved analysis unambiguously identifies constructively interfering $3p$-$3d$ ($m=0,\pm 1$) giant resonance transitions as the origin of the RH, as also implied by its position in the spectra. Time-frequency analysis indicates that the recolliding electron combines with the parent ion to form the upper state of the transitions. In addition, this study shows that the TD-CASSCF and TD-ORMAS methods can be applied to open-shell atoms with many unpaired inner electrons.