Reexamining the Lyman-Birge-Hopfield band of N2

Abstract

Motivated by fundamental molecular physics and by atmospheric and planetary sciences, the valence excitations of N${}_{2}$ gas have seen several decades of intensive study, especially by electron-energy-loss spectroscopy (EELS). It was consequently surprising when a comparison of nonresonant inelastic x-ray scattering (NIXS) and nonresonant EELS found strong evidence for violations of the first Born approximation for EELS when leaving the dipole scattering limit. Here we reassess the relative strengths of the constituent resonances of the lowest-energy excitations of N${}_{2}$, encompassed by the so-called Lyman-Birge-Hopfield (LBH) band, expanding on the prior, qualitative interpretation of the NIXS results for N${}_{2}$ by both quantifying the generalized oscillator strength of the lowest-energy excitations and also presenting a time-dependent density functional theory (TDDFT) calculation of the $q$ dependence of the entire low-energy electronic excitation spectrum. At high $q$, we find that the LBH band has an unexpectedly large contribution from the octupolar $w{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Delta}}_{u}$ resonance exactly in the regime where theory and EELS experiment for the presumed-dominant $a{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Pi}}_{g}$ resonance have previously had substantial disagreement, and also where the EELS results must now be expected to show violations of the Born approximation. After correcting for this contamination, the $a{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Pi}}_{g}$ generalized oscillator strength from the NIXS results is in good agreement with prior theory. The NIXS spectra, over their entire $q$ range, also find satisfactory agreement with the TDDFT calculations for both bound and continuum excitations.