Direct Analytical Evaluation of Electron-Impact Excitation Cross Sections via Multiconfigurational Binary Encounter Approach: Applications to Benzene and Naphthalene

Abstract

We present a multiconfigurational binary-encounter (MC-BE) framework for direct analytical evaluation of electron-impact electronic-excitation cross sections for dipole-allowed transitions from ab initio excited-state data. The method combines the threshold-modified Mott-Massey (TMMM) approximation with binary-encounter (BE/BE$f$) scaling. The effective binding energy in the BE/BE$f$ prefactor is obtained from amplitude-weighted occupied-orbital contributions computed by linear-response time-dependent density functional theory (LR-TDDFT), without system-specific fitting parameters. For benzene, MC-BE/TMMM cross sections for the dominant $1{}^{1}\!E_{\mathrm{1u}}$ ($π\!\to\!π^{\ast}$) band agree well with experiment at incident energies $T=10$-$20$ eV and improve on the Schwinger multichannel/truncated configuration-interaction singles results of Falkowski et al. [J. Chem. Phys. 159, 194301 (2023)] for this band and energy range. For naphthalene, the calculated total excitation cross section reproduces the onset and principal maximum of the gas-phase apparent fluorescence cross section, used as an emission-based proxy under dipole-dominated conditions, without empirical energy shifts or intensity scaling. Analytic peak-position and peak-height expressions, parameterized by $r=\langle B\rangle/ΔE$, show that typical valence excitations peak at incident energies $T\simeq 1.5$-$1.6ΔE$ with substantial BE attenuation, providing a diagnostic for relating measured cross-section profiles to excitation energies. Although demonstrated with LR-TDDFT, the framework is transferable to other excited-state theories that provide compatible amplitudes and well-defined orbital energies. These results support MC-BE/TMMM as a practical, inexpensive route for modeling electron-impact excitation of polyatomic molecules with finite oscillator strength.