Theoretical study of molecular vibrations in electron momentum spectroscopy experiments on furan: An analytical versus a molecular dynamical approach

Abstract

The influence of thermally induced nuclear dynamics (molecular vibrations) in the initial electronic ground state on the valence orbital momentum profiles of furan has been theoretically investigated using two different approaches. The first of these approaches employs the principles of Born-Oppenheimer molecular dynamics, whereas the so-called harmonic analytical quantum mechanical approach resorts to an analytical decomposition of contributions arising from quantized harmonic vibrational eigenstates. In spite of their intrinsic differences, the two approaches enable consistent insights into the electron momentum distributions inferred from new measurements employing electron momentum spectroscopy and an electron impact energy of 1.2 keV. Both approaches point out in particular an appreciable influence of a few specific molecular vibrations of A1 symmetry on the 9a1 momentum profile, which can be unravelled from considerations on the symmetry characteristics of orbitals and their energy spacing.

Influence of molecular vibrations on the valence electron momentum distributions of adamantane

“…It is immediately clear from inspecting the figures that the HAQM and BOMD approaches consistently quantify the influence of nuclear dynamics on the momentum profiles. The good accordance of the HAQM calculation, which is based on the harmonic approximation, with the BOMD calculation strongly suggests that the influence of vibrational anharmonicity is negligibly small for these momentum profiles, being consistent with our earlier studies on furan 35 and dimethyl ether. 36 wave effects may possibly be appreciable even at small p. In principle, the effects can be assessed by examining the incident electron energy dependence of the momentum profile; 27,28,63 however, it is beyond the scope of the present study.…”

“…analyze vibrational effects on electron momentum profiles. The first of these, known as the harmonic analytical quantum mechanical (HAQM) method, 30,35 is based on the harmonic approximation and the second approach relies on Born-Oppenheimer molecular dynamics (BOMD). [41][42][43]…”

“…Since the theory behind the HAQM approach has been fully described elsewhere, 30,34,35 only a short account is given here. Under the assumption of the PWIA the EMS cross section can be written as…”

“…where f ee is the electron-electron collision factor and Μ(p) is the structure factor corresponding to a momentum profile. 23 In the frame of the Born-Oppenheimer approximation, the electron momentum profile for a transition from the initial neutral electronic state i to the final ion state f can be expressed as follows: 30,34,35 ( )…”

“…[25][26][27][28] Because of its unique ability to image individual electron orbitals in momentum space, EMS can provide a powerful means to investigate how molecular orbital patterns are affected by the vibrational motions of molecules. Indeed, recent EMS studies on various polyatomic molecules [29][30][31][32][33][34][35][36][37][38] have shown that electron momentum profiles may considerably be affected by molecular vibrations, and that EMS experiments in conjunction with recently developed theoretical approaches are capable of disentangling the interplay between the electronic and nuclear dynamics. 30,31,[34][35][36][37][38] It is therefore of interest to apply the EMS technique to the study of the nuclear dynamics effects for diamondoids.…”