Determination of the electronic structure of atoms and molecules in the ground state: Measurement of molecular hydrogen by high-resolution x-ray scattering

Abstract

The high-resolution x-ray-scattering technique is used to study the elastic scattering of atoms and molecules in the gas phase. The elastic squared form factor, which is the square of the Fourier transformation of the electron density distribution in position space and reveals the pure electronic structure of atoms and molecules in the ground state, of molecular hydrogen is measured at an incident photon energy of about 9889 eV and an energy resolution of about 70 meV. Although it is generally thought that the x-ray-scattering technique is identical to high-energy electron scattering, at least for elastic scattering these two techniques have an apparent difference, i.e., the pure electronic structure of a molecule in the ground state can be determined by x-ray scattering while it cannot be obtained by the high-energy electron impact method due to the interference between the scattering of separate nuclei and of the electrons in the target. The present experimental results match the theoretical calculations very well, which demonstrates that high-resolution x-ray scattering is a powerful tool to study the electronic structure of atoms and molecules in the ground state.

Integral cross sections of the dipole‐allowed excitations of nitrogen molecule studied by the fast electron scattering

“…The vibronic states can be resolved with the good energy resolution in Xu et al [], but the moderate incident electron energy of 300 eV may not be high enough to approach the first Born approximation. With the dramatic development of third generation synchrotron radiation and the crystal spectrometer, the brightness and the energy resolution of the X‐ray scattering technique have been greatly improved, which provides the possibility for the measurements of the dynamic parameters of atoms and molecules [ Xie et al , ; Bradley et al , ; Zhu et al , ; Liu et al , ; Peng et al , ; Kang et al , ; Xu et al , ; Liu et al , ]. Recently, the X‐ray scattering results, which are free from the high‐order Born terms, were obtained by Bradley et al [] and Peng et al [] at the energy resolutions of 1 eV and 70 meV, respectively.…”

Ab initio calculation of inelastic scattering

“…2 Recently, new doubledifferential, high energy-resolution X-ray scattering measurements at synchrotrons have begun to provide an increasingly detailed picture of electronic structure and dynamics in gas-phase atoms and molecules. [3][4][5][6][7][8][9][10][11][12] One particular strength of inelastic X-ray scattering (IXS) is the ability to access optically forbidden transitions. New X-ray Free-Electron Lasers (XFELs), in turn, generate high intensity and short duration pulses [13][14][15][16][17][18][19] that enable timeresolved X-ray scattering, [20][21][22][23][24][25] and thus ultrafast imaging of photochemical dynamics.…”

Ab Initio Calculation of Total X-ray Scattering from Molecules

“…The H 2 molecule is a well-established benchmark system both for experiments [56][57][58][59] and theory. [19][20][21]31,38,55,[60][61][62] In Fig.…”

“…2, both experimental elastic 56 and inelastic 57 scattering d and calculated total 19 and elastic. 31 The small difference between our present calculations and those performed by Bentley et al is likely to be attributed to the lack of dynamical correlation in the Figure 2: Total, elastic and inelastic scattering for the H 2 molecule, showing experimental results for elastic 56 and inelastic, 57 our own MRCI(2,7)/aug-cc-pVTZ-level calculations, previous ab-initio calculations of elastic 31 and total scattering, 19 and the independent atom model (IAM) results.…”