This type of molecular scale interference was first proposed by Cohen and Fano 18 in photoionization and was successively demonstrated in the ionization of molecules induced by heavy ions 19, 20, 21, 22, 23, 24, 25, photons 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, as well as electrons 36, 37, 38. This oscillation phenomenon is usually referred to as bond oscillation 17, which can also be regarded as a result of the Cohen-Fano type 18 or the Young-type interference effect originated from the coherent superposition of the ( e, 2 e) amplitudes from the atoms in the molecule. Therefore the electron momentum distribution of a MO will be modulated by a cosine or sine function with periodicity of 2, where is the distance between atoms J a and J b. In momentum space, for a MO which can be approximated by a linear combination of atomic orbitals (LCAOs), the information about the equilibrium nuclear positions R J is only present in the phase factors exp(− i p ⋅ R J) introduced by Fourier transform of the wavefunction from position space to momentum space (see Methods for details). However, the geometry information of molecule is usually veiled due to the single-centered character of the momentum space wavefunction for MO. This unique ability of imaging MOs makes the EMS a robust technique for exploring the electronic structures of molecules in gas phase 16.
Information about the ionizing orbital of neutral molecule is also imprinted on the high-harmonic radiation produced by the recombination of the re-collision electron with the parent ion in the laser field and allows the three-dimensional shape of the highest electronic orbital to be measured 12.Įlectron momentum spectroscopy (EMS), which is based on the electron-impact single ionization or ( e, 2 e) experiment near the Bethe ridge, is a well-established technique that can obtain the spherically averaged electron momentum distributions, or electron momentum profiles (see Supplementary Information Note 1), for any individual molecular orbitals (MOs) in principle 13, 14, 15. Thus one set of measurements simultaneously identifies the orbital wavefunction of molecule and the position of the atoms in the molecule in this laser induced electron tunneling and diffraction technique. By measuring the momentum distribution for these direct electrons, the fingerprint of the highest occupied molecular orbital can be observed through the filter of the suppressed binding potential through which the electron tunnels 9. On the other hand, the tunneled electron wave packet that directly emerges into the vacuum retains information about the orbital from which the electron is ionized 9. The well-established method in the conventional electron diffraction is then applicable to retrieve the bond lengths of molecule. In this technique, an intense laser field is employed to extract electron from a molecule itself, and within one laser period a fraction of the tunneled electron wave packet will be forced back to re-collide and diffract from the parent molecular ion.
An alternative imaging approach emerged in the past decade, which is referred to as the laser induced electron diffraction 7, 8, 9, 10, 11, has also been demonstrated to image molecular structures with sub-Ångström precision. The geometry of a molecule is conventionally obtained by the methods of X-ray 1, 2 or electron diffraction 3, 4, 5, 6, from which the atomic positions are determined with sub-Ångström spatial resolution. The physical and chemical properties of molecules directly depend on their geometries and electronic structures that both have always been the central issues in molecular physics. Our approach provides a new robust tool for imaging molecules with high precision and has potential to apply to ultrafast imaging of molecular dynamics if combined with ultrashort electron pulses in the future. Thus, using one spectrometer, and in one measurement, the electron density distributions of MOs and the molecular geometry information can be obtained simultaneously. A very sensitive dependence of the oscillation period on interatomic distance is observed, which is used to determine F-F distance in CF 4 and O-O distance in CO 2 with sub-Ångström precision. Here we demonstrate the retrieval of interatomic distances from the multicenter interference effect revealed in the ratios of electron momentum profiles between two MOs with symmetric and anti-symmetric characters. However, the molecular geometry information is usually veiled due to the single-centered character of momentum space wavefunction of molecular orbital (MO).
Electron momentum spectroscopy is a unique tool for imaging orbital-specific electron density of molecule in momentum space.
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