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Curated by RSF Research Staff

Direct imaging of the wave function of an hydrogen molecule

The wave function is a mathematical object containing all the measurable information about the particle it describes. Used with the Schrodinger equation, it predicts the behavior of a dynamic system using conservation and Newtonian laws. As a theoretical object, wave function can’t be observed. However, the square of the function representing the probability to find the particle at a particular place is an observable and has recently been directly imaged by a team from Frankfurt in Germany.

The scientists choose to observe the hydrogen molecule, the simplest one, presenting two protons and two electrons. In this configuration, two molecular orbitals are created via the linear combinations of atomic orbitals approximation. The hydrogen molecule has as many molecular orbitals as there are atomic orbitals creating constructive interference between the two waves of the two hydrogen atoms. Thus, the internuclear electron probability density is increased.

Molecular Orbitals for the H2 Molecule. (a) This diagram shows the formation of a bonding molecular orbital. (b) This plot of the square of the wave function (Ψ2) for the bonding of molecular orbital illustrates the increased electron probability density between the two hydrogen nuclei. (c) This diagram shows the formation of an antibonding molecular orbital. (d) This plot of the square of the wave function for the antibonding molecular orbital illustrates the node corresponding to zero electron probability density between the two hydrogen nuclei.

Imaging the wave function of electrons give detailed information on the properties of matter. In solid state physics photoionization is used as a powerful tool for single-electron density imaging. Photon-based techniques can be implemented to go from still images to movies. For example, photoion mass spectrometry can fragment molecules over the energy excitation.

The wave function is not an observable in quantum physics, so it cannot be observed. Only the square of the wave function is an observable (if you have the tools to do it). This is one of the basic principles of quantum physics. Those who claim that they are able to observe the wave function are not using the proper language because this is not possible: what they do is to reconstruct it from some measured spectra by making some approximations. It can never be a direct observation.

M. Martins from the University of Hamburg, Germany

On the contrary, the reverse process of photoionization, namely high harmonic generation, can be used for orbital imaging such as other technic like electron momentum spectroscopy or strong field tunnel ionization. The novelty of the recent discovery made by the team of M. Martins was to be able to directly observe the wave function of a many-body systems. They succeeded in measuring the correlation between the constituents and the spatial and the momentum distribution of one electron depending on those of the other electrons and the nuclei. They have implemented an imaging scheme which allows to visualize these correlations between electrons. With this technique, they examined the H2 two-electron wave function and showed the dependence of the wave function on the internuclear distance.

Obviously, the natural step to follow is to try a similar method in more complicated molecules," Martín said. "Most likely, the method will work for small molecules, but it is not clear if it will work in very complex molecules. Not because of limitations in the basic idea, but mainly because of experimental limitations, since coincidence experiments in complex molecules are much more difficult to analyze due to the many nuclear degrees of freedom.

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