Hydrogen atoms under the magnifying glass:

Direct Observation of the Nodal Structures of Electronic States of the Hydrogen Atom

21st May 2013

To describe the microscopic properties of matter and its interaction with the external world, quantum mechanics uses wave functions, whose structure and time dependence is governed by the Schrödinger equation. In atoms, electronic wave functions describe - among other things - charge distributions existing on length-scales that are many orders of magnitude removed from our daily experience. In physics laboratories, experimental observations of charge distributions are usually precluded by the fact that the process of taking a measurement changes a wave function and selects one of its many possible realizations. For this reason, physicists usually know the shape of charge distributions through calculations that are shown in textbooks. That is to say, until now. An international team coordinated by researchers from the Max Born Institute has succeeded in building a microscope that allows magnifying the wave function of excited electronic states of the hydrogen atom by a factor of more than twenty-thousand, leading to a situation where the nodal structure of these electronic states can be visualized on a two-dimensional detector. The results were published in Physical Review Letters (http://physics.aps.org/articles/v6/58) and on physicsworld.com and provide the realization of an idea proposed approximately three decades ago.

The development of quantum mechanics in the early part of the last century has had a profound influence on the way that scientists understand the world. Quantum mechanics extended the existing worldview based on classical, Newtonian mechanics by providing an alternative description of the micro-scale world, containing numerous elements that cannot be classically intuited, such as wave-particle duality, the importance of interference and entanglement, the Heisenberg uncertainty principle and the Pauli exclusion principle. Central to quantum mechanics is the concept of a wave function that satisfies the time-dependent Schrödinger equation. According to the Copenhagen interpretation, the wave function describes the probability of observing the outcome of measurements that are performed on a quantum mechanical system, such as measurements of the energy of the system or the position or momenta of its constituents. This allows reconciling the occurrence of non-classical phenomena on the micro-scale with manifestations and observations made on the macro-scale, which correspond to viewing one or more of countless realizations allowed for by the wave function.
Despite the overwhelming impact on modern electronics and photonics, grasping quantum mechanics and the many possibilities that it describes continues to be intellectually challenging, and has over the years motivated numerous experiments illustrating the intriguing predictions contained in the theory. For example, the 2012 Nobel Prize in Physics was awarded to Haroche and Wineland for their work on the measurement and control of individual quantum systems in quantum non-demolition experiments, paving the way to more accurate optical clocks and, potentially, the future realization of quantum computers. Using short laser pulses, experiments have been performed illustrating how coherent superpositions of quantum mechanical stationary states describe electrons that move on periodic orbits around nuclei. The wave function of each of these electronic stationary states is a standing wave, with a nodal pattern that reflects the quantum numbers of the state. The observation of such nodal patterns has included the use of scanning tunneling methods on surfaces and recent laser ionization experiments, where electrons were pulled out of and driven back towards their parent atoms and molecules by using an intense laser field, leading to the production of light in the extreme ultra-violet wavelength region that encoded the initial wave function of the atom or molecule at rest.
About thirty years ago, Russian theoreticians proposed an alternative experimental method for measuring properties of wave functions. They suggested that experiments ought to be performed studying laser ionization of atomic hydrogen in a static electric field. They predicted that projecting the electrons onto a two-dimensional detector placed perpendicularly to the static electric field would allow the experimental measurement of interference patterns directly reflecting the nodal structure of the electronic wave function. The fact that this is so, is due to the special status of hydrogen as nature‘s only single-electron atom. Due to this circumstance, the hydrogen wave functions can be written as the product of two wave functions that describe how the wave function changes as a function of two, so-called “parabolic coordinates”, which are linear combinations of the distance of the electron from the H+ nucleus “r”, and the displacement of the electron along the electric field axis “z”. Importantly, the shape of the two parabolic wave functions is independent of the strength of the static electric field, and therefore stays the same as the electron travels (over a distance of about half a meter, in our experimental realization!!) from the place where the ionization takes place to the two-dimensional detector.
To turn this appealing idea into experimental reality was by no means simple. Since hydrogen atoms do not exist as a chemically stable species, they first had to be produced by laser dissociation of a suitable precursor molecule (hydrogen di-sulfide). Next, the hydrogen atoms had to be optically excited to the electronic states of interest, requiring another two, precisely tunable laser sources. Finally, once this optical excitation had launched the electrons, a delicate electrostatic lens was needed to magnify the physical dimensions of the wave function to millimeter-scale dimensions where they could be observed with the naked eye on a two-dimensional image intensifier and recorded with a camera system. The main result is shown in the figure below. This figure shows raw camera data for four measurements, where the hydrogen atoms were excited to states with 0, 1, 2 and 3 nodes in the wave function for the ξ = r+z parabolic coordinate. As the experimentally measured projections on the two-dimensional detector show, the nodes can be easily recognized in the measurement. As this point, the experimental arrangement served as a microscope, allowing us to look deep inside the hydrogen atom, with a magnification of approximately a factor twenty-thousand.
Besides validating an idea that was theoretically proposed more than 30 years ago, our experiment provides a beautiful demonstration of the intricacies of quantum mechanics, as well as a fruitful playground for further research, where fundamental implications of quantum mechanics can be further explored, including for example situations where the hydrogen atoms are exposed at the same time to both electric and magnetic fields. The simplest atom in nature still has a lot of exciting physics to offer!

Figure: (left) two-dimensional projection of electrons resulting from excitation of hydrogen atoms to four electronic states labeled with a set of quantum numbers (n1,n2,m) and having (from top to bottom) 0, 1, 2 and 3 nodes in the wave function for the ξ = r+z parabolic coordinate; (right) comparison of the experimentally measured radial distributions (solid lines) with results from quantum mechanical calculations (dashed lines), illustrating that the experiment has measured the nodal structure of the quantum mechanical wave function.

Contact

Aneta Stodolna, FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
Prof. Marc J.J. Vrakking, Tel: +49-30-6392 1200, Max-Born-Institut, Max Born Straße 2A, D-12489 Berlin, Germany

Neighbors move electrons jointly - an ultrafast molecular movie on metal complexes in a crystal

Applying femtosecond x-ray methods, researchers at the Max-Born-Institute in Berlin (Germany) and the Ecole Polytechnique Federale de Lausanne (Switzerland) observed an extremely fast, collective electron transfer of ~100 molecular ions after excitation of a single electron in a crystal of transition metal complexes.

15th April 2013

Photochemistry and molecular photovoltaics make frequent use of so-called transition metal complexes which consist of a central metal ion bonded to a group of surrounding ligands. Such materials display a strong absorption of ultraviolet or visible light, making them attractive as primary light absorbers in molecular solar cells and other devices of molecular optoelectronics. Absorption of light is followed by an extremely fast shift of electrons from the metal ion to the ligands, a mechanism that is essential for generating an electric voltage. All applications rely on solid state materials in which transition metal complexes are densely packed and can interact with each other. So far, the influence of this interaction on the very fast electron motions following the absorption of light has remained unclear.

To observe ultrafast electron motions in space and time, one needs to measure the position of electrons in the material with a precision of the order of 0.1 nm (0.1 nm =10^-10 m), roughly corresponding to the distance between neighboring atoms, and on a sub-100 fs time scale (1 fs = 10^-15s). This is possible by imaging the material with extremely short x-ray pulses which are scattered from the electrons and provide their spatial arrangement. The electron motions are initiated by an ultrashort optical pulse which excites an electron on an individual complex. In the current issue of Journal of Chemical Physics 138, 144504 (2013) (free download), Benjamin Freyer, Flavio Zamponi, Vincent Juve, Johannes Stingl, Michael Woerner, Thomas Elsaesser and Majed Chergui report the first in-situ x-ray imaging of electron and atom motions induced by such an electron transfer excitation. For the prototype material [Fe(bpy)₃]²⁺(PF_6-)₂, they show time-dependent 'electron maps' derived from x-ray snapshots taken with 100 fs long hard x-ray flashes. Taking x-ray snapshots at various times during and after the optical pulse that triggers the charge transfer, creates a molecular movie of electron and atom motions.

To the big surprise of the researchers, the time-dependent 'electron maps' reveal a transfer of electronic charge not only from the Fe atoms to the bipyridine units but - so far unknown -  an even larger amount of electronic charge from the PF_6- counterions to the bipyridine units. The analysis of the x-ray snapshots shows that the charge transfer affects approximately 30 complexes around the directly photo-excited one. This collective electron response is caused by the electric Coulomb forces between the different ions and minimizes the total electrostatic energy in the crystal. Such behavior is highly favorable for charge collection and injection in optoelectronic devices.

Contact

Michael Woerner, Tel: +49-30-6392 1470
Thomas Elsaesser, Tel: +49-30-6392 1400

Figures and movie: Upper panels: sticks and balls model of the transition metal complex iron(II)-tris-bipyridine [Fe(bpy)₃]²⁺. Iron-atoms (Fe) are brown, nitrogen (N) blue, carbon grey, and hydrogen (H) white. The six nitrogen atoms are at the corners of an octahedron around the Fe atom. The planes of the 3 bipyridine subunits (N₂C₁₀H₈) are mutually perpendicular. Left lower panel: the counterions in our crystal are two hexa-fluoro-phosphate (PF_6-) molecular subunits [phosphorus (P), fluorine (F)]. Again, the six F atoms are at the corners of an octahedron around the P atom. We show here a 3-dimensional surface of constant electron density ρ(r,t) = ρ_C = const. ρ_C was chosen in such a way that we are most sensitive to the motion of electronic charge located at the PF_6- anion. In the attached movie we observe upon photo excitation a pronounced reduction of the electron density on that PF6- anion, i.e. a shrinkage of the iso-electron density surface. Right lower panel: 3-dimensional surface of constant electron density of the unit cell showing the spatial arrangement of Fe atoms (balls), bipyridine subunits (pretzel-like objects), and PF_6- anions (octahedron-like stars).



Bottom: cartoon of the collective charge transfer in [Fe(bpy)₃]²⁺(PF_6-)₂ which affects approximately 30 complexes around the directly photo-excited one. Blue: reduction of electron density, red increase of electron density.