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ScienceWeek
CHEMICAL PHYSICS: TOMOGRAPHIC ANALYSIS OF ELECTRON ORBITALS
The following points are made by Henrik Stapelfeldt (Nature 2004 432:809):
1) In medical tomography, the three-dimensional shape of a person's interior organs is derived from a series of two-dimensional X-ray images recorded at different angles. Itatani et al[1] have demonstrated how a new version of tomography, using laser pulses instead of X-ray beams, can determine the three-dimensional structure of a much smaller object: one of the electron clouds, or orbitals, in a nitrogen molecule (N2).
2) The tomographic orbital reconstruction is based on a series of images of the orbital shadow in different directions. It is obtained by irradiating a molecule, fixed in space, from different angles with an intense ultrashort laser pulse. A remarkable feature of the technique is that the laser pulse records the orbital image in less than a femtosecond (10^(-15) seconds). This time is so short that electrons in motion are frozen in the tomographic snapshot. In the near future, therefore, it should be possible to watch directly how electron clouds -- that is, the bonds of molecules -- change during chemical reactions. This would be progress indeed, and provide insight into one of the most fundamental steps in chemistry.
3) But how can a pulse from an optical laser image an electron cloud that is more than a thousand times smaller than the laser's wavelength? The answer lies in recent advances in understanding the interaction between molecules and intense laser pulses. The strong electric field of the laser pulse forces the most loosely bound electron away from the molecule. When the field reverses its direction, half an optical period later (about 1.3 femtoseconds for the pulse used by Itatani et al[1]), the electron is forced back to collide with its parent molecule. The electron gains so much energy from the laser field that its wavelength at the moment of recollision is about 0.14 nanometers -- short enough to probe the structure of the electron cloud through self-diffraction on the molecule.
4) It might seem most obvious to record the diffracted electrons. Instead, the authors measured the spectrum of the extreme "overtones" of the laser light emitted in the spectral range between the ultraviolet and the X-ray regime. These overtones result from the recollision process and have been termed "high harmonics"[2]. The high harmonic spectrum turns out to be extremely useful because, as the authors demonstrate, the orbital structure is mapped onto the spectrum. More precisely, for a given angle between the molecule and the direction of the recolliding electron, the shadow of the orbital can be extracted from the harmonics spectrum. The experimental strategy is to record the harmonics spectrum for a large number of collision angles. The orbital's three-dimensional shape is then reconstructed from all the corresponding shadows using a mathematical procedure that is essentially identical to that used in medical tomography.[3-5]
References (abridged):
1. Itatani, J. et al. Nature 432, 867-871 (2004)
2. Brabec, T. & Krausz, F. Rev. Mod. Phys. 72, 545-591 (2000)
3. Stapelfeldt, H. & Seideman, T. Rev. Mod. Phys. 75, 543-557 (2003)
4. Stolow, A. & Jonas, D. M. Science 305, 1575-1577 (2004)
5. Siwick, B. J. et al. Science 302, 1382-1385 (2003)
Nature http://www.nature.com/nature
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DIRECT VISUALIZATION OF THE SHAPES OF ELECTRON ORBITALS
Notes by ScienceWeek:
It is an old and often repeated adage that the most important piece of information possessed by the human species is that everything is made of atoms. Indeed, much of the physical sciences of the past 200 years has been devoted to providing the details concerning atoms, and much of the technology of this period has been devoted to exploiting these details.
The idea that matter is made of discrete and further indivisible building blocks goes back to the Greek philosopher Democritus of the 5th century BC. The joining of this philosophical idea with the analytical methods of physics began in the late 18th and early 19th centuries, with John Dalton (1766-1844) beginning the systematic development of the atomic theory. Then, in 1897, J.J. Thomson (1856-1940) clearly demonstrated that atoms are electromagnetically constituted, and that from atoms can be extracted fundamental material units bearing electric charge, the units called "electrons". The electrons of an atom account for only a negligible fraction of its mass, so that by virtue of the electrical neutrality of every atom, most of the mass must reside in a compensating positively charged component -- the atomic nucleus.
In the early years of this century, Niels Bohr (1885-1962) and others constructed "solar system" models of atoms containing planetary point-like electrons orbiting around a positive core, but these models were ultimately superseded by modern non-particulate wave quantum theories of both electrons and atomic nuclei. According to contemporary quantum mechanics, it is not possible to provide a definite path for an electron. According to wave quantum mechanics, the electron has a certain probability of being in a given element of space, and the probabilities of finding electrons in different regions can be obtained by solving the Schroedinger wave equation to give the wave function Psi, and the probability of location per unit volume is then proportional to the square of the absolute magnitude of Psi. Thus the idea of electrons in fixed orbits was replaced by that of a probability distribution around a nucleus -- an atomic orbital. Essentially, an atomic orbital (electron orbital) can be thought of as an electric charge distribution averaged over time, and in representing orbitals it is convenient to describe a surface enclosing the space in which the electron is likely to be found with a high probability.
The following points are made by J.M. Zuo et al (Nature 1999 401:49):
1) The authors report what is apparently the first experimental determination of the shapes of electron orbitals.
2) The authors used a combination of electron and x-ray diffraction to study the shape and bonding of copper atoms in copper oxide. The authors point out that their methods can be used to determine bonding in high-temperature copper oxide superconductors, a satisfactory theory for which has eluded researchers for more than a decade.
In a commentary on the work of Zuo et al, Colin J. Humphreys (Nature 1999 401:21) suggests that the paper by Zuo et al is remarkable because the quality of their charge-density maps allows, for the first time, a direct experimental "picture" to be taken of the complex shape of a higher level orbital (the d(subz)2 orbital), and that the correspondence between the experimental charge density map of Zuo et al and the usual textbook diagram of the d(subz)2 orbital is striking. Humphreys points out that although in crystals x-ray diffraction can reveal the main peaks of charge density, x-ray diffraction is normally unable to provide details concerning the shape of the charge distribution, in particular the shape of the bonds. The main reason for this is that crystals contain defects such as dislocations, and the x-ray scattering from such defects is greater than the scattering from bonding electrons. What Zuo et al have done is to use an electron microscope to image a crystal, select a perfect region between crystal defects, and then form a diffraction pattern from this perfect region. Using this method, it is possible to make very accurate charge density maps that reveal the shapes of electron bonds.
Nature http://www.nature.com/nature
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QUANTUM PHYSICS: ON ORBITS OF ELECTRONS AND PLANETS
The following points are made by C.R. Stroud Jr (Science 2004 303: 778):
1) An atom with many electrons is like a complex ballet, displaying an often chaotic interplay of orbits. Owing to the effects of quantum mechanics, the lowest energy orbits (or ground states) of many-electron atoms are stable. Excited states of the atoms do experience interactions, however, in which one of the electrons is liberated while the other falls to a lower state. The connection between these so-called autoionization processes and the classical orbits is generally obscured by the same quantum effects that stabilize the ground states.
2) In classical mechanics, a multielectron atom is similar to a planetary system [for a description of the classical planetary three-body problem, see (2)]. There are some differences, particularly the fact that the gravitational forces coupling planets with each other and with the Sun are always attractive, whereas the electrons in an atom all are attracted to the nucleus but repel each other. The classical orbits of these two systems have many similarities, including the presence of chaos (i.e., a sensitivity to initial conditions that leads to wildly different outcomes). There are also collisions between planets or electrons that can throw them free of their respective systems.
3) We observe in nature that our Solar System is relatively stable, and furthermore that the ground states of multielectron atoms are stable. The reasons for this stability are different in the two cases. In the Solar System the planets are in nearly circular orbits, each with a different radius, so that they are never very near each other. The gravitational force between each pair of bodies is proportional to the product of their masses, and because the planetary masses are much smaller than that of the Sun, the coupling with the Sun is much stronger than the planets' mutual attraction unless they get very close together indeed. Were the planets to have very eccentric orbits so that they crossed, the probability of a close collision would be much greater and the planetary system would be unstable (3).
4) In contrast, the ground-state atomic electrons are in highly eccentric crossing orbits with low angular momenta; these electrons also venture near the nucleus where their kinetic energy is very large, allowing large exchanges of kinetic energy in collisions. It is therefore rather surprising that atoms are stable. The classical description of the simplest multielectron atom, helium, was extensively investigated at the beginning of the last century in an attempt to apply the rules of the old Bohr atomic model (4). The attempt failed and ultimately led to the development of modern quantum theory, in which the smearing effects of Heisenberg's uncertainty principle and wave function symmetrization stabilize the ground state. Excited states of the two-electron atom, in which each electron is in a bound state but the sum of the energies of the two excited electrons is larger than the binding of a single electron, can be unstable. In this case, they would undergo autoionization in which one electron takes the energy of both electrons and is ejected while the second electron drops back to the ion ground state.(5)
References (abridged):
1. S. N. Pisharody, R. R. Jones, Science 303, 813 (2004)
2. M. C. Gutzwiller, Rev. Mod. Phys. 70, 589 (1998) [APS]
3. The orbits of Pluto and Neptune do indeed cross, but their orbits are extremely large, making a near-collision relatively less likely, and the planets are moving relatively slowly so that the kinetic energy available for exchange in a collision is rather small.
4. M. Born, Atomic Physics, authorized translation from the German edition by J. Dougall (G. E. Stechert, New York, 1936)
5. G. Tanner, K. Richter, J.-M. Rost, Rev. Mod. Phys. 72, 497 (2000)
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