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Douglas B. Cameron
A Casual Introduction
When arbitrary objects are packed into a container, the container might not hold an exact integral number of objects, but it has some excess space too small for one more object. Were the container elastic it could be stretched to hold an additional object or contracted to remove the extra space. The external shape of the filled container might be a compromise between the packing of objects inside the container and the natural shape of the container itself.
A similar phenomenon occurs at the quantum scale. At very cold temperatures or small scales, the wavelength of the objects to be packed can be comparable to the dimensions of the container. At this quantum scale, objects no longer have sharp delineations but have gently varying probabilities of being at any particular position. This probability distribution is best represented as a wave function or density curve. Packing quantum objects into a container is best thought of as packing these probability densities into the container.
Obviously, objects at common human scales cannot be simultaneously placed at the same position. However, on the quantum scale the pressure of the bounding container causes probability densities to overlap.* The external shape of a container of quantum objects is a compromise between the packing of these probability densities.
The compromise between packing and distortions of electrons in atomic containers is the basis for the structural and optical properties of all molecules. In the context of this work the containers are small metal particles. The objects to be packed are the outer electrons of the metal atoms. In metals these outer electrons roam freely across atoms. (Unlike the inner electrons which are bound tightly to the atom and can be ignored as a first approximation.) For historical reasons these are not traditionally referred to as molecules but as metal clusters.
If a number of electrons fit within a container without encouraging distortion the number is termed a closed shell. Open shells distort their containers. Certain symmetric containers could distort in any of a number of equal ways to satisfy distorting forces. The arbitrary distortions that result are known as Jahn-Teller distortions.1 For example a circular volume remains circular with a closed shell number of electrons, but with an open shell undergoes ellipsoidal distortions along an arbitrary axis.
Schematically portrayed as:
The same phenomena would occur for "boxes" of electrons:
Small metal particles or clusters of 3-100 atoms that are not in contact with a surface behave as such quantum containers. These analogies are most accurate for metals whose valence electron density is relatively symmetric about the atom - independent of the underlying d-orbital electrons. This includes the alkali and coinage (Cu, Ag, Au) metals.
In this work, experiments determined the energy required to remove an electron from gas phase silver clusters. An apparatus was built to generate and detect clusters of the coinage metals. A pulsed laser was used to vaporize a metallic surface, then material from the surface was condensed into clusters inside a pulse of helium. Clusters were detected with time-of-flight mass spectroscopic techniques.
The energy to extract an electron from a neutral cluster was obtained by laser irradiation of the cluster to determine photoionization energy. Such ionization potentials were determined for most clusters in the range Ag3-Ag100.
|A theoretical model based on ellipsoidal distortions of a ductile volume containing an equivalent number of valence electrons explains almost all the observed photoionization patterns.|
|A comparison of this model to experimental results suggests the existence of shape isomers in metal cluster structure.|
Overall, the similarity to the experimental results is remarkable. Below is a comparison (from Chapter 4) of experimental () and calculated () photoionization potentials. The oscillations are reproduced with surprising fidelity, although little attempt has been made to make the model accurate in an absolute sense, .
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Douglas B. Cameron
1) H. A. Jahn, E. Teller, Pro. R. Soc. London Ser. A, 1937, 161, 220.