Thomas Crawford
Superatoms
Senior Comprehensive Paper
4/11/07
Abstract
Superatoms are clusters of ions which, as a whole, can exhibit properties of specific
chemical families, such as halides and alkaline earth metal ions. The unique mimicking
characteristics of superatomic clusters are due to their ionization potentials, which act
similarly to electron shell closings. Al13- was found to exhibit properties of the halides,
whereas Al14++ exhibits alkaline earth metal properties, and have great electronic and
geometric stability. Clusters of M@Au14 (M= Zr, Hf) and M@Au14 (M=Sc, Y) (where @
symbolizes a single atom encapsulated within a compound) were found to have very
large HOMO-LUMO gaps, with the latter set of clusters having an electron affinity
greater than that of elemental chlorine. [As@Ni12@As20]3- is a cluster whose superatomic
core is protected by a cage, possibly allowing for rather unstable superatomic clusters or
atoms to be stabilized. These superatoms will help pave new avenues of discovery across
many fields in science.
2
I. Introduction
Though superatoms have been developed and created only recently, they offer a
new path of study in inorganic materials production. Superatoms are defined as “clusters
of atoms which seem to exhibit some of the properties of elemental atoms.” 1 As opposed
to when two separate substances come together and form a compound whose properties
are different than their constituents, such as sodium and chlorine, these clusters can come
together to form compounds which can mimic the properties of elements. The purpose of
this paper is to bring to light recent developments of a phenomenon which is currently
being pursued by many different fields in science.
The beginning of the creation of superatomic clusters began in the 1960’s and
1970’s and were considered only as small molecules with no observed special properties
or periodicity. Independent studies in the early 1980’s began to develop the image of a
superatom as having a free-electron structure with the positive ionic cores spread
throughout the cluster, within an equally distributed, finite volume, ignoring the ionic
bonding characteristics of the cluster.
2,3,4
The nuclei and core electrons are spread out
over a predefined potential well, with valence electrons filling up electronic shells,5 and
the electron energy levels are grouped in a fashion similar to the nuclear shell model.6
The jellium model treats the cluster of atoms as a jelly-like blob, hence the name jellium.7
Clusters on the order of thousands of molecules began to be developed, and little to no
change in properties was observed between the gigantic and the tiny clusters.2
The creation and separation of metal clusters can be achieved by a variety of
means. When necessary, the clusters are separated by means of mass analyzers as a wide
variety of cluster sizes are produced.2 In general, the production of metal clusters relies
3
on the vaporization of a metal source and the subsequent cooling of the vapor to allow for
aggregation. Experimental procedures for cluster creation are discussed on page 23,
section V. 2
These superatoms fill their electron shells in the exact same manner as would
normal atoms. However, studies have focused on ionization potentials of the metal cluster,
as these potentials act similarly to filled electron shells (Figure 1). This is due to the fact
that these ionization potentials have characteristic local maxima that match electron shell
closures.3
Figure 1. Graph which shows the degeneracy of the states within the jellium model on the momentum scale,
which are subshells. Shows how many electrons are required for an ionization potential subshell closure
along with the corresponding subshell. 8
Metal cluster chemistry follows a different method of defining the principal
quantum number n, called the nuclear convention, whereas the most general and well
known method for chemists is the atomic convention. In the nuclear convention, the
shells created are denoted by both an n and l. For l, the lowest possible state is n = 1. No
4
physical analog exists between the atomic and nuclear principle number, n. l is also not
bound by n, so states which would not normally be seen in the atomic orbital diagram
appear in the nuclear orbital diagram.9,10 Figure 2 displays the difference between the
atomic orbital and the nuclear orbital energy diagram.
Figure 2. A. Energy diagram for atomic orbital. B. Energy diagram for nuclear orbital. Not to
scale.11
The occupancy for each level is determined by the equation
ms(2l+1) = ml (Equation 1)
or
2(2l+1) = ml (Equation 2)9
5
Similar to the stability characteristic of the filling of atomic orbitals, the nucleus may also
have stability at certain filled shells. Figure 3 provides a look at how the degeneracy of
some states varies depending on the shape of the potential well for the jellium cluster,
specifically three-dimensional harmonic, intermediate and square-well potentials. Also, it
is important to note that depending on the well’s shape state, the spaces between shell
closings, as well as ordering of potentials may vary significantly. 2
Figure 3. From left to right, occupation of various energy levels in a three dimensional spherical,
intermediate, and square potential well. Note that depending on the shape of the potential well, the ordering
of states may be modified. 2
According to the Aufbau principle, or the build-up principle, each electron
introduced to the atom should enter into the lowest energy filled orbital. The general
order of filling proceeds as 1s22s22p63s23p64s23d10… and so on until there are no more
6
electrons added to the atom. And each time an orbital is filled, the atom exhibits a certain
stability which is mainly found in the noble gases. Therefore, there are “magic numbers”
which dictate the point at which one shell is completely filled. For examples, helium has
a full 1s orbital and neon has a full 2s and 2p orbital. These magic numbers correspond to
each filled shell: Thus the magic number for helium would be 2 for 2 electrons filling the
1s orbital; and the number for neon would be 8, for the filled 1s, 2s, and 2p orbitals. The
sequence for these numbers is 2, 10, 18, 36, 54 and 86, corresponding to filled shells
(Figure 4). 12
Figure 4. Image of the concept of the Aufbau or building up principle. 12
To summarize, superatoms rely heavily on the idea of magic numbers. That is, at
certain points of cluster size, some clusters are more stable than other cluster sizes that
preceded or anteceded the original. This is due to the fact that at some point, there is a
closing of an electron shell, a shell in terms of ionization potential, or a structural shell.
These closures occur at a specific number of atoms or electrons and are termed ‘magic
7
numbers’ for their marked stability. The numbers vary, however, depending on the
property focused on, either the structure or electron count. One point to remember is that
there are no set list magic numbers; that is, the list is not arbitrarily made. These numbers
are recorded and observed because they constantly arise from spectroscopy or
experimental data for which there is a great abundance. For example, focusing on the
number of electrons in shell closures will show that the noble gases are the most stable,
as they have completed an electron shell. The quantum number shell closures would
occur at every noble gas, being 2, 10, 18, 36, 54 and 86 electrons. Focusing on ionization
potentials will lead to a different picture of stability, with stability being reached with
every subshell closures. Closures of this kind occur at 2, 8, 18, 20, 34, 40, 58, 68, 90, 92,
106, 132, 138, and 156 electrons, which, following the nuclear convention, would
translate to 1s1p1d2s1f2p1g2d1h3s2f1i3p2g electron configurations2. Structural closures
vary greatly, though, as one must take into account a vast assortment of high-order
geometric shapes. Icosahedra and cuboctahedra shell closures occur at 13, 55 and 147
atoms, whereas a tetrahedral structure needs 4, 10 and 20 atoms.8 For example,
Icosahedra and cuboctahedra structures can be determined by the equation
N(K) = 1/3(10K3
+ 15K2 + 11K + 3)
1
(Equation 3) 8
where N is the number of atoms, and K is the shell index. So, for the first appearance of
an icosahedra or cuboctahedra, K = 1, and when used in the equation, the number of
atoms needed is 13. For K = 2, the number required is 55. Table 1 displays a list of the
numbers required for a complete shell in various structures. 8
8
Table 1: List of number of atoms needed to create a variety of geometric figures. 8
II. Characteristics
Depending on the number of neutrons and/or protons in the nucleus, specific
combinations give rise to a structure within the nucleus which exhibits an enhanced
stability. For instance, helium has 2 protons and 2 neutrons, which are both magic
numbers. Oxygen has 8 neutrons or 8 protons, which are also both magic numbers. In the
case of these two, the magic number is reached when a geometric figure with a high
degree of order is created by the protons or neutrons - for instance, a bipyramidal figure
or an icosohedron.13, 14
Also, to add to the image of cluster stability, it is important to look at the effects
of different subshells, sizes, and shapes. When adding in all intermediates to figure 1, a
pattern emerges, which appears to be alternating bands of light and dark. However, more
than just a graphical pattern, as depicted in Figure 5, at certain points, subshells build up
to create a bunched state, known as a supershell.8
9
Figure 5. Bunching of subshells into states as depicted by the alternation of dark and light bands. 8
This creation of an electronic shell was also observed in the 1984 Knight et al. paper,
which stated that these structures can be seen when there is either a large dip in ionization
energy with an increasing cluster size or a sharp increase or decrease in mass spectra
peak intensity, as seen in Figure 6.8, 15
Figure 6. Graph of change in electronic energy versus number of sodium atoms. Each labeled peak
represents a shell closure.15
10
Another characteristic of the supershell is its enhancement through a phenomenon
called supershell beating. Due to the fact that components of an atom exhibit a waveparticle duality, the possibility exists of the potential for constructive and destructive
interference that could occur between different orbital patterns. Specifically, interference
exists between square and triangular wave orbitals inside a well of potential.4 The
constructive interference creates a large amplitude curve in the area of binding energies,
whereas the destructive interference only provides a small amount of total interference.
When plotted as a shell correction factor δF (being the difference between the cluster
energy and the average part) versus N1/3 (where N is the number of atoms in the cluster),
a sine-wave like pattern begins to emerge. When extrapolated to fit different temperatures,
and in this figure at absolute zero, a pattern is clearly visible with steps occurring at the
magic number sequence, 2, 8, 20, 34, 58, 92 etc. (Figure 7).4
Figure 7. Shell Correction Factor (energy difference) versus N1/3. 4
11
Finally, the shape of the cluster must be taken into account. As stated previously,
there exists an enhanced stability to some clusters of a specific size. Upon the addition of
an extra atom to a closed-shell cluster, a new shell is created, with a size increase
generally proportional to the cluster element’s interatomic distance. Clusters with an
enhanced stability will have a central atom which may pose a problem with evennumbered clusters. Simply put, more elaborate schemes are necessary to create an evennumbered stable cluster. Clusters with high-order geometry, such as icosahedrons or
cuboctohedrons, are also a great source of stability. According to a paper by Martin, et al.,
the first point at which a complete encapsulated icosahedral complex is formed from a
total of 13 atoms (which can be viewed as Al@Al12, where @ symbolizes a single atom
encapsulated within a compound), which is of great import due to topics addressed later
in this paper. 8
To bolster the experimental data, a mathematical system known as DFT, or
Density-Functional Theory, is employed to explain the observed experimental results.
DFT was created to discern the structure of multi-component systems, especially for the
condensed matter phase. Previously, the most common method to describe many-bodied
systems looked at the wave-function properties of the atoms, which relied on Cartesian
coordinates for every electron in the system to be properly described. Instead, DFT
simply looks at the density as a function of three variables, easing the work load.16
Within DFT, there are two other commonly used forms of the construct - KohnSham DFT and Local Density Approximation (LDA). First, Kohn-Sham is used to
simplify the problem of many bodies interacting in a given cluster. Instead of looking at
the many-bodied cluster as having interacting electrons and a static potential, Kohn-Sham
12
defines the cluster as having non-interacting electrons within an effective potential. This
effective potential includes Coulomb interactions between the electrons and the effective
potential. LDA comes into play when these Coulomb interactions have to be determined,
as defining the interactions otherwise requires a great deal of work. With LDA any
energy exchange within the system is given an exact number easily matching the results
of the interactions had they been obtained experimentally.16 The LDA model is actually
derived from the jellium model, as it treats the interaction energy in every point in the
cluster’s space as an interaction energy of a non-interacting cloud of electrons.17
In relation to other methods of calculations, DFT is a more efficient system than
previous means of determining structure, reactivity, and other properties. The HartreeFock method focuses on the wave functions of the electrons by using a complicated set of
equations. These equations are processed until all possible combinations of wave
functions are agreed upon within a certain criteria defined by the user. Another set of
calculations are semi-empirical methods and ab initio methods. Semi-empirical methods
rely mainly on using estimated integrals based on spectroscopy or physical properties of
the atom and work within a series of parameters that set specific integrals within the
calculations to zero. Ab initio methods attempt to calculate all secular determinant
integrals. Again, while the results prove to be rather close to experimental results, it takes
a large amount of computational calculations which require a good deal of time and
computing power.18
13
III. Current Research
Walter Knight’s group was among the first to begin research on superatoms.
Knight et al. published a paper in 1984 which focused on producing clusters of sodium
atoms. The results showed that there were large peaks in mass spectra which occurred at
NaN where N = 8, 20, 40, 58 and 92 (Figure 8). Other peaks were found to occur at 18, 34,
68, and 70, but were weaker due to the sensitivity of the parameters from the equation
used to calculate these potentials. 15
Figure 8. Mass spectrum of Sodium ions. Note that each step shows the amount of cluster ions and not
electron count, so each peak noted above is one step above the observed magic numbers. Peaks for 18, 34,
68, and 70 actually were found, but were weaker than the rest of the peak absorbencies. 8, 15
They realized that the peaks occurred at those intervals because the structure exhibited a
free-electron model with the 3s valence electrons were delocalized throughout the
cluster.15 This pioneering work helped spark the recent development into the field of
metal cluster chemistry.
Castleman’s group has recently published a paper on aluminum clusters following
the example of Leuchtner, et al. whose paper proposed that a special inertness of certain
anionic aluminum clusters, specifically clusters Al13- , Al27-, and Al37- exists. They were
14
testing the reactivity of aluminum clusters to oxygen etching; that is, clusters were
formed and then stripped away oxidatively of single aluminum atoms, one by one. Al13- ,
Al27-, and Al37- clusters could not be reduced further. As stated previously, the jellium
model allowed for stable clusters in accordance with the magic number rule. In this case,
Aluminum, having 13 electrons (of them, three valence electrons), provides a total of 39
valence electrons in the Al13 cluster, one electron short of the jellium magic number of 40.
Figure 1 illustrates that an electron ionization potential shell closure occurs at 40
electrons, which fills the 2p6 electron in the series 1s21p61d101f142s22p6. The addition of
an extra electron, making the compound Al13-, satisfies this closed electron rule, causing
it to become a very stable compound. In this respect, the Al13- cluster is similar to a halide,
in that it has 1 valence electron to donate toward a compound.9
Apart from having characteristics of halide ions, these aluminum clusters do not
form polyhalide-like compounds. For example, polyiodides form according to the
equation I2n+1- in chains, with an I2 molecule as the center and either I- or I3- attaching to
this center. I5- forms a chain with a V-shape, having two iodides attached to a single
iodide between the two arms. As it was predicted that Al13- can act as a halide, it would
seem that the cluster could also form these polyhalide chains.3 However, such is not the
case. Upon the addition of I2, the cluster favors the breaking of the I-I bond and the
formation of an Al-I bond. By looking at the atomization energies of these two
compounds, one can see that Al-I and I2, show that Al-I has a total energy of 3.83 eV,
whereas I2 only has a 2.21 eV atomization energy. In addition, the compound Al-I3
exhibits an atomization energy of 8.75 eV, bringing the Al-I atomization energy to 2.92
eV per iodide atom. On an interesting note, though, while the Al-I bonding may not be
15
structurally similar to polyhalide molecules, it maintains a certain stability for a total odd
number of atoms in the molecule, for these Al-I clusters are most stable with an even
number of iodine ions.3,19 The charge density of the HOMO and the addition of the 40th
electron to the Al13 cluster were analyzed and it was found that the extra negative charge
was delocalized throughout the cluster, further adding to this image of aluminum having
a superhalide character.19 In addition, another paper reported the electron affinity of the
Al13- cluster as being 3.57 eV, which is just a few hundredths of an eV under the electron
affinity of Cl, 3.61 eV.20
Upon the addition of more iodides, the Al13In- cluster exhibited an interesting
pattern. It seemed that when Al13In-, with the addition of an even number n of iodine,
showed a greater stability than odd number n (See figure 9B). When the Al13In- cluster
has an odd number of n, the reaction produces an active site, an area of charge density,
opposite from where the odd numbered atom is placed, as seen in Figure 9A. Also, when
this cluster has an odd number of I, it bonds in a sigma-like fashion; when there is an
even number, the bond exhibits a pi-like character. In each case of n up to 13, the cluster
maintains an almost perfect icosohedral structure. 3,19
16
Figure 9. A. Charge density maps of Al13In- (n= 1-12). The arrows point to where active sites are created
after addition of an odd number of I atoms. B. Plot in Energy required to remove an I from the cluster, from
1-12. 19
Conflicting evidence exists as to whether or not Al14++ can be regarded as
a superatom. Both Castleman, et al. papers suggest that Al14++ adheres to the jellium
magic number rule, as 14 Al would give the total valence shell count of 42, with the 2+
charge giving it a character of the alkaline earth metals. The Al14++ cluster also exhibits
the odd-even characteristic of halogen bonding as the Al13- cluster; however, instead of
being stable at every even step, its maximum stability is reached with an odd number of
iodine (Figure 10B). Al14 may be viewed as Al@(Al13) (where @ symbolizes a single
atom encapsulated within a compound) if one still considers the Al13 core as a halide,
with the 14th aluminum occupying a triangular face of the icosahedron (Figure 10A). 19
17
Figure 10. A. Structure and bond length characteristics of Al14In- (n= 1-3) B. Change in energy required to
remove an I atom from the cluster, for x = 1-12. Notice that its strongest peak does not start until x=3. 19
Figure 11. Charge density plots and the activation of active sites during even/odd I addition. 3
18
Han and Jung contest, however, that the Al14In- cluster does not fit the jellium
model. Rather, they argue that it is a stabilized metal-ligand cluster, as there is little
difference between the Al14 compound and Al14I3-.
6
Also, there are structural and
electrical dissimilarities between the Al14 and Al13 cores; Addition of iodine to the Al14
cluster changes the electrical identity of the cluster from anionic to cationic and its
structure from a capped-icosohedron to a “wheel” shape cluster respectively, as seen in
figure 12.6 Furthermore, the only point at which the Al14 core can be considered as a
jellium model is when three iodides are added to the Al14 cluster, making it a 40 electron
closed shell. 3, 19
Figure 12. Progression of icosahedral structure of Al14In- (n = 4-11) to wheel like structure upon successive
addition of I. 6
A paper by Gao et al. provided some research on gold cage clusters which
exhibited properties of superatoms. They first noted that Au clusters exhibited a very
19
large HOMO-LUMO gap, indicative of a very stable structure. They reported that the
icosohedral W@Au12 had a measured HOMO-LUMO gap of 1.68 eV, and the tetrahedral
Au20 cluster had a gap of 1.77eV; according to the Gao’s group the latter is the largest
gap among similar size cluster structures. They further reported two new types of Au
clusters - a gold-caged structure of M@Au14 (M= Zr, Hf) and an anionic cage cluster
M@Au14- (M=Sc, Y). Also, according to DFT calculations, these two new clusters
should exhibit a HOMO-LUMO gap larger than that of W@Au12 and Au20. Perhaps,
even more interesting, the M@Au14- (M=Sc, Y) have an electron affinity of 3.97eV,
which is not only greater than the Al13 cluster (3.57 eV), but even higher than elemental
Cl (3.61 eV). Table 2 lists the various properties of the gold caged structures and the
aluminum cluster species. 20
Table 2: List of experimental and calculated results for various atomic properties.20
Another group, King and Zhao, provided an interesting structure in which one
part, the icosahedral [As@Ni12@As20] 3- cluster, exhibits superatomic properties, depicted
in Figure 13.
20
Figure 13. Image of the equilibrium icosahedron structure of [As@Ni12@As20] 3-. Bonds between the Ni
layer and the outer As layer are removed to allow for a better image. 21
They related the structure of the cluster to that of the matryoshka nesting doll, a Russian
toy, whereupon taking apart one layer revealed a smaller layer, on until the smallest
component was reached. The outer layer of the cluster is an As20 dodecahedron, which
encompasses a Ni12 inner layer, which in turn contains an As3- ion. The arrangement of
the electrons is such that they can be allocated among each layer, allowing for a closed
electron shell layers. The As3- anion has an electron configuration of Krypton. There are a
total of 100 electrons in the As20 dodecahedron shell: 60 electrons for 2c-2e bonds, 40
electrons as lone pairs on each of the arsenic atoms, and negligible interactions with the
Ni12@As3-. As20 uses its lone electron pairs to act as an icosadentate ligand to the Ni12
layer, which brings about a jellium-like configuration of 40 electrons similar to the Al13cluster. 21
Noteworthy in this compound is the protecting feature of its shell. The As20
stabilizes the inner two layers, which under normal circumstances would collapse and
form other compounds. This protection could be extended to other compounds which
21
exhibit superatomic properties but cannot exist either stably or outside of the gaseous
phase. 21
IV. Applications
Castleman and Jena produced a 2006 paper which outlines a few potential
applications for clusters and cluster chemistry. Much like ionic crystals, these clusters
have a stable and highly uniform structure. The uses of these metal clusters are being
looked into as new sources of materials for their stability and properties as either stacked
crystalline structures or as a gigantic cluster system. Once these clusters are able to be
stabilized, they will become a great source of new materials. Covalently bonded clusters,
such as the fullerene C60, have already been tested extensively for their ability to
encapsulate metals, which would provide a new source for conductive materials.22
Also, it is speculated that clusters will have a great impact on the medical
community, specifically for cancer therapies. A problem that arises in current cancer
therapy is the non-specificity of some cancer treatments which do achieve their desired
goal of destroying the cancer, but also destroy a wealth of healthy cells. One suggested
method is to create nanoparticles that specifically target any malignant bodies. One group
has created a method which utilized silica coated with gold particles to perform this task.
The gold modifies the HOMO-LUMO gap in the silica; the silica is then able to react to
small amounts of infrared radiation and thus heat up and destroy the desired target.
Another method developed to treat for brain tumors uses radio frequencies instead of
infrared radiation to heat the embedded metal cluster molecules.22
22
V. Methods of Cluster Creation
Sources of cluster production:
Seeded supersonic nozzle source (Figure 14): The metal to be used is vaporized in
an oven and is then introduced to an inert gas (like a seed into a field) as the oven is
pressurized with the inert gas to the order of several atmospheres. This gaseous mixture is
then ejected at a high speed through a small hole into a vacuum, which then cools the
metallic vapor adiabatically. Metallic clusters then form from the supersaturated vapor
until the vapor density decreases to a small amount. This technique is the most common
and high-yield method of cluster production.2
Figure 14. Seeded supersonic nozzle source basic diagram. 2
Gas-aggregation cluster source (Figure 15): Metal is vaporized and then
combined to a cold inert gas, causing the vapor to become supersaturated. Clusters form
by means of metal atoms stacking together one by one.2
23
Figure 15. Gas-aggregation cluster source basic diagram. 2
Laser vaporization cluster source (Figure 16): A rod of the metal to be used is
inserted in a screw-like manner into apparatus. A pulsed laser is focused on the rod which
vaporizes the metal. A pulsed stream of cold helium is then applied to the metal vapor,
which causes the vapor to become supersaturated, with cluster formation proceeding by
single atom addition. This means of cluster production is viewed as a hybrid of the
previous two cluster producing methods.2
Figure 16. Laser vaporization source basic diagram.2
24
Sputtering source (Figure 17): A metal disk is bombarded by a beam of excited
inert gas ions. This method, unlike the previous ones, does not utilize the inert gas to
allow for condensation of the metal vapor. Unfortunately, the means by which cluster
formation occurs with the sputtering source method is not very well understood.2
Figure 17. Sputtering source basic diagram. 2
Liquid metal ion source (Figure 18): A small sample of metal is placed at the
head of a needle and then heated beyond its normal melting point. An electric potential is
applied, causing the liquid metal to spray in minute quantities from the tip. This multiplyionized and hot metal vapor then begins to condense by means of evaporative cooling. 2
25
Figure 18. Liquid-metal ion source basic diagram. 2
Sources of cluster differentiation:
Wien filter (Figure 19): A beam of clusters is propelled along uniform electric
and magnetic fields, with the uniform electric field perpendicular to the magnetic field,.
These two fields are perpendicular to the cluster beam. The ions are then sorted
depending on the charge-to-mass ratio, enabling only a specific m/z to pass through the
filter undeflected. 2
Figure 19. Wien filter basic diagram. 2
26
Quadrupole mass filter (Figure 20): A cluster beam is propelled through a field of
DC and AC energy. Clusters with a specified m/z ratio that corresponds to the AC/DC
current field will be allowed to pass through the filter. 2
Figure 20. Quadrupole mass filter basic diagram.2
Time-of-flight mass spectrometry (Figure 21): The clusters are ionized by means
of an ultraviolet light or electron beam and then fired out of an ion gun. The charged
beam accelerates through a field-free empty space and impacts on an ion detector. The
flight-of-time, the amount of time the cluster takes to reach the detector, determines its
m/z ratio. 2
Figure 21. A. Time-of-flight mass spectrometer. B. Reflectron mass spectrometer. This allows for
a greater resolution than the TOF mass spectrometer. 2
27
Ion cyclotron resonance mass spectroscopy: Cluster ions are enclosed in a threedimensional trap. A static quadrupole electric field and a uniform magnetic field are
applied to the trap to produce a resonant frequency of the clusters. This frequency is
picked up by an antenna and is Fourier analyzed. It directly correlates to the m/z ratio of
the cluster. 2
Molecular-beam “chromatography”:
Cluster ions are produced by laser
vaporization and sorted by mass selection. They are then introduced into a tube with
pinhole exit and entry pathways containing an inert gas and are propelled by a weak
electric field. Mobility of the metal clusters is affected by the inert gas due to the shape of
the cluster. Thus, clusters of a similar mass are separated temporarily by geometric
isometry. This method will be an immense help with certain metal clusters with similar
composition but varying shape. 2
VI. Conclusion
With further research, superatoms will have a major impact on the entire future of
science. Their amazing ability to mimic elements of the periodic table will yield the
production of designer materials. Many of the papers consulted for this report either
explicitly stated or have referenced a paper that stated that these clusters with
superatomic properties will help transform Mendeleev’s 2-dimensional periodic table into
a 3-dimensional one. Already, it has been reported that there are Aluminum clusters with
enhanced stability and exhibited alkaline earth metal and halogen-like activity. Gold
clusters, too, have provided many interesting properties, whether a greater electron
28
affinity than that of elemental chlorine or, when encasing silica, the ability to absorb
energy and act as a chemical scalpel to remove malignant growths. I believe that
development of this new science will revolutionize many sciences and markets in the
near future.
29
References:
1. Superatom. http://en.wikipedia.org/wiki/Superatom, Oct. 2, 2006.
2. de Heer, W.A. Rev. Mod. Phys. [Online] 1993, 65, 611-676.
3. Bergeron, D.E.; Roach, P.J.; Castleman, Jr., A.W.; Jones, N.O.; Reveles, J. U.;
Khanna, S.N. J. Chem. Phys. [Online] 2006, 124, 154311 1-8.
4. Brack, M. Rev. Mod. Phys. [Online] 1993, 677-732.
5. Harms, A. C.; Leuchtner, R. E.; Sigsworth, S. W.; Castleman, Jr, A. W. J. Am.
Chem. Soc. [Online] 1990, 112, 5673-5674.
6. Han, Y.K.; Jung, J. J. Chem. Phys. [Online] 2006, 125, 084101-1-7.
7. Ball, P. A new kind of alchemy. New Scientist. [Online] 2005, 186, 30-33.
8. Bergmann, T.; Gohlich, H; Martin, T.P.; Lange, T. J. Phys. Chem [Online] 1991,
95, 6421-6429.
9. Watts, D. Nuclear and Particle Physics: Lecture 7.
http://www.ph.ed.ac.uk/~dwatts1/np3_07_l7.pdf, 4/2/2007.
10. Nave, C. Shell model of nucleus. http://hyperphysics.phyastr.gsu.edu/hbase/nuclear/shell.html 4/2/2007.
11. Tomlin, B.E. Nuclear structure below 132Sn: An investigation of neutron-rich
nuclides via βand isomeric decay. Ph. D. Dissertation, Michigan State
University, East Lansing, Michigan, 2006.
12. Aufbau Principle. http://en.wikipedia.org/wiki/Aufbau_Principle, Oct. 4, 2006.
13. Borg, Xavier. The Particle - The wrong turn that led physics to a dead end.
http://www.blazelabs.com/f-p-magic.asp. 3/01/07.
14. Borg, Xavier. Magic numbers derived from a variable phase nuclear model.
http://www.blazelabs.com/magicnumbers.pdf 3/01/07.
15. Knight, W.D.; de Heer, W.A.; Saunders, W.A.; Clemenger, K; Chou, M.Y.;
Cohen, M.L. Phys. Rev. Let. [Online] 1984, 52, 2141-2143.
16. Density functional theory.
http://en.wikipedia.org/wiki/Density_functional_theory, Oct. 26, 2006.
17. Local-density Approximation. http://en.wikipedia.org/wiki/Localdensity_approximation, Oct. 26, 2006.
18. Atkins, P.; de Paula, J. Physical Chemistry. 7th ed. W.H. Freeman and Company:
N.Y., 2002, 441-445.
19. Bergeron, D.E.; Roach, P.J.; Castleman, Jr., A.W.; Jones, N.O.; Khanna, S.N.
Science. [Online] 2005, 307, 231-235.
20. Gao, Y.; Bulusu, S.; Zeng, X.C. J. Am. Chem. Soc. [Online] 2005, 127, 1568015681.
21. King, B.R.; Zhao, J. Chem. Comm. [Online] 2006, 4204-4205.
22. Castleman, Jr., AW; Jena, P. PNAS. [Online] 2006, 103, 10554-10559.
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