Article
pubs.acs.org/JPCC
Al12Cu Superatom as Stable Building Block of Ionic Salts
J. U. Reveles,*,†,‡ Tunna Baruah,‡,§ and Rajendra R. Zope‡,∥
†
Department of Physics, Virginia Commonwealth University, 701 West Grace Street, Richmond, Virginia 23284, United States
Department of Physics, University of Texas El Paso, 500 West University Avenue, El Paso, Texas 79968 United States
‡
S Supporting Information
*
ABSTRACT: The neutral copper aluminum cluster complex
Al12CuM3 [M = K, K3O, and K(2,2,2-crypt)] has been
investigated at the PBE96 level of theory. It is found that
Al12Cu could be considered a superatom mimic of a
phosphorus atom. It shows large electron affinity and is able
to receive three electrons from elements or compounds with
low ionization energies like K, K3O, or K(2,2,2-crypt) to
become a stable electronic closed shell with a large gap
between the highest occupied and lowest unoccupied
molecular orbitals (HOMO−LUMO gap). Theoretical calculations confirm that similar to the phosphorus atom in PK3, the
superatom Al12Cu cluster could form ionic salts, as shown from stable dimers, trimers, and tetramers of the Al12Cu{K(2,2,2crypt)}3 complex. On the basis of the maintenance of its integrity in these assemblies it could be predicted that Al12CuM3 holds
great potential as a building block for the development of future nanostructured materials. Furthermore, the choice of the
K(2,2,2-crypt) molecules to stabilize the salt opens a route to experimentally generate cluster base ionic salts, and we expect that
our work motivates experimental investigations of these assemblies.
1. INTRODUCTION
The search for stable clusters is one of the most active fields in
experimental and theoretical materials science today aimed to
develop nanostructured materials with tailored properties.1−8 It
has been found that collective phenomena exhibited in bulk
materials break down for very small sizes. For example, small
clusters of Rh, a nonmagnetic material, are magnetic,9 noble
elements like gold and platinum turn active catalysts when
reduced on the nanoscale,10,11 and highly reactive elements like
aluminum, which is readily oxidized by oxygen, are unreactive
for selected anionic cluster sizes.1,6 Because the properties of
the clusters depend on its size, geometry, composition, and
charge state, one can envision designing novel materials made
of stable clusters with selected catalytic, magnetic, and
structural properties.
Given the vast possibilities of sizes, composition, and charge
states, developing an understanding of the factors that govern
the structural and electronic stability is a critical step toward a
rational search of stable species. Previous experimental studies
of gas-phase sodium (Nan) clusters by Knight and coworkers12
showed noticeable peaks in the mass spectra at sizes of 2, 8, 18,
20, 40, and 58 atoms. The abundance of clusters of particular
sizes indicated that these clusters must be more stable than
others. Further investigations of the electronic properties were
undertaken and the ionization energy, electron affinity,
polarizability, and fragmentation patterns of these species
were determined to obtain an understanding of this stability. A
drop in ionization energies at sizes corresponding to electronic
count one above the stable species as well as low values of
electronic affinities at the stable sizes were observed.13
© 2015 American Chemical Society
Furthermore, experiments on the dissociation of clusters
showed that the stable sizes were the favored fragmentation
products and that more energy was required to fragment these
sizes.14,15
In simple metals, a confined free electron (CFE) model is a
good representation of the electronic spectrum, and Knight and
Ekardt12,16 proposed such a model to explain the experimentally observed stability of the alkali clusters. In this model,
the nuclei together with the innermost electrons form a
positively charged background that acts over the valence
electrons of the system, resulting in the arrangement of the
cluster’s valence electrons into 1S2, 1P6, 1D10, 2S2, 1F14, 2P6, ...
subshells similarly to the 1s2, 2s2, 2p6, 3s2, 3p6, ... subshells
found in individual atoms. Because each alkali atom contributes
with one electron to the valence pool, the stable sizes at 2, 8,
18, 20, 40... all correspond to electron counts that result in filled
electronic shells. At larger cluster sizes the extended cluster
orbitals tend to condense into highly degenerated shells and
geometrical effects begin to contribute to the stability.17−19 For
example, experiments on sodium clusters containing up to
several hundred atoms showed that the principal peaks in the
mass spectrum could be reconciled as being due to geometric
effects.17
These principles that rule electronic and geometrical stability
have been successfully applied to other metallic clusters.
Experimental observations by Castleman and coworkers1 on
Received: December 9, 2014
Revised: January 30, 2015
Published: February 4, 2015
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likely that random orientations of the clusters will favor
configurations in which the metal−metal intermolecular
interactions will collapse the building units toward the more
stable global minimum.
The aim of this paper is to explore if truly stable ionic
superatomic assemblies are indeed possible. Motivated by the
work of Kumar and Yoshiyuki that reported a high-spin
icosahedral ground state for Al12Cu with a magnetic moment of
3 μB,42 we investigate if Al12Cu, being able to accept three
electrons from elements and compounds with a low ionization
energy to form ionic (Al12Cu)3−(M+)3 species, may be a
suitable candidate to form stable nanostructures. In particular,
the following questions are addressed: Is the large negative
charge in the anionic (Al12Cu)3−superatom able to overcome
the intermolecular attractions in the ionic salts preserving its
identity? How large should an ideal cationic M species needs to
be to help sustaining the assembly through steric hindrance?
Our study shows that neither K nor K3O cations can avoid
collapse of the ionic species in the cluster assemblies and that it
is only the bulkier K(crypt-222) cation that allows the
formation of chemically and energetically stable ionic salts
[Al12Cu{K(crypt-222)}3]n (n = 1−4) of the Al12Cu cluster
superatom in a similar way as phosphorus does in PK3.
the reactivity of aluminum cluster anions with oxygen found
that while most clusters were etched away by oxygen, clusters
containing 13 and 23 atoms were relatively intact. Subsequent
theoretical studies by Khanna and Jena20 and Gong and
Kumar21 showed that both Al13− and Al23− clusters correspond
to closed-shell systems. For example, Al13− is a stable chemical
cluster that would neither give nor receive electrons as has a
large HOMO−LUMO gap of 1.87 eV. The cluster also showed
to be energetically stable as it would take almost 4.65 eV to
remove an Al atom from Al13− as opposed to 3.02 and 2.08 eV
required to remove an atom from Al 12 − and Al 14 − ,
respectively.20,22 Furthermore, the electronic structure of
Al13− showed 40 valence electrons (three valence electrons
per Al atom) that can be arranged according to the CFE model
in an 1S2, 1P6, 1D10, 2S2, 1F14, and 2P6 closed-shell
configuration. Subsequent theoretical23 and experimental
studies24 indicated that Al13 has a large electron affinity of
3.57 eV, and having 39 valence electrons is only one electron
short of a 40 electron closed shell. These results raised the
question of whether the neutral Al13 and anionic Al13− clusters
may be considered as mimics of halogen and noble-gas
elements, respectively, and led to the proposition that selected
clusters resembling the electronic and chemical behavior of
different atoms could be regarded as their superatom mimics
with the formation of a third dimension in the periodic table.
Over the past few years, superatoms resembling alkaline
earth,25 multiple valence,26 superalkali,27 transition metals,28−30
and halogen,6,31 atoms have been proposed.
Superatom complexes have also been investigated toward the
goal of building nanostructure materials with tailored properties. Khanna and Jena proposed that Al13− being analogous to
Cl− could form an ionic species similar to K+Cl−.32 Their
results showed that Al13−K+ is a stable ionic species with an
intact Al13− anionic moiety and that Al13K has a large HOMO−
LUMO gap of 1.72 eV being consistent with an ionic salt.
Calculations by Liu et al.,33 however, showed that the alkali
cations are not large enough to form a stable lattice. Further
experimental and theoretical studies have reported other Al13M
(M = Li, Na, and Cs) species,34−37 and Zheng et al.38
successfully produced Al13K in the gas phase. All of these
systems are, in fact, stepping stones toward the formation of
ionic cluster assemblies composed of aluminum-based
superatoms and appropriate cations. However, one has to
realize that strong metal−metal interactions between clusters
favor interatomic bonding rather than the stabilization of
separate units. For instance, Seo and Corbett showed that small
aluminum clusters tend to collapse with an increased number of
Al−Al contacts,39 and Ashman et al. studied the formation of
ionic compounds of Al7C− with alkali metals, finding hardly any
distortion in the original cluster unit; nevertheless, dimers and
tetramers of the Al7CLi species formed intermolecular Al−Al
bonds.40
Reber et al.41 reported Al13M3O as a strongly bound
molecule that can be used to form stable superatom assemblies
(Al13M3O)n (M = Na and K, n = 1−5) with Al13− and M3O+ as
the superatom building blocks, and Qiong31 showed that the
halogen superatom Al3C maintains its integrity in ionic
complexes with K atoms: [(Al3C)(KCAl3)n] (n = 1−5).
These reports are certainly encouraging; they, however, are
also indicative of the challenges in designing superatom
assemblies. Both Reber et al. and Qiong found local minima
resulting from a unique orientation of the cationic and anionic
units in their cluster assemblies. In experiments, however, it is
2. COMPUTATIONAL METHOD
The theoretical calculations are carried out within the density
functional formalism with the description of exchangecorrelation effects at the generalized gradient approximation
level by means of the Perdew, Burke, and Ernzerhof (PBE96)
functional.43 The electronic orbitals and eigenstates are
determined by using a linear combination of Gaussian
atomic-type orbital molecular orbital (LCGTO) approach in
the deMon2k software.44,45 The calculation of four-center
electron repulsion integrals is avoided using a variational fitting
of the Coulomb potential,46 and the exchange correlation
energy and potential are calculated via a numerical integration
of the fitted density47 using the GEN-A2 auxiliary function
set.48 All electrons of the Al, Cu, K, and O atoms are treated
explicitly using the double-ζ valence plus polarization (DZVP)
basis sets.49 Relativistic effective core potentials with 1, 4, 5, 6,
3, and 19 valence electrons for K, C, N, O, Al and Cu were
employed, respectively, with their corresponding basis sets50 to
speed up the calculations of the larger [Al12Cu{K(crypt222)}3]n (n = 1−4) systems, which range from 202 to 808
atoms. The geometry optimization used a quasi-Newton
method in internal delocalized coordinates and all possible
spin configurations were investigated to determine the most
stable states.51,52 Partial charges were determined using a
natural bond orbital (NBO) analysis.53
To further eliminate any uncertainty associated with the
choice of basis set, the numerical procedure, and the use of
pseudo potentials, we carried out supplementary all-electron
calculations using the Naval Research Laboratory Molecular
Orbital Library (NRLMOL) set of codes developed by
Pederson and coworkers.54−56 For these calculations the same
PBE96-generalized gradient approximation used in deMon2k
was employed.43 We found excellent agreement in the
optimized geometries and energy order of the investigated
spin states for the clusters between deMon2k and NRLMOL
calculations.
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Figure 1. Optimized geometries for Al12Cu and Al12CuXn (X = K, K3O, and Crypt; n = 1−3). Molecular spin multiplicity is given by the superscripts.
The electronic charges are marked next to the Al12Cu and X fragments. Light-blue, yellow, brown, gray, red, dark-blue, and white circles represent Al,
Cu, K, C, O, N, and H atoms, respectively.
that the filled 3d states of Cu are located between the 1P6and
1D10 states. Notably, the highest occupied energy levels
correspond to triple-degenerate 2P3 states three electrons
short to complete the shell, similar to a phosphorus atom with a
[Ne] 4s23p3 configuration. Moreover, our calculated electron
affinity of 2.92 eV, in good agreement with the experimental
value of 3.24 ± 0.03 eV reported by Pal et al.,57 indicated a
larger tendency of Al12Cu to receive electrons. Pal et al. also
employed a Basin-hopping global optimization method and
found a slightly distorted icosahedral with D3d symmetry to be
ground-state geometry of the anionic Al12Cu−. The gas-phase
anionic Al12Cu− has also been produced as reported in an
experimental and theoretical study by Roach et al.58 The
authors, however, noted that the cluster was oxygen-etched and
did not show signs of chemical stability, presenting a small
HOMO−LUMO gap of only 0.2 eV. The rationale for this
behavior is rooted in its electronic structure. One extra electron
is not enough to complete the cluster’s 2P subshell to generate
a stable species. The 2P subshell of Al12Cu cluster can, however,
be completed by the addition of three electrons, as discussed
later.
3.2. Al12CuKn Clusters and Its Assemblies. With the goal
to obtain a closed-shell cluster, we studied the interaction of K
atoms (an electron donor with low ionization energy) with the
Al12Cu cluster. We investigated the charge transfer by
calculating NBO charges and the energy gained with successive
3. RESULTS AND DISCUSSION
3.1. Al12Cu Superatom. As previously noted, several
studies have explored Al superatoms as potential building
blocks of ionic materials, but strong intermolecular interactions
between these have limited the potential to build truly stable
cluster assemblies. In this work we study the Al12Cu neutral
species with a goal to design a stable superatom with a large
negative charge because such a system can result in ionic
compounds with increased stability. Kumar and Kawazoe
reported the finding of a high-spin icosahedral ground state for
Al12Cu with a magnetic moment of 3 μB in accordance with the
Hund’s rule of maximum spin at half-filling of a P shell forming
an open-shell superatom.42 Several possible geometries and
spin states were investigated in our study, and it was found that
the most stable structure for Al12Cu did correspond to the Cu
atom inside a slightly distorted icosahedral cage with D3d
symmetry and Al−Al and Al−Cu bonds of 2.79 and 2.65 Å,
respectively, as shown in Figure 1, and presenting a quartet spin
state (having three unpaired electrons), in agreement with the
previous report.42 An analysis of the electronic structure of
Al12Cu accounts for a total of 37 delocalized valence electrons
(three electrons for each Al and one electron for the Cu atom)
arranged in 1S2, 1P6, 1D10, 2S2, 1F14, and 2P3 subshells
according to the CFE model, as shown by the one-electron
energy levels and molecular orbital isosurfaces in Figure 2. Note
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Figure 3. One-electron energy levels near to the HOMO level for the
Al12Cu, K, Al12CuK, Al12CuK2, and Al12CuK3 species. Molecular spin
multiplicity is given by the superscripts. Main and angular quantum
numbers are given for selected levels showing the progressive filling of
the 2P superorbitals marked in a blue rectangle. Solid black lines and
dotted red lines represent, respectively, occupied and unoccupied
states.
Figure 2. One-electron energy levels and molecular orbital isosurfaces
for Al12Cu. The main and angular quantum numbers for the
delocalized superorbitals and the 3d Cu localized orbitals are also
given. The 2P superorbitals are marked in a blue rectangle. Solid black
lines and dotted red lines represent, respectively, occupied and
unoccupied states.
Our next step in the investigation of ionic cluster assemblies
was to study the structural and electronic properties of dimers
of the ionic Al12CuK3 cluster. Several initial orientations of the
(Al12CuK3)−(Al12CuK3) dimer were prepared and fullgeometry optimizations were performed. The initial geometries
showed signs of structural stability, and we did actually find a
stable dimer in which the Al12CuK3 units remain separated and
exhibit a large HOMO−LUMO gap of 1.36 eV, as shown in
Figure 5a. However, because of the metal−metal interactions
between the Al12Cu units, another more stable complex was
also found with an Al−Al bonding between adjacent cores at a
short distance of 2.90 Å. This structure resulted in being more
stable by 1.21 eV and had a smaller HOMO−LUMO gap of
only 0.64 eV, which is indicative of less chemical stability
(Figure 5a). This result is also consistent with a report by
Ashman et al.22 that studied the mobility of alkali atoms on the
Al13 surface. The authors found that the barrier for the motion
of a K atom from one hollow site to another is <0.13 eV,
indicating that it may be possible for K atoms to be mobile at
ordinary temperatures and hence are not good protecting
cations for the aluminum core.
3.3. Al12Cu(K3O)n Clusters and Its Assemblies. We then
changed our strategy by turning efforts to the use of molecular
counterions rather than atomic ions. These ions have two main
advantages. First, they present low ionization energies like
single alkali atoms assuring a good charge transfer when
forming a molecular salt. Second, and the more important
advantage, is that the bulkier nature of these molecular
counterions increases the steric hindrance, which helps in
avoiding the agglomeration of separate clusters into a bulk
material.
Motivated by the work of Reber et al.,41 who reported
Al13M3O as a strongly bound molecule that retains its integrity
in ionic complexes of the type (Al13M3O)n (M = Na and K, n =
1−5) with separated Al13− and M3O units; we first studied the
binding of the super alkali K3O molecule with our Al12Cu
superatom aimed to form a stable closed-shell species like the
one found for Al12CuK3. We begin by investigating the charge
transfer and the energy gained with successive additions of K3O
additions of K atoms to Al12Cu, incremental binding energy
(IBE), in Al12CuKn by using the equation
IBE = E[Al12CuK n] − E[K] − E[Al12CuK n − 1], with n = 1−5
Here E[X] represents the total energy of the gas-phase
species. Note that according to this definition a positive IBE
corresponds to a bound structure and a larger value of IBE is
indicative of an energetically more stable structure. Addition of
one K atom resulted in a large energy gain of 2.0 eV to form
Al12CuK in which the K sits on top of a hole of a slightly
distorted Al12Cu cage (Figure 1). The one-electron energy
levels indicate that one electron was transferred to the 2P
subshell of Al12CuK that now presents a triplet state with two
still unpaired electrons and a small HOMO−LUMO gap of
0.24 eV (Figure 3). Our population analysis supports this
conclusion with −0.97 and 0.97 electronic charges for the
Al12Cu and K fragments. Further addition of K atoms also
showed large energy gains for the second and third K atoms of
1.93 and 1.85 eV, respectively, and a drop in the IBE after 3 K
atoms to only ∼0.7 eV (Figure 4a). The optimized geometries
and electronic charges for these species are presented in Figure
1. Moreover, the calculations also indicate a progressive
increase in the HOMO−LUMO gap (and thus in the chemical
stability) with each addition of K atoms as the 2P subshell gets
filled with the charge given by the K atoms, reaching a
maximum gap of 1.44 eV for the compact closed-shell Al12CuK3
cluster (Figures 1 and 3). We confirm the ionic nature of this
species via our population analysis that found −2.88 and 0.96
electronic charges in Al12Cu and each K atom, respectively.
Figure 4a graphically presents the calculated IBE and HOMO−
LUMO gap for the Al12CuKn clusters attesting for both the
energetic and chemical stability of the Al12CuK3 species that
presents maxima compared with neighboring sizes.
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6a, a set of occupied energy levels of K3O lies above the
unoccupied 2P levels of Al12Cu. The bonding combinations of
these levels give rise to an Al12CuK3O complex that exhibits a
polar covalent interaction between the two units. The polar
nature of the bonding is attested by the calculated charge
transfer and the covalent character is attested by the observed
bonding between Al and O. Furthermore, the stronger
interaction in this case becomes evident from the large energy
gain of 6.16 eV for the addition of K3O to Al12Cu. This energy
is three times larger than the energy gain (1.99 eV) for the
addition of a single K to Al12Cu. The addition of another K3O
to Al12CuK3O also resulted in a large energy gain of 4.61 eV.
The population analysis of the optimized Al12Cu(K3O)2 cluster
indicates an increase in the charge transfer toward the Al12Cu
core, which now acquires a negative −2.49 electronic charge
(Figure 1). The energy levels for this cluster reveal a 2P5
configuration for the highest occupied subshell in a doublet
state with still one unpaired electron and a smaller HOMO−
LUMO gap of 0.33 eV. Finally, the addition of a third K3O
resulted in an energy gain of 4.46 eV accompanied by
additional charge transfer such that the Al12Cu core now
acquires a negative −3.38 charge in the closed-shell Al12Cu(K3O)3 species with a HOMO−LUMO gap of 0.67 eV. Further
addition of K3O resulted in smaller energy gains and species
with smaller HOMO−LUMO gaps, as shown in Figure 4b.
These results suggested that the stable closed-shell Al12Cu(K3O)3 cluster can be a promising candidate as a building block
of ionic assemblies. To explore this we prepared several initial
orientations of the Al12Cu(K3O)3−Al12Cu(K3O)3 dimer, which
were then fully optimized. Notably, we again found the
formation of a stable complex with separated Al12Cu(K3O)3
units exhibiting a HOMO−LUMO gap of only 0.47 eV, as
shown in Figure 5b. However, as in the case of the (Al12CuK3)2
dimer, strong metal−metal interactions between the Al12Cu
units conducted to another more stable complex with the
presence of Al−Al bonding between adjacent cores at a
distance of 2.69 Å. This structure resulted in being more stable
by 0.76 eV and had a smaller HOMO−LUMO gap of only 0.15
eV in a triplet-state configuration (Figure 5b).
Interestingly, our results disagree with the report of Reber et
al.,41 wherein the lowest energy dimer of (K3OAl13)2 was found
to be a bent structure with oxygen occupying on-top positions
at the Al13 surface and with an energy barrier of >0.14 eV
toward the formation of the Al26−K6O3 species. To investigate
the cause of discrepancy, we also calculated the Al13K3O−
Al13K3O dimers starting from several initial configurations and
found that it is only when the species are disposed such that the
K3O on one Al13K3O is oriented toward the Al13 side of the
second Al13K3O that we are able to reproduce the results of ref
41. All other possible configurations of the dimers led to the
formation of more stable Al26−K6O3 species without any
energy barrier. In actual experiments, it is likely that random
orientations of the clusters will favor configurations in which
the metal−metal intermolecular interactions will collapse the
building units toward the more stable global minimum with the
loss of the individual cluster identities and properties.
Similarly, another study by Qiong31 showed that the halogen
superatom Al3C maintains its integrity in ionic complexes when
bonding with K atoms in the form [(Al3C)(KCAl3)n] (n = 1−
5). We again calculated these clusters and found that it is only
in the structural configuration given by the author that the
species retains its identity and that other possibilities resulted in
collapsing of the aluminum clusters into more stable
Figure 4. HOMO−LUMO gap (HL gap) and incremental binding
energies (IBEs) for the (a) Al12CuKn, (b) Al12Cu(K3O)n, and (c)
Al12Cu(Crypt)n, n = 1−5 clusters.
molecules (IBE) in forming Al12Cu(K3O)n by using the
equation
IBE = E[Al12Cu(K3O)n ] − E[K3O] − E[Al12Cu(K3O)n − 1],
with n = 1−5
The addition of the first K3O resulted in a large energy gain
of 6.19 eV to form Al12CuK3O in which the O atom strongly
binds to an Al atom at a short distance of 1.77 Å. This distance
is within the range of 1.7 to 2.0 Å reported for the Al−O bond
in AlnO2 (n = 1−5) clusters by Sun et al.59 Surprisingly,
Al12CuK3O presented a closed-shell configuration (Figure 1)
with a HOMO−LUMO gap of 0.7 eV. This result is intriguing
given that according to our population analysis only 1.43
electrons are transferred from the K3O superalkali cluster into
Al12Cu, which is in need of three electrons to complete its 2P
subshell as previously mentioned. The analysis of the electronic
structure sheds light onto this apparent contradiction.
According to the one-electron energy levels shown in Figure
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Figure 5. Optimized geometries for dimers of the (a) Al12CuK3 and (b) Al12Cu(K3O)3 clusters. Molecular spin multiplicity is given by the
superscripts. The relative energies (Erel) and HOMO−LUMO gaps (HL gap) are also given.
Al12Cu fragments, respectively. The calculated energy gain of
3.19 eV for the addition of Crypt to Al12Cu is >1 eV larger than
the energy gain for the addition of a single K atom to Al12Cu of
only 1.99 eV.
The addition of second Crypt to Al12Cu(Crypt) resulted in
an energy gain of 2.63 eV, and the resultant structure of
Al12Cu(Crypt)2 has the K atom of the second Crypt sitting on
top of an Al atom of the Al12Cu cage. The one-electron energy
levels of Al12Cu(Crypt)2 in Figure 6b indicate that an additional
electron from the second Crypt has been transferred to fill
another empty 2P level of Al12Cu such that the Al12Cu(Crypt)2
complex now presents a doublet spin state with only one
unpaired electron in a 2P5 electronic configuration and with a
small HOMO−LUMO gap of 0.19 eV. The population analysis
in this case shows that the Al12Cu core acquires a negative
charge of −2.03 electrons from the Crypt molecules, and each
Crypt molecule has a positive electronic charge of nearly one
electron (Figure 1). Finally, the addition of the third Crypt
resulted in an energy gain of 2.2 eV, where the Al12Cu core has
a −2.98 charge in the closed-shell Al12Cu(Crypt)3 species that
presented a rather large HOMO−LUMO gap of 1.38 eV. The
addition of a fourth Crypt resulted in a smaller energy gain of
1.1 eV and the formation of an Al12Cu(Crypt)4 less stable
species with a smaller HOMO−LUMO gap of 0.27 eV. Further
addition of a Crypt resulted in a nonbonded species, showing
that the maximum number of Crypt molecules that can bind
the Al12Cu core is four. These results are collected in Figure 4c.
We then directed our efforts to explore the potential of the
closed-shell Al12Cu(Crypt)3 species as a resilient building block
of ionic assemblies. We prepared several initial orientations of
the Al12Cu(Crypt)3−Al12Cu(Crypt)3 dimer that were then fully
optimized. In this case and for the first time in our studies we
found that the Al12Cu(Crypt)3 units were able to retain their
identity toward the formation of the {Al12Cu(Crypt)3}2 dimer,
as shown Figure 7, and with a binding energy of 1.41 eV.
configurations. These results suggest that an even larger
molecular cation is needed to prohibit fusion of aluminum
clusters in the formation of ionic solids.
3.4. Al12Cu(Crypt)n Clusters and Their Assemblies. The
results in previous sections indicate that the K and K3O ions
cannot prevent coalescence of the Al12CuM3 (M = K and K3O)
cluster due to their smaller sizes and we therefore choose the
bulkier K encapsulated K(2.2.2-cryptand), from now on called
Crypt, as the electron donor for our Al12Cu superatom with the
hope that its larger size could stabilize the ionic assemblies.
Cryptands are a family of synthetic bi- and polycyclic
multidentate ligands for a variety of cations.60 These molecules
are 3D analogues of crown ethers but are more selective,
complex the guest ions more strongly, and exhibit low
ionization energies. We begin by studying the binding of the
Crypt molecules with our Al12Cu superatom with a goal to
obtain a stable closed species like the ones found for Al12CuK3
and Al12Cu(K3O)3. We investigated the charge transfer and the
energy gained with successive additions of Crypt molecules
(IBE) in forming Al12Cu(Crypt)n in a similar way as we did
above for the K and K3O electron donors.
The addition of the first Crypt resulted in a large energy gain
of 3.19 eV to form the Al12CuCrypt complex in which the K
atom of the Crypt sits on top of an Al atom of the Al12Cu cage
at a distance of 4.56 Å (Figure 1). The optimized Al12CuCrypt
has multiplicity of 3 and a small HOMO−LUMO gap of 0.14
eV. The state with spin multiplicity of 1 is energetically
degenerate with this state. Figure 6b presents the one-electron
energy levels for Al12Cu, Crypt, and Al12Cu(Crypt)n, n = 1−3.
It can be seen that a single occupied energy level from the
Crypt lies above the 2P unoccupied states of Al12Cu and that it
is this Crypt state that transfers one electron to form a 2P4
configuration in the triplet state of Al12CuCrypt. The
population analysis results are consistent with this observation
and show 1.04 and −1.04 electronic charges for the Crypt and
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Notably, the assembly is also chemically stable, presenting a
large HOMO−LUMO gap of 1.09 eV. Further additions of
Al12Cu(Crypt)3 units to form trimers and tetramers were
investigated by approaching the additional Crypt units from the
possible orientations and fully optimizing the geometries. We
found that as in the case of the dimer both trimer and tetramer
resulted in stable assemblies with energy gains of 0.26 and 0.95
eV for the addition of Al12Cu(Crypt)3 units to the dimer and
trimer, respectively. The dimer, trimer, and tetramers also had
relatively large HOMO−LUMO gaps of 1.09, 0.97, and 0.93
eV, respectively (Table 1). Most importantly for the formation
Table 1. Gap between the Highest Occupied and Lowest
Unoccupied Molecular Orbitals (HOMO−LUMO gap) for
the {Al12CuCryptx}y (x = 1−4, y = 1−4) Complexa
HOMO−LUMO gap (eV)
1
Al12Cu(Crypt)
Al12Cu(Crypt)2
1
Al12Cu(Crypt)3
2
Al12Cu(Crypt)4
1
{Al12Cu(Crypt)3}2
1
{Al12Cu(Crypt)3}3
1
{Al12Cu(Crypt)3}4
2
a
0.14
0.19
1.38
0.27
1.09
0.91
0.93
Molecular spin multiplicity is given by the superscripts.
of stable ionic salts is that the Al12Cu(Crypt)3 cluster retained
its identity in all of the optimized geometries, as shown in
Figure 7. On the basis of these results, we confirm that similar
to the phosphorus atom in PK3 the superatom Al12Cu cluster
could indeed form truly ionic salts of the Al12Cu(Crypt)3
complex and that assemblies of the Al12CuM3 type hold great
potential as building blocks for the development of novel
nanostructured materials with tailored properties.
Figure 6. One-electron energy levels for the (a) Al12Cu, K3O,
Al12Cu(K3O)n and (b) Al12Cu, Crypt, Al12Cu(Crypt)n, n = 1−3
clusters. Molecular spin multiplicity is given by the superscripts. Main
and angular quantum numbers are given for selected levels showing
the progressive filling of the 2P superorbitals marked in a blue
rectangle. Solid black lines and dotted red lines represent, respectively,
occupied and unoccupied states.
4. CONCLUSIONS
Our theoretical study demonstrates that Al12Cu exhibits
electronic and chemical behavior similar to that of a
phosphorus atom and can be considered its superatom
mimic. Al12Cu being a 37-valence-electron system corresponds
to an open-shell system three electrons short to complete its
Figure 7. Optimized geometries for the ionic solids formed by the successive addition of Al12Cu(Crypt)3 units. Molecular spin multiplicity is given
by the superscripts.
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superatomic 2P subshell. It forms ionic compounds with K,
K3O, or Crypt with a high energetic and chemical stability. Our
results show that although both K and K3O provide the
required number of electrons, the size of these ions is not large
enough to keep strong metal−metal intermolecular interactions
from collapsing the cluster during the formation of cluster
assemblies. Notably, the larger Crypt ion is found to be the
ideal cation to donate the needed electrons and to prevent the
Al12Cu core from coalescing. Our studies confirm that similar
to the phosphorus atom in PK3 the superatom Al12Cu cluster
could then form truly stable ionic salts, as shown from dimers,
trimers, and tetramers of the Al12Cu(Crypt)3 complex
calculated from several random possible initial orientations.
The integrity of Al12Cu(Crypt)3 unit in the cluster assemblies
shows that the Al12Cu(Crypt)3 clusters hold a great potential as
a building block for the development of novel nanostructured
materials.
We believe that the understanding of the interplay between
the electronic and geometrical structure and the chemical
stability of the investigated systems has the potential to provide
a descriptor (or template) toward the computational discovery
and design of families of novel nanostructured materials with
potential applications. The choice of the Crypt molecules to
stabilize the salt opens a route to experimentally generate
cluster base ionic salts, and we hope that new ionic assemblies
may be developed by extending our findings and that this work
motivates experimental investigations that confirm our results.
■
ASSOCIATED CONTENT
S Supporting Information
*
Full citations for refs 11, 44, and 45. This material is available
free of charge via the Internet at http://pubs.acs.org.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected].
Notes
The authors declare no competing financial interest.
§
T.B.: E-mail: [email protected].
∥
R.R.Z.: E-mail:[email protected].
■
ACKNOWLEDGMENTS
This work was partially supported by the DOE Basic Energy
Science under award DE-SC0006818 (R.R.Z.) and DESC0002168 (T.B.) and the NSF PREM program between
UCSB and UTEP (DMR-1205302) (T.B.) and the University
of Texas at El Paso (J.U.R.). We thank the Texas Advanced
Computing Center (TACC) from the National Science
Foundation (NSF) (Grant No. TG-DMR090071) and
NERSC for the computational time.
■
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