Article
pubs.acs.org/JPCA
Theoretical Study of Small Scandium-Doped Silver Clusters ScAgn
with n = 1−7: σ‑Aromatic Feature
Hung Tan Pham,† Loc Quang Ngo,† My Phuong Pham-Ho,*,† and Minh Tho Nguyen*,‡
†
Institute for Computational Science and Technology (ICST), Ho Chi Minh City, Vietnam
Department of Chemistry, KU Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium
‡
ABSTRACT: Geometry, chemical bonding, and aromatic feature of a
series of small silver clusters doped by an Sc atom (ScAgn with n = 1−7)
were investigated by means of density functional theory calculations. A
planar shape is found for ScAgn including n from 4 to 7. The growth
mechanism is established for the formation of the hexagonal and
heptagonal metallic cycles following increase of the number of Ag atoms.
Particularly, both clusters ScAg6− and ScAg7 present a planar cyclic form
in which the Sc atom is situated at the central position of the Ag6 and Ag7
cycles. The σ aromaticity is unambiguously demonstrated by the
existence of strongly diatropic current flows within the ring in both
ScAg6− and ScAg7. The isovalent ScCu7 cluster has a similar ring current
characteristic. In the Sc-doped ScAgn clusters, a delocalized bonding pattern is found as a connector between the dopant Sc and
the Agn host, as indicated by an ELI_D analysis.
B72− and B@B8−, both sets of σ and π delocalized MOs are
considered to be aromatic as indicated by ring current
calculations.18 Additionally, by exploring the ring current
maps of both delocalized σ and π orbitals, the M@B6H6q and
M@B7H7q planar cycles with M = Cr, Mn and Fe and q
(charge) = −1, 0, and +1 provide us with another kind of
double aromaticity.19
As indicated by CMO analyses and mostly by negative NICS
values, the dianions Zn32−, Cd32−, and Hg32− were classified as π
aromatic with two π electrons.20 The planar transition metal
centered five-membered ring [Fe(Sb) 5]+ and [Fe(Bi)5]+
clusters were characterized to be π aromatic in agreement
with the existence of 10 delocalized π electrons.21
While the main group elements can lead to either a single π
or a double π and σ aromaticity, the δ aromaticity, which is
formed by d−d interactions, has been observed for planar
cycles containing transition metals. The Hf3 (1A1′ D3h) cluster
was shown to exhibit a triple σ, π, and δ aromaticity.22 The δ
aromatic character was identified by canonical MO analysis and
negative NICS value for the W32− and W3O92− clusters.23,24 In
the latter, a combination of 5d-AOs of W atoms produces
delocalized MOs that turn out to be responsible for a δ
aromaticity with two delocalized electrons. The 5d-AOs
generate delocalized δ MOs occupied by two electrons in the
anion Ta3− and its oxides including Ta3O− and Ta3O3−. As a
result, they are considered as δ aromatic species.25,26 Although
d−d interactions tend to induce a δ aromaticity, both σ and π
aromatic characters are mainly found in metallic cycles.
1. INTRODUCTION
The concept of aromaticity was introduced by Kekule in 1865
in an attempt to rationalize the particular thermodynamic
stability and chemical reactivity of benzene and its derivatives.1−3 With the aim of theoretically predicting the
aromaticity of monocyclic hydrocarbons, Hückel established
in 1931 the milestone formula of (4N + 2) to count their π
electrons.4,5 This simple rule points out that, if an unsaturated
cyclic hydrocarbon molecule has a number of π electrons
satisfying the (4N + 2) count, this species is aromatic and has
thereby a high stability and low reactivity. Subsequently,
Breslow defined in 1970 the associated concept of antiaromaticity in which a molecule containing 4N π electrons is
thermodynamically unstable and highly reactive.6 Since then,
the 4N/4N + 2 electron count rules emerged as the simplest
and most popular indicator for the aromatic character of not
only hydrocarbons but also of different classes of organic and
inorganic compounds.
The emergence of elemental clusters has given an
unexpected expansion of the aromatic character. As for a
prototype of aromatic cycle containing metal atoms, the
dianion Al42− has been the subject of several experimental
and theoretical studies.7−17 Based on an MO analysis and NICS
calculations, the tetra-atomic cluster Al42− has been considered
as having a triple aromaticity involving σ-radial, σ-tangential,
and π-planar aromaticity.9 However, subsequent ring current
calculations that evaluated the orbital contributions to the
magnetic responses of the electron density clearly demonstrated that Al42− is an σ-aromatic species rather than a triple
aromatic compound.15−17 Planar metallic cycles not only
contain a high coordination but also involve often a double σ
and π aromaticity. For instance, let us consider the species B@
© 2016 American Chemical Society
Received: August 10, 2016
Published: September 20, 2016
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Figure 1. Shape of lower-lying isomers of Ag2Sc− and AgnSc clusters with n = 1, 3, and 4. Geometry optimizations were performed using B3LYP/ccpVTZ:Sc and cc-pVTZ-PP:Ag computations.
central position of a six-membered ring, is also σ aromatic with
10 delocalized σ electrons.39 In this context, a legitimate
question emerges as to whether an σ aromaticity can be
recovered in isovalent species of YAu6− and ScCu7 containing
silver atoms such as ScAg6− and ScAg7, respectively.
For silver clusters, the sizes of six and seven Ag atoms have
been identified as structures in which a transition from 2D to
3D form of small sizes occurs.40−44 A systematic investigation
of the neutral and charged Agn−/0/+ clusters with n = 1−15
showed that these clusters undergo a transition from spherical
to prolate to oblate form.45 The pure and mixed silver clusters
have been the subject of several experimental and theoretical
studies.46−48 However, study of silver cluster doped by 3d
transition metals is quite limited. An extensive search on
Ag5M0/− with M being a 3d transition metal using both
experiment and DFT calculations showed that both 2D and 3D
structures coexist.49 Particularly, of the 3d transition metaldoped MAgn+ clusters, the size CoAg10+ presents an endohedral
structure with singlet spin state.50 The quenching and high
stability of CoAg10+ was rationalized in terms of the 18-electron
rule. More recently, the V-doped clusters VAg14+ and VAg15 are
identified to have high stability with 18 and 20 electrons shells,
respectively.51
In this context, we set out to search for Ag clusters featuring
only an σ aromatic character. For this aim, we perform a
systematic investigation on the geometric and electronic
structure of small scandium-doped silver clusters ScAgn using
quantum chemical calculations. The Sc atom is selected in view
of its behavior in the ScCun clusters. Concerning the
rationalization of aromaticity, it has recently been shown that
the one-point NICS values often draw incorrect predictions for
cyclic metallic systems, whereas the ring current maps appear to
behave as consistent magnetic indicators.16,17,19,52
There is a debate on the aromatic character of hydrometallic
and transition metal cycles. On the basis of a NICS and CMO
analysis, the CunHn hydrometallic cycles, which is in perfect
planar shape with high Dnh symmetry, are classified as the triple
σ, π, and δ aromatic feature.27 Similar phenomena were also
observed for the isovalent clusters AunHn and AgnHn again with
n = 3−6.28 In particular, the mixed coinage metal clusters
CunAg3−nH3, CunAg4−nH4, and CunAg5−nH5 were found to be
stable in planar geometry, and their triple aromaticity is
contributed by σ, π, and δ components.29 However, these
hydrometallic cycles are considered as nonaromatic species
according to the GIMIC, 30 MCI,31 and CMO−NICS
calculations.32−34
Transition metal clusters containing only σ aromaticity are
rather scarce.35,36 The trimeric cationic trimers of coinage
metals Cu3+, Ag3+, and Au3+ were characterized as σ aromatic
cycles.37 However, the ring current analysis clearly showed that
these species present strong local paramagnetic currents around
the atomic nuclei rather than moving through the whole cluster.
As a consequence, they should be classified as nonaromatic
clusters.38
The aromatic feature of planar Cu42−, Ag42−, and Au42−
clusters was rationalized by using magnetic responses that
pointed out that six delocalized σ electrons are the main
contributors to the ring current flows. Accordingly, these planar
coinage metal clusters are classified as σ aromatic. Structural
identifications demonstrated that the scandium-doped copper
cluster ScCu7 is a beautiful heptagonal cycle in which the Sc
atom is located at the center of the ring, whereas the smaller
analogues ScCu6 and ScCu5 were found to be in a 3D form.
Perhaps more interestingly is the fact that the seven-membered
ScCu7 cycle is an σ aromatic species containing 10 delocalized σ
electrons as supported by NICS calculations and ELI_D
analysis.36 The yttrium-doped gold cluster YAu6− cluster,
characterized as a D6h planar structure with Y occupying the
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Figure 2. Shape of lower-lying isomers of Ag6Sc− and AgnSc clusters with n = 5 and 7. Geometry optimizations were performed using B3LYP/ccpVTZ:Sc and cc-pVTZ-PP:Ag computations.
2. COMPUTATIONAL METHODS
All geometry optimizations and energy calculations are
performed using the Gaussian 09 suite of programs.53 A
stochastic genetic algorithm is used to generate the initial
geometries for the ScAgn clusters.54 They are first optimized
using density functional theory (DFT) with the hybrid
functional B3LYP and the small LAN2DZ basis set.55,56 The
lower-energy isomers identified at this level, within a range of
50 kcal/mol on relative energies with respect to the lowestlying isomer, are subsequently reoptimized using the same
functional but in conjunction with the larger cc-pVTZ basis set
for the Sc atom and the cc-pVTZ-PP for Ag atom.57 In the
latter, PP stands for an effective core potential, which also
includes the relativistic effects. The electronic structure and
chemical bonding features of the ScAgn global energy minimum
structures are then explored carrying out a partition of the
electron density. This is achieved by using the electron
localizability indicator (ELI_D)58 and the magnetic responses
expressed in terms of ring currents. Calculations on the ring
current maps are carried out using the SYSMO program,59,60
which is connected to the GAMESS-UK package.61 As for a
convention, a diatropic current density corresponds to an
aromatic character, whereas a paratropic current indicates an
antiaromatic character. For the sake of comparison, the σ
aromatic character of the ScCu7 cluster, which was pointed out
in previous studies, is also revisited by ring current calculations.
electron distribution and chemical bonding phenomena in
these clusters will be examined, with a particular focus on their
aromatic character.
3.1. Geometrical Aspects. The shape, electronic state, and
relative energies of the lower-lying isomers of the clusters ScAgn
considered are displayed in Figure 1 for n = 1−4 and Figure 2
for n = 5−7.
ScAg and ScAg2. The diatomic Sc−Ag is identified to have a
triplet ground state with an equilibrium distance of 2.7 Å. The
closed-shell singlet state is ∼8 kcal/mol above. For the
triatomic ScAg2 and its anion, the linear structure in which
the Sc atom is located in the middle turns out to be the lowestenergy isomer.
ScAg3. The global minimum structure 3.A is planar in which
the Sc dopant occupies the central position of the equilateral
Ag3 cycle. The tetra-atomic 3.A can thus be formed upon
adding the Sc atom to the Ag3 cluster. The next isomer 3.B has
also a planar shape and is located at ∼5 and ∼9 kcal/mol above
the ground state for the triplet and singlet states, respectively.
The 3.B form was previously predicted as the global minimum
structure of the PdAg3 cluster.62 However, the Sc dopant does
not favor this shape.
ScAg4. Extensive search on the isomers of the penta-atomic
ScAg4 cluster results in the planar 4.A (C2v 2B2) as the most
stable structure. Basically 4.A could be generated by
substitution of an Ag atom of the Ag5 structure, which has
the highest coordination state.45 The same shape is also found
for the penta-atomic PdAg4 and VAg4 clusters in which either
the Pd62 or the V63 dopant is surrounded by four Ag atoms.
The 4.B shown in Figure 1 results from attachment of a Sc
atom into the Ag4 square and is at ∼10 kcal/mol above 4.A.
3. RESULTS AND DISCUSSION
We first briefly describe the geometries of a series of the
smallest scandium-doped silver clusters considered and
establish their growth pattern. In the following sections, the
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The isomers including 4.C and 4.D seen in Figure 1 have 3D
shape and are much less stable.
ScAg5. As shown in Figure 2, the incomplete planar hexagon
5.A (C2v 1A1), as the lowest-lying energy isomer, is consistent
with previous results on the geometry of the ScAg50/−
clusters.49
ScAg6−. DFT calculations indicate that the singlet and high
symmetry 6.A (D6h 1A1g) is the lowest energy isomer. This
structure presents a particular shape in which the Sc dopant is
situated at the central position of the hexagonal Ag6 ring. Let us
mention that the pure neutral Ag7 cluster was identified as a
pentagonal bipyramid.45 Accordingly, the Sc atom strongly
affects the geometry of when replacing an Ag atom. The next
isomers including 6.B, 6.C, and 6.D that are formed by adding
an Ag atom to the ScAg5 cluster at various sites are highly
unstable. This behavior of ScAg6− differs thus from the
isovalent ScCu6−, which has a 3D shape,64 but similar to the
isovalent YAu6−, which has high symmetry planar form (D6h).39
It is apparent that the larger size of the Ag6 and Au6 rings allows
the metal dopant to be endohedrally incorporated.
ScAg7. There is a competition for the ground state in the
case of ScAg7 cluster. The planar 7.B (D7h 1A1g) in which the Sc
atom is located at the center of a planar heptagonal Ag7 ring is
only ∼2 kcal/mol higher than 7.A. In a view, 7.A actually arises
from a strong distortion of 7.B. With the expected accuracy of
DFT calculations (∼3−4 kcal/mol), both of them can be
regarded as competitive for the ground state of ScAg7. Because
the Ag7 ring is large, it tends to undergo distortion upon
doping.
3.2. Growth Pattern: Formation of Hexagonal and
Heptagonal Cycles. From geometrical characteristics described above, the growth pattern of the ScAgn clusters can thus
be revealed and are illustrated in Figure 3. The ScAg2 structure
is generated following addition of an Ag atom to the diatomic
Sc−Ag. Then the ScAg3 cyclic structure results from an
attachment of one more Ag to the trimer ScAg2. The ScAg4
cluster arises from both addition and substitution pathways.
Replacement of an Ag site on Ag5 by Sc or addition of one Ag
atom to ScAg3 equally ends up in the ScAg4 global minimum.
More interestingly, this structure is actually a fragment of
hexagonal and heptagonal cycles. As a matter of fact, addition of
two and three Ag atoms to the ScAg4 unit results in the
hexagonal and heptagonal cycles of ScAg6 and ScAg7,
respectively. It is obvious that the incomplete hexagonal
ScAg5 cluster is formed by a combination of an Ag atom with
the most stable ScAg4 structure. Finally, the planar hexagonal
cycle ScAg6 is produced upon addition of one Ag atom to the
ScAg5. Attachment of Ag to the hexagonal ScAg6 cycle gives
subsequent rise to the heptagonal cycle. Overall, upon doping
of a Sc atom, the resulting ScAgn clusters up to the sizes of n =
6 and 7 follow a rather simple route leading to formation of
hexagonal and heptagonal cycles.
3.3. Electronic Shell Model. The high thermodynamic
stability of the planar form of singly doped MAgn clusters,
whose dopant is a transition metal atom, was previously
rationalized as a result of a strong stabilizing orbital interaction
of the metal atom with the Agn hosts.50,51 Such an interaction
gives rise to a MO pattern of MAgn satisfying the eigenstates
inherently produced by the electron shell model. We thus use
this simple approach to probe the stability of the planar ScAg6
and ScAg7 cycles. In the shell model, nuclei are ignored and
replaced by a mean field, while electrons are considered to
move freely within this mean field. The S, P, D, F, etc., orbitals
according to the angular momentum numbers L = 0, 1, 2, 3,
etc., are generated and successively filled by the valence
electrons. With a given quantum number L, the lowest-lying
level has a principle number N = 1. In the framework of the
shell model, a successive occupation of a level, giving rise to a
magic number, leads to a stabilized cluster.
In order to determine the electron shells, partial densities of
state (pDOS) are calculated for Sc atom and Agn cycle with n =
6 and 7 and displayed in Figures 4 and 5. Total densities of
state (DOS) involving all contributions from both the dopant
Sc and the Ag6 and Ag7 hosts are displayed in the same Figures
4 and 5. Combining with the MO shape, the electron shell
configurations of these clusters can unambiguously be
established. The orbital overlap between Ag and Sc (Figures
4 and 5) yields the shell configuration as [1S2 1P4 1D4...]
occupied by 10 electrons for both the anion ScAg6− and the
neutral ScAg7. The same shell configuration was found in the
case of the planar isovalent YAu6− and ScCu7 clusters. The
valence electrons of both Sc or Y dopants and the Cu7, Ag6,7, or
Au6 hosts can then fully occupy the electron shell of [1S2 1P4
1D4...] and, consequently, stabilize the resulting planar clusters.
3.4. Chemical Bonding Analysis Using Orbital Interaction. To obtain a deeper understanding on chemical
bonding of Sc@Ag7 and Sc@Ag6− planar cycles, the orbital
interactions of the Sc atom with the Ag7 and Ag6− cycles are
constructed. As shown in Figure 6, the 1S level of Ag7 and Ag6−
combines with the 4s orbital of Sc, and thereby establish the 1S
subshell for Sc@Ag7 and Sc@Ag6− clusters. Clearly, the 1P
subshells of Sc@Ag7 and Sc@Ag6− clusters are mainly
contributed by the 1P level Ag7 and Ag6− cycles. The 3d
orbitals of Sc dopant enjoy a stabilizing interaction with the 1D
levels of Ag7 and Ag6− strings and, subsequently, give rise to the
1D subshells, each of which is occupied by four electrons of
either Sc@Ag7 or Sc@Ag6− planar structure. As a result, orbital
interactions between Sc and Ag7 and Ag6− cycles induce a
thermodynamic stability for the resulting clusters.
Figure 3. Growth mechanism of the series of small Sc-doped silver
clusters.
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Figure 4. DOS and pDOS plots of ScAg6− planar cluster.
Figure 5. DOS and pDOS plots of ScAg7 planar cluster.
3.5. Electron Partition Using the Electron Localizability Indicator (ELI_D) and WBI. In order to obtain a
deeper understanding of the bonding pattern of the ScAgn
clusters, we now use the electron localizability indicator
(ELI_D) to probe the electron distribution. This method
includes a partition of the total electron density into basins
where electrons are populated. As given in Figure 7, the ELI_D
maps that are plotted at the bifurcation of 1.15 of the ScAg,
ScAg2, and ScAg3 clusters clearly indicate the localization
domains between Sc and Ag. In these systems the Sc dopant
connects to the Ag hosts through localized bonds.
At the bifurcation value of 0.98, the ELI_D map of ScAg4
illustrates a localization domain, which is distributed over the
region between Ag atoms and the Sc center. In other words, in
the ScAg4 cluster, the Sc dopant induces a delocalized bond
with the Ag4 host. A similar result is recovered for the hexaatomic ScAg5 cluster in which a localization domain populated
in the space between Sc and Ag5 host is present. This indicates
the existence of a delocalized bond.
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Figure 6. Orbital interactions of the Sc atom with Ag6− and Ag7 strings giving the Sc@Ag6− and Sc@Ag7 cycles.
existence of electron sharing between Ag atoms in Sc@Ag6−
and Sc@Ag7 cycles.
3.6. σ-Aromaticity of Planar ScAg6− and ScAg7. A
Comparison with ScCu7. Let us now probe the aromatic
feature of the planar ScAg6− and ScAg7 metallic cycles using the
magnetic responses of the electron density as expressed by ring
current flows. As for a comparison with the behavior of the
isovalent ScCu7, the ring current maps of the latter are also
generated.
The total ring current flow, which is contributed by all
valence electrons of both ScAg7 and ScCu7, is displayed in
Figure 8. Both species generate strongly diatropic current maps
in terms of magnetic responses. Therefore, they can be
classified as aromatic species. The most remarkable feature is
that total ring current of ScAg7 and ScCu7 is entirely
contributed by σ valence electrons, due to the fact that these
clusters do not contain π electrons. It is obvious that both
clusters bear an σ aromatic character. As indicated by both
DOS and ELI_D analysis, the valence electrons of either ScAg7
or ScCu7 are not only delocalized over whole cluster but also
satisfy the (4N + 2) electron count. In the present case, the
classical (4N + 2) rule draws a consistent conclusion with the
ring current criteria.
In order to further probe their aromatic feature, the orbital
contributions to the ring currents are performed and displayed
in Figure 8. It thus appears that the doubly degenerate HOMO
and HOMO′ constitute the main contributors to the ring
current maps, whereas the HOMO−1,1′ and HOMO−2 are
not active in magnetic response.
For a comparison of the electron circulation within the ring,
the ring current maps of the planar Ag73− and Cu73− heptagonal
trianions, which are isovalent to both ScCu7 and ScAg7 clusters,
are also performed (Figure 9). As expected, strongly diatropic
current density are also identified for both Ag73− and Cu73−
cycles indicating also their σ aromatic feature. This result
confirms that the Sc dopant supplies all of its three valence
electrons to the whole molecular σ system.
In order to quantify the aromaticity level of both Sc@Cu7
and Sc@Ag7, the jmax values are calculated and compared to
Al42−, which is considered as a typical all-metal aromaticity.
This quantity can be regarded as a measure of the maximum
strength of the current per unit inducing field. It should be
noted that the current maps mainly convey qualitative
information about aromaticity, whereas the jmax values are a
Figure 7. ELI_D surfaces: ScAg5, ScAg6, and ScAg7 are plotted at
bifurcation value ELI_D = 0.925; ScAg, ScAg2, and ScAg3 at ELI_D =
1.15; and ScAg4 at ELI_D = 0.98.
At the bifurcation value of ELI_D = 0.925, the localization
domain, which is distributed over the region covering the Sc
dopant and the Agn host, is again found for both ScAg6− and
ScAg7. The connection between the Sc atom to each of the Ag6
and Ag7 cycle is thus made by delocalized electrons. The fact
that the Sc dopant tends to connect with the Agn hosts, from
the size of ScAg4, through delocalized bonding pattern is
consistent with the results derived from the DOS analysis
described in the previous section.
To obtain a deeper insight into the bonding features of Sc@
Ag6− and Sc@Ag7 planar clusters, the Wiberg bond indices
(WBI) are calculated for the relevant Ag−Ag and Sc−Ag
connections. As a result, all Sc−Ag connections of Sc@Ag7
have a WBI value of 1.0, whereas in Sc@Ag6− the six Sc−Ag
bonds have the same WBI value of 0.8. Additionally, WBI
values of ∼0.8 are calculated for all Ag−Ag connections in both
Sc@Ag6− and Sc@Ag7. These results clearly point out the
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Figure 8. Total ring currents of (a) ScCu7 and Cu73− and (b) ScAg7 and Ag73− cycles.
Sc@Ag7 and Sc@Cu7 cycles have a comparable level of
aromaticity as Al42−.
4. CONCLUSIONS
In the present theoretical study, we have investigated the
geometry, chemical bonding, and aromatic feature of the
smallest Sc-doped silver clusters ScAgn with n = 2−7.
Geometric identifications show that all ScAgn clusters have a
planar shape in which the Sc dopant prefers a high coordination
position. In particular, Sc@Ag6− and Sc@Ag7 present planar
metallic cyclic forms in which the Sc atom is located at the
central position of the Ag6 and Ag7 cycles. The growth
mechanism can be established in which formation of the
hexagonal and heptagonal metallic cycles can be achieved
following increase of the number of Ag atoms. The partition of
the total electron density using the ELI_D approach
demonstrates that the Sc dopant connects to the Agn hosts
through a delocalized orbital pattern. Magnetic ring current
calculations show that both the Sc@Ag6− and Sc@Ag7 clusters
exhibit a σ aromatic character, similar to the isovalent species
Y@Au6− and Sc@Cu7.
■
AUTHOR INFORMATION
Corresponding Authors
*E-mail: [email protected].
*E-mail: [email protected].
Figure 9. Orbital contributions to the ring currents of (a) ScAg7 and
(b) ScCu7.
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
The authors thank the Department of Science and Technology
of Ho Chi Minh City, Vietnam, for supporting our work at
ICST. M.T.N. is indebted to the KU Leuven Research Council
(GOA program) and FWO-Vlaanderen. We greatly appreciate
more quantitative criterion. In other words, the jmax value could
also be used to quantitatively evaluate the degree of aromaticity.
Both Sc@Ag7 and Sc@Cu7 have a jmax value of 0.06, whereas
the jmax of Al42− is found to be 0.05. As a consequence, both
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