Structures and Stability of Doped Gallium Nanoclusters - The Journal

Subscriber access provided by DUKE UNIV

Article

Structures and Stability of Doped Gallium Nanoclusters David James Henry J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 07 Nov 2012 Downloaded from http://pubs.acs.org on November 10, 2012

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 37

The Journal of Physical Chemistry

Structures and Stability of Doped-Ga Nano-clusters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Structures and Stability of Doped Gallium Nanoclusters

David J. Henry∗

School of Chemical and Mathematical Sciences, Murdoch University, WA, 6150, Australia

Abstract The stability and reactivity of metal nanoclusters is critically dependant on the valence electronic configuration of the cluster. Many “magic” electronic configurations are inaccessible for pure trivalent metal clusters. However, doping is one method by which the electronic configuration and properties of a cluster can be significantly modified or even tailored. Density functional theory is used in this study to investigate the structures, stabilities and electronic properties of doped gallium nanoclusters, Ga12X (X = B, C, N, Al, Si, P, Ga, Ge, and As). In all cases doping of the cluster leads to increased stability relative to Ga13. Stabilisation is largely due to electronic contributions, although for many of the clusters the dopant also induces a small increase in the stability of the Ga12 framework. Generally the endohedrally doped isomers are either lower in energy or close in energy to the isomers with the dopant at the surface of the cluster. Endohedral Ga12C is the most stable cluster and exhibits the most Jellium-like orbital structure. Trends in vertical ionization potentials and electron affinities can be explained in terms of the interactions in frontier orbitals and generally adhere to the predictions of the Jellium model.

Keywords: Endohedral doping, Exohedral doping, Jellium model, Cluster bonding, Stabilization ∗

Corresponding author email: [email protected]

1

ACS Paragon Plus Environment



1.

Introduction The Jellium model predicts that for small clusters of atoms there are certain valence

electronic configurations (8, 20, 34, 40, 58, …) know as magic numbers, that exhibit increased stability relative to their neigbouring configurations, in the same way that noble gas electronic configurations exhibit increased stability.1 These electronic configurations are easily achieved with integer numbers of Group 1 or Group 2 elements. However, each group 13 atom in a cluster contributes 3 valence electrons to the cluster electronic configuration making many of these magic electronic configurations inaccessible. Nevertheless, the properties and reactivity of boron and aluminium nanoclusters have been extensively studied by experimental and theoretical procedures. 2-10

However, there has been relatively less attention paid to gallium clusters.

Experimental studies reveal that Ga13 exhibits particular stability because it is the smallest cluster that combines a geometric shell like structure with an almost closed shell “magic” electronic configuration.11 Theoretical calculations support this observation but there appears to be some debate regarding the structure of the Ga13 cluster. Gong et al.12 carried out ab initio molecular dynamics on the Ga13 cluster using the Perdew and Zunger exchange-correlation functional with non-local norm-conserving pseudopotential plane-wave basis. They found that the icosahedral structure was the lowest energy isomer followed by the hcp-like and fcc-like structures. Molecular dynamics simmulations in the range 100 - 200 K did not result in any structural transformations from one symmetry to another. However, slight distortions from ideal symmetry did lead to a lowering of the total energies of the respective structures, particularly for the Ih structure. This is most likely due to Jahn-Teller distortion of the incompletely filled Highest Occupied Molecular Orbital (HOMO), as observed for Al13. However, Yi13 investigated the stability and structure of Ga13 using Car-Parrinello density functional theory and found that the lowest energy isomer of Ga13 is a distorted decahedron. Nevertheless, they also noted that only small activation energies exist for structural transformations, which means that Ga13 exhibits considerable flexibility and floppiness. 2


Page 2 of 37

Page 3 of 37



Reaction of the decahedral cluster with a Ga atom was found to induce structural change of the substrate towards a more ideal decahedron. In comparison, reaction with an arsenic atom was found to induce a transformation of the substrate to a distorted icosahedron. Recently, Song and Cao14 investigated the geometries and electronic structures of Gan clusters for n = 2 - 26 using the PW91/DNP level of theory. They also found that the ground state structure is a decahedron with the icosahedral structure 0.38 eV higher in energy.

If the pure gallium cluster is ionized to Ga13- then the cluster has a true magic number electronic configuration and exhibits increased stability. Cha et al.11 experimentally determined the photoelectron spectra of Aln- and Gan- clusters for n = 1 – 15 and found that the vertical electron detachment energies (VDE) of Al13- and Ga13- were 3.75 eV and 3.50 eV, respectively, indicating significant stability for the anion configurations. They also found that while the photoelectron spectrum of Al13- exhibited only a single broad feature, suggesting high symmetry, Ga13- exhibited a double peak, which can be attributed to reduced symmetry. Theoretical calculations confirm that Al13- has icosahedral symmetry with a single Al atom at the core of the cluster surrounded by 12 Al atoms equidistant from the core.9a In comparison, theoretical calculations of Ga13- reveal that only the bicapped pentagonal prism (D5h) is a minimum on the potential energy surface.15

Doping of aluminium clusters with other elements has been found to have a significant effect on the stability and reactivity of the cluster.9,10 In this regard, doping of both Al13 and Ga13 with group 14 elements leads to the formation of a 40 valence electron cluster that should exhibit enhanced stability analogous to Al13- and Ga13-, respectively.16,17 Weiß et al.15 investigated pure and silicon-doped gallium cluster anions by performing fourier-transform ion cyclotron resonance-mass spectrometry on a metalloid cluster [Ga19(C(SiMe3)3)6][Li2Br(THF)6]. They found that the spectrum was dominated by pure gallium cluster anions Gan- (n ≤ 50) but also contained mixed galliumsilicon cluster anions GanSi-, GanSi2-, and GanSi3- (n ≤ 43). For the pure Gan- clusters a maximum is 3




observed in the spectra for Ga13- which is due to the stability of the closed shell 40 electron valence configuration. Generally the clusters with an odd number of gallium atoms exhibit higher intensity peaks compared with the neighboring even numbered clusters. For the spectrum of mixed Ga-Si clusters, the major product is Ga12Si-, however, the abundance of the GanSi- clusters is generally significantly less than the Gan- clusters while GanSi2- and GanSi3- species only occur in extremely low abundance.

Theoretical investigations of doped gallium clusters include the work of Guo18 who carried out a computational study of GanAl (n=1-15) clusters at the B3LYP/Lanl2DZ level of theory. Guo found that for Ga13 and Ga12Al the lowest energy structures are distorted decahedrons with the latter structure having the Al atom at the core of the cluster. However, the corresponding structure with the Al atom on the surface of the cluster is only 0.01 eV higher in energy. Similarly, Wang et al19 carried out an experimental investigation of nitrogen-doped gallium cluster anions (GaxNy-, x = 4 12, y = 1 and x = 7 - 12, y = 2) combined with theoretical studies of a subset of these clusters. Song et al.20 investigated neutral nitrogen-doped clusters (GanN, n = 1 - 19) at the PBE/DNP level of theory. They found that the lowest energy structure of Ga12N is a distorted decahedron with the N atom at the surface of the cluster. They also found that when the N atom was placed in the core of the cluster the optimum structure has icosahedral symmetry and is 0.16 eV higher in energy. However, their calculations indicate that clusters with n = 3, 7 and 15 are particularly stable despite the fact that these clusters have 14, 26 and 50 valence electrons and therefore do not conform to the predictions of the Jellium model. There are clearly a number of issues to consider when investigating doped metal clusters including, electronic configuration, stability, bonding and structural isomerism.

This study uses density functional theory to investigate the structures, stability and electronic properties of endohedral and exohedral doped gallium clusters Ga12X (X = B, C, N, Al, 4


Page 4 of 37

Page 5 of 37



Si, P, Ge, Al). This current series of clusters were selected on the basis of the information they can provide with regards to using dopants to tune the properties of small gallium clusters. In particular, the boron and aluminium doped clusters are isoelectronic with Ga13 and therefore provide insight as to the importance of dopant size and orbital energy levels on structure and properties. The group 14 dopants (X = C, Si, and Ge) lead to 40 valence electron configurations which are predicted to exhibit enhanced stability within the Jellium model. In comparison, group 15 dopants are important in the context of semiconductor materials and quantum dots. For all of these clusters, stability is measured in terms of binding energies, stabilization energies, distortion energies, ionization potentials, electron affinities and HOMO-LUMO gaps. Trends are analysed in terms of cluster bonding and orbital interactions and compared to the already well studied aluminium analogues (Al12X).

2.

Computational Procedures Standard density functional theory calculations were performed using the GAUSSIAN03

and GAUSSIAN09 computer programs.21,22 In this study a range of structural isomers of Ga12X (X = B, C, N, Al, Si, P, Ga, Ge, and As) were studied. Geometries for all neutral Ga12X clusters were determined with the PBE0 functional using the 6-311G(d) basis set. All structures were fully optimized with no geometry restrictions. Low-spin and higher spin electronic states were investigated to determine the multiplicity of the ground state. However, in all cases the ground state was found to have low-spin multiplicity. Geometry optimizations were started from an extensive range of isomers including, icosahedral and decahedral structures with endohedral dopants, “inverted” structures with the dopant atoms located exohedrally as well as, peripheral structures with the dopant located at a vertex of icosahedron, or decahedron structures, and distorted structures with the dopant located over a face or edge of the Ga12 cage. Vibrational frequency analysis was performed to characterize all stationary points reported here as true minima. In the following discussion, structural formula of the form endo-Ga12X indicate that the dopant atom X is located at the core of the cluster, whereas formula of the form exo-XGa12 indicate that X is at the surface of the cluster. Key geometric parameters of the different structural isomers are defined in Figure 1. 5



Page 6 of 37


Binding energies are defined by the enthalpy change for the following reaction:

12Ga + X → Ga12X

(1)

where X = B, C, N, Al, Si, P, Ga, Ge, and As. The enthalpy of the substitution reaction (2) can also be used as a valuable measure of the stability of doped clusters relative to Ga13 because there should be significant cancellation of errors in the energies of both the atoms and the clusters.

Ga13 + X → Ga12X + Ga

∆Hsubst

(2)

Consequently, an exothermic substitution reaction indicates that the dopant X stabilises the cluster whereas an endothermic enthalpy indicates that X de-stabilises the cluster. The stabilization energy provides an overall measure of the combined electronic and structural stabilization as a result of doping the cluster. All binding energies and ∆Hsubst values have been corrected for zeropoint vibrational energy.

The distortion energy (∆Hdist) can be used to “isolate” energy contributions arising from structural changes as a result of doping. The distortion energy is defined as the energy of the Ga12 conformation in the doped cluster (Ga12X) minus the energy of the same Ga12 atoms in the corresponding conformation of the Ga13 cluster. Therefore, a negative value for ∆Hdist indicates structural stabilization of the gallium framework as a result of doping i.e. the Ga12 conformation in the doped cluster is more stable than in the undoped Ga13 cluster. Likewise, a positive value for ∆Hdist indicates destabilization of the gallium framework of the cluster.

6


Page 7 of 37



Vertical ionization energies, and vertical electron affinities were determined by the difference in energy of the ions and the neutral clusters at the geometry of the ground state neutral species. 3.

Results and Discussion The lowest energy stable endo- and exo-hedral isomers of Ga12X clusters identified in this

study are displayed in Figure 2 as well as the energy of the exohedral isomers relative to the corresponding endohedral isomers. Key structural parameters for the endo-Ga12X clusters are presented in Table 1 .

The pure Ga13 cluster has a distorted decahedral structure with one Ga atom at the core of the cluster, two of the 12 outer atoms are aligned along the principal axis and the remaining 10 atoms are arranged into two eclipsed 5-membered rings perpendicular to the principal axis. The deviation from ideal D5h symmetry arises from a Jahn-Teller distortion that leads to a displacement of the core Ga atom towards one of the axial Ga atoms. Consequently, one of the axial Ga-Ga bonds is shorter (2.685 Å) than the other (2.743 Å). There is also an elongation of the Gaeq-Gaeq distance for one pair of Ga atoms leading to a slightly larger inter-ring separation (2.659 Å) for this pair of atoms compared to the remaining Ga ring atoms (~2.595 Å). A number of other studies also support a distorted decahedral ground state structure for Ga13, with the relaxed icosahedral and cuboctahedral structures higher energy saddle points.13-15

Analysis of clusters of different sizes generally reveals an evolution from localized covalent type bonding through to bulk metallic type bonding. In individual Ga2 molecules where the bonding is fully covalent, the Ga-Ga bond length is 2.685 Å.23 In comparison, the bulk structure of gallium metal is orthorhombic in which each gallium atom has one very close neighbor at ~2.44 Å with the remaining neighbors at 2.70 – 2.79 Å.24 The structure of bulk gallium is therefore similar to that of iodine, and might be considered to consist of diatomic subunits that arise from pair-wise interaction 7




of the 4p electrons. The shortest Ga-Ga distances in Ga13 are intermediate between these two values providing an indication of the degree to which the bonding has evolved from fully covalent to bulk-like. Isoelectronic aluminum and Al12X clusters have been extensively studied and therefore provide an interesting comparison between these closely related but quite different metals. To begin with bulk aluminium has an fcc metallic structure with uniform Al-Al distances of 2.86 Å.24 The Al13 cluster also exhibits a Jahn-Teller distortion but this lowers the symmetry from icosahedral to D3d symmetry. Nevertheless the average X-Al and Al-Al bond lengths of Al13 are 2.68 and ~2.86, respectively,9,25,31

indicating significant development of a spherical free-electron or metallic

bonding environment in the cluster. It is important to note that gallium exhibits a “d-block contraction” in atomic size as a result of a higher effective nuclear charge and this has a bearing on the structure and properties of gallium based species. The preference for almost D5h symmetry in Ga13 can be considered a balance between the preference for formation of Ga2 subunits and having a spherical free-electron bonding environment.

Endohedral doping of Ga13 with second row elements (B, C and N) results in a contraction of the cluster dimensions and transformation from D5h symmetry to Ih or the closely related D3d symmetry (Table 1). Endo-Ga12B is isoelectronic with Ga13 but has a structural motif closer to that of Al13, with a Jahn-Teller distortion that lowers the symmetry from Ih to D3d. The bond lengths between the boron atom at the core of the cluster and the external Ga atoms (X-Gaeq) range from 2.540 – 2.600 Å and are substantially shorter than the corresponding distances in Ga13. This is analogous to the behavior observed for endo-Al12B, where there is a contraction of the X-Al distances relative to the Al13, due to the smaller size of the dopant atom at the core of the cluster.25,26 The closed shell endo-Ga12C cluster also exhibits significant contraction of the cluster geometry and conversion to perfect Ih symmetry. This behavior closely resembles endo-Al12C that also exhibits a contraction.17,27-31 The endo-Ga12C and endo-Al12C clusters are unusual in that the centrally located carbon atom is effectively bonded to all twelve atoms of the cluster cage. There has been some 8


Page 8 of 37

Page 9 of 37



discussion in the literature about the high symmetry of endo-Al12C and the possibility that this structure may only represent a local minimum protected by a high barrier from lower energy and lower symmetry structures in which the carbon exhibits typical 4-coordinate bonding. However, several ab initio molecular dynamics studies have confirmed the stability of the endo-Al12C cluster up to quite high temperatures.17,29-30 Nevertheless, exohedral structures for both Al12C

30

and Ga12C

have been identified and will be discussed in more detail in the subsequent sections. Surprisingly the endohedral Ga12N cluster, with 41 valence electrons, exhibits only a very minor deviation from Ih symmetry with X-Ga and Ga-Ga bond lengths that are marginally longer than observed in endoGa12C. The PBE0/6-311G(d) structure of the present study is in good agreement with that reported previously by Song et al.20 at the PBE/DNP level. Again this behavior is identical to that observed for the corresponding isomer of the aluminum analogue, endo-Al12N.32 The shorter X-Ga distances in all three endo-Ga12X clusters relative to Ga13, reflects the smaller size of the core atom but also implies increased bonding between the core and the surface atoms. However, there is a slight overall elongation of the surface Ga-Ga distances indicating a weakening of the surface bonds. This contrasts with the observed behavior in the analogous Al12X clusters where the endohedral dopants lead to a contraction of both the X-Al and Al-Al bond lengths.

Endohedral doping of the gallium cluster with third row elements has a much smaller effect on the structure of the cluster relative to Ga13. Ga12Al is isoelectronic with Ga13 and also exhibits distortion away from ideal D5h symmetry, however, the distortion is much less severe than exhibited by Ga13. In particular, the axial X-Gaax distances are now equivalent in endo-Ga12Al and the main evidence of a distortion is in the elongation of Gaeq-Gaeq for one pair of Ga atoms. Unlike endoGa12C, the closed shell endo-Ga12Si cluster exhibits decahedral symmetry and in fact the icosahedral isomer represents a higher energy saddle-point. Nevertheless, endohedral Ga12Si shows a contraction of the axial X-Gaax distances relative to both Ga13 and Ga12Al and a significant decrease in the inter-ring separation. In fact endo-Ga12Si has the smallest inter-ring separation of all of the endohedral Ga12X clusters investigated. For the analogous endo-Al12Si cluster, both the Ih 9




and D5h structures are local minima with the icosahedral structure slightly favoured.31 However, in agreement with endo-Ga12Si, the formation of a closed shell 40 valence electron configuration leads to a contraction of bond distances relative to its parent cluster (Al13).25,29,31,33,34 The 41 valence electron endohedral Ga12P cluster also has D5h symmetry but exhibits a significant elongation of the X-Gaax bonds and a contraction of the X-Gaeq distances relative to Ga13. Consequently, both endoGa12Si and endo-Ga12P exhibit a shortening of the Gaeq-Gaeq distances that indicates enhanced bonding in the inter-ring region between pairs of gallium atoms. Several studies report that the corresponding aluminum cluster (endo-Al12P) also preferentially adopts a high symmetry structure34,35 and Molina et al.36 note that for 41 valence electron endo-Al12X clusters, there is generally an elongation of two X-Alax bonds and a contraction of 10 X-Aleq bonds, similar to that observed for endo-Ga12P.

Doping the cluster with fourth row elements (Ge and As) generally has a relatively small effect on the overall dimensions of the cluster relative to Ga13. The 40 valence electron endoGa12Ge cluster is slightly more compact than Ga13, with shorter average X-Gaeq and X-Gaax distances and a smaller inter-ring separation (Gaeq-Gaeq). However, the degree of contraction is somewhat smaller than observed for isoelectronic endo-Ga12C and endo-Ga12Si, due to the larger size of germanium. In comparison, Kumar and co-workers report25,33 that endo-Al12Ge has icosahedral symmetry characteristic of Al12X clusters but that the X-Al bond lengths are identical to endo-Al12Si. Charkin et al.31 also found that the Ih endo-Al12Ge cluster was the most stable but that the decahedral isomer was only 0.13 eV higher in energy. However, the icosahedral structure for endo-Ga12Ge represents a higher energy saddle-point. The endohedral Ga12As cluster exhibits similar elongation of the X-Gaax distances as noted for endo-Ga12P and an overall contraction of the X-Gaeq distances. This implies decreased bonding between the core (P or As) and the axial gallium atoms but increased bonding between the core and equatorial atoms compared to Ga13. As noted

10


Page 10 of 37

Page 11 of 37



above, a similar distortion of cluster geometry is observed in a number of 41 valence electron endoAl12X clusters.36

Several clear structural trends emerge from the above analysis. Endohedral doping of Ga13 with lighter elements generally results in an Ih/D3d structure, while doping with heavier main group elements generally leads to D5h based structures. In contrast, endo-Al12X clusters exhibit a clear preference for Ih/D3d based symmetry for the same series of main group element dopants. However, several features are common to both endo-Al12X and endo-Ga12X clusters. For a series of dopants from the same period, the cluster with the group 14 dopant (C, Si, Ge), has the most compact and symmetric structure, consistent with a stable 40 valence electron configuration within the Jellium model. Group 13 and group 15 dopants lead to deviations away from these highly symmetric structures. Comparison of isoelectronic structures reveals not surprisingly that the heavier dopant atoms lead to either smaller contractions or alternatively slight expansions of the cluster dimensions and larger deviations from ideal symmetry.

A number of exohedral structures were also identified and the key structural parameters for these species are presented in Table 2. Of the second row dopants, carbon and nitrogen lead to stable low energy exohedral XGa12 structures. The only stable exohedral CGa12 structure identified in this study has a distorted Ga12 cage with the carbon atom bonded to four gallium atoms of a square face of the cluster, analogous to the “common” exohedral CAl12 structure reported by Charkin and coworkers.31 For the gallium based clusters the energy difference between endo-Ga12C and exo-CGa12 is 0.70 eV and a notable feature of the exo-CGa12 structure is the fact that the gallium atoms adopt positions similar to those of a distorted decahedron with one atom removed. In comparison, the low symmetry exo-CAl12 structure is only marginally higher in energy (0.06 eV) than the high symmetry endo-Al12C structure, and has been important in providing an explanation of the shape of the first peak in the photoelectron spectrum of the corresponding anion. 27,31 11




For exohedral NGa12, the nitrogen dopant atom is located in an equatorial position in one of the five-atom rings. However, the cluster is significantly distorted in this region with quite short Gaax-X and X-Gaeq distances indicating that the nitrogen is strongly bonded to 2 surface gallium atoms as well as the core gallium atom. Consequently, the dopant atom also has the effect of causing an elongation of the axial bond lengths (Gaax-Gaax). Further from the dopant, the Ga-Ga bond lengths are generally closer to those found in Ga13 indicating that the dopant has quite a localized effect on the bonding within the cluster. Despite this significant structural distortion, exoNGa12 is 0.10 eV lower in energy than the much more symmetric endo-Ga12N cluster. This is in agreement with Song et al.20 who found exo-NGa12 to be the lowest energy structure at the PBE/DNP level with the endohedral structure 0.16 eV higher in energy. Interestingly, the difference in energy between endohedral and exohedral isomers of Al12N is significantly larger. Bai et al.37 report that the irregular exo-NAl12 structure, with nitrogen bonded to 3 surface Al atoms is ~0.75 eV lower in energy than the N-centered structure. They suggest that the higher electronegativity of nitrogen and preference to participate in covalent bonding strongly favours the exohedral structure over the more metallic endo-Al12N. This preference appears to also be true for NGa12 but to a lesser extent.

The exohedral AlGa12 cluster has a distorted decahedral structure and is marginally higher in energy (0.02 eV) than the corresponding endohedral structure. However, in exo-AlGa12 the Al dopant atom is located in an axial position. The overall structure and dimensions of exo-AlGa12 are similar to those of Ga13. The core gallium atom is displaced towards the aluminium atom with a corresponding elongation of the Gaax-Gaax distance. The inter-ring distances (Gaeq-Gaeq) are marginally shorter in exo-AlGa12 than in Ga13. The study of Guo18 at the B3LYP/Lanl2DZ level of theory also found that the exohedral and endohedral Ga12Al structures were very close in energy with endo-Ga12Al marginally (0.01 eV) favored over exo-AlGa12. 12


Page 12 of 37

Page 13 of 37



The exohedral silicon doped cluster also has a distorted decahedral structure, however, as for exo-NGa12, the dopant atom is located in one of the equatorial rings rather than in an axial position. Like its endohedral counterpart, exo-SiGa12 has a magic number of valence electrons but now lacks the overall geometric symmetry of the endohedral structure. Consequently the Si dopant atom now acts more as an electronegative impurity, leading to a higher energy (+0.61 eV) structure and significant structural distortions in the region of the dopant. In particular, the Gaax–X and XGaeq distances are significantly shorter than for the endohedral structure and there is an inequivalence in the Gaax-Gaax distances. However, the Ga-Ga bonds more remote from the Si dopant are similar in length to surface Ga-Ga bonds in endohedral Ga12Si. Interestingly, Charkin et al.31 identified several stable exohedral Al12Si isomers. The lowest energy of these was an inverted icosahedron with the silicon dopant in an axial position and an Al atom at the core. This structure was 0.65 eV higher in energy than the Si-centered Ih structure and was followed by a marquee type structure and a significantly distorted exohedral structure.

The exohedral phosphorous, germanium and arsenic doped Ga12X clusters exhibit similar structures to exo-Ga12Si with the dopant atom located in an equatorial position in one of the fivemembered rings of distorted decahedral structures. Exo-GeGa12 exhibits longer Gaax-X and X-Gaeq distances than exo-SiGa12 but the other dimensions of the two clusters are generally similar. Exohedral GeGa12 is only slightly higher in energy (+0.14 eV) than the endohedral isomer. Similarly, Charkin et al.31 found that the icosahedral endo-Al12Ge was the lowest energy aluminium analogue but that a range of low lying exohedral isomers also existed. They concluded that the size and electronegativity difference between aluminium and germanium has a significant effect on bonding in the cluster. These effects will be smaller in the gallium based clusters which could explain the smaller number of isomers. In comparison, the exohedrally doped phosphorus- and arsenic-doped clusters exhibit quite short Gaax-X and X-Gaeq distances, indicating strong bonding 13




between the dopant and neighboring Ga atoms. The dopants also cause a significant elongation of the Gaax-Gaax distances with a slight shortening of the inter-ring separation. The difference in energy between endo-Ga12P and exo-PGa12 (+0.40 eV) is similar to that for the corresponding Al12P isomers (+0.35 eV).35 However, exo-PAl12 exhibits a significantly more distorted structure than exo-PGa12.

Binding energies (BE) for all of the clusters are presented in Table 3. Ga13 with 39 valence electrons has the lowest binding energy of the systems considered in this study. The isoelectronic Al and B doped systems have successively larger binding energies indicating greater overall stability. The systems doped with group 14 elements at the core, leading to closed-shell 40 valence electron configurations, generally exhibit high binding energies. However, within this group there is a successive decrease in binding energy as the dopant is changed from C through to Ge as observed for Al12X clusters.25 Systems doped with group 15 elements (N, P and As) also exhibit increased binding relative to Ga13 but not to the same level as the group 14 doped systems. The absolute binding energies for Ga12X clusters are generally smaller than the corresponding Al12X values reported here but there are consistent trends as a function of dopant for the two systems.

One of the experimental techniques for the formation of small metallic clusters involves laser ablation of metals/ alloys with subsequent aggregation of the ejected atoms into clusters of different sizes, compositions and/or isomers.2 For a given cluster composition, one of the factors that will determine the abundance of different isomers is the relative energies of these species. In this regard, a Boltzmann distribution can be used to estimate the relative proportions of different conformations forming at different temperatures. As shown in Figure 1, the relative energies of endo- and exo-hedral isomers vary significantly for different dopants. Carbon, silicon, phosphorous and germanium exhibit the greatest preference for the dopant atom to be located at the core of the cluster. The energy differences between the isomers for these clusters is sufficiently large that a 14


Page 14 of 37

Page 15 of 37



Boltzmann distribution indicates that less than 1 % of the exohedral isomers would be formed at 298 K. In fact even at 1000 K, still less than 1 % of the exohedral isomers, CGa12, SiGa12 and PGa12, would be formed. For Ga12Ge the energy difference is smaller and 17 % of the exohedral isomer is predicted at this elevated temperature. As noted earlier the exohedral NGa12 is lower in energy than the endohedral isomer and the energy difference between isomers is sufficiently large that less than 2 % of the endohedral isomer is predicted to form from the atoms at 298 K. However, at 1000 K, up to 23 % of the endohedral isomer is predicted. For the aluminium and arsenic doped clusters, the energy differences between isomers are much smaller. Consequently, a Boltzmann distribution indicates that ~32 % and ~14% of the exo-Ga12Al and endo-Ga12As, isomers, respectively, would be formed from the atoms at 298 K. In comparison, 44% and 37% of these isomers would be formed from the atoms at 1000 K, respectively. While these ratios are based solely on the relative energies of the isomers and do not take into account other factors such as reaction kinetics and higher energy isomers, they do suggest that very high endohedral/exohedral isomer selectivity may be possible for some compositions over a large temperature range using atomization techniques.

Generally the trends in ∆Hsubst reflect the trends in binding energies. Endohedral doping of the cluster with carbon leads to the largest stabilizing effect (∆Hsubst = -3.44 eV). This results in a 40 valence electron cluster that is predicted to be particularly stable within the Jellium model. Doping the cluster with other Group 14 elements (Si and Ge) also has a stabilizing effect but the magnitude of this stabilization decreases substantially for these third and fourth row dopants. Doping the cluster with a group 13 element will not lead to a change in the total number of valence electrons relative to Ga13 and therefore should have a minimal effect on the stability of the cluster. However, doping the cluster with Al actually leads to an increase in stability (~0.4 eV) while doping with boron leads to an even greater increase in stability (2.59 eV). In fact endo-Ga12B is slightly more stable than endo-Ga12Si, despite the latter having a closed shell magic electronic configuration. 15




Likewise, doping Ga13 with a group 15 element leads to a 41 valence electron system and would not be expected to lead to a significant increase in stability. However, it is clear from Table 3 that in each case (X = N, P and As) that the dopant does in fact increase the stability of the cluster.

Inspection of Table 3 reveals a broad correlation between distortion energies (∆Hdist) and atomic size for the endohedrally doped clusters. Systems with second row dopants exhibit the largest stabilization of the Ga12 framework followed by systems with third row dopants. This indicates that in these systems there is less strain in the Ga12 framework as a consequence of doping. For the clusters with fifth row dopants, endo-Ga12Ge exhibits negligible stabilization of the gallium cage, whereas the framework of endo-Ga12As is slightly destabilized. Despite this broad correlation between ∆Hdist and dopant size, there is no clear trend within a series of clusters with dopants from the same row of the periodic table.

With the exception of exo-CGa12, the exohedrally doped clusters exhibit the opposite trend in ∆Hdist. The clusters with fourth row dopants show large stabilization of the framework followed by exo-XGa12 with third row dopants, while the Ga12 framework of exo-NGa12 is actually destabilized relative to Ga13. Exo-CGa12 exhibits the largest stabilization of the Ga12 framework because the highly distorted structure allows for an increased number of close Ga-Ga bonds. However, while ∆Hdist does make a contribution to the overall stability of both the endohedral and exohedral doped clusters, this is relatively small compared to ∆Hsubst, indicating that electronic effects are much more important than structural effects.

Analysis of eigenvalues of the endo-Ga12X clusters reveals that endo-Ga12C exhibits a Jellium-like eigenvalue spectrum with a high degree of degeneracy (Fig. 3a), which correlates well with its high stability. The 1s, 1p, 2s, 1d and 2p shells have clearly formed, predominantly from the 4s orbitals of the gallium atoms. However, as Chandrachud et al.17 noted, the levels near the HOMO 16


Page 16 of 37

Page 17 of 37



are predominantly formed from p-type orbitals of the surface atoms rather than fully hybridized Jellium-type orbitals. In comparison, endo-Al12C has a clearly defined shell structure with distinct 1s, 1p, 2s, 1d, 2p and 1f Jellium orbitals, indicating a well developed, spherical free electron / metallic bonding environment. The closed shell endo-Ga12Si and endo-Ga12Ge clusters exhibit much less degeneracy indicating less developed formation of Jellium-like orbitals, which equates with their smaller stabilization energies.

The eigenvalue spectra of endo-Ga12B and endo-Ga12N have a number of features in common with endo-Ga12C including p-type orbitals near the HOMO but lack the overall simplicity of the latter. For the endo-Ga12X clusters with X = Al, Si, Ga and Ge, the outer orbitals appear to form a very broad (~0.6 – 0.9 eV) 1f shell. The differences in the band structure of the outer orbitals appears to influence the symmetry of the cluster framework with p-type shells leading to icosahedral structures and broad f-type shells leading to decahedral type structures. Molina et al.36 note that for 40 valence electron Al12X clusters the energy of the 1d and 1f shells are relatively constant while the other shells (1s, 1p, 2s, 2d etc) are generally shifted towards the HOMO as a function of dopant size. In fact analysis of bonding between the core and surface atoms of Al12X clusters reveals that it is strongly metallic in nature and that the shifts of the 2s and 2p orbitals are strongly related to the electronic contributions of the central atom. It is clear from Figure 3a that for endohedral Ga12X, the 1p, 1d and 2p shells are relatively constant in energy. In comparison, the 1s and 2s shells show shifts towards the HOMO level as a function of dopant size, indicating a significant interaction between core and surface atoms, analogous to Al12X systems. The top of the 2p level falls within a relatively narrow band (~-6.8 - -7.3 eV) for the 39 and 40 valence electron Ga12X clusters but is substantially lower for endo-Ga12N and is not clearly defined for endo-Ga12P and endo-Ga12As due to merging of the bands.

17




The eigenvalue spectra of the exohedral systems (Fig. 3b) do show some clustering of orbital energies but there is far less degeneracy than observed for the endohedral clusters. However, for the 41 valence electron systems (X = N, P and As) the separation between the HOMO-group of orbitals and the next band is noticiceably smaller than for other clusters, indicating a significant deviation from Jellium-type bonding.

Analysis of the total electron density can also provide insight to the nature of the bonding in Ga12X clusters. At an isosurface value of 0.088, charge is localized around all of the atoms individually (Fig. 4a) except for the dopants of endo-Ga12Si and endo-Ga12Al. At 50% of this value, the picture remains the same for many clusters with electron density localized around individual atoms. However, for endo-Ga12Si, endo-Ga12P, endo-Ga12Ge and endo-Ga12As, there is significant localization of charge between pairs of atoms in the inter-ring region corresponding to Gaeq-Gaeq bonds (Fig. 4b). This reflects the tendency of gallium to form covalently bound Ga2 dimer subunits. For most clusters, direct bonding between the core and surface atoms is only observed at isovalues lower than that for Ga-Ga inter-ring bonding. However, for endo-Ga12X clusters with first row dopants, bonding between the core and the surface Ga’s is evident at higher or similar isosurface values to that of Ga-Ga bonding, reflecting greater charge transfer with the dopant atoms. These observations are consistent with Jellium-like bonding in the systems with endohedral second row dopants and more localized bonding in the systems with heavier element dopants. Trends in electron density are consistent with trends in bond lengths. In comparison, Al12X clusters generally exhibit delocalized charge density that is well spread over the cluster, consistent with predominantly metallic bonding.9d,17 For the exohedrally doped clusters with 41 valence electrons, the isosurfaces indicate significant localized bonding between the dopant and neighbouring gallium atoms, with little evidence of Jellium-like structure.

18


Page 18 of 37

Page 19 of 37



Ionization potentials and electron affinities also give an indication of the stability and potential reactivity of a cluster. Generally ionization processes that bring the electronic configuration of a cluster closer to a closed shell magic number are favored because this leads to increased stability. Table 4 presents vertical ionization potentials (vIP) and vertical electron affinities (vEA) for each of the clusters identified in this study.

The vertical ionization potentials for all of the clusters are quite large (Table 4). Nevertheless, it is clear that the 41 valence electron systems (Group 15 dopants) have the lowest vIPs of the systems studied, reflecting the stability of the corresponding 40 valence electron cations. However, it is notable that within this group of systems, the clusters with endohedral dopants have lower vIPs than the corresponding exohedral systems. In fact the vIPs for the endohedral clusters (X = N, P, and As) are less than the ionization potential for gallium atom (5.997 eV).24 This also reflects the increased stabilization achieved from combining spherical symmetry with a closed shell magic electronic configuration. The vIPs for the corresponding Al12X systems exhibit similar trends. For example, Molina et al.36 reported vertical ionization potentials for the series of endoAl12X clusters where X = Al, Si and P as 6.68 eV, 6.93 eV and 5.21 eV, respectively. Clearly, the vIP value for the 41 valence electron Al12X cluster is significantly lower than for the 39 and 40 valence electron clusters, again reflecting the high stability of the corresponding closed shell cation. It is also notable that the vIPs for the endohedral systems with 39 and 40 valence electrons can be split into two groups. The first group, with second row dopants (B and C), have vIPs of ~ 7.0 eV, while the second group with third and fourth row core atoms have vIPs of ~ 6.7 eV. Charkin et al.31 reported the vIPs for endo-Al12X with X = C, Si and Ge as 6.76, 6.78 and 6.94 eV, which indicates an increase in vIP with dopant size. This is the opposite of that for the corresponding endo-Ga12X clusters and reflects differences in the bonding within the different systems. In comparison, the ionization potentials of the exohedral systems show greater variation and are more closely aligned with the number of valence electrons of the clusters. 19




It is clear from Table 4 that the 39 valence electron systems have the highest vertical electron affinities, again reflecting the significant stability of the corresponding ions. As for the vIPs, the electron affinities for the exohedral clusters follow a logical trend with the 40 valence electron clusters (group 14 dopants) having the lowest values, while the 41 valence electron systems (group 15 dopants) are slightly higher and values for the 39 valence electron systems higher again. For the endohedral systems, there is a clear distinction in the vEAs of systems doped with second row atoms and those with heavier atoms. The vEAs for the 40 and 41 valence electron systems are all ~1.8 eV. However, the vEA for endo-Ga12C is very low at 1.28 eV reflecting the significant destabilization introduced by addition of a single electron. In comparison, endo-Ga12N has a substantially higher vertical electron affinity. The aluminium analogues exhibit similar trends with the 39 valence electron systems having the highest vEAs, however, the absolute values for the endo-Al12X systems are generally significantly higher.9,27,34,38

The observed trends in vIP and vEA can generally be explained in terms of the frontier orbitals of the clusters. The bonding in the Ga12 framework of the endohedral clusters is dominated by a group of orbitals at or just below the HOMO (Fig. 5a, 5b). This is particularly true for the endohedral 40 electron systems where the HOMO is two- or fourfold degenerate. Ionization breaks the degeneracy of these key orbitals (Jahn-Teller distortion), weakening the bonding in the Ga12 framework making it energetically unfavourable.

For the 41 valence electron systems, the HOMO is in fact a singly occupied molecular orbital (SOMO) (Fig. 5c). The SOMO on endo-Ga12N is weakly bonding between the gallium atoms but anti-bonding with nitrogen, as shown in the cutaway in Figure 5d. Ionisation of endoGa12N is more favourable than for endo-Ga12C because it removes this interaction without disrupting the underlying orbitals, which are more important to the bonding and stability of the 20


Page 20 of 37

Page 21 of 37



cluster framework. The SOMOs of endo-Ga12P and endo-Ga12As involve a bonding interaction between a dz2 orbital on P or As, respectively, and p-type orbitals of the equatorial gallium atoms (Fig. 5e). However, there is an antibonding interaction with the axial gallium atoms. Once again, ionization removes this interaction without disrupting the critical bonding interactions of the underlying orbitals. The anti-bonding interaction in the SOMO of endo-Ga12P and endo-Ga12As also accounts for the elongation of the axial bonds in these clusters. The SOMO of the 39 valence electron clusters involves a bonding interaction between the core atom and the Ga12 framework. Therefore, ionization weakens the overall framework of the cluster. However, addition of an electron to this orbital significantly increases stability which accounts for the large vertical electron affinities. The LUMOs of the 40 valence electron clusters are generally similar to the SOMOs of the corresponding 41 electron clusters. Addition of an electron leads to an anti-bonding interaction with the core that is energetically unfavourable.

The frontier orbitals of a number of the exohedral clusters share features with the endohedral counterparts. In particular, the SOMO of exo-AlGa12 is bonding between the core and the equatorial gallium atoms. Ionisation therefore weakens the bonding of the central framework but addition of an electron substantially strengthens the cluster. The aluminium atom in the axial position is not involved in this interaction. The HOMOs and LUMOs of exo-SiGa12 and exoGeGa12 are also similar to their endohedral counterparts. However, the electronegative dopant in one of the 5-membered rings, polarizes the bond with the gallium atom in the opposing ring and this leads to a slight increase in both vIP and vEA. The 41 electron exohedral systems all have very similar SOMOs with an anti-bonding interaction between the dopant and the neighbouring gallium atoms but bonding interactions between the gallium atoms further from the dopant (Fig. 5f). The anti-bonding interaction is more localized in the exohedral clusters, so the vIPs and vEAs are higher than in their endohedral counterparts. The values decrease going down the group because the p-type

21




orbitals from the dopant are successively less contracted and they interact more strongly with the Ga12 framework.

The calculated vEA of Ga13 is smaller (0.5 eV) than the experimental vertical detachment energy (vDE) of Ga13- reported by Cha et al.11 However, the latter is relative to the more stable and symmetric closed shell cluster, where removal of an electron and the corresponding loss of degeneracy would be expected to have a larger effect. The BP86/SVP adiabatic electron affinities of Ga12Si- reported by Weiß et al.15 are larger than the vEAs reported here but the difference in energy between the endohedral and exohedral isomers is quite similar.

The calculated HOMO-LUMO gaps (EHL) for each of the cluster are presented in Table 4. For the endohedral systems, the trends in EHL tend to follow those of the vIPs. The endo-Ga12B and endo-Ga12C clusters have large HOMO-LUMO gaps of > 3 eV. In comparison, endo-Ga12N has a much lower EHL of only 1.85 eV. The remaining systems with Group 13 and 14 core atoms have EHL values in the range 2.50 – 2.63 eV, while endo-Ga12P and endo-Ga12As have EHL values of ~2.25 eV. The EHL values for exohedral Al, Si and Ge doped systems are similar to those of the corresponding endohderal isomers, consistent with the similar bonding in all of these systems. For the exohedral group 15 doped systems the HOMO-LUMO gap is larger for exo-NGa12 but smaller for exo-PGa12 and exo-AsGa12, compared to the endohedral isomers, respectively. The HOMOLUMO gaps of endo-Al12X analogues are generally significantly smaller than their endo-Ga12X counterparts. Nevertheless, similar trends are observed for systematic variations of dopant.36

4. Conclusions In this study the structures and stability of doped gallium clusters Ga12X (X= B, C, N, Al, Si, P, Ga, Ge and As) were investigated using density functional theory. Clusters doped with lighter elements (X = B, C and N) have high symmetry Ih/D3d structures while those with heavy element 22


Page 22 of 37

Page 23 of 37



dopants generally have decahedral based structures similar to Ga13. This arises from differences in the exchange of electron density between the core and the Ga12 cage as well as differences in the band structure of the orbitals near the HOMO. Clusters with group 14 dopants generally have the most compact structures, in line with their closed-shell “magic” electronic configurations. Exohedral doping with lighter elements generally causes greater structural distortion than doping with heavier elements.

Binding and stabilization energies generally follow the trends predicted by the Jellium model with the 40 valence electron systems being the most stable and the 39 valence electron systems the least stable. However, for isoelectronic systems there is a successive decrease in binding/stabilization as the dopant is changed from a second row element through to a fourth row element. With the exception of exo-NGa12 and exo-AlGa12, the endohedral isomers are generally favoured or close in energy to their exohedral counterparts.

Endohedral Ga12C shows the most Jellium-like structure with high degeneracy of orbitals. In comparison, exo-NGa12 exhibits the least Jellium-like structure with very localized bonding around the nitrogen dopent. While there are a number of similarities in the properties of Ga12X clusters and Al12X clusters a number of significant differences also exist. These differences are largely due to the less developed s-p hybridization in the Ga12X clusters. Trends in vertical ionization potentials and electron affinities can be explained in terms of the interactions in frontier orbitals and generally adhere to the predictions of the Jellium model.

Acknowledgements The author acknowledges generous allocations of computing time from the Australian National Computational Infrastructure (NCI) facility.

23




References

1

(a) Knight, W. D.; Clemenger, K.; de Heer, W. A.; Saunders, W. A.; Chou, M. Y.; Cohen, M.

L. Phys. Rev. Lett. 1984, 52, 2141-2143. (b) Beck, D. E. Solid State Comm. 1984, 49, 381-385. (c) Chou, M. Y.; Cohen, M. L. Phys. Lett. A 1986, 113A, 420-424. 2

Lau, K. C.; Pandey, R. Comput. Lett. 2005, 1, 259-270.

3

Teixidor, F.; Vinas, C.; Demonceau, A.; Kivekaes, R.; Sillanpaeae, R.; Nunez, R. In Boron

Chemistry at the Beginning of the 21st Century; Bubnov, Yu. N. Ed.; Russ. Acad. Sci. 2003. 4

(a) Jarrold, M. F.; Bower, J. E. J. Chem. Phys. 1986, 85, 5373-5375. (b) Jarrold, M. F.; Bower,

J. E. J. Chem. Phys. 1987, 87, 5728-5738. (c) Jarrold, M. F.; Bower, J. E. Chem. Phys. Lett. 1988, 144, 311-316. (d) Jarrold, M. F.; Bower, J. E. J. Am. Chem. Soc. 1988, 110, 70-78. 5

Rao, B. K.; Jena, P. J. Chem. Phys. 1999, 111, 1890-1904.

6

Ahlrichs, R.; Elliott, S. D. Phys. Chem. Chem. Phys. 1998, 1, 13 - 21.

7

Cox, D. M.; Trevor, D. J.; Whetten, R. L.; Kaldor, A. J. Phys. Chem. 1988, 92, 421-429.

8

Taylor, K. J.; Pettiette, C. L.; Craycraft, M. J.; Chesnovsky, O.; Smalley, R. E. Chem. Phys.

Lett. 1988, 152, 347-352. 9

(a) Henry, D. J.; Varano, A.; Yarovsky, I. J. Phys. Chem. A 2008, 112, 9835-9844. (b) Henry,

D. J.; Yarovsky, I. J. Phys. Chem. A, 2009, 113, 2565-2571. (c) Henry, D. J.; Varano, A.; Yarovsky, I. J. Phys. Chem. A 2009, 113, 5832-5837. (d) Henry, D. J.; Szarek, P.; Hirai, K.; Ichikawa, K.; Tachibana, A.; Yarovsky, I. J. Chem. Phys. C 2011, 115, 1714-1723. 10

Wang, L.; Zhao, J.; Zhou, Z.; Zhang, S.; Chen, Z. J. Comput. Chem. 2009, 30, 2509-2514.

11

Cha, C.Y.; Gantefor, G.; Eberhardt, W. J. Chem. Phys. 1994, 100, 995-1010.

12

Gong, X. G.; Zheng, Q. Q.; Han, R. S. Solid State Comm. 1995, 94, 735-739.

13

Yi, J.-Y. Phys. Rev. B 2000, 61, 7277-7279.

14

Song, B.; Cao, P.-I. J. Chem. Phys. 2005, 123, 144312.

15

Weiß, K.; Köppe, R.; Schnöckel, H. Int. J. Mass. Spectrom. 2002, 214, 383-395.

16

(a) Khanna, S. N.; Jena, P. Phys. Rev. Lett. 1992, 69, 1664-1667. (b) Gong, X. G.; Kumar, V.

Phys. Rev. Lett. 1993, 70, 2078-2081. (c) Kumar, V.; Sundararajan, V. Phys. Rev. B 1998, 57, 49394942. (d) Li, S. F.; Gong, X. G. Phys. Rev. B 2004, 70, 075404-1 - 075404-5. (e) Li, S. F.; Gong, X. G. Phys. Rev. B 2006, 74, 045432-1 - 045432-5. 24


Page 24 of 37

Page 25 of 37



17

Chandrachud, P.; Joshi, K.; Kanhere, D. G. Phys. Rev. B 2007, 76, 235423-1 - 235423-8.

18

Guo, L. Comput. Materials Sci. 2009, 45, 951-958.

19

Wang, H.; Ko, Y. J.; Bowen, K. H.; Sergeeva, A. P.; Averkiev, B. B.; Boldyrev, A. I. J. Phys.

Chem. 2010, 114, 11070-11077. 20

Song, B.; Yao, C.H.; Cao, P.-l. Phys. Rev. B 2006, 74, 035306-1 - 035306-8.

21

Gaussian 03, Revision C.02, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.;

Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; et al. Gaussian, Inc., Wallingford CT, 2004. 22

Gaussian 09, Revision A.02, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.;

Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian, Inc., Wallingford CT, 2009. 23

Ghosh, T. K.; Tanaka, K.; Mochizuki, Y. J. Mol. Struct. (THEOCHEM) 1998, 451, 61-71.

24

Greenwood, N. N.; Earnshaw, A. Chemistry of the Elements; Pergamon Press: Oxford, U.K.,

1984. 25

Gong, X. G.; Kumar, V. Phys. Rev. Lett. 1993, 70, 2078 – 2081.

26

Lei, X.L. J. Cluster Sci. 2011, 22, 159-172.

27

Li, X.; Wang, L.-S. Phys. Rev. B 2002, 65, 153404-1 - 153404-4.

28

Rao, B. K.; Jena, P. J. Chem. Phys. 2001, 115, 778-83.

29

Gong, X. G. Phys. Rev. B 1997, 56, 1091 – 1094.

30

Seitsonen, A. P.; Laasonen, L.; Nieminen, R. M.; Klein, M. L. J. Chem. Phys. 1995, 103, 8075

– 8080. 31

Charkin, O. P.; Charkin, D. O.; Klimenko, N. M.; Mebel, A. M. Faraday Discuss.. 2003, 124,

215-237. Charkin, O. P.; Klimenko, N. M.; Charkin, D. O.; Mebel, A. M. Russ. J. Inorg. Chem. 2004, 49, 1382 – 1391. 32

Wang, B.; Zhao, J.; Shi, D.; Chen, X.; Wang, G. Phys. Rev. A 2005, 72, 023204-1 - 023204-5.

33

Kumar, V.; Sundararajan, V. Phys. Rev. B 1998, 57, 4939 – 4942.

34

Akutsu, M.; Koyasu, K.; Atobe, J.; Hosoya, N.; Miyajima, K.; Mitsui, M.; Nakajima, A. J.

Phys. Chem. A 2006, 110, 12073 – 12076. 35

Guo, L.; Wu, H. J. Nanopart. Res. 2008, 10, 341 – 351. 25




36

Molina, B.; Soto, J. R.; Castro, J. J. J. Phys. Chem. C 2012, 116, 9290 – 9299.

37

Bai, Q.; Song, B.; Hou, J.; He, P. Phys. Lett A 2008, 372, 4545 – 4552.

38

Guo, L. J. Alloys Compounds 2012, 527, 197-203.

26


Page 26 of 37

Page 27 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1. Key Structural Properties of Endohedral Substituted Gallium Clusters (Ga12X) (Å). Symmetry

X-Gaax

X-Gaeq

Gaax-Gaeq

Gaeq-Gaeq

Ga13

C1

2.685, 2.743

2.702 – 2.796

2.731 – 2.857

2.587 – 2.659

Ga12B

D3d

Ga12C

Ih

2.547

2.547

2.678

2.678

Ga12N

D3d (~Ih)

2.559

2.558

2.690

2.690

Ga12Al

Cs

2.721

2.703 – 2.789

2.730 – 2.782

2.586 – 2.686

Ga12Si

D5h

2.670

2.714

2.776

2.542

Ga12P

D5h

2.916

2.683

2.874

2.552

Ga12Ge

D5h

2.693

2.739

2.803

2.561

Ga12As

D5h

2.944

2.726

2.916

2.580

2.540 – 2.600

2.643 – 2.808

27 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 37

Table 2. Key Structural Properties of Exohedral Substituted Gallium Clusters (Ga12X) (Å) Symmetry

Gaax-X

Gaax-Gaax

X-Gaeq

Gaeq-Gaeq

Ga13

C1

2.743

2.685

2.731 – 2.857

2.587 – 2.659

CGa12

Cs

2.309

2.701, 2.800

2.011 – 2.122

2.594 – 2.863

NGa12

Cs

1.992

2.709, 2.859

1.945

2.577 – 2.681

AlGa12

Cs (dist C5)

2.687

2.722

2.723 – 2.736

2.580 - 2.641

SiGa12

Cs

2.501

2.673,2.704

2.476

2.547, 2.556

PGa12

Cs

2.374

2.974, 2.843

2.431 - 2.780

2.582, 2.548

GeGa12

Cs

2.571

2.673, 2.708

2.561

2.544, 2.552

AsGa12

Cs

2.477

2.865, 3.001

2.588

2.558, 2.559


Page 29 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3. Key Energetic Properties of Substituted Gallium Clusters (Ga12X) (eV). Endohedral

Exohedral

Ga12B

Ga12C

Ga12N

BGa12

CGa12

NGa12

BE

-30.31

-31.15

-28.91

-

-30.48

-29.01

∆Hsubst

-2.59

-3.44

-1.19

-

-2.74

-1.29

∆Hdist

-0.39

-0.36

-0.38

-

-0.46

+0.22

Ga12Al

Ga12Si

Ga12P

AlGa12

SiGa12

PGa12

BE

-28.12

-30.28

-29.24

-28.10

-29.67

-28.84

∆Hsubst

-0.40

-2.57

-1.52

-0.38

-1.95

-1.12

∆Hdist

+0.03

-0.15

-0.07

-0.01

-0.23

-0.16

Ga13

Ga12Ge

Ga12As

Ga13

GeGa12

AsGa12

BE

-27.72

-29.54

-28.54

-27.72

-29.40

-28.58

∆Hsubst

0.0

-1.82

-0.82

0.0

-1.68

-0.87

∆Hdist

0.0

-0.01

+0.23

0.0

-0.39

-0.41



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 37

Table 4. Vertical Ionisation Potentials (vIP), Vertical Electron Affinities (vEA) and HOMOLUMO gaps (EH-L)a for Substituted Gallium Clusters (eV). Endohedral

a

Exohedral

Ga12B

Ga12C

Ga12N

BGa12

CGa12

NGa12

vIP

7.03

7.00

5.51

-

6.70

6.15

vEA

3.10

1.28

2.21

-

1.94

2.53

EH-L

3.09

3.28

1.85

-

2.52

2.04

Ga12Al

Ga12Si

Ga12P

AlGa12

SiGa12

PGa12

vIP

6.76

6.75

5.78

6.69

6.86

6.03

vEA

3.02

1.81

1.81

3.03

2.01

2.20

EH-L

2.50

2.63

2.27

2.64

2.54

1.81

Ga13

Ga12Ge

Ga12As

Ga13

GeGa12

AsGa12

vIP

6.71

6.72

5.77

6.71

6.90

5.98

vEA

3.02

1.82

1.86

3.02

1.97

2.14

EH-L

2.55

2.60

2.21

2.55

2.62

1.89

EH-L for open-shell systems is calculated as the difference in energy of the SOMO and the lowest

energy virtual α-orbital.


Page 31 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure Captions:

Figure 1. Key geometric parameters of Ga12X clusters with (a) endohedral dopant (b) exohedral dopant in axial position and (c) exohedral dopant in equatorial position.

Figure 2. Lowest energy endo-Ga12X (left) and exo-XGa12 (right) clusters and energies of exohedral isomers relative to corresponding endohedral isomers.

Figure 3. Eigenvalue spectra for (a) endo-Ga12X clusters and (b) exo-Ga12X clusters.

Figure 4. Electron Density for endo-Ga12P (a) 0.088 electrons/Å3 isosurface and (b) 0.044 electrons/Å3 isosurface.

Figure 5. Selected cluster frontier orbitals: (a) HOMO endo-Ga12C, (b) HOMO-2 endo-Ga12C, (c) SOMO endo-Ga12N (d) SOMO endo-Ga12N cutaway (e) SOMO endo-Ga12P and (f) SOMO exoGa12P.



Figure 1. Key geometric parameters of Ga12X clusters with (a) endohedral dopant (b) exohedral dopant in axial position and (c) exohedral dopant in equatorial position.

Gaeq -Gaeq

Gaax -Gaeq

X-Gaax

(a)

X

X-Gaeq

X

Gaeq -Gaeq

Gaax-Gaax

X-Gaax

(c)

X-Gaeq Gaeq -Gaeq

Gaax-Gaax X-Gaax

(b)

X-Gaeq

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 37

X

Gaax-Gaax


Page 33 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2. Lowest energy endo-Ga12X (left) and exo-XGa12 (right) clusters and energies of exohedral isomers relative to corresponding endohedral isomers.

endo-Ga12 B

endo-Ga12 C

exo-CGa12 +0.70

endo-Ga12 N

exo-NGa12 –0.10

endo-Ga12 Al

exo-AlGa12 +0.02

exo-SiGa12

endo-Ga12 Si

+0.61

endo-Ga12 P

exo-PGa12 +0.40

Ga13

endo-Ga12 Ge

exo-GeGa12 +0.14 exo-AsGa12

endo-Ga12 As

–0.05



Figure 3. Eigenvalue spectra for (a) endo-Ga12X clusters and (b) exo-Ga12X clusters.

-2

-4

-4

-6

-6

Eigenvalue Energies (eV)

-2

-8 -10 -12 -14 -16

-8 -10 -12 -14 -16

-18

-18

-20

-20

-22

-22

(a)

(b)


PGa12

AsGa12

SiGa12

GeGa12

AlGa12

PGa12

NGa12 AsGa12

SiGa12

Ga13 GeGa12

AlGa12

NGa12

Ga13

Ga12As

Ga12Ge

Ga12P

Exohedral

Ga12Si

Ga12Al

Ga12N

Ga12C

Ga12B

Ga13

Endohedral

Eigenvalue Energies (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 37

Page 35 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4. Electron Density for endo-Ga12P (a) 0.088 electrons/Å3 isosurface and (b) 0.044 electrons/Å3 isosurface.

(a)

(b)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 5. Selected cluster frontier orbitals: (a) HOMO endo-Ga12C, (b) HOMO-2 endo-Ga12C, (c) SOMO endo-Ga12N (d) SOMO endo-Ga12N cutaway (e) SOMO endo-Ga12P and (f) SOMO exoGa12P.

(a)

(b)

(c)

(d)

(e)

(f)


Page 36 of 37

Page 37 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table of Contents Graphic


Structures and Stability of Doped Gallium Nanoclusters - The Journal

Recommend Documents