Doped Aluminum Cluster Anions: Size Matters - American Chemical

Article pubs.acs.org/JPCA

Doped Aluminum Cluster Anions: Size Matters Elisa Jimenez-Izal,*,† Diego Moreno,‡ Jose M. Mercero,¶ Jon M. Matxain,† Martha Audiffred,‡ Gabriel Merino,*,‡ and Jesus M. Ugalde† †

Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU) and Donostia International Physics Center (DIPC), P.K. 1072, Donostia, Euskadi 20008, Spain ‡ Departamento de Fı ́sica Aplicada, Centro de Investigación y de Estudios Avanzados, Unidad Mérida. Km 6 Antigua Carretera a Progreso. Apdo. Postal 73, Cordemex, Mérida, Yucatán, 97310, México ¶ IZO-SGI Sgiker, Euskal Herriko Unibertsitatea (UPV/EHU), P. K. 1072, Donostia, Euskadi 20080, Spain S Supporting Information *

ABSTRACT: The global minima of the cluster anions with the generic chemical formula (XAl12)2−, where X = Be, Mg, Ca, Sr, Ba, and Zn, are determined by an extensive search of their potential energy surfaces using the Gradient Embedded Genetic Algorithm (GEGA). All the characterized global minima have an icosahedral-like structure, resembling that of the Al−13 cluster. These cages comprise closed-shell electronic configurations with 40 electrons, therefore, in accordance to the jellium model, they are predicted to be highly stable and amenable to experimental detection. The two preferred sites for the dopant species, at the center and at surface of the icosahedral cage, are stabilized depending on the atomic radius of X. Thus, while the small dopants (X = Be, Zn) sit preferably at the center of the cage, the preferred site for X = Mg, Ca, Sr, and Ba is at the surface. Since these dianions are not stable towards electron detachment, one Li cation is added in order to yield stable systems. Our computations show that in the global minimum form of Li(XAl12)−, the lithium cation, ionically bonded to the Al atoms, does not change the structure of the (XAl12)2− core.

■

INTRODUCTION Clusters with a (pseudo)spherical structure and a number of valence electrons that match those required to have an electronic closed-shell have been found to be particularly stable, receiving the generic name of “magic clusters”.1,2 Al−13 is one of the most attractive magic clusters.3 It has a perfect icosahedral symmetry with an aluminum atom at the center,4 a closed-shell electronic configuration (40 electrons), and a large highest occupied molecular orbital−lowest unoccupied molecular orbital (HOMO−LUMO) gap.5 These features result in an unusual stability and chemical inertness, similar to noble gases, that make the clusters inert toward coalescence. Recent studies showed that the chemical and electronic properties of aluminum clusters could be tuned by doping. In fact, it has been proven that several doped aluminum clusters with formula XAl12 have a higher stability when the dopant X is placed at the center of the cage. Using density functional theory (DFT) computations, Charkin et al.6 and Gong et al.7 studied independently some doped aluminum clusters (XAl12, X = Be, Mg, Zn, B, Al, Ga, C, Si, Ge, N, P, As) with different charges to yield isoelectronic 40 valence electrons systems. The authors concluded that the X-centered icosahedral structure, Ih, is the most favorable for the majority of the selected stoichiometries, even though the relative energy between the other low-lying isomers rapidly decreases when X moves down through the periodic subgroup. In 2008, Lu et al. reported that the stability of aluminum cluster hydrides is greatly increased © 2014 American Chemical Society

when Mg or Ca atoms are embbeding into the cage. Furthermore, the resulting doped clusters are predicted to be promising building block candidates for the synthesis of new nanocluster materials by self-assembling.8 Varano et al. showed that Al@MgAl11 is lower in energy than its parent Mg@Al12. Nonetheless, they noticed that the former isomer features significant structural distortion.9 Despite these reports, studies on aluminum clusters using global geometry optimization techniques are scarce, and consequently great uncertainty remains as to deciphering which are their most stable structure. In this sense, Khanna and Jena10 have studied AlnC clusters and found that Al4C and Al12C possess an enhanced stability with respect to their neighboring size species. In Al12C, the carbon atom occupies the central site of a perfect icosahedron with no direct bonding with any of the cage aluminum atoms. Likewise, Pal et al.11 have studied various systems with the general formula (MAl12)−, M = Li, Cu, and Au, using the basin-hopping global optimization method in combination with DFT computations. They found that (LiAl12)− can be described as a barely distorted icosahedral (Al@LiAl11)− cluster, where the lithium atom replaces one of surface’s atom. Conversely, copper prefers the central site and forms an icosahedral (Cu@Al12)− cluster. Finally, gold also Received: February 11, 2014 Revised: May 5, 2014 Published: May 19, 2014 4309

dx.doi.org/10.1021/jp501496b | J. Phys. Chem. A 2014, 118, 4309−4314

The Journal of Physical Chemistry A

Article

prefers sites at the cage’s center yielding a severely distorted (Au@Al12)− cluster. The aim of this work is to unveil the most stable structures of the doped aluminum cluster dianions with the general formula (XAl12)2− (X = Be, Mg, Ca, Sr, Ba, and Zn) by performing an extensive stochastic search of their minimum energy forms. These species possess 40 valence electrons, hence, according to the jellium model, they should exhibit highly electronic and structural stability. Finally, the global minimum structures of the ionically bonded Li(XAl12)− monoanionic clusters are also found. These species might be more amenable for experimental detection due to their reduced charge. Interestingly, the addition of lithium does not alter the geometrical shapes of their parent clusters.

Table 2. Atomic Charges, HOMO−LUMO Gaps, and Electron Energy Detachment of the XAl12− Global Minimum Structuresa 2−

(Be@Al12) (Al@MgAl11)2− (Al@CaAl11)2− (Al@SrAl11)2− (Al@BaAl11)2− (Zn@Al12)2−

Table 1. Relative Energy between the (X@Al12)2− and (Al@ XAl11)2− Isomers (ΔE) in kcal/mola (Al@Al12) (Be@Al12)2− (Al@BeAl11)2− (Mg@Al12)2− (Al@MgAl11)2− (Al@CaAl11)2− (Al@SrAl11)2− (Al@BaAl11)2− (Zn@Al12)2− (Al@ZnAl11)2−

0.0 32.0 33.3 0.0

0.0 5.2

rcavity

rXb

rAl−Al

rAl−X

Ih Ih C5v Ih C5v C5v C5v C5v C1 C5v

2.65(0.00) 2.57(0.00) 2.63(0.03) 2.68(0.00) 2.68(0.03) 2.72(0.05) 2.77(0.08) 2.83(0.13) 2.63(0.01) 2.67(0.06)

1.21 0.96 0.96 1.41 1.41 1.76 1.95 2.15 1.22 1.22

2.78 2.71 2.81 2.82 2.80 2.80 2.79 2.79 2.77 2.80

2.65 2.57 2.51 2.68 2.93 3.20 3.36 3.48 2.63 2.77

EDEGF

PS

MO

−2.41 0.38 0.08 0.45 b −1.46

−1.41 −1.27 −1.35 b

3.03 2.31 1.64 1.47 1.09 2.84

−0.022 −0.114 −0.037 −0.028 c −0.030

0.979 0.923 0.924 0.922

t1u e2 e2 e2

0.955

a

PBE0/LANL2DZ level were subsequently reoptimized at the PBE0/def2-TZVPD20 level using Gaussian 09 program.21 Harmonic vibrational frequencies were computed by analytical differentiation of gradients to determine whether the structures are true minima and to estimate zero-point and thermal corrections for the energies. The electron detachment energies (EDE) were computed using the outer valence green function (OVGF) approach. Large values, close to 1, of the pole strengths obtained in the OVGF calculations suggested that the electron detachment channels correspond to one-electron processes and, thus, OVGF values should be reliable.22 Furthermore, in order to disclose the nature of the bonding between (XAl12 )2− and Li +, we performed an energy decomposition analysis using the Ziegler-Rauk23,24 scheme, as implemented in the ADF10.02 package.25 We used PBE0 hybrid functional15−17 and a triple-ζ basis-set plus two polarization functions, TZ2P. Structures involving Sr and Ba atoms were treated with the scalar relativistic ZORA approximation.26−28 The interaction energy between the fragments, ΔEint, is the energy difference between the molecule and the fragments in their electronic reference state and frozen geometry of the supermolecule. This interaction energy can be divided into four main components:

Figure 1. Global minimum structures of (Be@Al12)2−, left, and (Al@ MgAl11)2−, right, clusters. Aluminum atoms are shown in pink, beryllium in yellow, and magnesium in red.

Symm

∈HL

q(X) is the NBO charge of the X atom and q(Al)C is the NBO charge of the central Al atom in the exohedral compounds. ∈HL stands for the HOMO−LUMO gap, in eV. The OVGF electron detachment energies, EDEGF, are given in eV. PS gives the pole strength and MO stands for the symmetry of the orbital. bOrthonormalization of MBS failed in NAO. cNot shown because of too small pole strength.

METHODS The potential energy surfaces of the (XAl12)2− (X = Be, Mg, Ca, Sr, Ba, and Zn) clusters have been explored in detail using the

ΔE

q(Al)C

a

■

−

q(X)

ΔE int = ΔE Pauli + ΔEelstat + ΔEorb + ΔEdisp

(1)

The first term, ΔEPauli, is computed by orthonormalizing and antisymmetrizing the fragment spin−orbitals of one moiety with the fragment spin−orbitals of the second moiety at the supermolecule’s equilibrium position. This step ensures that same spin electrons do not occupy the same region of space. Usually this term is responsible for the increase in kinetic energy upon formation of a chemical bond and is always positive. The second term, ΔEelstat, is computed as the electrostatic interaction between the unperturbed fragments at the supermolecules’s equilibrium position. The last term, ΔEorb, is computed by relaxing the orthonormalized density to the full optimized electron density of the entire supermolecule. This contribution includes the charge transfer between the occupied orbitals of one fragment and the unoccupied orbitals of the other fragment. It also includes charge transfer within the occupied and unoccupied orbitals of the same fragment, the socalled intrafragment polarization. Finally, the dispersion corrections are taken into consideration using the corrections suggested by Grimme et al.,29 DFT-D3.

a

Other parameters: symmetry of the molecule (Symm); the average distance between the central atom and the cage, i.e., the cavity radius (rcavity) along its standard deviation in parentheses; the covalent radius of X (rX); the average Al−Al distance (rAl−Al); the distance between X and the closest aluminum atoms (rAl−X). All distances are in Å. bFrom ref 30.

Gradient Embedded Genetic Algorithm (GEGA),12,13 as is implemented in the Kaxan code.14 We used the PBE015−17 functional and the LANL2DZ18 basis set for the energy, gradient, and force computations involved in the GEGA procedure. These computations were performed using the GAMESS program.19 The geometries from GEGA at the 4310



Article

atom, two forms are obtained: the dopant sits at the center of the cage or replaces one of the aluminum atoms in the surface. These structures are depicted in Figure 1. Table 1 collects the energy differences between these two isomers for all of the considered dopant atoms, X. For the sake of comparison, data for (Al@Al12)−, computed at the same level, are also shown. Beryllium and zinc prefer to be hosted inside the icosahedron. These structures are 32.0 and 5.2 kcal/ mol more stable, respectively, than their corresponding exoclusters, where the Be and Zn atoms replace one aluminum of the cage. Magnesium, on the other hand, prefers to be located on the top of the cage. Actually, (Al@MgAl11)2− is 33.2 kcal/mol more stable than its icosahedral (Mg@Al12)2− isomer. Finally, the most stable arrangement for calcium, strontium, and barium are those where an Al atom of the surface is substituted for the dopant to give (Al@XAl11)2− isomer. Isomers with other different structures were also found, but they are much higher in energy (see the Supporting Information). This behavior can be rationalized in terms of the size of the dopant atoms. Let us take the well-characterized (Al@Al12)− cluster as the reference structure. The atomic radius of aluminum is 1.21 Å. Since beryllium has a smaller atomic radius (0.96 Å), it can be accommodated inside the cage very easily. On the other hand, when an Al atom is replaced by a Be, the difference between the size of these two atoms leads to a substantial deformation of the cage. Consequently, beryllium sits preferably at the center of the cage, and the isomer resulting from cage’s atom substitution lies higher in energy by 32.0 kcal/mol (see Table 1). Now let us consider zinc. The atomic radius of Zn is very similar to that of Al (1.22 Å vs 1.21 Å, respectively); therefore, zinc may almost equally well replace the center and any of the cage’s surface aluminum atoms of our reference (Al@Al12)− cluster yielding (Zn@Al12)2− or (Al@ ZnAl11)2−. The estimated relative energy between them is only 5.2 kcal/mol, as shown in Table 1. Magnesium, with a radius of 1.41 Å, is bigger than aluminum. Therefore, replacement of the central aluminum atom of our reference (Al@Al12)− structure induces a very large steric repulsion with the cage’s atoms making it an energetically more favorable surface replacement of the cage. Indeed, the relative energy between the lowest lying (Al@MgAl11)− isomer and (Mg@Al12)− is 33.3 kcal/mol. For Ca, Sr, and Ba atoms, there is simply not enough space inside the cage to fit them, so, the only stable icosahedral form found is the one resulting from the cage’s surface atom replacement (see Table 1). The Natural Population Analysis (NPA) charges show that all atoms at the cage center have negative charges, ranging from −1.27|e| (Ca) to −2.41|e| (Be). It reveals that for the beryllium cluster, the charge is concentrated at the beryllium atom and the cage bears a total positive charge of 0.41|e|. The situation is different when X = Zn, because the charge at the zinc atom is −1.46|e|, meaning that the surface has still a negative charge (−0.54|e|). For the (Al@XAl11) 2− clusters, the central aluminum atom is negative and the dopant surface atom X is positive (see Table 2). The HOMO−LUMO gaps are also an indicative of electronic stability of these species (see Table 2). Nonetheless, one should not forget that DFT tends to underestimate the gaps. The one-electron detachment energies of the lowest-lying isomers of the (XAl12)2− clusters are also shown in Table 2. It was previously reported that the Green’s function method is capable of predicting photoelectron spectral features fairly

Figure 2. HOMO, left, and LUMO, right, of the lowest lying isomers of (XAl12)2− clusters. The isosurface corresponds to 0.02 e/Å3.

Doped Aluminum (XAl12)2− Cluster Anions. From all the numerous structures characterized in this study, the global minima have an icosahedral structure, as it is the case for the (Al@Al12)− magic cluster.4 However, depending on the dopant 4311



Article

Figure 3. Lowest lying geometries of Li(XAl12)− structures, with X = Be, Mg, Ca, Sr, Ba and Zn. Al in pink, Li in purple, Be in yellow, Mg in red, Ca in green, Sr in dark yellow, Ba in brown, and Zn in blue.

Table 3. Relative Energy between the First and Second Most Stable Isomers of the Li(XAl12)− Anions (ΔE) in kcal/mola Li(Be@Al12)− Li(Al@MgAl11)− Li(Al@CaAl11)− Li(Al@SrAl11)− Li(Al@BaAl11)− Li(Zn@Al12)−

ΔE

rcavity

rAl−Li

rAl−X

∈HL

EDEGF

PS

16.3 0.30 1.10 1.39 1.85 1.67

2.57(0.04) 2.70(0.08) 2.72(0.14) 2.76(0.23) 2.82(0.35) 2.63(0.03)

2.70 2.59 2.56 2.56 2.55 2.72

2.57 2.92 3.17 3.31 3.44 2.62

2.91 2.59 2.18 2.08 1.93 2.72

3.428 2.754 2.201 2.048 1.869 2.931

0.878 0.934 0.954 0.956 0.978 0.939

a

Other properties: the average distance between the X and the cage’s surface atoms, i.e., the cavity radius (rcavity) along with the standard deviation in parentheses; the average Al−Li distance (rAl−Li); the distance between X and the closest aluminum atoms, (rAl−X). All are distances in (Å). ∈HL stands for the HOMO−LUMO gap, in eV. The OVGF electron detachment energies, EDEGF, are in eV. PS stands for the OVGF pole strengths.

Table 4. Energy Decomposition Analysis of the Li(XAl12)− Anionsa qX Li(Be@Al12)− Li(Al@MgAl11)− Li(Al@CaAl11)− Li(Al@SrAl11)− Li(Al@BaAl11)− Li(Zn@Al12)−

−2.44 0.55 0.37 0.85 b −1.47

qAlC

qLi

ΔEPauli

ΔEelstat

ΔEorb

ΔEdisp

ΔEint

−1.43 −1.28 −1.37 b

0.65 0.44 0.46 0.46 b 0.65

25.81 26.38 26.19 26.62 25.38 25.55

−154.63(71.7) −157.46(69.9) −155.90(68.4) −158.36(69.0) −158.27(68.9) −153.13(71.5)

−59.39(27.5) −66.02(29.3) −70.13(30.8) −69.44(30.3) −69.70(30.3) −59.43(27.7)

−1.57(0.7) −1.75(0.8) −1.75(0.8) −1.74(0.8) −1.73(0.8) −1.71(0.8)

−189.77 −198.85 −201.59 −202.92 −204.33 −188.71

ΔEint is the total interaction energy. ΔEPauli is the Pauli repulsion energy. The attractive interaction energies are, ΔEelstat: the electrostatic interaction, ΔEorb: the orbital interaction and, ΔEdisp: the dispersion energy. All energy values are given in kcal/mol. Values in parentheses are the percentage of the total attractive energy carried by each of the attractive components. bOrthonormalization of MBS failed in NAO. a

accurately.31 Thus, the vertical electron detachment energies measured from the peak maxima of experimental spectra can be directly compared to the results of the ab initio computations discussed here. Note that the smallest electron detachment energies of all the (XAl12)2− dianionic species considered here are negative, indicating that they will lose an electron spontaneously, given that the repulsive Coulomb barrier for detachment32 will not prevent it. Figure 2 shows the HOMO and LUMO of lowest energy isomers of the XAl2− 12 dianionic clusters. Notice that for (X@ Al12)2−, X = Be, Zn, their corresponding HOMO and LUMO

have 2P- and 2D-type symmetry, respectively, in accordance with the jellium model orbital occupation scheme,33 1S2 1P6 1D10 2S2 1F14 2P6 1G0. The HOMO of the (Al@XAl11)2− (X = Mg, Ca, Sr, Ba) closely resembles 2P-type symmetry but its corresponding LUMO strongly deviates from the 1G-type symmetry predicted by the jellium model. Li(XAl12)− Anions. Laser vaporization coupled with negative ion photoelectron spectroscopy,34 is a very powerful experimental technique to study monoanionic cluster species. Indeed, the negative ion technique affords convenient size selectivity, and photoelectron spectroscopy is very appropriate 4312



■

Article

CONCLUSIONS We have characterized the lowest-lying energy structures of the (XAl12)2−, X = Be, Mg, Ca, Sr, Ba, and Zn, cluster anions by means of a search on the their corresponding potential energy surfaces with the Gradient Embedded Genetic Algorithm (GEGA) as implemented in the Kaxan code. The minimum energy structures found resemble an icosahedron moiety with one atom at the center. For X = Be, Mg, and Zn, two isomers with the icosahedral shape were found close in energy. For X = Ca, Sr, and Ba only one icosahedral isomer was found. The size of the atomic radii of the X atoms explains the preferred structure of the (XAl12)2− cluster anions. Thus, small atoms like Be and Zn sit preferentially at the center of the cage and the isomer where X replaces an aluminum atom of the cluster cage’s surface are found to be less stable by 32.0 and 5.2 kcal/mol, respectively. For the next atom, Mg, the opposite is found, and the surface-substituted cluster at 33.3 kcal/mol is the more stable one. Finally, for Ca, Sr, and Ba, there is simply not enough room for them to be accommodated within the cage, and the surface-substituted isomer is found to be the only icosahedron-like isomer. All these (XAl12)2− cluster anions are found to be unstable toward spontaneous electron detachment. However, coordination with lithium to yield Li(XAl12)− molecules stabilizes them and renders amenable structures for experimental detection. Remarkably, we found that these cluster anions undergo very little structural change in forming the Li(XAl12)− anions. The resulting global minima are best described as a Li+ cation ionically coordinated to the icosahedral (XAl12)2− cluster anion moiety.

for providing unique electronic structure information. Thus, the combination of this technique and ab initio computations offers a particularly powerful approach to investigate the structure and bonding of cluster species.31 Furthermore, dianionic clusters, unstable toward electron detachment, are greatly stabilized by an alkali cation. The global minima are shown in Figure 3. Table 3 shows the geometric and electronic properties of each of these lowest-energy structures. Interestingly, the shape of the lowest-lying lithiated cluster anions remains unchanged when it is compared to that of the parent (XAl12)2− dianions (Figures 1 and 3). Thus, both beryllium and zinc sit inside the aluminum icosahedral cage, while the remainder of the alkaline earth metals substitute one of the cage’s surface aluminum atoms. Moreover, the calculated cavity radii of the lithium complexed clusters, as well as the AlX distances, do not change appreciably upon lithium complexation. A remarkable distinctive feature between (X@Al12)2− and (Al@XAl11)2− formal moieties of the lithium complexed clusters is that the Al−Li distance is considerably shorter for the latter group of clusters, see rAl−Li in Table 3, a fact that reflects the more negative partial charge borne by the surface aluminum atoms of the latter clusters, vide supra. Nevertheless, the addition of Li+ has greatly increased the electron detachment energies (both vertical and the calculated using OVGF). As it can be seen in Table 3, all the values are positive which means that the monoanions are stable toward electron detachment. The increase of the HOMO−LUMO gaps for the anions further confirms the enhancement of the stability ascribed to the lithinum cation. In Table 4, the NPA charges are given along with the energy components of the energy decomposition analysis. Careful analysis of the NPA charges reveals that the charge borne by the central atom of the cluster moiety remains almost unchanged upon lithium coordination, compare q(X) and q(Al)C in Tables 2 and 4. Additionally, lithium appears to be positively charged and may formally be seen as a lithium cation. The icosahedral (XAl12)2− cluster anions seem to undergo very little structural change when they are Li(XAl12)− clusters. This is further confirmed by the energy decomposition analysis data shown in Table 4. Let us recall that the two fragments chosen to examine the interaction are the lithium cation and the remaining cluster moiety. Note that the electrostatic interaction energy component, ΔEelstat, amounts to ∼70% of the sum of the attractive interaction energies for all the species, strongly supporting an ionic interaction between these two fragments. The so-called orbital interaction energy, ΔEorb, associated with covalent and charge transfer interactions35 represents less than one-third of the total attractive interaction energy. Finally, the dispersion effects have a negligible contribution to the bonding of these molecules, which are best described as a Li+ cation ionically coordinated to the icosahedral (XAl12)2− cluster anion moiety. Note that the Pauli repulsion and the dispersion terms are almost constant. The electrostatic contribution changes less than 5 kcal/mol. The most pronounced change is computed for the orbital contribution (more than 10 kcal/mol). Although ΔEorb is only one-third of the total attractive interaction, this is the component justifying the different ΔEint between systems with the X at the center (ΔEint ≈ 189 kcal/mol) and those with X at the surface (ΔEint ≈ 200 kcal/mol)

■

ASSOCIATED CONTENT

* Supporting Information S

Structures of the isomers discussed in this work. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Financial support comes from Eusko Jaurlaritza and the Spanish Office for Scientific Research. The SGI/IZO-SGIker UPV/ EHU is gratefully acknowledged for generous allocation of computational resources. J.M.M. would like to thank the Spanish Ministery of Science and Innovation for funding through a Ramón y Cajal fellow grant (RYC 2008-03216). E.J.I. would like to thank the Basque Government for a Ph.D. fellowship. Moshinsky Foundation, and Conacyt (Grant INFRA-2013-01-204586) supported the work in México. The CGSTIC (Xiuhcoalt) at Cinvestav is gratefully acknowledged for generous allocation of computational resources. M.A. and D.M. thank Conacyt for the Ph.D. fellowship.

■

REFERENCES

(1) Knight, W. D.; de Heer, W. A.; Saunders, W. A. Shell Structure and Response Properties of Metal Clusters. Z. Phys. D 1986, 3, 109− 114.

4313



Article

(23) Ziegler, T.; Rauk, A. CO, CS, N2, PF3, and CNCH3 as σ Donors and π Acceptors. A Theoretical Study by the Hartree−Fock−Slater Transition-State Method. Inorg. Chem. 1979, 18, 1755−1759. (24) Ziegler, T.; Rauk, A. On the Calculation of Bonding Energies by the Hartree−Fock−Slater Method. Theoret. Chim. Acta 1977, 46, 1− 10. (25) Velde, G. T.; Bickelhaupt, F. M.; Baeredens, E. J.; Guerra, C. F.; Giesbergen, J. A. V.; Snijders, J. G.; Ziegler, T. Chemistry with ADF. J. Comput. Chem. 2001, 22, 931−967. (26) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. Relativistic Regular Two-Component Hamiltonians. J. Chem. Phys. 1993, 99, 4597−4610. (27) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. Relativistic Total Energy Using Regular Approximations. J. Chem. Phys. 1994, 101, 9783−9792. (28) van Lenthe, E.; Ehlers, A. E.; Baerends, E. J. Geometry Optimizations in the Zero Order Regular Approximation for Relativistic Effects. J. Chem. Phys. 1999, 110, 8943−8953. (29) Grimme, S.; Anthony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 154104. (30) Cordero, B.; Gomez, V.; Platero-Prats, A. E.; Reves, M.; Echeverria, J.; Cremades, E.; Barragan, F.; Alvarez, S. Covalent Radii Revisited. Dalton Trans. 2008, 21, 2832−2838. (31) Wang, L. S.; Boldyrev, A. I.; Li, X.; Simons, J. Experimental Observation of Penta-atomic Tetracoordinate Planar Carbon-Containing Molecules. J. Am. Chem. Soc. 2000, 122, 7681−7687. (32) Simons, J. Coulomb Potentials have Strong Effects on Anion Electronic States. J. P. Phys. Chem. C 2013, 117, 22314−22324. (33) Rao, B. K.; Khanna, S. N.; Jena, P. Designing New Materials Using Atomic Clusters. J. Cluster Sci. 1999, 10, 477−491. (34) Wang, L. S.; Hu, H. In In Advances in Metal and Semiconductor Clusters. IV. Cluster Materials; Duncan, M., Ed.; JAI Press: Greenwich, CT, 1998; pp 299−343. (35) Frenking, G.; Wichmann, K.; Frohlich, N.; Loschen, C.; Lein, M.; Frunzke, J.; Rayon, V. M. Towards a Rigorously Defined Quantum Chemical Analysis of the Chemical Bond in Donor−Acceptor Complexes. Coord. Chem. Rev. 2003, 238, 55.

(2) Brack, M. The Physics of Simple Metal Clusters: Self-Consistent Jellium Model and Semiclassical Approaches. Rev. Mod. Phys. 1993, 65, 677−732. (3) Rao, B. K.; Jena, P. Evolution of the Electronic Structure and Properties of Neutral and Charged Aluminum Clusters: A Comprehensive Analysis. J. Chem. Phys. 1999, 111, 1890−1904. (4) Fowler, J. E.; Ugalde, J. M. Al12 and the Al@Al12 Clusters. Phys. Rev. A 1998, 58, 383−388. (5) Leuchtner, R. E.; Harms, A. C.; Castleman, A. W. Thermal Metal Cluster Anion Reactions: Behavior of Aluminum Clusters with Oxygen. J. Chem. Phys. 1989, 91, 2753−2754. (6) Charkin, O. P.; Charkin, D. O.; Klimenko, N. M.; Mebel, A. M. A Theoretical Study of Isomerism in Doped Aluminum MAl12 and MAl12X12 Clusters with 40 and 50 Valence Electrons. Faraday Discuss. 2003, 124, 215−237. (7) Gong, X.; Kumar, V. Enhanced Stability of Magic ClustersA Case-Study of Icosahedral Al12X, X = B, Al, Ga, C, Si, Ge, Ti, As. Phys. Rev. Lett. 1993, 70, 2078−2081. (8) Lu, Q. L.; Jalbout, A. F.; Luo, Q. Q.; Wan, J. G.; Wang, G. H. “Sliding Kinetics” of Single-Walled Carbon Nanotubes on SelfAssembled Monolayer Patterns: Beyond Random Adsorption. J. Chem. Phys. 2008, 128, 224707. (9) Varano, A.; Henry, D. J.; Yarovsky, I. DFT Study of H Adsorption on Magnesium-Doped Aluminum Clusters. J. Phys. Chem. A 2010, 114, 3602−3608. (10) Khanna, S. N.; Jena, P. Assembling Crystals from Clusters. Phys. Rev. Lett. 1992, 69, 1664−1667. (11) Pal, R.; Cui, L.; Bulusu, S.; Zhai, H.; Wang, L.; Zeng, X. C. Probing the Electronic and Structural Properties of Doped Aluminum Clusters: MAl12− (M = Li, Cu, and Au). J. Chem. Phys. 2008, 128, 024305. (12) Alexandrova, A. N.; Boldyrev, A. I.; Fu, Y.; Yang, X.; Wang, X.; Wang, L. S. Structure of the NaxClx+1(x = 1−4) Clusters via ab initio Genetic Algorithm and Photoelectron Spectroscopy. J. Chem. Phys. 2004, 121, 5709. (13) Alexandrova, A. N.; Boldyrev, A. I. Search for the Lin(0/+1/−1) (n = 5−7) Lowest-Energy Structures Using the ab initio Gradient Embedded Genetic Algorithm (GEGA). Elucidation of the Chemical Bonding in the Lithium Clusters. J. Chem. Theory Comput. 2005, 1, 566−580. (14) Moreno, D.; Ramirez-Manzanares, A.; Merino, G. Kaxan 0.1; Cinvestav, Unidad Mérida: Mérida, Yucatán, México, 2012. (15) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (16) Perdew, J. P.; Burke, K.; Ernzerhof, M. Errata. Generalized Gradient Approximation made Simple. Phys. Rev. Lett. 1997, 78, 1396. (17) Adamo, C.; Barone, V. Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model. J. Chem. Phys. 1999, 110, 6158. (18) Hay, P. J.; Wadt, W. R. Ab Initio Effective Core Potentials for Molecular Calculations. Potentials for K to Au Including the Outermost Core Orbitals. J. Chem. Phys. 1985, 82, 299−310. (19) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. J.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. General Atomic and Molecular Electronic Structure System. J. Comput. Chem. 1993, 14, 1347−1363. (20) Rappoport, D.; Furche, F. Property-Optimized Gaussian Basis Sets for Molecular Response Calculations. J. Chem. Phys. 2010, 133, 134105. (21) 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.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F. et al. Gaussian 09; Gaussian, Inc.: Wallingford, CT, 2009. (22) Ortiz, J. V. Advances in Quantum Chemistry; Elsevier Inc: Waltham, MA, USA, 1999; Vol. 35; pp 33−52. 4314


Doped Aluminum Cluster Anions: Size Matters - American Chemical

Recommend Documents