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Understanding the Bonding and Reactivity of Gallium Nanoclusters using RDFT
David J. [email protected]
Hydrogen Economy2
Challenges
Production: Cheaply and efficiently from H2O
Storage: Light weight / high volume
Conversion: Fuel cells or combustion
Solid State Storage
Metal hydrides e.g. NaBH4 - High storage - slow k
TM dopants - Fast kinetics - Low storage
Storage
High pressure gas tanks - 350 and 700 bar
Liquid hydrogen - requires energy to cool
Light-metal Nanomaterials
Chemical and electronic properties differ from bulk
High surface areas for adsorption
Metal Nanoparticles3
Laser ablation
Metal
He
LaserLaser directed at metal surface
- atoms ejected into He carrier gas
Atoms recombine to form small clusters
Analysed by MS
Clusters are ionised
_
Number of sodium atoms per cluster, N
Knight, et al. Phys. Rev. Lett. 52 (1984) 2141
de Heer, Rev. Mod. Phys. 65 (1993) 6118 20 34 40 58
Some sizes more abundantLi, Na, K : 8, 18, 20, 34, 40, … atoms
Mg : 10, 17, 20, 29, 46, … atoms
Al : 6, 7, 13, 19, 23, 31, … atoms
Jellium Model4
- valence electrons of each metal atom loosely bound when the cluster is formed
- delocalise across the whole cluster
- act like “super atoms”
He 1s2
Ne 2s2 2p6
Ar 3s2 3p6
Na2 1s2
Na8 1s2 1p6
Na18 1s2 1p6 1d10
Na20 1s2 1p6 1d10 2s2
Na34 1s2 1p6 1d10 2s2 1f14
Na40 1s2 1p6 1d10 2s2 1f14 2p6
“one-electron shell model in which independent delocalised electrons are bound in a spherically symmetrical potential well”
Knight, et al. Phys. Rev. Lett. 52 (1984) 2141
Chou, et al. Solid State Comm. 52 (1984) 645
Chou, Cohen Phys. Rev. Lett. 113 (1986) 420
Aln clusters5
Electronic structure of Al: [Ne]3s23p1
3s - 3p energy separation: ~ 3.6 eV
Shell model will only be valid when band overlap occurs
Li, et al. Phys. Rev. Lett. 81 (1998) 1909
Akola, et al. Phys. Rev. B 60 (1999) R11297
Akola, et al. Phys. Rev. B 58 (1998) 3601
Ganteför, et al. Phys. Rev. A 37 (1988) 2716
Schriver, et al. Phys. Rev. Lett. 64 (1990) 2539
VOLUME 81, NUMBER 9 PHY S I CA L REV I EW LE T T ER S 31 AUGUST 1998
a 10 atm backing pressure. A cold cluster beam was pro-duced by a supersonic expansion of the cluster/carrier gasmixture through a 2 mmdiam nozzle and collimated by a6 mmdiam skimmer. The anions were extracted from thebeam at 90± and mass analyzed by a time-of-flight (TOF)mass spectrometer. The clusters of interest were sizeselected and decelerated before irradiated by a 193 nmphoton beam from an ArF excimer laser. PhotoelectronTOF spectra were collected for each size-selected clusterfor 10 000 to 30 000 laser shots at 20 Hz repetition rate.The vaporization laser was off at alternating detachmentlaser shots for background subtraction. For the verysmall clusters, the anion mass abundance was weak andhigher photon flux was needed, causing a more severenoise problem (see Fig. 2). The electron TOF spectrawere converted to kinetic energy �Ke� spectra calibratedby the known spectra of Cu2. The presented bindingenergy (BE) spectra were obtained by subtracting the Kespectra from the photon energy (6.42 eV). The electronenergy resolution of our apparatus was about 30 meV at1.5 eV Ke and deteriorates according to �Ke�3�2 for highKe (low BE) features.Figure 2 shows the PES spectra of Alx2 for x � 1 12.
We measured spectra of size-selected Alx2 for x � 1to 162 systematically. For the very large clusters, thespectra became broad with few changes between spectraof neighboring clusters. The Al2 anion has an electronconfiguration of �Ne�3s23p2. The peak labeled “p” inthe spectrum of Al2 corresponds to the detachment ofa 3p electron, giving rise to the ground state of the Alatom �3s23p1, 2P�. The peak labeled “s” correspondsto the removal of a 3s electron, resulting in an excitedAl atom �3s13p2, 4P�. The measured separation (3.6 eV)between the “p” and “s” bands agrees with the opticalmeasurement of the 2P-4P separation for Al atoms[5]. However, bulk Al is known to have a completelyhybridized s-p band with nearly free electron characters[4]. Thus, we anticipated that the p- and s-derivedorbitals in small Al clusters would broaden and approacheach other, eventually forming a unified s-p hybridizedband at very large sizes.In small Al clusters, the 3s orbitals of Al form bonding
and antibonding molecular orbitals (MOs) which are fullyoccupied, whereas only the bonding MOs derived fromthe 3p are partially filled. The PES features from p-and s-derived MOs are labeled in Fig. 2 with “p” and“s”, respectively. The s features are characterized bytheir high binding energies and low detachment crosssections. The gap between the p- and s-“bands” is seento be reduced significantly in Al2, and rapidly approacheseach other with increasing cluster size. At Al8, the p-and s-derived features already begin to overlap partially,and they are completely mixed starting at Al9. Detailedquantum calculations have been performed for the atomicstructures of small Al clusters [12,14]. Those with n , 6were found to be planner. A 2D to 3D structural transition
FIG. 2. Photoelectron spectra of Alx2 �x � 1 12� at6.42 eV. The “p” and “s” labels indicate features derivedfrom the Al 3p and 3s, respectively. Note the overlap of thep- and s-derived features in Al9.
occurs between Al5 and Al6. The rapid s-p convergenceis accompanied by the structural changes. The completes-p mixing starting at Al9 is probably due to the highcoordination numbers possible for the larger clusters.According to Fig. 1, the first spherical shell closing
occurs at Al112 with the filling of the 1f shell. The PES
spectrum of Al112 does show a slightly higher binding
energy relative to its neighbors with numerous well-resolved features. However, the shell closing effect inAl11
2 is not as strong as observed in the larger clusters(Fig. 2), probably because Al11
2 is still quite small andits electronic structure is likely to be dictated more byits detailed molecular structure. A much stronger shellclosing effect was observed at Al13
2 and larger clustersas shown in Figs. 3 and 4. Figure 3 shows the PESspectra of the closed shell anions (left column) comparedto those one atom larger (right column). The closedshell anion clusters �Alx2� exhibit high binding energies
1910
s - p begin to overlap
Photoelectron Spectra of closed shell Aln-
odd number of atoms, respectively. The only exceptions aredimer and 13-atom ion �icosahedron� with S�1.18 Of thetwo size regimes discussed in this paper the smaller clustersare interesting due to the hybridization effects whence for thelarger ones competing structural motifs were found by com-paring the calculated and measured IP values.The structures were obtained for Al2–Al7 by a conjugate-
gradient search among a number of plausible candidates. Forthe size-range Al12–Al23 we used a classical molecular dy-namics program in conjunction with a potential derived fromthe effective medium theory �EMT� �Refs. 19 and 20� toproduce a number of low-energy isomers, the best ones ofwhich were selected as starting geometries for the BO-LSD-MD calculations. The structures were obtained by cool-ing from hot liquid clusters. The vast number of the lowestenergy structures produced by EMT potential wereicosahedral-based structures. As is well known, certain sizes
�13,19,23� are particularly interesting since they match filledatomic-shell structures of either icosahedral, decahedral, orfcc-based ��cub�octahedral� symmetry �see Fig. 2�. For thesesizes we started optimization directly from these symmetries.All the structure optimizations were done without any con-straints to the symmetry.To analyze the hybridization of the KS states, � i
KS , forthe smallest clusters we projected each occupied state ontospherical harmonic components according to
� iKS�r���
l ,m� l ,mi �r �Y l ,m���, �1�
with l up to 3 �atomic f state�, from which a weight wli of a
given angular momentum component in the charge density is
wli� �
m��l
l � �� l ,mi �r ��2r2dr . �2�
We performed this analysis from dimer to tetramer the originfor the expansion �1� set at the atoms. We wish to note herethat the plane-wave basis set prevents us from a full Mul-liken analysis common in traditional quantum chemical
TABLE I. Symmetry, average bond length �in Å�, experimental�Ref. 4� and calculated vertical �vIP� and adiabatic �aIP� ionizationpotential �in eV� for ground states of Al–Al7.
N Symmetry �d� IP�exp� vIP�LSD� aIP�LSD�
1 5.99 6.122 D� 2.46 6.20 6.83 6.253 C3v 2.48 6.45 6.91 6.794 D2h 2.58 6.55 6.80 6.695 C2v 2.58 6.45 6.77 6.686 O 2.73 6.45 7.03 6.937 O 2.69 6.20 6.38 5.90
TABLE II. Ionization potentials for Al12–Al23 �in eV�. The tableshows experimental values �Ref. 4� together with the calculated vIPand aIP for ICS and COS structures. Also shown is the energydifference �E�E�cubo��E�ico� �in K�. In addition, results fordecahedral structures are shown in parentheses for N�13�15,22,23. In that case �E�E�deca��E�ico�. The values in bold-face are plotted in Fig. 1 for reasons explained in the text.
N IP�exp�vIP�LSD�ico
aIP�LSD�ico
vIP�LSD�cubo
aIP�LSD�cubo �E
12 6.20 6.45 6.30 6.42 6.28 46013 6.45 7.00 6.92 6.39 85013 �6.85� �6.42� �70�14 5.80 6.46 6.09 5.87 5.58 40014 �6.27� �5.89� �30�15 5.76 6.15 5.74 6.41 5.77 43015 �6.21� �5.97� �80�16 5.90 6.15 6.06 5.72 5.54 50017 5.62 6.11 5.63 5.96 5.77 518 5.76 6.17 6.06 5.88 5.69 �52019 5.56 6.20 6.14 5.82 5.62 6020 5.73 6.19 6.08 5.89 5.80 11021 5.56 6.23 5.99 5.84 5.71 222 5.72 6.30 5.93 5.87 5.72 46022 �5.94� �5.86� ��90�23 5.38 5.94 5.76 5.86 5.62 68023 �6.27� �5.95� ��130�
FIG. 1. Ionization potential of aluminum clusters �in eV�. Opencircles, threshold photoionization experiment �Ref. 4�; solid dots,BO-LSD-MD results; open squares, Car-Parrinello calculations�Ref. 11�; and crosses, X� results �Ref. 12�.
FIG. 2. Closed atomic shell structures. Top from left: 13-atomicosahedron, decahedron, and cuboctahedron. Bottom: 19-atomdouble icosahedron, octahedron, and 23-atom decahedron.
3602 PRB 58BRIEF REPORTSIonisation potentials of closed shell Aln-
Neutral Al13
Al13 cluster6
VOLUME 81, NUMBER 9 PHY S I CA L REV I EW LE T T ER S 31 AUGUST 1998
FIG. 3. Photoelectron spectra of the expected closed shellAlx2 anions compared to those of the Alx11
2 clusters. Notethe high binding energies of the closed shell Alx2 clusters andthe appearance of low binding energy features and energy gapsin the Alx11
2 clusters.
and high degeneracy, whereas those clusters one atomlarger �Alx11
2� show weak low energy features withenergy gaps, suggesting partial occupation of the nexthigher shells according to Fig. 1. Al13
2, with 40 valenceelectrons, exhibits the strongest shell closing effect. Theelectron affinity derived for Al13 is 3.62 eV, the highestof all the Al clusters we investigated. The spectrumof Al13
2 shows the fewest features, indicating a highdegeneracy and high symmetry, consistent with the knownicosahedral geometry �Ih� for Al13 [12,13]. Al14
2, with43 valence electrons, was expected to partially fill the 1gshell, which should undergo ellipsoidal splitting [16]. Thespectrum of Al14
2 is almost identical to that of Al132
except for the three weak low energy features (Fig. 3)which are consistent with the anticipated splitting of the1g level. Ellipsoidal distortion in open-shell clusters leadsto subshell structures and subshell closings [16]. The
FIG. 4. Photoelectron spectra of Alx2 anions for which thecorresponding neutrals are expected to be closed shell and thoseof larger Alx2 clusters �x � 99 112�.
PES spectra of the other Alx112 clusters in Fig. 3 suggest
that the neutral Alx11 clusters are all closed shell witha substantial energy gap. In particular, Al36 exhibits anunusually large energy gap (1.02 eV). The PES spectraof those clusters, for which the neutrals were expectedto be closed shell in the spherical shell model (Fig. 1),are shown in Fig. 4 along with those of several largeclusters. For Al46
2, Al522, and Al66
2, a weak low energyfeature was clearly resolved with a significant energy gap,indicating the neutral clusters are indeed closed shell. ForAl56
2 alone, the weak low energy feature was not wellresolved and only a shoulder was observed, suggesting asmaller energy gap between the 4s and 1j shells (Fig. 1).We observed additional closed shell neutral clusters, Al26,Al28, Al32, Al42, Al54, Al68, and Al72, probably due tosubshell closings.However, the spectra of Al78
2 and Al802 (Fig. 4)
do not show a similar energy gap even though the
1911
Al13 is the smallest neutral Al cluster with near spherical
symmetry (D3d)
Stable
Not Stable
+1.03 eV
+0.21 eV
+2.69 eV
Computational
Details
PBE / DNP
PBE0 / 6-311G(d)
Benchmark
Geometries
CCSD / 6-31G(d)
Benchmark
Energies
G3(MP2)-RAD
Li, et al. Phys. Rev. Lett. 81 (1998) 1909
“The spectrum of Al13− shows the fewest
features, indicating a high degeneracy and high symmetry”
“Al13− has icosahedral symmetry”
Upton, J. Chem. Phys. 86, 7054 (1987)Pettersson, et al. J Chem. Phys 87, 2205 (1987)Yi, et al. Phys. Rev. Lett. 67, 1594 (1991);
Altering Electronic Structure - Dopants
7
d(Al-X) Valenceelectrons
Binding Energy
(eV)
SubstitutionΔH1 , ΔH2
(eV)
HOMO-LUMO (eV)
Al12Mg 2.703 38 27.81 +3.45+2.72 1.45
Al13 2.698 39 31.31 ----
1.99
Al12Si 2.643 40 33.96 -2.15-1.38 2.06
Al13 + X Al12X + Al ΔH1
2Al13 + X2 2Al12X + Al2 ΔH2
Metallic bonding observed in all three clusters
Thermal stability of these materials needs to be considered
Dopants can be used to change the electronic configuration
Al12Mg575 K
Hydrogen Adsorption8
0.030electrons Å-3
Al12MgH Al13H Al12SiH
H B.E (eV) H-L (eV) IP (eV) EA (eV)
Al12MgH 2.47 0.73 6.23 2.60Al12MgH2 5.10 1.48
Al13H 2.34 1.50 6.31 2.00Al13H2 5.35 1.99 6.72 3.05
Al12SiH 1.88 1.32 6.90 2.60
Al12SiH2 4.77 2.06
H binds to all 3 clusters
Al12MgH and Al12SiH - Atop
Al13H - Bridge and Hollow
Transfer of density from the cluster to H atom - disrupts metallic bonding
Increased binding for two H atoms
Henry, Varano, Yarovsky J. Phys. Chem. A 112 (2008) 9838 Varano, Henry, Yarovsky J. Phys. Chem. A 114 (2010) 3602
Al12MgH 375 K
Chemisorption of H2 to Al12X9
Hollow TS
Bridge TSFront
Front
TransitionState
Product
-1
-0.5
0
0.5
1
1.5(eV)
Al13+
Al13
Al13-TS
Product
Reactants
atop(1)-hollow(1,2,2) atop(1)-bridge(2,2)
or
or or
atop(1)-atop(2) atop(1)-bridge(1,2) atop(1)-hollow(2,2,3)
PBE/DNP Al12X No.Valence e-
ForwardBarrier (eV)
Reverse Barrier (eV)
Enthalpy(eV)
Al12Mg+ + H2 → Al12MgH2+ 37 0.60 0.97 -0.37
Al12Mg + H2 → Al12MgH2 38 0.45 0.87 -0.42
Al12Mg- + H2 → Al12MgH2- 39 1.06 1.11 -0.05
Al13+ + H2 → Al13H2
+ 38 0.08 0.58 -0.50Al13 + H2 → Al13H2 39 0.98 0.93 +0.05
Al13- + H2 → Al13H2
- 40 1.77 1.18 +0.59
Al12Si+ + H2 → Al12SiH2+ 39 1.01 0.91 +0.10
Al12Si + H2 → Al12SiH2 40 1.80 1.18 +0.62
Al12Si- + H2 → Al12SiH2- 41 1.57 1.55 +0.02
Regional DFT10
A. Tachibana, J. Chem. Phys.
115, (2001) 3497.
Total Edensity
KEdensity
External PEdensity
Interelectron PEdensity
The kinetic energy density obtained in this scheme provides a new outlook at the chemical bond
Partitioning of space into mutually disjoint regions
Electronic drop (RD) and atmosphere (RA) regions
separated by the interface S.
-
+
RD
RAS
Classical movement of electron
Turning point
Quantum tunnellingregion
Repulsive electronic tensioncompensates the attractive electric
field of atomic nuclei
A
SLagrange surface
RA
RD B
Kinetic energy density
Chemical Potential
Stress Tensor
Bond Strengths
)(ˆ)(ˆ)(ˆ rLrrF SSS !!!!!!!!! " +=
Total force on electrons
Tension Lorentz
Stationary state 0)( =rF !
!
)(ˆ rS !!!" )(ˆ rLS !
!!
Bonding region = = 0
Lagrange point can characterise interaction between atoms
Covalent bond - spindle structure - a geometrical region where the principal electronic tensile stress is positive along the axis between a pair of atom or molecule RD’s.
Transition State Distances11
TS Distance (Al1 - H1) v Barrier
R2 = 0.7282
0.0
0.4
0.8
1.2
1.6
2.0
1.68 1.7 1.72 1.74 1.76 1.78
Distance (Å)
Barrier (eV)
Al12Si
Al12MgAl12Mg+
Al12Si+ Al12Si-
Al13+
Al13 Al13-
Al12Mg-
Decreasing Covalent Character of Surface Bonds
Decreasing C
ovalent Character of Surface B
onds
Stress Tensor provides measure of electron pairing b/w pairs of atoms
Indicates degree of covalent character
No covalency b/w core and surface
Varying covalency in surface bonds
As covalency lowered so is the tendency for addition type reactions
longer d(Al1-H1)
H1
Al1Correlation between d(Al1-H1) and reaction barriers
No correlation with other TS distances
Henry, Yarovsky J. Phys. Chem. A 113 (2009) 2565
Charge Transfer12
Al1H1
H2
Al2
-0.10
-0.15
Al12Mg+
Al13+
Al12Si+
Al12Mg
Al13
Al12Mg-
Al13-
Al12Si-
µ
Al12Si
Increasing nucleophilicity in atop sites
Surface Chemical Potential provides a measure of the electron affinity of a region
electrophilic nucleophilic
Cluster cations - less charge transfer in TS - earlier TS - Lower barrier
Cluster anions - more charge transfer - later TS - higher barrier
Charge
Correlation between charge on H1 in TS and reaction barriers
No correlation with other TS charges
Henry, Yarovsky J. Phys. Chem. A 113 (2009) 2565Henry et al. J. Phys. Chem. C 115 (2011) 1714
Distortion Energy13
Al12Si
0.65
0.40
Al12MgAl12Mg+
Al12Si-
Al13+
Al13 Al13-
bµ
Al12Mg-
Al12Si+
Henry, Yarovsky J. Phys. Chem. A 113 (2009) 2565Henry et al. J. Phys. Chem. C 115 (2011) 1714
Strong bonds between core and surface atoms
Surface bonds are weaker and have varying degrees of covalent character
Addition of H2 occurs preferentially on edges and / or faces with the highest covalent character
Correlation between distortion energy and barrier heights
- most interatomic
distances 2.71 - 2.79 Å
!"#$%&'()*#+'&,-.'()
*#(/0%1)
Gallium14
Bulk gallium
- low m.p. (29.7 °C)
- Ga2 atoms at 2.437 Å
- molecular solid (Ga2)n
1σg+
1σu+
πu
2σg+
πg
2σu+
Molecular Orbitals
Bonding πu and 2σg+
!"#$%"&$'&%()(*% ()+*%
Bonding is intermediate between covalent and
metallic
!"#$$
!"#$$%&%!"#''
!"#''%&%!"#((
)*+%,%(+-.%
&)*+%,%(+-.%
+*+%
(+-.%
(+-$%
(+-'%
(+-.%
(+-$%
(+-'%
τeS33 slightly negative - electrons are not strongly localised
Gallium15
1000 Cha, Gantefljr, and Eberhardt: Small aluminum and gallium clusters
. ..c ro >-.j...J
en c (])
.j...J C
4 3 2 0 4 3 2
Binding Energy [eV]
Ga 9
Ga" 10
Ga" 1 1
Ga 13
Ga" 14
o
FIG. 5. Photoelectron spectra ofGa; clusters with n=2-15. The photon energy is 5.0 eV (KrF laser). All features correspond to photodetachment from 4p derived orbitals of Ga. In contrast to Al for Ga; up to n= II, a distinct gap between the feature at highest BE and the limit of the exper" imental range (4.5 eV) is observed, indicating a clear separation of the 4s and 4p bands.
The spectrum of Ali obtained with hv= 5.0 eV [Figs. 2(n) and 4] displays two prominent broad peaks at 2.5 eV (A, B, and C) and 3.5 eV (D) BE. The feature at 2.5 eV BE exhibits a splitting into three components marked A, B, and C. Peak C is only visible as a shoulder located at the high BE side of feature B. The spectrum of Ali taken at hv=3.68 eV [Fig. 2(c)] displays the same features with peak D cut off at 3.4 eV BE due to the reduced transmis-sion of the spectrometer for low energy electrons. The rel-ative intensities of the three components A, B, and Care altered slightly. At hv=5.0 eV, peak B has a lower inten-sity with respect to peak A.
The three features A, B, and C in Fig. 2(c) (hv=3.68 eV) are less well resolved than in the measurement at hv =5.0 eV [Fig. 2(n)]. This behavior is surprising because the energy resolution of the spectrometer is enhanced due to the lower kinetic energy of the electrons corresponding to the same transitions at lower photon energy. In addi-tion, the tail observed at the low BE side of peak A has a higher intensity in the 3.68 eV spectrum. These observa-tions might be explained by temperature effects. The source is usually adjusted to a maximum anion signal for each cluster size. Depending on the parameters of the source (seeding gas pressure and timing), the effectivity of the vibrational cooling varies between different measurements. If during the measurement using hv=3.68 eV the source had run at less effective cooling conditions, the vibrational temperature of the anions would be higher. The peaks would then be broadened and hot band transitions may cause the appearance of an exponential tail at the low BE side of the ground state transition.
The tail at low BE observed for Ali taken at hv= 3.68 eV [Fig. 2(c)] exhibits a width of about 0.5 eV, which corresponds to an extremely high vibrational temperature if the feature is caused by hot band vibrational transitions. Also, the shape deviates from the typical exponential shape of a hot band progression. These tails and a nonstructured smooth photoemission signal at higher BE are observed in several photoelectron spectra of cluster anions (Ag; and eu;) .15,37 A possible explanation is the appearance of an increasing number of different isomers in the beam at finite vibrational temperatures. The BE of a certain transition in the PE spectrum depends strongly on the geometry (see below). If the spectrum consists of contributions from sev-eral isomers different from the ground state geometry, this may cause a nonstructured smooth photoemission signal starting at a BE corresponding to the isomer with the low-est VDE. As long as at lower internal temperature the ground state isomer is still predominant in the beam, a structured photoelectron spectrum can be superimposed to give the featureless sum of spectra of different isomers. These considerations can be verified by calculations using simulated annealing. 1
We should like to point out here that the difference between the VDE of the isomer with the lowest VDE com-pared with the VDE of the ground state isomer does not correspond to the difference in total energy of the two isomers. If one single particle orbital is lowered in BE by a change of the geometry, others may be shifted to higher BE. Thus, even if an isomer has a 1 eV lower VDE, the appearance of this isomer in the beam may be due to a much lower thermal excitation energy. This can be dem-onstrated using the calculations of Al3 single particle or-bitals displayed schematically in Fig. 6. Only the 3p de-rived orbitals are displayed in Fig. 6. The linear isomer of neutral Al3 (three 3p electrons) exhibits a low VDE due to the single electron occupying the ITT u orbital. However, the total BE of the linear isomer is relatively high due to the gain of stability corresponding to the increased BE of the two electrons occupying the 20' u orbital (for a detailed discussion s.b.). Thus we are able to explain the appear-
J. Chern. Phys., Vol. 100, No.2, 15 January 1994
Downloaded 27 Aug 2010 to 131.170.90.2. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions
Ga13− can be assigned to a "magic number" cluster, but the structural symmetry could possibly be lower than in Al13−.
Cha, et al. J. Chem. Phys. 100 (1994) 995
Ga13− adopts decahedral geometry in gas phase
Photoelectron Spectra of Gan-
2.586 -2.660 Å
2.684 Å
2.694 - 3.185 Å
2.796 ÅPBE0/6-311G(d,p)
Ga13
Yi Phys. Rev. B 61 (2000) 7277
Drebov et al. J. Chem. Phys. 135 (2011) 044314
Gallium16
Schnepf et al. Angew. Chem. Int Ed. 40 (2001) 1241
[Ga19(C(SiMe3)3)6][Li2Br(THF)6]
Schnepf, Stösser, Schnöckel JACS. 122 (2000) 9178
Can dopants be used to change the
structure and stability of the
cluster?
Ga13 + X Ga12X + Ga
Endohedral Dopant Axial Exohedral Equatorial Exohedral
X
XX
17
B-2.59
C-3.44
N-1.19
Al-0.40
Si-2.57
P-1.52
Ga0
Ge-1.82
As-0.82
Ga13 + X Ga12X + Ga ∆H (eV)
Substitution Energy
B-0.39
C-0.36
N-0.38
Al+0.03
Si-0.15
P-0.07
Ga0
Ge-0.01
As+0.23
Distortion Energy (eV)
Endohedral Ga12X
Third- and Fourth row dopants D5h symmetry
Second-row dopants lead to a contraction of cluster and
transformation to Ih symmetry
B C N
Al Si P
Ge As
Henry J. Phys. Chem. C 116 (2012) 24814
Third- and Fourth row dopants D5h symmetry
Second-row dopants lead to a contraction of cluster and
transformation to Ih symmetry
18
Endohedral Ga12X
B C N
Al Si P
Ge As
Henry J. Phys. Chem. C 116 (2012) 24814
-22
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
Eige
nval
ue E
nerg
ies
(eV)
Ga 1
3
Ga 1
2N
Ga 1
2Al
Ga 1
2Si
Ga 1
2P
Ga 1
2Ge
Ga 1
2As
Ga 1
2C
Ga 1
2B
Endohedral
(a) Ga12C has the most developed Jellium
structure followed by Ga12N
Ga12Si and Ga12Ge exhibit degeneracy in core Jellium orbitals but broad bands of
outer orbitals
Ga12B Ga12C Ga12N
Ga12Al Ga12Si Ga12P
Ga13 Ga12Ge Ga12As
Metallic electron density framework for X = B, C and N
!"#$
!%#$
Metallic
Covalent
Semi-metal
Electron Deformation Density
Ga12B Ga12C Ga12N
Ga12Al Ga12Si Ga12P
Ga13 Ga12Ge Ga12As
τeS33 slightly negative
- electrons are not
strongly localised
Electronic Stress Tensor
Henry, Ichikawa, Nozaki, Tachibana Comput. Mater. Sci. 115 (2016) 145
RDFT Analysis of Ga12X
Distorted
Equatorial X
20
B C-2.74
N-1.29
Al-0.38
Si-1.95
P-1.12
Ga0
Ge-1.68
As-0.87
Ga13 + X Ga12X + Ga ∆H (eV)
Substitution Energy
B C-0.46
N+0.22
Al-0.01
Si-0.23
P-0.16
Ga0
Ge-0.39
As-0.41
Distortion Energy (eV)
Exohedral Ga12X
+0.62 +0.41
+0.13
–0.02
–0.11
–0.05
C N
Al Si P
Ge As
+0.70Energy
relative to endo-Ga12X
(eV)
Henry J. Phys. Chem. C 116 (2012) 24814
Distorted
Equatorial X
21
Exohedral Ga12X
+0.62 +0.41
+0.13
–0.02
–0.11
–0.05
C N
Al Si P
Ge As
+0.70Energy
relative to endo-Ga12X
(eV)
Henry J. Phys. Chem. C 116 (2012) 24814
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
Eige
nval
ue E
nerg
ies
(eV)
Ga13 Ga12C CGa12 Ga12N NGa12 Ga12Si SiGa12
Henry, Ichikawa, Nozaki, Tachibana Comput. Mater. Sci. 115 (2016) 145
Hollow 2Hollow 1Bridge 3Bridge 2Bridge 1Atop 2Atop 1
22
H atom AdsorptionGa12X + H Ga12XH ∆H (eV)
Adsorption of a single atom can also lead to a closed shell structure.
Henry, J. Phys. Chem. C 117 (2013) 26269
X = Ga -2.54 -2.34 -2.46 -2.23
Hollow 2Hollow 1Bridge 3Bridge 2Bridge 1Atop 2Atop 1
X = Ga -2.54 -2.34 -2.46 -2.23
X = Si -1.46 -1.49 -1.31 -1.52
Hollow 2Hollow 1Bridge 3Bridge 2Bridge 1Atop 2Atop 1 Hollow 2Hollow 1Bridge 3Bridge 2Bridge 1Atop 2Atop 1
X = Ga -2.54 -2.34 -2.46 -2.23
X = Si -1.46 -1.49 -1.31 -1.52
X = P -2.55 -2.53 -1.83
Cluster Bonding
0.044 electrons A-3
Atop 2 Bridge 2
Hollow 2Bridge 3
Ga13H
Electron Density
0.088 electrons A-3
Cluster (Jellium) Orbitals1s2 1p6 1d10 2s2 1f14 2p6
Ga13 A2 B2 B3 H2
Covalent bonding between H and Ga
Increased degeneracy in electronic structure
Variations with adsorption site
Less covalency in Ga - Ga bonds
Cluster (Jellium) Orbitals1s2 1p6 1d10 2s2 1f14 2p6
Cluster BondingElectron Density
LUMO X = Si, Ge
Ga13 A2 B2 B3 H2
Ga12B Ga12C Ga12N
Ga12Al Ga12Si Ga12P
Ga13 Ga12Ge Ga12As
Bond orders
5 - 15% of H2
Bond orders correlate with
number of valence
electrons
Increase in equatorial bonds
Decrease in axial bonds
Ga13 ΔE≠fwd (eV) ΔE≠rev (eV) ΔH (eV)
Brg1 1.283 1.204 0.078
Brg2 1.036
Brg3
Hol1 1.012 0.840 0.171
Hol2 0.962 0.790 0.172
Hol3 1.093 0.972 0.121
25
Ga13 + H2 Ga13H2
Bridge 1 ΔE≠fwd (eV) ΔE≠rev (eV) ΔH (eV)
Ga13 1.283 1.204 0.078
Ga12Si 1.479 1.051 0.429
Ga12P 1.558 1.437 0.121
Bridge 2 ΔE≠fwd (eV) ΔE≠rev (eV) ΔH (eV)
Ga13 1.036
Ga12Si 1.498 0.958 0.540
Ga12P 1.411 0.955 0.456
PBE0/6-311G(d,p)
Similar trend to Al12X
Correlation between barrier
(ΔH≠) and enthalpy (ΔH) Late
transition state ???
Ga12X + H2 Ga12XH2
Distortion Energy Structure energy change in TS
Charge TransferBond Strengths
Ga12Al Ga12Si Ga12P
0.5 0.8
Correlation b/w charge on H1 in TS and ΔH≠
Correlation b/w ΔH≠ and distortion E
Ga12X + H2 Ga12XH2
[Ga19(C(SiMe3)3)6][Li2Br(THF)6]Ga13(GaR)6
−
Exohedral Coordination
Ga13 ΔH (eV)
A1 - BH3 −
A2 - BH3 -0.52
Ga13 as Lewis base
Ga13 ΔH (eV)
A1 - NH3 -0.53
A2 - NH3 -0.47
Ga13 as Lewis acid
Cluster Stabilisation
Ga12Si
with
24-crown-8 as stabilising ligand
Exohedral Coordination
Reaction Modulation
Bridge 1 ΔE≠fwd (eV) ΔE≠rev (eV) ΔH (eV)
Ga12P 1.411 0.955 0.456
Ga12P-BH3 1.298
30
Acknowledgements
Prof Akitomo Tachibana
Dr Kazuhide Ichikawa
Dr Pawel Szarek
Kosuke Hirai
Hiroo Nozaki
RMIT University (Aust)Prof Irene YarovskyAdrian Varano
Tim Varano
Kyoto University
Murdoch University (Aust)
David Zeelenberg
Summary
Stability and Reactivity of Gallium clusters is tuneable with dopants and ligands
Trends in reactivity and regioselectivity can be explained by variation in surface bond strengths
RDFT/Electronic Stress Tensor method is a valuable tool for understanding bonding in metalloid (metallic and covalent) systems
Dimers
• All of the aggregates are lower in energy than the isolated clusters and hydrogen
• This will have implications for cluster assembled materials
2Al13 + H
Al13-Hatop-Al13
Al13-Hbdg-Al13
Al13-Hhol-Al13
(Al13)2 + H
Al13Hatop + Al13 Al13Hbdg + Al13
Al13Hhol + Al13
+2.2 eV
−1.9 eV
