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4 Void Reactivity of 20-Nanogold Cages: Few Approaches for Measuring

4 Void Reactivity of 20-Nanogold Cages: Few Approaches for Measuring

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E.S. Kryachko and F. Remacle

30.4.1 HOMO and LUMO Patterns

The patterns of the HOMOs and LUMOs of cages II, III, and IV are shown in

Figs. 30.8 and 30.9. The HOMO of II is mainly composed of: (i) the 6s AOs of the

‘top’ and ‘bottom’ gold atoms Au4−0.37 and Au8−0.37 where the superscript indicates

the Mulliken charge; (ii) the 6 p AOs of Au1−0.06 , Au3−0.01 , Au7−0.01 , Au0.38

13 , and




Au14 , and largely of Au5 and Au15 ; and (iii) the 5d AOs localized on Au3 ,

Au5 , Au7 , Au14 , and Au15 . The latter two AOs partly protrude into the void of

cage II where a hole can therefore partially appear under the ionization. In this

sense, the void of cage II can be treated as a polarizable ‘sphere’, by analogy with

the C60 cage [46]. In contrast, the LUMO of cage II lies substantially ‘outdoors’,

in the outer space, thus emphasizing that the electron attachment may primarily

contributes to the outer reactivity of cage II. This LUMO is mainly composed of

the 6s AOs localized on almost all gold atoms, except Au3 , Au5−7 , Au1 , Au16−18 ,

and Au20 , and 6 p AOs on Au2,3 , Au5,7 , Au11,13 , and Au15,20 . A small part of the

LUMO, determined by the 5d AOs of Au3 , Au7 , Au8 , Au12 , and Au17 , is however

placed within the void.

The shapes of the HOMO and LUMO of cage III are rather spectacular.

They are mostly composed of AOs Au1,7,14,16 0.75 (6 px 0.19 ), Au2,8,13,15−0.25 (6s0.21 ),

Au3,5,9,12 −0.45 (6s0.48 ), and the 6-folded Au17,18,19,200.41 (6 py 0.11 5d−2 0.14 ) for the

HOMO and Au1,7,14,16 (6s0.43 6 py 0.14 ), Au4,6,10,11(6s0.22 ) and Au17,18,19,20(6 py 0.16 )

for the LUMO. The HOMO and LUMO are mostly localized in the outer space

around the Au3,5,9,12 and Au1,4,6,7,10,11,14,16, respectively. Juxtaposing the HOMO

and LUMO of cage III in Fig. 30.8, one readily concludes that the void portion of

its HOMO is larger than the LUMO one.

In addition, the HOMO − 2–HOMO − 4 of cage III which, due to their 5p and

5d AOs, that are largely localized in its void region are displayed in Fig. 30.9. Since

these HOMO-2 – HOMO-4 lie within 0.8–1.6 eV from the HOMO, they participate

in the first – at least, HOMO-2 – and second ionization processes of cage III. These

are therefore the processes where the void reactivity of cage III can be detected.

Distinguishably different are the HOMO and LUMO of cage IV. The outer part of its

HOMO is sharply localized on the opposite vertex gold atoms Au3−0.40 (6s0.62 ) and


(6s0.68 ). The rest of the HOMO lies in the void. Its LUMO is considerably


localized on the side vertex atoms outward.

30.4.2 Molecular Electrostatic Potential Patterns

The MEPs of the cages II, III, and IV are shown in Fig. 30.10 for the different

charge states Z = 0, ±1, and −2, where, for the latter, the MEP of I−2 is added for

comparison, bearing in mind Fig. 30.7. It is seen in this figure that the MEPs of the

cages’ outer space are nonnegative – that is indicated by blue regions converging

to the green ones. The void MEP of cage II is of both signs: negative is shown in

30 20-Nanogold Au20 (Td ) and Low-Energy Hollow Cages: Void Reactivity


Fig. 30.8 The HOMOs and LUMOs of cages II-IV: (a) and (b) plot the HOMO and LUMO of

cage II, respectively; (c) and (d) the HOMO and LUMO of cage III; and (e) and (f) plot the HOMO

and LUMO of cage IV


E.S. Kryachko and F. Remacle

Fig. 30.9 The HOMO-2 (a), HOMO-3 (b), and HOMO-4 (c) of cage III. Their orbital eigenvalues

are correspondingly equal to −6.29, −6.42, and −7.06 eV

30 20-Nanogold Au20 (Td ) and Low-Energy Hollow Cages: Void Reactivity


Fig. 30.10 The B3LYP MEPs of the cages II, III, and V which are mapped either from

−0.01(red) to +0.01(blue)|e|/(4πε0 a0 ) for the Z = 0 charge state or from −0.1(red) to

+0.1(blue)|e|/(4πε0 a0 ) for the Z = ±1 and −2 (including, as the reference, the MEP of the hollow

˚ −3 isosurface of the one-electron density ρ (r)

cage I−2 ) charge states onto 0.001|e| · A


E.S. Kryachko and F. Remacle

red, as e.g. in the neighborhood of Au1 and Au5 , and positive, in blue, as e.g. in a

small and deep ‘pocket’ in the neighborhood of Au17 . Hence, the latter may confine

some atom.

The MEP of III is positive outside and takes both signs in the void. In Fig. 30.10,

there exists a pair of symmetric negative MEP regions in the neighborhood of Au12 ,

Au14 , Au20 , and Au3 , Au7 , and Au19 . And there are the other two regions, close to

Au13 , Au17 , and Au10 , Au18 , which are positive. This implies the existence of two

different ‘pockets’ for trapping. For cage IV, in addition, there appear a ‘pocket’

with a slightly negative charge in the center of the MEP and the essentially positive

surface which is mapped on the ρ (r) = 0.004 isocontour. Therefore, the MEPs of

II, III and IV definitely demonstrate a capability of their voids to trap neutral, as

well as both, positively and negatively, charged atomic and molecular guests.

30.4.3 Endohedrality: Space-Filled Au20 (Td ) vs. Au20

Hollow Cages

Due to a space-filled shape of the ground-state structure Au20 (Td ) on the neutral

20-gold PES, the latter is seemingly not able to confine any guest atom or molecule.

This is not consistent with the existence of some endohedral fullerenes X@Au20 (Td )

that was computationally proven in [37,38]. Actually, there is no contradiction. True,

any hollow cage enables to trap, by the definition, a guest. It may however happen

that the interaction of a space-filled cluster with a guest is so strong that the latter

pushes aside the cluster interior, creates there a void and becomes trapped therein.

We illustrate this statement ad absurdum, in some sense.

Let consider in Fig. 30.11 two stable structures, both composed of 21 gold

atoms and both initially chosen as endohedral: the left-hand one as Au@AuII20

and the right-hand as Au@Au20 (Td ). That is, in the other words, one gold atom

was initially trapped either in the void of the hollow cage AuII20 or inside the

space-filled Au20 (Td ), where it substitutes the atom of Li in the endo-fullerene

Li@Au20 (Td ) discussed in Introduction. As a result of optimization, the former

remains endohedral, i.e. as Au@AuII20 , where the trapped gold atom Au+5.29 , ca.

+5 positively charged according to its Mulliken charge, forms nine void bonds with

AuII20 via transferring its nearly five electrons to the latter cluster. This encaging

gains the energy of 1.645 eV. In contrast, the latter structure converts to the exobonded Au&Au20 (Td ), implying that the interior of Au20 (Td ) repels the guest gold

atom to the outer space where it becomes bonded by three bonds. This effect

of repulsion of Au by the Au20 (Td ) interior is naturally anticipated because the

energy that is needed to distort the interior of Au20 (Td ), roughly estimated from the

frequencies of the Au-Au bonds forming it and being equal to ∼90–100 cm−1 , is

approximately the same as the energy of interaction between the initially trapped

gold atom and those atoms of Au20 (Td ). That is why this atom was repelled and

30 20-Nanogold Au20 (Td ) and Low-Energy Hollow Cages: Void Reactivity




Fig. 30.11 Left: The endohedral golden fullerene Au@AuII20 , formed by trapping of the guest gold

atom (blue circle) in the void of cage II. The trapped atom Au+5.29 bears a Mulliken charge of

+5.29 that implies that the nine void bonds it forms with AuII20 by means of electron transfer to

˚ Au@AuII20

cage II which becomes negatively charged. The bond lengths fall within {2.90, 3.05} A.

is slightly polar, of 0.74 D. Right: The exo-bonded Au&Au20 (Td ). Its dipole moment is equal to

˚ The energy gap

0.25 D. The exo-bonding includes three Au-Au bonds with bond lengths of 2.85A.

Δ = 1.714 and 2.017 eV for spin-up and spin-down electrons

the resultant structure is Au&Au20 (Td ) with three exo-bonds, characterized by the

binding energy of −1.149 eV, that is less than Au@AuII20 , though it is placed below

the latter by 1.030 eV.

30.5 Summary and Conclusions

Due to their exceptional reactivity, gold nano-particles in all their diverse size,

shape, and charge state are currently at the forefront of theoretical and experimental

nanoscience. The gold hollow cages – golden fullerenes – turn out to be interesting

systems with bifunctional reactivity–the void and the outer ones which can be

manipulated by doping. Obviously, manipulation with reactivity does actually

demand a way or ways to measure it. Unfortunately, this problem has not been

rigorously and consistently formulated so far and that is why remains not welldefined.

In the present work, we have identified five 20-nanogold low-energy hollow

cages at the BP86, B3LYP, and PW91PW91 density functional levels by a detailed

examination of the 20-nanogold PESs in the different charge states and their

thorough comparison. As primarily thought, the PES search was performed in two


E.S. Kryachko and F. Remacle

directions. One is to build hollow cages in the neutral charge state directly, from

blocks, such as 10-nanogold Au10 , and to investigate their stability and closeness, in

energy, to the ground-state tetrahedron Au20 (Td ). This way the hollow cage III has

been created. The other is to proceed to the dianionic PES, which is experimentally

accessible (see [38] and references therein), and to search it for the ground state –

this direction was explored in [38] and it was resulted in the hollow cage II. It

then appeared that under the vertical electron detachment (VED), the reorganization

energy of cage III becomes negative: ΔEreorg B3LYP(III|VED) = −0.17 eV, either

implying a collapse of void or an existence of a new stable isomer that must lie

on the neutral PES below cage III. The latter was actually the case that gives rise to

the cage IV which, as neutral, is placed below cage III by 2.5–3.6 kcal · mol−1 . On

the anionic PES, cages III and IV coincide with each other. The origin of cage V

is outlined in the legend to Fig. 30.5 as implying the stable endohedral cage under

encaging LiF into cage II. The history of appearance of the last cage VI is described

in the legend to Fig. 30.6 and in [26]. All these cages are stable in the charge states

Z = 0, ±1, and −2 since, according to Tables 30.1–30.5, their owest modes are

strictly positive.

In the present work, we have suggested few different approaches to measure

the void reactivity of 20-nanogold cages: on the one hand, these are ionization

energy and electron affinity, which are definitely the global characteristics, and on

the other, the local, such as the HOMO and LUMO, and the MEP. All of them

have been compared with C60 . It has been demonstrated that the MEP, which

patterns of the studied hollow cages look quite different from that of C60 , is useful

to assess the electrostatic nature of possible dopants. We thus anticipate that this

concept might be rather useful in designing golden fullerene-type nanomaterials

with the tailored void and doping-controlled properties. It is definitely useful for

metal M@Au−1

N golden fullerenes where metal atom is inside the anionic cage and

where the bonding scenario is largely governed by the MEP since the metal – cage

interaction is dominantly ionic (see [48] and references therein) and determines the

metal position.

It has also been fully answered the question why the space-filled cluster Au20 (Td )

enables to trap guest atoms [48], answered in a manner that makes the partition

of a 3D golden shape either in a space-filled or hollow one rather smeared, quite

inapplicable or even ill-defined. The reason of that is rather simple – it lies in a

relative softness of its ‘interior’ bonds, which stretches fall within the interval of

{90 cm−1 , 100 cm−1 }. This softness has been probed by the guest atom of gold.

Since its interaction with these bonds of Au20 (Td ) is of approximately the same

magnitude as the bond dissociation energies, the guest gold atom is repelled by the

‘interior’ and becomes exo-bonded. The situation between the hollow cage II of

Au20 and the guest gold atom is different: the latter is naturally trapped in a void

and forms therein nine rather strong void bonds.

Acknowledgments This work was partially supported by the AIP ‘Clusters and Nanowires’

Project of the Belgian Federal Government and the EC FET proactive NanoICT Project ‘MOLOC’.

One of the authors, E. S. K., gratefully thanks FNRS (Belgium) and the FRFC project 2.4.594.10.F

30 20-Nanogold Au20 (Td ) and Low-Energy Hollow Cages: Void Reactivity


for supporting his stay at the University of Li`ege and the Organizing Committee of the QSCP-XV,

in particular the Chair Philip E. Hoggan, for the kind invitation, the generous hospitality, and the

excellent organization. E. S. K. also thanks Benjamin Soul´e de Bas, Mike J. Ford, Alessandro

Fortunelli, Uzi Landman, Pekka Pyykkăo, Gernot Frenking, and the reviewer for the valuable

suggestions and comments.


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