The aim of this paper is to report a study of the reactivity of Pt(100) cluster and the same system modified by a nickel tetramer towards the atomic hydrogen adsorption. This study was carried out in the framework of density functional theory which provides global and local indexes that can be used to characterize the reactivity. The analyzed reactivity descriptors were: chemical potential, chemical hardness, electrophilicity index and Fukui function. The results showed that the global reactivity descriptor predicts that the platinum cluster modified by nickel is more reactive than the pure platinum cluster and that the local Fukui function provides information about the most susceptible site to electrophilic attack in platinum cluster.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

Castro, Eduardo Alberto

Lopez, M. B.

Ortiz, E. V.

Journal of Physics Conference Series

English

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XIX Latin American Symposium on Solid State Physics (SLAFES XIX) IOP Publishing
Journal of Physics: Conference Series 167 (2009) 012021 doi: 10.1088/1742-6596/167/1/012021
Reactivity of a Pt(100) cluster modified by adsorption of a 
Nickel tetramer
EV Ortiz12, MB Lopez1, EA Castro3
1 Centro de Investigaciones Fisicoquímicas, Teóricas y Aplicadas (CIFTA), Facultad 
de Ciencias Exactas y Naturales, Universidad Nacional de Catamarca, Av. Belgrano 
300, (4700), Catamarca, Argentina.
2 Facultad de Tecnología y Ciencias Aplicadas, Universidad Nacional de Catamarca, 
Maximio Victoria 55, (4700), Catamarca, Argentina.
3INIFTA, CONICET, Universidad Nacional de la Plata, Diag. 113 y 64, Suc.4, C.C. 
16, (1900), La Plata, Argentina.
E-mail: mblopez@fcasuser.unca.edu.ar
Abstract. The aim of this paper is to report a study of the reactivity of Pt(lOO) cluster and the 
same system modified by a nickel tetramer towards the atomic hydrogen adsorption. This study 
was carried out in the framework of density functional theory which provides global and local 
indexes that can be used to characterize the reactivity. The analyzed reactivity descriptors 
were: chemical potential, chemical hardness, electrophilicity index and Fukui function. The 
results showed that the global reactivity descriptor predicts that the platinum cluster modified 
by nickel is more reactive than the pure platinum cluster and that the local Fukui function 
provides information about the most susceptible site to electrophilic attack in platinum cluster.
1. Introduction
There is a strong current interest in the study of supported metal nanoclusters, not only from a 
fundamental point of view but also because of their technological relevance in, e.g., heterogeneous 
catalysis or the design of nanoscale magnetic storage devices. Systems with reduced dimensions can 
exhibit surprising properties [1].
The increase in catalytic properties resulting from the formation of intermetallic compounds is 
attributed to the alteration of the electronic structure and physicochemical properties, such as work 
function and density of states at the Fermi level [2],
The system Pt/Ni has been widely studied in its various forms: Alloy surface [3], pseudomorphic 
overlayer [4] and supported nanoparticles [5], Recent studies have revealed that the Pt-Ni alloy surface 
presents a considerable increase in the catalytic activity versus Pt pure compared to the reaction of 
oxygen reduction [6] and Ni-Pt nanoparticles which are more reactive compared to the oxidation of 
methanol on the surface of Pt(100) surface [7], It is therefore of great interest to know the microscopic 
mechanisms responsible for the modification of the reactivity in this bimetallic system since this 
knowledge will allow the design of catalysts composition and specific structures.
The Density Functional Theory (DFT) has provided the basis for rigorous mathematical definitions of 
reactivity descriptors like chemical potential, electronegativity, chemical hardness, softness, etc., [8],
© 2009 IOP Publishing Ltd 1
XIX Latin American Symposium on Solid State Physics (SLAFES XIX) IOP Publishing
Journal of Physics: Conference Series 167 (2009) 012021 doi: 10.1088/1742-6596/167/1/012021
All of these are well established global indicators in chemical reactivity studies and are going to be 
used in this paper to characterize the reactivity of Pt(100)n cluster and Pt(100)nNim (n=25, m=4) toward 
the adsorption hydrogen atom.
Also local indicators have been introduced in the theory to explain the reactivity or selectivity at a 
particular site of the system. In this work, we adopted the Fukui function to analyze the reactivity of 
the surfaces against a hydrogen atom.
2. Theoretical background
In DFT, the chemical potential and hardness for the N-electrons system with total energy E and 
external potential v(r) are defined as the first and second derivatives of the energy with respect to N
[8-11]:
a«La' (i>
and
2F.U (2)
In numerical applications, p and pare calculated through the following approximate version of Eqs.
(1) and (2), based upon the finite difference approximation and the Koopmans theorems [8],
and
-|(/P+E4) = +
(3)
(4)
IP is the ionization potential, EA is the electron affinity, £H and £L are the energies of the highest 
occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), 
respectively. The electrofilicity index is defined as [11]:
2?7
(5)
This quantity is a measure of the propensity of systems to acquire electronic charge from the 
surroundings. Considering clusters or metallic surfaces as binding environments, (0 can be useful for 
analyzing the interaction with small molecules.
The condensed Fukui functions are denoted as [10]:
A+ = qk(N+ 1)- qk(N)
A = qk(N)- qk(N-l)
(6)
where qi(M) is the atomic electron population at atom k for either the neutral system (M=N), the 
cation (M=N-1), orthe anion (M=N+1).
3. Computational methods
Density functional theory (DFT) as implemented in Gaussian03 [12] has been used for all the 
calculations. The hybrid B3LYP density functional method was used, which includes Becke's 3- 
parameter nonlocal-exchange functional [13] with the correlation functional of Lee et al [14], The 
effective-core-potential LANL2DZ [15] is used for the atoms of Ni and Pt and the bases 6-31G** for 
hydrogen atom.
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XIX Latin American Symposium on Solid State Physics (SLAFES XIX) IOP Publishing
Journal of Physics: Conference Series 167 (2009) 012021 doi:10.1088/1742-6596/167/l/012021
The Pt surfaces with (100) crystalline plane were modeled using Pt(100)25 clusters and Ni 
nanoparticles was simulated by a nickel tetramer, Ni4, Figure 1. Since the reactivity of the surface is 
evaluated in terms of global and local indices based on well localized processes of charge transfer 
between adsorbate-substrate the use of an atomic bilayer was not considered.
Figure 1. PtnNim (n=25, m=4) system
In all calculations the nearest neighbor Pt-Pt distance was fixed at the experimental value [16] of 0.277 
nm for platinum. The optimization of the geometry of the Ni ad-atoms was carried out maintaining the 
geometry of the substrate fixed. The effects of relaxation of the substrate atoms were not considered. 
The interaction of the hydrogen atom on Pt (100)n and Pt (100)nNim surfaces was optimized in different 
adsorption sites: on top, bridge and hollow. At each site the H-surface distance was optimized, while 
all other parameters of these systems were kept frozen. In all cases, harmonic frequency analysis was 
performed to verify that the optimized structures are local minima.
The binding energy of hydrogen atom to the M-H systems (M= P(100)n, and Pt(100)nNim) was 
calculated as:
Ead ~ H ~ ~ (7)
Where, EM-h is the energy of hydrogen adsorbed on M system, EM energy from the M system and EH is 
the energy of hydrogen to an infinite distance from the surface, respectively.
4. Results
Table 1 shows the values of the global reactivity descriptors -chemical potential (p), chemical 
hardness (r|) and electrofilicity index (co)- for the pure and modified surfaces, Ptn and PtnNm, 
respectively, and the binding energy (Ead) of hydrogen atom on PtnH and modified surface, PtnNimH. 
The adsorption site of hydrogen atom is indicated as T (on top) and B (bridge), Figure 2. Not found 
adsorption on the Hollow site.
Figure 2. Hydrogen 
adsorption site (a) 
Pt„H(B), (b) PtnH(T), 
(C) PtnNim H(B), (d) 
PtnNim H(T)
The reactivity of global indicators is an intrinsic electronic property of the system and indicates their 
availability for a chemical change that may occur. The chemical potential measures the escaping
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XIX Latin American Symposium on Solid State Physics (SLAFES XIX) IOP Publishing
Journal of Physics: Conference Series 167 (2009) 012021 doi:10.1088/1742-6596/167/l/012021
tendency of electrons from the equilibrium systems then as ji becomes more negative, it is more 
difficult to lose an electron but easier to gain one.
The chemical hardness can be seen as the strength of a system to charge transfer; therefore it 
characterizes the stability of the systems under study. The electrophilicity index is a measure of 
stabilization energy of the system when it is saturated with electrons which come from the external 
environment, i.e., it measures the tendency of a system to capture electrons.
The chemical potential, the negative of the absolute electronegativity, of the hydrogen atom is -7.20 
eV and the chemical potential of Ptn and PtnNim systems are -6.03 eV and -5.92 eV, respectively 
(Table 1). Therefore it can be expected that Ptn and PtnNim systems act as a donor system and the donor 
Fukui function /k should indicate the reactivity of different regions of Ptn cluster.
The Ptn system had a greater value of chemical hardness, 0.56 eV, that the PtnNim, 0.46 eV, hence the 
latter system is more reactive or softer. The hydrogen adsorption stabilizes Ptn systems, being PtnH(T) 
more stable than PtnH(B) with a chemical hardness value equal to 0.61 eV and 0.59 eV, respectively. 
The same trend is observed for the modified surface but in this case the PtnNimH(B) is more stable than 
PtnNimH(T) with a chemical hardness value equal to 0.55 eV and 0.49 eV, respectively.
The values of the electrophilicity index confirm the tendency of the system, noting that the lower 
values of co are for PtnH(T) and PtnNm H (B).
An analysis of the binding energy of hydrogen atom in different sites covering the surface under study 
confirms that site energetically favorable for Ptn cluster is on top and for PtnNim is on bridge.
Table 1. Global reactivity descriptors, chemical potential (p), 
chemical hardness (T|), electrophilicity index (co) and binding 
energy (Ea<i) for the systems: Ptn, PtnNim, PtnH and PtnNimH (n = 25, 
m = 4),
System R
(eV)
n
(eV)
CO
(eV)
Ea[| 
(eV)
Pt„ -6.03 0.56 32.41 -
Pt„Nim -5.95 0.46 37.93 -
Pt„H(T) -6.02 0.61 29.70 -4. 64
Pt„H (B) -5.93 0.59 29.80 -4.45
Pt„NimH(T) -5.92 0.49 37.76 -4.53
Pt„NiraH (B) -5.84 0.55 31.00 -6.56
00^1 QMa'j
Figure 3. Fukui function (fk ) of Ptn and Ptn Nim systems.
The Fukui function (/k ) allows identifying the most active sites in the surface. The greater reactivity 
of cluster Pt (100)25 is located in the center with maximum value of Fukui function equal to 0.407, 
Figure 3. This site is the most susceptible to electrophilic attack and this result is in agreement with the 
previous one for hydrogen adsorption on platinum cluster, PtnH(T). Reactivity observed in the edge of 
the platinum cluster atoms can be considered artificial because the border atoms have unsaturated
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XIX Latin American Symposium on Solid State Physics (SLAFES XIX) IOP Publishing
Journal of Physics: Conference Series 167 (2009) 012021 doi: 10.1088/1742-6596/167/1/012021
valences which can cause additional reactivity. The modified surface Ptn Nim presents the greater 
reactivity on Ni tetramer with the same value of Fukui function for each Ni atom. The four Ni atom 
have obviously the same probability to be attacked by electrophylic species, therefore in this case they 
do not provide the adsorption hydrogen site.
Future studies using larger cluster and effects of relaxation between adsorbate-substrate will allow us 
to make up a further analysis on the impact of the localized Fukui function to predict energetically 
favorable adsorption sites.
5. Conclusions
The study of the reactivity of Pt(100) cluster and of the same system modified by a nickel tetramer 
towards the atomic hydrogen using the global and local reactivity descriptors, allows us to arrive at the 
following conclusions:
-The global reactivity descriptors, chemical potential, chemical hardness and electrophilicity index 
confirm that the Pt cluster modified by nickel tetramer is more reactive than the pure Pt cluster.
-The local reactivity descriptor, Fukui function (/k), predicts that the greater reactivity of pure Pt 
cluster is located in the central atom and for PtnNim surfaces in the Ni tetramer.
6. Reference
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Reactivity of a Pt(100) cluster modified by adsorption of a nickel tetramer

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Reactivity of a Pt(100) cluster modified by adsorption of a nickel tetramer

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