DENSITY FUNCTIONAL THEORY (DFT) APPLIED TO THE STUDY
OF THE REACTIVITY OF PLATINUM SURFACE MODIFIED BY
NICKEL NANOPARTICLES
Ortiz, Erlinda del Vallea,b and López, María Beatrízb
a
Facultad de Tecnología y Ciencias Aplicadas, Universidad Nacional de Catamarca, Maximio
Victoria 55, Catamarca, Argentina, [email protected], http://www.tecnología.unca.edu.ar
b
CIFTA, Facultad de Cs. Exactas y Naturales, Universidad Nacional de Catamarca, Av. Belgrano
300, Catamarca, Argentina, [email protected], http://www.exactas.unca.edu.ar
Keywords: Reactivity, Nanoparticles, Pt-Ni, DFT .
Abstract
Density functional theory (DFT) has provided the basis for rigorous mathematical definitions of
reactivity descriptors like chemical potential, electronegativity, chemical hardness, softness, etc. In this
work the density functional descriptors of chemical reactivity are reported to characterize the clean
platinum surfaces, Pt(100) and Pt(111), and Pt surface modified by nickel nanoparticles. We found
that the modified surfaces are more reactive than the clean Pt surfaces and the active sites are located
in the centre of the cluster which favours the formation of islands of atoms onto these surfaces.
1-
INTRODUCTION
The catalytic properties of metal surfaces can be significantly modified by metallic
nanoparticles deposition (Guczi, 2005). In electrocatalysis the electrodeposition of metal
nanoparticles on the electrode surface has been suggested as an attractive process for
enhancing the electrode conductivity, facilitating the electron transfer and improving the
analytical sensitivity and selectivity (López et al, 2007, Chikaea et al, 2006).
A bimetallic system of great importance in electrocatalysis is the Pt-Ni alloy nanoparticles
by its application like electrocatalyst in the oxidation of methane. It is demonstrated that the
platinum surface modified by Nickel nanoparticles is more reactive than the clean platinum
surface in the oxidation of methanol (Lee et al, 2002). Therefore, a detailed understanding of
the underlying microscopic mechanisms responsible for the modification of the reactivity in
bimetallic systems is highly desirable. It might lead to the design of better catalysts, in
particular since bimetallic systems might offer the possibility to tailor the reactivity by
preparing specific surface compositions and structures.
Density functional theory (DFT) has provided the basis for rigorous mathematical
definitions of reactivity descriptors like chemical potential, electronegativity, chemical
hardness, softness, etc. (Yang et al, 1985). All of these are well established global quantities
in chemical reactivity studies and are going to be used in this paper to characterize the clean
and modifies Pt surface. Although local and nonlocal quantities such as the condensed Fukui
function and local softness, have also been introduced in the theory to characterize specific
sites in the catalytic surfaces.
The present work refers to DFT calculations for describing the reactivity of Pt(100) and
Pt(111) surfaces modified by nickel nanoparticles deposition. We have considered two model
systems: i) a clean platinum surface, ii) modified platinum surface adsorbing a Ni atoms.
Changes in the work function (HOMO) of Pt (100) and Pt (111) induced by the adsorption
of metallic ad-atoms allow to analyzing the interaction adsorbate-substrate. The reactivity of
the clean and modified surfaces were analyzed by: i) energy levels of the highest occupied
molecular orbital (HOMO), ii) softness and local softness.
2-METHODOLOGY
2.1 Theoretical Background
Density functional theory has been successfully applied to study the electronic structures of
a wide variety of chemical systems. The success of this theory is mainly due to (i) the
significantly less computational effort required in carrying out the accurate electronic
structure calculations through its practical implementation, (ii) the fact that a natural set of
indices can be defined within the theory which are useful descriptors of reactivity of chemical
systems.
According to the Hohenberg and Kohn (HK) theorems (Hohenberg and Kohn, 1964), the
ground state energy functional of an N- electron system with density ρ(r) in an external
potential u, is given by
E [ ρ ( r ) ] = F [ ρ ( r ) ] + ∫ υ ( r ) ρ ( r ) dr
(1)
where F [ ρ ( r ) ] is called the universal HK-functional containing the contribution of the
kinetic energy (T) and the electron-electron interaction (Vee) of the system. The usual
minimization of the energy functional of (1) using the method of Lagrange multipliers subject
to the constraint, N =
∫ ρ ( r ) dr , leads to the Euler–Lagrange equation,
µ = [δ E / δ ρ
]υ
= υ ( r) + δ F[ ρ ( r)] / δ ρ ( r)
(2)
where the constant µ has been identified, in the grand canonical ensemble at 0 K, as the
electronic chemical potential (Parr and Yang, 1989). This quantity arising within the DFT,
measures the escaping tendency of an electronic cloud in the ground state system. Being a
constant over all space for the ground state of an atom or molecule, μ, is recognized as a
global reactivity index. It has been also shown, that the chemical potential is the slope of m
the curve E versus N at a fixed external potential (Parr et al, 1978)
µ = ( ∂ E / ∂ N )υ .
(3)
Within the finite difference approximation this slope can be written in terms of the
ionization potential IP, and the electron affinity EA. In this way, the DFT chemical potential
can be associated with the negative of the Mulliken electronegativity ( χ ) (Parr et al, 1978),
as
µ ≈ − ( IP + EA) / 2 = − χ .
(4)
The chemical potential can be considered as a function of N and υ , and describe a change
in the system from [ N ,υ ] → [ N + dN , υ + ∂ υ ] , according to
dµ = η dN + ∫ ∂ υ ( r ) f ( r ) dr .
(5)
This consideration leads to the definition of another two important indices, which have
been used to study chemical reactivity. The global hardness, η , and the local reactivity index
f , called the Fukui function (Parr and Yang, 1984).
Parr and Pearson (Parr and Pearson, 1983) have defined the former as,
η =
(
)
1 2
∂ E/∂N2 υ .
2
(6)
The factor 1/2 is arbitrary in the original definition and it is not considered in this paper.
From (6), η is the curvature of the curve E versus N, which is always positive (Parr and
Yang, 1989). Within the finite difference approximation,
η ≈ IP − EA .
(7)
The inverse of global hardness defines the global softness (Parr and Yang, 1989),
S = 1/η = ( ∂ N / ∂ µ
)v .
(8)
Hardness and softness are concepts that have been used to explain chemical reactivity for
many years (Pearson, 1973).
In numerical applications, µ and η are calculated through the following approximate
versions of Eqs. (3) and (6), based upon the finite difference approximation and the
Koopmans theorem (Pearson, 1973),
µ ≈ −
and
1
( IP + EA) ≈ 1 ( ε L + ε
2
2
H
)
(9)
η ≈
1
( IP − EA) ≈ 1 ( ε L − ε
2
2
H
)
(10)
IP is the ionization potential, EA is the electron affinity, ε L and ε H are the energies of the
highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital
(LUMO), respectively.
Form DFT, local descriptor, such as local hardness, local softness and Fukui function
indices, were derived to explain the reactivity or selectivity at a particular site of the system.
In this work, we adopted the local softness to describe the local reactivity of the surfaces.
The local softness is defined as
 ∂ ρ(r) 

s (r) = 
 ∂ μ  υ (r )
(11)
where ρ ( r ) is the electron density at the site r. Based on Eq. (8), and the fact that the local
softness should be integrated to give the global softness, then
S=
∫ s (r) dr .
(12)
The local softness s( r ) can be identified as
 ∂ρ
 ∂ N


s (r) = 
* 
= f (r )*S
 ∂ N  υ (r )  ∂ μ  υ (r )
(13)
where f ( r ) is the Fukui function, the intramolecular reactivity index introduced by Parr and
Yang (Yang and Parr, 1985). Because s( r ) is obtained by multiplying f ( r ) with the softness
S, then s( r ) contains information about the intramolecular reactivity, as well as the
intermolecular reactivity. Consequently, we used the local softness to compare the reactivity
of each site of the two systems, that is, clean Pt surfaces and a modified surface with metallic
ad-atoms. Because of the discontinuity in the derivative at the N-value of Eq. (13), we used
two definitions for Fukui Function,
+
 ∂ ρ(r) 

f (r ) = 
(derivative as N increases from N 0 → N 0 + δ)
 ∂ N  υ (r )
+
(14)
for a nucleophylic attack, and
−
 ∂ ρ(r) 

f (r ) = 
 ∂ N  υ (r )
−
(derivative as N increases from N 0 → N 0 − δ)
(15)
for an electrophilic attack. In a finite difference approximation, these indices can be written as
f + (r ) = ρ N + 1 (r) − ρ N (r)
f − (r ) = ρ N (r) − ρ N − 1 (r)
(16)
where ρ N ( r ) is the electronic –density function of the atomic or molecular anion (M=N+1)
or cation (M=N-1) calculated at the geometry of the neutral system (M=N).
Because we are interested in the reactivity of the atomic sites, we considered the numbers
obtained by approximate integrations of the Fukui function over atomic regions (these
numbers are called condensed Fukui functions). The Mulliken population analysis (MPA)
scheme was used to define the atomic region.
The condensed Fukui functions are denoted as
f k+ = q k (N + 1) − q k (N)
(17)
f k− = q k (N) − q k (N - 1)
where qK (M) is the atomic electron population at atom k for either the neutral system
(M=N), the cation (M=N-1), or the anion M=(N+1). Consequently, the local softness can be
represented as
s +k = f k+ * S
(18)
s −k = f k− * S
(19)
for a nucleophilic attack, and
for an electrophilic attack.
2.2 Computational Methods
Density function theory (DFT) as implemented in Gaussian 03 (Revision C 0.2, 2004) has
been used for all the calculations. The hybrid B3LYP density functional method was used,
which includes Becke´s 3-parameter nonlocal-exchange functional (Becke, 1993) with the
correlation functional of Lee (Lee et al, 1988). The effective-core-potential LANL2DZ basis
set (Hay and Wadt, 1985) is used for the Ni and Pt atoms.
The Pt surfaces (substrate) with (100) and (111) crystalline plane were modelled using
Pt(100)25 and Pt(111)21 clusters and Ni nanoparticles was simulated by a Ni tetramer, Figure 1.
The optimization of the geometry of the Ni ad-atoms was carried out maintaining fixed the
geometry of the substrate. This optimization allows to predict the adsorbate structural changes
when Ni atoms interacting with the surface Pt (100) and Pt (111).
a)
b)
Figure 1: Pt surface modified by the adsorption Ni nanoparticles: a) Pt(100)25Ni4 and b) Pt(111)21Ni4
3 RESULTS
HOMO´s energy of a finite cluster model can directly be related with the work function of
the extended system (Hashimoto et al, 2001). Table 1 shows the HOMO energy levels, the
chemical potential (μ) and global softness (S) by the four systems: Pt(100)25, Pt(111)21,
Pt(100)25Ni4 and Pt(111)21Ni4.
System
Pt(100)25
Pt(111)21
Pt(100)25Ni4
Pt(111)21Ni4
HOMO
(eV)
-6,313
-6,285
-5,877
-5,768
µ
(eV)
-6
-5,972
-5,632
-5,469
S
(eV)
3,195
3,2
4,09
3,344
Table 1 – Reactivity global descriptors: HOMO (highest occupied molecular orbital), Chemical potential (μ) and
global softness (S).
According to the HOMO energy values, the clean Pt (100)25 surfaces is more stable than
the clean Pt (111)21 surface. The nickel nanoparticles adsorption destabilize the HOMO level
of both surface in 0.44 eV for Pt(100)25Ni4 and 0.52 eV for Pt(111)21Ni4 . This means that the
modified surfaces are more reactive that the clean surfaces.
The chemical potential measure the escaping tendency of electrons from the equilibrium
systems them as μ becomes more negative, it is more difficult to lose an electron but easier to
gain one. In particular Pt(111)21 presents the highest values of chemical potential, -5,97 eV
them these systems are able to transfer electrons.
The softness of the surface modified increases being Pt(111) 21Ni4 the more reactive one.
The local softness values (s+ y s-) are plotted in Figure 2 a, b respectively, against each atom
of the Pt(100)25 ad Pt(111)21 surfaces.
The local softness allows to identify the most active sites in the surface. The greater
reactivity of cluster Pt (111)21 is located in the center . We can observe that the central atoms
have the greatest values of local softness, therefore we can assign the greater activity to that
site. Nevertheless, atoms near these central atoms present great values of local softness,
consequently a zone of greater reactivity could be identified. The presence of active sites or
active zone (group of atoms) favours the formation of island atoms onto this surface. This
would allow to speculate with the possible formation of nickel islands on platinum surfaces
before de Ni bulk deposition.
The Ni nanoparticles adsorption increase the local softness in the more active site and zone
on Pt(111)21. The clean Pt(100)25 surface presents a centralized concentration of the reactivity
and when it is deposited the nickel nanoparticles is observed an increase in the local softness
for central atoms. These atoms define the hollow site in the surface consequently this site
could be identified as the most active site.
Softness
20
18
16
14
Pt(100)25
Pt(111)21
Pt(100)25Ni4
Pt(111)21Ni4
s-(eV)
12
10
8
6
4
2
0
Pt 1
Pt 3
Pt 5
Pt 7
Pt 9
Pt 11 Pt 13 Pt 15 Pt 17 Pt 19 Pt 21 Pt 23 Pt 25
2-a)
Softness
18
16
14
Pt(100)25
Pt(111)21
Pt(100)25Ni4
Pt(111)21Ni4
s+(eV)
12
10
8
6
4
2
0
Pt 1
Pt 3
Pt 5
Pt 7
Pt 9
Pt 11 Pt 13 Pt 15 Pt 17 Pt 19 Pt 21 Pt 23 Pt 25
2-b)
Figure 2 -Local softness: a)in the case of electrophilic reaction, and b) in the case of nucleophilic reaction
4. CONCLUSIONS
We have investigated the reactivity of Pt(100) and Pt(111) surfaces modified by nickel
nanoparticles deposition. The reactivity of the clean and modified surface was analyzed by
energy levels of the highest occupied molecular orbital (HOMO), softness and local softness.
All our calculations were made using hybrid B3LYP density functional theory method.
The reactivity of the clean Pt(100) and Pt(111) surfaces increases with the nickel
nanoparticles adsorbed. We found that the active sites and active zones are located in the
centre of the cluster which favours the formation of island of atoms onto these surfaces.
Comparing the reactivity of the clean surfaces, the (111) face is more reactive than the
(100) face. The modification of the surfaces by adsorbed nanoparticles reactivates both
surfaces but the (111) face is the one that presents greater reactivity.
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