Introduction
Methodology
Partial Results
Multi-dimensional PES determination for N2 reacting on a
tungsten surface using the modified shepard interpolation method
Preliminary results
Alejandro Peña Torres
Universidad Nacional de Colombia - Université Bordeaux 1
[email protected]
August, 2014
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N2 on W(100)
August, 2014
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Introduction
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Theoretical Chemistry & Modeling Group
Research interests of the group include:
Ultra-cold collisions and electron molecule scattering
Reaction dynamics in the gas phase and on surfaces
Quantum chemistry of reaction mechanisms
Quantum chemistry of electron and exciton transport in organic materials
Linear scaling density functional theory and density matrix
Nuclear magnetic resonance parameters computations and simulations
Modeling and Simulation of Condensed Phases
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Surface science
Definition?
Region that separates two 3D homogeneous phases with different chemical or physical
properties.
Geometry
Surface electronic structure
Processes that occur on it (Catalysis, Bond breaking/formation, Oxidation, Diffusion,
Charge/Atom transportation...)
”God made solids, but surfaces were the work of the devil”
W. Pauli
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August, 2014
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Gas-surface reactions
Heterogeneus catalysis
Key role in modern technology
To control it and design better catalysts we have to understand several number of
processes at a microscopic level in the gas-surface interface.
Superposition of processes = Complex study
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August, 2014
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Gas-surface reactions
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N2 on W(100)
August, 2014
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Spaceships
Increasing temperature due to
adsorption and recombination of
molecules on the thermal shield.
(≈ 40%)
It is required an understanding of
the reaction involving molecules
present in the atmosphere (N2 and
O2 ) on metallic surfaces.
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N2 on W(100)
August, 2014
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Gas-surface reactions: Multi-dimensional problems!
Determination of multi-dimensional PES: ?
System: N2 + W (100)
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N2 on W(100)
August, 2014
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Multi-dimensional problems
Basic approximation
I
I
I
BOA
No energy exchange with phonons (rigid surface)
No electron/hole pair excitation
PES = DFT + Interpolation or Fitting method
Method
Modified Shepard interpolation scheme
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N2 on W(100)
August, 2014
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System
8 possible approaches: Top (θ = 0, 90◦ ), Hollow (θ = 0, 45, 90◦ ), Bridge
(θ = 0, 90◦ (φ = 0, 90◦ ))
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N2 on W(100)
August, 2014
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Introduction
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Modified Shepard (MS) scheme
The system is described by linear combinatios of interatomic distances Zk =
Alejandro Peña Torres (UN)
N2 on W(100)
1
Rk
August, 2014
10 / 24
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Second order Taylor expansions
The potential energy V , at a given configuration Z, in the vicinity of an ab initio data
point Z(i), can be expanded as:
N (N −1)/2
X
δV Ti (Z) = V [Z(i)] +
[Zk − Zk (i)]
δZk Z=Z(i)
k=1
1
+
2!
N (N −1)/2 N (N −1)/2
X
X
k=1
j=1
δ 2 V [Zk − Zk (i)][Zj − Zj (i)]
δZk δZj Z=Z(i)
An accurate evaluation of V can be obtained by the MS method, where the potential
energy is obtained as a weighted average of the different Taylor series calculated from each
data point of our space sample and their symmetry equivalent points
V (Z) =
Nd
XX
ωg◦i (Z)Tg◦i (Z)
g∈G i=1
Alejandro Peña Torres (UN)
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August, 2014
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Selection criteria
Region most frequently visited
PNtraj
h(k) =
m=1,m6=k vm [Z(k)]
PNdata
i=1
vi [Z(k)]
Region where the PES is the most inaccurate (Variance where the weighted average is
largest)
σ 2 (k) =
NX
data
[Z(k)]{Ti [Z(k)] − E[Z(k)]}2
i=1
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August, 2014
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Iterative procedure of the PES growth
Alejandro Peña Torres (UN)
N2 on W(100)
August, 2014
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C. Crespos et al. Chemical Physics Letters 376 (2003) 566575
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August, 2014
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MS Advantages
No a priori analytical form
Non uniform sampling = less ab initio data
Interpolation method = accuracy increases with the number of data points.
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N2 on W(100)
August, 2014
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VASP calculations
Functional:
PW91
Type: UltraSoft
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August, 2014
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Pseudopotentials
Chemical properties of a system are defined by its valence electrons, given that the
internal barely take part in the interactions.
An effective potential which represents the influence of the internal electrons on the
valence electrons.
Lower calculation time.
So, what can be done to ’improve’ the results?
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August, 2014
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Adding more electrons
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August, 2014
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Using Quantum Espresso
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August, 2014
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VASP vs. QE
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August, 2014
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2D cut of the PES: DFT vs. CRP
Position: Bridge Parallel (φ = 90◦ )
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August, 2014
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2D cut of the PES: DFT vs. CRP
Position: Hollow Parallel
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August, 2014
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To do...
Optimize the ab initio set of data points
Test the code
Compare with other methods
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August, 2014
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Thank you all for coming
Questions?
Suggestions?
Comments?
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August, 2014
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