Dynamics of H2 on Ti/Al(100) surfaces
Chen, J.C.
Citation
Chen, J. C. (2011, October 19). Dynamics of H2 on Ti/Al(100) surfaces. Retrieved from https://hdl.handle.net/1887/17956
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Dynamics of H 2 on Ti/Al(100) surfaces
PROEFSCHRIFT
ter verkrijging van
de graad van Doctor aan de Universiteit Leiden,
op gezag van de Rector Magnificus prof. mr. P. F. van der Heijden, volgens besluit van het College voor Promoties
te verdedigen op woensdag 19 oktober 2011 klokke 15.00 uur
door
Jian-Cheng Chen
geboren te Shaanxi in 1977
Promotiecommissie
Promotores: Prof. dr. G. J. Kroes Prof. dr. R. A. Olsen Co-promotor: Dr. J. C. Juanes-Marcos Overige leden: Prof. dr. M. T. Koper
Dr. G. C. Groenenboom Prof. dr. J. Brouwer
Prof. dr. J. J. C. Geerlings Dr. L. B. F. Juurlink
Prof. dr. M. C. van Hemert
This research described in this thesis was performed at the Theoretical Chemistry Group of the Leiden Institute of Chemistry (LIC), Leiden University, 2300 RA Leiden. This work was made possible by financial support from the “Marie Curie Research Training Network:
HYDROGEN” under contract No. 032474. The “Stichting Nationale Computerfaciliteiten” (NCF) is acknowledged for grants of computer time.
Productie en vormgeving omslag: F&N Boekservice
To my parents
Contents
1 Introduction 9
1.1 Hydrogen production and storage . . . 9
1.1.1 Hydrogen production . . . 10
1.1.2 Hydrogen storage . . . 10
1.2 H2–surface reactions . . . 13
1.2.1 Gas–surface reaction mechanisms . . . 14
1.2.2 Scattering of H2on metal surfaces . . . 16
1.2.3 Dissociation of H2on metal surfaces . . . 18
1.3 Scope and major results . . . 19
1.4 Outlook . . . 22
1.5 References . . . 24
2 Theoretical methods 31 2.1 The Born-Oppenheimer approximation . . . 31
2.2 Brief density functional theory . . . 32
2.2.1 From Hartree approximation to density functional theory . . . 32
2.2.2 Density functional theory . . . 35
2.2.3 Plane wave DFT . . . 37
2.2.4 Two-center projected density of states . . . 39
2.3 Quasi-Newton optimization . . . 40
2.4 Barrier search methods . . . 42
2.5 Potential energy surface building . . . 44 v
CONTENTS CONTENTS
2.5.1 The “grow” method . . . 46
2.5.2 Corrugation reducing procedure . . . 49
2.6 Quasi-classical trajectory method . . . 50
2.7 Time-dependent wave packet . . . 51
2.7.1 Hamiltonian and the time-dependent wave packet . . . 51
2.7.2 Methods to propagate the time-dependent wave packet . . . 54
2.7.3 Representation of the wave packet . . . 55
2.7.4 Asymptotic analysis . . . 59
2.8 Transition state theory . . . 61
2.9 Molecular beam simulations . . . 63
2.10 References . . . 64
3 A DFT study of H2reacting on Ti/Al(100) surfaces 69 3.1 Introduction . . . 69
3.2 Methodology and numerical details . . . 72
3.3 Results and discussion . . . 74
3.3.1 Slab models . . . 74
3.3.2 H2dissociation barriers . . . 77
3.3.3 A molecular orbital view of the H2 approach to the surface and the subsequent dissociation . . . 83
3.4 Conclusions . . . 85
3.5 References . . . 86
4 Six-dimensional quasi-classical and quantum dynamics for H2 dissociation on the 1 monolayer covered c(2 × 2)-Ti/Al(100) surface 89 4.1 Introduction . . . 90
4.2 Methodology and numerical details . . . 92
4.2.1 Electronic structure calculations and slab model . . . 92
4.2.2 Modified Shepard interpolation method and “growing” of the six- dimensional PES . . . 93
4.2.3 CT and QCT calculations . . . 97 vi
CONTENTS CONTENTS
4.2.4 TDWP calculations . . . 100
4.3 Results and discussion . . . 103
4.3.1 PES obtained from the “Grow” method . . . 103
4.3.2 Quasi-classical H2 dissociation probabilities . . . 105
4.3.3 Quantum dynamics of H2dissociation probability . . . 110
4.4 Conclusions . . . 114
4.5 References . . . 115
5 Dynamics of H2 dissociation on the 1/2 ML Ti-covered c(2 × 2)-Ti/Al(100) surface 121 5.1 Introduction . . . 122
5.2 Methodology and details . . . 124
5.2.1 Electronic structure calculations and slab model . . . 124
5.2.2 The interpolation of the 6D PESs . . . 125
5.2.3 CT and QCT calculations . . . 128
5.2.4 Effective barrier heights and rovibrational efficacies in QCT cal- culations . . . 128
5.2.5 TDWP calculations . . . 129
5.2.6 Molecular beam simulations . . . 131
5.2.7 H2 dissociation rate constant calculations by transition state the- ory and quasi-classical trajectories . . . 132
5.3 Results and discussion . . . 134
5.3.1 PES obtained from the corrugation reducing procedure . . . 134
5.3.2 Quasi-classical H2 dissociation probabilities . . . 137
5.3.3 Stereodynamic effects and rovibrational efficacies from the QCT calculations . . . 141
5.3.4 Quantum dynamics of H2dissociation . . . 144
5.3.5 Molecular beam simulations results . . . 146
5.3.6 Reaction rate constant calculations by transition state theory and quasi-classical dynamics . . . 147
5.4 Conclusions . . . 150 vii
CONTENTS CONTENTS
5.5 References . . . 152
viii
