Selective excitation of adsorbate vibrations on dissipative surfaces [Elektronische Ressource] / von Stephanie Beyvers
163 pages
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Selective excitation of adsorbate vibrations on dissipative surfaces [Elektronische Ressource] / von Stephanie Beyvers

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163 pages
English
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Selective excitation of adsorbate vibrations ondissipative surfacesDissertationzur Erlangung des akademischen Grades“doctor rerum naturalium”(Dr. rer. nat.)in der Wissenschaftsdisziplin Theoretische Chemieeingereicht an derMathematisch-Naturwissenschaftlichen Fakult¨atder Universit¨at PotsdamvonStephanie Beyversaus Mallersdorf-PfaffenbergPotsdam, im Juli 2008beyvers@rz.uni-potsdam.de 1. Gutachter: Prof. Dr. P. Saalfrank2. Gutachter: Prof. Dr. T. Klu¨ner3. Gutachter: Prof. Dr. R. MarquardtTag der Disputation: 29. Oktober 2008This work is licensed under a Creative Commons License: Attribution - Noncommercial - Share Alike 2.0 Germany To view a copy of this license visit http://creativecommons.org/licenses/by-nc-sa/2.0/de/deed.en Online published at the Institutional Repository of the Potsdam University: http://opus.kobv.de/ubp/volltexte/2008/2551/ urn:nbn:de:kobv:517-opus-25516 [http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25516] PublicationsPublications (7)1 “Quantum dynamics of laser-induced desorption from metal andsemiconductor surfaces, and related phenomena”P. Saalfrank, M. Nest, I. Andrianov, T. Klamroth, D. Kr¨oner, and S. BeyversJ. Phys.: Condens. Matter 18, 1425 (2006)2 “Optimal control in a dissipative system: Vibrational excitation ofCO/Cu(100) by IR pulses”S. Beyvers, Y. Ohtsuki, and P. SaalfrankJ. Chem. Phys.

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Publié par
Publié le 01 janvier 2008
Nombre de lectures 32
Langue English
Poids de l'ouvrage 7 Mo

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Selective excitation of adsorbate vibrations on
dissipative surfaces
Dissertation
zur Erlangung des akademischen Grades
“doctor rerum naturalium”
(Dr. rer. nat.)
in der Wissenschaftsdisziplin Theoretische Chemie
eingereicht an der
Mathematisch-Naturwissenschaftlichen Fakult¨at
der Universit¨at Potsdam
von
Stephanie Beyvers
aus Mallersdorf-Pfaffenberg
Potsdam, im Juli 2008
beyvers@rz.uni-potsdam.de 1. Gutachter: Prof. Dr. P. Saalfrank
2. Gutachter: Prof. Dr. T. Klu¨ner
3. Gutachter: Prof. Dr. R. Marquardt
Tag der Disputation: 29. Oktober 2008This work is licensed under a Creative Commons License:
Attribution - Noncommercial - Share Alike 2.0 Germany
To view a copy of this license visit
http://creativecommons.org/licenses/by-nc-sa/2.0/de/deed.en










































Online published at the
Institutional Repository of the Potsdam University:
http://opus.kobv.de/ubp/volltexte/2008/2551/
urn:nbn:de:kobv:517-opus-25516
[http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25516] Publications
Publications (7)
1 “Quantum dynamics of laser-induced desorption from metal and
semiconductor surfaces, and related phenomena”
P. Saalfrank, M. Nest, I. Andrianov, T. Klamroth, D. Kr¨oner, and S. Beyvers
J. Phys.: Condens. Matter 18, 1425 (2006)
2 “Optimal control in a dissipative system: Vibrational excitation of
CO/Cu(100) by IR pulses”
S. Beyvers, Y. Ohtsuki, and P. Saalfrank
J. Chem. Phys. 124, 234706 (2006)
3 “Mode-selective excitation of hydrogen atoms on a Si surface:
Non-Markovian and Markovian treatment of infrared-laser driven
dissipative quantum dynamics”
G. K. Paramonov, S. Beyvers, I. Andrianov, and P. Saalfrank
Phys. Rev. B 75, 045405 (2007)
4 “Vibrationally enhanced associative photodesorption of molecular
hydrogen from Ru(0001)”
T. Vazhappilly, S. Beyvers, T. Klamroth, M. Luppi, and P. Saalfrank
Chem. Phys. 338, 299 (2007)ii
5 “A hybrid local / global control algorithm for dissipative systems
with time-dependent targets”
S. Beyvers and P. Saalfrank
J. Chem. Phys. 128, 074104 (2008)
6 “Selective excitation of coupled CO vibrations on a dissipative
Cu(100) surface by shaped infrared laser”
J. C. Tremblay, S. Beyvers, and P. Saalfrank
J. Chem. Phys. 128, 194709 (2008)
7 “Controlling the photodesorption of adspecies from surfaces”
P. Saalfrank, T. Vazhappilly, S. Beyvers, G. K. Paramonov, and T. Klamroth
Surf. Sci. 602, 3153 (2008)Contents
1 Introduction 1
2 Theoretical methods 5
2.1 Stationary solution of the adsorbate/surface system . . . . . . . . . . . . . . 6
2.1.1 Time-independent Schr¨odinger equation . . . . . . . . . . . . . . . . . 6
2.1.2 Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Dissipative dynamics: The Liouville-von Neumann equation . . . . . . . . . . 7
2.3 Dissipation model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.1 Nonadiabaticmolecularorbitaltheoryforthecalculationofvibrational
lifetimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.2 Harmonic and anharmonic approaches for higher rates . . . . . . . . . 13
2.4 Optimal control theory (OCT) . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.1 Global and local optimal control for wavefunctions . . . . . . . . . . . 17
2.4.2 Global optimal control for density matrices . . . . . . . . . . . . . . . 18
iCONTENTS ii
2.4.3 Pulse analysis by Husimi quasiprobability distribution . . . . . . . . . 20
3 Adsorbate/surface systems 22
3.1 CO/Cu(100) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.1 Potential energy surface and stationary solution . . . . . . . . . . . . 24
3.1.2 Dipole function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.1.3 Dissipation and dephasing rates . . . . . . . . . . . . . . . . . . . . . . 33
3.2 H/Si(100) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.1 Potential energy surface and vibrational states . . . . . . . . . . . . . 38
3.2.2 Dipole function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.3 Dissipation and dephasing rates . . . . . . . . . . . . . . . . . . . . . . 40
3.3 2H/Ru(0001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.1 Potential energy surface, stationary solution and dipole function . . . 43
3.3.2 Calculation of vibrational lifetimes . . . . . . . . . . . . . . . . . . . . 45
4 Control of vibrational excitation in dissipative systems 50
4.1 CO/Cu(100) [96,97] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.1.1 One-dimensional model (r) [96] . . . . . . . . . . . . . . . . . . . . . 51
4.1.2 Two-dimensional model (r,Z) . . . . . . . . . . . . . . . . . . . . . . . 54
4.1.3 Three-dimensional model (r,Z,X) [96] . . . . . . . . . . . . . . . . . 59CONTENTS iii
4.1.4 Four-dimensional model (r,Z,θ,φ) [97] . . . . . . . . . . . . . . . . . 65
4.2 H/Si(100) [104] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2.1 One-dimensional model (r) . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2.2 Two-dimensional model (r,φ) [104] . . . . . . . . . . . . . . . . . . . 72
4.3 2H/Ru(0001) [111] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.3.1 Excitation of the Z mode . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3.2 Excitation of the r mode . . . . . . . . . . . . . . . . . . . . . . . . . 82
5 Optimal control with time-dependent targets 85
5.1 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.2 Numerical tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.3.1 Creation and preservation of a wavepacket . . . . . . . . . . . . . . . . 92
5.3.2 Controlling a multi-level system. . . . . . . . . . . . . . . . . . . . . . 94
6 Summary 96
A Numerical methods for solving the stationary problem 102
A.1 Sinc-function discrete variable representation . . . . . . . . . . . . . . . . . . 102
A.2 Fourier Grid Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
A.3 Iterative two-term Lanczos eigensolver . . . . . . . . . . . . . . . . . . . . . . 107CONTENTS iv
B Boundstate calculations for CO/Cu(100) 109
C Numerical methods to solve the Liouville-von Neumann equation 113
D Numerical method to solve the TDSE: The split-operator propagator
method 118
E Quantum chemical methods 119
E.1 Hartree-Fock theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
E.1.1 Hartree-Fock Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 120
E.2 Density functional theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
E.2.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
E.2.2 Kohn-Sham equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
E.3 Effective core potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
F A new parametrization of the CO/Cu(100) dipole function 125
G Non-Markovian theory 130
H Local control of vibrational excitation in a non-dissipative system 134

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