Electron spin-spin coupling from multireference CI wave functions [Elektronische Ressource] / vorgelegt von Natalie Gilka

Informations

• Publié par: heinrich-heine-universitat_dusseldorf
• Publié le: 01 janvier 2008
• Nombre de lectures: 17
• Langue: English
• Poids de l'ouvrage: 9 Mo

Extrait

Electron Spin-Spin Coupling
from Multireference CI Wave Functions
Inaugural-Dissertation
zur
Erlangung des Doktorgrades der
Mathematisch-Naturwissenschaftlichen Fakult¨at
der Heinrich-Heine-Universit¨at Dusseldo¨ rf
vorgelegt von
Natalie Gilka
aus Bydgoszcz (Polen)
April 2008Aus dem Institut fur¨ Theoretische Chemie und Computerchemie
der Heinrich-Heine-Universit¨at Duss¨ eldorf
Gedruckt mit der Genehmigung der
Mathematisch-Naturwissenschaftlichen Fakult¨at
der Heinrich-Heine-Universit¨at Duss¨ eldorf
Referentin: Prof. Dr. Christel M. Marian
Korreferent: Prof. Dr. Walter Thiel
Externer Referent: Prof. Dr. Frank Neese
Tag der mundlichen¨ Prufung:¨ 23.06.2008Contents
Introduction 1
1 Framework 3
1.1 Electron Spin-Spin Coupling: General Framework . . . . . . . . . . . . 4
1.1.1 Primary Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.2 Assessment of the Experimental Framework . . . . . . . . . . . 7
1.1.3 Historically: Calculations of Electron Spin-Spin Coupling . . . . 10
1.1.4 Present Theoretical Work . . . . . . . . . . . . . . . . . . . . . 13
1.1.5 Conclusion: Concerted Considerations . . . . . . . . . . . . . . 19
1.2 Theoretical Chemistry at Dusseldorf¨ – SFB 663 . . . . . . . . . . . . . 20
1.3 Computational Considerations . . . . . . . . . . . . . . . . . . . . . . . 22
1.4 Program Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.5 Theoretical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.5.1 Expression of the Operator . . . . . . . . . . . . . . . . . . . . . 28
Wigner-Eckart Theorem . . . . . . . . . . . . . . . . . . . . . . 30
Second Quantization . . . . . . . . . . . . . . . . . . . . . . . . 31
1.5.2 Matrix Elements . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Algorithm: η-Pattern: spin-free . . . . . . . . . . . . . . . . . . 33 η-P spin-dependent . . . . . . . . . . . . . . 35
1.6 Experimental Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 36
1.7 Final Remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2 Computational Structure 41
2.1 Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2 Calculation of Matrix Elements . . . . . . . . . . . . . . . . . . . . . . 45
2.2.1 Spin-Spin Operator . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.2.2 Derivation – Part (I) . . . . . . . . . . . . . . . . . . . . . . . . 52
Selection Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Contribution of Closed Shells . . . . . . . . . . . . . . . . . . . 55
Permutational Relation . . . . . . . . . . . . . . . . . . . . . . . 57
2.2.3 Derivation – Part (II). . . . . . . . . . . . . . . . . . . . . . . . 61
Anticommutation . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Insertion of Resolution of Identity . . . . . . . . . . . . . . . . . 63
Sequence of Spin Terms . . . . . . . . . . . . . . . . . . . . . . 63
ΔS =2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
ΔS =1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
56 Contents
ΔS =0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.2.4 Implemented Formulas . . . . . . . . . . . . . . . . . . . . . . . 75
2.2.5 Spatial Integrals. . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Principal scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Existing Approach in Dalton . . . . . . . . . . . . . . . . . . . . 81
2.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
2.3.1 Program Execution . . . . . . . . . . . . . . . . . . . . . . . . . 91
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3 Calculations 93
3.1 O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 942
3.1.1 One- vs. Two-Center Contributions . . . . . . . . . . . . . . . . 95
3.1.2 Augmented vs. Non-Augmented Basis Sets . . . . . . . . . . . . 97
3.1.3 Effect of Selected Reference Configurations . . . . . . . . . . . . 98
3.1.4 Convergence with Space . . . . . . . . . . . . . . . . 100
3.1.5 Evaluation of Results for O . . . . . . . . . . . . . . . . . . . . 1022
3.2 NH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.3 All-trans Polyenes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.3.1 Discussion of MOs . . . . . . . . . . . . . . . . . . . . . . . . . 108
3.3.2 Hexatriene: Comparison of dft/mrci, hf/mrci, and CASSCF 111
3.3.3 dft/mrci: Basis Set Comparison . . . . . . . . . . . . . . . . . 113
3.3.4ci: Results for C H – C H . . . . . . . . . . . . . . 1156 8 16 34
3.3.5 All-trans Polyenes: Conclusions . . . . . . . . . . . . . . . . . . 116
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Summary and Outlook 119
List of Tables 121
List of Figures 123
Acknowledgement 141Introduction
Understanding the laws of nature and elucidating their functioning is the fundamental
motivation in the natural sciences. In the evolution of life, this functioning is strongly
determinedbyourmainnaturalsourceofenergy, thesun. Onabiochemicallevel, sun-
light initiates a multitude of processes involving excited states of molecules, thereby
constituting the driving force in the astonishing complexity of what we simply call
“living”.
Theseprocessesusuallyinvolvedirectexcitationofmolecularsystems,followedbysub-
sequentde-excitationthroughavarietyofpossiblemechanisms. Consideringespecially
the numerous pathways molecules in biological environments can follow in redistribut-
ingtheirexcessenergy,itisnotsurprisingtoreflectthatwearefarfromunderstanding
the functioning of biological organisms. Nonetheless, concerted efforts from both the
experimental and theoretical sides constitute a promising approach, successively re-
vealing facets of the entire composition.
Thetheoreticalcommunityhasaprofoundrecordofsuccessintheconsiderationofsys-
tems at equilibrium. Investigation of excited states, in particular the of
reaction mechanisms, necessitates entirely different approaches, however. A molecule
undergoes conformational reorientations accompanied by changes in the structure of
its energy levels, opening possibilities for intricate energy redistributions and coupling
to different states, conceivably involving neighbouring molecules. Excitation from the
singlet to the triplet manifold can be a crucial aspect in this process and necessitates
the consideration of spin interactions. From a theoretical perspective, this involves the
evaluationofspincouplingeffectsfrequentlysmallinmagnitude, theconceptualorigin
of which lies in the consideration of special relativity.
ThegroupofTheoreticalandComputationalChemistryattheUniversityofDusseldorf¨
provides profound competence in the sophisticated electronic structure treatment of
excited states of medium-sized systems through the efficient dft/mrci approach [1].
This is combined with considerable experience in the calculation of spin-orbit coupling
effects employing the program spock [2–4]. This expertise is brought to applications
in the Sonderforschungsbereich (SFB) 663 “Molecular Response to Electronic Excita-
tion”. The incentive of the SFB 663 is the investigation of processes of photostability
and photoreactivity; its particular strength lies in the interdisciplinary approach of
experimental and theoretical fields.
The present work is motivated by an extension of the capabilities of our group. It
12 Introduction
presents the development and theoretical consideration of the calculation of coupling
effects between the spins of unpaired electrons (spin-spin coupling). The impact of
this work is twofold: First, electron spin-spin interaction, like spin-orbit interaction,
constitutes a possible coupling mechanism in processes of excitation and de-excitation.
Understanding the origin of these transitions is mandatory for an explanation of bio-
chemical reactions. Second, spin-spin coupling can be employed as a means of investi-
gatingthestructureofexcitedstates. Themagnitudeofthisinteractionisanindicator
of the distance between unpaired electrons. This has already been employed in an ex-
perimental context and the combination with the theoretical approach is particularly
promising for obtaining insight into the location of radical electrons in molecular sys-
tems, thereby clarifying processes of energy dissipation.
Calculations in the field of electron spin-spin coupling have been very limited. This
observation is related to the high demand that the implementation of this operator
poses, motivated by its complicated structure. The present work represents one of the
first efforts in the implementation of this effect based on a computational treatment
that considers dynamical as well as non-dynamical correlation contributions and al-
lows for the computation of medium-sized systems. It is novel as it is one of the few
approaches that considers the relevant correlation effects on an equal basis, allows for
the calculation of excited states due to its multireference approach, and furthermore
enables the consideration of larger systems due to the efficient selecting algorithm of
the underlying correlation treatment. The present work will thereby not only assist in
theultimateelucidationofthei