Wave function based relativistic multi-reference electron correlation methods [Elektronische Ressource] : development and application to atomic and molecular properties / Timo Fleig

Informations

• Publié par: heinrich-heine-universitat_dusseldorf
• Publié le: 01 janvier 2007
• Nombre de lectures: 17
• Langue: English

Extrait

Wave Function Based
Relativistic Multi-Reference
Electron Correlation Methods.
Development and Application
to Atomic and Molecular
Properties.
Habilitationsschrift
zur Erlangung der venia legendi
fur¨ das Fach Theoretische Chemie
an der Mathematisch–Naturwissenschaftlichen Fakult¨at
der Heinrich-Heine-Universit¨at Dus¨ seldorf
Timo Fleig
Dusseldorf¨ 2006Angefertigt mit Genehmigung der
Mathematisch-Naturwissenschaftlichen Fakult¨at
der Heinrich-Heine-Universit¨at Duss¨ eldorffor my beloved wife and children[about thought and deception; science defined]
We conclude, therefore, that the argument from religious experience is altogether
fallacious. The fact that people have religious experiences is interesting from the
psychological point of view, but it does not in any way imply that there is such a
thing as religious knowledge, any more than our having moral experiences implies
that there is such a thing as moral knowledge. The theist, like the moralist, may
believe that his experiences are cognitive experiences, but, unless he can formulate
his “knowledge” in propositions that are empirically verifiable, we may be sure that
he is deceiving himself. It follows that those philosophers who fill their books with
assertions that they intuitively “know” this or that moral or religious “truth” are
merely providing material for the psycho-analyst. For no act of intuition can be
said to reveal a truth about any matter of fact unless it issues in verifiable propo-
sitions. And all such propositions are to be incorporated in the system of empirical
propositions which constitutes science.
Alfred Jules Ayer [1]Contents
Introduction 1
I State of the Art 5
1 Heavy-Element Properties and Methods 9
1.1 Spectroscopic Properties . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.1.1 Density Functional Theory . . . . . . . . . . . . . . . . . . . . 9
1.1.2 Wave Function Based Correlation Methods . . . . . . . . . . . 12
1.2 Electric Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
II Method Development 17
2 Relativistic MRCI 21
2.1 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1.1 Previous relativistic implementations . . . . . . . . . . . . . . 22
2.1.2 Scope of the Method . . . . . . . . . . . . . . . . . . . . . . . 24
2.2 Relativistic CI Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.1 Generalized Active Spaces (GAS) . . . . . . . . . . . . . . . . 27
2.2.2 Excitation Class Formalism . . . . . . . . . . . . . . . . . . . 30
2.2.3 Projected Vectors and Density Matrices . . . . . . . . . . . . 33
2.2.4 Relativistic GASCI in an overview . . . . . . . . . . . . . . . 35
2.3 Approximate Schemes: Spin-orbit Free CI . . . . . . . . . . . . . . . 36
2.3.1 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3.2 Previous Implementations . . . . . . . . . . . . . . . . . . . . 37
2.3.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3.4 Scope of the Method . . . . . . . . . . . . . . . . . . . . . . . 38
2.3.5 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3 Relativistic MCSCF Technique 41
3.1 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.1.1 Previous Relativistic Implementations . . . . . . . . . . . . . 42
3.1.2 Scope of the Method . . . . . . . . . . . . . . . . . . . . . . . 43
v3.2 Relativistic MCSCF Theory . . . . . . . . . . . . . . . . . . . . . . . 44
3.2.1 Furry picture . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2.2 MCSCF Parameterization . . . . . . . . . . . . . . . . . . . . 44
3.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.1 Optimization algorithm. . . . . . . . . . . . . . . . . . . . . . 45
3.3.2 Direct MCSCF algorithm . . . . . . . . . . . . . . . . . . . . 46
3.3.3 Large-scale MCSCF implementation . . . . . . . . . . . . . . 48
3.3.4 Further technical remarks . . . . . . . . . . . . . . . . . . . . 50
4 Relativistic MRCC Theory 51
4.1 General Coupled Cluster Theory. . . . . . . . . . . . . . . . . . . . . 51
4.1.1 Previous Relativistic Implementations . . . . . . . . . . . . . 52
4.1.2 Scope of the Method . . . . . . . . . . . . . . . . . . . . . . . 52
4.2 State-Selective Multi-Reference Approach . . . . . . . . . . . . . . . . 53
4.3 Spin-Dependent MRCC Implementation . . . . . . . . . . . . . . . . 54
4.3.1 Unrestricted Generalization . . . . . . . . . . . . . . . . . . . 54
4.3.2 Kramers-Restricted Formalism . . . . . . . . . . . . . . . . . . 55
4.3.3 Kramers-Adapted Fo . . . . . . . . . . . . . . . . . . 57
4.4 Spin-Free MRCC Implementation . . . . . . . . . . . . . . . . . . . . 58
4.4.1 Previous Implementations . . . . . . . . . . . . . . . . . . . . 59
4.4.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4.3 Scope of the Method . . . . . . . . . . . . . . . . . . . . . . . 59
4.4.4 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
III Application 61
5 Spectroscopic Properties 65
5.1 Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.1.1 Main group atoms . . . . . . . . . . . . . . . . . . . . . . . . 66
5.1.2 Lanthanide and actinide atoms . . . . . . . . . . . . . . . . . 68
5.2 Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2.1 Small Molecules with Light Atoms . . . . . . . . . . . . . . . 70
5.2.2 Molecules with One Heavy Atom . . . . . . . . . . . . . . . . 71
5.2.3s with Two Heavy Atoms . . . . . . . . . . . . . . . . 80
6 Electric Properties 83
6.1 Methods for Property Calculations . . . . . . . . . . . . . . . . . . . 83
6.1.1 Analytical Methods . . . . . . . . . . . . . . . . . . . . . . . . 83
6.1.2 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . 84
6.2 Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.2.1 Electric Dipole Polarizabilities . . . . . . . . . . . . . . . . . . 85
6.3 Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 906.3.1 Electric Dipole Moments . . . . . . . . . . . . . . . . . . . . . 90
6.3.2 Electric Dipole Polarizabilities . . . . . . . . . . . . . . . . . . 90
6.3.3 Electric Field Gradients . . . . . . . . . . . . . . . . . . . . . 91
Summary (in german) 93List of Figures
1.1 Wave function based quantum chemical models . . . . . . . . . . . . 12
1.2 4-Component Electron Correlation Methods . . . . . . . . . . . . . . 20
2.1 Generalized Active Spaces . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2 Hamiltonian matrix for a 6-particle system . . . . . . . . . . . . . . . 35
3.1 MCSCF program flow chart . . . . . . . . . . . . . . . . . . . . . . . 47
5.1 CASSCF potential curves of AuO . . . . . . . . . . . . . . . . . . . . 73
5.2 GAS setup for core-valence-type of correlation treatments . . . . . . . 77
5.3 Relativistic and correlation effects in CsLi . . . . . . . . . . . . . . . 79
6.1 Group-13 polarizabilities and polarizability anisotropy components . . 89
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