Mulak / Gajek The Effective Crystal Field Potential

1. Auflage 2000
ISBN: 978-0-08-053071-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 316 Seiten, Web PDF

As it results from the very nature of things, the spherical symmetry of the surrounding of a site in a crystal lattice or an atom in a molecule can never occur. Therefore, the eigenfunctions and eigenvalues of any bound ion or atom have to differ from those of spherically symmetric respective free ions. In this way, the most simplified concept of the crystal field effect or ligand field effect in the case of individual molecules can be introduced.
The conventional notion of the crystal field potential is narrowed to its non-spherical part only through ignoring the dominating spherical part which produces only a uniform energy shift of gravity centres of the free ion terms. It is well understood that the non-spherical part of the effective potential 'seen' by open-shell electrons localized on a metal ion plays an essential role in most observed properties. Light adsorption, electron paramagnetic resonance, inelastic neutron scattering and basic characteristics derived from magnetic and thermal measurements, are only examples of a much wider class of experimental results dependent on it. The influence is discerned in all kinds of materials containing unpaired localized electrons: ionic crystals, semiconductors and metallic compounds including materials as intriguing as high-Tc superconductors, or heavy fermion systems. It is evident from the above that we deal with a widespread effect relative to all free ion terms except those which can stand the lowered symmetry, e.g. S-terms.
Despite the universality of the phenomenon, the available handbooks on solid state physics pay only marginal attention to it, merely making mention of its occurrence. Present understanding of the origins of the crystal field potential differs essentially from the pioneering electrostatic picture postulated in the twenties. The considerable development of the theory that has been put forward since then can be traced in many regular articles scattered throughout the literature. The last two decades have left their impression as well but, to the authors' best knowledge, this period has not been closed with a more extended review. This has also motivated us to compile the main achievements in the field in the form of a book.

Autoren/Hrsg.

Mulak, J.

Gajek, Z.

Inhaltsverzeichnis

1;Cover;1
2;Contents ;10
3;Chapter 1. Introduction;16
4;Chapter 2. Parameterization of crystal field Hamiltonian;26
4.1;2.1. Operators and parameters of the crystal field Hamiltonian;27
4.2;2.2. Basic parameterizations;29
4.3;2.3. Symmetry transformations of the operators;33
4.4;2.4. The number of independent crystal field parameters;38
4.5;2.5. Standardization of the crystal field Hamiltonian;41
4.6;2.6. Final remark;44
5;Chapter 3. The effective crystal field potential. Chronological development of crystal field models;46
6;Chapter 4. Ionic complex or quasi-molecular cluster. Generalized product function;56
6.1;4.1 Concept of the generalized product function;56
6.2;4.2 The density functions and the transition density functions;58
6.3;4.3 Model of the generalized product functions;59
6.4;4.4 Crystal field effect in the product function model;64
7;Chapter 5. Point charge model (PCM);68
7.1;5.1 PCM potential and its parameters;68
7.2;5.2 Simple partial PCM potentials;71
7.3;5.3 Extension of PCM–higher point multipole contribution;76
8;Chapter 6. One-configurational model with neglecting the non-orthogonality. The charge penetration and exchange effects;80
8.1;6.1 Classical electrostatic potential produced by the ligand charge distribution;80
8.2;6.2 The charge penetration effect and the exchange interaction in the generalized product function model;83
8.3;6.3 The weight of the penetration and exchange effects in the crystal field potential;86
8.4;6.4 Calculation of the two-centre integrals;88
8.5;6.5 Final remarks;89
9;Chapter 7. The exclusion model. One-configurational approach with regard to non-orthogonality of the wave functions;92
9.1;7.1 Three types of the non-orthogonality;92
9.2;7.2 The renormalization of the open-shell Hamiltonian Ha owing to the non-orthogonality of the one-electron functions;94
9.3;7.3 The contact-covalency–the main component of the crystal field potential;99
9.4;7.4 The contact-shielding;102
9.5;7.5 The contact-polarization;103
9.6;7.6 Mechanisms of the contact-shielding and contact-polarization in terms of the exchange charge notion;103
10;Chapter 8. Covalency contribution, i.e. the charge transfer effect;106
10.1;8.1 The one-electron excitations. Group product function for the excited state;106
10.2;8.2 The renormalization of the open-shell Hamiltonian due to the covalency effect;109
10.3;8.3 Basic approximations;111
10.4;8.4 The one-electron covalency potential Vcov;112
10.5;8.5 The one-electron covalency potential V cov in the molecular-orbital formalism;116
10.6;8.6 Remarks on the covalency mechanism;117
11;Chapter 9. Schielding and antishielding effect: contributions from closed electron shells;120
11.1;9.1 Phenomenological quantification of the screening effect;121
11.2;9.2 Microscopic model of the screening effect;122
11.3;9.3 General expressions for the screening factors;124
11.4;9.4 The screening factors;131
12;Chapter 10. Electrostatic crystal field contributions with consistent multipolar effects. Polarization;134
12.1;10.1 Expansion of the electrostatic potential of point charge system into the multipole series;134
12.2;10.2 Extended formula for the crystal field parameters including all multipole moments of the surroundings;136
12.3;10.3 The self-consistent system of permanent and induced multipole moments in crystal lattice;141
12.4;10.4 The off-axial polarization terms in local coordinate systems.;142
12.5;10.5 Typical examples of dipole and quadrupole polarization contributions to the crystal field potential;144
13;Chapter 11. Crystal field effect in the Stevens perturbation approach;146
13.1;11.1 The Wannier functions;147
13.2;11.2 The perturbation scheme for degenerate systems employing projection operators;148
13.3;11.3 The crystal field effect;151
14;Chapter 12. Specific mechanisms of metallic states contributing to the crystal field potential;158
15;Chapter 13. Screening the crystal field in metallic materials;162
15.1;13.1 The Fourier form of the crystal lattice potential;164
15.2;13.2 The dielectric static screening function e(q);168
15.3;13.3 The dynamic mechanism of the screening - zero-point plasmon;174
16;Chapter 14. Virtual bound state contribution to the crystal field potential;178
16.1;14.1 The resonance scattering of conduction electrons by a central potential;178
16.2;14.2 The nature of the virtual bound state;181
16.3;14.3 Spin-polarization of the virtual bound state;182
16.4;14.4 Experimental manifestations of existing the virtual bound states and methods of estimating their localization degree;182
16.5;14.5 The crystal field splitting of the virtual bound state;183
16.6;14.6 The primary crystal field effect relative to the open-shell states (4f);184
16.7;14.7 Corrections to the simple model of the virtual bound state mechanism;189
17;Chapter 15. Hybridization or covalent mixing between localized states and conduction band states in metallic crystals;192
17.1;15.1 The essence of the hybridization;192
17.2;15.2 Hybridization contribution to the crystal field parameters;193
17.3;15.3 The scale of the hybridization effect;197
17.4;15.4 Contribution to the crystal field potential from a split-off state from the conduction band in impurity systems;199
18;Chapter 16. Density functional theory approach;200
18.1;16.1 Electron density as a key variable;200
18.2;16.2 The Kohn–Sham equations;203
18.3;16.3 Local density approximation;205
18.4;16.4 Extensions;207
18.5;16.5 Exchange-correlation energy;216
18.6;16.6 Mapping DFT on effective Hamiltonian;219
18.7;16.7 Applications;221
19;Chapter 17. Analysis of the experimental data . Interpretation of crystal field parameters with additive models;226
19.1;17.1 Phenomenological Hamiltonian;227
19.2;17.2 Simplified crystal field models;230
19.3;17.3 Towards applications;239
20;Chapter 18. Lattice dynamics contribution;244
20.1;18.1 Adiabatic and harmonic approximations;245
20.2;18.2 Collective (normal) coordinates and the "quasi-molecular" model;248
20.3;18.3 The Jahn-Teller effect;250
20.4;18.4 Lattice dynamics and the crystal field effect;256
21;Chapter 19. Extension of the crystal field potential beyond the one-electron model;262
21.1;19.1 Two-electron correlation effect in the crystal field model;262
21.2;19.2 Parameterization of the two-electron potential;263
21.3;19.3 The term dependent crystal field;265
21.4;19.4 Spin correlated crystal field (SCCF);267
21.5;19.5 Many-electron approach to the crystal field effect;269
22;Chapter 20. Appendices;272
22.1;A. Transformation from local to the global coordinate system;272
22.2;B. 3n-j symbols;274
22.3;C. Methods of orthogonalization of functions;276
23;References;278
24;Author Index;302
25;Subject Index;308