Computational methods in lanthanide and actinide chemistry

Contributors xiii Preface xvii 1 Relativistic Configuration Interaction Calculations for Lanthanide and Actinide Anions 1 Donald R. Beck, Steven M. O’Malley and Lin Pan 1.1 Introduction 1 1.2 Bound Rare Earth Anion States 2 1.3 Lanthanide and Actinide Anion Survey 3 1.3.1 Prior Results and Motivation for the Survey 3 1.3.2 Techniques for Basis Set Construction and Analysis 6 1.3.3 Discussion of Results 9 1.4 Resonance and Photodetachment Cross Section of Anions 12 1.4.1 The Configuration Interaction in the Continuum Formalism 13 1.4.2 Calculation of the Final State Wavefunctions 15 2 Study of Actinides by Relativistic Coupled Cluster Methods 23 Ephraim Eliav and Uzi Kaldor 2.1 Introduction 23 2.2 Methodology 25 2.2.1 The Relativistic Hamiltonian 25 2.2.2 Fock-Space Coupled Cluster Approach 25 2.2.3 The Intermediate Hamiltonian CC method 27 2.3 Applications to Actinides 30 2.3.1 Actinium and Its Homologues: Interplay of Relativity and Correlation 31 2.3.2 Thorium and Eka-thorium: Different Level Structure 35 2.3.3 Rn-like actinide ions 39 2.3.4 Electronic Spectrum of Superheavy Elements Nobelium (Z=102) and Lawrencium (Z=103) 42 2.3.5 The Levels of U4+ and U5+: Dynamic Correlation and Breit Interaction 45 2.3.6 Relativistic Coupled Cluster Approach to Actinide Molecules 48 2.4 Summary and Conclusion 49 3 Relativistic All-Electron Approaches to the Study of f Element Chemistry 55 Trond Saue and Lucas Visscher 3.1 Introduction 55 3.2 Relativistic Hamiltonians 59 3.2.1 General Aspects 59 3.2.2 Four-Component Hamiltonians 61 3.2.3 Two-Component Hamiltonians 65 3.2.4 Numerical Example 69 3.3 Choice of Basis Sets 71 3.4 Electronic Structure Methods 73 3.4.1 Coupled Cluster Approaches 75 3.4.2 Multi-Reference Perturbation Theory 80 3.4.3 (Time-Dependent) Density Functional Theory 82 3.5 Conclusions and Outlook 83 4 Low-Lying Excited States of Lanthanide Diatomics Studied by Four-Component Relativistic Configuration Interaction Methods 89 Hiroshi Tatewaki, Shigeyoshi Yamamoto and Hiroko Moriyama 4.1 Introduction 89 4.2 Method of Calculation 90 4.2.1 Quaternion Symmetry 90 4.2.2 Basis Set and HFR/DC Method 91 4.2.3 GOSCI and RASCI Methods 91 4.3 Ground State 92 4.3.1 CeO Ground State 92 4.3.2 CeF Ground State 97 4.3.3 Discussion of Bonding in CeO and CeF 101 4.3.4 GdF Ground State 102 4.3.5 Summary of the Chemical Bonds, of CeO, CeF, GdF 104 4.4 Excited States 106 4.4.1 CeO Excited States 106 4.4.2 CeF Excited States 108 4.4.3 GdF Excited States 108 4.5 Conclusion 116 5 The Complete-Active-Space Self-Consistent-Field Approach and Its Application to Molecular Complexes of the f-Elements 121 Andrew Kerridge 5.1 Introduction 121 5.1.1 Treatment of Relativistic Effects 123 5.1.2 Basis Sets 123 5.2 Identifying and Incorporating Electron Correlation 124 5.2.1 The Hartree Product Wavefunction 124 5.2.2 Slater Determinants and Fermi Correlation 124 5.2.3 Coulomb Correlation 126 5.3 Configuration Interaction and the Multiconfigurational Wavefunction 127 5.3.1 The Configuration Interaction Approach 127 5.3.2 CI and the Dissociation of H2 128 5.3.3 Static Correlation and Crystal Field Splitting 130 5.3.4 Size Inconsistency and Coupled Cluster Theory 131 5.3.5 Computational Expense of CI and the Need for Truncation 132 5.4 CASSCF and Related Approaches 133 5.4.1 The Natural Orbitals 133 5.4.2 Optimisation of the CASSCF Wavefunction 133 5.4.3 Variants and Generalisations of CASSCF 137 5.5 Selection of Active Spaces 138 5.5.1 Chemical Intuition and Björn’s Rules 138 5.5.2 Natural Orbital Occupations 139 5.5.3 RAS Probing 139 5.6 Dynamical Correlation 139 5.6.1 Multireference Configuration Interaction 140 5.6.2 Multireference Second Order Perturbation Theory 140 5.7 Applications 141 5.7.1 Bonding in Actinide Dimers 141 5.7.2 Covalent Interactions in the U-O Bond of Uranyl 142 5.7.3 Covalency and Oxidation State in f-Element Metallocenes 143 5.8 Concluding Remarks 144 6 Relativistic Pseudopotentials and Their Applications 147 Xiaoyan Cao and Anna Weigand 6.1 Introduction 147 6.2 Valence-only Model Hamiltonian 149 6.2.1 Pseudopotentials 150 6.2.2 Approximations 151 6.2.3 Choice of the Core 153 6.3 Pseudopotential Adjustment 155 6.3.1 Energy-Consistent Pseudopotentials 155 6.3.2 Shape-Consistent Pseudopotentials 158 6.4 Valence Basis Sets for Pseudopotentials 161 6.5 Selected Applications 162 6.5.1 DFT Calculated M–X (M = Ln, An; X = O, S, I) Bond Lengths 163 6.5.2 Lanthanide(III) and Actinide(III) Hydration 166 6.5.3 Lanthanide(III) and Actinide(III) Separation 170 6.6 Conclusions and Outlook 172 7 Error-Balanced Segmented Contracted Gaussian Basis Sets: A Concept and Its Extension to the Lanthanides 181 Florian Weigend 7.1 Introduction 181 7.2 Core and Valence Shells: General and Segmented Contraction Scheme 182 7.3 Polarization Functions and Error Balancing 185 7.4 Considerations for Lanthanides 187 8 Gaussian Basis Sets for Lanthanide and Actinide Elements: Strategies for Their Development and Use 195 Kirk A. Peterson and Kenneth G. Dyall 8.1 Introduction 195 8.2 Basis Set Design 196 8.2.1 General Considerations 196 8.2.2 Basis Sets for the f Block 197 8.3 Overview of Existing Basis Sets for Lanthanides and Actinide Elements 204 8.3.1 All-Electron Treatments 204 8.3.2 Effective Core Potential Treatments 205 8.4 Systematically Convergent Basis Sets for the f Block 206 8.4.1 All-Electron 207 8.4.2 Pseudopotential-Based 208 8.5 Basis Set Convergence in Molecular Calculations 210 8.6 Conclusions 213 9 4f, 5d, 6s, and Impurity-Trapped Exciton States of Lanthanides in Solids 217 Zoila Barandiarán and Luis Seijo 9.1 Introduction 217 9.2 Methods 220 9.2.1 Embedded-Cluster Methods 221 9.2.2 Combined Use of Periodic Boundary Condition Methods and Embedded Cluster Methods 227 9.2.3 Absorption and Emission Spectra 227 9.3 Applications 228 9.3.1 Bond Lengths 228 9.3.2 Energy Gaps 231 9.3.3 Impurity-Trapped Excitons 232 9.3.4 Solid-State-Lighting Phosphors 234 10 Judd-Ofelt Theory — The Golden (and the Only One) Theoretical Tool of f-Electron Spectroscopy 241 Lidia Smentek 10.1 Introduction 241 10.2 Non-relativistic Approach 245 10.2.1 Standard Judd-Ofelt Theory and Its Original Formulation of 1962 248 10.2.2 Challenges of ab initio Calculations 251 10.2.3 Problems with the Interpretation of the f -Spectra 255 10.3 Third-Order Contributions 257 10.3.1 Third-Order Electron Correlation Effective Operators 259 10.4 Relativistic Approach 260 10.5 Parameterizations of the f -Spectra 262 11 Applied Computational Actinide Chemistry 269 André Severo Pereira Gomes, Florent Réal, Bernd Schimmelpfennig, Ulf Wahlgren and Valérie Vallet 11.1 Introduction 269 11.1.1 Relativistic Correlated Methods for Ground and Excited States 270 11.1.2 Spin-Orbit Effects on Heavy Elements 272 11.2 Valence Spectroscopy and Excited States 273 11.2.1 Accuracy of Electron Correlation Methods for Actinide Excited States: WFT and DFT Methods 273 11.2.2 Valence Spectra of Larger Molecular Systems 275 11.2.3 Effects of the Condensed-Phase Environment 276 11.2.4 Current Challenges for Electronic Structure Calculations of Heavy Elements 278 11.3 Core Spectroscopies 278 11.3.1 X-ray Photoelectron Spectroscopy (XPS) 279 11.3.2 X-ray Absorption Spectroscopies 280 11.4 Complex Formation and Ligand-Exchange Reactions 283 11.5 Calculations of Standard Reduction Potential and Studies of Redox Chemical Processes 286 11.6 General Conclusions 288 12 Computational Tools for Predictive Modeling of Properties in Complex Actinide Systems 299 Jochen Autschbach, Niranjan Govind, Raymond Atta-Fynn, Eric J. Bylaska, John W. Weare and Wibe A. de Jong 12.1 Introduction 299 12.2 ZORA Hamiltonian and Magnetic Property Calculations 300 12.2.1 ZORA Hamiltonian 300 12.2.2 Magnetic properties 303 12.3 X2C Hamiltonian and Molecular Properties from X2C Calculations 312 12.4 Role of Dynamics on Thermodynamic Properties 319 12.4.1 Sampling Free Energy Space with Metadynamics 319 12.4.2 Hydrolysis constants for U(IV), U(V), and U(VI) 320 12.4.3 Effects of Counter Ions on the Coordination of Cm(III) in Aqueous Solution 322 12.5 Modeling of XAS (EXAFS, XANES) Properties 325 12.5.1 EXAFS of U(IV) and U(V) Species 327 12.5.2 XANES Spectra of Actinide Complexes 330 13 Theoretical Treatment of the Redox Chemistry of Low Valent Lanthanide and Actinide Complexes 343 Christos E. Kefalidis, Ludovic Castro, Ahmed Yahia, Lionel Perrin and Laurent Maron 13.1 Introduction 343 13.2 Divalent Lanthanides 349 13.2.1 Computing the Nature of the Ground State 349 13.2.2 Single Electron Transfer Energy Determination in Divalent Lanthanide Chemistry 352 13.3 Low-Valent Actinides 356 13.3.1 Actinide(III) Reactivity 356 13.3.2 Other Oxidation State (Uranyl…) 361 13.4 Conclusions 365 14 Computational Studies of Bonding and Reactivity in Actinide Molecular Complexes 375 Enrique R. Batista, Richard L. Martin and Ping Yang 14.1 Introduction 375 14.2 Basic Considerations 376 14.2.1 Bond Energies 376 14.2.2 Effect of Scalar Relativistic Corrections 377 14.2.3 Spin-Orbit Corrections 378 14.2.4 Relativistic Effective Core Potentials (RECP) 379 14.2.5 Basis Sets 380 14.2.6 Density Functional Approximations for Use with f-Element Complexes 381 14.2.7 Example of application: Performance in Sample Situation (UF6→UF5 +F) [39, 40] 382 14.2.8 Molecular Systems with Unpaired Electrons 384 14.3 Nature of Bonding Interactions 385 14.4 Chemistry Application: Reactivity 387 14.4.1 First Example: Study of C–H Bond Activation Reaction 387 14.4.2 Study of Imido-Exchange Reaction Mechanism 395 14.5 Final Remarks 397 15 The 32-Electron Principle: A New Magic Number 401 Pekka Pyykkö, Carine Clavaguéra and Jean-Pierre Dognon 15.1 Introduction 401 15.1.1 Mononuclear, MLn systems 401 15.1.2 Metal Clusters as ‘Superatoms’ 402 15.1.3 The Present Review: An@Ln-Type Systems 404 15.2 Cases So Far Studied 404 15.2.1 The Early Years: Pb2−12 and Sn2−12 Clusters 404 15.2.2 The Validation: An@C28 (An = Th, Pa+, U2+, Pu4+) Series 410 15.2.3 The Confirmation: [U@Si20]6−-like Isoelectronic Series 413 15.3 Influence of Relativity 418 15.4 A Survey of the Current Literature on Lanthanideand Actinide-Centered Clusters 420 15.5 Concluding Remarks 421 16 Shell Structure, Relativistic and Electron Correlation Effects in f Elements and Their Importance for Cerium(III)-based Molecular Kondo Systems 425 Michael Dolg 16.1 Introduction 425 16.2 Shell Structure, Relativistic and Electron Correlation Effects 429 16.2.1 Shell Structure 430 16.2.2 Relativistic Effects 433 16.2.3 Electron Correlation Effects 437 16.3 Molecular Kondo-type Systems 439 16.3.1 Bis(η8-cyclooctatetraenyl)cerium 440 16.3.2 Bis(η8-pentalene)cerium 443 16.4 Conclusions 446 Index 451 Color plates appear between pages 342 and 343