Computational Methods in Lanthanide and Actinide Chemistry

Michael Dolg, Institute for Theoretical Chemistry, University of Cologne, Germany. Professor Dolg works in the field of relativistic ab initio pseudopotentials, both their development and their applications. He performed the first wavefunction-based relativistic and correlated ab initio calculations on lanthanide compounds, in 1989, and in 1994 he extended his studies to actinides. He is currently working on various topics in lanthanide and actinide computational chemistry and is one of the leading scientists in this field.

• Contributors xiii Preface xvii1 Relativistic Configuration Interaction Calculations for Lanthanide and Actinide Anions 1Donald R. Beck, Steven M. O’Malley and Lin Pan1.1 Introduction 11.2 Bound Rare Earth Anion States 21.3 Lanthanide and Actinide Anion Survey 31.3.1 Prior Results and Motivation for the Survey 31.3.2 Techniques for Basis Set Construction and Analysis 61.3.3 Discussion of Results 91.4 Resonance and Photodetachment Cross Section of Anions 121.4.1 The Configuration Interaction in the Continuum Formalism 131.4.2 Calculation of the Final State Wavefunctions 152 Study of Actinides by Relativistic Coupled Cluster Methods 23Ephraim Eliav and Uzi Kaldor2.1 Introduction 232.2 Methodology 252.2.1 The Relativistic Hamiltonian 252.2.2 Fock-Space Coupled Cluster Approach 252.2.3 The Intermediate Hamiltonian CC method 272.3 Applications to Actinides 302.3.1 Actinium and Its Homologues: Interplay of Relativity and Correlation 312.3.2 Thorium and Eka-thorium: Different Level Structure 352.3.3 Rn-like actinide ions 392.3.4 Electronic Spectrum of Superheavy Elements Nobelium (Z=102) and Lawrencium (Z=103) 422.3.5 The Levels of U4+ and U5+: Dynamic Correlation and Breit Interaction 452.3.6 Relativistic Coupled Cluster Approach to Actinide Molecules 482.4 Summary and Conclusion 493 Relativistic All-Electron Approaches to the Study of f Element Chemistry 55Trond Saue and Lucas Visscher3.1 Introduction 553.2 Relativistic Hamiltonians 593.2.1 General Aspects 593.2.2 Four-Component Hamiltonians 613.2.3 Two-Component Hamiltonians 653.2.4 Numerical Example 693.3 Choice of Basis Sets 713.4 Electronic Structure Methods 733.4.1 Coupled Cluster Approaches 753.4.2 Multi-Reference Perturbation Theory 803.4.3 (Time-Dependent) Density Functional Theory 823.5 Conclusions and Outlook 834 Low-Lying Excited States of Lanthanide Diatomics Studied by Four-Component Relativistic Configuration Interaction Methods 89Hiroshi Tatewaki, Shigeyoshi Yamamoto and Hiroko Moriyama4.1 Introduction 894.2 Method of Calculation 904.2.1 Quaternion Symmetry 904.2.2 Basis Set and HFR/DC Method 914.2.3 GOSCI and RASCI Methods 914.3 Ground State 924.3.1 CeO Ground State 924.3.2 CeF Ground State 974.3.3 Discussion of Bonding in CeO and CeF 1014.3.4 GdF Ground State 1024.3.5 Summary of the Chemical Bonds, of CeO, CeF, GdF 1044.4 Excited States 1064.4.1 CeO Excited States 1064.4.2 CeF Excited States 1084.4.3 GdF Excited States 1084.5 Conclusion 1165 The Complete-Active-Space Self-Consistent-Field Approach and Its Application to Molecular Complexes of the f-Elements 121Andrew Kerridge5.1 Introduction 1215.1.1 Treatment of Relativistic Effects 1235.1.2 Basis Sets 1235.2 Identifying and Incorporating Electron Correlation 1245.2.1 The Hartree Product Wavefunction 1245.2.2 Slater Determinants and Fermi Correlation 1245.2.3 Coulomb Correlation 1265.3 Configuration Interaction and the Multiconfigurational Wavefunction 1275.3.1 The Configuration Interaction Approach 1275.3.2 CI and the Dissociation of H2 1285.3.3 Static Correlation and Crystal Field Splitting 1305.3.4 Size Inconsistency and Coupled Cluster Theory 1315.3.5 Computational Expense of CI and the Need for Truncation 1325.4 CASSCF and Related Approaches 1335.4.1 The Natural Orbitals 1335.4.2 Optimisation of the CASSCF Wavefunction 1335.4.3 Variants and Generalisations of CASSCF 1375.5 Selection of Active Spaces 1385.5.1 Chemical Intuition and Björn’s Rules 1385.5.2 Natural Orbital Occupations 1395.5.3 RAS Probing 1395.6 Dynamical Correlation 1395.6.1 Multireference Configuration Interaction 1405.6.2 Multireference Second Order Perturbation Theory 1405.7 Applications 1415.7.1 Bonding in Actinide Dimers 1415.7.2 Covalent Interactions in the U-O Bond of Uranyl 1425.7.3 Covalency and Oxidation State in f-Element Metallocenes 1435.8 Concluding Remarks 1446 Relativistic Pseudopotentials and Their Applications 147Xiaoyan Cao and Anna Weigand6.1 Introduction 1476.2 Valence-only Model Hamiltonian 1496.2.1 Pseudopotentials 1506.2.2 Approximations 1516.2.3 Choice of the Core 1536.3 Pseudopotential Adjustment 1556.3.1 Energy-Consistent Pseudopotentials 1556.3.2 Shape-Consistent Pseudopotentials 1586.4 Valence Basis Sets for Pseudopotentials 1616.5 Selected Applications 1626.5.1 DFT Calculated M–X (M = Ln, An; X = O, S, I) Bond Lengths 1636.5.2 Lanthanide(III) and Actinide(III) Hydration 1666.5.3 Lanthanide(III) and Actinide(III) Separation 1706.6 Conclusions and Outlook 1727 Error-Balanced Segmented Contracted Gaussian Basis Sets: A Concept and Its Extension to the Lanthanides 181Florian Weigend7.1 Introduction 1817.2 Core and Valence Shells: General and Segmented Contraction Scheme 1827.3 Polarization Functions and Error Balancing 1857.4 Considerations for Lanthanides 1878 Gaussian Basis Sets for Lanthanide and Actinide Elements: Strategies for Their Development and Use 195Kirk A. Peterson and Kenneth G. Dyall8.1 Introduction 1958.2 Basis Set Design 1968.2.1 General Considerations 1968.2.2 Basis Sets for the f Block 1978.3 Overview of Existing Basis Sets for Lanthanides and Actinide Elements 2048.3.1 All-Electron Treatments 2048.3.2 Effective Core Potential Treatments 2058.4 Systematically Convergent Basis Sets for the f Block 2068.4.1 All-Electron 2078.4.2 Pseudopotential-Based 2088.5 Basis Set Convergence in Molecular Calculations 2108.6 Conclusions 2139 4f, 5d, 6s, and Impurity-Trapped Exciton States of Lanthanides in Solids 217Zoila Barandiarán and Luis Seijo9.1 Introduction 2179.2 Methods 2209.2.1 Embedded-Cluster Methods 2219.2.2 Combined Use of Periodic Boundary Condition Methods and Embedded Cluster Methods 2279.2.3 Absorption and Emission Spectra 2279.3 Applications 2289.3.1 Bond Lengths 2289.3.2 Energy Gaps 2319.3.3 Impurity-Trapped Excitons 2329.3.4 Solid-State-Lighting Phosphors 23410 Judd-Ofelt Theory — The Golden (and the Only One) Theoretical Tool of f-Electron Spectroscopy 241Lidia Smentek10.1 Introduction 24110.2 Non-relativistic Approach 24510.2.1 Standard Judd-Ofelt Theory and Its Original Formulation of 1962 24810.2.2 Challenges of ab initio Calculations 25110.2.3 Problems with the Interpretation of the f -Spectra 25510.3 Third-Order Contributions 25710.3.1 Third-Order Electron Correlation Effective Operators 25910.4 Relativistic Approach 26010.5 Parameterizations of the f -Spectra 26211 Applied Computational Actinide Chemistry 269André Severo Pereira Gomes, Florent Réal, Bernd Schimmelpfennig, Ulf Wahlgren and Valérie Vallet11.1 Introduction 26911.1.1 Relativistic Correlated Methods for Ground and Excited States 27011.1.2 Spin-Orbit Effects on Heavy Elements 27211.2 Valence Spectroscopy and Excited States 27311.2.1 Accuracy of Electron Correlation Methods for Actinide Excited States: WFT and DFT Methods 27311.2.2 Valence Spectra of Larger Molecular Systems 27511.2.3 Effects of the Condensed-Phase Environment 27611.2.4 Current Challenges for Electronic Structure Calculations of Heavy Elements 27811.3 Core Spectroscopies 27811.3.1 X-ray Photoelectron Spectroscopy (XPS) 27911.3.2 X-ray Absorption Spectroscopies 28011.4 Complex Formation and Ligand-Exchange Reactions 28311.5 Calculations of Standard Reduction Potential and Studies of Redox Chemical Processes 28611.6 General Conclusions 28812 Computational Tools for Predictive Modeling of Properties in Complex Actinide Systems 299Jochen Autschbach, Niranjan Govind, Raymond Atta-Fynn, Eric J. Bylaska, John W. Weare and Wibe A. de Jong12.1 Introduction 29912.2 ZORA Hamiltonian and Magnetic Property Calculations 30012.2.1 ZORA Hamiltonian 30012.2.2 Magnetic properties 30312.3 X2C Hamiltonian and Molecular Properties from X2C Calculations 31212.4 Role of Dynamics on Thermodynamic Properties 31912.4.1 Sampling Free Energy Space with Metadynamics 31912.4.2 Hydrolysis constants for U(IV), U(V), and U(VI) 32012.4.3 Effects of Counter Ions on the Coordination of Cm(III) in Aqueous Solution 32212.5 Modeling of XAS (EXAFS, XANES) Properties 32512.5.1 EXAFS of U(IV) and U(V) Species 32712.5.2 XANES Spectra of Actinide Complexes 33013 Theoretical Treatment of the Redox Chemistry of Low Valent Lanthanide and Actinide Complexes 343Christos E. Kefalidis, Ludovic Castro, Ahmed Yahia, Lionel Perrin and Laurent Maron13.1 Introduction 34313.2 Divalent Lanthanides 34913.2.1 Computing the Nature of the Ground State 34913.2.2 Single Electron Transfer Energy Determination in Divalent Lanthanide Chemistry 35213.3 Low-Valent Actinides 35613.3.1 Actinide(III) Reactivity 35613.3.2 Other Oxidation State (Uranyl…) 36113.4 Conclusions 36514 Computational Studies of Bonding and Reactivity in Actinide Molecular Complexes 375Enrique R. Batista, Richard L. Martin and Ping Yang14.1 Introduction 37514.2 Basic Considerations 37614.2.1 Bond Energies 37614.2.2 Effect of Scalar Relativistic Corrections 37714.2.3 Spin-Orbit Corrections 37814.2.4 Relativistic Effective Core Potentials (RECP) 37914.2.5 Basis Sets 38014.2.6 Density Functional Approximations for Use with f-Element Complexes 38114.2.7 Example of application: Performance in Sample Situation (UF6→UF5 +F) [39, 40] 38214.2.8 Molecular Systems with Unpaired Electrons 38414.3 Nature of Bonding Interactions 38514.4 Chemistry Application: Reactivity 38714.4.1 First Example: Study of C–H Bond Activation Reaction 38714.4.2 Study of Imido-Exchange Reaction Mechanism 39514.5 Final Remarks 39715 The 32-Electron Principle: A New Magic Number 401Pekka Pyykkö, Carine Clavaguéra and Jean-Pierre Dognon15.1 Introduction 40115.1.1 Mononuclear, MLn systems 40115.1.2 Metal Clusters as ‘Superatoms’ 40215.1.3 The Present Review: An@Ln-Type Systems 40415.2 Cases So Far Studied 40415.2.1 The Early Years: Pb2−12 and Sn2−12 Clusters 40415.2.2 The Validation: An@C28 (An = Th, Pa+, U2+, Pu4+) Series 41015.2.3 The Confirmation: [U@Si20]6−-like Isoelectronic Series 41315.3 Influence of Relativity 41815.4 A Survey of the Current Literature on Lanthanideand Actinide-Centered Clusters 42015.5 Concluding Remarks 42116 Shell Structure, Relativistic and Electron Correlation Effects in f Elements and Their Importance for Cerium(III)-based Molecular Kondo Systems 425Michael Dolg16.1 Introduction 42516.2 Shell Structure, Relativistic and Electron Correlation Effects 42916.2.1 Shell Structure 43016.2.2 Relativistic Effects 43316.2.3 Electron Correlation Effects 43716.3 Molecular Kondo-type Systems 43916.3.1 Bis(η8-cyclooctatetraenyl)cerium 44016.3.2 Bis(η8-pentalene)cerium 44316.4 Conclusions 446Index 451Color plates appear between pages 342 and 343