- Presents surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology
- Features detailed reviews written by leading international researchers
Advances in Quantum Chemistry presents surveys of current topics in this rapidly developing field one that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology. It features detailed reviews written by leading international researchers. In this volume the readers are presented with an exciting combination of themes. Presents surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology Features detailed reviews written by leading international researchers
Front Cover 1
Advances in Quantum Chemistry 4
Copyright 5
Contents 6
Preface 10
Contributors 14
Chapter 1: Electronic Structure Calculations for Antiferromagnetism of Cuprates Using SIWB Method for Anions in DV and a ... 16
1. Introduction 17
2. Hubbard Model and DV Method in a DFT for Antiferromagnetism 20
3. SIWB Method in DV Method of a DFT for Antiferromagnetism 26
4. Examination of the SIWB Results from the FEM 35
5. Conclusions 39
Acknowledgment 40
References 40
Chapter 2: Quantum Chemistry in Proton-Conductors: Mechanism Elucidation and Materials Design 46
1. Introduction 47
1.1. Fuel Cell 47
1.2. Operation Temperature of Solid Oxide Fuel Cell 47
1.3. Proton-Conduction and Oxide Ion-Conduction in Solid Electrolyte 48
2. Theoretical Background 49
2.1. Hybrid Kohn-Sham DFT 49
2.2. Chemical Bonding Rule 50
2.3. Ionics Model III: Proton 51
3. Proton-Conduction in LaAlO3 Perovskite 52
3.1. Proton-Conductor of Aluminum Oxide 52
3.2. Two-Dimensional Proton-Conduction within Al4O4 Square 52
3.3. Three-Dimensional Proton-Conduction Crossing Al4O4 Square 55
3.4. Activation Energy for Proton-Conduction 56
3.5. Proton-Pumping Effect 58
3.6. Doping Effect 60
3.7. Conflict with Oxide Ion-Conduction 70
4. Conventional Perovskite-Type Proton-Conductors 73
4.1. Conventional Perovskite-Type Proton-Conductors 73
4.2. Proton-Conduction in BaZrO3 Perovskite 73
4.3. Proton-Conduction in SrTiO3 Perovskite 76
5. Concluding Remarks 77
5.1. Mechanism Elucidation 77
5.2. Quantum Effect 78
5.3. Materials Design 78
5.4. Conflict with Oxide Ion-Conduction: Safety Aspect 79
5.5. Practical Application 79
Acknowledgments 79
References 80
Chapter 3: Time-Dependent Treatment of Molecular Processes 84
1. Introduction 85
2. Molecular Hamiltonian 88
3. The Time-Dependent Variational Principle 94
4. Coherent States 98
4.1. Gaussian Wave Packet as a Coherent State 99
4.2. The Determinant Coherent State for N Electrons 103
4.3. Vector Hartree–Fock 106
4.4. Singularities 112
5. Minimal END 113
6. Rendering of Dynamics 120
Acknowledgments 122
References 122
Chapter 4: Stretching and Breaking of Chemical Bonds, Correlation of Electrons, and Radical Properties of Covalent Species 126
1. Introduction 127
2. Basic Theoretical Concept 130
3. Covalent Bonds in Light of Their Stretching and Breaking 134
3.1. C.C Bonds 134
3.2. C—O, C—H, and F—F Bonds 141
3.3. X.X Covalent Bonds of Heavier Tetrels (X=Si, Ge, and Sn) 142
4. Stretched Bonds in Covalent Compounds 151
4.1. Quantum-chemical Aspect of Bond Stretching 151
4.2. Chemically Stretched Covalent Bonds 152
4.2.1. Single Bonds 152
4.2.1.1. Polyderivatives of Fullerene C60 152
4.2.1.2. Polyderivatization of Graphene 154
4.2.2. Double and Triple Bonds 156
4.2.2.1. Dimerization of p-diethylbenzene 157
4.2.2.2. Diphenylacetylenes, Graphyne, and Graphdiyne 161
5. Mechanical Stretching of Covalent Bonds 166
5.1. Dynamic Stretching 166
5.2. Static Stretching 170
6. Conclusion 171
Acknowledgments 173
References 173
Chapter 5: Mechanistic Radiobiological Models for Repair of Cellular Radiation Damage 178
1. Introduction 180
1.1. Hypofractionation and Small-Dose Conventional Fractionation 180
1.2. Stereotactic Radiosurgery for Large-Dose NonconventionalFractionation 182
1.3. Stereotactic Body Radiotherapy with Ablative Doses 183
2. Biological Aspects of Radiotherapy and the Need for Biophysical Models 184
2.1. Multifaceted Tasks of Radiobiological Models in Radiotherapy 187
2.2. The LQ Cell Response Versus the Conditions Imposed onto Radiobiological Models 189
2.2.1. Validity Restriction to Low Doses and Obstacles at High Doses 189
2.2.2. Bias of the LQ Parameters 193
2.3. The PLQ Model: Validity at All Doses 198
3. Modeling Tumor Cell Proliferation 199
3.1. The Exponential Tumor Growth Law 199
3.2. The Gompertz Tumor Growth Law 202
4. Cell Death Probability After Irradiation by a Dose D + dD Oncethe Same Cell Survived a Dose D 208
5. Multiple Radiation–Cell Interactions in the Realm of the Poisson Statistics 216
6. Dynamics of Radiosensitivity 218
6.1. Nested Differential Equation for SFs 218
6.2. The Weilbull and the Gompertz ProbabilityDistribution Functions 221
7. Methods of Discrete Mathematics for Cell Surviving Fractions 223
7.1. Direct Problem: Derivation of Generating Functions from DifferenceEquations for Counting Functions 225
7.2. The Linear Model for Event Counting 225
7.3. The LQ Model for Event Counting 227
7.4. The LQC Model for Event Counting 229
7.5. The MPE Model for Event Counting 231
7.6. The MSE Model for Event Counting 231
8. Inverse Problem: Reconstruction of Difference Equations for CountingFunctions from Generating Functions 232
9. Determination of the Radiosensitivity Parameters from Experimental Data 234
10. BED During Acute Irradiation 236
11. Fractionation of Irradiation 238
11.1. Isoeffect for Dose per Fraction Tending to Zero (d . 0) 239
11.2. Isoeffect for Standard Dose per Fraction: dst = 2Gy 241
11.3. Low-Order Approaches to BED 242
11.4. Small- and Large-Dose Behaviors of Low-Order Biological Effect and SF 243
12. Cell Blocking Mechanism and Reduced Effectiveness of Radiation 245
12.1. Wasted Quanta, Delayed Cell Response 245
12.2. The Euler Delayed Dynamics Model for Cell Survival 248
12.3. Delayed Dynamics and DDEs 254
12.4. The Formalism of Paralyzable Dead Time in Delayed Dynamics 254
12.5. The LDD Model 256
13. The IMM Model 259
14. Results and Discussion 263
15. Conclusions and Perspectives 269
Appendix A. The Lambert W Function and Its Basic Characteristics 270
Chapter 6: Molecular Integrals for Exponential-Type Orbitals Using Hyperspherical Harmonics 280
1. Introduction 281
2. Evaluation of Molecular Integrals Using Coulomb Sturmians 283
2.1. Definition of Coulomb Sturmians 283
2.2. Fourier Transforms of Coulomb Sturmians 284
2.3. Many Center Sturmians 286
2.4. Overlap Integrals Involving Coulomb Sturmians 287
2.5. Shibuya–Wulfman Integrals 289
2.6. Matrices Representing Kinetic Energy and Nuclear Attraction 293
2.7. Pre-Evaluation and Storage of the Matrix cµ'' µ'
2.8. One-Center Densities in Terms of 2k Sturmians 296
2.9. Interelectron Repulsion Integrals Between Two One-Center Densities 298
2.10. Two-Center Densities in Terms of 2k Sturmians 301
2.11. The Integral Transformation to m.o. Repulsion Integrals 303
2.12. Checks 304
2.13. Three-Center Nuclear Attraction Integrals 305
3. Results 305
3.1. Accuracy 306
3.2. Efficiency 308
4. Extension to Slater-Type Orbitals 309
4.1. Definition of STO's 309
4.2. Expansion of an Arbitrary Function of s = kr in Terms of SturmianRadial Functions 310
4.3. Evaluation of STO Molecular Integrals 312
4.4. STO Overlap and Kinetic Energy Integrals 315
5. Angular and Hyperangular Integration 318
5.1. The Volume Element and Solid Angle 318
5.2. Theorem 319
5.3. Proof 319
5.4. Comments 319
6. An Alternative Method for Evaluating I1 and I2 320
6.1. Evaluation in Direct Space 320
6.2. Expansion of 1k Coulomb Sturmians in Terms of 3k Coulomb Sturmians 321
6.3. Evaluation of the Coefficients b'µ'' µ'
6.4. Putting n-sums Inside the Hyperangular Integrals 323
6.5. Some Simple Examples 326
6.6. Checks 327
7. Repeating with Real Spherical Harmonics 328
7.1. Real Spherical Harmonics and their Associated Hyperspherical Harmonics 328
7.2. Expansion of 1k Sturmians in Terms of 3k Sturmians with RealSpherical Harmonics 330
7.3. Other Modifications Needed with Real Spherical Harmonics 333
8. Discussion 335
Chapter 7: Large-Scale QM/MM Calculations of Hydrogen Bonding Networks for Proton Transfer and Water Inlet Channels for W ... 340
1. Introduction 342
2. Computational Model 345
2.1. Theoretical Modeling of the CaMn4O5 Cluster in OEC of PSII 345
2.2. Computational Methods of the CaMn4O5 Cluster in OEC of PSII 352
3. Computational Results 352
3.1. Hydrogen Bonding Network Optimized by the QM/MM Calculations 352
3.2. Proton Wire for PRP 356
3.3. Hydrogen Bonding Interaction Between O(4) and Water Molecule W(11) 359
3.4. Hydrogen Bonding interaction Between O(2) and Arg357, and Between O(3) and His337 362
3.5. Hydrogen Bonding Interaction Between O(1) and Water Molecule W(10) 365
3.6. Hydrogen Bonding Interaction Around Chloride Anion Cl(2) 367
3.7. Hydrophobic Interaction Around the O(5) Site 369
4. Results and Discussions 370
4.1. Comparisons of XRD Results 370
4.2. Comparison with High-resolution XRD and EXAFS Results 372
4.3. Theoretical System Models of OEC of PSII 374
4.4. Mutation Experiments 375
4.4.1. Amino Acids in the First Coordination Sphere of the CaMn4O5 Cluster 375
4.4.2. His190 and Tyr161 377
4.4.3. His337 and Arg357 377
4.4.4. Asp61, Lys317, and Chloride Anion 378
4.4.5. Val185 380
4.5. Structural Symmetry Breaking and Reaction Pathways 381
4.5.1. Labile Mn—O(5)—Mn bond of the CaMn4O5 Cluster 381
4.5.2. Transition Structures for Left- and Right-Hand Scenarios of Water Oxidation 383
4.6. Artificial Water Oxidation Systems 386
5. Concluding Remarks 388
Acknowledgments 389
Appendices 390
A1. Photosynthetic System 390
A1.1. System Structure of Photosystem 390
A1.2. Kok Cycle for Water Oxidation 391
A2. Structure and Bonding of the Catalytic Site for Water Oxidation 392
A2.1. Hydrogen Bonding Networks of the CaMn4O5 Cluster 392
A2.2. Structural Symmetry Breaking of the Mna—O—Mnd Bond 393
A3. System Structures of Photosynthesis 394
A3.1. Necessity of System Modeling 394
A3.2. Channel Structures of OEC of PSII Revealed by the XRD Experiments 395
A4. Mechanisms of Water Oxidations 401
A4.1. Importance of Val185 401
A4.2. Mechanisms of Water Oxidation 401
References 421
Index 430
Electronic Structure Calculations for Antiferromagnetism of Cuprates Using SIWB Method for Anions in DV and a Density Functional Theory Confirming from Finite Element Method
Kimichika Fukushima1 Advanced Reactor System Engineering Department, Toshiba Nuclear Engineering Service Corporation, Yokohama, Japan
1 Corresponding author: email address: kimichika1a.fukushima@glb.toshiba.co.jp
Abstract
Describing antiferromagnetism in density functional theory (DFT) had been an unsolved problem since the 1930s until recently. This chapter containing a significant review reports the SIWB (surrounding or solid Coulomb potential-induced well for basis set) method for the antiferromagnetic state derivation in copper oxides. SIWB uses the discrete variational (DV) method, which employs numerical atomic orbital basis functions in a DFT. Within Cu oxides, O2 − is stable, whereas in a vacuum only the O− state is experimentally observed, although O2 − is not observed in a vacuum. DV adds a well potential to the electron potential to generate an anion basis set without predicting the radius and depth of the well. The present SIWB method theoretically determines the radius and depth of the well for an anion (negative ion), and this derived well is shallower than the conventional well, leading to antiferromagnetism. We confirm the effectiveness of SIWB approach using the finite element method.
Keywords
Antiferromagnetism
Density functional theory
SIWB
Well potential
Well depth
Well radius
Shannon ionic radii
Anion
Ionic radius
Copper oxides
1 Introduction
Metal compounds, such as metal oxides, show various forms of magnetism, such as ferrimagnetism, which is observed in ferrites with strong permanent magnetic moment. In ferrimagnetism, magnetic moments that originate from the intrinsic magnetic moment of electrons on metal atoms are partially canceled by the antiparallel magnetic moments on near metal atoms, but the significant magnetic moments remain. Ferrimagnetism includes antiferromagnetism as a special case, which was experimentally observed by means of the neutron diffraction1,2 along with other theoretical researches.3–19 Antiferromagnetism is seen in copper oxides, which are mother materials for high-temperature superconductors found in 1986.20 Ferrimagnetism and antiferromagnetism show potential for magnetic data storage devices21 and advancing technologies in spintronics.
The semi-empirical Hubbard model was proposed for a system with one conduction electron per metal atom.11–16 This model predicts the antiferromagnetic state for the stronger on-site Coulomb repulsion between electrons with opposite spins on the same metal atom site than the transfer integral corresponding to the overlap integral between atomic orbitals on the concerned metal atom and its nearest-neighbor metal atom. The model also shows a nonmagnetic metallic state for the smaller on-site Coulomb repulsion compared to the transfer integral. Parallel to the semi-empirical model, density functional theory (DFT) has greatly succeeded in predicting electronic structures of atoms, molecules, as well as solids.22–40 DFT is supported by Hohenberg–Kohn's theorem that the ground state of electron systems under external nuclear Coulomb fields is expressed in terms of the electron density. It had been difficult to describe the antiferromagnetic insulating state using DFT or similar corresponding schemes, since the 1930s.41 Electronic structure calculations in DFT for antiferromagnetic cuprates showed that the magnetic moment on a metal site is canceled from the antiparallel magnetic moment on the same metal site and the energy gap closes resulting in the metallic state.
The present author, however, found that DFT can derive antiferromagnetism of cuprates, incorporating the delocalization of electrons on oxygen sites between Cu metal atoms42–49 using the DV method50–53 in a scheme of LCAO (linear combination of atomic orbitals). Conventionally, the DV method employs atomic orbital basis functions calculated numerically for a separated atom/ion in a vacuum. The oxygen in Cu oxides is in the form of O2 − in a solid/molecule, whereas in a vacuum O2 − is not observed in spite of the experimental observation of O− in a vacuum.54–56 Attached electrons in the O2 − anion in a vacuum cannot be bound with the nuclear attractive Coulomb force, and an electron is detached. The LCAO analysis of O2 − in a solid requires stabilized O2 − atomic orbital basis functions, which are different from the unstable atomic orbital in a vacuum. The atomic orbitals in the DV method are obtained numerically by solving the quantum one-electron wave equation for electrons on an anion (negative ion) in a vacuum.57 For O2 −, the well potential with an appropriate depth within a well radius is added to the self-consistent potential forced on electrons at the anion. The theoretical method was unable to determine the radius and depth of the well potential.
The present author performed the spin-polarized electronic state calculations using the DV method for a molecule and clusters of hydrogen at elongated interatomic distances. These molecule/clusters are simple models for transition metals in metal oxides, which have one conduction electron per metal atom. The DFT scheme is the original Kohn–Sham formalism, whose results are similar to the suitable formalism58 of the generalized gradient approximation (GGA),31–40 compared to the Vosko–Wilk–Nusair (VWN) formalism29 for magnetism. The DV analysis derived the antiferromagnetic state for elongated H molecule/cluster, but the analysis using the conventional depth and radius of the well potential could not show antiferromagnetism for Cu oxides.
The author further developed the SIWB method (surrounding or solid Coulomb-induced well for basis set), which theoretically determines the radius and depth of the well potential. At the first version, the well radius for anions was assigned to the Shannon radius (Shannon radii)59–61 based on the Pauling's ionic radius (ionic radii)62–64 following Goldschmidt's experimental data.65,66 The average depth of the well potential for anions is determined by summing the Coulomb potential produced from nuclear charges and extended electron charges obtained from the self-consistent quantum calculations around the concerned anion. In the case of a periodic system, the summation is performed with the help of Evjen's method67–70 for nuclear charges and quantum extended electron charges around the central anion. The summation of the above Coulomb potential averaged over the well radius converges rapidly with the increase of the shell of charge unit cells surrounding the anion. The well depth is measured from the minimum level of the potential, under which an unbound electron moves freely around the central anion when the potential expect for the remaining well potential is removed from the potential acting on electrons on the anion. This SIWB method reveals a shallower well depth compared to the conventional well depth and leads to the antiferromagnetic insulating state. The attraction between the nearest antiparallel spins on metal atom sites with a gap decreases the total energy of the system compared to the nonmagnetic metallic state. The decrease in the total energy exhibiting antiferromagnetism implies the improvement of atomic orbital basis functions. This analysis shows that the DFT derives antiferromagnetism even for the case where oxygen exists between metals.
At the second version, the anion radius was theoretically determined independently of the Shannon radii. The starting well radius is set to the Shannon's anion radius in the self-consistent field (charge) iterations, and the well radius at each iteration is assigned to the derived radius, Req, the distance from an anion nucleus to the point where the electron charge density belonging to the anion is equal to the electron charge density belonging to the nearest-neighbor cation (positive ion). The calculated anion radii, Req, for fluorides, chlorides, and oxides of the NaCl crystal structure with six-coordinated nearest-neighbor atoms were similar to the Shannon radii. This second version of the SIWB method thus made it possible to predict the well radius, which is independent of the Shannon radius.
The electronic structure calculations using the SIWB method, which derived the antiferromagnetism, indicate improved atomic orbital basis functions to suitably describe the delocalization of electrons on anion sites. This improvement is confirmed through the finite element method (FEM)49,71–73 for a small molecule. FEM is similar to the finite difference method and in some sense FEM is an improved flexible version of the finite difference method. Atomic orbital basis functions are defined in a large region with an atomic size around a nucleus, while the basis functions for FEM extend over a very tiny domain around a grid (lattice) point in space. When the lattice spacing goes...
| Erscheint lt. Verlag | 29.1.2015 |
|---|---|
| Mitarbeit |
Herausgeber (Serie): Erkki J. Brandas, John R. Sabin |
| Sprache | englisch |
| Themenwelt | Naturwissenschaften ► Biologie |
| Naturwissenschaften ► Chemie ► Physikalische Chemie | |
| Naturwissenschaften ► Physik / Astronomie ► Angewandte Physik | |
| Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik | |
| Technik | |
| ISBN-10 | 0-12-801915-8 / 0128019158 |
| ISBN-13 | 978-0-12-801915-3 / 9780128019153 |
| Haben Sie eine Frage zum Produkt? |
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