Advances in Quantum Chemistry

1. Auflage 2015
ISBN: 978-0-12-801915-3
Verlag: William Andrew Publishing
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, Band Volume 70, 440 Seiten, Format (B × H): 152 mm x 229 mm

Reihe: Advances in Quantum Chemistry

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. This volume focuses on the theory of heavy ion physics in medicine.


- 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

Zielgruppe

Quantum chemists, physical chemists, physicists

Autoren/Hrsg.

Weitere Mitwirkende

Sabin, John R.

Brandas, Erkki J.

Fachgebiete

• Naturwissenschaften Chemie Physikalische Chemie Quantenchemie, Theoretische Chemie

Inhaltsverzeichnis

- 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 Fukushima

- Quantum Chemistry In Proton Conductors: Mechanism Elucidation and Materials Design

Taku Onishi

- Time-Dependent Treatment of Molecular Processes

Yngve Öhrn

- Stretching and Breaking of Chemical Bonds, Correlation of Electrons, and Radical Properties of Covalent Species

Elena Sheka

- Mechanistic Radiobiological Models for Repair of Cellular Radiation Damage

Dzevad Belkic and Karen Belkic

- Molecular Integrals for Exponential-Type Orbitals Using Hyperspherical Harmonics

James Emil Avery and John Scales Avery

- Large Scale QM/MM Calculations of Hydrogen Bonding Networks for Proton Transfer and Water Inlet Channels for Water Oxidation. Theoretical System Models of the Oxygen Evolving Complex of Photosystem II Mitsuo Shoji, Hiroshi Isobe, Shusuke Yamanaka, Yasufumi Umena, Keisuke Kawakami, Nobuo Kamiya, Jian-Ren Shen, Takahito Nakajima and Kizashi Yamaguchi

Leseproben

Chapter One 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: [e-mail] 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...

Über Autor(innen)

Sabin, John R.
I was born in Springfield, Mass, and Educated at Williams College (BA) and the University of New Hampshire (PhD). Following that, I was a postdoctoral at Uppsala University in Sweden, and at Northwestern University in Evanston. For the past four decades, I have worked in the Quantum Theory Project, Department of Physics, at the University of Florida. My interests have always been in the theory of molecular electronic structure. More recently, I have been working on the interaction of fast particles, mostly protons and alpha particles, with proto-biological molecules, in terms of the transfer of energy from the projectile to the molecular target, and the outcome of that energy transfer. Such energy transfer is primarily electronic, and the initial electronic excitation results in target electronic and vibrational excitation, ionization, fragmentation, charge exchange, and other processes. The study of these processes, known as stopping power, has applications in fields from microelectronics to tumor therapy. The investigations are interesting and continue.