The hydrogen molecule in strong magnetic fields: optimizations of anisotropic Gaussian basis sets

The anisotropic Gaussian basis sets were optimized for the H atom and the hydrogen molecule in strong magnetic fields of 0-1000 a.u. We used five-parameter fit functions to generate anisotropic Gaussian exponents of hydrogenic atomic orbitals. These functions provided errors of energy that were comparable to the independent optimization of all the exponents. The optimal exponents were used to calculate the Hartree-Fock energies of H2 at arbitrary orientations, with respect to the magnetic field. Furthermore, the double-exponential transformation was applied to calculate highly anisotropic Coulomb integrals. Between magnetic field strengths of 1 a.u. and 100 a.u., a molecule in a triplet ground state continuously changed its stable orientation from the perpendicular geometry to the parallel geometry.     

Resonant states of the hydrogen atom in strong magnetic fields

Resonant states of atomic hydrogen in strong magnetic fields have been computed by semiclassical methods. Eigenvalues are obtained by using an adiabatic separation of variables and standard WKB methods; these are confirmed by semiclassical quantization of numerically computed quasiperiodic trajectories. Large numbers of resonant states are found at B = 10 kT for L_z values above 20.     

Edges of two-dimensional electron systems under strong magnetic fields

Two-dimensional electron systems, which exist e.g. at interlaces between two different semiconductors, exhibit interesting physical properties under strong magnetic fields. In interpreting the quantum Hall effect the role of one-dimensional system edges begins to be taken into account.

The electron structure, connected with Landau quantization of 2D electron states under magnetic field, has been studied in the vicinity of system edges. Model systems with abrupt confinement barriers exhibit electron dispersions with edge plateaus above the barrier tops, accompanied by regions of substantially reduced gaps between neighbouring Landau branches. Selfconsistent results for smoothly confined systems provide alternating channels of compressible and incompressible Fermi liquids along the system edges. Recent investigation illustrates the transition between the two limiting confinement barrier cases.

In order to evaluate the Hall conductivity, the Kubo formula has been adopted in a straightforward manner to two-dimensional stripes confined by arbitrary barriers. Total deviation of the Hall conductivity from the integer values is given by the product of two factors: the geometrical factor is inversely proportional to the sample width and the edge factor is proportional to the derivative of the electron dispersion at the Fermi level and is thus governed by the shape of the confinement barrier. The deviations have been evaluated for model systems of various widths and a qualitative agreement with recent experimental data for quantum wires has been found.

The formulas provide also current densities and this enables to investigate spatial distributions of the electron current across the Hall stripes. Application to the abruptly confined model shows that the quantized part of the total current takes place within the interior of the stripe whereas the edge currents distribution is affected by the confinement barrier.     

Spectra of atomic Rydberg states in strong magnetic fields

Transition frequencies and intensities for exited states of atomic hydrogen in a strong magnetic field are calculated by Fourier transformation of dipole moments computed using classical trajectories. We consider states with n = 30 and L_z = 1 for fields of up to 7 T. Spectra for states labeled as librators and rotators are found to be qualitatively different, especially for the spectral component perpendicular to the field. In addition to the zero-field Kepler line, a new intra-manifold transition is located at low frequency. The frequencies and intensities are found to be sensitive functions of the field strength, and of the particular state of the Coulomb manifold involved.     

Investigations of the sodium and lithium D-lines in strong magnetic fields

Experimental and theoretical investigations of the splitting of the hyperfine structure of the sodium and lithium-D-lines in magnetic fields between 0 and 1 T were performed. In this magnetic field region the fine structure levelsJ=1/2 andJ=3/2 of the excited term² P begin to influence each other. In case of lithium crossings and anticrossings of hyperfine states stemming from different fine structure energy levelsJ=1/2 andJ=3/2 can be observed. The measurements were performed by laseratomic-beam spectroscopy in dependence on the applied external magnetic field strength. The experimental spectra were compared with computed spectra. Spectra were simulated by calculations using for the hyperfine hamiltonian two hyperfine constantsA andB in case of sodium and four hyperfine constantsa _c ,a _d ,a ₀ andb in case of lithium. Values for this constants could be derived by fitting the theoretical splittings to the experimental ones. For the first time theg _I — factor of sodium could be determined in a purely optical way.     

Magnetic properties of the fullerene organic compounds in strong magnetic fields

Magnetisation study of the C₆₀·TMTSF·2CS₂ molecular complex in magnetic field up to 47 T for the temperature range 1.8–300 K and ESR spectroscopy of the molecular complex (ET)₂C₆₀ at T=1.8 K for the frequency range 60–90 GHz in magnetic field up to 32 T provide the experimental evidence that a paramagnetic centers with the reduced g-factor values g<1 control magnetic properties of these solids. Anomalous g-factor values may be caused by dynamic Jan-Teller effect on the negative C₆₀ ions, which appear as defects in crystalline structure with a weak charge transfer.     

Ring current effects on nuclear magnetic shielding of carbon in the benzene molecule

The differential Biot-Savart law of classical electrodynamics was applied to develop a ring current model for the magnetic shielding of the carbon nucleus in benzene. It is shown that the local effect of the pi currents, induced by a magnetic field normal to the molecular plane, on the sigmaC out-of-plane shielding tensor component vanishes. However, approximately 10% of sigmaC is due to the shielding contributions from pi current density in the region of the other carbon atoms. Magnetic shielding density maps obtained via quantum mechanical procedures confirm the predictions of the classical model. Copyright (c) 2004 John Wiley & Sons, Ltd.     

Analytical GIAO and hybrid-basis integral derivatives: application to geometry optimization of molecules in strong magnetic fields

Analytical integral evaluation is a central task of modern quantum chemistry. Here we present a general method for evaluating differentiated integrals over standard Gaussian and mixed Gaussian/plane-wave hybrid orbitals. The main idea is to have a representation of basis sets that is flexible enough to enable differentiated integrals to be reinterpreted as standard integrals over modified basis functions. As an illustration of the method, we report a very simple implementation of Hartree-Fock level geometrical derivatives in finite magnetic fields for gauge-origin independent atomic orbitals, within the London program. As a quantum-chemical application, we optimize the structure of helium clusters and some well-known covalently bound molecules (water, ammonia and benzene) subject to strong magnetic fields.     

QED contributions to the atomic structure at strong central fields

Precise determination of the accurate structure of highly charged, very heavy ions is the basis for a detailed understanding of QED at strong fields. The experimental advances in this field will be reviewed with special emphasis given to H-, He- and Li-like very heavy ions. For the heaviest species, U, the ground-state Lamb shift for H-like ions is measured with an accuracy of about 1%, the two-electron QED terms for He-like system are just being touched, and for the Li-like species already two-loop QED terms have been probed with ultimate accuracy. The different approaches to measure the strong field QED contributions will be elucidated and the results compared to theory. Emphasis will be given to results from the heavy ion storage ring ESR.     

Hydrogenic Rydberg atoms in strong magnetic fields: Theoretical and experimental spectra in the transition region from regularity to irregularity

For deuterium Rydberg atoms in a magnetic field of ～6 T we compare the complete experimental spectrum in the range ?190 cm^?1 to ?20 cm^?1 with the positions and oscillator strengths of the corresponding quantum theoretically calculated photoabsorption lines. The agreement is excellent. The range of energy covered extends from the end of thel-mixing regime up to the regions where the approximate integrability of the problem is completely lost, and the corresponding classical system undergoes a transition to chaos.     

Generalized Sturmians applied to atoms in strong external fields

The generalized Sturmian approach to quantum mechanical many‐body problems is described. The method allows correlated solutions to the many‐particle Schrödinger equation to be obtained directly, without the use of the self‐consistent‐field approximation. As an illustrative example, spectra and polarizabilities are calculated for atoms and ions in the 2‐electron and 3‐electron isoelectronic series under the influence of very strong external electric fields.     

Structure,dynamics and quantum chaos in atoms and molecules under strong magnetic fields

Although studies on the interaction of atoms and molecules with external magnetic fields are more than 100 years old, beginning from the pre-quantum-mechanical days to the era of quantum mechanics, interest in the application of strong, static magnetic fields on atoms and molecules is only about three decades old. Although a great deal of insight has been obtained on the consequent changes in electronic structure and chemical bonds by such strong fields, the more realistic, dynamic, strong magnetic fields were not studied. Based on our own works in the last decade, we will discuss in this article how strong static as well as oscillating, strong magnetic fields on atoms and molecules affect electron density and chemical bonds. The dynamic fields generate completely new, hitherto unknown exciting phenomena. Our discussions will be based on three inter-linked, fundamental aspects of matter-external-magnetic-field interactions, viz., (1) action of static, strong magnetic fields as well as associated changes in electronic structure and the chemical bond, (2) Dynamics of electron density, and (3) Non-linear effects inherent in these interactions. Each aspect, although discussed separately for clarity, is a part of a larger intertwining picture.     

Water-annealing regulated protein-based magnetic nanofiber materials: tuning silk structure and properties to enhance cell response under magnetic fields

In this study, flexible silk fibroin protein and biocompatible barium hexaferrite (BaM) nanoparticles were combined and electrospun into nanofibers, and their physical properties could be tuned through the mixing ratios and a water annealing process. Structural analysis indicates that the protein structure of the materials is fully controllable by the annealing process. The mechanical properties of the electrospun composites can be significantly improved by annealing, while the magnetic properties of barium hexaferrite are maintained in the composite. Notably, in the absence of a magnetic field, cell growth increased slightly with increasing BaM content. Application of an external magnetic field during in vitro cell biocompatibility study of the materials demonstrated significantly larger cell growth. We propose a mechanism to explain the effects of water annealing and magnetic field on cell growth. This study indicates that these composite electrospun fibers may be widely used in the biomedical field for controllable cell response through applying different external magnetic fields.