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.     

Rydberg atoms in crossed external magnetic and electric fields: Experimental observation of an outer potential minimum

Rydberg atoms in crossed magnetic and electric fields have been investigated. The existence of field induced bound states with a large electric dipole moment was demonstrated. For this purpose the highly excited atoms were deflected by means of an inhomogeneous electric field.     

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.     

Stability of the Rydberg atom in the crossed magnetic and electric fields

The stability of equilibrium positions of the Rydberg atom exposed to the uniform crossed electric and magnetic fields is analyzed. The dynamics of the system is described by an autonomous Hamiltonian depending on parameters a and f. By the normalization of the quadratic part of the Hamiltonian expansion in the neighborhood of the equilibrium position it is proved that for any f < 0 and ${1 \over 2} < a < {1 \over 2} + {{( - f)^{3/2} } \over {3\sqrt 3 }}$ , the equilibrium solution of the equations of motion is stable in Liapunov sense, while for f > 0 and a < 1/2, there is a domain of instability in the plain of parameters Ofa bounded by the curve d₃ = 0. In the domain of linear stability, it is proved that there are two curves in the plane Ofa, where the resonance conditions of third (ω₁ = 2ω₂) and fourth (ω₁ = 3ω₂) order are fulfilled. Moreover, by the normalization of the third‐ and fourth‐order terms in the Hamiltonian expansion it is proved that in the case of the third‐order resonance, the equilibrium position is unstable for all f > 0 different from f = 0.111572 and f = 0.281144, for which the stability takes place. In the case of the fourth‐order resonance, there are two intervals of parameters for which the equilibrium position is unstable. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Study of the magnetic state of transition element atoms in compounds and alloys usingKα 1 spectra

A review is given for investigations of the magnetic state of transition element atoms in compounds and alloys using K₁ spectra. The shift and width of the K₁ line are used for determining changes in the spin and charge density on the emitting atom depending on the type and concentration of the components. This method permits us to determine the local magnetic moment at an atom with precision of 0.1–0.2 _B . The electron state density in the conductance band affects the spin density formed on the resonance 3d level of an atom in the field of a 2p vacancy. Localization of 3d states was observed upon the transition of an atom to an impurity state. The contribution to the spin state on the emitting atom in Pauli paramagnetics is proportional to the state density on the Fermi level. The width of the K₁ line of transition element atoms was found to depend on the magnetic moment on the atoms of the immediate environment and on the magnitude and sign of the exchange interaction between them, which permits us to study magnetic phase transitions.Institute of the Mineralogy, Geochemistry, and Crystal Chemistry of Rare Elements. Translated from Zhurnal Strukturnoi Khimii, Vol. 30, No. 6, pp. 122–137, November–December, 1989.     

Study of the nmr spectra of mono- and oligosaccharides in the region of a strong magnetic field

Conclusions An investigation of the NMR spectra of mono- and oligosaccharides in the region of a strong magnetic field permits a judgment of the conformational and configurational changes in the structure of monosaccharides, as well as the order and conformation of the bonds between monosaceharide residues in oligosaccharides.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 8, pp. 1854–1856, August, 1969.     

Nonlinear response of the benzene molecule to strong magnetic fields

The fourth-rank hypermagnetizability tensor of the benzene molecule has been evaluated at the coupled Hartree-Fock level of accuracy within the conventional common-origin approach, adopting gaugeless basis sets of increasing size and flexibility. The degree of convergence of theoretical tensor components has been estimated allowing for two different coordinate systems. It is shown that a strong magnetic field perpendicular to the plane of the molecule causes a distortion of the electron charge density, which tends to concentrate in the region of the C-C bonds. This charge contraction has a dynamical origin, and can be interpreted as a feedback effect in terms of the classical Lorentz force acting on the electron current density.     

Theoretical study on regularity of changes in quantum defects in Rydberg state series of many‐valence electron atoms within WBEPM theory

Within the scheme of the weakest bound electron potential model theory, the regularity of changes in quantum defects in 40 “spectrum‐level‐like series” of several many‐valence electron atoms of the third period was studied. The n–δ curves of the 40 spectrum‐level‐like series could be classified into three types; for all such series the quantum defects δ could be expanded as a polynomial of the principal quantum number n in a spectrum‐level‐like series. With regularity, the level energies of high Rydberg states in a series can be predicted accurately. By carefully studying and explaining the three types of 40 n–δ curves, the conclusion was reached: the type of the n–δ curve, i.e., the regularity of changes in quantum defects in a spectrum‐level‐like series, was determined by both the energy level and the azimuthal quantum number l of the weakest bound electron. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 232–237, 2001     

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.     

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.     

Theoretical and experimental investigations of the electronic Rydberg states of diazomethane: assignments and state interactions

The electronic states of diazomethane in the region 3.00-8.00 eV have been characterized by ab initio calculations, and electronic transitions in the region 6.32-7.30 eV have been examined experimentally using a combination of 2 + 1 REMPI spectroscopy and photoelectron imaging in a molecular beam. In the examined region, three Rydberg states of 3p character contribute to the transitions, 2(1)A2(3p(y) <-- pi), 2(1)B1(3p(z) <-- pi), and 3(1)A1(3p(x) <-- pi). The former two states are of mostly pure Rydberg character and exhibit a resolved K structure, whereas the 3(1)A1(3p(x) <-- pi) state is mixed with the valence 2(1)A1(pi* <-- pi) state, which is unbound and is strongly predissociative. Analyses of photoelectron kinetic energy distributions indicate that the ground vibrational level of the 2(1)B1(3p(z)) state is mixed with the 2(1)A2(3p(y)) nu(9) level, which is of B1 vibronic symmetry. The other 2(1)A2(3p(y)) vibronic states exhibit pure Rydberg character, generating ions in single vibrational levels. The photoelectron spectra of the 3(1)A1(3p(x) <-- pi) state, on the other hand, give rise to many states of the ion as a result of strong mixing with the valence state, as evidenced also in the ab initio calculations. The equilibrium geometries of the electronic states of neutral diazomethane were calculated by CCSD(T), using the cc-pVTZ basis, and by B3LYP, using the 6-311G(2df,p) basis. Geometry and frequencies of the ground state of the cation were calculated by CCSD(T)/cc-pVTZ, using the unrestricted (UHF) reference. Vertical excitation energies were calculated using EOM-CCSD/6-311(3+,+)G* at the B3LYP optimized geometry. The theoretical results show that the 2(1)A2(3p(y) <-- pi) and 2(1)B1(3p(z) <-- pi) states have geometries similar to the ion, which has C(2v) symmetry, with slight differences due to the interactions of the electron in the 3p orbital with the nuclei charge distributions. The geometry of the 3(1)A1(3p(x) <-- pi) state is quite different and has Cs symmetry. The experimental and theoretical results agree very well, both in regard to excitation energies and to vibrational modes of the ion.     

Structural colors in nature: the role of regularity and irregularity in the structure.

Coloring in nature mostly comes from the inherent colors of materials, but it sometimes has a purely physical origin, such as diffraction or interference of light. The latter, called structural color or iridescence, has long been a problem of scientific interest. Recently, structural colors have attracted great interest because their applications have been rapidly progressing in many fields related to vision, such as the paint, automobile, cosmetics, and textile industries. As the research progresses, however, it has become clear that these colors are due to the presence of surprisingly minute microstructures, which are hardly attainable even by ultramodern nanotechnology. Fundamentally, most of the structural colors originate from basic optical processes represented by thin-film interference, multilayer interference, a diffraction grating effect, photonic crystals, light scattering, and so on. However, to enhance the perception of the eyes, natural creatures have produced various designs, in the course of evolution, to fulfill simultaneously high reflectivity in a specific wavelength range and the generation of diffusive light in a wide angular range. At a glance, these two characteristics seem to contradict each other in the usual optical sense, but these seemingly conflicting requirements are realized by combining appropriate amounts of regularity and irregularity of the structure. In this Review, we first explain the fundamental optical properties underlying the structural colors, and then survey these mysteries of nature from the viewpoint of regularity and irregularity of the structure. Finally, we propose a general principle of structural colors based on structural hierarchy and show their up-to-date applications.     

Theoretical study of shake-up in the core photoelectron spectra of the alkali atoms

Relativistic and non-relativistic Hartree-Fock calculations have been performed for the shake-up lines relative to core ionization of the alkali atoms. Good general agreement with the experimental data is achieved both for the energy and the intensity. Relativistic effects are found to be small, amounting TO = 0.2 eV in Cs. As concerns the shake-up energies, a correlation effect is detected, the magnitude of which increases along the series.     

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.     

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.     

Effects of static electric fields on the photoionization spectra of two-electron atoms and ions

The simultaneous photoexcitation of two electrons is a highly correlated process, producing doubly excited states, observed as resonant structure in the ionization cross-section. This review paper explores the ability of a static electric field to affect these correlations, as evidenced by changes in the shape and energy of resonances. A comparison of field effects on the spectra of H⁻, Ps⁻, He, Ba and Cs⁻ summarizes current understanding of the processes and the capability of theory to predict the cross-sectional features.     

Observation of new Rydberg series in the many-electron transition region of N(2)

Fluorescence excitation spectra produced through photoexcitation of N(2) using synchrotron radiation in the spectral region between 50 and 62.5 nm have been obtained with a resolution of 0.004?nm. A broadband detector (in the 115-180 nm region) was employed to monitor fluorescence originated from neutral excited atomic nitrogen fragments which are produced through direct dissociation processes and predissociation from the well-known many-electron excited Rydberg states. We have identified a new Rydberg series (2 (2)Π(g)) 4sσ, a better resolved Rydberg (D (2)Π(g)) npσ series, and also the prominent Codling series converging to the D (2)Π(g), and C (2)Σ(u) (+) states of N(2) (+), respectively. By normalizing our relative fluorescence intensities to previously measured absolute fluorescence cross-section data we obtain the cross-section data of undispersed fluorescence in the 115-180?nm region. The fluorescence quantum yields for the present photodissociative excitation processes are found to be less than 0.05. The present results may provide important data for our understanding of competitions among the various decay channels of the many-electron transition states of N(2).