Wave Functions Of Levels Research Articles

High-Dimensional Topological Insulators with Quaternionic Analytic Landau Levels

We study the three-dimensional topological insulators in the continuum by coupling spin-1/2 fermions to the Aharonov-Casher SU(2) gauge field. They exhibit flat Landau levels in which orbital angular momentum and spin are coupled with a fixed helicity. The three-dimensional lowest Landau level wave functions exhibit the quaternionic analyticity as a generalization of the complex analyticity of the two-dimensional case. Each Landau level contributes one branch of gapless helical Dirac modes to the surface spectra, whose topological properties belong to the Z(2) class. The flat Landau levels can be generalized to an arbitrary dimension. Interaction effects and experimental realizations are also studied.

Plunger lifetimes and electromagnetic transition strengths in odd 167Yb

Abstract Nine lifetimes have been determined for the first time in the 5 / 2 − [ 523 ] and 5 / 2 + [ 642 ] bands of 167Yb by means of Recoil distance Doppler-shift measurements carried out at the Cologne FN tandem. For the data analysis, a dedicated version of the Differential decay curve method was used. The newly deduced transition strengths and the level scheme are reasonably described by the Particle plus triaxial rotor model (PTRM) calculations except for the behavior of the quadrupole collectivity in the two signatures of the 5 / 2 + [ 642 ] band. The stretched B(E2)ʼs in the favored signature are appreciably larger than those in the unfavored signature. The effect increases with spin. In the PTRM calculations, the wave functions of the favored signature levels contain larger contribution of low-Ω orbitals from ν i 13 / 2 parentage than those of the unfavored levels. This could selectively increase the deformation of the favored signature band members. If so, rotation and Coriolis interaction would give rise to a dynamic shape coexistence taking place between the two signatures.

Insights into the ultraviolet spectrum of liquid water from model calculations: The different roles of donor and acceptor hydrogen bonds in water pentamers

With a view toward a better understanding of changes in the peak position and shape of the first absorption band of water with condensation or temperature, results from electronic structure calculations using high level wavefunction based and time-dependent density functional methods are reported for water pentamers. Excitation energies, oscillator strengths, and redistributions of electron density are determined for the quasitetrahedral water pentamer in its C(2v) equilibrium geometry and for many pentamer configurations sampled from molecular simulation of liquid water. Excitations associated with surface molecules are removed in order to focus on those states associated with the central molecule, which are the most representative of the liquid environment. The effect of hydrogen bonding on the lowest excited state associated with the central molecule is studied by adding acceptor or donor hydrogen bonds to tetramer and trimer substructures of the C(2v) pentamer, and by sampling liquid-like configurations having increasing number of acceptor or donor hydrogen bonds of the central molecule. Our results provide clear evidence that the blueshift of excitation energies upon condensation is essentially determined by acceptor hydrogen bonds, and the magnitudes of these shifts are determined by the number of such, whereas donor hydrogen bonds do not induce significant shifts in excitation energies. This qualitatively different role of donor and acceptor hydrogen bonds is understood in terms of the different roles of the 1b(1) monomer molecular orbitals, which establishes an intimate connection between the valence hole and excitation energy shifts. Since the valence hole of the lowest excitation associated with the central molecule is found to be well localized in all liquid-like hydrogen bonding environments, with an average radius of gyration of ~1.6 Å that is much lower than the nearest neighbor O-O distance, a clear and unambiguous connection between hydrogen bonding environments and excitation energy shifts can be established. Based on these results, it is concluded that peak position of the first absorption band is mainly determined by the relative distribution of single and double acceptor hydrogen bonding environments, whereas the shape of the first absorption band is mainly determined by the relative distribution of acceptor and broken acceptor hydrogen bonding environments. The temperature dependence of the peak position and shape of the first absorption band can be readily understood in terms of changes to these relative populations.

Rational Design of Single-Ion Magnets and Spin Qubits Based on Mononuclear Lanthanoid Complexes

Here we develop a general approach to calculating the energy spectrum and the wave functions of the low-lying magnetic levels of a lanthanoid ion submitted to the crystal field created by the surrounding ligands. This model allows us to propose general criteria for the rational design of new mononuclear lanthanoid complexes behaving as single-molecule magnets (SMMs) or acting as robust spin qubits. Three typical environments exhibited by these metal complexes are considered, namely, (a) square antiprism, (b) triangular dodecahedron, and (c) trigonal prism. The developed model is used to explain the properties of some representative examples showing these geometries. Key questions in this area, such as the chemical tailoring of the superparamagnetic energy barrier, tunneling gap, or spin relaxation time, are discussed. Finally, in order to take into account delocalization and/or covalent effects of the ligands, this point-charge model is complemented with ab initio calculations, which provide accurate information on the charge distribution around the metal, allowing for an explanation of the SMM behavior displayed by some sandwich-type organometallic compounds.

Equidistance of the complex two-dimensional anharmonic oscillator spectrum: the exact solution

We study a class of quantum two-dimensional models with complex potentials of a specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to the conventional separation of variables. In the present case, the property of shape invariance provides the equidistant form of the spectrum and the algorithm to construct eigenfunctions analytically. It is shown that the Hamiltonian is non-diagonalizable, and the resolution of identity must also include the corresponding associated functions. In the specific case of anharmonic second plus fourth-order interaction, expressions for the wavefunctions and associated functions are constructed explicitly for the lowest levels, and the recursive algorithm to produce higher level wavefunctions is given.

Graphene under spatially varying external potentials: Landau levels, magnetotransport, and topological modes

Superlattices (SLs) in monolayer and bilayer graphene, formed by spatially periodic potential variations, lead to a modified bandstructure with extra finite-energy and zero-energy Dirac fermions with tunable anisotropic velocities. We theoretically show that transport in a weak perpendicular (orbital) magnetic field allows one to not only probe the number of emergent Dirac points but also yields further information about their dispersion. or monolayer graphene, we find that a moderate magnetic field can lead to a strong reversal of the transport anisotropy imposed by the SL potential, an effect which arises due to the SL induced dispersion of the zero energy Landau levels. This effect may find useful applications in switching or other devices. For bilayer graphene, we discuss the structure of Landau level wave functions and local density of states in the presence of a uniform bias, as well as in the presence of a kink in the bias which leads to topologically bound `edge states'. We consider implications of these results for scanning tunneling spectroscopy measurements, valley filtering, and impurity induced breakdown of the quantum Hall effect in bilayer graphene.

Ultrathin Amorphous Alumina Nanoparticles with Quantum-Confined Oxygen-Vacancy-Induced Blue Photoluminescence as Fluorescent Biological Labels

Ultrathin alumina nanoparticles (NPs) with an average size of less than 4 nm are produced from porous anodic alumina membranes. The alumina NPs in a suspension produce strong blue tunable photoluminescence (PL) with a high quantum efficiency of ∼15% and Stokes shift as large as 1.0 eV. An obvious blue-shift and diminished line width are observed after storing the suspension in air. The tunable blue PL which is closely related to the oxygen vacancy (OV) defect centers at different depths beneath the surface depends on the NP size. The experimental observations are corroborated by theoretical derivation demonstrating that the electron wave functions of the OV-induced defect levels are extended in space, and quantum confinement takes place when the alumina NP is smaller than the spread of the wave functions. It is thus possible to control the PL behavior by changing the NP size and OV depth distribution and the alumina NPs are experimentally demonstrated to be robust and nontoxic biological probes.

ROVIBRATIONAL QUENCHING RATE COEFFICIENTS OF HD IN COLLISIONS WITH He

Along with H2, HD has been found to play an important role in the cooling of the primordial gas for the formation of the first stars and galaxies. It has also been observed in a variety of cool molecular astrophysical environments. The rate of cooling by HD molecules requires knowledge of collisional rate coefficients with the primary impactors, H, He, and H2. To improve knowledge of the collisional properties of HD, we present rate coefficients for the He-HD collision system over a range of collision energies from 10–5 to 5 × 103 cm–1. Fully quantum mechanical scattering calculations were performed for initial HD rovibrational states of j = 0 and 1 for v = 0-17 which utilized accurate diatom rovibrational wave functions. Rate coefficients of all Δv = 0, –1, and –2 transitions are reported. Significant discrepancies with previous calculations, which adopted a small basis and harmonic HD wave functions for excited vibrational levels, were found for the highest previously considered vibrational state of v = 3. Applications of the He-HD rate coefficients in various astrophysical environments are briefly discussed.

Fully Computational Lead-Development of Fluoro-Olefin Polymerization Catalysts

Coordinative polymerization of fluorinated olefins is still a challenging task. We analyzed the catalytic properties of diimido chromium VI compounds computationally by density functional methods. It was found that reactivity predictions depend strongly on the density functional chosen for the computations. Therefore, DFT calculations were calibrated to high level wave function theory calculations. Then geometrical parameters, which can be tuned by a ligand, were scanned to elucidate their influence on the catalytic activity. Having arrived at an optimal parameter set, we randomly assembled chromium complexes from a fragments database and automatically checked for their activities. This led to the proposal of three exemplary catalyst candidates.

Energy level diagram, wavefunctions, and probabilities of optical transitions in KCuF3

Using modern concepts of the crystal field in ion-covalent compounds, we calculate the energy level diagram, wavefunctions, and probabilities of optical transitions in the orbital ordering phase of KCuF3. On this basis, we discuss the possible mechanisms by which an optical absorption sideband structure forms, accompanied by the creation of magnons.

“Adiabatic-hindered-rotor” treatment of the parahydrogen-water complex

Inspired by a recent successful adiabatic-hindered-rotor treatment for parahydrogen pH(2) in CO(2)-H(2) complexes [H. Li, P.-N. Roy, and R. J. Le Roy, J. Chem. Phys. 133, 104305 (2010); H. Li, R. J. Le Roy, P.-N. Roy, and A. R. W. McKellar, Phys. Rev. Lett. 105, 133401 (2010)], we apply the same approximation to the more challenging H(2)O-H(2) system. This approximation reduces the dimension of the H(2)O-H(2) potential from 5D to 3D and greatly enhances the computational efficiency. The global minimum of the original 5D potential is missing from the adiabatic 3D potential for reasons based on solution of the hindered-rotor Schrödinger equation of the pH(2). Energies and wave functions of the discrete rovibrational levels of H(2)O-pH(2) complexes obtained from the adiabatic 3D potential are in good agreement with the results from calculations with the full 5D potential. This comparison validates our approximation, although it is a relatively cruder treatment for pH(2)-H(2)O than it is for pH(2)-CO(2). This adiabatic approximation makes large-scale simulations of H(2)O-pH(2) systems possible via a pairwise additive interaction model in which pH(2) is treated as a point-like particle. The poor performance of the diabatically spherical treatment of pH(2) rotation excludes the possibility of approximating pH(2) as a simple sphere in its interaction with H(2)O.

Isomerization Mechanism in Hydrazone-Based Rotary Switches: Lateral Shift, Rotation, or Tautomerization?

Two intramolecularly hydrogen-bonded arylhydrazone (aryl = phenyl or naphthyl) molecular switches have been synthesized, and their full and reversible switching between the E and Z configurations have been demonstrated. These chemically controlled configurational rotary switches exist primarily as the E isomer at equilibrium and can be switched to the protonated Z configuration (Z-H(+)) by the addition of trifluoroacetic acid. The protonation of the pyridine moiety in the switch induces a rotation around the hydrazone C=N double bond, leading to isomerization. Treating Z-H(+) with base (K(2)CO(3)) yields a mixture of E and "metastable" Z isomers. The latter thermally equilibrates to reinstate the initial isomer ratio. The rate of the Z → E isomerization process showed small changes as a function of solvent polarity, indicating that the isomerization might be going through the inversion mechanism (nonpolar transition state). However, the plot of the logarithm of the rate constant k vs the Dimroth parameter (E(T)) gave a linear fit, demonstrating the involvement of a polar transition state (rotation mechanism). These two seemingly contradicting kinetic data were not enough to determine whether the isomerization mechanism goes through the rotation or inversion pathways. The highly negative entropy values obtained for both the forward (E → Z-H(+)) and backward (Z → E) processes strongly suggest that the isomerization involves a polarized transition state that is highly organized (possibly involving a high degree of solvent organization), and hence it proceeds via a rotation mechanism as opposed to inversion. Computations of the Z ↔ E isomerization using density functional theory (DFT) at the M06/cc-pVTZ level and natural bond orbital (NBO) wave function analyses have shown that the favorable isomerization mechanism in these hydrogen-bonded systems is hydrazone-azo tautomerization followed by rotation around a C-N single bond, as opposed to the more common rotation mechanism around the C=N double bond.

Insights into the ultraviolet spectrum of liquid water from model calculations

With a view toward a better molecular level understanding of the effects of hydrogen bonding on the ultraviolet absorption spectrum of liquid water, benchmark electronic structure calculations using high level wave function based methods and systematically enlarged basis sets are reported for excitation energies and oscillator strengths of valence excited states in the equilibrium water monomer and dimer and in a selection of liquid-like dimer structures. Analysis of the electron density redistribution associated with the two lowest valence excitations of the water dimer shows that these are usually localized on one or the other monomer, although valence hole delocalization can occur for certain relative orientations of the water molecules. The lowest excited state is mostly associated with the hydrogen bond donor and the significantly higher energy second excited state mostly with the acceptor. The magnitude of the lowest excitation energies is strongly dependent on where the valence hole is created, and only to a lesser degree on the perturbation of the excited electron density distribution by the neighboring water molecule. These results suggest that the lowest excitation energies in clusters and liquid water can be associated with broken acceptor hydrogen bonds, which provide energetically favorable locations for the formation of a valence hole. Higher valence excited states of the dimer typically involve delocalization of the valence hole and/or delocalization of the excited electron and/or charge transfer. Two of the higher valence excited states that involve delocalized valence holes always have particularly large oscillator strengths. Due to the pervasive delocalization and charge transfer, it is suggested that most condensed phase water valence excitations intimately involve more than one water molecule and, as a consequence, will not be adequately described by models based on perturbation of free water monomer states. The benchmark calculations are further used to evaluate a series of representative semilocal, global hybrid, and range separated hybrid functionals used in efficient time-dependent density functional methods. It is shown that such an evaluation is only meaningful when comparison is made at or near the complete basis set limit of the wave function based reference method. A functional is found that quantitatively describes the two lowest excitations of water dimer and also provides a semiquantitative description of the higher energy valence excited states. This functional is recommended for use in further studies on the absorption spectrum of large water clusters and of condensed phase water.

Application of high level wavefunction methods in quantum mechanics/molecular mechanics hybrid schemes

In this Perspective, several developments in the field of quantum mechanics/molecular mechanics (QM/MM) approaches are reviewed. Emphasis is placed on the use of correlated wavefunction theory and new state of the art methods for the treatment of large quantum systems. Until recently, computational chemistry approaches to large/complex chemical problems have seldom been considered as tools for quantitative predictions. However, due to the tremendous development of computational resources and new quantum chemical methods, it is nowadays possible to describe the electronic structure of biomolecules at levels of theory which a decade ago were only possible for system sizes of up to 20 atoms. These advances are here outlined in the context of QM/MM. The article concludes with a short outlook on upcoming developments and possible bottlenecks for future applications.

The origin of the conformational preference of N,N′-diaryl-N,N′-dimethyl ureas

Poly aromatic ureas and poly aromatic amides are important classes of foldamers-oligomers with well defined conformations. We have explored the origins of the conformational preference of some N,N'-diaryl-N,N'-dimethyl ureas by a combination of NMR spectroscopy and electronic structure calculations using both a recently developed density functional (M06-2X) and a DFT approach (DFT-D) having empirical corrections for dispersive interactions. We have validated the DFT-D approach for structures of this type using high level wavefunction calculations, (CCSD(T)), of the unsubstituted N,N'-diphenyl-N,N'-dimethyl urea. For the N,N'-diaryl-N,N'-dimethyl ureas we have identified a number of 'endo' conformers (i.e. having an E,E geometrical conformation about the two urea C-N bonds), both π- and tert-butyl-stacked, as well as 'exo' structures (having a Z geometrical conformation about at least one of the C-N bonds), and have computed the relative energies of these conformers as well as the barriers for their interconversion. We find that the relative energies of the 'endo' structures closely follow the relative values of the dispersive interactions. The calculations have allowed us to associate different conformers with the various peaks in the NMR spectra, which point to relatively small differences in energy between the conformers. Somewhat larger energy differences are predicted by the two computational approaches, with the M06-2X functional performing the better of the two. It is suggested that the continuum model employed may not be sufficiently accurate to reflect the solvation of the various conformers.

The effects of perfluorination on carbohydrate–π interactions: computational studies of the interaction of benzene and hexafluorobenzene with fucose and cyclodextrin

The effect of benzene fluorination on C-H...pi interactions is studied using a number of computational methods applied to a range of intermolecular complexes. High level wavefunction methods (CCSD(T)) predict a slightly greater interaction energy for complexes of benzene with methane or fucose, compared to corresponding complexes involving hexafluorobenzene. A number of more approximate treatments, DFT with the M06-2X functional, PM3-D* and MM methods, give interaction energies within 1 kcal mol(-1) of the high level values, and also correctly predict that the interaction energy is slightly greater for benzene compared to hexafluorobenzene. However, the DFT-D model used here predicts that the interaction energy is slightly greater for hexafluorobenzene. Molecular dynamics simulations, employing the GLYCAM-06 force field, validated here, are used to model the complexes of benzene and hexafluorobenzene with beta-cyclodextrin in aqueous solution. We predict the binding free energies of the complexes to be within 0.5 kcal mol(-1), and suggest that the different chemical shifts of the H5 protons observed in the two complexes arise from their slightly different structures, rather than from different binding energies.

RENORMALIZED LANDAU LEVELS AND PARTICLE-HOLE SYMMETRY IN GRAPHENE

In this proceedings paper we report on a calculation of graphene's Landau levels in a magnetic field. Our calculations are based on a self-consistent Hartree-Fock approximation for graphene's massless-Dirac continuum model. We find that because of graphene's chiral band structure interactions not only shift Landau-level energies, as in a non-relativistic electron gas, but also alter Landau level wavefunctions. We comment on the subtle continuum model regularization procedure necessary to correctly maintain the lattice-model's particle hole symmetry properties.

Possible Verification of Tilted Anisotropic Dirac Cone in α-(BEDT-TTF)2I3 Using Interlayer Magnetoresistance

It is proposed that the presence of a tilted and anisotropic Dirac cone can be verified using the interlayer magnetoresistance in the layered Dirac fermion system, which is realized in quasi-two-dimensional organic compound α-(BEDT-TTF) 2 I 3 . Theoretical formula for the interlayer magnetoresistance is derived using the analytic Landau level wave functions and assuming local tunneling of electrons. It is shown that the resistivity as a function of the azimuthal angle of the magnetic field takes the maximum in the direction of the tilt if anisotropy of the Fermi velocity of the Dirac cone is small. The procedure is described to determine the parameters of the tilt and anisotropy.

Potential energy curves and electronic structure of 3d transition metal hydrides and their cations

We investigate gas-phase neutral and cationic hydrides formed by 3d transition metals from Sc to Cu with density functional theory (DFT) methods. The performance of two exchange-correlation functionals, Boese-Martin for kinetics (BMK) and Tao-Perdew-Staroverov-Scuseria (TPSS), in predicting bond lengths and energetics, electronic structures, dipole moments, and ionization potentials is evaluated in comparison with available experimental data. To ensure a unique self-consistent field (SCF) solution, we use stability analysis, Fermi smearing, and continuity analysis of the potential energy curves. Broken-symmetry approach was adapted in order to get the qualitatively correct description of the bond dissociation. We found that on average BMK predicted values of dissociation energies and ionization potentials are closer to experiment than those obtained with high level wave function theory methods. This agreement deteriorates quickly when the fraction of the Hartree-Fock exchange in DFT functional is decreased. Natural bond orbital (NBO) population analysis was used to describe the details of chemical bonding in the systems studied. The multireference character in the wave function description of the hydrides is reproduced in broken-symmetry DFT description, as evidenced by NBO analysis. We also propose a new scheme to correct for spin contamination arising in broken-symmetry DFT approach. Unlike conventional schemes, our spin correction is introduced for each spin-polarized electron pair individually and therefore is expected to yield more accurate energy values. We derive an expression to extract the energy of the pure singlet state from the energy of the broken-symmetry DFT description of the low spin state and the energies of the high spin states (pentuplet and two spin-contaminated triplets in the case of two spin-polarized electron pairs). The high spin states are build with canonical natural orbitals and do not require SCF convergence.

QUANTUM HALL EFFECT ON THE FLAG MANIFOLD F2

The Landau problem on the flag manifold F2 = SU (3)/ U (1)× U (1) is analyzed from an algebraic point of view. The involved magnetic background is induced by two U(1) Abelian connections. In quantizing the theory, we show that the wave functions, of a nonrelativistic particle living on F2, are the SU(3) Wigner [Formula: see text]-functions satisfying two constraints. Using the F2 algebraic and geometrical structures, we derive the Landau Hamiltonian as well as its energy levels. The lowest Landau level (LLL) wave functions coincide with the coherent states for the mixed SU(3) representations. We discuss the quantum Hall effect for a filling factor ν = 1, where the obtained particle density is constant and finite for a strong magnetic field. In this limit, we also show that the system behaves like an incompressible fluid. We study the semiclassical properties of the system confined in LLL. These will be used to discuss the edge excitations and construct the corresponding Wess–Zumino–Witten action.