Energy-band structure of CdTe and Si: a sp(s)k.p model

The energy bands of the direct-band-gap semiconductor (CdTe) as well as the indirect-band-gap semiconductor (Si), throughout the entire Brillouin zone, have been obtained by diagonalizing a 24×24 k.p Hamiltonian referred to basis states at We extend the sp³s^∗ basis functions by the inclusion of orbitals. We find that the sp³‘d’(s^∗)²k.p model is fairly sufficient to describe the electronic structure of these systems over a wide energy range, obviating the use of any d orbitals. Finally, the comparison with available theoretical results shows that the present model reproduces known results for bulk CdTe and Si, that is, their band structure, including s and p valence bands and the lowest two conduction bands.     

Resonance states of atomic anions

We study destabilization of an atom in its ground state with decrease of its nuclear charge. By analytic continuation from bound to resonance states, we obtain complex energies of unstable atomic anions with nuclear charge that is less than the minimum “critical” charge necessary to bind N electrons. We use an extrapolating scheme with a simple model potential for the electron, which is loosely bound outside the atomic core. Results for O^2? and S^2? are in good agreement with earlier estimates. Alternatively, we use the Hylleraas basis variational technique with three complex nonlinear parameters to find accurately the energy of two‐electron atoms as the nuclear charge decreases. Results are used to check the less accurate one‐electron model. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 255–261, 2001     

Entanglement of polar symmetric top molecules as candidate qubits

Proposals for quantum computing using rotational states of polar molecules as qubits have previously considered only diatomic molecules. For these the Stark effect is second-order, so a sizable external electric field is required to produce the requisite dipole moments in the laboratory frame. Here we consider use of polar symmetric top molecules. These offer advantages resulting from a first-order Stark effect, which renders the effective dipole moments nearly independent of the field strength. That permits use of much lower external field strengths for addressing sites. Moreover, for a particular choice of qubits, the electric dipole interactions become isomorphous with NMR systems for which many techniques enhancing logic gate operations have been developed. Also inviting is the wider chemical scope, since many symmetric top organic molecules provide options for auxiliary storage qubits in spin and hyperfine structure or in internal rotation states.     

Efficient Remote Preparation of Four-Qubit Cluster-Type Entangled States with Multi-Party Over Partially Entangled Channels

We present a strategy for realizing multiparty-controlled remote state preparation (MCRSP) for a family of four-qubit cluster-type states by taking a pair of partial entanglements as the quantum channels. In this scenario, the encoded information is transmitted from the sender to a spatially separated receiver with control of the transmission by multiple parties. Predicated on the collaboration of all participants, the desired state can be faithfully restored at the receiver’s location with high success probability by application of additional appropriate local operations and necessary classical communication. Moreover, this proposal for MCRSP can be faithfully achieved with unit total success probability when the quantum channels are distilled to maximally entangled ones.     

Kinetic energy density for orbital‐free density functional calculations by axiomatic approach

An axiomatic approach is herein used to determine the physically acceptable forms for general D‐dimensional kinetic energy density functionals (KEDF). The resulted expansion captures most of the known forms of one‐point KEDFs. By statistically training the KEDF forms on a model problem of noninteracting kinetic energy in 1D (six terms only), the mean relative accuracy for 1000 randomly generated potentials is found to be better than the standard KEDF by several orders of magnitudes. The accuracy improves with the number of occupied states and was found to be better than for a system with four occupied states. Furthermore, we show that free fitting of the coefficients associated with known KEDFs approaches the exactly analytic values. The presented approach can open a new route to search for physically acceptable kinetic energy density functionals and provide an essential step toward more accurate large‐scale orbital free density functional theory calculations.     

Dimensional scaling treatment with relativistic corrections for stable multiply charged atomic ions in high-frequency super-intense laser fields

We present a theoretical framework which describes multiply charged atomic ions, their stability within super-intense laser fields, and also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H(-), H(2 -), He, He(-), He(2 -), He(3 -) within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind "additional" electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown. These nodes are spaced far enough from each other to minimize the electronic repulsion of the electrons, while still providing adequate enough attraction so as to bind the excess electrons into orbitals. We have found that even with relativistic considerations these species are stably bound within the field. It was also found that performing the dimensional scaling calculations for systems within the confines of laser fields to be a much simpler and more cost-effective method than the supporting D = 3 SCF method. The dimensional scaling method is general and can be extended to include relativistic corrections to describe the stability of simple molecular systems in super-intense laser fields.     

Effects of Hawking Radiation on the Entropic Uncertainty in a Schwarzschild Space‐Time

The Heisenberg uncertainty principle describes a basic restriction on an observer's ability of precisely predicting the measurement of a pair of noncommuting observables, and virtually is at the core of quantum mechanics. Herein, the aim is to study the entropic uncertainty relation (EUR) under the background of a Schwarzschild black hole and its control. Explicitly, dynamical features of the measuring uncertainty via entropy are developed in a practical model where a stationary particle interacts with its surrounding environment while another particle—serving as a quantum memory reservoir—undergoes free fall in the vicinity of the event horizon of the Schwarzschild space‐time. It shows higher Hawking temperatures would give rise to an inflation of the entropic uncertainty on the measured particle. This is suggestive of the fact the measurement uncertainty is strongly correlated with degree of mixing present in the evolving particles. Additionally, based on information flow theory, a physical interpretation for the observed dynamical behaviors related with the entropic uncertainty in such a genuine scenario is provided. Finally, an efficient strategy is proposed to reduce the uncertainty by non‐tracing‐preserved operations. Therefore, our explorations may improve the understanding of the dynamic entropic uncertainty in a curved space‐time, and illustrate predictions of quantum measurements in relativistic quantum information sciences.     

Primität und Homomorphie von ebenen Dreiecksgraphen

Ohne Zusammenfassung     

Achieving high circularly polarized luminescence with push–pull helicenic systems: from rationalized design to top-emission CP-OLED applications

While the development of chiral molecules displaying circularly polarized luminescence (CPL) has received considerable attention, the corresponding CPL intensity, g_lum, hardly exceeds 10⁻² at the molecular level owing to the difficulty in optimizing the key parameters governing such a luminescence process. To address this challenge, we report here the synthesis and chiroptical properties of a new family of π-helical push–pull systems based on carbo[6]helicene, where the latter acts as either a chiral electron acceptor or a donor unit. This comprehensive experimental and theoretical investigation shows that the magnitude and relative orientation of the electric (μ_e) and magnetic (μ_m) dipole transition moments can be tuned efficiently with regard to the molecular chiroptical properties, which results in high g_lum values, i.e. up to 3–4 × 10⁻². Our investigations revealed that the optimized mutual orientation of the electric and magnetic dipoles in the excited state is a crucial parameter to achieve intense helicene-mediated exciton coupling, which is a major contributor to the obtained strong CPL. Finally, top-emission CP-OLEDs were fabricated through vapor deposition, which afforded a promising g_El of around 8 × 10⁻³. These results bring about further molecular design guidelines to reach high CPL intensity and offer new insights into the development of innovative CP-OLED architectures.

A CPL intensity of up to 3 × 10⁻² is achieved in π-extended 6-helicene derivatives, owing to an intense helicene-mediated exciton coupling. Corresponding top-emission CP-OLEDs afforded a promising g_El of around 8 × 10⁻³.

The design of chiral emitters displaying intense circularly polarized luminescence (CPL) has attracted significant interest, thanks to the potential of CP light in a diverse range of applications going from chiroptoelectronics (organic light-emitting diodes (OLEDs), optical information processing, etc.) to bio-imaging and chiral sensing.¹ Recently, designing OLEDs with CP electroluminescence (CP-OLEDs) has emerged as an interesting approach to improve high-resolution display performance. Namely, using unpolarised OLEDs, up to 50% of the emitted light can be lost due to the use of antiglare polarized filters.² In CP-OLEDs, the electro-generated light can pass these filters with less attenuation owing to its circular polarization and thus lead to an increase of the image brightness with lower power consumption.³ To develop CP-OLED devices, the main approach relies on the doping of the device''s emitting layer by a CPL emitter, which should ensure simultaneously high exciton conversion and a high degree of circular polarization. The harvesting of both singlet and triplet excitons has been successfully addressed using either chiral phosphorescent materials or thermally activated delayed fluorescence (CP-TADF) emitters with device efficiencies of up to 32%.⁴ However, the intensity of circularly polarized electroluminescence (CPEL), evaluated by the corresponding dissymmetry factor g_El, remains inefficient and typically falls within the range of 10⁻³ with limited examples reaching g_El > 10⁻² based on polymeric materials and lanthanide complexes.⁵ For CP-OLEDs using a molecular chiral emissive dopant, g_El, defined as the ratio between the intensity difference of left- and right-CPEL, and the total generated electroluminescence, 2(El_L − El_R)/(El_L + El_R), can be generally related to the luminescence dissymmetry factor g_lum measured in diluted solution.² Accordingly, it is of crucial importance to design luminescent molecules with high g_lum values,^3,28a–d,29 in order to reach strong CP electro-luminescence when going to practical devices. However, structural and electronic factors that govern the CPL of chiral compounds are still poorly understood even if a few studies have recently tried to rationalize and establish molecular guidelines to obtain high g_lum values.⁶Our team has contributed to the research in this area by developing extended π-helical molecular architectures resulting from the association of carbo[6]helicene and achiral dyes,⁷ which afforded enhanced chiroptical properties, with notably a g_lum up to 10⁻², owing to an uncommon chiral exciton coupling process mediated by the chiral helicenic unit.⁸ In addition, we also described an unusual solvent effect on the intensity of CPL of π-helical push–pull helicene–naphthalimide derivatives,^7b which showed a decrease of g_lum from 10⁻² to 10⁻³ upon increasing the polarity of solvent.^7b This solvatochromism effect was shown to be related to a symmetry breaking of the chiral excited state before emission,⁹ which modifies the relative intensity of the magnetic (μ_m) and electric (μ_e) dipole transition moments, and the angle, θ, between them (Fig. 1), ultimately impacting g_lum. The latter is well approximated as 4|m|cos θ/(|μ|) for an electric dipole-allowed transition.¹⁰Open in a separate windowFig. 1Chemical structures of “push–pull” 2,15-diethynylhexahelicene-based emitters with their polarized luminescence characteristics including their calculated electric and magnetic transition dipole moments and the angle between them corresponding to the S₁ → S₀ transition.While these results highlight interesting aspects regarding the key parameters influencing the CPL of organic emitters, this type of “helical push–pull design” remains limited to only one example, which render the systematic rationalization of these findings difficult. Accordingly, we decided to develop a complete family of new chiral push–pull compounds to explore the structural and electronic impact of the grafted substituents on the helical π-conjugated system. In addition, we went a step further and incorporated the designed chiral emitter into proof-of-concept CP-OLEDs using a top-emission architecture,¹¹ which remains scarcely explored for CP-light generation despite its considerable potential for micro-display applications. To the best of our knowledge, only one example of such type of electroluminescent device has been reported, using a CP-TADF emitter, affording a modest g_El of 10⁻³.^11aHerein, we report the synthesis and chiroptical properties of a new family of π-helical push–pull systems based on chiral carbo[6]helicene, functionalized by either electron donor or acceptor units. Interestingly, the chiral π-conjugated system of the helicene may act as either an electron acceptor or a donor, depending on the nature of the attached substituents, thereby impacting the chiroptical properties, notably the resulting CPL. By optimizing the chiral exciton coupling process through the modulation of the magnitude and relative orientation of the electric (μ) and magnetic (m) dipoles, the chiroptical properties of classical carbo[6]helicene-based emitters can be dramatically enhanced and reach high g_lum values at the molecular level, i.e. up to 3–4 × 10⁻². Experimental and theoretical investigations revealed that the mutual orientation of the electric and magnetic dipoles in the excited-state is a crucial parameter and is optimal when the substituents attached to the helicene core possess a rather weak electron withdrawing or donating ability. Finally, proof of concept top-emission CP-OLEDs were fabricated through vapor deposition of π-helical push–pull derivatives and afforded a g_El of around 8 × 10⁻³, which represents a significant improvement for the polarization of electroluminescence emitted using this device architecture.     

Large-Z and -N dependence of atomic energies from renormalization of the large-dimension limit

By combining Hartree–Fock results for nonrelativistic ground-state energies of N-electron atoms with analytic expressions for the large-dimension limit, we have obtained a simple renormalization procedure. For neutral atoms, this yields energies typically threefold more accurate than the Hartree–Fock approximation. Here, we examine the dependence on Z and N of the renormalized energies E(N, Z) for atoms and cations over the range Z, N = 2 → 290. We find that this gives for large Z = N an expansion of the same form as the Thomas–Fermi statistical model, E → Z^7/2(C₀ + C₁Z^?1/3 + C₂Z^?2/3 + C₃Z^?3/3 + ?), with similar values of the coefficients for the three leading terms. Use of the renormalized large-D limit enables us to derive three further terms. This provides an analogous expansion for the correlation energy of the form δE δZ^4/3(δC₃ + δC₅Z^?2/3 + δC₆Z^?3/3 + ?); comparison with accurate values of δE available for the range Z ? 36 indicates the mean error is only about 10%. Oscillatory terms in E and δE are also evaluated. © 1994 John Wiley & Sons, Inc.