Ground State Energy Levels Research Articles

Tuning the Protein-Induced Absorption Shifts of Retinal in Engineered Rhodopsin Mimics.

Rational design of light-capturing properties requires understanding the molecular and electronic structure of chromophores in their native chemical or biological environment. We employ here large-scale quantum chemical calculations to study the light-capturing properties of retinal in recently designed human cellular retinol binding protein II (hCRBPII) variants (Wang et al. Science, 2012, 338, 1340-1343). Our calculations show that these proteins absorb across a large part of the visible spectrum by combined polarization and electrostatic effects. These effects stabilize the ground or excited state energy levels of the retinal by perturbing the Schiff-base or β-ionone moieties of the chromophore, which in turn modulates the amount of charge transfer within the molecule. Based on the predicted tuning principles, we design putative in silico mutations that further shift the absorption properties of retinal in hCRBPII towards the ultraviolet and infrared regions of the spectrum.

Diamagnetic Raman Optical Activity of Chlorine, Bromine, and Iodine Gases.

Magnetic Raman optical activity of gases provides unique information about their electric and magnetic properties. Magnetic Raman optical activity has recently been observed in a paramagnetic gas (Angew. Chem. Int. Ed. 2012, 51, 11058; Angew. Chem. 2012, 124, 11220). In diamagnetic molecules, it has been considered too weak to be measurable. However, in chlorine, bromine and iodine vapors, we could detect a significant signal as well. Zeeman splitting of electronic ground-state energy levels cannot rationalize the observed circular intensity difference (CID) values of about 10(-4). These are explicable by participation of paramagnetic excited electronic states. Then a simple model including one electronic excited state provides reasonable spectral intensities. The results suggest that this kind of scattering by diamagnetic molecules is a general event observable under resonance conditions. The phenomenon sheds new light on the role of excited states in the Raman scattering, and may be used to probe molecular geometry and electronic structure.

Ground states of critical and supercritical problems of Brezis–Nirenberg type

We study the existence of symmetric ground states to the supercritical problem $$\begin{aligned} -\Delta v=\lambda v+\left| v\right| ^{p-2}v\;\text {in}\;\Omega ,\quad v=0\;\text {on}\;\partial \Omega , \end{aligned}$$ in a domain of the form $$\begin{aligned} \Omega =\{(y,z)\in \mathbb {R}^{k+1}\times \mathbb {R}^{N-k-1}:\left( \left| y\right| ,z \right) \in \Theta \}, \end{aligned}$$ where \(\Theta \) is a bounded smooth domain such that \(\overline{\Theta } \subset \left( 0,\infty \right) \times \mathbb {R}^{N-k-1}\), \(1\le k\le N-3\), \(\lambda \in \mathbb {R}\), and \(p=\frac{2(N-k)}{N-k-2}\) is the \((k+1)\)-st critical exponent. We show that symmetric ground states exist for \(\lambda \) in some interval to the left of each symmetric eigenvalue and that no symmetric ground states exist in some interval \((-\infty ,\lambda _{*})\) with \(\lambda _{*}>0\) if \(k\ge 2\). Related to this question is the existence of ground states to the anisotropic critical problem $$\begin{aligned} -\text {div}(a(x)\nabla u)=\lambda b(x)u+c(x)\left| u\right| ^{2^{*}-2}u\;\text {in}\; \Theta ,\quad u=0\;\text {on}\; \partial \Theta , \end{aligned}$$ where a, b, c are positive continuous functions on \(\overline{\Theta }\). We give a minimax characterization for the ground states of this problem, study the ground state energy level as a function of \(\lambda \), and obtain a bifurcation result for ground states.

On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schrödinger Equation for Interdiffused Quantum Wells and Quantum Wires**Supported by the Ministry of Education, Science, and Technological Development of Serbia and the Flemish fund for Scientific Research (FWO Vlaanderen)

We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schrödinger equation. The accuracy of the solution is explored as it varies with the range of the numerical domain. The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires. Also, the model of a linear harmonic oscillator is considered for comparison reasons. It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range, which is thus considered to be optimal. This range is found to depend on the number of mesh nodes N approximately as α0 logeα1(α2N), where the values of the constants α0, α1, and α2 are determined by fitting the numerical data. And the optimal range is found to be a weak function of the diffusion length. Moreover, it was demonstrated that a domain range adaptation to the optimal value leads to substantial improvement of accuracy of the solution of the Schrödinger equation.

On Dipolar Quantum Gases in the Unstable Regime

We study the nonlinear Schrödinger equation arising in dipolar Bose--Einstein condensate in the unstable regime. Two cases are studied: the first when the system is free, the second when gradually a trapping potential is added. In both cases we first focus on the existence and stability/instability properties of standing waves. Our approach leads to the search of critical points of a constrained functional which is unbounded from below on the constraint. In the free case, by showing that the constrained functional has a so-called mountain pass geometry, we prove the existence of standing states with least energy, the ground states, and show that any ground state is orbitally unstable. Moreover, when the system is free, we show that small data in the energy space scatter in all regimes, stable and unstable. In the second case, if the trapping potential is small, we prove that two different kinds of standing waves appear: one corresponds to a topological local minimizer of the constrained energy functional and consists in ground states, and the other is again of mountain pass type but now corresponds to excited states. We also prove that any ground state is a topological local minimizer. Despite the problem being mass supercritical and the functional being unbounded from below, the standing waves associated to the set of ground states turn out to be orbitally stable. Actually, from the physical point of view, the introduction of the trapping potential stabilizes the system that is initially unstable. Related to this we observe that it also creates a gap in the ground state energy level of the system. In addition when the trapping potential is active the presence of standing waves with arbitrary small norm does not permit small data scattering. Eventually some asymptotic results are also given.

Thiophene-bithiazole based metal-free dye as DSSC sensitizer: Effect of co-adsorbents on photovoltaic efficiency

A new molecule consisting of a bithiazole chromophore sandwiched between two thiophenes, functionalized with benzothiophene unit at one end and cyanoacrylic acid at the other end (BT1) was synthesized, photophysical properties were studied and employed as a photosensitizer in dye-sensitized solar cells (DSSCs). The molecule exhibited an intense absorption in the UV-visible region with absorption extending up to 500 nm. The ground and excited state potentials of BT1 were calculated to be 1.29 and -0.65 V, respectively vs. NHE using cyclic voltammetry. The ground state energy level is more positive than the triiodide electrolyte and excited state energy level is considerably more negative than the TiO2 satisfying the energetic requirements for a photosensitizer in DSSC. The solar cells fabricated from BT1 exhibited an efficiency of 1.13%. The effect of various co-adsorbents (CDCA,TP1 andTP2) on the DSSC performance was investigated in detail. In the presence of CDCA, the photovoltaic efficiency was enhanced to 1.25%, whereas, in the presence of TP1 and TP2, the efficiency lowered to 0.20% and 0.59%, respectively. The increased efficiency in the presence of CDCA could be attributed to the prevention of the aggregation of dye molecules induced by CDCA. On the other hand, TP1 and TP2 were found to be not as effective as CDCA to prevent aggregation leading to the lowering of photoconversion efficiency.

Germanium–vacancy color center in isotopically enriched diamonds synthesized at high pressures

We report on the high-pressure synthesis of novel nano- and microcrystalline diamonds with germanium–vacancy (Ge–V) color centers emitting at 602 nm. The synthesis was carried out in non-metallic growth systems C–H–Ge and C–H–O–Ge enriched with germanium and carbon isotopes. We demonstrate germanium and carbon isotope shifts in the fine structure of the luminescence, which allows us to unambiguously associate the center with the germanium impurity entering into the diamond lattice. We show that there are two ground-state energy levels with the separation of 0.7 meV and two excited-state levels separated by 4.6 meV in the electronic structure of the center and suggest a split-vacancy structure of this center. High-intensity and narrow-line emission of high-pressure synthesized small diamonds with Ge–V centers makes them promising candidates for single-photon emitters.

Theoretical and Experimental Optimization of InGaAs Channels in GaAs PHEMT Structure

The ground-state energy level (GEL) and electron distribution of GaAs pseudomorphic high-electron-mobility transistors (PHEMTs) are analyzed by a self-consistent solution to the Schrödinger—Poisson equations. The indium composition and thickness of the InGaAs channel are optimized according to the GEL position. The GEL position is not in direct proportion to 1/d2 (d is the channel thickness) by considering the influence of electron distribution in the InGaAs channel. Indium composition 0.22 and channel thickness 9nm are obtained by considering the mismatch between InGaAs and AlGaAs. Several PHEMT samples are grown according to the theoretical results and mobility 6300 cm2/V·s is achieved.

Ring planarity problem of 2-oxazoline revisited using microwave spectroscopy and quantum chemical calculations.

In a previous infrared, Raman, and microwave spectroscopic work,1 it was claimed that 2-oxazoline has a planar ring equilibrium conformation, and the ring-puckering potential function V(z) = 22.2(z(4) + 1.31z(2)) cm(-1), where z is a dimensionless reduced coordinate, was derived. This function poorly reproduces the rotational constants of the lowest and most important puckering states. The microwave spectrum has been reinvestigated and largely extended to include more than 4600 transitions of the ground state and six excited states of the ring-puckering vibration allowing accurate centrifugal distortion constants to be obtained for the first time. A new potential function V(z) = 38.8(z(4) - 0.65z(2)) cm(-1) has been determined. This function yields much better agreement between calculated and observed rotational constants, especially for the lowest puckering states, than the previous function and predicts a nonplanar ring equilibrium conformation. The barrier to ring planarity is determined to be 49(8) J/mol. The ground-state energy level is 35 cm(-1) above the barrier maximum. Theory predicts that three of the five Watson centrifugal distortion constants, ΔJK, ΔK, and δK, should vary with the puckering state, whereas ΔJ and δJ should be unaffected. It was found that ΔJK and ΔK indeed behave in the expected manner, while deviations were seen for the three other centrifugal distortion constants. The ab initio methods HF, MP2, CCSD, CCSD(T), and CCSD(T)-F12 with large basis sets as well as several DFT methods were used in an attempt to reproduce the low experimental barrier to the planar ring. Only the MP2 method yielded a satisfactory prediction of the barrier. The CCSD and the CCSD(T) calculations predict a planar ring, whereas the energy differences between a planar and a nonplanar ring obtained in the CCSD(T)-F12 computations are so small that a definite conclusion cannot be drawn.

Isomeric and ground state energy level measurements of natural tellurium isotopes via (γ,n) reaction

We have planned to measure isomeric and ground state energy levels in 120Te(γ,n)119m,gTe, 122Te(γ,n)121m,gTe, 128Te(γ,n)127m,gTe, 130Te(γ,n)129m,gTe photonuclear reactions of natural tellurium induced by bremsstrahlung photons with end-point energy at 18 MeV. The sample was irradiated in the clinical linear electron accelerator (Philips SLi-25) at Akdeniz University Hospital. The gamma spectrum of the tellurium sample was measured using HP(Ge) semiconductor detector (ORTEC) and multi channel analyzer. We used both MAESTRO (ORTEC) and home made root based gui program (Theia) for data analyzing. The obtained experimental data values are compared with NUDAT energy values.

Two-electronn−pdouble quantum dots in carbon nanotubes

We consider electron states in $n\text{\ensuremath{-}}p$ double quantum dots defined in a semiconducting carbon nanotube (CNT) by an external potential. We describe formation of extended single-electron orbitals originating from the conduction and valence bands confined in a minimum and a maximum of the external potential, respectively. We solve the problem of a confined electron pair using an exact diagonalization method within the tight-binding approach, which allows for a straightforward treatment of the conduction- and valence-band states, keeping an exact account for the intervalley scattering mediated by the atomic defects and the electron-electron interaction. The exchange interaction, which in the unipolar double dots is nearly independent of the axial magnetic field ($B$) and forms singletlike and tripletlike states, in the $n\text{\ensuremath{-}}p$ system appears only for selected states and narrow intervals of $B$. In particular, the ground-state energy level of a $n\text{\ensuremath{-}}p$ double dot is not split by the exchange interaction and remains fourfold degenerate at zero magnetic field also for a strong tunnel coupling between the dots.

Effect of Interdiffusion on Optoelectronic Properties of In1-xGaxAs/InAs/In1-yAlyAs Quantum Well

The effect of interdiffusion of Al, Ga and In atoms on confining potential, ground state energy level of electron and interband light absorption coefficient in In1-xGaxAs/InAs/In1-yAlyAs quantum well is investigated in the framework of variational method and Wood-Saxon potential model. It is shown that the interdiffusion leads to the smearing of potential rectangular profile, to the rising up of ground state energy level and to the significant decrease in the interband absorption coefficient.

Wigner Measures Approach to the Classical Limit of the Nelson Model: Convergence of Dynamics and Ground State Energy

We consider the classical limit of the Nelson model, a system of stable nucleons interacting with a meson field. We prove convergence of the quantum dynamics towards the evolution of the coupled Klein-Gordon-Schr\"odinger equation. Also, we show that the ground state energy level of $N$ nucleons, when $N$ is large and the meson field approaches its classical value, is given by the infimum of the classical energy functional at a fixed density of particles. Our study relies on a recently elaborated approach for mean field theory and uses Wigner measures.

Born-Oppenheimer approximation for theXYZmesons

Many of the XYZ mesons discovered in the last decade can be identified as bound states in Born-Oppenheimer (B-O) potentials for a heavy quark and antiquark. They include quarkonium hybrids, which are bound states in excited flavor-singlet B-O potentials, and quarkonium tetraquarks, which are bound states in flavor-nonsinglet B-O potentials. We present simple parameterizations of the deepest flavor-singlet B-O potentials. We infer the deepest flavor-nonsinglet B-O potentials from lattice QCD calculations of static adjoint mesons. Selection rules for hadronic transitions are used to identify XYZ mesons that are candidates for ground-state energy levels in the B-O potentials for charmonium hybrids and tetraquarks. The energies of the lowest-energy charmonium hybrids are predicted by using the results of lattice QCD calculations to calculate the energy splittings between the ground states of different B-O potentials and using the Schroedinger equation to determine the splittings between energy levels within a B-O potential.

One order enhancement of detectivity in quaternary capped InAs/GaAs quantum dot infrared photodetectors due to vertical coupling of quantum dot layers

The spectral and electrical properties of vertically coupled quaternary (InAlGaAs) capped InAs/GaAs quantum dot infrared photodetector with different capping thicknesses are investigated, and compared with a conventional quaternary capped uncoupled detector. Electronic coupling between quantum dot layers leads to a reduction in the ground state energy level and hence greater electronic confinement, which reduces the dark current and enhances the detectivity. These expectations are confirmed by our experimental results. Most significantly one order enhancement in peak detectivity (from 1.1×109cmHz1/2/W to 2.48×1010cmHz1/2/W) is observed for optimized coupled quantum dot infrared photodetector compared to uncoupled device. The optimal interlayer barrier thickness which gives maximum detectivity is explained in terms of the interplay between electronic coupling and strain buildup in the heterostructure.

Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space

Based on the Bogoliubov non-ideal gas model, we discuss the energy spectrum and phase transition of the superfluid Fermi gas of atoms with a weak attractive interaction on the canonical noncommutative space. Because the interaction of a BCS-type superfluid Fermi gas originates from a pair of Fermionic quasi-particles with opposite momenta and spins, the Hamiltonian of the Fermi gas on the noncommutative space can be described in terms of the ordinary creation and annihilation operators related to the commutative space, while the noncommutative effect appears only in the coefficients of the interacting Hamiltonian. As a result, we can rigorously solve the energy spectrum of the Fermi gas on the noncommutative space exactly following the way adopted on the commutative space without the use of perturbation theory. In particular, different from the previous results on the noncommutative degenerate electron gas and superconductor where only the first order corrections of the ground state energy level and energy gap were derived, we obtain the nonperturbative energy spectrum for the noncommutative superfluid Fermi gas, and find that each energy level contains a corrected factor of cosine function of noncommutative parameters. In addition, our result shows that the energy gap becomes narrow and the critical temperature of phase transition from a superfluid state to an ordinary fluid state decreases when compared with that in the commutative case.

Measurement of proton tunneling in short hydrogen bonds in single crystals of 3,5 pyridinedicarboxylic acid using nuclear magnetic resonance spectroscopy.

In this Letter, we present NMR spin-lattice and relaxometry data for proton transfer in one of the shortest known N-H⋯O hydrogen bonds in a single crystal of 3,5 pyridinedicarboxylic acid (35PDCA). It is widely believed that proton transfer by quantum tunneling does not occur in short hydrogen bonds since the ground state energy level lies above the potential barrier, yet these data show a temperature independent, proton tunneling rate below 77K and a clear deviation from classical dynamics below 91K. This study therefore suggests that proton tunneling occurs in all hydrogen bonds at low temperature and the crossover temperature to classical hopping must be determined when evaluating whether proton tunneling persists at higher temperature, for example in enzyme catalysis under physiological conditions.

LiTaO3단결정 내의 Fe3+상자성 불순물 이온에 대한 에너지 준위 계산

Ground state energy levels of the Fe paramagnetic impurity ion in stoichiometric LiTaO3 and in congruent LiTaO3 single crystals were calculated with electron paramagnetic resonance constants. Energy levels between six energy levels were obtained with spectroscopic splitting parameter g and zero field splitting constant D for Fe ion. The energy diagrams of Fe ion were different from different magnetic field directions ([100], [001], [111]) when magnetic field increases. The calculated ZFS energies of Fe ion in stoichiometric and congruent LiTaO3 single crystals for |± 5/2> ↔ |± 3/2> and |± 3/2> ↔ |± 1/2> transitions were 12.300 GHz and 6.150 GHz, and 59.358 GHz and 29.679 GHz, respectively. It turns out that energy levels of Fe paramagnetic impurity in LiTaO3 crystal are different from different crystal growing condition.

Selection Rules for Hadronic Transitions ofXYZMesons

Many of the XYZ mesons discovered in the last decade can be identified as bound states of a heavy quark and antiquark in Born-Oppenheimer (BO) potentials defined by the energy of gluon and light-quark fields in the presence of static color sources. The mesons include quarkonium hybrids, which are bound states in excited flavor-singlet BO potentials, and quarkonium tetraquarks, which are bound states in BO potentials with light-quark+antiquark flavor. The deepest hybrid potentials are known from lattice QCD calculations. The deepest tetraquark potentials can be inferred from lattice QCD calculations of static adjoint mesons. Selection rules for hadronic transitions are derived and used to identify XYZ mesons that are candidates for ground-state energy levels in the BO potentials for charmonium hybrids and tetraquarks.

An optically modulated zero-field atomic magnetometer with suppressed spin-exchange broadening

We demonstrate an optically pumped (87)Rb magnetometer in a microfabricated vapor cell based on a zero-field dispersive resonance generated by optical modulation of the (87)Rb ground state energy levels. The magnetometer is operated in the spin-exchange relaxation-free regime where high magnetic field sensitivities can be achieved. This device can be useful in applications requiring array-based magnetometers where radio frequency magnetic fields can induce cross-talk among adjacent sensors or affect the source of the magnetic field being measured.