Orbital Wave Functions Research Articles

One- and Two-Photon Absorption: Physical Principle and Applications.

We introduce the principle and applications of one-photon absorption (OPA) and two-photon absorption (TPA) controlled by external electric fields. The physical mechanism of OPA and TPA are firstly introduced, which can visually promote thoroughly understanding of principle and physical analysis. Secondly, the applications of different molecules in OPA and TPA with and without external electric field are introduced in detail. The effect of the external electric field on the charge transfer during the absorption process is also exemplified. Furthermore, the external electric field on the molecular orbital wave function is visualized through the charge transfer process in the excited state transitions. The purpose of this review is to deepen the understanding of the types of charge transfer under linear and non-linear absorption in different systems.

Study on the Decomposition Mechanism of the HFO1234zeE/N2 Gas Mixture

HFO1234zeE is an environmental-friendly gas with the potential to replace sulfur hexafluoride (SF6). Therefore, research on the breakdown and decomposition characteristics of the HFO1234zeE gas mixture was conducted. The breakdown experiments of the 20% HFO1234zeE/80% N2 gas mixture under different electric fields were performed, and the feasibility of replacing SF6 with HFO1234zeE was verified in terms of insulation strength. Based on the density functional theory, the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) wave function distributions of the HFO1234zeE molecule were obtained. According to the frontier orbital theory, the possible position of reaction in the molecule may occur at the carbon–carbon double bond and carbon–hydrogen bond. Moreover, reaction force field-molecular dynamics (ReaxFF-MD) was used to simulate the decomposition of the 20% HFO1234zeE/80% N2 gas mixture, the effect of the temperature and pressure on the decomposition reaction was studied, and the main decomposition paths were analyzed. The research results show that the main decomposition products are C2F2, CN, CNF, H, N, F, and HN2. With the increase in temperature and pressure, the number of molecules decomposed increases. The conclusions provide the theoretical basis for the application of HFO1234zeE.

Relativistic Approximations for Quantization and Harmony in the Schrödinger Equation, and Why Mechanics Is Quantized

The initial purpose is to add two physical origins for the outstandingly clear mathematical description that Dirac has left in his Principles of Quantum Mechanics. The first is the “internal motion” in the wave function of the electron that is now expressed through dispersion dynamics; the second is the physical origin for mathematical quantization. Bohr’s model for the hydrogen atom was “the greatest single step in the development of the theory of atomic structure.” It leads to the Schrodinger equation which is non-relativistic, but which conveniently equates together momentum and electrostatic potential in a representation containing mixed powers. Firstly, we show how the equation is expansible to approximate relativistic form by applying solutions for the dilation of time in special relativity, and for the contraction of space. The adaptation is to invariant “harmonic events” that are digitally quantized. Secondly, the internal motion of the electron is described by a stable wave packet that implies wave-particle duality. The duality includes uncertainty that is precisely described with some variance from Heisenberg’s axiomatic limit. Harmonic orbital wave functions are self-constructive. This is the physical origin of quantization.

Elastic Scattering of Electrons by Helium Atoms in Born Approximation

Elastic scattering phenomena arising in electron-helium scattering are dominant processes. The determination of accurate elastic differential cross sections for electron-helium scattering has a considerable importance. An accurate calculation of the plane-wave first Born exchange amplitude of electrons elastic scattering by helium atoms is reported. The direct and exchange amplitudes are calculated analytically from the Hartree-Fock orbital wave functions by using a variational method. The forms of these wave functions are very suitable for analytical calculations and powerful to generalize to more complex atomic systems. The interaction potential is modelled by the static Coulomb interaction between the incident electron and the atomic system. The differential cross sections are calculated at intermediate energies taking into account the exchange effects. We have established in the high energies region, by neglecting the exchange effects, the analytical expressions of the total and momentum transport cross sections suitable for the calculation of the plasma transport properties. A very compact form of the Born amplitude has been proposed as a finite series of Gaussian functions, which represents a major tool in the calculations of differential cross sections of two-electron atomic systems. Numerical results are used to analyze the contribution of the exchange amplitude to the differential cross sections at intermediate and high energies. The differential cross sections are calculated for the energy range 30-400 eV. We find good agreement in high energy domain scattering with experimental results and other sophisticated calculations without using any adjustable parameter.

Effect of Deposition Parameters on the Structure of ZnCo Alloy Nanowires and Growth Mechanism

To elucidate the effect of voltage and concentration on the elctrodeposition of ZnCo nanowires, we have studied the deposition of ZnCo nanowires by XRD and SEM. The structure of ZnCo alloy nanowires changes by changing the concentration of electrolyte as 100-x g/l Co100-xZnx (0≤x≤15), at constant voltage -1.6, and fixed pH 3. XRD results show that change in concentration can transform the crystal structure of electrodeposited Co100-xZnx from crystalline to amorphous. Furthermore, similar behavior from crystalline to amorphous was also observed for ZnCo electrodeposited nanowires at various potentials (-1.6V, - 2.5V, and - 3.0V) from the bath containing Co95g/l and Zn5g/l, pH 3 and at room temperature. We argued that this change in structure of ZnCo nanowires can be attributed to the faster growth rate of Zn than Co. These results can be explained by the electron tunneling theory. The workfunction of Zn (4.33eV) is smaller than Co (5.0eV) and the wavefunction of Zn metal has a larger overlap with orbital wavefunction of Zn ions, which leads the faster growth rate of Zn and hence influenced the structure of ZnCo alloy nanowires.

Landau levels of bilayer graphene in a WSe2 /bilayer graphene van der Waals heterostructure

Heterostructures formed between two different van der Waals materials enable interactions and functionalities absent in each component. In this work we show that vicinity to an atomically thin WSe$_2$ sheet dramatically impacts the energies of the symmetry-broken low Landau levels of bilayer graphene, possibly due to screening. We present a systematic study of the magnetic field and electrical displacement field dependences of the Landau level gaps at filling factor $\nu$ = 1, 2, 3, and compare to BN encapsulated pristine bilayer graphene. The exchange-dominated energy splitting between the N = 0 and 1 orbital wave functions is significantly enhanced, which leads to a modified phase diagram at filling factor $\nu$ = 0 and larger energy gaps at $\nu$ = 1 and 3 in WSe$_2$/bilayer graphene heterostructures. The exchange-enhanced spin gap at $\nu$ = 2, on the other hand, is reduced by approximately two-fold. Our results demonstrate a possible way to engineer quantum Hall phenomena via van der Waals heterostructures.

Valley drift and valley current modulation in strained monolayer MoS2

Elastic-mechanical deformations are found to dramatically alter the electronic properties of monolayer (ML) $\mathrm{Mo}{\mathrm{S}}_{2}$; particularly, the low-energy Bloch bands are responsive to a directional strain. In this study, in-plane uniaxial deformation is found to drift the low-energy electron/hole valleys of strained $\mathrm{ML}\text{\ensuremath{-}}\mathrm{Mo}{\mathrm{S}}_{2}$ far away from $K/K'$ points in the Brillouin zone (BZ). The amount of drift differs notably from hole to electron bands, where the conduction band minimum (CBM) drifts nearly 2 times more than the valence band maximum (VBM) in response to a progressively increasing strain field (0--10%). The resulting strain-induced valley asymmetry/decoherence can lift the momentum degeneracy of valley carriers at the $K$ point, thereby affecting the low-energy valley excitations ($K$-valley polarization) in a strained $\mathrm{ML}\text{\ensuremath{-}}\mathrm{Mo}{\mathrm{S}}_{2}$ lattice. The quantum origin of this decoherent valley arises from the differences in the Bloch orbital wave functions of electron and hole states at the exciton band edges and their deformation under strain. A higher drift (g1.5 times) is noticed when strain is along the zigzag (ZZ) axis relative to the armchair (AC) axis, which is attributed to a faster decline in Young's modulus and Poisson's ratio (PR) along the ZZ direction. A similar valley drift only in the VBM of uniaxially strained $\mathrm{ML}\text{\ensuremath{-}}\mathrm{Mo}{\mathrm{S}}_{2}$ was reported in an earlier local density approximation (LDA) based density functional theory (DFT) study [Q. Zhang et al., Phys. Rev. B 88, 245447 (2013)], where a massive valley drift occurring at the CBM was fully overlooked. Moreover, the giant VBM drift reported therein is 6 times the drift observed in our DFT studies based on spin-orbit coupling (SOC) and Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) functionals. The physical origin of valley drift has been ascertained in our thorough investigations. The robustness of our approach is substantiated as follows. With progressive increase in strain magnitude (0--10%), the band gap remains direct up to 2% uniaxial tensile strain, under SOC, which accurately reproduces the experimental strain-induced direct-to-indirect band gap transitions occurring at \ensuremath{\sim}2% strain. Based on LDA-DFT [Q. Zhang et al., Phys. Rev. B 88, 245447 (2013)], this crossover in band gap has been incorrectly reported to occur at a higher value of uniaxial strain of 4%. Moreover, the direct SOC band gap shows a linear redshift at a rate of 51--53 meV/(% of strain), under uniaxial tensile strain, which is in excellent quantitative agreement with experimentally observed rates in the redshift of direct excitonic transitions measured in several optical absorption and photoluminescence (PL) spectroscopy experiments. In addition, the Berry curvature \textohm{}($k$) of electron/hole bands gets significantly modulated in strained $\mathrm{ML}\text{\ensuremath{-}}\mathrm{Mo}{\mathrm{S}}_{2}$, where the intensity of the flux profile increases as a function of the magnitude of strain with an opposite drift around $K/K'$, when strained along the ZZ/AC direction. A strong strain-valley coupling leads to an enhancement in the strength of spin-orbit induced spin splitting of bands at VBM/CBM, which is sizably enhanced (\ensuremath{\sim}7 meV) simply by the strain-controlled orbital motions. Our findings are of prime importance in the valley physics of $\mathrm{Mo}{\mathrm{S}}_{2}$. Besides, the important theoretical insights emerging from this work will trigger further experimental investigations on $\mathrm{ML}\text{\ensuremath{-}}\mathrm{Mo}{\mathrm{S}}_{2}$ to realize its novel technological potential in nanoelectronics, spintronics, and valleytronics.

NBO 7.0: New vistas in localized and delocalized chemical bonding theory.

We briefly outline some leading features of the newest version, NBO 7.0, of the natural bond orbital (NBO) wavefunction analysis program. Major extensions include: (1) a new NPEPA module implementing Karafiloglou's "polyelectron population analysis" in the NBO framework; (2) new RDM2 program infrastructure for describing electron correlation effects based on full evaluation of the second-order reduced density matrix; (3) improved convex-solver implementation of natural resonance theory (NRT), allowing a greatly expanded range of applications and associated "resonance NBO" (RNBO) visualization of chemical reactivity; (4) a variety of other improvements in well-established NBO algorithms. We also provide brief introduction to the new NBOPro@Jmol utility program, a plugin to the Jmol chemical structure viewer that serves as a convenient tool to provide on-demand NBO descriptors or orbital visualizations for a broad variety of chemical inquiries in research or classroom applications. © 2019 Wiley Periodicals, Inc.

Observation of strong relativistic and distorted-wave effects in (e,2e) electron-momentum spectroscopy of mercury

We report a measurement of the valence orbital-momentum profiles of mercury (Hg) using a high-sensitivity binary $(e,2e)$ electron-momentum spectrometer at incident energies of 600 and 1200 eV plus the binding energy. The $6{s}_{1/2}$ orbital and the spin-orbit components of $5{d}_{5/2}$ and $5{d}_{3/2}$ orbitals are well separated in the measured binding-energy spectra. The experimental momentum distributions for the individual orbitals and the branching ratio of $5{d}_{5/2}$ to $5{d}_{3/2}$ are obtained and compared with predictions from a plane-wave impulse approximation (PWIA) in which the orbital wave functions are calculated using the nonrelativistic (NR) and spin-orbital (SO) relativistic theories. The SO relativistic calculations are in better agreement with experiment than the NR, indicating clearly the importance of relativistic effects in the electronic structure of Hg. We also observe some discrepancies between experiment and PWIA calculations in the high-momentum region of $6{s}_{1/2}$ and the low-momentum region of $5d$ orbitals which display a dynamic dependence on the impact energy. These discrepancies become smaller at a higher energy of about 1200 eV and thus can be qualitatively assigned to the distorted-wave effect in the $(e,2e)$ reaction of Hg.

Attosecond imaging of molecules using high harmonic spectroscopy

The availability of attosecond-duration extreme ultraviolet or soft X-ray light sources has opened up new fields of research in atomic and molecular physics. These pulses can be as short as 50 as, fast enough to freeze the motion of electrons within molecules, to resolve how electrons rearrange themselves after the removal of an electron and to study electron–electron correlations. Gas-phase molecules can be aligned in space using short laser pulses, permitting the measurement of molecular parameters in the molecular frame. Aligned molecules can be photoionized using a train of attosecond pulses, enabling the complete characterization of the partial waves making up the photoelectron angular distributions. Using a recolliding electron in the high harmonic process allows complex transition dipole matrix elements to be recorded (including their amplitude and phase) in the molecular frame. High harmonic spectroscopy makes it possible to image molecular orbitals and for unimolecular chemical reactions to be followed with femtosecond resolution. For example, the behaviour around conical intersections can be probed. Charge migration within molecules can be observed with sub-femtosecond resolution. High harmonic spectroscopy is a femtosecond laser technique that reveals details of valence electron orbital wavefunctions in gas-phase molecules. It makes it possible to image molecular orbitals and for unimolecular chemical reactions to be followed with femtosecond resolution.

Hopping parameters for tunnel coupling in 2D materials

Using Bardeen’s approach and orbital wave functions obtained by the algorithm of Herman and Skillman, we calculated interatomic matrix elements for tunnel interaction between the atoms from the set of B, C, N, Si, P, S, Ti, V, Se, Mo, Te and W, which constitute many 2D materials. In a wide range of interatomic distances, these values are approximated by simple functions with a small set of parameters. The results are presented in reference tables. These results will be useful for describing different tunnel phenomena in low-dimensional materials using the tight-binding approach.

An animated visualization of orbital angular momentum and spin‐orbit coupling

This paper presents an approach toward visualizing a complex orbital based on animation using a time‐dependent phase factor. This makes orbital angular momentum clearly visible, in a way that reflects the nature of the orbital angular momentum wavefunction. Visualization of this quantity is also useful for examining the effects of spin‐orbit coupling (SOC), in which higher orbital angular momentum states are admixed into the orbital; in this case, however, scaling of one phase‐component is needed. The phase orientation of a complex orbital, which is generally not guaranteed by the SCF procedure, must be considered when doing this. The method of visualization presented here may prove useful when analyzing properties where SOC is important, such as magnetic resonance parameters. Animated visualizations are performed, and compared with the method of phase‐colored isosurfaces, first for a model p‐orbital to explain the idea, and then for the singly‐occupied molecular orbitals of two small doublet radicals.

Metastable bound states of the interacting two-dimensional magnetoexcitons

The possible formation of two-dimensional (2D) magnetic biexcitons composed of two 2D magnetoexcitons with electrons and holes on the lowest Landau levels (LLLs) with opposite center-of-mass wave vectors k→ and −k→ and with antiparallel electric dipole moments perpendicular to the corresponding wave vectors was investigated. Two spinor structures of two electrons and of two holes were considered. In the singlet-singlet state the spins of two electrons as well as the effective spins of two holes create the combinations with the total spin S=0 and its projection on the magnetic field Sz=0. The triplet-triplet state corresponds to S=1 and Sz=0. Two orbital Gaussian variational wave functions depending on |k→| and describing the relative motion of two magnetoexcitons inside the molecule were used. Analytical calculations show that in the LLLs approximation the stable bound states of bimagnetoexcitons do not exist, but there is a metastable bound state with the orbital wave function, having the maximum on the in-plane ring for the triplet-triplet spin configuration. The metastable bound state has an energy activation barrier comparable with the magnetoexciton ionization potential and gives rise to the new luminescence band due to the metastable biexciton-para exciton conversion with the frequencies higher than those of the para magnetoexciton luminescence line.

Ab initio electron-phonon interactions using atomic orbital wave functions

The interaction between electrons and lattice vibrations determines key physical properties of materials, including their electrical and heat transport, excited electron dynamics, phase transitions, and superconductivity. We present a new ab initio method that employs atomic orbital (AO) wavefunctions to compute the electron-phonon (e-ph) interactions in materials and interpolate the e-ph coupling matrix elements to fine Brillouin zone grids. We detail the numerical implementation of such AO-based e-ph calculations, and benchmark them against direct density functional theory calculations and Wannier function (WF) interpolation. The key advantages of AOs over WFs for e-ph calculations are outlined. Since AOs are fixed basis functions associated with the atoms, they circumvent the need to generate a material-specific localized basis set with a trial-and-error approach, as is needed in WFs. Therefore, AOs are ideal to compute e-ph interactions in chemically and structurally complex materials for which WFs are challenging to generate, and are also promising for high-throughput materials discovery. While our results focus on AOs, the formalism we present generalizes e-ph calculations to arbitrary localized basis sets, with WFs recovered as a special case.

Exciton Polaritons in a Two-Dimensional Lieb Lattice with Spin-Orbit Coupling.

We study exciton polaritons in a two-dimensional Lieb lattice of micropillars. The energy spectrum of the system features two flat bands formed from S and P_{x,y} photonic orbitals, into which we trigger bosonic condensation under high power excitation. The symmetry of the orbital wave functions combined with photonic spin-orbit coupling gives rise to emission patterns with pseudospin texture in the flat band condensates. Our Letter shows the potential of polariton lattices for emulating flat band Hamiltonians with spin-orbit coupling, orbital degrees of freedom, and interactions.

Influence of VO2+ ions on structural and optical properties of potassium succinate-succinic acid single crystal for non-linear optical applications

A transparent and good optical quality semi organic single crystal of vanadium doped potassium succinate-succinic acid (KSSA) was synthesized by slow evaporation technique at room temperature. The structural perfection was supported by the powder XRD of the KSSA-VO2+ single crystal. Optical behavior of the material was discovered from the absorption and transmission spectra of UV–vis–NIR characterization. Functional group and presence of metal ion in the specimen are depicted from FTIR traces. From the photoluminescence studies, emission of wavelength in the violet region (418 nm) at the excitation of 243 nm could be ascertained. EDAX, SEM measurements identify presence of elements and pictures the step-line growth and the imperfection presents in the grown crystal. EPR analysis extracts the information about the local site symmetry around the impurity ion, molecular orbital coefficients, admixture coefficients and ground state wave function of VO2+ doped KSSA single crystal. Second harmonic generation (SHG) efficiency of the grown crystal was investigated to explore the NLO characteristic of the material.

Rovibrational spectrum calculations of four electronic states in carbon monoxide molecule: Comparison of two effect correction methods

Accurate calculation of molecular energy is of great significance for studying molecular spectral properties. In this work, the potential energy curve and rovibrational spectrum (Gν) of the ground state X1∑+ and the excited states a3Π, a'3∑+ and A1Π of carbon monoxide molecule are calculated by the multi-reference configuration interaction method. In the calculation, the core-valence correlation correction (CV) effect and scalar relativistic (SR) effect are included.In order to obtain an accurate energy of molecule, two computational schemes are adopted. In the first scheme, i.e. (m MRCI+Q/CBS(TQ5)+CV+SR), the molecular orbital wavefunction is obtained from the Hartree-Fock self-consistent field method by using the basis set aug-cc-pVnZ. The wavefunction is first calculated by the state-averaged complete active space self-consistent field approach. Then the multi-reference configuration interaction method (MRCI) is adopted to calculate the dynamic correlation energy in the potential energy curve. Finally, we use the basis set cc-pCVQZ and aug-cc-pVQZ to calculate the CV effect and SR effect by the MRCI method. In the second scheme (aug-cc-pwCVnZ-DK (n=T, Q, 5)), the potential energy curves (PECs) of these four electronic states are calculated by the MRCI method whose basis set (aug-cc-pwCVnZ-DK) contains the CV effect and SR effect. Finally, in order to reduce the error caused by the basis set, we extrapolate the basis sets of the two computational schemes to the complete basis set. On the basis of the PECs plotted by the different methods, we obtain the spectroscopic parameters of the X1∑+, a3Π, a'3∑+ and A1Π states of the carbon monoxide by solving the internuclear Schrödinger equations through utilizing the numerical integration program “LEVEL”.In this paper, we calculate the SR effect and the CV effect by using different schemes, and the latter is indispensable for accurately calculating the molecular structure. For the lowest two electronic states, we consider the dependence of the two effects on the calculation of the Gaussian basis group (Method B), and find that the accuracy of the rovibrational spectrum is improved. It can be seen that these electronic states have higher requirements for electronic correlation calculation. For higher electronic states, the electron cloud distribution is relatively loose, and the electronic correlation obtained by a single Gaussian basis group can achieve the corresponding calculation accuracy. Of course, since the calculation of the rovibrational spectra is essentially only the relative energy, the offset effect of the electronic correlation effect of different electronic states is also included here in this paper.

The spin pairing symmetry of d-wave superconductor indicated by tunneling spectroscopy

Andreev reflection on the interface of ferromagnet/superconductor ([Formula: see text]) junction provides a tool for exhibiting the spin pairing symmetry in superconductors. The triplet tunneling in [Formula: see text]-wave [Formula: see text] junction observed in recent experiments revived a fundamental interest: the pairing mechanism of the superconducting cuprate. Here we show that in a doped cuprate, the effective spin coupling between the doped holes on the O sites yields a symmetric bound pair state [Formula: see text] with quantum numbers [Formula: see text], [Formula: see text] in the CuO2 layer, which explains the origin of the resonating valence bound state in cuprates, as well as the tunneling experiments. In addition, the [Formula: see text]-wave is consistent with the triplet pairing since the observable orbital wavefunction is a projection from the total odd-frequency wavefunction onto the quasi-2D superconducting CuO[Formula: see text] layer. High-temperature superconductivity as a long-standing puzzle touches upon a hiding symmetry: the triplet state ([Formula: see text], [Formula: see text]) is indistinguishable from the singlet ([Formula: see text]) either in NMR measurements, or in muon detections, but can be identified by tunneling spectroscopy of [Formula: see text] junction.

Modulation effect on the effective mass of free carriers induced by multicomponent elements in In2O3-based transparent conducting oxides

Motivated by extensive investigations on the In2O3-based multicomponent transparent conducting oxides (TCOs), we want to know the carrier transport properties in these systems and how they evolve with adjusting of geometric structure and constituent elements. Guided by the empirical minimum effective mass physics, we select nine impurities M (M=Sn, Zn, Cd, Hg, Mn, Ni, Co, Ga and Ge) to tune the effective mass (m∗) of In2O3-based TCOs. By means of systematic theoretical investigations, we find that in impurity M isolated or corporately doped In2O3 materials, the substitutional position for dopant M is determined by the charge state. Codoping Sn and other eight impurities into In2O3 (to form IMTO) is an effective strategy to reduce the indium content in In2O3-based TCOs materials. For the recognized n-type carrier contributor, namely, VO defect, it induce spatial localization and orbital localization effects in electronic structures and thus enlarge m∗, which are caused by the large lattice distortion and complicated orbital wavefunction hybridizations. However, for IMTO:VO (M=Zn, Ga and Hg) systems, both localization effects are weakened, leading to a decrease of m∗. It even reduces by half value for In-Hg-Sn-O:VO systems. This systematic work in In2O3-based materials may be helpful in designing of a new range of high performance TCOs.

Direct mapping of spin and orbital entangled wave functions under interband spin-orbit coupling of giant Rashba spin-split surface states

We use spin- and angle-resolved photoemission spectroscopy (SARPES) combined with polarization-variable laser and investigate the spin-orbit coupling effect under interband hybridization of Rashba spin-split states for the surface alloys Bi/Ag(111) and Bi/Cu(111). In addition to the conventional band mapping of photoemission for Rashba spin-splitting, the different orbital and spin parts of the surface wavefucntion are directly imaged into energy-momentum space. It is unambiguously revealed that the interband spin-orbit coupling modifies the spin and orbital character of the Rashba surface states leading to the enriched spin-orbital entanglement and the pronounced momentum dependence of the spin-polarization. The hybridization thus strongly deviates the spin and orbital characters from the standard Rashba model. The complex spin texture under interband spin-orbit hybridyzation proposed by first-principles calculation is experimentally unraveled by SARPES with a combination of p- and s-polarized light.