Strong State Mixing Research Articles

Observation of quantum-confined exciton states in monolayer WS2 quantum dots by ultrafast spectroscopy.

Monolayer transition metal dichalcogenide quantum dots (TMDC QDs) could exhibit unique photophysical properties, because of both lateral quantum confinement effect and edge effect. However, there is little fundamental study on the quantum-confined exciton dynamics in monolayer TMDC QDs, to date. Here, by selective excitations of monolayer WS2 QDs in broadband transient absorption (TA) spectroscopy experiments, the excitation-wavelength-dependent ground state bleaching signals corresponding to the quantum-confined exciton states are directly observed. Compared to the time-resolved photophysical properties of WS2 nanosheets, the selected monolayer WS2 QDs only show one ground state bleaching peak with larger initial values for the linear polarization anisotropy of band-edge excitons, probably due to the expired spin-orbit coupling. This suggests a complete change of the band structure for monolayer WS2 QDs. In the femtosecond time-resolved circular polarization anisotropy experiments, a valley depolarization time of ∼100 fs is observed for WS2 nanosheets at room temperature, which is not observed for monolayer WS2 QDs. Our findings suggest a strong state-mixing of band-edge valley excitons responsible for the large linear polarization in monolayer WS2 QDs, which could be helpful for understanding the exciton relaxation mechanisms in colloidal monolayer TMDC QDs.

Statistical and analytical approaches to finite-temperature magnetic properties of the compound SmFe12

To investigate the magnetic properties of $\mathrm{Sm}{\mathrm{Fe}}_{12}$, we construct an effective spin model, where magnetic moments, crystal-field (CF) parameters, and exchange fields at 0 K are determined by first-principles calculations. Finite-temperature magnetic properties are investigated by using this model. We further develop an analytical method with strong mixing of states with a different quantum number of angular momentum $J$ ($J$-mixing), which is caused by a strong exchange field acting on the spin component of $4f$ electrons. Comparing our analytical results with those calculated by Boltzmann statistics, we clarify that the previous analytical studies for Sm transition-metal compounds overestimate the $J$-mixing effects. The present method enables us to perform a quantitative analysis of the temperature dependence of magnetic anisotropy (MA) with high reliability. The analytical method with model approximations reveals that the $J$-mixing caused by the exchange field increases the spin angular momentum, which enhances the absolute value of the orbital angular momentum and MA constants via spin-orbit interaction. It is also clarified that these $J$-mixing effects remain even above room temperature. Magnetization of $\mathrm{Sm}{\mathrm{Fe}}_{12}$ shows a peculiar field dependence known as the first-order magnetization process (FOMP), where the magnetization shows an abrupt change at a certain magnetic field. The result of the analysis shows that the origin of FOMP is attributed to competitive MA constants between positive ${K}_{1}$ and negative ${K}_{2}$. The sign of ${K}_{1(2)}$ appears due to an increase in the CF potential denoted by the parameter ${A}_{2}^{0}\ensuremath{\langle}{r}^{2}\ensuremath{\rangle}$ (${A}_{4}^{0}\ensuremath{\langle}{r}^{4}\ensuremath{\rangle}$) caused by hybridization between $3d$-electrons of Fe on the $8i$ ($8j$) site and $5d$ and $6p$ valence electrons on the Sm site. It is verified that the requirement for the appearance of FOMP is given as $\ensuremath{-}{K}_{2}<{K}_{1}<\ensuremath{-}6{K}_{2}$.

Periodic Orbits and Bifurcations of the Vibrational Modes of the Ozone Molecule at High Energies

The study of quantum states near the dissociation threshold is necessary both to understand the formation of molecules and to explore accurately chemical reactions. Quantum calculations of highly excited states can be complemented by methods of nonlinear classical mechanics that help revealing the stable modes of molecular vibrations and their transformations (bifurcations) during excitation of a molecule. The classical approach is particularly efficient at high energies where due to their high density, strong state mixing could occur, and simple assignment in terms of the standard normal modes becomes impossible. In this work we present first results for periodic orbits of the main isotopologue of the ozone molecule (16O3) using recent accurate ab initio potential energy surface. Along with the principle families of the periodic orbits corresponding to the symmetric, antisymmetric, and bending types of molecular vibrations, we have located bifurcations corresponding to the transition to local modes as well as resonance orbits that are responsible for new types of vibrational motions in the high energy range. The classical trajectories of nuclei and their correspondence to the wave functions of the quantum states are also discussed.

Two-dimensional infrared study of the C[sbnd]D and C[dbnd]O stretching vibrations in strongly hydrogen-bonded complexes

We report a study of the CD and CO stretching modes of formyl deuterated formic acid (DCOOH) hydrogen bonded to nitrogenous bases. These modes are spectators to the hydrogen bond itself but are sensitive to the strength of that interaction. Using 2D IR spectroscopy, we show that in strongly hydrogen bonded complexes the CD stretching vibration becomes anharmonically coupled to low-order combination states leading to strong state mixing resulting in Fermi resonance transitions in the 2D IR spectra. In contrast, the CO vibrations show multiple peaks as a result of conformational heterogeneity associated with internal rotation about the hydrogen bond. For both modes, the population relaxation rates tend to be quite short, ∼1 ps or less. Having characterized the vibrational spectroscopy of these spectator vibrations, we conclude that they are quite sensitive to details of the hydrogen bonding interactions though their utility is limited by spectral complexity and short population lifetimes.

Time-dependent view of an isotope effect in electron-nuclear nonequilibrium dynamics with applications to N2

Isotopic fractionation in the photodissociation of N2 could explain the considerable variation in the 14N/15N ratio in different regions of our galaxy. We previously proposed that such an isotope effect is due to coupling of photoexcited bound valence and Rydberg electronic states in the frequency range where there is strong state mixing. We here identify features of the role of the mass in the dynamics through a time-dependent quantum-mechanical simulation. The photoexcitation of N2 is by an ultrashort pulse so that the process has a sharply defined origin in time and so that we can monitor the isolated molecule dynamics in time. An ultrafast pulse is necessarily broad in frequency and spans several excited electronic states. Each excited molecule is therefore not in a given electronic state but in a superposition state. A short time after excitation, there is a fairly sharp onset of a mass-dependent large population transfer when wave packets on two different electronic states in the same molecule overlap. This coherent overlap of the wave packets on different electronic states in the region of strong coupling allows an effective transfer of population that is very mass dependent. The extent of the transfer depends on the product of the populations on the two different electronic states and on their relative phase. It is as if two molecules collide but the process occurs within one molecule, a molecule that is simultaneously in both states. An analytical toy model recovers the (strong) mass and energy dependence.

CI+MBPT calculations of Ar I energies, g factors, and transition line strengths

Excited states of noble gas atoms present certain challenges to atomic theory for several reasons: first, relativistic effects are important and LS coupling is not optimal; second, energy intervals can be quite small, leading to strong mixing of states; third, many-body perturbation theory for hole states does not converge well. Previously, some attempts were made to solve this problem, using for example the all-order coupled-cluster approach and particle-hole configuration-interaction many-body perturbation theory (CI-MBPT) with modified denominators. However, while these approaches were promising, the accuracy was still limited. In this paper, we calculate Ar I energies, g factors, and transition amplitudes using ab initio CI-MBPT with eight valence electrons to avoid the problem of slow convergence of MBPT due to strong interaction between 3p and 3s states. We also included in CI many dominant states obtained by double excitations of the ground state configuration. Thus perturbation corrections were needed only for 1s, 2s, 2p core electrons non-included in valence-valence CI, which are quite small. We found that energy, g factors, and electric dipole matrix elements are in reasonable agreement with experiments. It is noteworthy that the theory agreed well with accurately measured g factors. Experimental oscillator strengths have large uncertainty, so in some cases we made a comparison with average values.

Uniaxial compression influence on valence sub-bands energy spectrum and electroluminescence in n-AlGaAs/GaAsP/p-AlGaAs diode structures

Numerical calculations of the valence band and conduction band size quantized levels in a strained p-AlxGa1-xAs/GaAs1-yPy/n-AlxGa1-xAs (y = 0.16) double heterostructure were performed for different values of the external uniaxial compression along [110] direction. They indicate that the two upper levels in the valence band merge at pressure about 4 kbar and a strong state mixing develops around the merging point. The results of calculations explain the nonlinear character of the photon energy shift and electroluminescence intensity increase that were experimentally observed in these structures under uniaxial compression up to 5 kbar.

Size quatized levels of the valence band and the optical gain in strained p-AlGaAs/GaAsP/n-AlGaAs structures under uniaxial compression

The band structure, size quatized levels, and wave functions in the conduction and valence bands of strained n-AlxGa1 − xAs/GaAsyP1 − y/p-AlxGa1 − xAs (y = 0.84) heterostructures are calculated numerically upon a uniaxial compression along the [110] direction. The calculation indicates a sublinear increase of the effective optical gap in the GaAs0.84P0.16 quantum well, strong mixing of states of light and heavy holes, and merging of the corresponding ground states in the quantum well of the valence band under a pressure of 4.5–5 kbar. The calculation of matrix elements of the electron-photon interaction operator for a system of possible interband transitions permits one to determine the optical gain for the TE and TM modes. The increase in this coefficient by two to fourfold under uniaxial compression agrees with the previously published experimental data on the increase of the electroluminescence intensity.

Carbon−Cobalt Bond Distance and Bond Cleavage in One-Electron Reduced Methylcobalamin: A Failure of the Conventional DFT Method

Geometry optimizations at the HF, B3LYP, and CASSCF levels of electronic structure theory have been performed for methylcobalamin (MeCbl) model compounds in both the Co(III) (MeCbl(III)) and Co(II) (MeCbl(II)) formal oxidation states. Since the HOMO-LUMO and C-Co sigma-sigma MO gaps are significantly smaller in the MeCbl(II) compounds compared with MeCbl(III), a pseudo-Jahn Teller effect is possible. CASSCF calculations show that there is strong coupling between C-Co sigma-sigma MOs for the MeCbl(II) models leading to strong state mixing with significant total charge density transfer (approximately 0.4 e-), mainly from the C-Co sigma MO to C-Co sigma MO (approximately 0.3 e-). CASSCF(9:7) calculations show that the strong state mixing leads to an increase in the C-Co bond length for MeCbl(II) model compounds from 1.969 A (DFT and HF calculations) to 2.164 A in the base-on MeCbl(II) model and from 1.938 A to 2.144 A in the base-off MeCbl(II) model. Concomitantly, the Co-N axial bond length increases from 2.121 A (DFT) to 2.344 A in the CASSCF calculation. This coupling interaction between states can be used to explain the much lower Co-C bond dissociation enthalpy and much faster bond cleavage rate for the one-electron reduced methylcobalamin radical anion compared to MeCbl(III). It may also be important for axial bond distances in other Co(II) compounds.

Effective-mass theory for hierarchical self-assembly ofGaAs∕AlxGa1−xAsquantum dots

The electronic structures in the hierarchical self-assembly of $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ quantum dots are investigated theoretically in the framework of effective-mass envelope function theory. The electron and hole energy levels and optical transition energies are calculated. In our calculation, the effect of finite offset, valence-band mixing, the effects due to the different effective masses of electrons and holes in different regions, and the real quantum dot structures are all taken into account. The results show that (1) electronic energy levels decrease monotonically, and the energy difference between the energy levels increases as the GaAs quantum dot (QD) height increases; (2) strong state mixing is found between the different energy levels as the GaAs QD width changes; (3) the hole energy levels decrease more quickly than those of the electrons as the GaAs QD size increases; (4) in excited states, the hole energy levels are closer to each other than the electron ones; (5) the first heavy- and light-hole transition energies are very close. Our theoretical results agree well with the available experimental data. Our calculated results are useful for the application of the hierarchical self-assembly of $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ quantum dots to photoelectric devices.

The photodissociation dynamics of CFBr excited into the Ã(1A″) state

The dynamics of the photolysis reaction, CFBr+hν→CF+Br, have been investigated for photolysis energies in the range, ν̄=23 500–26 000 cm−1 (λ=385–435 nm). These energies correspond to excitation into the Ã(1A″) state of CFBr with 2500–5000 cm−1 of excess vibrational energy. Following dissociation of jet-cooled CFBr, the internal energy (Ω, Λ, J) of the nascent CF fragments (X 2Π, υ=0) was probed by laser induced fluorescence spectroscopy. Two distinct types of product state distributions were observed. At energies above T00+3360 cm−1 the populations of the Π1/22 and Π3/22 spin–orbit states of CF were equal, while A″ lambda doublet states were preferred over A′. These populations are consistent with a direct dissociation mechanism on the à state, over a barrier with a height of 3360 cm−1. The strong state mixing in the vicinity of the barrier ensures a statistical mixture of final spin–orbit states. The preference for the A″ lambda doublet states is consistent with the two lone electrons in in-plane orbitals pairing up in the final CF product, leaving one unpaired electron in an out-of-plane orbital, lying parallel to the J vector of the recoiling fragment. For excitation at energies below T00+3360 cm−1 the ground spin–orbit state of CF (2Π1/2) is preferred, while the lambda doublet populations are equal. The interpretation of these populations is that at these energies à state CFBr is stable with respect to dissociation over the barrier. The molecule crosses to either the X̃ or ã state where it encounters a deep attractive potential well. The subsequent slower dissociation rate allows the molecule to follow a more adiabatic pathway producing the lowest spin–orbit state of CF, and for any preference for lambda doublet states to be lost.

On the electronic energy disposal of calcium excited atom reactions with halogen-containing compounds: Electronic branching ratio and spin–orbit state populations

This paper reports on the electronic energy disposal of the Ca( 1D 2)+RX → CaX ∗+R reaction system in which R=CH 3, H and X=Cl, Br and I. The chemiluminescence yield was collected from either beam–gas or beam–beam reactions resolving the A and B electronically excited CaX states as well as the 2 Π 3/2, 1/2 spin–orbit states. The experimentally observed branching ratio, i.e. Γ(A/B) deviates significantly from the statistical value of 2 and hardly changes with collision energy. This deviation has been attributed to an increased role of Σ→Π transitions, i.e. the lack of orbital following as the impact parameter increases. In relation to the spin–orbit state population the overall behaviour is a nearly equally state population which, in principle, seems to be due to strong state mixing in these excited alkaline-earth halide reaction products. These findings are discussed in light of dynamical models currently used to interpret the reaction dynamics of excited species.

Quantum relaxation of multilevel particles

A non-perturbative model of the relaxation of a multilevel particle between collisionally isolated Hilbert subspaces has been developed using the density matrix formalism. The relaxation between these subspaces can be induced by internal state mixing. Under appropriate conditions a particle can be confined inside one subspace even in the case of strong state mixing. The particular case of nuclear spin conversion in CH 3F molecules is proposed as a simple and convenient system to study experimentally this type of relaxation for a wide range of parameters.

Plucking a hydrogen bond: A near infrared study of all four intermolecular modes in (DF)2

The near ir combination band spectra of supersonically cooled (DF)2 in the 2900 to 3300 cm−1 region have been recorded with a high resolution slit jet spectrometer. Twelve vibration–rotation–tunneling (VRT) bands are observed, representing each of the four intermolecular modes (van der Waals stretch ν4, geared bend ν5, out-of-plane torsion ν6, and antigeared bend ν3) built as combination bands on either the ν1 (free) or ν2 (bound) DF stretches. Analysis of the rotationally resolved spectra provide spectroscopic constants, intermolecular frequencies, tunneling splittings, and predissociation rates as a function of both intra- and intermolecular excitation. The intermolecular frequencies demonstrate a small but systematic dependence on intramolecular mode, which is exploited to yield frequency predictions relevant to far-ir studies, as well as facilitate direct comparison with full 6-D quantum calculations on trial potential surfaces. The tunneling splittings demonstrate a much stronger dependence upon intermolecular mode, increasing by as much as an order of magnitude for geared bend excitation. Conversely, high resolution line shape analysis reveals that vibrational predissociation broadening is only modestly affected by intermolecular excitation, and instead exhibits mode specific behavior controlled predominantly by intramolecular excitation. Detailed H/D isotopic vibrational shifts are obtained by comparison with previous combination band studies of all four intermolecular modes in (HF)2. In contrast to the strong state mixing previously observed for (HF)2, the van der Waals stretch and geared bend degrees of freedom are largely decoupled in (DF)2, due to isotopically ‘‘detuning’’ of resonances between bend–stretch intermolecular vibrations. Four-dimensional quantum calculations of the (HF)2 and (DF)2 eigenfunctions indicate that the isotopic dependence of this bend–stretch resonance behavior is incorrectly predicted by current hydrogen bond potential surfaces.

Probing hydrogen bond potentials via combination band spectroscopy: A near infrared study of the geared bend/van der Waals stretch intermolecular modes in (HF)2

High resolution near infrared spectra of the two lowest frequency intermolecular modes in HF-stretch excited states of (HF)2 have been characterized using a slit-jet infrared spectrometer. In the spectral region surveyed, ten vibration–rotation–tunneling (VRT) bands are observed and assigned to the low frequency ‘‘van der Waals stretch’’ (ν4) and ‘‘geared bend’’ (ν5) intermolecular modes, in combination with either the hydrogen bond acceptor (ν1) or donor (ν2) high-frequency intramolecular HF stretches. Analysis of the rotationally resolved spectra provide intermolecular frequencies, rotational constants, tunneling splittings, and predissociation rates for the ν4/ν5 intermolecular excited states. The intermolecular vibrational frequencies in the combination states display a systematic dependence on intramolecular redshift that allows far-IR intermolecular frequencies to be reliably extrapolated from the near-IR data. Approximately tenfold increases in the hydrogen bond interconversion tunneling splittings with either ν4 or ν5 excitation indicate that both intermolecular modes correlate strongly to the tunneling coordinate. The high resolution VRT line shapes reveal mode specific predissociation broadening sensitive predominantly to intramolecular excitation, with weaker but significant additional effects due to low frequency intermolecular excitation. Analysis of the high resolution spectroscopic data for these ν4 and ν5 combination bands suggests strong state mixing between what has previously been considered van der Waals stretch and geared bend degrees of freedom.

High-spin rotational states in 177, 173Lu and evidence for ΔK = 2 and ΔK = 4 mixings

The level schemes of the deformed odd-proton nuclei 171Lu and 173Lu have been studied by in-beam spectroscopy. Measurements of singles γ-ray spectra, angular distributions and γ-γ coincidences were performed in the 169Tm(α, 2nγ) 171Lu reaction at 27 MeV α-particle energy. In the reaction 173Yb(d, 2nγ) 173Lu singles spectra and γ-γ coincidences were measured. Additional γ-ray spectra were taken for the reactions 169Tm(α, 2nγ) 171Lu at E α = 23 MeV and 173Yb(p, nγ) 173Lu. The proposed level schemes of 171Lu and 173Lu involve rotational bands of the intrinsic states 7 2 +[404] , 1 2 +[411] , 5 2 +[402] , 1 2 −[541] and 9 2 −[514] up to spin 25 2 , 23 2 , 23 2 , 29 2 and 21 2 , respectively, in 171Lu and up to spin 23 2 , 17 2 , 19 2 , 25 2 , and 23 2 , respectively, in 173Lu. Transitions between some states of the 1 2 +[411] and 5 2 +[402] bands in 171Lu indicate a strong mixing of states with ΔK = 2. Similarly, a ΔK = 4 mixing between states of the 1 2 −[541] and 9 2 −[514] bands in 171Lu is indicated by interband transitions. These mixings are described in terms of the rotation-particle coupling, considering only the interaction between states with K and K±1. The dependence of the side feeding to the 1 2 −[541] and 7 2 +[404] bands on the level spins and energies was investigated.

NMR study of the electronic structure of solid and liquid metals

NMR was used to study the effect of melting on the electronic structure of copper and aluminium. The Knight shift and spin—lattice relaxation time were measured as a function of temperature in the solid and in the liquid state. From these measurements the temperature dependence of K(x). the reciprocal enhancement factor of the Korringa relation, is obtained. In the case of copper it is shown that the main temperature effect is indirectly through thermal expansion. It is shown that the conduction electrons density of states and spin density at the nucleus are strongly influenced by sd hybridization. Their temperature dependence is explained as due to the volume dependence of the hybridization. In aluminium, in contrast to copper, the results of K(oc) as a function of temperature cannot be explained as due to volume change, but rather a direct temperature effect. The explanation is based on the strong mixing of states near the Brillouin zone. This mechanism should prevail only in polyvalent metals such as aluminium, in contrast to monovalent metals such as copper, where this effect can be neglected. The behaviour of other metals upon melting is discussed. About twenty years ago, W. D. Knight discovered that the nmr line of a nucleus in a metal is shifted relative to its line in a nonmetal. This is the wellknown Knight shift. This discovery made the nmr technique an important research tool in the study of the electronic structure of metals. The study of nmr in metals has become a very broad and active field. We would like to discuss one problem in this field: the effect of melting on the electronic structure of metals. This is a problem to which nmr has made a significant contribution. When a metal is heated, two major processes occur. The first is an increase in the lattice volume, which is gradual in the solid state and changes abruptly on reaching the melting point. The second is an increase in the amplitude of atomic vibrations, which can be looked upon as a gradual deviation from the order typical of the crystalline state, till a completely disordered state is reached at the melting point. We will discuss the effect of each of these two processes. In fact, a good test for any theory of electronic structure is its ability to explain the effect of a change of atomic volume and of order on

Strong perturbations in NMR double quantum spectra

The nuclear magnetic resonance double quantum spectra for cases in which the double quantum line falls close to a transition with which it has an energy level in common are discussed. It is shown that the strong mixing of states, occurring in this case, leads to large frequency shifts of the double quantum lines and, in addition, to the appearance of multiplets in the double quantum spectrum. The transition frequencies can be derived by a first order treatment of the rotating frame Hamiltonian. Double quantum spectra from 2-bromothieno[3,2- b]thiophene are compared with theory.