Dipole Transition Matrix Elements Research Articles

Exploring the Influence of Approximations for Simulating Valence Excited X-ray Spectra.

First-principles simulations of excited-state X-ray spectra are becoming increasingly important to interpret the wealth of electronic and geometric information contained within femtosecond X-ray absorption spectra recorded at X-ray Free Electron Lasers (X-FELs). However, because the transition dipole matrix elements must be calculated between two excited states (i.e., the valence excited state and the final core excited state arising from the initial valence excited state) of very different energies, this can be challenging and time-consuming to compute. Herein using two molecules, protonated formaldimine and cyclobutanone, we assess the ability of n-electron valence-state perturbation theory (NEVPT2), equation-of-motion coupled-cluster theory (EOM-CCSD), linear-response time-dependent density functional theory (LR-TDDFT) and the maximum overlap method (MOM) to describe excited state X-ray spectra. Our study focuses in particular on the behavior of these methods away from the Franck-Condon geometry and in the vicinity of important topological features of excited-state potential energy surfaces, namely, conical intersections. We demonstrate that the primary feature of excited-state X-ray spectra is associated with the core electron filling the hole created by the initial valence excitation, a process that all of the methods can capture. Higher energy states are generally weaker, but importantly much more sensitive to the nature of the reference electronic wave function. As molecular structures evolve away from the Franck-Condon geometry, changes in the spectral shape closely follow the underlying valence excitation, highlighting the importance of accurately describing the initial valence excitation to simulate the excited-state X-ray absorption spectra.

The Nonlinear Optical Properties of Self-Assembled InAs/GaAs Quantum Dot: Effect of Hydrostatic Pressure and Temperature

In this study, we have investigated the effects of temperature (T) and hydrostatic pressure (P) on both the nonlinear and linear optical properties of an InAs/GaAs core/shell quantum dot (QD) system with a Screened-Modified Kratzer potential (SMKP). To achieve this objective, we calculated the energy levels and their corresponding wave functions of the structure using the diagonalization method within the framework of the effective mass approximation. Analytical expressions for the absorption coefficients (ACs) and relative refractive index changes (RRICs) were derived using the compact-density-matrix approach. In our numerical calculations, we first determined the variation of the SMKP dependence, the dipole transition matrix element, and the electron energies of the ground (1s) and first excited state (1p) over a range of hydrostatic pressure (P) and temperature (T). As a result, the obtained numerical calculations revealed that changes in P and T influence both the magnitude and position of the resonant peaks that define the ACs and RRICs

Cooper minima in high-Z atoms: effects of correlation and relativity on np photoionization

Photoionization dipole transition matrix elements pass through a zero or attain a minimum that leaves imprints on photoionization parameters like the cross-section, angular distribution asymmetry parameter, phase shift, and photoionization time delay. This minimum is commonly known as the ‘Cooper minimum’ (CM). The CM, in general, is strongly affected by relativistic and correlation effects. Previous works investigated CM in the 6p and 5p subshell photoionization up to Z = 100 using the single-particle Dirac-Slater (DS) method. The present work extends the earlier work to Z up to 120 using more accurate methods; Dirac–Hartree–Fock (DHF) which includes the relativistic effects and exchange correlations, and the relativistic random phase approximation (RRPA) which includes both initial and final state electron-electron correlations along with relativistic effects. In addition to the study of photoionization from the 6p and 5p subshells, the 4p subshell has also been investigated in the present work. To demonstrate the prominent effects in the high-Z atoms, Rn (Z = 86), Ra (Z = 88), No (Z = 102), Cn (Z = 112), Og (Z = 118), and Ubn (Z = 120) are investigated.

Measurement of relative transition strengths of 133Cs Rydberg D states using electromagnetically induced transparency

Transition strengths between states are fundamental physical properties of atomic spectra. The differences in fine structure splitting of certain states are mainly attributed to the angular momentum parts of transition dipole matrix elements. These can be calculated by integrating the wave-functions theoretically and can be accessed by selecting corresponding polarizations of the exciting lasers experimentally. We measured the transition strengths ratios of nD5/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{5/2}$$\\end{document}/nD3/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{3/2}$$\\end{document} via Rydberg electromagnetically induced transparency (EIT) by changing the powers and polarizations of probing and coupling lasers in a room temperature cesium vapor cell. The variation of the ratios on the principal quantum number n which ranges from 40 to 62 is also investigated. Theoretical and experimental results agreed with each other.

Direct bandgap emission from strain-doped germanium

Germanium (Ge) is an attractive material for Silicon (Si) compatible optoelectronics, but the nature of its indirect bandgap renders it an inefficient light emitter. Drawing inspiration from the significant expansion of Ge volume upon lithiation as a Lithium (Li) ion battery anode, here, we propose incorporating Li atoms into the Ge to cause lattice expansion to achieve the desired tensile strain for a transition from an indirect to a direct bandgap. Our first-principles calculations show that a minimal amount of 3 at.% Li can convert Ge from an indirect to a direct bandgap to possess a dipole transition matrix element comparable to that of typical direct bandgap semiconductors. To enhance compatibility with Si Complementary-Metal-Oxide-Semiconductors (CMOS) technology, we additionally suggest implanting noble gas atoms instead of Li atoms. We also demonstrate the tunability of the direct-bandgap emission wavelength through the manipulation of dopant concentration, enabling coverage of the mid-infrared to far-infrared spectrum. This Ge-based light-emitting approach presents exciting prospects for surpassing the physical limitations of Si technology in the field of photonics and calls for experimental proof-of-concept studies.

Extended Analytical Model for the Description of Light Absorption Spectra of Linear Molecular Aggregates

We study optical properties of linear dye aggregates in which the transition dipole matrix elements of two monomer molecules forming their unit cell are not coplanar with the aggregate axis, and the Frenkel exciton is delocalized along this axis. An analytical model has been developed for the description of polarization effects in the light absorption spectra of such aggregates. It is shown that the nature of their optical spectra differs drastically from previously studied linear aggregates with a single molecule per unit cell. The developed theory contains simple formulas of the well-known Davydov–McRae–Kasha model for conventional linear aggregates as a particular case. A quantitative explanation of the experimental data is given for the absorption spectra of the pseudoisocyanine bromide dye aggregate.

Tailoring light-induced charge transfer and intersystem crossing in FeCO using time-dependent spin-orbit configuration interaction.

Real-time (RT) electronic structure methods provide a natural framework for describing light-matter interactions in arbitrary time-dependent electromagnetic fields (EMF). Optically induced excited state transitions are of particular interest, which require tuned EMF to drive population transfer to and from the specific state(s) of interest. Intersystem crossing, or spin-flip, may be driven through shaped EMF or laser pulses. These transitions can result in long-lived "spin-trapped" excited states, which are especially useful for materials requiring charge separation or protracted excited state lifetimes. Time-dependent configuration interaction (TDCI) is unique among RT methods in that it may be implemented in a basis of eigenstates, allowing for rapid propagation of the time-dependent Schrödinger equation. The recent spin-orbit TDCI (TD-SOCI) enables a real-time description of spin-flip dynamics in an arbitrary EMF and, therefore, provides an ideal framework for rational pulse design. The present study explores the mechanism of multiple spin-flip pathways for a model transition metal complex, FeCO, using shaped pulses designed to drive controlled intersystem crossing and charge transfer. These results show that extremely tunable excited state dynamics can be achieved by considering the dipole transition matrix elements between the states of interest.

Precision Spectroscopy of Radiation Transitions between Singlet Rydberg States of the Group IIb and Yb Atoms

The measurements of microwave (μw) and radio-frequency (RF) radiation quantitative parameters may be based on the quantum–optical approach to determine the spectral characteristics of radiation transitions between the Rydberg states of atoms. Frequencies and matrix elements are calculated for dipole transitions between opposite-parity Rydberg states nL 1L and n′L±1 1L±1 (where n′= n,n±1,n±2) of the singlet series in the alkaline–earth–metal-like atoms of group IIb (Zn, Cd, Hg) and Yb. The matrix elements determine the shifts of Rydberg-state energy levels in the field of resonance μw or RF radiation, splitting the resonance of electromagnetically induced transparency (EIT) for intensely absorbed probe radiation. Numerical computations based on the single-electron quantum defect method (QDM) and the Fues’ model potential (FMP) approach with the use of the most reliable data from the current literature on quantum defect values are performed for frequencies and matrix elements of transitions between singlet Rydberg states of 1S0-, 1P1-, 1D2-, and 1F3-series in Zn, Cd, Hg, and Yb atoms. The calculated data are approximated by polynomials in the powers of the principal quantum numbers. The polynomial coefficients are determined with the use of a standard curve-fitting interpolation polynomial procedure for numerically calculated functions. These approximation expressions provide new possibilities for accurately evaluating the frequencies and matrix elements of dipole transitions between Rydberg states over a wide range of quantum numbers n >> 1, accompanied by the emission and absorption of μw and RF photons.

Quadrupole Effects in the Photoionisation of Sodium 3s in the Vicinity of the Dipole Cooper Minimum

A procedure to obtain relativistic expressions for photoionisation angular distribution parameters using the helicity formulation is discussed for open-shell atoms. Electric dipole and quadrupole transition matrix elements were considered in the present work, to study the photoionisation dynamics of the 3s electron of the sodium atom in the vicinity of the dipole Cooper minimum. We studied dipole–quadrupole interference effects on the photoelectron angular distribution in the region of the dipole Cooper minimum. Interference with quadrupole transitions was found to alter the photoelectron angular distribution, even at rather low photon energies. The initial ground and final ionised state discrete wavefunctions of the atom were obtained in the present work using GRASP, and we employed RATIP with discrete wavefunctions, to construct continuum wavefunctions and to calculate transition amplitudes, total cross-sections and angular distribution asymmetry parameters.

Topological-insulator nanocylinders

Nanostructures, such a quantum dots or nanoparticles, made of three-dimensional topological insulators (3DTIs) have been recently attracting increasing interest, especially for their optical properties. In this paper we calculate the energy spectrum, the surface states and the dipole matrix elements for optical transitions with in-plane polarization of 3DTI nanocylinders of finite height LL and radius RR. We first derive an effective 2D Hamiltonian by exploiting the cylindrical symmetry of the problem. We develop two approaches: the first one is an exact numerical tight-binding model obtained by discretising the Hamiltonian. The second one, which allows us to obtain analytical results, is an approximated model based on a large-RR expansion and on an effective boundary condition to account for the finite height of the nanocylinder. We find that the agreement between the two models, as far as eigenenergies and eigenfunctions are concerned, is excellent for the lowest absolute value of the longitudinal component of the angular momentum. Finally, we derive analytical expressions for the dipole matrix elements by first considering the lateral surface alone and the bases alone, and then for the whole nanocylinder. In particular, we focus on the two limiting cases of tall and squat nanocylinders. The latter case is compared with the numerical results finding a good agreement.

Theory for all-optical responses in topological materials: The velocity gauge picture

High Harmonic Generation (HHG), which has been widely used in atomic gas, has recently expanded to solids as a means to study highly nonlinear electronic response in condensed matter and produce coherent high frequency radiation with new properties. Most recently, attention has turned to Topological Materials (TMs) and the use of HHG to characterize topological bands and invariants. Theoretical interpretation of nonlinear electronic response in TMs, however, presents many challenges. In particular, the Bloch wavefunction phase of TMs has undefined points in the Brillouin Zone. This leads to singularities in calculating the inter-band and intra-band transition dipole matrix elements of Semiconductor Bloch Equations (SBEs). Here, we use the laser-electromagnetic velocity gauge ${\boldsymbol p}\cdot {\bf A}(t)$ to numerically integrate the SBEs and treat the singularity in the production of the electrical currents and HHG spectra. We use a prototype of Chern Insulators (CIs), the Haldane model, to demonstrate our approach. We find good qualitative agreement of the velocity gauge compared to the length gauge and the Time-Dependent Density Functional theory in the case of topologically trivial materials such as MoS$_2$. For velocity gauge and length gauge, our two-band Haldane model reproduces key HHG spectra features: ($\textit i$) The selection rules for linear and circular light drivers, ($\textit ii$) The linear cut-off law scaling and ($\textit iii$) The anomalous circular dichroism. We conclude that the velocity-gauge approach captures experimental observations and provides theoretical tools to investigate topological materials.

Singular-connection approach to topological phases and resonant optical responses

We introduce a class of singular connections as an alternative to the Berry connection for any family of quantum states defined over a parameter space. We find a natural application of the singular connection in the context of transition dipoles between two bands. We find that the shift vector is nothing but the difference between the singular connection and the connection induced from the Berry connections of involved bands; the gauge invariance of the shift vector is transparent from this expression. We show, using singular connections, that the topological invariant in two dimensions associated with optical transitions between the two bands can be computed, by means of this connection, by algebraically counting the points in the zero locus of a transition dipole matrix element of the two bands involved. It follows that this invariant provides a natural topological lower bound on the number of momenta in the Brillouin zone for which an electron cannot be excited from one Bloch band to the other by absorbing a photon.

Continuous absorption and emission of light by the heteronuclear rare gas (ArXe)+ and (KrXe)+ ions

Studies of radiative transitions between ground and charge transfer excited terms of heteronuclear rare-gas (ArXe)+ and (KrXe)+ ions with small and moderate dissociation energies (D0 ArXe+ =179 and D0 KrXe+ =389 meV) are reported. Potential energy curves and dipole transition matrix elements are evaluated using ab initio calculations based on the CASSCF method followed by the NEVPT2 treatment and perturbative description of relativistic effects as implemented in the ORCA suite. We develop an efficient approach for the calculations of Boltzmann-averaged cross sections, rate constants, and absorption and emission coefficients associated with the integral contributions of bound-bound and bound-free transitions from a manifold of rovibrational states of the (RgXe)+ ion. A similar approach is used for the description of the free-free and free-bound transitions between different electronic terms of a quasimolecular (RgXe)+ ion temporarily formed during a collision of Ar or Kr atoms with Xe+ ions. Our method is based on the quantal version of the theory of non-adiabatic transitions in molecular and quasimolecular systems combined with the approximation of a quasicontinuum for rovibrational energy levels. This allowed us to obtain a semianalytic expression for the integral absorption properties particularly relevant at elevated temperatures. We perform a comprehensive analysis of the identified radiative processes in local thermodynamic equilibrium plasmas of rare gas Rg/Xe mixtures containing both atomic, Xe+, and molecular, RgXe+, ions and determine their role in the formation of the absorption and emission spectra in a wide range of wavelengths and gas temperatures. The results obtained are in good agreement with the available experimental data.

Unified master equation for molecules in phonon and radiation baths

We have developed a unified quantum optical master equation that includes the dissipative mechanisms of an impurity molecule in crystals. Our theory applies generally to polyatomic molecules where several vibrational modes give rise to intramolecular vibrational redistributions. The usual assumption on identical shapes of the nuclear potentials in ground and excited electronic states and the rotating wave approximation have been relaxed, i.e. the vibrational coordinates are different in the ground and excited states, with counter-rotating terms included for generality. Linear vibrational coupling to the lattice phonons accounts for dissipations via non-radiative transitions. The interaction of a molecule with photons includes Herzberg–Teller coupling as the first order non-Condon interaction where the transition dipole matrix elements depend linearly on vibrational coordinates. We obtain new cross terms as the result of mixing the terms from the zeroth-order (Condon) and first-order (non-Condon) approximations. The corresponding Lamb shifts for all Liouvilleans are derived explicitly including the contributions of counter-rotating terms. The computed absorption and emission spectra for carbon monoxide is in good agreement with experimental data. We use our unified model to obtain the spectra for nitrogen dioxide, demonstrating the capability of our theory to incorporate all typical dissipative relaxation and decoherence mechanisms for polyatomic molecules. The molecular quantum master equation is a promising theory for studying molecular quantum memory.

Nontrivial quantum geometry of degenerate flat bands

The importance of the quantum metric in flat-band systems has been noticed recently in many contexts such as the superfluid stiffness, the dc electrical conductivity, and ideal Chern insulators. Both the quantum metric of degenerate and nondegenerate bands can be naturally described via the geometry of different Grassmannian manifolds, specific to the band degeneracies. Contrary to the (Abelian) Berry curvature, the quantum metric of a degenerate band resulting from the collapse of a collection of bands is not simply the sum of the individual quantum metrics. We provide a physical interpretation of this phenomenon in terms of transition dipole matrix elements between two bands. By considering a toy model, we show that the quantum metric gets enhanced, reduced, or remains unaffected depending on which bands collapse. The dc longitudinal conductivity and the superfluid stiffness are known to be proportional to the quantum metric for flat-band systems, which makes them suitable candidates for the observation of this phenomenon.

Rashba effect on linear and nonlinear optical properties of a cylindrical core/shell heterojunction quantum dot

Rashba effect may play an important role in the nonlinear optical properties of heterojunction quantum dots. In this work, we have theoretically examined the effects of Rashba spin-orbit interaction on an electron in a cylindrical core/shell quantum dot (CCSQD). The modifications of various properties of cylindrical core/shell quantum dot such as transition energies, dipole transition matrix elements and linear and nonlinear optical properties due to change in Rashba coupling parameter, magnetic field and effective Rydberg energy were studied. We solved the Schrödinger equation using numerical methods and obtained energy eigenvalues as functions of the aforementioned parameters. It was observed that, the magnetic field has a considerable effect on absorption coefficients and refractive index. It was also observed that increasing the magnetic field shifts the resonances towards higher energies. Additionally, increasing in the Rashba coupling coefficient (αR) was found out to result an increase in absorption coefficients and refractive index. Our results demonstrated that, we can manipulate optical properties of cylindrical core/shell quantum dot using an external magnetic field.

Character of the OH Bend-Stretch Combination Band in the Vibrational Spectra of the "Magic" Number H3O+(H2O)20 and D3O+(D2O)20 Cluster Ions.

The fundamental transitions that contribute to the diffuse OH stretching spectrum of water are known to increase in width and intensity with increasing red shift from the free OH frequency. In contrast, the profile of the higher-energy combination band involving the OH stretching and the intramolecular HOH bending modes displays a qualitatively different spectral shape with a much faster falloff on the lower-energy side. We elucidate the molecular origin of this difference by analyzing the shapes of the combination bands in the IR spectra of cryogenically cooled H3O+(H2O)20 and D3O+(D2O)20 clusters. The difference in the shapes of the bands is traced to differences in the dependence of their transition dipole matrix elements on the hydrogen-bonding environment. The fact that individual transitions across the combination band envelope have similar intensities makes it a useful way to determine the participation of various sites in extended H-bonding networks.

High Harmonic Generation in Monolayer and Bilayer of Transition Metal Dichalcogenide

In transition metal dichalcogenides (TMDCs), charge carriers have spin, pseudospin, and valley degrees of freedom associated with magnetic moments. The monolayers and bilayers of the TMDCs, in particular, MoS2, lead to strong couplings between the spin and pseudospin effects. This feature has drawn attention to TMDCs for their potential use in advanced tech devices. Meanwhile, high-order harmonic generation (HHG) has recently been applied to the characterization of the electronic structure of solids, such as energy dispersion, Berry-curvature, and topological properties. Here, we show theoretical results obtained with the ‘philosophy’ of using HHG to investigate the structural effects of the monolayer and bilayers of MoS2 on nonlinear optical emission. We use a simple model for MoS2 in the 3R AB staking. We find that the pseudospin and valley indexes (the Berry curvature and the dipole transition matrix element) in TMDC driven by a circularly polarized laser (CPL) can encode in the high-energy photon emissions. This theoretical investigation is expected to pave the way for the ultrafast manipulation of valleytronics and lead to new questions concerning the spin-obit-coupling (SOC) effects on TMDC materials, Weyl Semimetals, and topological phases and transitions in topological insulators.

Orbital−energy splitting in Ruddlesden−Popper layered halide perovskites for tunable optoelectronic properties

The electronic orbital characteristics at the band edges play an important role in determining the electrical, optical and defect properties of perovskite photovoltaic materials. It is highly desirable to establish the relationship between the underlying atomic orbitals and the optoelectronic properties as a guide to maximize the photovoltaic performance. Here, using first-principles calculations and taking Ruddlesden-Popper (RP) phase layered perovskites Cs n +1 Ge n I n +1 Cl 2n as examples, we demonstrate how to rationally optimize the optoelectronic properties (e.g., band gap, transition dipole matrix elements, carrier effective masses, bandwidth) through a simple band structure parameter. Our results show that reducing the splitting energy |Δ c | between the in-plane p x , y and out-of-plane p z orbitals at the conduction band minimum (CBM) can effectively reduce the band gap and carrier effective masses while greatly improving the optical absorption in the visible region. Thereby, the orbital-property relationship with Δ c is well established through biaxial compressive strain. Finally, it is shown that this approach can be reasonably extended to several other non-cubic halide perovskites with similar p orbitals characteristics at the conduction band edge. Therefore, we believe that our proposed orbital engineering approach will provide atomic-level guidance for understanding the performance limits of layered perovskite solar cells. • Orbital−energy splitting in Ruddlesden−Popper layered halide perovskites. • Optimizing the optoelectronic properties through a simple band structure parameter. • Reducing the splitting energy .|Δ c | can effectively tune the optoelectronic properties.

Large Inverted Singlet–Triplet Energy Gaps Are Not Always Favorable for Triplet Harvesting: Vibronic Coupling Drives the (Reverse) Intersystem Crossing in Heptazine Derivatives

Heptazine derivatives are promising dopants for electroluminescent devices. Recent studies raised the question whether heptazines exhibit a small regular or an inverted singlet-triplet (IST) gap. It was argued that the S1 ← T1 reverse intersystem crossing (RISC) is a downhill process in IST emitters and therefore does not require thermal activation, thus enabling efficient harvesting of triplet excitons. Rate constants were not determined in these studies. Modeling the excited-state properties of heptazine proves challenging because fluorescence and intersystem crossing (ISC) are symmetry-forbidden in first order. In this work, we present a comprehensive theoretical study of the photophysics of heptazine and its derivative HAP-3MF. The calculations of electronic excitation energies and vibronic coupling matrix elements have been conducted at the density functional theory/multireference configuration interaction (DFT/MRCI) level of theory. We have employed a finite difference approach to determine nonadiabatic couplings and derivatives of spin-orbit coupling and electric dipole transition matrix elements with respect to normal coordinate displacements. Kinetic constants for fluorescence, phosphorescence, internal conversion (IC), ISC, and RISC have been computed in the framework of a static approach. Radiative S1 ↔ S0 transitions borrow intensity mainly from optically bright E' π → π* states, while S1 ↔ T1 (R)ISC is mediated by E″ states of n → π* character. Test calculations show that IST gaps as large as those reported in the literature are counterproductive and slow down the S1 ← T1 RISC process. Using the adiabatic DFT/MRCI singlet-triplet splitting of -0.02 eV, we find vibronically enhanced ISC and RISC to be fast in the heptazine core compound. Nevertheless, its photo- and electroluminescence quantum yields are predicted to be very low because S1 → S0 IC efficiently quenches the luminescence. In contrast, fluorescence, IC, ISC, and RISC proceed at similar time scales in HAP-3MF.