Dipole Moment Matrix Elements Research Articles

Electronic transition dipole moment and radiative lifetime calculations of sodium dimer ion-pair states.

We report here ab initio calculated electronic transition dipole moments for the sodium dimer ion pair states of (1)Σg (+) symmetry. They vary strongly as a function of internuclear distance because of the effect of the Na(+) + Na(-) ion pair potential, which also causes the formation of additional wells and shoulders in the molecular potential energy curves. We also present a computational study of the transition dipole moment matrix elements and lifetimes for these ion-pair states.

Design of white LED using GaN/InxGa(1−x)N multiquantum well

In this paper, we report white light extraction from multiquantum well (MQW) light emitting diode (LED). Our proposed white LED is composed of InxGa(1−x)N well layers with different widths and mole fractions, emitting red, green, and blue (RGB) colors. The barrier layer is composed of GaN material. Regarding piezoelectric and spontaneous polarizations internal fields, we have employed 6×6 k.p. method, for solving Schrödinger and Poisson equations self consistently. Then, we have calculated electron and hole eigen energies and waves functions. By evaluating dipole moment matrix elements, the output intensity has been calculated due to the interband transition between two energy levels. We have adjusted RGB quantum wells (QW) dimensions and material compositions such that the output light is close to the ideal white light in the chromaticity diagram. Also, effects of temperature deviations as a key parameter on the output color and also chromaticity coordinates have been investigated. We have demonstrated that temperature variation in the range of 250–350°K decreases output intensities and causes a redshift in the spectrums of RGB colors. As a result, temperature variations deviate (x, y) coordinate in the chromaticity diagram, but still the output color remains close to white.

Linear and nonlinear optical absorption coefficients and refractive index changes in double parabolic-square quantum well as dependent on intense laser field

In this study, for double parabolic-square quantum well (DPSQW) the linear and nonlinear intersubband optical absorption coefficients and the refractive index changes are calculated as dependent on the intense laser field (ILF). Our results show that the location and the size of all absorption coefficients and refractive index changes depend on ILF. Also, we show that ILF provides an important effect on the electronic and optical properties of DPSQW, and the changes of the energy levels and the dipole moment matrix elements are dependent on the shape of the confinement potential. Such effects can provide methods to drive tunable semiconductor lasers, which may be tailored by quantum potential well parameters and by ILF values.

How to Calculate Molecular Column Density

The calculation of the molecular column density from molecular spectral (rotational or ro-vibrational) transition measurements is one of the most basic quantities derived from molecular spectroscopy. Starting from first principles where we describe the basic physics behind the radiative and collisional excitation of molecules and the radiative transfer of their emission, we derive a general expression for the molecular column density. As the calculation of the molecular column density involves a knowledge of the molecular energy level degeneracies, rotational partition functions, dipole moment matrix elements, and line strengths, we include generalized derivations of these molecule-specific quantities. Given that approximations to the column density equation are often useful, we explore the optically thin, optically thick, and low-frequency limits to our derived general molecular column density relation. We also evaluate the limitations of the common assumption that the molecular excitation temperature is constant and address the distinction between beam-averaged and source-averaged column densities. As non-LTE approaches to the calculation of molecular spectral line column density have become quite common, we summarize non-LTE models that calculate molecular cloud volume densities, kinetic temperatures, and molecular column densities. We conclude our discussion of the molecular column density with worked examples for C18O, C17O, N2H+, NH3, and H2CO. Ancillary information on some subtleties involving line profile functions, conversion between integrated flux and brightness temperature, the calculation of the uncertainty associated with an integrated intensity measurement, the calculation of spectral line optical depth using hyperfine or isotopologue measurements, the calculation of the kinetic temperature from a symmetric molecule excitation temperature measurement, and relative hyperfine intensity calculations for NH3 are presented in appendices. The intent of this document is to provide a reference for researchers studying astrophysical molecular spectroscopic measurements.

Resonant peaks of the linear optical absorption and rectification coefficients in GaAs/GaAlAs quantum well: Combined effects of intense laser, electric and magnetic fields

In this study, the resonant peaks of the linear optical absorption (OA) and rectification coefficients in GaAs/GaAlAs quantum well are calculated as dependent on the applied electric field (F), the magnetic field (B) and the laser field intensity parameter (α0). Our results show that the shape of confined potential profile, the energy levels and the dipole moment matrix elements are changed as dependent on the F, B and α0. Also, the resonant peaks of the OA and rectification coefficients depend on the applied external field effects. Therefore, the variation of the resonant peaks of these coefficients which can be appropriate for various optical modulators and infrared optical device applications can be smoothly obtained by the alteration electric, magnetic and intense laser field.

Properties of Stark Resonant States in Exactly Solvable Systems

Properties of Stark resonant states are studied in two exactly solvable systems. These resonances are shown to form a biorthogonal system with respect to a pairing defined by a contour integral that selects states with outgoing wave boundary conditions. Analytic expressions are derived for the pseudonorm, dipole moment, and coupling matrix elements which relate systems with different strengths of the external field. All results are based on explicit calculations made possible by a newly designed integration method for combinations of Airy functions representing resonant eigenstates. Generalizations for one-dimensional systems with short-range potentials are presented, and relations are identified which are likely to hold in systems with three spatial dimensions.

Parameterization of the effective dipole moment matrix elements in the case of the asymmetric top molecules. Application to NO2 molecule

A new parameterization of the effective dipole moment matrix elements for the asymmetric top molecules is suggested. It is based on the introduction of the Herman-Wallis type factors for the matrix elements. The advantage of this new parameterization consists in the utilization of the matrix element parameters which describe explicitly the dependence of the principal matrix element parameter on the rotational quantum numbers J and K. The application of this approach to the open-shell NO2 molecule is discussed.

Studies of singlet Rydberg series of LiH derived from Li(nl) + H(1s), with n ≤ 6 and l ≤ 4.

The 50 singlet states of LiH composed of 49 Rydberg states and one non-Rydberg ionic state derivable from Li(nl) + H(1s), with n ≤ 6 and l ≤ 4, are studied using the multi-reference configuration interaction method combined with the Stuttgart/Köln group's effective core potential/core polarization potential method. Basis functions that can yield energy levels up to the 6g orbital of Li have been developed, and they are used with a huge number of universal Kaufmann basis functions for Rydberg states. The systematics and regularities of the physical properties such as potential energies, quantum defects, permanent dipole moments, transition dipole moments, and nonadiabatic coupling matrix elements of the Rydberg series are studied. The behaviors of potential energy curves and quantum defect curves are explained using the Fermi approximation. The permanent dipole moments of the Rydberg series reveal that they are determined by the sizes of the Rydberg orbitals, which are proportional to n(2). Interesting mirror relationships of the dipole moments are observed between l-mixed Rydberg series, with the rule Δl = ±1, except for s-d mixing, which is also accompanied by n-mixing. The members of the l-mixed Rydberg series have dipole moments with opposite directions. The first derivatives of the dipole moment curves, which show the charge-transfer component, clearly show not only mirror relationships in terms of direction but also oscillations. The transition dipole moment matrix elements of the Rydberg series are determined by the small-r region, with two consequences. One is that the transition dipole moment matrix elements show n(-3/2) dependence. The other is that the magnitudes of the transition dipole moment matrix elements decrease rapidly as l increases.

Simultaneous effects of the intense laser field and the electric field on the nonlinear optical properties in GaAs/GaAlAs quantum well

In this study, both the linear and nonlinear intersubband optical absorption coefficients and the refractive index changes are calculated as dependent on the applied electric field (F) and the laser field intensity parameter (α0). Our results show that the location and the size of the linear and total absorption coefficients and refractive index changes depend on the applied external field effects. The shape of confined potential profile, the energy levels and the squared dipole moment matrix elements are changed as dependent on the F and α0. We have found that the intense laser field and the applied electric field can be used as a way to control the linear, nonlinear and total optical properties of the quantum well structures. While for F=0 the intersubband absorption spectrum shows blue-shift up to the critical laser field value ( for about α0<L/3), this spectrum shows red-shift for laser field values greater than this certain value. In the presence F, we obtain two critical laser field values (for about α0<L/3 and α0>2L/3). The absorption spectra display blue-shift up to the first critical laser field values, these spectra indicate red-shift up to the second critical values and show again blue-shift for the laser field values greater than these second certain values. Therefore, the variation of the absorption coefficients and refraction index changes which can be appropriate for various optical modulators and infrared optical device applications can be smooth obtained by the alteration of electric field and intense laser field.

Electron–phonon interaction influence on optical properties of parallelogram quantum wires

In the present work, we have studied the effect of electron–phonon (e–p) interaction on optical properties of a GaAs quantum wire with parallelogram cross-section. For this goal, we have calculated refractive index changes and absorption coefficients by using compact-density-matrix approach and iterative method. The results show that the refractive index changes and absorption coefficients are obviously increased and the peak positions shift toward higher energies after considering the e–p interaction. We have also studied polaronic effect on electric dipole moment matrix elements and the energy levels for different quantum wire sizes. We have found that the line-width of absorption coefficients and refractive index changes is approximately constant after considering e–p interaction.

Electron-related optical responses in triangular quantum dots

The linear and nonlinear coefficients for the optical absorption and relative refractive index change associated with intersubband transitions of electrons in the conduction band of a two-dimensional quantum dot of triangular shape are calculated for x-polarization and y-polarization of the incident light. Both the effective mass and parabolic band approximations have been considered. The results show that the increase in the size of the triangular quantum dot leads to the expected fall of the intersubband energy transition and that there is an increment in the values of the associated off-diagonal electric dipole moment matrix elements. All this reflects in the increase of the amplitude of the nonlinear optical absorption resonant peak, as well as in the growth of the total relative refractive index in the system.

Einstein A-values and oscillator strengths of the A2П–X2Σ+ system of CP

Line strengths for bands of the A2П–X2Σ+ transition of CP, including the effect of rotation on the vibrational wavefunctions (the Herman–Wallis effect), have been calculated using Western׳s PGOPHER program and Le Roy׳s LEVEL program. The potential energy functions for the A2П and X2Σ+ state were computed using spectroscopic constants obtained from high resolution spectra. The RKR potentials of the two states, and the electronic transition dipole moments of this transition calculated in a recent ab initio study have been used in Le Roy׳s LEVEL program to produce transition dipole moment matrix elements. The matrix elements have been converted from Hund׳s case (b) to (a), and then used in PGOPHER to generate a line list containing observed and calculated wavenumbers, Einstein A coefficients and f-values for 75 bands with v=0–8 for both states. The Einstein A coefficients have been used to compute radiative lifetimes for v=0–5 in the A2П state. The line list may be useful for computing the molecular opacities of CP needed to simulate the spectra of stellar and substellar sources.

EINSTEIN A COEFFICIENTS AND OSCILLATOR STRENGTHS FOR THE A 2 Π- X 2 Σ + (RED) AND B 2 Σ + -X 2 Σ + (VIOLET) SYSTEMS AND ROVIBRATIONAL TRANSITIONS IN THE X 2 Σ + STATE OF CN

Line strengths have been calculated in the form of Einstein A coefficients and f-values for a large number of bands of the A 2Π-X 2Σ+ and B 2Σ+-X 2Σ+ systems and rovibrational transitions within the X 2Σ+ state of CN using Western's PGOPHER program. The J dependence of the transition dipole moment matrix elements (the Herman-Wallis effect) has been taken into account. Rydberg-Klein-Rees potential energy functions for the A 2Π, B 2Σ+ , and X 2Σ+ states were computed using spectroscopic constants from the A 2Π-X 2Σ+ and B 2Σ+-X 2Σ+ transitions. New electronic transition dipole moment functions for these systems and a dipole moment function for the X 2Σ+ state were generated from high level ab initio calculations and have been used in Le Roy's LEVEL program to produce transition dipole moment matrix elements (including their J dependence) for a large number of vibrational bands. The program PGOPHER was used to calculate Einstein A coefficients, and a line list was generated containing the observed and calculated wavenumbers, Einstein A coefficients and f-values for 290 bands of the A 2Π-X 2Σ+ transition with v' = 0-22, v'' = 0-15, 250 bands of the B 2Σ+-X 2Σ+ transition with v' = 0-15, v'' = 0-15 and 120 bands of the rovibrational transitions within the X 2Σ+ state with v = 0-15. The Einstein A coefficients have been used to compute radiative lifetimes of several vibrational levels of the A 2Π and B 2Σ+ states and the values compared with those available from previous experimental and theoretical studies.

The effect of electron–phonon interaction on optical properties of a triangular quantum wire

The influence of electron–phonon interaction on refractive index changes and absorption coefficients in a GaAs quantum wire with triangular cross-section is investigated by using compact-density-matrix approach and iterative method. The results show that the refractive index changes and absorption coefficients are obviously enhanced and the peak positions shift toward higher energy after considering the electron–phonon interaction. In this paper, we also investigate polaron effect on the energy levels and electric dipole moment matrix elements for different length sides of quantum wire.

Donor impurity-related linear and nonlinear optical absorption coefficients in [formula omitted] concentric double quantum rings: Effects of geometry, hydrostatic pressure, and aluminum concentration

The linear and nonlinear optical absorption associated with the transition between 1s and 2s states corresponding to the electron-donor-impurity complex in GaAs/Ga1−xAlxAs three-dimensional concentric double quantum rings are investigated. Taking into account the combined effects of hydrostatic pressure and the variation of the aluminum concentration, the energies of the ground and first excited s-like states of a donor impurity in such a system have been calculated using the effective mass approximation and a variational method. The energies of these states and the corresponding threshold energy of the optical transitions are examined as functions of hydrostatic pressure, aluminum concentration, radial impurity position, as well as the geometrical dimensions of the structure. The dependencies of the linear, nonlinear and total optical absorption coefficients as functions of the incident photon energy are investigated for different values of those mentioned parameters. It is found that the influences mentioned above lead to either redshifts or blueshifts of the resonant peaks of the optical absorption spectrum. It is particularly discussed the unusual property exhibited by the third-order nonlinear of becoming positive for photon energies below the resonant transition one. It is shown that this phenomenon is associated with the particular features of the system under study, which determine the values of the electric dipole moment matrix elements.

Linear and nonlinear optical properties of a hydrogenic impurity confined in a two-dimensional quantum dot: Effects of hydrostatic pressure, external electric and magnetic fields

In this work, combined effects of external electric and magnetic fields, and hydrostatic pressure on the refractive index changes and optical absorption coefficients of a hydrogenic impurity confined in a two-dimensional parabolic quantum dot are studied. Energy eigenvalues and eigenvectors are calculated using the direct matrix diagonalization method and optical properties are obtained using the compact density matrix approach. It is found that the confinement potential strength, hydrogenic impurity, hydrostatic pressure, external electric and magnetic fields and the tilt angle θ considerably change the transition energy between the subbands and dipole moment matrix elements. Therefore, these parameters have a great influence on the linear and the third-order nonlinear optical absorption coefficients as well as the refractive index changes of the system.

Temperature effects on output characteristics of quantum dot white light emitting diode

In this paper, we proposed quantum dot (QD) based structure for implementation of white light emitting diode (WLED) based on InGaN/GaN. The proposed structure included three layers of InGaN QD with box shapes and GaN barriers. By using of single band effective mass method and considering strain effect, piezoelectric and spontaneous polarizations internal fields, then solving Schrodinger and Poisson equations self consistently, we obtained electron and hole eigen energies and wave functions. By evaluating dipole moment matrix elements for interband transitions, the output intensity was calculated due to the interband transition between two energy levels with highest emission probability. We adjusted QDs dimensions and material compositions so that the output light can be close to the ideal white light in chromaticity diagrams. Finally, effects of temperature variations on output spectrum and chromaticity coordinates were studied. We demonstrated that temperature variations in the range of 100 to 400 K decrease output intensity, broaden output spectral profile and cause a red shift in three main colors spectrums. This temperature variation deviates (x, y) are coordinated in the chromaticity diagram, but the output color still remains close to white.

Accurate ab initio ro-vibronic spectroscopy of the $\tilde X^2 \Pi$X̃2Π CCN radical using explicitly correlated methods

Explicitly correlated CCSD(T)-F12b calculations have been carried out with systematic sequences of correlation consistent basis sets to determine accurate near-equilibrium potential energy surfaces for the X(2)Π and a(4)Σ(-) electronic states of the CCN radical. After including contributions due to core correlation, scalar relativity, and higher order electron correlation effects, the latter utilizing large-scale multireference configuration interaction calculations, the resulting surfaces were employed in variational calculations of the ro-vibronic spectra. These calculations also included the use of accurate spin-orbit and dipole moment matrix elements. The resulting ro-vibronic transition energies, including the Renner-Teller sub-bands involving the bending mode, agree with the available experimental data to within 3 cm(-1) in all cases. Full sets of spectroscopic constants are reported using the usual second-order perturbation theory expressions. Integrated absorption intensities are given for a number of selected vibronic band origins. A computational procedure similar to that used in the determination of the potential energy functions was also utilized to predict the formation enthalpy of CCN, ΔH(f)(0K) = 161.7 ± 0.5 kcal/mol.

Einstein A coefficients and absolute line intensities for the E 2Π–X 2Σ + transition of CaH

Einstein A coefficients and absolute line intensities have been calculated for the E 2Π–X 2Σ + transition of CaH. Using wavefunctions derived from the Rydberg–Klein–Rees (RKR) method and electronic transition dipole moment functions obtained from high-level ab initio calculations, rotationless transition dipole moment matrix elements have been calculated for all 10 bands involving v′=0,1 of the E 2Π state and v″=0,1,2,3,4 of the X 2Σ state. The rotational line strength factors (Hönl–London factors) are derived for the intermediate coupling case between Hund's case (a) and (b) for the E 2Π–X 2Σ + transition. The computed transition dipole moments and the spectroscopic constants from a recent study [Ram et al., Journal of Molecular Spectroscopy 2011;266:86–91] have been combined to generate line lists containing Einstein A coefficients and absolute line intensities for 10 bands of the E 2Π–X 2Σ + transition of CaH for J-values up to 50.5. The absolute line intensities have been used to determine a rotational temperature of 778±3 °C for the CaH sample in the recent study.

Direct fit of experimental ro-vibrational intensities to the dipole moment function: Application to HCl

A dipole moment function (DMF) for hydrogen chloride (HCl) has been obtained using a direct fit approach that fits the best available and appropriately weighted experimental data for individual ro-vibrational transitions. Combining wavefunctions derived from the Rydberg–Klein–Rees (RKR) numerical method and a semi-empirical DMF, line intensities were calculated numerically for bands with Δ v=0, 1, 2, 3, 4, 5, 6, 7 up to v′=7. The results have demonstrated the effectiveness of inclusion of rotational dipole moment matrix elements and appropriate weighting of the experimental data in the DMF fitting. The new method is shown to be superior to the common method of fitting only the rotationless dipole moment elements, while at the same time being simple to implement.