Rydberg-Klein-Rees Research Articles

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.

Rotational analysis and deperturbation of the A 2Π → X 2Σ+ and B′ 2Σ+ → X 2Σ+ emission spectra of MgH

Deperturbation analysis of the A(2)Π → X(2)Σ(+) and B(')(2)Σ(+) → X(2)Σ(+) emission spectra of (24)MgH is reported. Spectroscopic data for the v = 0 to 3 levels of the A (2)Π state and the v = 0 to 4 levels of the B'(2)Σ(+) state were fitted together using a single Hamiltonian matrix that includes (2)Π and (2)Σ(+) matrix elements, as well as off-diagonal elements coupling several vibrational levels of the two states. A Dunham-type fit was performed and the resulting Y(l,0) and Y(l,1) coefficients were used to generate Rydberg-Klein-Rees (RKR) potential curves for the A (2)Π and the B'(2)Σ(+) states. Vibrational overlap integrals were computed from the RKR potentials, and the off-diagonal matrix elements coupling the electronic wavefunctions (a(+) and b) were determined. Zero point dissociation energies (D(0)) of the A(2)Π and B'(2)Σ(+) states of (24)MgH were determined to be 12,957.5 ± 0.5 and 10,133.6 ± 0.5 cm(-1), respectively. Using the Y(0,1) coefficients, the equilibrium internuclear distances (r(e)) of the A(2)Π and B'(2)Σ(+) states were determined to be 1.67827(1) Å and 2.59404(4) Å, respectively.

Spectroscopic constants and molecular properties of A3 Σu + , B3 Πg , W3 Δu , and B′3 Σu − electronic states of the N2 molecule

The potential energy curves (PECs) of A3Σ, B3Πg, W3Δu, and B′3Σ electronic states of the N2 molecule have been studied for internuclear separations from 0.05 to 2.0 nm using the full valence complete active space self-consistent-field method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in conjunction with the correlation-consistent basis sets. Effects on the PECs by the core–valence correlation and relativistic corrections are taken into account. The way to consider the relativistic correction is to use the second-order Douglas-Kroll Hamiltonian approximation. The core–valence correlation correction is made with the cc-pCV5Z basis set. And the relativistic correction is performed at the level of cc-pV5Z basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size-extensivity errors by the Davidson modification (MRCI+Q). These PECs are extrapolated to the complete basis set limit. The spectroscopic parameters of 14N2, 14N15N, and 15N2 isotopologs have been evaluated and compared with those reported in the literature. Excellent agreement has been found between the present results and the Rydberg-Klein-Rees (RKR) data. With the PECs obtained by the MRCI+Q/CV+DK+56 calculations, the first 30 vibrational states for three species are computed for each electronic state. And for each electronic state of each species, the vibrational level G(ν), inertial rotation constant Bν, and centrifugal distortion constant Dν have been determined, which agree well with the RKR data. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

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.

Photoautoionization structure in the halogen systems Br2, I2, BrCl, ICl, and IBr

The photoabsorption ion-yield spectra of the titled molecules have been recorded in the threshold ionization region between the two spin-orbit components of the ground states of the molecular ions. All ion-yield spectra display rather simple autoionization structure superimposed on a smoothly rising continuum in the ionization energy region. The structure was analyzed in terms of autoionizing Rydberg states and their vibrational profiles simulated using Rydberg–Klein–Rees (RKR) derived potential energy curves and calculated Franck–Condon factors using Gaussian line-shape functions. All of the structure observed is attributed to spin-orbit autoionization. There seems to be a propensity for autoionization of sσ Rydberg states in all of the interhalogen molecules studied.

Franck–Condon factors and radiative lifetime of the A2Π1/2–X2Σ+ transition of ytterbium monofluoride, YbF

The fluorescence spectrum resulting from laser excitation of the A(2)Π(1/2)←X(2)Σ(+) (0,0) band of ytterbium monofluoride, YbF, has been recorded and analyzed to determine the Franck-Condon factors. The measured values are compared with those predicted from Rydberg-Klein-Rees (RKR) potential energy curves. From the fluorescence decay curve the radiative lifetime of the A(2)Π(1/2) state is measured to be 28 ± 2 ns, and the corresponding transition dipole moment is 4.39 ± 0.16 D. The implications for laser cooling YbF are discussed.

Characterization of the outer well of NaH C 1Σ + state by fluorescence depletion spectroscopy

The outer well of the NaH C 1Σ + excited state was determined using pulsed optical–optical double resonance fluorescence depletion spectroscopy. The level-selected fluorescence of the A 1Σ + state is depleted back to the ground state when a probe laser excites the molecules to the C 1Σ + state. A total of 456 rovibrational levels, v = 5–33 and J = 1–11, were observed. A set of Dunham constants and the Rydberg–Klein–Rees (RKR) potential curve for the outer well were reported.

Vibrational distributions in N 2 with an improved calculation of energy levels using the RKR method

The potential curve of the N 2 ground state ( X 1 Σ g + ) has been accurately reconstructed using the Rydberg–Klein–Rees (RKR) method extrapolated by a Hulburt and Hirschfelder potential for longer internuclear distances. Solving the corresponding radial Schrödinger equation yields 60 bound levels above v = 0, whose energies may be fitted by the following polynomial expansion: G ( v ) = ∑ i = 1 5 a i ( v + 1 / 2 ) i , with the coefficients a i in cm −1 equal to 2378.1, −18.516, 0.26662, −6.2127 × 10 −3, and 3.4215 × 10 −5, respectively, for i = 1–5. The effects of considering this more accurate potential on the vibrational distribution function of N 2(X, v) molecules obtained in nitrogen microwave discharges and post-discharges are compared with previous calculations, using a smaller vibrational manifold.

Franck-Condon factors and r-centroids for the diatomic fluorides of germanium and silicon

A suitable potential energy function was found by analysing the potential functions proposed by Morse, Mohammad and Rafi et al. for the A2?+-X2?3/2 and B2?+-X2?3/2 band systems of GeF and the 1?-1? band system of SiF. It was found that the potential proposed by Rafi et al. is in close agreement with the Rydberg-Klein-Rees (R-K-R) potential. Using this potential, the wave functions were evaluated by the Wentzel-Kramer-Brillouin (W-K-B) method. The Franck-Condon factors and r-centroids were computed by a numerical integration technique. The results are compared with available theoretical values. The intensities of the various bands were investigated.

The 5 1Π u electronic state of the lithium dimer

Polarisation labelling spectroscopy has been used to study the previously unobserved 5 1Π u state of the Li 2 molecule. Molecular constants are derived from a Dunham expansion and the Rydberg-Klein-Rees (RKR) potential curve is constructed. Absolute vibrational numbering of the 5 1Π u state is determined by observation of the isotope effect. The values of T e, ω e and B e are 36390.97(2), 232.03(3) and 0.46832(4) cm −1, respectively.

A universal analytic potential-energy function based on a phase factor

Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of face-centered cubic (fcc) metals - Al, Cu, Ag, etc. are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.

Construction of RKR-QDT atomic model potentials for the calculation of Lithium polarizabilities and hyper-polarizabilities

Atomic local model potentials, reproducing experimental energy levels, are built by a combination of the Rydberg–Klein–Rees (RKR) inversion method with the quantum defect theory (QDT). An efficient iterative procedure leads to the production of spectrum-equivalent potentials containing a number of free parameters. These parameters can be adjusted in order to improve the accuracy of other physical properties, calculated via the constructed potentials. The high efficiency of the method is demonstrated by calculating the lifetimes of singly excited states as well as the dipole and quadrupole polarizability and hyper-polarizability of the ground 1s22s and first excited 1s22p state of Lithium. The obtained value γ = 3390 au for the ground state hyper-polarizability is in excellent agreement with other elaborate theoretical calculations. The scalar hyper-polarizability of 1s22p acquires a much higher value, γ0 = 1.002 × 107 au, while its tensor part is γ2 = −0.621 × 107 au.

Observation and analysis of the 2g(1D) ion-pair state of I2: the g/u mixing between the 1u(1D) and 2g(1D) states.

We report the analysis of the 2g(1D) ion-pair state of I2 by perturbation-facilitated optical-optical double resonance. The present study began with the observation of the 2g(1D)-A' 3Pi(2u) emission at around 230 nm during the analysis of the ultraviolet emissions originating form the 1u(1D) ion-pair state. The identification of this new transition helped us to specify the wavelengths for detecting the 2g(1D) state by emission, and also to estimate its absolute position. The intermediate states used to observe the 2g(1D) state were the B 3Pi(0u(+))-b' 2u mixed states by the hyperfine interaction, which allowed us to combine the X 1Sigmag(+) ground state with the 2g(1D) state in the (1+1) photon excitation following the optical selection rules for one-photon transitions: 2g(1D)<--b' 2u-B 3Pi(0u(+))<--X 1Sigmag(+). Our analysis covered the 2g(1D) state in the 0< or =v< or =12 and 9< or =J< or =40 ranges. The molecular constants and Rydberg-Klein-Rees (RKR) potential of the 2g(1D) state were reported. We discussed the occurrence of the 2g(1D)-A' 3Pi(2u) emission, when exciting to the 1u(1D) v=0 state, and attributed it to the g/u mixing between the 2g(1D) and 1u(1D) states by the hyperfine interaction. The effect of the perturbation on measured line intensities and lifetimes was evident.

Comparison of spectroscopic potentials and an a priori analytical function. The potential energy curve of the ground state of the sodium dimer, X1Sigmag(+) Na2.

The results of a "universal" potential energy function, one that incorporates electronegativity and Slater's effective nuclear charge into a Morse-type function, are compared to spectroscopically derived potential energy curves of the X1Sigmag(+) state of Na2. The function is a priori in that it does not require prior knowledge of the actual potential and has no adjustable parameters. Criteria used to evaluate the performance of the function are comparisons of predicted versus spectroscopic energies at Rydberg-Klein-Rees (RKR) procedure turning points, predicted distances at measured energies versus RKR distances, and eigenvalues derived from the a priori potential versus spectroscopically deduced energy levels. The a priori function describes the Na2 potential with deviations approaching the magnitude of those found among some spectroscopic potentials from different sources. By examining the behavior of the "spectroscopic" parameter of the Morse function, irregularities are found in five of the seven spectroscopic potentials examined. A new procedure is demonstrated for correcting irregularities on the inner branch of spectroscopic potentials at high extents of dissociation and for extending reliably the potential in this region beyond the domain of the measurements.

Improved LeRoy-Bernstein near-dissociation expansion formula, and prospect for photoassociation spectroscopy.

NDE (Near-dissociation expansion) including LeRoy-Bernstein formulas are improved by taking into account the multipole expansion coefficients and the nonasymptotic part of the potential curve. The theory is tested with the Rydberg-Klein-Rees (RKR) potential curve of the Cs(2)(0(g) (-)6s+6p(3/2)) state. Results indicate that the formula could be used to improve the determination of the asymptotic coefficient (within a 1% accuracy) and to extract relativistic correction from photoassociation spectra of long-range potential curve of diatomic molecules.

Studies on the analytical potential energy function of diatomic molecular ion XY+ using variational method

A new analytical potential energy function for diatomic molecular ion XY+ is proposed based on the energy consistent method (ECM). The Coulomb potential included in the new ionic potential contains multipole corrections, converges quickly and is variationally, changeable. The new potential and the ECM are applied to variationally studying the potential energies of eight electronic states of several diatomic molecular ions: the A2π state of CO+, the X2∑g+ state of Li2+, the X2∑g+ state of He2+, the 12∏u state of Na2+, the A2∏u state of N2+, the X1∑+ state of KrH+, the X2∑+ state of SiO+ and the A2π state of SO+ ion. The present results agree excellently with the experiment-based Rydberg-Klein-Rees (RKR) potentials, and are superior to the commonly used Huxley-Murrell-Sorbie (HMS) analytical potentials, and are better in some cases than some quantum mechanicalab initio potentials in the ionic asymptotic and dissociation regions.

The deperturbation analysis of the [formula omitted] system of TiO: new [formula omitted] state near 3 eV

Transition wavenumbers of several vibronic bands associated with v ′=0 to 5 for the C 3 Δ–X 3 Δ system were analyzed to determine the molecular parameters for the C 3 Δ state. It was found that the Ω=3 spin sublevel in the C 3 Δ , v ′=2 to 4 levels is perturbed by the state having the 1 Φ symmetry via the spin–orbit interaction. It was also found that the Ω=1 sublevel in the C 3 Δ , v ′=4 and 5 levels is perturbed by the state having the 1 Π symmetry via the spin–orbit interaction. Taking into account these perturbations, the C 3 Δ–X 3 Δ , C 3 Δ–a 1 Δ , and c 1 Φ–a 1 Δ systems were simultaneously analyzed, from which the experimentally unknown 1 Π state lying near 3 eV on the X 3 Δ state was found. The Rydberg–Klein–Rees (RKR) potentials for the C 3 Δ and c 1 Φ states were evaluated using the newly determined rotational and vibrational parameters. Using these potentials, the spin–orbit interaction A( r) of the C 3 Δ state, and the spin–orbit interaction H so el( r), between the C 3 Δ and c 1 Φ states, were determined as functions of the internuclear distance r. The electronic structures of the C 3 Δ and c 1 Φ states are discussed.

Transition Probabilities in the B1Σ+–X1Σ+ and the B1Σ+–A1Π Electronic Systems of MgO

Transition probabilities for the B1Σ+–X1Σ+ and the B1Σ+–A1Π electronic systems are presented for v=0–4 and J=0–150 in each electronic state. The functional form of the electronic transition moment for the B–X transition is taken from published ab initio results. The B–A moment is assumed to have the same form and is scaled using empirical branching ratio data. The Re(r) are used with Rydberg–Klein–Rees (RKR) wavefunctions to calculate transition probabilities for v=0–4 and J=0–150. The RKR potentials were calculated based on empirical spectroscopic constants.

Accurate radial atomic modelpotentials by means of a novel RKR-QDT combined approach

The age-old semiclassical Rydberg-Klein-Rees (RKR) inversespectrum method, which has been, so far, widely applied todiatomic molecules only, is combined with the quantum defecttheory (QDT) formalism so that highly accurate radial modelpotentials supporting experimental bound spectra of atoms andatomic ions are constructed. There are two main steps in ourapproach. The first step consists in constructing, by inversion,the best first-order WKB potential. The high quality of thispotential is attested by the fact that the standard WKB quantizationcondition for bound states perfectly reproduces the input data.The second step deals with how to improve further, on aquantum-mechanical level, this RKR potential energy so that theeigenvalues of the radial Schrödinger equation for thequantum-mechanical analogue of the RKR curve, obtained from thelatter after subtraction of Langer's correction, are inagreement with the input data. To this purpose, a rapidlyconverging iterative QDT procedure is developed, according towhich the input quantum defects are, at each iteration,corrected by the difference between the experimental and thecalculated quantum defects. The so-constructed convergedpotential curves are able to reproduce with spectroscopicaccuracy the bulk of available experimental spectra. Demonstrativeexamples from the structure of the high-l 9snl series ofBa and for selected low-l Rydberg series of the Ba+ion are given.

On the 5 [formula omitted] state of NaK

Polarization labelling spectroscopy is applied to study the previously unobserved 5 1Σ + state of the NaK molecule. Molecular constants and a Rydberg–Klein–Rees (RKR) potential energy curve based on these constants are determined. The values of T e, ω e and R e are 23530.62(6) cm −1, 115.60(6) cm −1 and 4.307 Å, respectively.