Inverted Perturbation Approach Research Articles

The E1Σg+ state of lithium dimer revised

This article describes the use of the inverted perturbation approach method for construction of an accurate potential energy curve of the E1Σg+ “shelf” state in Li2. Contrary to previous reports the applied method provides a potential curve free of unphysical oscillations and reproduces energies of all the levels known from previous experiments. Our results confirm the possibility of describing the E state within the Born–Oppenheimer approximation.

The Li2 F 1Σg+ “shelf” state: Accurate potential energy curve based on the inverted perturbation approach

We report an accurate inverted perturbation approach (IPA) potential energy curve for the “shelf” F 1Σg+ state in Li2 which reproduces positions of the experimental energy levels available in the literature for all three isotopomers Li27, Li76Li, and Li26 with a standard deviation of 0.11 cm−1. Our analysis significantly improves the shape of the recently reported Rydberg–Klein–Rees (RKR) potential curve of the F 1Σg+ state [Antonova et al., J. Chem. Phys. 112, 7080 (2000)] and provides evidence for the existence of a shallow minimum in the shelf region. Using our IPA potential curve we were able to localize and identify some local perturbations in the spectra, as well as to correct the assignment of several spectral lines previously observed experimentally.

Doppler-free UV-visible optical–optical double resonance polarization spectroscopy of the 2 1Σu+ double minimum state and the C 1Πu state of Li2

Doppler-free UV-visible optical–optical double resonance polarization spectra of the 2 1Σu+←X 1Σg+ and C 1Πu←X 1Σg+ transitions in Li27 molecules were measured. In the case of the double minimum 2 1Σu+ state transitions to all vibrational levels (except the lowest two) localized in the inner potential well, to several levels in the outer well and some levels beyond the potential barrier were observed. Potential energy curves of the C 1Πu(v=0–10) state and the inner well of the 2 1Σu+ state are determined by the RKR method. A V(R) curve describing the whole potential of the 2 1Σu+ state (including both wells) is constructed using the Inverted Perturbation Approach (IPA). Tunneling splittings and energy shifts of the 2 1Σu+ levels were observed, and their magnitudes are well represented in a semiclassical model using the IPA potential. Perturbations between the C 1Πu(v,J) and 2 1Σu+(v′,J) levels were detected in the region above the potential barrier of the 2 1Σu+ state, where the rotational constant of the 2 1Σu+ state is much smaller than that of the C 1Πu state.

Spectroscopic investigation of the double-minimum21Σu+state of the potassium dimer

The double-minimum $2{}^{1}{\ensuremath{\Sigma}}_{u}^{+}$ state was investigated in ${}^{39}{\mathrm{K}}_{2}$ and ${}^{39}{\mathrm{K}}^{41}\mathrm{K}$ molecules by analyzing spectra of the $2{}^{1}{\ensuremath{\Sigma}}_{u}^{+}\ensuremath{\leftarrow}X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ band system, simplified by polarization labeling. A wide range of rovibrational levels 21\ensuremath{\leqslant}v\ensuremath{\leqslant}97, 18\ensuremath{\leqslant}J\ensuremath{\leqslant}159 was observed. By using the inverted perturbation approach to construct the exotic potential-energy curve, an accurate, isotopically consistent description of the $2{}^{1}{\ensuremath{\Sigma}}_{u}^{+}$ state has been obtained.

An improved potential energy curve for the ground stateof NaK

This paper presents an accurate potential curve for the groundstate of the NaK molecule. A series of resolved laser-inducedfluorescence spectra of the A-X system allowed a spread ofrotational levels in the lowest 70 vibrational levels (99.9%of the total well depth) to be observed. A variational methodcombining the inverted perturbation approach of Vidal andScheingraber (Vidal C R andScheingraber H 1977 J. Mol. Spectrosc. 65 46) forshort internuclear distances with an analytical expression forinternuclear distances beyond 8.5 Å has been used to constructa potential energy curve which reproduces the measured groundstate energies with an rms error of 0.003 cm-1. The dissociation energy and coulombicparameters governing the Na(3s) + K(4s) interactionderived from this potential curve are compared with recentvalues.

Construction of potential curves for diatomic molecular states by the IPA method

A program package is presented which utilizes the Inverted Perturbation Approach (IPA) method for construction of potential energy curves of 1Σ and 1Π states of diatomic molecules directly from the experimental data. In most cases using the constructed IPA potential one can reproduce the experimental energy levels within the accuracy of measurement. The package is successfully tested in case of double minimum potential where the traditional RKR method is not applicable.

STUDY ON THE POTENTIAL ENERGY CURVES OF ALKALI DIATOMIC MOLECULES WITH ENERGY CO NSISTENT METHOD

The studies on the potential energy curves of the electronic excited states 21Πg, 43Πg, b3Πu of Na2, the states a3Σ+u, 21 Πg, B1Πu, A1Σ+u of K2 and the state 11Πg of Cs 2 molecules by using the energy consistent method (ECM) are reported here . The results show that the present ECM potentials agree very well with the know n Rydberg-Klein-Rees data or the inverted perturbation approach data, and that they are much better than other analytical potentials such as the Morse and the Huxley-Murrell-Sorbie potentials for the electronic excited states of alkali dia tomic molecules.

Rotational Analysis of the LiHg 22Π3/2–X2Σ+1/2 (v′ = 0 ← v" = 0, 1, 2) Vibronic Bands

We present a complete analysis of the previously reported LiHg 22Π3/2–X2Σ+ excitation spectrum [X. Li, P. Pircher, D. Gruber, and L. Windholz, Chem. Phys. Lett. 263, 463 (1996)]. The v′ = 0 − v" = 0, 1, 2 vibronic bands are analyzed and the rotational transitions are identified. The assigned rotational transitions are initially fitted on a band-to-band basis. A global fit is performed afterwards for all the known vibronic transitions of the LiHg molecules. In the fit the ground state molecular constants are separated into spin–rotation coupling terms and Dunham-type coefficients. The obtained Dunham coefficients are used to derive the molecular potential for the ground electronic state using the inverted perturbation approach (IPA). The equilibrium bond length was found to be 2.9528(6) Å for the LiHg ground state.

The RbCs X1Σ+ Ground Electronic State: New Spectroscopic Study

In this paper a new spectroscopic investigation on the X1Σ+ electronic ground state of the RbCs molecule is reported. This study is conducted by using laser-induced fluorescence combined with Fourier transform spectroscopy (LIF–FTS). More than 23000 spectral data are used in a global linear reduction to molecular constants. With these new and improved molecular constants, the potential energy curve has been calculated by the inverted perturbation approach (IPA). Accurate values for the dissociation energy and the long-range parameters have been derived.

Quasibound levels and shape resonances of 39K2(B 1Πu) crossed laser-molecular beam studies and analytical interpretation

Quasibound levels and shape resonances in the (B 1Πu −X 1Σ+g) band system of 39K2 have been recorded by crossed laser-molecular beam techniques. Using optical–optical double resonance, individual rovibrational levels (v″=15–18, J″=3–25) of the K2 state are prepared by Franck–Condon pumping (FCP) in a supersonic nozzle beam. Excitation into quasibound levels below and above the (B 1Πu) state barrier is detected as molecular and atomic (K4 2P3/2→4 2S1/2 only) fluorescence. The resonance transition frequencies and shapes are measured and the results are used (a) to determine the scattering resonance energies, widths, and lifetimes; (b) to compare them with values obtained by a ‘‘maximum internal amplitude’’ approach [R. J. LeRoy and R. B. Bernstein, J. Chem. Phys. 54, 5114 (1971)]; and (c) to check the agreement with exact calculations of the B state potential using the ‘‘inverted perturbation approach (IPA).’’ The bound and quasibound part of the B 1Πu state including the locus (R=8.08±0.05 Å) of the barrier maximum (298±8 cm−1 above the adiabatic dissociation limit) is found in excellent agreement with previous results. The shape resonances are not highly sensitive to the long-range interatomic forces, here the repulsive dipole–dipole resonance interaction.

Spectroscopic study of the E 1Σ+g ‘‘shelf’’ state in 7Li2

The E 1Σ+g ‘‘shelf ’’ state of the 7Li2 molecule was investigated using a pulsed optical optical double resonance technique. The measurements cover the vibrational levels in the range 0≤v≤29 including the shelf region around 13≤v≤15. Molecular constants have been determined. Using an inverted perturbation approach, an effective potential energy curve has been generated within the adiabatic approximation whose quantum mechanical energy eigenvalues reproduce all the measured term values to within 0.113 cm−1 for the range 0≤v≤23 and 0≤J≤47.

Inverted perturbation approach (IPA) potentials and adiabatic corrections of the X 1Σ+ state of the lithium hydrides near the dissociation limits

Laser-induced fluorescence (LIF) spectra of the A–X system of the LiH isotopes, excited by the UV lines of an argon and a krypton ion laser, were observed and analyzed. Three long LIF series of different LiH isotopes were taken with a 3.4 m high resolution spectrograph. The results were combined with previous experimental data to study the breakdown of the Born–Oppenheimer approximation in the X 1Σ+ electronic ground state of the isotopic LiH molecules. Using a quantum mechanical variational method, potential energy curves of the four LiH isotopes were extended almost up to the dissociation limits.

Improvement of the RKR procedure obtained by semi-classical calculations

In this letter we present a new technique to improve RKR molecular potential curve calculations. The potential curve obtained gives calculated G(ν) and B(ν) values extremely close to the measured ones. The aim of these calculations is the same as that of the inverted perturbation approach of Vidal and Sheingraber, but the potential-well corrections are calculated by using Watson's semi-classical inversion procedure.

Determination of diatomic molecular constants using an inverted perturbation approach: Application to the [formula omitted] system of Mg 2

The measurements of the A 1 Σ u +-X 1 Σ g + system of the Mg 2 molecule of Balfour and Douglas have been reevaluated and molecular constants have been determined using a variational procedure which is based on an inverted perturbation approach. The method provides a leastsquares fit of the experimental term values to the calculated quantum mechanical energy eigenvalues of a rotating vibrator. All measured line positions of the system are fitted with two rotationless potentials U o which yield G v and B v values and which are independent of any centrifugal distortion parameters. The latter are determined in a separate least-squares fit in which the previously determined G v and B v values are held fixed. A comparison of the quantum mechanical U o and the semiclassical first-order RKR potential is carried out. The method provides dissociation energies which are more accurate than previous extrapolation procedures, and allows a self-consistency test of the experimental term values. The 24Mg 2 and 26Mg 2 molecules have been fitted using mass reduced variables, and an electronic isotope shift of 0.17 cm −1 has been obtained.