The ground X 1Sigmag+ electronic state of the cesium dimer: application of a direct potential fitting procedure.

A collection of 16,544 fluorescence series spectroscopic line positions involving the A (1)Sigma(u)(+)-->X (1)Sigma(g)(+) transition in Cs(2) has been analyzed by a modern direct potential fitting procedure to generate the first fully analytical potential energy function for the ground electronic state, and precise energy term values for the excited A (1)Sigma(u)(+) state. The potential function yields an accurate representation of spectroscopic data that span 99.24% of the well depth and the number of fitted parameters is significantly less than half the number of parameters determined in conventional Dunham analyses. A novel variant of the Morse/long-range potential model has been employed in the representation of the ground state potential, and a critical comparison has been made with an extended modified Lennard-Jones potential model. Proper account has been taken of the known long-range van der Waals form of the potential, and our final potential function is determined with constrained literature values of the C(8) and C(10) dispersion energy coefficients, along with a fitted value of C(6)=3.31(5) x 10(7) cm(-1) A(6)=6870(100) a.u. The fitted dissociation energy (D(e)) is compared with the precisely known value based on the recent analysis of data from a two-photon transfer process (STIRAP) in ultracold Cs atoms. It is concluded that hyperfine effects in the X (1)Sigma(g)(+) state are not negligible, and that the estimate of D(e)=3649.84(7) cm(-1) obtained in this work represents an effective dissociation limit lying between the two lowest hyperfine limits. Precise rotational and centrifugal distortion constants for the ground electronic state have also been calculated through conventional perturbation theory. These estimates are fully consistent with the derived potential function and the experimental spectroscopic information.

Accurate analytic potentials for Li(2)(X (1)Sigma(g) (+)) and Li(2)(A (1)Sigma(u) (+)) from 2 to 90 A, and the radiative lifetime of Li(2p).

Extensions of the recently introduced "Morse/long-range" (MLR) potential function form allow a straightforward treatment of a molecular state for which the inverse-power long-range potential changes character with internuclear separation. Use of this function in a direct-potential-fit analysis of a combination of new fluorescence data for (7,7)Li(2), (6,6)Li(2), and (6,7)Li(2) with previously reported data for the A((1)Sigma(u) (+)) and X((1)Sigma(g) (+)) states yields accurate, fully analytic potentials for both states, together with the analytic "adiabatic" Born-Oppenheimer breakdown radial correction functions which are responsible for the difference between the interaction potentials and well depths for the different isotopologues. This analysis yields accurate well depths of D(e)=8516.709(+/-0.004) and 8516.774(+/-0.004) cm(-1) and scattering lengths of 18.11(+/-0.05) and 23.84(+/-0.05) A for the ground-states of (7,7)Li(2) and (6,6)Li(2), respectively, as well as improved atomic radiative lifetimes of tau(2p)=27.1018(+/-0.0014) ns for (7)Li(2p) and 27.1024(+/-0.0014) ns for (6)Li(2p).

The B 1sigma+ and X 1sigma+ electronic states of hydrogen fluoride: a direct potential fit analysis.

All literature pure rotational and vibration-rotational spectroscopic data on the ground X (1)Sigma(+) electronic state of HF and DF, together with the entire set of spectroscopic line positions from analyses of the B (1)Sigma(+) --> X (1)Sigma(+) emission band systems of HF and DF, have been used in a global least-squares fit to the radial Hamiltonian operators, in compact analytic form, for both electronic states. With a data set consisting of 6157 spectroscopic line positions, the reduced standard deviation of the fit was sigma = 1.028. Sets of quantum mechanically significant rotational and centrifugal distortion constants were calculated for both electronic states using Rayleigh-Schrödinger perturbation theory.

Application of direct potential fitting to line position data for the X (1)Sigma(+) and A (1)Sigma(+) states of LiH.

A collection of 9089 spectroscopic LiH line positions, of widely varying precision, which sample 84.9% and 98.6% of the A and X state well depths, respectively, have been employed in a direct least-squares fit of the effective potential energy and Born-Oppenheimer breakdown functions for the two states. For the four isotopomers (6)LiH, (7)LiH, (6)LiD, and (7)LiD, the data comprise both pure rotational and vibration-rotational transitions within the ground state, as well as rotationally resolved transitions in the A-X system. Despite the unusual shape and associated anomalous properties of the A state potential, no special features or considerations were required in the direct potential fitting approach. The reduced standard deviation of the fit was close to unity, indicating that the quantum mechanical eigenvalues calculated from the fully analytical functions of the Hamiltonians of the two states, which are characterized by a total of only 53 fitted parameters, represent the line positions, on average, to within the estimated uncertainties. A quantum mechanical calculation of the molecular constants G(nu), B(nu), D(nu), H(nu), L(nu), M(nu), N(nu), and O(nu) from the fitted potential for the A state of (7)LiH confirms that the usual polynomial expansion in J(J+1) is an unsatisfactory representation for the rotational terms of the lowest vibrational levels.

Direct potential fit analysis of the X1sigma+ ground state of CO.

A collection of 21,559 highly precise spectroscopic line positions from pure rotational and vibration-rotational spectra for seven isotopomers of carbon monoxide in the X1sigma+ ground electronic state has been employed in direct least-squares fits of the rovibrational Hamiltonian operator obtained from Watson's work [J. Mol. Spectrosc. 80, 411 (1980)] and that obtained by Herman and Ogilvie [Adv. Chem. Phys 103, 187 (1998)]. Fully analytical models are used for the various functions, including the Born-Oppenheimer internuclear potential function, and an account is taken of breakdown of the Born-Oppenheimer approximation. The resulting representations are more compact than currently available traditional Ukl/deltakl extended Dunham descriptions, and they generate quantum-mechanical eigenvalues that reproduce reliably the spectroscopic line positions to within the associated measurement uncertainties. Rayleigh-Schrodinger perturbation theory has been used to calculate highly accurate rotational and centrifugal distortion constants Bupsilon-Oupsilon for nine isotopomers of carbon monoxide. These constants are just as successful at reconstructing the observed spectroscopic information as the quantum-mechanical eigenvalues of the fitted Hamiltonian operators.

A numerical test of analytical methods for reduction of IR and MW spectra of NaCl chi1sigma+ to parameters of radial functions.

Two methods for direct inversion of IR and MW spectra of diatomic molecules--a deformational self-consistent procedure (DS-cP) and a computer program RADIATOM based on hypervirial perturbation theory are tested numerically. The test calculations for NaCl chi1sigma+ confirm that the RADIATOM program does not produce sufficiently accurate radial parameters and energy term values for their export to other utilities employed in the spectral analysis of diatomic systems.