Born-Oppenheimer Breakdown Functions Research Articles

The ground electronic state of ClF: Updated molecular constants and potential curves for 35ClF and 37ClF

A comprehensive assessment of available literature spectroscopic data and molecular constants for the X 1Σ+ ground electronic states of isotopologues 35ClF and 37ClF is undertaken. Three different approaches are employed in the analysis of the available information. The first approach involves merging molecular constants from various studies to yield an optimized set of Dunham coefficients {Y01, Y02, Y03, Y10, Y11, Y21, Y02 and Y12}. Utilizing these updated constants, vibrational energies (Gυ) and rotational constants (Bυ) for υ = 0–9 are calculated, and RKR potentials are determined for both isotopologues. The second approach involves calculating synthetic spectroscopic line positions using literature molecular constants, with normally distributed random errors added on, and subjecting these to a modern direct-potential-fit analysis. This analysis produces a precise analytical potential energy function for 35ClF, and Born-Oppenheimer breakdown functions that characterize adiabatic and non-adiabatic corrections. The third approach involves fitting the synthetic spectroscopic data directly to Dunham coefficients. The results of the three approaches are compared and discussed.

DPotFit: A computer program to fit diatomic molecule spectral data to potential energy functions

This paper describes program dPotFit, which performs least-squares fits of diatomic molecule spectroscopic data consisting of any combination of microwave, infrared or electronic vibrational bands, fluorescence series, and tunneling predissociation level widths, involving one or more electronic states and one or more isotopologs, and for appropriate systems, second virial coefficient data, to determine analytic potential energy functions defining the observed levels and other properties of each state. Four families of analytical potential functions are available for fitting in the current version of dPotFit: the Expanded Morse Oscillator (EMO) function, the Morse/Long-Range (MLR) function, the Double-Exponential/Long-Range (DELR) function, and the ‘Generalized Potential Energy Function׳ (GPEF) of Šurkus, which incorporates a variety of polynomial functional forms. In addition, dPotFit allows sets of experimental data to be tested against predictions generated from three other families of analytic functions, namely, the ‘Hannover Polynomial’ (or “X-expansion”) function, and the ‘Tang–Toennies’ and Scoles–Aziz ‘HFD’, exponential-plus-van der Waals functions, and from interpolation-smoothed pointwise potential energies, such as those obtained from ab initio or RKR calculations. dPotFit also allows the fits to determine atomic-mass-dependent Born–Oppenheimer breakdown functions, and singlet-state Λ-doubling, or Σ2 splitting radial strength functions for one or more electronic states.dPotFit always reports both the 95% confidence limit uncertainty and the “sensitivity” of each fitted parameter; the latter indicates the number of significant digits that must be retained when rounding fitted parameters, in order to ensure that predictions remain in full agreement with experiment. It will also, if requested, apply a “sequential rounding and refitting” procedure to yield a final parameter set defined by a minimum number of significant digits, while ensuring no significant loss of accuracy in the predictions yielded by those parameters.

Full empirical potential curves for the X(1)Σ(+) and A(1)Π states of CH(+) from a direct-potential-fit analysis.

All available "conventional" absorption/emission spectroscopic data have been combined with photodissociation data and translational spectroscopy data in a global analysis that yields analytic potential energy and Born-Oppenheimer breakdown functions for the X(1)Σ(+) and A(1)Π states of CH(+) and its isotopologues that reproduce all of the data (on average) within their assigned uncertainties. For the ground X(1)Σ(+) state, this fully quantum mechanical "Direct-Potential-Fit" analysis yielded an improved empirical well depth of 𝔇e = 34 362.8(3) cm(-1) and equilibrium bond length of re = 1.128 462 5 (58) Å. For the A(1)Π state, the resulting well depth and equilibrium bond length are 𝔇e = 10 303.7(3) cm(-1) and re = 1.235 896 (14) Å, while the electronic isotope shift from the hydride to the deuteride is ΔTe = - 5.99(±0.08) cm(-1).

Improved direct potential fit analyses for the ground electronic states of the hydrogen halides: HF/DF/TF, HCl/DCl/TCl, HBr/DBr/TBr and HI/DI/TI

The potential energy and Born–Oppenheimer breakdown functions for the X1Σ+ ground electronic states of the hydrogen halides HF, HCl, HBr, and HI are reported in full analytic form. All available pure rotational and vibrational–rotational spectroscopic data for the various isotopologues of the four HX molecules, as well as the B1Σ+→X1Σ+ emission band system data for HF/DF and HCl/DCl, were employed in direct potential fit determinations of the various radial functions. Significant improvements over previous work have been made to the mathematical models for these functions, particularly with respect to the behavior of the potential energy in the long-range region where dispersion forces between the component atoms dominate. The MLR3 model for the potential energy is employed, allowing for constraint of the three leading dispersion coefficients C6, C8, and C10, for the X states of HF and HCl. Quantum-mechanical rotational and centrifugal distortion constants are calculated for all isotopologues considered in the non-linear least-squares fitting procedures. Computer code is provided in order that precise calculation of all functions for all isotopologues is possible for a user-specified radial grid. Precise estimates are obtained for X state equilibrium internuclear separations for the principal isotopologues of all four halides, namely re(HF)=0.91683897±0.00000004Å, re(H35Cl)=1.27454677±0.00000006Å, re(H79Br)=1.4144292±0.0000001Å, and re(HI)=1.6290588±0.0000004Å.

Accurate Analytic Potential and Born–Oppenheimer Breakdown Functions for MgH and MgD from a Direct-Potential-Fit Data Analysis

New high-resolution visible Fourier transform emission spectra of the A (2)Π → X (2)Σ(+) and B' (2)Σ(+) → X (2)Σ(+) systems of (24)MgD and of the B' (2)Σ(+) → X (2)Σ(+) systems of (25,26)MgD and (25,26)MgH have been combined with earlier results for (24)MgH in a multi-isotopologue direct-potential-fit analysis to yield improved analytic potential energy and Born-Oppenheimer breakdown functions for the ground X (2)Σ(+) state of MgH. Vibrational levels of the ground state of (24)MgD were observed up to v" = 15, which is bound by only 30.6 ± 0.10 cm(-1). Including deuteride and minor magnesium isotopologue data allowed us also to determine the adiabatic Born-Oppenheimer breakdown effects in this molecule. The fitting procedure used the recently developed Morse/Long-Range (MLR) potential energy function, whose asymptotic behavior incorporates the correct inverse-power form. A spin-splitting radial correction function to take account of the (2)Σ spin-rotation interaction was also determined. Our refined value for the ground-state dissociation energy of the dominant isotopologue ((24)MgH) is D(e) = 11,104.25 ± 0.8 cm (-1), in which the uncertainty also accounts for the model dependence of the fitted D(e) values for a range of physically acceptable fits. We were also able to determine the marked difference in the well depths of (24)MgH and (24)MgD (with the deuteride potential curve being 7.58 ± 0.30 cm(-1) deeper than that of the hydride) as well as smaller well-depth differences for the minor (25,26)Mg isotopologues. This analytic potential function also predicts that the highest bound level of (24)MgD is v" = 16 and that it is bound by only 2.73 ± 0.10 cm(-1).

Erratum: “Potential energy, Λ doubling and Born–Oppenheimer breakdown functions for the BΠu1 ‘barrier’ state of Li2” [J. Chem. Phys. 119, 7398 (2003)

Erratum: “Potential energy, Λ doubling and Born–Oppenheimer breakdown functions for the BΠu1 ‘barrier’ state of Li2” [J. Chem. Phys. 119, 7398 (2003)

Application of direct potential fitting to line position data for the [formula omitted] and [formula omitted] states of Li 2

A collection of 15 222 spectroscopic Li 2 line positions, all with measurement precision in the range 0.005–0.02 cm −1, and which sample 99.97 and 99.98% 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. The fully analytical potential function for the A state of 6Li 2 is determined out to R ≈ 55 Å, well into the long-range region. For the three isotopologues, 6Li 2, 6Li 7Li, and 7Li 2, most of the data are comprised of rotationally resolved transitions in the A– X system recorded by Fourier transform spectroscopies. For 6Li 2 and 7Li 2, complementary fluorescence data are also included for high vibrational levels of both the A and X states. The reduced standard deviation of the fit was close to unity, indicating that the quantum mechanical eigenvalues calculated from the analytical functions of the Hamiltonians of the two states, which are described by a total of only 45 fitted parameters, represent the line positions, on average, to within the estimated uncertainties. The dissociation energies for 6Li 2 are estimated precisely as D e( X) = 8516.74(1) cm −1 and D e( A) = 9351.96(1) cm −1.

Application of direct potential fitting to line position data for the X 1Σ+ and A 1Σ+ 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.

The inversion of diatomic Born–Oppenheimer-breakdown corrections

The inversion of diatomic vibration–rotation data to give the r dependence of operators is considered. For the Born–Oppenheimer energy levels E vJ and for the expectation values 〈 vJ| X( r)| vJ〉 of an operator X( r), the inversion is unambiguous if the reduced mass is known, leading to the potential energy function V( r) and to X( r). The breakdown of the Born–Oppenheimer approximation is represented in terms of three functions Q i ( r), R i ( r), and S i ( r) for each atom i. The function Q i ( r) can be removed by a transformation that changes the other functions to R ̃ i(r) and S ̃ i(r) , which still have one degree of indeterminacy. The effects of this indeterminacy in fits to truncated Hamiltonians is considered for the extensive data for isotopomers of the LiH molecule. This discussion is relevant to a recent claim that the dipole moment and rotational g J factor of LiH can be determined from a fit to field-free vibration–rotation spectra. The values obtained for these quantities are unreliable because they are strongly dependent on the constraints used in the Born–Oppenheimer-breakdown functions.

Potential energy, Λ doubling and Born–Oppenheimer breakdown functions for the B 1Πu “barrier” state of Li2

The potential energy curve for the B 1Πu state of Li2 has a rotationless barrier which protrudes above its energy asymptote. A direct fit to spectroscopic data for all three isotopomers of this species, including Λ-doubling splittings and tunneling predissociation line widths, is used to determine an accurate analytic potential energy function plus Born–Oppenheimer breakdown and Λ-doubling perturbation radial strength functions for this system. This analysis introduces an analytic model for representing a potential function with a rotationless barrier, and shows that a radial perturbation function treatment can determine the symmetry of the perturbing state giving rise to Λ-doubling splittings.

The application of direct potential fitting to the X1∑ + ground electronic states of LiCl, TlCl, RbF and CsF

A procedure for directly fitting the potential energy curve of a diatomic molecule has been applied to the X 1∑ + ground states of LiCl, TlCl, RbF and CsF. Extensive, high-precision infrared and pure-rotational data sets for all isotopomers of the aforementioned molecules have been employed in direct least-squares fits of a radially dependent Hamiltonian operator. The Born–Oppenheimer potentials are represented by a modified Lennard–Jones function that is shown to be flexible and provide the proper behavior in the long-range region of the potential. While the potential fits of LiCl and TlCl required the inclusion of Born–Oppenheimer breakdown functions, no such functions were necessary for either RbF or CsF.

Experimental Born–Oppenheimer Potential for theX1Σ+Ground State of HeH+: Comparison with theAb InitioPotential

All literature on vibration–rotational and pure rotational transition energies for theX1Σ+state of4HeH+,3HeH+,4HeD+, and3HeD+have been employed in a direct least-squares fit of the radially dependent Hamiltonian. The Born–Oppenheimer potential is represented by a modified Lennard–Jones function that provides for correct behavior in the near dissociation long-range region. Only 19 adjustable parameters were required to represent the 166 measured transition energies, which are reproduced almost to within the measurement accuracies. The fitted potential and Born–Oppenheimer breakdown functions are shown to be in good agreement with the results ofab initiocalculations. The results are used to obtain high-order centrifugal distortion constants as well as level widths for quasi-bound levels.

Application of an improved fitting procedure for diatomic internuclear potentials and Born-Oppenheimer breakdown functions: The B1Σ+ → X1Σ+ system of H35Cl and H37Cl

A numerical procedure for direct fitting of effective 1Σ Hamiltonians to spectroscopic data of diatomic molecules is described. Approximate Hamiltonians for the X and B states of H37Cl, derived from fitted Hamiltonians for H35Cl, provided predicted line positions in the B → X system of H37Cl that were accurate to about 0.05 cm−1. These calculations permitted the first extensive rotational assignments for 31 bands of this isotopomer (0 ≤ v′ ≤ 6; 7 ≤ v″ ≤ 17) in spectra recorded previously using HCl prepared from naturally occurring chlorine. The entire B → X data set for H35Cl (2010 line positions) and H37Cl (928 line positions), together with 573 vibration-rotation and pure rotation transitions in the X state, has been employed simultaneously in fits to the effective X- and B-state Hamiltonians of the two isotopomers. It is concluded that Born-Oppenheimer breakdown effects in the X1Σ+ state of HCl are dominated at large internuclear separations by coupling to the repulsive 1 1Π state correlating with ground state atoms. Ab initio calculations of the radial variation of matrix elements coupling the X state with excited electronic states would be of much value.