dParFit: A computer program for fitting diatomic molecule spectral data to parameterized level energy expressions

- Computer program for performing direct least-squares fits of multi-state, multi-isotopologue spectroscopic data to parametric level-energy expressions.
- Readily treats all types of spectroscopic data: pure rotational (MW) vibrotational (IR), electronic band or fluorescence series data, and photoassociation spectroscopy (PAS) binding energies.
- Can perform fits using four families of analytic expressions (i) Term values T(v,J,p,is) for every observed vib-rotational level of every isotopologue of a given electronic state; (ii) sets of “band constants” Gv, Bv, −Dv, Hv,… for every vibrational level of every isotopologue of that state; (iii) a Dunham polynomial for thr vibrational energies Gv, for the inertial rotational constants Bv, and for as many centrifugal distortion constants as desired; (iv) near-dissociation expansions (NDEs); (v) Tellinghuisen׳s mixed Dunham-NDE “MXS” functions for Gv and Bv.
- The various expansions described above can be chosen independently for (a) the vibrational energies; (b) the inertial rotational constants Bv; (c) the centrifugal distortion constants.
- Multi-isotopologue Dunham, NDE and MXS fits treat the parameters of a chosen reference isotopologue as independent parameters, with this for other isotopologues linked by semiclassical reduced mass scaling.
- Multi-isotopologue Dunham, NDE and MXS fits can also determine Born-Oppenheimer Breakdown parameters.
- Analyses an fit to properties of multiple electronic states simultaneously

This paper describes Fortran program dParFit, which performs least-squares fits of diatomic molecule spectroscopic data involving one or more electronic states and one or more isotopologues, to parameterized expressions for the level energies. The data may consist of any combination of microwave, infrared or electronic vibrotational bands, fluorescence series or binding energies (from photo-association spectroscopy). The level energies for each electronic state may be described by one of: (i) band constants {Gv,Bv,Dv,…} for each vibrational level, (ii) generalized Dunham expansions, (iii) pure near-dissociation expansions (NDEs), (iv) mixed Dunham/NDE expressions, or (v) individual term values for each distinct level of each isotopologue. Different representations may be used for different electronic states and/or for different types of constants in a given fit (e.g., Gv and Bv may be represented one way and centrifugal distortion constants another). The effect of Λ-doubling or 2Σ splittings may be represented either by band constants (qvB or γvB, qvD or γvD, etc.) for each vibrational level of each isotopologue, or by using power series expansions in (v+12) to represent those constants. Fits to Dunham or NDE expressions automatically incorporate normal first-order semiclassical mass scaling to allow combined analyses of multi-isotopologue data. In addition, dParFit may fit to determine atomic-mass-dependent terms required to account for breakdown of the Born-Oppenheimer and first-order semiclassical approximations. In any of these types of fits, one or more subsets of these parameters for one or more of the electronic states may be held fixed, while a limited parameter set is varied. The program can also use a set of read-in constants to make predictions and calculate deviations [ycalc−yobs] for any chosen input data set, or to generate predictions of arbitrary data sets.