The reduced potential curve (RPC) method and its applications

Three-Parameter Electric Dipole Moment Function for the CO Molecule

A global electric dipole moment function of the ground electronic state of carbon monoxide is constructed by morphing its best theoretical approximants from the literature to the best available experimental data within the framework of the reduced radial curve approach. The resulting functions coincide with their best many-parameter empirical counterparts so closely that they can be used as highly accurate three-parameter representations. Apparently, given the mathematical nature of the problem addressed, this approach can be applied equally well to all radial molecular functions that have similarly cumbersome shapes as the function probed. This means that the property characteristics of diatomic molecules can, in principle, be described with high precision even when as few as three pertinent experimental data points are accurately known. To date, no such functional approximants are available in the literature.

Reduced Radial Curves of Diatomic Molecules

The prospect of using the concept of a universal reduced potential energy curve (RPC) for a broader class of radial molecular functions is explored by performing appropriate model calculations for the electric dipole moment functions of the hydrogen halides HF, HCl, and HBr. The reduced radial functions of the model systems, constructed from their best available theoretical approximants, coincide so closely that they can be used as few-parameter universal representations of functions available in the literature. Given the mathematical nature of the problem addressed here, the results are not limited to the functions studied but can be applied equally well to all radial molecular functions that have similar shapes, such as electric quadrupole moment and dipole polarizability functions.

The Infrared Spectrum of CN in Its Ground Electronic State

12C14N vibration-rotation bands for the sequences (1-0) through (9-8) were observed in the spectral region 1800-2200 cm-1 using a Bruker 120 HR Fourier transform spectrometer at an unapodized resolution of 0.027 cm-1. Of the 362 lines observed, the wavenumbers of 237 lines were least-squares fitted using the Dunham expansion coefficients with a root-mean-square deviation of 0.00093 cm-1. Together with most accurate data from the literature, the data were also fitted in the framework of the reduced potential curve (RPC) method. The global potential energy function resulting from this fit provides a fairly quantitative description of the experimental data, at least up to 30 000 cm-1. In addition to global fitting, the RPC approach was also used for fully quantitative fitting of the data pertaining to the lowest three vibrational states. The effective potential energy curves obtained in this way allow for very accurate predictions of highly excited rotational states.

Critical Evaluation of the Prediction of the Dissociation Energy and the Energy Spectrum of the Ground State of KRb by the Reduced Potential Curve Method

The estimates of the value of the dissociation energy and the energy spectrum of the KRb molecule made previously (O. Bludský, M. Ju&rbreve;ek, V. Spirko, B. A. Brandt, and F. Jen&cbreve;, 1995, J. Mol. Spectrosc. 169, 555-582) are compared with the new experimental data (C. Amiot and J. Vergès, 2000, J. Chem. Phys. 112, 7068-7074) and the efficacy of the reduced potential curve (RPC) method is demonstrated. Copyright 2001 Academic Press.

Gauge symmetry, chirality and parity effects in four-particle systems: Coulomb's law as a universal function for diatomic molecules

Following recent work in search for a universal function (Van Hooydonk, Eur. J. Inorg. Chem., (1999), 1617), we test four symmetric +/- a(n)Rn potentials for reproducing molecular potential energy curves (PECs). Classical gauge symmetry for 1/R-potentials results in generic left right asymmetric PECs. A pair of symmetric perturbed Coulomb potentials is quantitatively in accordance with observed PECs. For a bond, a four-particle system, charge inversion (a parity effect, atom chirality) is the key to explain this shape generically. A parity adapted Hamiltonian reduces from ten to two terms and to a soluble Bohr-like formula, a Kratzer (1 - Re/R)2 potential. The result is similar to the combined action of spin and wave function symmetry upon the Hamiltonian in Heitler-London theory. Analytical perturbed Coulomb functions varying with (1 - Re/R) scale attractive and repulsive branches of PECs for 13 bonds H2, HF, LiH, KH, AuH, Li2, LiF, KLi, NaCs, Rb2, RbCs, Cs2 and I2 in a single straight line. The 400 turning points for 13 bonds are reproduced with a deviation of 0.007 A at both branches. For 230 points at the repulsive side, the deviation is 0.003 A. The perturbed electrostatic Coulomb law is a universal molecular function. Ab initio zero molecular parameter functions give PECs of acceptable quality, just using atomic ionisation energies. The function can be used as a model potential for inverting levels and gives a first principle's comparison of short- and long-range interactions, important for the study of cold atoms. Wave-packet dynamics, femto-chemistry applied to the crossing of covalent and ionic curves, can provide evidence for this theory. We anticipate this scale/shape invariant scheme applies to smaller scales in nuclear and high-energy particle physics. For larger gravitational scales (Newton 1/R potentials), problems with super-unification are discussed. Reactions between hydrogen and antihydrogen, feasible in the near future, will probably produce normal H2.

The RbCs X(1)Sigma(+) Ground Electronic State: New Spectroscopic Study

In this paper a new spectroscopic investigation on the X(1)Sigma(+) 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 23 000 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. Copyright 1999 Academic Press.