A general transformation to canonical form for potentials in pairwise interatomic interactions

Weakly bound (red; (i) Ar₂ (ii) Ar–HBr (iii) OC–Cl₂ (iv) OC–HF) and strongly bound (blue; (i) H₂ (ii) H₂⁺ (iii) LiH (iv) HF) pairwise interactions transformed to one canonical potential.

Anharmonic electron-phonon coupling in condensed media: 1. Formalism

Three different schemes for calculating anharmonic line shape functions are reported and discussed for the first time in this article using eigenstate representation. First, the linear dipole-moment time correlation function (DMTCF), homogeneous (single-site) absorption line shape function, and the respective Franck-Condon factors (FCF) are derived and explored as a molecule makes a transition from a harmonic to an anharmonic (Morse potential) electronic state. Second, the linear DMTCF, homogeneous absorption line shape function, and FCFs are also derived as a molecule makes a transition from one anharmonic to another linearly displaced anharmonic state; FCFs in this case are reported in an exact closed-form expressed in terms of Appell's hypergeometric function. Third, same as the latter set of results are reported but with both linearly displaced and distorted shape of the upper Morse potential. FCFs of the zero-phonon line in all three cases are reported. The first case is rather mathematically complex as a result of taking the overlap integral of the Morse oscillator eigenfunctions, whose spatial decay is a simple exponential, with those of harmonic oscillator, whose decay is a Gaussian. This form of a functional disparity gives rise to some challenges. Model calculations are presented and discussed.

Universal scaling features of spectroscopic constants for diatomic systems

Based on a new criterion that was proposed to search for the universality of spectroscopic constants for bound ground-state diatomics [R. H. Xie and P. S. Hsu, Phys. Rev. Lett. 96, 243201 (2006)], we have found universal scaling relations between spectroscopic constants of diatomic systems with s-, p-, and d-type valence-shell constituents. Our study suggests a useful empirical approach for the prediction of molecular spectroscopic constants.

Comparison of spectroscopic potentials and an a priori analytical function. The potential energy curve of the ground state of the sodium dimer, X 1Σg+ Na2

The results of a "universal" potential energy function, one that incorporates electronegativity and Slater's effective nuclear charge into a Morse-type function, are compared to spectroscopically derived potential energy curves of the X1Sigmag(+) state of Na2. The function is a priori in that it does not require prior knowledge of the actual potential and has no adjustable parameters. Criteria used to evaluate the performance of the function are comparisons of predicted versus spectroscopic energies at Rydberg-Klein-Rees (RKR) procedure turning points, predicted distances at measured energies versus RKR distances, and eigenvalues derived from the a priori potential versus spectroscopically deduced energy levels. The a priori function describes the Na2 potential with deviations approaching the magnitude of those found among some spectroscopic potentials from different sources. By examining the behavior of the "spectroscopic" parameter of the Morse function, irregularities are found in five of the seven spectroscopic potentials examined. A new procedure is demonstrated for correcting irregularities on the inner branch of spectroscopic potentials at high extents of dissociation and for extending reliably the potential in this region beyond the domain of the measurements.

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.