A proper account of core-polarization with pseudopotentials: single valence-electron alkali compounds

Theoretical calculations for the ground state and for 83 excited states of the Na2 molecule are presented in the framework of two independent approaches. The electron–core interaction is represented either by a pseudopotential or by a model potential, and a core polarization potential is introduced in both cases. The basis set contains either Gaussian orbitals or two‐center generalized Slater orbitals. The two methods appear to give similar results, one being more accurate for the ground and first excited states, the other being better adapted to the intermediate Rydberg states. A very good agreement is obtained with the experimental spectroscopic constants determined for 26 states, the mean deviation being ΔRe=0.05a0, Δωe=0.86 cm−1, and ΔDe=57 cm−1.

Potential curves for the ground and excited states of the Na2 molecule up to the (3s+5p) dissociation limit: Results of two different effective potential calculations

Publisher Summary This chapter discusses several experimental studies conducted on cluster ions. Cluster ions comprise a nonrigid assembly of components having properties between those of large gas phase molecules and the bulk condensed state. Research on the properties of cluster ions is valuable in obtaining a complete understanding of the forces between ions and neutral atoms or molecules, where, for example, data on energetics provide a direct measure of the depth of the potential well of interaction between the ion and the collection of neutral molecules. There are three types of experimental approaches to produce and study these cluster ions depending on different degrees of physical isolation, that is, clusters moving freely in space (gas phase studies), clusters supported upon a substrate surface, and clusters existing in solids and liquids. Moreover, the use of cluster ions for fuel injection into fusion reactors and cluster ions are also present in other high-temperature systems such as those designed as sources of energy employing magnets and hydrodynamics.

Experimental studies on cluster ions

Two-step polarization-labeling spectroscopy of diatomic molecules is described. Formulas for relative transition intensities are derived, and their use in determining angular momenta of molecular states is discussed. The experimental apparatus and procedure used to identify twenty-four new $^{1}\ensuremath{\Sigma}_{g}^{+}$, $^{1}\ensuremath{\Pi}_{g}$, and $^{1}\ensuremath{\Delta}_{g}$ states in ${\mathrm{Na}}_{2}$ are described. The states are identified as low-lying members, $n=3 \mathrm{to} 14$, of several molecular Rydberg series, and the dependence of their properties on principal quantum numbers is shown. These results are extrapolated to yield constants for the ground state of $\mathrm{Na}_{2}^{}{}_{}{}^{+}$.

Two-step polarization-labeling spectroscopy of excited states of Na 2

Although the diatomic halogens are endowed with a wide range of intravalence-shell electronic states, the number and variety of these states is far from obvious in one-photon absorption from the ground state where only a few regions of structured absorption are present at visible and UV wavelengths. Selection rules on angular momentum and parity are key players in enforcing this sparse structure, but Franck- Condon effects also exercise considerable influence by directing transitions into regions where the transition dipole is small o r into a continuum where much of the detail is lost: further, a simultaneous excitation of two o r more electrons is formally forbidden in single-photon transitions. Some of the obstacles to one-photon absorption are avoided in the sequential absorption of two o r three photons using the conveniently placed, low-lying excited sQtes in the visible region for the initial step, in effect broadening the perspective from the ground state to include that from the lower ex...

Multiphoton Spectra and States of Halogens

Even small molecules produce spectra complicated enough so that their analysis is complex and difficult. In Nat, for instance, only six excited singlet electronic states have been identified by conventional spectroscopy. We have, therefore, studied several methods of using lasers to identify a selected energy level, and thereby simplify the spectrum.

Selective Spectrum Simplification by Laser Level Labeling

The new excited $^{1}\ensuremath{\Delta}_{g}$ states and five new excited $^{1}\ensuremath{\Pi}_{g}$ states of ${\mathrm{Na}}_{2}$ have been identified with the use of the two-step polarization labeling technique. The electronic energies of these states form a molecular Rydberg series. By extrapolating the dissociation energies, vibrational constants, and rotational constants of these Rydberg states it is possible to obtain good estimates of the same quantities for the $X^{2}\ensuremath{\Sigma}_{g}$ ground state of ${\mathrm{Na}}_{2}^{+}$.

Identification of Rydberg States in Na 2 by Two-Step Polarization Labeling

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Two-step polarization-labeling spectroscopy of excited states of Na 2

Selective Spectrum Simplification by Laser Level Labeling

Identification of Rydberg States in Na 2 by Two-Step Polarization Labeling