Corresponding States Principle for the Alkaline Earth Dimers and the van der Waals Potential of Ba₂

Abstract

A simple method based on the corresponding states principle and the Tang-Toennies potential model is used for the determination of the ground state van der Waals potential of barium dimer. The potential energy curve calculated from the theoretical dispersion coefficients and the experimental vibrational frequency is comparable to other quantum chemical calculations. To assess its validity, the same method is used to calculate the potential of the strontium dimer, for which there are many theoretical and experimental determinations. A comparison with experimental measurements suggests that the present method is highly accurate. The potentials of five alkaline earth dimers are compared. The potentials of Mg(2), Ca(2), Sr(2), and Ba(2) are shown to be nearly conformal with each other. The potential of Be(2) has a different shape.

Scattering lengths of calcium and barium isotopes

“…For Ca 2 , an analytic representation of the X 1 + g potential based on an extensive set of experimental data from the Tiemann group is available [23]. For Ba 2 , [24]. The used Ca 2 and Ba 2 potentials are shown in Fig.…”

“…3). Note that these adjustments in C 6 also require small changes in A and b [24]. The uncertainty in C 6 gives rise to a large spread in the scattering length, which can also be seen as a large shift along the mass axis, as indicated by the arrow.…”

The van der Waals potentials of MgCa, MgSr, MgBa, CaSr, CaBa, and SrBa

“…Recently, we have shown that the ground state potential energy curves of Ba 2 , Mg 2 , Ca 2 , and Sr 2 can also be described by this model with spectroscopic precision [2,[7][8][9]. The reduced potentials of these group 2 dimers also conform with each other within a few percent, although the shape of these reduced potentials is different from that of the rare gas dimers.…”

“…It is seen that the parameters (except b * ) of the reduced potentials are much closer to each other than those of the potentials themselves. Although they are not identical, but because the slight differences in the repulsive part are compensated by the differences in the attractive parts, when U(x) is plotted against x, the four curves almost coincide with each other [2]. This invariance with respect to the shape of the potential is not to be construed as resulting from the use of the same potential Table 2 Parameters of the reduced TT potential for the homo-nuclear dimers listed in Table 1.…”

“…Since the potentials of the group 2 (IIA) dimers, except Be 2 , are also conformal [2], in this Letter we will use the same combining rules to determine the ground state potentials of MgCa, MgSr, MgBa, CaSr, CaBa, and SrBa from the potentials of Mg 2 , Ca 2 , Sr 2 , and Ba 2 . The results are in a surprisingly good agreement with the potential determined by the laser induced fluorescence spectra of MgCa [3], which is the only experimental result of these molecules that we can find in literature.…”