Gerade-ungerade symmetry breaking in HD: Bound states supported by the I′Πg1 outer potential well

Abstract

Gerade-ungerade symmetry breaking in HD for the bound states supported by the shallow outer I' (1)Pi(g) potential is studied theoretically. By clarifying the asymptotic behavior of the relevant nonadiabatic couplings among the stats correlating to the n=2 dissociation limit, simple two-state (for f-parity) and three-state (for e-parity) approximations are formulated. They reproduce binding energies in very good agreement with recent spectroscopic measurements. Comparisons with the calculations based on a single model potential are presented and the dependence of the results on the used ab initio Born-Oppenheimer (clamped nuclei) potentials is discussed.

Gerade-ungerade symmetry breaking in HD: States close to N=2 dissociation limit

“…1 shows the results of the calculated term values for the f-parity states, with the assumed dissociation energy D=118664.80 cm -1 . It can be seen that the agreement with experiments [8,9] is excellent and that the close-coupling method [10] is superior to calculations using a single semi-empirical potential [8] .…”

“…In particular, in the case of the state (v=1, J=1), we see the largest deviation (-1.19 cm -1 ) of the semi-empirical value from the experimental result. The reason for this is that this state has an inherent two-channel character due to the quasi-resonance with an energy level in the C 1 Π u potential [10] and therefore can be precisely described only by the coupled-state method.…”

“…The authors have also constructed a single semi-empirical potential in order to theoretically interpret their results [7,8]. Recently, we have solved the coupled equations (10) in order to go beyond the singleeffective potential description [10]. The binding energies of f-parity rovibrational states have been calculated by solving two coupled equations (10) with α,β=1,2.…”

“…While for the BO potentials and adiabatic corrections there are ab initio [11,12] and asymptotic [13] results in the literature , this is not the case for the coupling matrix element (12) which in this case involves only H gu . Since we are interested here in the states localized in the outer well of the II' 1 Π g potential, that is, at large internuclear distances, we shall replace V 12 (R) with its (constant) asymptotic value at R→∞ [10]: To solve the coupled equations (10) we used the particle-in-the-box discrete variable representation (DVR) of Colbert and Miller [14]. The converged results were obtained by using N DVR =600 equidistant grid points spanning the interval from R min =0.5 to R max =75.…”

Gerade–ungerade symmetry breaking in bound states localized in the II′ 1Πg outer potential well of HD

“…The column E d concerns the energy relative to the lower dissociation limit H * (n = 2) + D(n = 1), while E a denotes the energy relative to the X 1 + g (v = 0, J = 0) ground state. The quantity denotes the difference between experimental results E obs [4,5] well can be found in [15].…”