The inversion of diatomic Born–Oppenheimer-breakdown corrections

On the X2Σ+, A2Π, and C2Σ+ states of BeH, BeD, and BeT

“…In this approach the observed level energy spacings are fitted directly to difference between eigenvalues obtained by solving the effective radial Schrö dinger equation [28,29] …”

Algebraic vs. numerical methods for analysing diatomic spectral data: a resolution of discrepancies

“…For a neutral diatomic molecule A-B in a 1 R electronic state, it may be written as [8,[41][42][43][44][45] …”

“…An alternate version of the above Hamiltonian in which the b(r)[E v,J À V CN (r)] term does not appear and the BOB radial functions have different formal definitions has been derived by Watson [43,45], and the present discussion applies equally to either formulation. The objective of any direct potential fit method is then to determine the optimum effective potential energy function (with or without the term b(r)[E v,J À V CN (r)])…”

“…On the other hand, according to the alternate version of Eq. (6) derived by Watson, the effects of the Q A (r) and Q B (r) kinetic-energy and R A (r) and R B (r) centrifugal BOB functions can not be distinguished from those of the adiabatic potential energy functions S A (r) and S B (r) [43,45,70]. This implies that unique values of t A 0 and t B 0 , and hence of the dipole moment and rotational g-factor, cannot be determined from transition energy data alone.…”

“…The results of the present RADIATOM ADIATOM analyses for GeS and BrCl shown in Table 2 also clearly support WatsonÕs conclusion. In particular, his derivations [45,70] show that the BOB parameters t A 0 and u A 1 both contribute additively to the same Z A l;m correction coefficients, which implies that they cannot be determined independently. This conclusion is supported by independent physical arguments [48], and by comparison of the present case (v) although the values of t A 0 and t B 0 yielded by the case (v) fits appear to be statistically significant (i.e., having uncertainties <100%), the fact that fits of equivalent quality are obtained when those parameters were fixed at zero and the parameters u A 1 varied in the fits shows that conclusion was an artifact of the choice of model Hamiltonian and the limited number of correction function coefficients considered.…”