Contribution of the Breakdown of the Born-Oppenheimer Approximation to Higher Order Dunham Coefficients

Analysis of rotational and vibrational-rotational spectra of HF based on the non-Born-Oppenheimer effective Hamiltonian

Rotational transitions of HF that are important as a wavenumber standard have been analyzed by simultaneous fitting of the reported rotational and vibrational-rotational transitions plus rotational measurements of the present study with the non-Born-Oppenheimer effective Hamiltonian expressed with the optimal parameters, i.e., the determinable clusters of the expansion coefficients of the correction functions for the breakdown of the Born-Oppenheimer approximation. Since the spectral fit is made with the analytical solution of the Schrödinger equation, one can easily reproduce the fitting procedure. This is the first example of the non-Born-Oppenheimer analysis of a single isotopologue with physically meaningful parameters based on the traditional concept of the molecular constants. Fitting of a data set for HF has generated 15 independent parameter values that include 4 determinable clusters of the expansion coefficients. These 15 parameters are sufficient to generate 41 Yij coefficients and 72 rotational constants, which provide comprehensive sets of molecular constants of HF.

Evaluation of Expansion Coefficients from Optimal Fitting Parameters for the Analysis of Spectra of Diatomic Molecules and an Application to LiH

To evaluate individual expansion coefficients composing fitting parameters of the Born-Oppenheimer corrections to Dunham's coefficients Y(ij) that have been given analytically with the Delta(B) and Delta(omega) formalism, we examined the consistency of analytic expressions for those corrections with Watson's assertion of the experimental inseparability of nonadiabatic corrections Q(a, b)(r) for a molecule AB. Derived analytic expressions in terms of optimal fitting parameters for the corrections are essential to evaluate individual expansion coefficients. These expressions also reveal redundancies between empirical correction parameters Delta(ij). A method of evaluating nonadiabatic vibrational corrections Q(a, b)(r) and adiabatic corrections S(a, b)(r) separately consistent with Watson's assertion of inseparability is presented and is applied to an analysis of spectral data of LiH. Functions Q(a, b) and S(a, b) for LiH are thus successfully evaluated; S(H, Li)(r) values agree well with those predicted simply by wobble-stretch theory. Experimental values for optimal fitting parameters r(H)(1q) and r(H)(2q) are nearly equal to those of r(Li)(1q) and r(Li)(2q), respectively, in agreement with a theoretical relation r(a)(iq)=r(b)(iq). Copyright 2001 Academic Press.

Dunham Treatment Including Effects of the Born-Oppenheimer Breakdown for Open-Shell Diatomic Molecules in 2Sigma States

A Dunham treatment of an effective Hamiltonian for diatomic molecules in 2Sigma states that includes contributions of the Born-Oppenheimer breakdown has yielded an expression for vibrational-rotational energy by an expansion in powers of (v + (1/2))i[N(N + 1)]j-k(N'/2)k, where N' is N for the J = N + (1/2) spin-doublet state and -(N + 1) for the J = N - (1/2) state and k = 0, 1, ellipsis, j. Analytic expressions for the expansion coefficients Y*vJijk provide a potential model appropriate for the spectral fits for molecules in 2Sigma states. The expansion coefficients Y*vJij0 for the k = 0 terms are exactly the same as the Y*vNij coefficients given for 1Sigma states, the Dunham coefficients Yij modified by the contributions of the Born-Oppenheimer breakdown, provided that a spin contribution originating from off-diagonal electronic corrections of the electronic part of the spin-orbit interaction can be ignored. Spin-rotation energy is given by the terms with coefficients Y*vJijk (k >/= 1). There are no Y*vJijk (k >/= 2) terms in the previously known methods of analysis for 2Sigma molecules. The present potential model is applied to the reported vibrational-rotational spectra of CaH and all spectral lines of 40CaH and 40CaD isotopomers are fitted to a single set of molecular constants simultaneously with significantly smaller standard deviations. Copyright 1998 Academic Press.