Theory of energy shifts associated with deviations from Born-Oppenheimer behavior in 1Σ-state diatomic molecules

Quantitative Analysis of Vibration-Rotational Spectra of Diatomic Molecules with (v,j)-Dependent Dynamical Reference Conformation. Application to LiH X1Σ+

“…The standard procedure for the reduction of spectral data, comprising wave numbers of pure rotational and vibration-rotational transitions, to parameters of radial functions (1)- (4) is based on the wave equation derived by Herman and Asgharian [6] or in an equivalent form [21] The nonadiabatic functions α(R), (3(R), appearing in (7), have the same absolute order (me /m) 2 according to the nature of electronic matrix elements that they represent [12,21]. However, relative to their addends of unity they appear in (9) as functions of intrinsic order m e /m; similarly adiabatic term V'(R) is of the same order me/m relative to BO potential V(R) [12].…”

“…Consequently, the wave equation (7) can be significantly simplified by applying the linear approximation [12] and ignoring all terms containing a ratio of electronic to nuclear mass to powers greater than me/m [12]. As a result we obtain the Schrödinger equation [12] amenable to semi-classical Wentzel-Kramers-Brillouin (WKB) treatment, provided that E,, J appearing in (14) is treated as a known power series expansion in J and v [6]. To this effect another approximation [6] is used, in which EBOvJ denotes the BO term values obtained by solving Eq.…”

“…As a result we obtain the Schrödinger equation [12] amenable to semi-classical Wentzel-Kramers-Brillouin (WKB) treatment, provided that E,, J appearing in (14) is treated as a known power series expansion in J and v [6]. To this effect another approximation [6] is used, in which EBOvJ denotes the BO term values obtained by solving Eq. (13) for…”

“…These data comprise 543 unduplicated rotational and vibration-rotational transitions measured with an individual precision from 1.67 x 10 -6 cm -1 to 1.0 x 10 -3 cm -1 [24][25][26][27][28]. Table I presents the values of radial parameters obtained in a standard approach employing Radiatom programme [5,6,12], and in a generalized DS-c scheme. The uncertainty in parentheses is a one-estimated standard error in units of the last quoted digit of the fitted values.…”

“…A standard procedure for evaluation of radial functions V(R), V'(R), c (R), ,3(R) from pure rotational and vibration-rotational spectra of diatomic species in an electronic ground state X "E+ or 0+ is based on a theoretical model developed by Herman and Asgharian [6] containing subsequent refinements by Bunker [7], Watson [8], Herman and Ogilvie [9], and by Ogilvie [10][11][12]. This approach applies an analytic formalism originated by Dunham [1] but with a treatment greatly extended to include adiabatic and nonadiabatic effects.…”