A Na₂ X ¹ Σ ⁺ _g and (1)¹Π _g electronic states long range analysis

Abstract

In this paper the Na₂ X ¹ Σ ⁺ _g and (1)¹Π _g electronic states long range tail functional behavior is analysed in the light of multipolar expansion theory combined with damping functions. The experimental data used here is the one reported by Barrow et al. [1]. In the present paper this experimental data is used in a nonlinear reduction to van der WaalsC _n constants using the multipolar expansion Σ _n C _n /r ⁿ. Since the internuclear distance reached by the biggest part of the data is still out of the Le Roy's region (where the internuclear distance must be greater thanr _lim:

$$r_{\lim } = 2\left( {\left\langle {r_A^2 } \right\rangle ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} + \left\langle {r_B^2 } \right\rangle ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } \right),$$

being the outermost electron orbital radii for the 〈r _A 〉 and 〈r _B 〉 two atoms), the exchange energy must be taken into account. Due to the fact that the 1/r ⁿ expansion diverges whenr→0, the damping functions has been included in order to prevent this. The obtained values for theC _n coefficients, as well as the exchange energy constants, show a good agreement with the theoretical available data, for both electronic states.