A comprehensive deperturbation analysis is made of the singlet-triplet D(1)
Pi similar to d(3)Pi complex of the (NaK)-Na-23-K-39 molecule. The depertur
bation model takes into account direct spin-orbit coupling between the sing
let and triplet states plus a spin-rotational interaction between different
Omega components of the triplet state. The direct inversion procedure prov
ides a self-consistent set of the Dunham molecular constants for both state
s and for the matrix elements of the spin-orbit interaction. The deperturba
tion analysis is supported by electronic structure calculations performed i
n the framework of the relativistic effective potential method combined wit
h many-body multipartitioning perturbation theory. The theoretical spin-orb
it matrix elements agree well with their experimental counterparts.