In order to describe the electronic states of metal (M)-rare gas (Rg) van der Waals dimers having an sp configuration with a strong spin-orbit interaction, we derived an elf parity adapted molecular Hamiltonian matrix by adopting a symmetry-adapted atomic orbital approach. The molecular Hamiltonian was constructed by introducing (i) the interaction between the p electron and the attached rare gas atom V-Rg, (ii) the exchange interaction between the s and p orbitals, e(2)/r(sp), and (iii) the spin-orbit interaction for the p electron. As a basis set, twelve molecular electronic wave functions were derived by taking into account their elf parities. We applied the derived molecular Hamiltonian matrix to the first excited 6s6p configuration of HgAr by performing a least-squares fit to the spectroscopically determined term values for the v = 0 levels of the a (II0-)-I-3, A (II0+)-I-3, B (II1)-I-3, b (II2)-I-3, and C (II1)-I-1 states. From the results of the least-squares fit, we clarified how the above interactions (i)-(iii) split twelve degenerate molecular wave functions into the eight electronic eigenstates; i.e., a (II0)-I-3, A (II0+)-I-3, B (II1)-I-3, b (II2)-I-3, c (3) Sigma(1)(+), d (3) Sigma(0)(+), C (II1)-I-1, and D (1) Sigma(0)(+). On the basis of (i) a critical comparison between the atomic Hamiltonian matrix for Hg and the determined molecular Hamiltonian matrix and (ii) an examination of the mixing among the symmetry-adapted molecular wave functions, characteristic features of the electronic structure arising from the formation of a van der Waals bond, were extracted.