The crucial problems of the diatomics-In-molcculcs method. i-e_ dhtomic state mixing and treatment of over& are analyzed using the quartet states of 113 as an example-A Ned version of mixing is proposed and results of Illustrative calculations are discussed_ 1. fntroduction C3IcuIations of potentia! surfrrces for poiyatomic systems by the diotomfes-in-mo!ecu!es (DIhl) mer!rod [I ! meet wit11 some difficulties due to diatomic state rni..ing prob!ems and treatment of overiap integra!s between polyzttomic basis functions (pbPs)_ The prob!em of diatomic state mixing arises 3t constructing fnrgment hamiItoni3n mstrices on tire basis of known diatomic potential energy values_ \then electronic st3teS of the diatomic fr3gment include two or more states of tire s3me symmetry, tire correspondin b!ock of the hamiltonian matrix mnnet be determined unnmbi~uous!y_ In t!lat me the theory suggests 3n introduction of specific p3r3meters of the D!M method, the so-&led diatomic srste mixirrg parameters_ These are either determined by soiving the diatomic prob!em using the valence bond teclmique [2] or varied to obtain the best fir of the DIhi potential surf3ces to results of independent ea!culations [S] _ The first appIic3tiom of tire DIhl method [4,5] r2ve3!ed th3t the neg!ect of overlap between pbfs !lad pr3cticaIIy no effect on the c3!cu!ated energy MIues of polyzrtomic mo!ecu!es_ However later on, serious difficulties were encountered in attempts to caIcu!ate some potential surfaces of H, taking into Xcount overlap integnds between pbfs which correspond to cov3Ient snd ionic corGigur3tion.s [2.6] _ The problem is compliczrted by the f3ct that bot!r