The difficulties involved in the Hartree-Fock method of calculation of the force constants for structures described by non-Roothaan type wave functions were an- alyzed. It was shown on the example of the C4(D4h) molecule that the Hartree- Fock potential surface in the vicinity of the stationary points studied is con- tinuous and smooth only in defined cross-sections. The formally-correct calcu- lation of these cross-sections requires the use of a special procedure described in the present article. A comparison has been made of the results of the calcu- lation of the force constants obtained by the Hartree-Fock method (in the MINDO/3) approximation) and by allowing for the minimal configurational interaction. There exist in systems with a cubic (T d, O, Oh, T, T h) and tetragonal (D~h , C4v, D2d) symmetry with an open electronic shell t b (N = 2, 3, 4) and e 2, the so-called "non-Roothaan" type states, in the calculation of which by the Hartree-Fock method special measures must be taken for matching the symmetry of the molecular skeleton and many-electron functions of state (3, 4). These measures consist in taking into account in the SCF equations in an explicit form the unitary transformation matrix U with an accuracy matching that upon which the basis of the degenerate MO of an open shell has been determined. (Depending on U are the vectorial bond coefficients amn(U) and bmn (u) in the expressions for the energy func- tional and the Fock operations, and also the coefficients of the expansion of the function of state with respect to Slater determinants (3).) With decrease in the symmetry of the system (for example, during structural distortions) the necessity of taking into account the above features is only partially eliminated. An- alysis shows that there is a unique memory effect, at low symmetry distortions, the systems seemingly "remembering" that in the high symmetry configufation they possessed on non- Roothaan type wave function character, with the characteristic dependence of the latter on U. The result of this is that in the vicinity of a symmetric nuclear configuration the ex- pressions for the energy of the system and its wave function (for one and the same spectro- scopic state) are different and depend on the character of the distorting coordinate Q. The last fact is of considerable importance in calculating the physical characteristics, which are derivatives of a Hamiltonian with respect to internuclear distances, in particular the force constants. In the present work, an analysis is made of the main difficulties arisin Z in the calculations of force constants for highly symmetric structures described by non-Roothaan type wave functions. As an application, an examination is made of the problem of the calculation of the force constants for a C~ (D4h) molecule in its lowest singlet non-Roothaan type state iBi~ (electronic configuration eg2). This problem is of interest in