The problem of taking into account different sizes of mixture component molecules is one of the key problems of the theory of multicomponent systems [1][2][3][4][5][6][7][8][9][10]. So called lattice models of solutions involving the concept of the blocking of separate lattice struc ture nodes have been used most extensively [1][2][3][4][5][10][11][12][13][14][15]. Blocking of several neighboring lattice structure centers by large molecules sharply complicates calcu lations of the number of existing molecule configura tions and their statistical weights at fixed number and energy of molecules. For this reason, the theory for large molecules has been developed to a much lesser extent than the theory for one node molecules model ing systems with approximately equal sizes. Earlier, molecules with comparatively simple shapes were con sidered, rigid rod and flexible chain (with length L), plate L 1 × L 2 (L 1 and L 2 are plate linear sizes), and rect angular parallelepiped (L 1 × L 2 × L 3 ) shapes.Various spatial orientations of molecules with fixed centers of mass should be considered in the construc tion of a theory of nonspherical molecules. In particu lar, three dimensional phase transitions of the nem atic and/or smectic)-disordered phase type occur in volume phases [11][12][13]. Close to the surface of a solid in the plane of the surface, an ordered arrangement of molecules with equal orientations of their long axes becomes more favorable. When large molecules are described statistically, each molecule orientation is included as a kind of some particle, and taking into account different orientations of molecules reduces to the theory of adsorption of a mixture of molecules even for a one component system. In [14,15], this approach was generalized to taking into account non uniformity of different surface regions, including mul tilayer regions. In [16], large molecule distributions close to solids and inside pores were studied.The equations obtained earlier presuppose discrete linear molecule i sizes , where α = x, y, z. In this work, an interpolation procedure from to + 1 along each α axis for molecule i with a rigid core and a parallelepiped shape is discussed. This procedure gen eralizes the equations obtained earlier to non integer molecule linear size values for molecules blocking more than one structure node. It retains the inclusion of lateral interactions between molecules and broad ens the range of theory applicability [14,15] (lateral interactions between the nearest neighbors are included).The essence of interpolation. For an arbitrarily dis crete fine mesh [17], differences in the shapes and vol umes of mixture components can fairly accurately be taken into account in terms of discrete molecule linear size values. This sharply increases problem mathemat ical complexity. Naturally, the question arises of the existence of a compromise between problem complex ity and accuracy of molecular distribution calcula tions.The real linear size of molecule i along axis α will be denoted by . Accordingly, the val...