On the application of a topological approach to analysis of poorly formalized problems for constructing algorithms for virtual screening of quantum-mechanical properties of organic molecules II: Comparison of formalism with constructions of quantum mechanics and experimental approbation of the proposed algorithms

Correspondences between descriptions of molecules in the framework of the theory of chemographs, internal coordinates of molecules, and $\psi$-functions are shown. The results obtained are comparable: ($i$) with the solutions of the one-electron Schrödinger equation on fragments of molecules with allowance for the overlap of fragments; ($ii$) with additive schemes for calculating electron density in the electron density functional theory; and ($iii$) with allowance for overlap integrals in the theory of molecular orbitals. Approbation of the algorithms on a sample of 134 thousand organic molecules showed rank correlations of the order of 0.75 (95%, reliable interval 0.67–0.85) between the results of calculations using the proposed algorithms and the values of the investigated quantum mechanical properties of molecules. The calculation speed of the proposed algorithms is several orders of magnitude higher than the speed of quantum mechanical calculations which is important for screening the molecules.