QUANTUM-CHEMICAL QUANTIFICATION OF MOLECULAR COMPLEXITY AND CHIRALITY

We introduce a number of molecular complexity indexes on the grounds o f quantization of notions known in the differential geometry of curves (specifically, electron trajectories). Mean lengths, L(psi) and L, re flect the general spatial extent of a many-electron system in a given state psi and, correspondingly, of the molecular structure as a whole. Analogously, mean curvatures, K(psi) and K, give a measure of the non -linearity of electron distribution. A mean torsion, t(psi), along wit h related indexes k and k(f), presents a degree of molecular dissymmet ry, i.e. a measure of chirality. In fact, all these indexes possess ad ditivity properties and correct asymptotics under decomposition into s eparate parts or individual atoms. A topological approach to a one-ele ctron hamiltonian through an adjacency matrix of the corresponding mol ecular graph is examined when calculating the above indexes. Some typi cal planar and nonplanar structures (Huckel-like systems, simple model s of chiral allenes and chiral octahedral complexes with bidentate lig ands) are studied.