Theoretical Reconstruction of the Electron Density of Large Molecules from Fragments Determined as Proper Open Quantum Systems: The Properties of the Oripavine PEO, Enkephalins, and Morphine

A new method of computing the properties of large molecules, not amenable to direct computation, is presented. The large molecule is reconstructed from judiciously chosen fragment molecules which are small enough for direct computation but large enough to retain good approximations to the electron density of the respective moieties in the large molecule. The atoms in the fragment molecules are determined as proper open systems according to the quantum theory of atoms-in-molecules (QT-AIM) developed by Bader. The properties of the atoms in the fragment molecules representing atoms in the large molecule are summed to obtain the properties of the large molecule. The computational effort is, thus, reduced from the n th power of a large number (the size of the basis set describing the large molecule) to the sum of the n th power of small numbers (the sizes of the basis sets describing each fragment molecule). The method is tested on the complicated oripavine molecule 7-α-[1-( R )-hydroxy-1-methyl-3-phenylpropyl]-6,14- endo -etheno-tetrahydrooripavine (PEO) and used to study some opioids. The properties of PEO computed from fragments are found to be remarkably close to those computed for the intact molecule. The success of this approach is the result of the transferability as well as the additivity of atomic properties. Three stable conformations of PEO are found to correspond closely to three conformations of enkephalins (Enk), each of the three PEO/Enk conformer pairs having key functional groups in very similar spatial disposition. These pairs can be candidate biologically active conformations at the three opioid receptor subtypes. The relationship between the concepts of transferability and similarity is discussed, and a new real-space “reactive similarity” index based on the Laplacian of the density is proposed. The extension of Carbó's similarity measures to pharmacophoric fragments of molecules is discussed. The results open the door for accurate theoretical studies of a multitude of large complicated biological molecules.