Momentum-Space Electron Densities
and Quantum Molecular Similarity

Quantum molecular similarity attempts to answer quantitatively the general question: How similar are two molecules?. In our new approach, molecular similarity and dissimilarity indices are obtained from numerical comparisons of momentum-space electron densities. Many of the problems associated with more conventional position-space procedures are avoided and particular emphasis is placed on the variation of the long-range position-space electron density. The momentum-space approach is particularly suited to problems for which the molecular activity depends less on the details of the bonding topology than on features of the long-range slowly-varying valence electron density.

Momentum-space concepts are not, in general, familiar to the chemist and so our review article outlines first the calculation of momentum-space electron densities, [[rho]](p), from ab initio wavefunctions. The form of [[rho]](p) for different molecules is discussed, using as examples (i) the ground state of H2, (ii) bond formation in BH+, and (iii) the [[pi]]-orbitals in large conjugated polyenes.

The construction and the evaluation of similarity and dissimilarity indices based on [[rho]](p) are described in some detail. Examples are presented involving the comparison of (i) the total or total valence electron densities of two molecules, (ii) the densities associated with particular molecular fragments or localised molecular orbitals, and (iii) the densities of two molecular orbitals in the same molecule. Results are reported for the model series (a) CH3CHsCH3, CH3OCH3 and CH3SCH3, and (b) C-H and C-F bonds in hydrofluoromethanes. Finally, two studies involving larger systems are presented. In the first, momentum-space similarity indices are used to rationalise anti-HIV1 virology data for a group of phospholipids. The technique proves to have predictive value for such systems. In the second application, a structure-activity relationship is generated for the hyperpolarizabilities of a range of non-centrosymmetric 1,4-substituted benzene derivatives.