Chemical reactivity from linear response eigenfunctions and eigenvalues

The atom-condensed linear response function matrix can be diagonalized, and the associated eigenvectors thus obtained form a complete basis set on which any density deformation can be projected. In this paper, one proposes to interpret these vectors as atom condensed Electron Density Deformation Modes. Each eigenvector represents a mode describing how electron density can deformed in response to an external potential perturbation. It is hypothesized that these modes can reveal the preferred direction or pattern of electron flow, helping identifying the reactive region of a molecule. A relationship between electron density polarization energy and hardness variation is also derived. Practical applications on organic reactions are provided.