An improved algorithm to locate critical points in a 3D scalar field as implemented in the program MORPHY

A new algorithm for location of the critical points in general scalar fields is described. The new method has been developed as part of an on-going process to exploit the topologic analysis of general 3D scalar fields. Part of this process involves the use of topologic information to seed the critical point search algorithm. The continuing move away from topologic studies of just the electron density requires more general algorithms and the ability to easily "plug in" new functions, for example, the Laplacian of the electron density ( triangle down (2)rho), the Electron Localisation Function (ELF), the Localised Orbital Locator (LOL), the Lennard-Jones function (LJF), as well as any new functions that may be proposed in the future. Another important aspect of the current algorithm is the retention of all possible intermediate information, for example, the paths describing the connectivity of critical points, as well as an ability to restart searches, something that becomes increasingly important when analysing larger systems. This new algorithm represents a core part of a new local version of the MORPHY code. We distinguish nine universal types of gradient paths.