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 (▿2ρ), 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. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 437–442, 2003

[1]  Paul L. A. Popelier,et al.  Atoms in molecules , 2000 .

[2]  William H. Press,et al.  Numerical recipes , 1990 .

[3]  R. Bader.  Atoms in molecules : a quantum theory , 1990 .

[4]  R. Bader,et al.  Prediction of the structures of hydrogen-bonded complexes using the laplacian of the charge density , 1988 .

[5]  Quantum topological atoms , 2002 .

[6]  Paul L. A. Popelier,et al.  A method to integrate an atom in a molecule without explicit representation of the interatomic surface , 1998 .

[7]  F. Escudero,et al.  Atoms in molecules , 1982 .

[8]  Paul L. A. Popelier,et al.  Quantum molecular similarity. 1. BCP space , 1999 .

[9]  Paul L. A. Popelier,et al.  MORPHY, a program for an automated “atoms in molecules” analysis , 1996 .

[10]  R. Bader,et al.  Core Distortions and Geometries of the Difluorides and Dihydrides of Ca, Sr, and Ba , 1995 .

[11]  T. Tang,et al.  A charge density topological approach on the equilibrium gas-phase basicity of selected nitrogen-containing organic molecules , 1990 .

[12]  J. Baker.  An algorithm for the location of transition states , 1986 .

[13]  Axel D. Becke,et al.  Chemical content of the kinetic energy density , 2000 .

[14]  Determination of protonation sites in bases from topological rules , 2000 .

[15]  J. Cioslowski,et al.  Topology of electron-electron interactions in atoms and molecules. II. The correlation cage , 1999 .

[16]  A. Savin,et al.  Classification of chemical bonds based on topological analysis of electron localization functions , 1994, Nature.

[17]  P. Popelier,et al.  Protonation energies and the Laplacian of the electron density: A critical examination , 2001 .

[18]  P. Popelier.  On the full topology of the Laplacian of the electron density , 2000 .

[19]  A. Becke,et al.  Two functions of the density matrix and their relation to the chemical bond , 2002 .

[20]  Paul L. A. Popelier,et al.  Integration of atoms in molecules: a critical examination , 1996 .

[21]  Axel D. Becke,et al.  A Simple Measure of Electron Localization in Atomic and Molecular-Systems , 1990 .

[22]  R. Shibaeva,et al.  X-ray study on the structure of p-bromobenzoyldimethylamine , 1968 .

[23]  R. Bader,et al.  The mapping of the conditional pair density onto the electron density , 1999 .

[24]  R. Bader,et al.  The Lennard-Jones Function: A Quantitative Description of the Spatial Correlation of Electrons As Determined by the Exclusion Principle , 1998 .

[25]  Boris R. Stefanov,et al.  An efficient approach to calculation of zero‐flux atomic surfaces and generation of atomic integration data , 1995, J. Comput. Chem..

[26]  Paul L. A. Popelier,et al.  Quantum Molecular Similarity. 3. QTMS Descriptors , 2001, J. Chem. Inf. Comput. Sci..

[27]  R. Bader,et al.  Similarity and complementarity in chemistry , 1992 .

[28]  Francesco Zerbetto,et al.  Controlling the Frequency of Macrocyclic Ring Rotation in Benzylic Amide [2]Catenanes , 1998 .

[29]  R. Osman,et al.  Nucleophilic addition to activated double bonds: predictions of reactivity from the Laplacian of the charge density , 1989 .

[30]  J. Platts,et al.  RELATIONSHIP BETWEEN PHOSPHINE PROTON AFFINITIES AND LONE PAIR DENSITY PROPERTIES , 1995 .

[31]  R. Bader,et al.  Structural homeomorphism between the electron density and the virial field , 1996 .

[32]  Todd A. Keith,et al.  Topological analysis of magnetically induced molecular current distributions , 1993 .

[33]  Paul L. A. Popelier,et al.  A ROBUST ALGORITHM TO LOCATE AUTOMATICALLY ALL TYPES OF CRITICAL-POINTS IN THE CHARGE-DENSITY AND ITS LAPLACIAN , 1994 .

[34]  Paul L. A. Popelier,et al.  Atoms in Molecules: An Introduction , 2000 .

[35]  Ronald J. Gillespie,et al.  Chemical Bonding and Molecular Geometry: From Lewis to Electron Densities , 1972 .

[36]  R. Bader,et al.  Quantum Theory of Atoms in Molecules–Dalton Revisited , 1981 .

[37]  Friedrich Biegler-König,et al.  Calculation of the average properties of atoms in molecules. II , 1982 .

[38]  Bernard Silvi,et al.  CHARACTERIZATION OF ELEMENTARY CHEMICAL PROCESSES BY CATASTROPHE THEORY , 1997 .

[39]  Paul L. A. Popelier,et al.  Atom–atom partitioning of intramolecular and intermolecular Coulomb energy , 2001 .