Popelier

Assistance with the illustrations for the second edition was provided by Drs R Groot, S McGrother and V Milman. Many of the figures from the first edition are also included here and so 1 would like to thank again Dr S E Greasley, Dr M M Harm, Dr H Jhoti, Dr S N Jordan, Professor G R Luckhurst, Dr P M McMeekin, Dr A Nicholls, Dr P Popelier, Dr A Robinson and Dr T E Klein. 

R. J. Gillespie, P. L. P. Popelier, Chemical Bonding and Molecular Geometry. Oxford University Press, 2001. 

Popelier, P.L.A. (1994) A robust algorithm to locate automatically all types of critical points in the charge density and its Laplacian, Chem. Phys. Lett., 228, 160-164. 

Popelier, P.L.A. (1996) MORPHY, a program for an automated Atoms in Molecules Analysis, Comput. Phys. Comm., 93,212. 

It has been recently shown [12] that the ELF topological analysis can also be used in the framework of a distributed moments analysis as was done for Atoms in Molecules (AIM) by Popelier and Bader [32, 33], That way, the Mo( 2) monopole term corresponds to the opposite of the population (denoted N) ... 

The five second-moment spherical tensor components can also be calculated and are defined as the quadrupolar polarization terms. They can be seen as the ELF basin equivalents to the atomic quadrupole moments introduced by Popelier [32] in the case of an AIM analysis ... 

Popelier PLA (2000) Atoms in molecules An introduction, Prentice-Hall, Harlow, UK... 

The classification of critical points in one dimension is based on the curvature or second derivative of the function evaluated at the critical point. The concept of local curvature can be extended to more than one dimension by considering partial second derivatives. d2f/dqidqj, where qt and qj are x or y in two dimensions, or x, y, or z in three dimensions. These partial curvatures are dependent on the choice of the local axis system. There is a mathematical procedure called matrix diagonalization that enables us to extract local intrinsic curvatures independent of the axis system (Popelier 1999). These local intrinsic curvatures are called eigenvalues. In three dimensions we have three eigenvalues, conventionally ranked as A < A2 < A3. Each eigenvalue corresponds to an eigenvector, which yields the direction in which the curvature is measured. 

Because of the irregular shape of an atom in a molecule, this integration is not trivial and can be time-consuming. For many molecules, however, it can now be carried out on a personal computer in a reasonably short time. A discussion of integration procedures is given by Popelier (1999). 

An important advantage of the finite atoms defined by AIM is that they do not overlap, which is not generally true for orbital-defined atoms. Each atom has a sharp and well-defined boundary inside the molecule, given by its interatomic surfaces. The atoms fit exactly into each other, leaving no gaps. In other words, the shape and the volume of the atoms are additive. This is true also for other physical properties of an atom, such as the electron population and the charge, as seen in Table 6.2 and as indeed has been shown to be true for all other properties. (Bader 1990, Popelier 1999). 

P. L. A. Popelier, Atoms in Molecules An Introduction, 2000, Pearson Education, Harlow,... 

P. Coppens, X-ray Charge Densities and Chemical Bonding, 1997, Oxford University Press, New York. P. L. A. Popelier, F. M. Aiken, and S. E. O Brien, Royal Society of Chemistry Specialist Periodical Report Vol 1, Ed. A. Hinchliffe, 143 (2000). 

This article gives a simple introduction to the electron densities of molecules and how they can be analyzed to obtain information on bonding and geometry. More detailed discussions can be found in the books by Bader (4), Popelier (5), and Gillespie and Popelier (6). Computational details to reproduce the results presented in this paper are presented in Appendix 1. 

Gillespie, R. J. Popelier, P. L. A. Molecular Geometry and Chemical Bonding jrom Lewis to Electron Densities Oxford University Press New York, 2001. 

Several methods have been used for analyzing the electron density in more detail than we have done in this paper. These methods are based on different functions of the electron density and also the kinetic energy of the electrons but they are beyond the scope of this article. They include the Laplacian of the electron density ( L = - V2p) (Bader, 1990 Popelier, 2000), the electron localization function ELF (Becke Edgecombe, 1990), and the localized orbital locator LOL (Schinder Becke, 2000). These methods could usefully be presented in advanced undergraduate quantum chemistry courses and at the graduate level. They provide further understanding of the physical basis of the VSEPR model, and give a more quantitative picture of electron pair domains. 

Chemical bonding and molecular geometry from Lewis to electron densities / R.J. Gillespie, P.L.A. Popelier. 

Chemical bonds—History. 2. Molecules—Models. I, Popelier, P.L.A. II. Title. III. Series... 

We welcome comments and suggestions from readers. Please send comments via e-mail to either gillespie mcmaster.ca or pla umist.ac.uk. For more information about our research, please visit our web sites—Ronald Gillespie at http //www.chemistrv.mcmaster.ca/facultv/giUespie and Paul Popelier at http //www.ch.umist.ac.uk/popelier.htm. 

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