Matta, Boyd. The quantum theory of atoms in molecules

The Quantum Theory

of Atoms in Molecules

Edited by

Che´rif F. Matta and Russell J. Boyd

The Quantum Theory

of Atoms in Molecules

From Solid State to DNA and Drug Design

Edited by

Che´rif F. Matta and Russell J. Boyd

This book is dedicated to

Professor Richard F.W. Bader

on the occasion of his 75th birthday, for his invaluable contributions to the physical theory of chemistry.

‘‘. . . it is in virtue of the form that the matter is some one definite thing, and this is the substance of the thing. What Aristotle means seems to be plain common sense: a ‘thing’ must be bounded, and the boundary constitutes its form. . . . We should not naturally say that it is the form that confers substantiality, but that is because the atomic hypothesis is ingrained in our imagination. Each atom, however, if it is a ‘thing’, is so in virtue of its being delimited from other atoms, and so having, in some sense, a ‘form’.’’

Bertrand Russell, A History of Western Philosophy;

Simon and Schuster, New York (1945).

VII

Foreword

As a graduate student at McMaster University in the years 1975–81 I had the good fortune of knowing Richard Bader as a member of my supervisory committee. The departments of chemistry and physics shared facilities in the building that was then called the Senior Sciences Building and is now called the A.N. Bourns Building. I was a student in the department of physics, in the theoretical physics group, with an o ce not far from the o ces of the Bader group.

Richard was the first theoretical chemist I ever met. In addition to the annual supervisory committee meetings, we chatted occasionally in his o ce. Looking back on those years, I wonder how di erently my own career might have turned out had I not been inspired by those conversations. And inspired I was!

Anyone who knows Richard would agree that the single word describing him best is passion. Richard Bader is passionate about science. His conviction and enthusiasm for his own science, the theory of chemical bonding, are particularly infectious. Every session with him left me exhilarated and, at the same time, exhausted! His energy far outstripped mine.

What inspired me most was his passion for ideas and concepts. Our conversations were not about technical matters such as basis sets or levels of electron correlation. We talked about densities and probabilities in chemical systems, what makes a chemical bond, what is an atom in a molecule, why are atoms of a given element similar in di erent molecular environments? Fundamental questions! Fundamental ideas! My own e orts at the time were far o the beaten track – basis-set-free computational schemes, Thomas Fermi-like molecular models, the Hartree–Fock–Slater approximation. As a theoretical physics student with no expertise in theoretical chemistry, I relied heavily on Richard’s feedback. Any other quantum chemist might have discouraged these unconventional projects, but not Richard. He was encouraging. He called the work important. He gave me confidence to pursue the unusual, ask the big questions, and, above all, seek out beautiful ideas.

Science is inherently beautiful. The most powerful ideas are also the simplest and the most beautiful. Early in the history of the density-functional theory of electronic structure, long before DFT was fashionable, Richard Bader followed his own path and developed some of the most beautiful ideas in chemistry. The boundaries of atoms in molecules are uniquely and rigorously defined by the

VIII Foreword

electron-density distribution. The topology of the density distribution also maps out all the bonds in a chemical system. Its Laplacian reveals the presence of localized electron pairs. Atoms in molecules, bonds, localized electron pairs – these are the most fundamental notions in chemistry. Richard Bader has taught us that the total electronic density defines them all.

It is a pleasure and an honor to help celebrate such a uniquely creative career. Thank you, Richard, for the inspiration and encouragement during my formative McMaster years and throughout my career. And thank you for the beautiful conceptual framework you gave to the theory of chemistry.

IX

Contents

1.1Introduction 1

1.3The Topology of the Electron Density Dictates the Form of Atoms in Molecules 5

1.6The Nodal Surface in the Laplacian as the Reactive Surface of a Molecule 10

1.7Bond Properties 10

1.7.6Electron Delocalization between Bonded Atoms: A Direct Measure of

Bond Order 13

1.8Atomic Properties 15

1.8.4Laplacian [L(W)] 17