Professor Emeritus at Uppsala University, Uppsala, Sweden.
On the long way from the Coulombic Hamiltonian to the intermolecular energy surfaces: Concluding remarks at the tromsø conference, June 20–22, 1989
Article first published online: 19 OCT 2004
Copyright © 1990 John Wiley & Sons, Inc.
International Journal of Quantum Chemistry
Volume 38, Issue 5, pages 741–758, November 1990
How to Cite
Löwdin, P.-o. (1990), On the long way from the Coulombic Hamiltonian to the intermolecular energy surfaces: Concluding remarks at the tromsø conference, June 20–22, 1989. Int. J. Quantum Chem., 38: 741–758. doi: 10.1002/qua.560380514
- Issue published online: 19 OCT 2004
- Article first published online: 19 OCT 2004
- Manuscript Accepted: 20 NOV 1989
- Manuscript Received: 24 JUN 1989
After a brief review of the main results given at the conference, the general properties of the Coulombic Hamiltonian for a system of electrons moving in a framework of moving atomic nuclei—considered as point charges—are discussed. Since this Hamiltonian is invariant under translations and rotations, the total momentum and the total angular momentum are constants of motion, which means that it is possible to separate the motion of the center of mass and the rotation of the system as a whole. Even if these separations are simple in principle, they lead to a mixing of the electronic and nuclear coordinates that complicates the transformed Hamiltonian. The general features of this Hamiltonian are discussed both in pure quantum mechanics and general quantum theory dealing with wave functions Ψ respective density matrices ρ or system operators T. The principles of the latter are derived from five simple axioms, and it is shown that pure quantum mechanics is a special case of the general theory and that the analogy between these two approaches is essential for the “economy of thinking.” It is indicated that the general theory of the shape and topology of the energy surface 〈H〉 = TrHΓ and its critical points, as a function of the system operator Γ involving both electronic and nuclear coordinates, is a very difficult mathematical problem and that calculation of this surface even for simple molecular systems represents a formidable computational problem, which has to be solved in order to be able to understand the nature of chemical reactions from first principles.