Chapter 1
The Potential Energy Surface in Molecular
Quantum Mechanics
Brian Sutcliffe and R. Guy Woolley
Abstract The idea of a Potential Energy Surface (PES) forms the basis of almost all accounts of the mechanisms of chemical reactions, and much of theoretical molecular spectroscopy. It is assumed that, in principle, the PES can be calculated by means of clamped-nuclei electronic structure calculations based upon the
Schrödinger Coulomb Hamiltonian. This article is devoted to a discussion of the
origin of the idea, its development in the context of the Old Quantum Theory, and
its present status in the quantum mechanics of molecules. It is argued that its present
status must be regarded as uncertain.
1.1 Introduction
The Coulombic Hamiltonian H does not provide much obvious information or guidance,
since there is [sic] no specific assignments of the electrons occurring in the systems to the
atomic nuclei involved—hence there are no atoms, isomers, conformations etc. In particular
one sees no molecular symmetry, and one may even wonder where it comes from. Still it is
evident that all of this information must be contained somehow in the Coulombic Hamiltonian H [1].
Per-Olov Löwdin, Pure. Appl. Chem. 61, 2071 (1989)
This paper addresses the question Löwdin wondered about in terms of what quantum mechanics has to say about molecules. A conventional chemical description
of a stable molecule is a collection of atoms held in a semi-rigid arrangement by
chemical bonds, which is summarized as a molecular structure. Whatever ‘chemical
bonds’ might be physically, it is natural to interpret this statement in terms of bonding forces which are conservative. Hence a stable molecule can be associated with
a potential energy function that has a minimum value below the energy of all the
clusters that the molecule can be decomposed into. Finding out about these forces,
or equivalently the associated potential energy, has been a major activity for the past
century. There is no a priori specification of atomic interactions from basic physical
laws so the approach has been necessarily indirect.
B. Sutcliffe (B)
Service de Chimie Quantique et Photophysique, Université Libre de Bruxelles, 1050 Bruxelles,
Belgium
e-mail: bsutclif@ulb.ac.be
M. Hotokka et al. (eds.), Advances in Quantum Methods and Applications in
Chemistry, Physics, and Biology, Progress in Theoretical Chemistry and Physics 27,
DOI 10.1007/978-3-319-01529-3_1,
© Springer International Publishing Switzerland 2013
3
The Potential Energy Surface in Molecular
Quantum Mechanics
Brian Sutcliffe and R. Guy Woolley
Abstract The idea of a Potential Energy Surface (PES) forms the basis of almost all accounts of the mechanisms of chemical reactions, and much of theoretical molecular spectroscopy. It is assumed that, in principle, the PES can be calculated by means of clamped-nuclei electronic structure calculations based upon the
Schrödinger Coulomb Hamiltonian. This article is devoted to a discussion of the
origin of the idea, its development in the context of the Old Quantum Theory, and
its present status in the quantum mechanics of molecules. It is argued that its present
status must be regarded as uncertain.
1.1 Introduction
The Coulombic Hamiltonian H does not provide much obvious information or guidance,
since there is [sic] no specific assignments of the electrons occurring in the systems to the
atomic nuclei involved—hence there are no atoms, isomers, conformations etc. In particular
one sees no molecular symmetry, and one may even wonder where it comes from. Still it is
evident that all of this information must be contained somehow in the Coulombic Hamiltonian H [1].
Per-Olov Löwdin, Pure. Appl. Chem. 61, 2071 (1989)
This paper addresses the question Löwdin wondered about in terms of what quantum mechanics has to say about molecules. A conventional chemical description
of a stable molecule is a collection of atoms held in a semi-rigid arrangement by
chemical bonds, which is summarized as a molecular structure. Whatever ‘chemical
bonds’ might be physically, it is natural to interpret this statement in terms of bonding forces which are conservative. Hence a stable molecule can be associated with
a potential energy function that has a minimum value below the energy of all the
clusters that the molecule can be decomposed into. Finding out about these forces,
or equivalently the associated potential energy, has been a major activity for the past
century. There is no a priori specification of atomic interactions from basic physical
laws so the approach has been necessarily indirect.
B. Sutcliffe (B)
Service de Chimie Quantique et Photophysique, Université Libre de Bruxelles, 1050 Bruxelles,
Belgium
e-mail: bsutclif@ulb.ac.be
M. Hotokka et al. (eds.), Advances in Quantum Methods and Applications in
Chemistry, Physics, and Biology, Progress in Theoretical Chemistry and Physics 27,
DOI 10.1007/978-3-319-01529-3_1,
© Springer International Publishing Switzerland 2013
3