The following abstracts outline the work in which I have been involved since the last CCP1 newsletter. Since that appeared I have retired from the University of York and, as will be clear from the addresses given below, have  gone to live in Brussels. I am still an Honorary Professor at the University of York and I am a visiting Professor at the ULB. Nothing so sordid as financial remuneration is involved in either appointment but it is a pleasantly novel feeling to be a Professor twice over and I am tempted to write (Prof)² on my correspondence. I don't have any students in either place and I don't have to give any lectures at ULB but I still teach a course in York for a week each year.

The ULB is the Francophone residue of the Free University of Brussels. It is "Libre'' simply in the sense that it is not necessary to subscribe to a particular religious view in order to be a member. The University was founded by rather anti-clerical free-masons in the early 19th century and was dominantly Francophone until 1968, when it split into two parts, a Dutch (Flemish)-speaking part, the VUB, and a French-speaking part the ULB. There is however cooperation between the two parts in matters such as library and computing provision.

I still seem to get sent plenty of refereeing and grant assessment work but I try to be retired by taking very long weekends and when in the Lab, working only on problems that I find interesting. I am at present engaged in developing the theory of two interacting groups
with arbitrarily placed particle origins within the groups, generalising, I hope, some earlier work in which I was involved (Molec. Phys.50, 1025 (1983)). I hope to be able to
continue working in this manner for at least as long as my appointment at ULB is continued and to remain a member of CCP1.
 

Abstracts

The idea of a potential energy surface.

The development of the idea of a potential energy surface is examined in the context of solutions to the full quantum mechanical problem specified by the Schrödinger Hamiltonian expressed in laboratory-fixed coordinates by considering the possibility of separating  nuclear and electronic motions.

Appeared In: A. F. Sax, ed. Potential Energy Surfaces,
Lecture Notes in Chemistry, Vol. 71,  Springer, Berlin, 61-96 (1998).
 

The Born-Oppenheimer correction terms for a triatomic system in the Sutcliffe-Tennyson formulation

An attempt is made to formulate the Born-Oppenheimer correction terms arising from the interaction of the electronic and nuclear motions in a triatomic system. The formulation for the nuclear motion problem is kept as general as possible while using the nuclei to define the
instantaneous the (x-z) plane, following the approach presented in Sutcliffe and Tennyson (Int. journ. quant. chem. 39 183 (1991)). The origin for the electronic coordinates is taken to be the centre-of-nuclear mass.

Appeared In: Int. journ. quant. chem. 74, 109-121 (1999)
 

Dipole moment surfaces and spectroscopic calculations.

Modern non-empirical calculations of the rotation-vibration spectra of small molecules often use a dipole moment surface computed from a clamped nuclei electronic structure calculation to determine the transition intensities. In this paper an attempt is made to analyse what exactly is involved in such an enterprise.

Appeared In: Int. journ. quant. chem. 74, 681-695 (1999).
 

The decoupling of electronic and nuclear motions in the isolated molecule Schrödinger Hamiltonian

The problem of approximately separating electronic from nuclear motion is considered. The standard method, in which the total wavefunction is written as a sum of products of electronic and nuclear parts, forms the basis of the discussion but it is made taking account of the symmetries and spectral properties of the full Hamiltonian. It is shown that a certain arbitrariness enters the discussion when the symmetries and spectral properties are considered properly and that problems also arise which would seem to limit the domain of validity of any wave function composed as a sum of such products.

To Appear In: I. Prigogine and S. Rice, eds. Advances in Chemical Physics 114, 1-121, (2000).
 

Is a molecule in Chemistry explicable as a broken symmetry in quantum mechanics?

It is argued that incorporating the molecular geometry into the transformation specifications for deriving the standard (Eckart) Hamiltonian used to describe molecular spectra, cannot generally be accomplished without breaking the permutational symmetry requirements on
identical nuclei.

To appear in C. le Bris and M. Defranceschi eds.  Mathematical models and methods for ab initio Quantum Chemistry, Lecture Notes in Chemistry, Vol 74 , Springer, (2000).
 

Some mathematical problems in the description of dissociating molecules.

When separating the centre of mass motion from the Schrödinger problem for a system, some apparently reasonable choices of space fixed coordinates have transformation properties under nuclear permutations that mix variables that are formally nuclear with those that are formally electronic variables. This renders the idea of a potential surface expressed in such coordinates, problematic. The problems are discussed and some solutions suggested.

To appear in P. O. Löwdin ed. Advances in Quantum Chemistry (2000).