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19 Dec 2022
updated 21 Dec 2022

I first encountered Joe Gerratt during my initial year of postgraduate work at UEA, which fortunately for me coincided with his year as a lecturer in the Department of Theoretical Chemistry. I attended his lectures avidly, and was immediately struck by his clarity of thought, precision of expression, and immaculate presentation on the white-boards despite his left-handedness! He moved on the following year to the University of Bristol, and it was there that I contacted him four years later to enquire about the possibility of working with him. The first year in 1972 / 73 was unfunded, and I was very much on probation. I spent a good deal of time initially on reading-up the history and mathematical background of the Barnett-Coulson expansion which was to be at centre-stage for the years that followed. Both these individuals had spent some part of their career at Kings College London, as had I, and this soon engendered in me a strong commitment to their legacy. Both their careers were exceptionally varied and make very interesting reading.

Please click links below to read and / or print further details about MPB and CAC:



C A Coulson obituary (Daily Telegraph)

Joe Gerratt's funding application to the SRC (Science Research Council) in 1972 / 73 makes very interesting reading and I apologise for the intrusive spill-marks that I haven't been able to cover-up entirely. This document emerged quite late in the history of the project but provides an excellent context for the work that was done.

Please click here to read and / or print the SRC Funding Research Application

Papers I - V were written during 1978 / 79. Paper VI wasn't completed until 1984 (although the section on the use of symmetry had its genesis in a brief paper written at Joe Gerratt's request back in 1974 and endlessly rewritten to meet his exacting requirements! It was eventually submitted to Mol. Phys. but was rejected, I think for lack of evidence for computational utility.

Writing-up a research project in ones spare time, whilst working for a living and helping to bring up a young family, is no mean feat. I'm well aware that there are some rough edges showing, particularly as regards the literature citations, but I've made no attempt to rectify this. These are personal testaments frozen in time and should be left as such.

Paper VI differs from the earlier Papers in that in some places it is more of a research progress report than a polished summary of work fully accomplished.

The original manuscripts were handwritten in pencil (though just a few pages were typed) on A4 paper. They have now been scanned on a Hewlett Packard Deskjet 3050, after careful experimentation with settings, and output to bitmap image (bmp) files. These were amalgamated to pdf files, one for each Paper, using the AVS Image Converter program. The FileZilla FTP Client software was then used to transmit the pdf files to the Web Developer's home server for incorporation into the website.

There is no doubt that Joe Gerratt thought very highly of this work. In a letter of recommendation to my first employer (who showed it to me) Joe said (and I'm quoting from memory) "There are not another dozen people in the world who could have done what Dr Waddell has achieved".

And this despite the undeniable incompleteness of the project, insofar as the computation of vibrational force-constants for 3-dimensional polyatomics was admittedly still just out of sight.

So, not entirely an ego-trip. My intention is simply to get this stuff into the public domain by giving it a pedigree, an endorsement from a theoretical chemist of great erudition and wide reknown in the quantum chemistry community.

But if you make use of it, I would appreciate an acknowledgement!

Following hallowed tradition I titled the series of manuscripts

"New developments in the Barnett-Coulson method
for calculating molecular integrals"

and their individual titles are itemised below.

Please click on the manuscript item you wish to read and / or print.

I.Expansions and transformations.
II.Further expansions and transformations;
Ancillary techniques and basic integrals.
III.One- and two-centre matrix elements
for overlap and related operators.
IV.One- and two-centre potential functions;
two- and three-centre nuclear attraction integrals.
V.One-, two- and three-centre integrals of the regular and irregular solid cubic harmonics;
Cartesian fields and multipole moments.
VI.One-, two-, three- and four-centre electron repulsion integrals;
Associated transformations over two and four indices.