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23 Jan 2024
updated 23 Jan 2024

Paper 0 (Symmetry), 1974

As already mentioned in Manuscripts / PostDoc I did make strenuous efforts, during the first quarter of 1974, to produce a brief paper (sufficiently punchy, succinct and stylish to satisfy Joe Gerratt's exacting requirements!) on the use of point-group symmetry to utilise symmetry-equivalence of molecular integrals whenever possible rather than heavy computation. And indeed, the program could also generate its own point-groups from the bare minimum of generic elements, using some rather ingenious 3D geometric formulae, though I think that came later. The really big deal, though, was that it took into account the behaviour of vector or tensor operators, and was totally relaxed about fractional rotational coefficients.

It was a huge distraction from the task in hand of getting the Model T version of the program on the road, and the time lost was later to cost me dearly. It was a big risk, and when the editor of Mol Phys bounced it back for revision I didn't bother with it any further.

Please click here to read and / or print the Mol Phys editorial response

(I seem to have mislaid the referee's annotated original manuscript referred to in Ian Mills' letter, but I think the major complaint related to lack of evidence for computational utility.)

Papers I — V, 1978 - 1981

The following sequence of extracts covers all six of the letters I received from Joe Gerratt after I left Bristol. Additionally, we met on several occasions during this period to hand over, or hand back, the various manuscripts rather than entrusting them to the post! And of course he rang me from time to time.

Joe's total enthusiasm, determination, commitment and involvement with the manuscripts I gave him and the somewhat incomplete program I bequeathed him emerge very clearly from these letters, and are all the more remarkable when one remembers all his other teaching, research and family activities. He always gave 100% to everything he took on, and never accepted anything less than perfection in what he or his research students achieved.

In the first letter from Joe, dated 30 November 1977, he said

"This is just a note to enquire about the progress of your promised write-up of your Barnett-Coulson integral package work. When do you think you will be able to let me have a copy? As you know, I think this is good work and I'm anxious for us to publish something together.

"In particular, I wonder if you could let me have a copy of your notes of the work on the zeta function power series expansion ... Our work on using the B-C expansion to transfer vibrational wave-functions from one coordinate system to another seems to be going well so far. For zeta functions up to [the order of] 40 I think that [this] expansion is probably the answer."

Please click here to see a passworded copy of the letter JG 30 Nov 1977

In the second letter from Joe, dated 6 April 1978, he said

"I've had a first look at the material you gave me yesterday. I realise that we were talking at cross-purposes! Originally you said that you would write up a complete report, and leave it to me to extract material for publication. However you have written up several complete papers!

"The work is very impressive. I think we should submit papers I and II to Phil Trans Roy Soc. They accept long articles of this nature. We could do it via (PB) at Daresbury: he has just been made an FRS, and I'm sure he would appreciate this kind of work. I could give it to (ED) to type out, but if (SW) is willing to do it, I'm sure that this would be much quicker."

Please click here to see a passworded copy of the letter JG 6 Apr 1978

In the third letter from Joe, dated 10 July 1978, he said

"(ED) has finished typing the first of the papers, and I took it up to Daresbury last week to show (PB) and ask whether he would submit it to Phil Trans Roy Soc for us. He said he wants to read it through first, but otherwise — yes, he would. I think he was rather impressed by it, actually.

"My purpose in writing to you is twofold. First of all to express my appreciation of all the work you put [into] producing these two papers. I've read them both through a couple of times, and I do feel very impressed by the immense amount of material. They also read very well: I usually have a very strong urge to rewrite things, but this is not the case here! ...

"The second (and more practical) purpose is to point out that Table 2 is missing in both papers. You told me that you have relevant numbers — could you send them to me please? (ED) is now well into Paper II, and I'd like to complete I as soon as possible and send a copy to (PB).

"Could you also jot down a short description of what the major routines do in your program? We've got the funding for a post-doc now, and an advert should appear in 'Nature' any week. I expect that when and if the person starts work, we'll come over to see you to talk to you about the program. (SW) is keen to get it to run at Daresbury. He hasn't much faith in (XX)'s Gaussian packages!!

"Thank you once more for your tremendous effort. ..."

Please click here to see a passworded copy of the letter JG 10 Jul 1978

After this letter there was no further mention of publication in Phil Trans Roy Soc, so presumably (PB) had decided not to sponsor Papers I and II after all.

In a letter to Joe dated 21 August 1978 I said

" ... The present state of the series is as follows:

"Papers I and II you have.

"Paper III 'One- and two-centre matrix elements for overlaps & related operators' is complete and ready for collection.

"Paper IV 'One- and two-centre potential functions; two- and three-centre nuclear attraction integrals' is also complete and ready for collection.

"Paper V 'One-, two- and three-centre integrals of the regular and irregular cubic harmonics; cartesian fields and multipole moments' is in preparation.

"Paper VI 'One-, two-, three- and four-centre electron-repulsion integrals; associated transformations over two and four indices' has not yet been started."

There is nothing to be gained by releasing a copy of the letter RW 21 Aug 1978

Sometime in the early spring of 1980, Joe sent me photocopies of two letters from William Montgomery, Physics Editor for the North-Holland Publishing Co. who were evidently willing to publish "an article on 'New Developments in the Barnett-Coulson Method for Calculating Molecular Integrals" in their journal Physics Reports — certainly a modest step in the right direction, though Joe's subsequent letter said that they'd be happy to publish the whole series!!!

Please click here to see a copy of the letter WM 10 Dec 1979
Please click here to see a copy of the letter pp WM 9 Jan 1980

In the fourth letter from Joe, dated 19 March 1980, he said

"... Since hearing from Montgomery, I have received a detailed report from two referees sent to me by the editor, Professor McDowell. The referees (I am reliably informed!) were Vic Saunders and Brian Sutcliffe. Most of their comments were just picking up odd 'nits', eg missing cross-references etc. However their one major comment was to suggest a reordering of some of the material, so that one could follow a particular type of integral through.

"I am not sure about this, and will want to think carefully about it. My feeling is that what is needed is perhaps an expanded introduction, stating explicitly how the sections are organised, and in particular saying that we do expect the reader to be familiar with Barnett's 1963 article.

"In any case, the upshot of this is that Papers I and II are still not in their final form. As soon as this is done, I will certainly send you a copy of the final manuscript. Meanwhile let me assure you that all your alterations have been incorporated. ...

"Your card decks are certainly not in the way. As a matter of fact, I want to get a copy of them onto disk and tape, and also a listing of the source. The deck is the only source I have and it is ageing. In time it will become unreadable — so I want to get this copying done as soon as I can. Do you want a tape copy?

"Meanwhile the one-electron properties package seems to be running quite well. What I would like to know is: would you send me a listing of the programs (or link-edit + input) to generate the constants files? I would like to feel that if these were ever erased by mistake I could regenerate them if necessary!

"McDowell indicated that he would accept the whole series of papers, but I and II are enough for everyone at present. As soon as we've got these finally out of the way, I'll turn my attention to the others. Hopefully this will be fairly soon.

... [Major medical issue indicated for JG]"

Please click here to see a passworded copy of the letter JG 19 Mar 1980

In the fifth letter from Joe, dated 2 June 1980, he said

"... I'm glad to say that I have now completely recovered. I've taken up the Barnett-Coulson papers again and hope that publication day will — at last — be in sight.

"I enclose the comments of the referees. Please do not upset yourself over them. The 'major changes' asked for really come down to inclusion of Papers III and IV. This I have now done. (ED) is in the toils of typing them out. I am myself in the midst of the various minor corrections detailed by Sutcliffe, and I have rewritten the Introduction to Paper I. I [will] send you a draft. You will see that what I've done is to talk about the problem more generally, before getting down to the details further on. In particular, the introduction should now serve for the series as a whole. McDowell has agreed to this, but the whole lot (I-IV) will go back to the referees. I am sure it will be alright this time!!

"You did say that you wanted to discuss Paper V. I'll be glad to come over and see you. Do you have a manuscript ready? Please let me know when it is convenient.

"Did you manage to root out for us the link-edit + main program for generating the integral constants? Disasters occasionally occur on disks — and we would like to be able to regenerate the constants if it should prove necessary"

Please click here to see a passworded copy of the letter JG 2 Jun 1980

and here to see a copy of the referees' comments1 on Papers I and II

and here to see a copy of Joe Gerratt's new collective Introduction

Please note that the referees are working from the typescripts rather than the manuscripts, so the paginations are likely to differ considerably.

In the sixth and final letter from Joe, dated 16 August 1981, he said

"... I have been doing a great deal of work, both on the Barnett-Coulson papers and on the program, and I would be very grateful indeed for your help at this stage.

"The papers [I — V] are all in a good state. I haven't been able to work on them until this last couple of months (for reasons which I shall explain below). I have thoroughly familiarised myself with all the material, and this has enabled me to answer the referee effectively.

"In particular, I have rewritten the section on rotations in Paper I to emphasise the convention you actually adopted is the same as that of Wigner and of Fano & Racah — but not that of Brink & Satchler and of Messiah. Edmonds is supposed to be the same as Wigner, but gets some things wrong, so I've down-pedalled on him. Furthermore, I have checked all the formulas against Wigner and Fano & Racah, and they all agree exactly. Which I think clinches the argument.

"I've re-worded bits of [Paper] II, again to emphasise, from Table 2, what a difference the Shanks-Wynn transformation makes.

"Papers III, IV and V are more or less OK as they stand. The major item missing is a table of sample integrals for each of the types of operators discussed. I have run the program for an h3O basis set with 1s, 2s, 2p, 3d on O and 1s on H for multipole moments — and that seems OK.

"I haven't yet run the RGRADE [module] for irregular solid harmonics — but I feel so familiar with the program that I don't anticipate much trouble.

"However I would be very grateful for some sample output for each of these types of operators — with the link-edit part: it's hard to reconstruct exactly what is needed with the 'LET' option as you have done. ...

"I have come unstuck with the TWOL [module] for multi-centre 2-electron integrals. I realise that this is something you haven't finished. The program fails in routine FRACTN which is supposed to fit the AA and AB potentials by continued fractions. The points x which should be kept in the array DUMMY(20) in COM001 in routine ELEC2C (for example) have not been assigned. This was something you were in the process of altering to use least-squares fitting. Would you please send me your notes on this — I am sure that I could carry out the necessary updates.

"It is important to have an alternative to STEVENS for a multicentre program — I can convert it for the CRAY machine at Daresbury.

"Finally, I would be grateful for a listing of the source to compare with mine. I copied the decks onto disk, as [they] were getting elderly. There seems to have been some mix-up with the routines GFUNCN and HFUNCN so I only have the object files for these.

"Completion of all this work has been hampered by all kinds of outside factors [major medical issues indicated for both JG and ZG] Also (GD) left in the middle of last year — and we had to take over his lectures. (GC) has been on sabbatical — so we were two people short.

"But I've been determined to finish the job over the summer. Please do reply as soon as you can — I can probably finish this all off over the next month before term begins. This has been a sizeable chunk of work out of both our lives, and it should be properly completed. In any case, I do feel that people are beginning to listen to the advantages of STO's — particularly the electron-molecule scattering group at Daresbury for whom Gaussian functions are quite wrong."

Please click here to see a passworded copy of the letter JG 16 Aug 1981

As far as my records show, this was the last letter that I ever received from Joe. I wrote him two further letters, dated 16 November 1981 and 11 December 1981, concerning the problems he'd mentioned in this letter and had also called me about.

And as far as I can tell, Papers I — V (let alone Paper VI) have never appeared in print, whether in Physics Reports or anywhere else.

Why didn't I grasp the nettle and get back to Joe to ask how the publication was progressing? After all, he'd said in his sixth letter that the Papers I — V were all in good shape. The stocks were sold, the Press was squared, the Middle Class was quite prepared ...

I don't really know. The underlying reason was that I was too embarrassed to do so, knowing that he and his wife had both been very seriously ill, and feeling that a pushy enquiry of this nature would be inappropriate. Another factor was the increasing remoteness of academic life and its ethos — the equally skewed world of corporate life was now the dominant factor in my daily life. But a subtler reason is also discernible in retrospect: by the mid 1980's my midlife crisis was in full swing, and I had become totally caught up by the fitness craze and was regularly involved in a great diversity of recreational sports, particularly long-distance running (serious 26.2 mile marathon events), and I began to feel that university life had been a bit of a vainglorious snare and a delusion, had ended messily, and was best forgotten.

1: A lot of the substantive comments related to missing literature references, missing textual cross-references, incomplete tabulations etc., that I had hoped would have been cleared up for me in the preparation of the typescripts. But what really stung was the dismissive attitude towards the Shanks transformation that was central to my advocacy of the Barnett-Coulson method as a competitive methodology for multicentre integrals. I'd successfully evaluated its effectiveness in regard to a number of well-known infinite series for standard functions, the very first in fact having been the notoriously slowly-convergent Gregory series for π, and you may be interested to visit the Wikipedia page for this very instance.

Paper VI, 1984

I did however complete Paper VI (well, with the usual ragged edges as regards the references) and this time posted a photocopy to Joe rather than handing it over in person. I certainly didn't make personal contact with him about it. On and off it had been about five years in gestation, and towards the end I had of course no real faith that it was going to make any impact back at base. It did however contain an improved and extended version of Paper 0 on the use of symmetry, but by this stage in history that was no longer cutting-edge.

Enter the Internet

Even in the most reactionary business corporations the internet eventually invaded the workplace, and one lunch-time in mid 1999 I idly googled Joe Gerratt's name, to see what he'd been up to over the past few years. It was a terrible shock to discover that he had died two years earlier. For several minutes I just couldn't bring myself to believe it. Even now I feel deeply emotional to think about it. He had been a wise and benevolent mentor, so extraordinarily clever and yet so down to earth, such a raconteur, with such a pithy turn of phrase, and with such deep cultural roots in his own background, his scientific relationships abroad, and of course his family connections. You don't meet many people like Joe in the course of a lifetime.

The reasons for non-publication of this Barnett-Coulson work may well have been complex, and in any case will almost certainly never emerge. It's all too long ago. However I am making every effort to ascertain what would have happened to the typescripts for Papers I to V, and to the source code upon which Joe also worked so assiduously. They were both part of his intellectual property at the time of his death, so should certainly have been respectfully archived somewhere.

And if and when I might be permitted an unrestricted copy of them, I shall have enormous pleasure in putting them into the public domain on this website!