Andre Julg - interview concerning : Early Ideas in the History of Quantum Chemistry.

After having finished my studies at the E.N.S. (Ecole Normale Supérieure) and at the Faculté des Sciences de Paris, I contacted in October 1952 the small Theoretical Chemistry group formed by Mr. and Mrs. Pullman and G. Berthier in order to prepare a thesis. In that period the non-benzenoid aromatic hydrocarbons were under study in that laboratory. As for most parts of work being performed in Theoretical Chemistry, the method in use was the one of Hückel (1). The introduction, on the one part, of the configuration interaction (CI) and, on the other, of the SCF Roothaan method incited the Pullmans to leave the simple Hückel area in order to see what these new techniques could bring to our research work. Berthier was charged to study fulvene, reduced to its 6 pi-electrons, by the SCF. method while I myself was directed to apply CI on the same molecule, starting from the Hückel functions, the only ones which were available at that time.

The work of Berthier (2) was conclusive for the dipole moment but the transition energies remained overestimated. Contrary to this, the CI proved disappointing. Independently of the extensive calculations which I did nearly all by hand, having at my disposal only occasionally a Peerless electromechanical calculator - the values obtained showed transition energies which oscillated in a disconcerting manner versus the number of configurations introduced (3). From which the decision in October 1953 to tackle azulene by means of the SCF method which had given good results for fulvene, at least in what concerned the dipole moment. Let me remind in this context that the Hückel method gives for this molecule a dipole moment which is too high, all the carbon atoms of the pentagonal ring being charged negatively while the others are positive.

The work was considerable: 10 pi-electrons, that was the largest SCF calculation ever attempted. More than 4500 two-electron integrals had to be calculated. And more, the non-orthogonality of the 2pz atomic functions presented great difficulties in the calculation which necessitated the inversion of matrices of orders 4 and 6. And further on, in contrast to what had happened for fulvene, the iterations of the energy matrix not only didn't converge, but also diverged. More than 15 months of work at the rate of about 10 hours a day, without taking any holidays! Finally, at the cost of using mathematical tricks, I obtained the convergence ... and a good dipole moment (4). I found quasi-alternating net charges which was confirmed many years later by experiment. But the transitions were overestimated. On the other hand, the method of Pariser and Parr very rapidly gave me good results for the transitions of heptafulvene (5).

I submitted my thesis in 1955. In October 1957 I have been appointed Professor of Theoretical Chemistry at the Faculté des Sciences at Marseille. My first research works were running in parallel whith my teaching. In 1964 I published my teaching in the book entitled Chimie théorique (6). I wanted to present to my students a coherent statement of the methods of quantum chemistry, persuaded that there existed a deep connection between the SCF method which I considered as the absolute reference, and the Hückel method. The question was the more important since, in that period, it was quite out of question for the students, in the absence of computers, to use a method other than the Hückel one and even only for simple cases (See the book Exercices de Chimie quantique (7) published in collaboration with my wife).

Although I did not intend to speak of the method of Parr and Pariser, my first work was to reflect on the recipes of these authors, especially in order to obtain electron repulsion integrals reduced with respect to their analytical values. To me it became clear very quickly that the simple formula of Pariser for the one-center Coulomb integral obtained from the ionization energy I and the electron affinity A: J=I-A , has to be corrected by an additional term. J=I-A-epsilon(I+A), where epsilon=s/Z, s being the screening constant (0.35) and Z the effective nuclear charge of the orbital under consideration. At first I considered that the self-consistency between the atomic charges and the corresponding Z's was necessary. But then I had the pleasant surprise to see that the values obtained for the different atoms (e.g. C, N, O) and their ions corresponded to the theoretical values deduced from the analytic expression of the orbitals, provided that one utilizes an effective charge reduced by the factor lambda_0 (Z'=lambda_0*Z), the latter being the same for all the atoms of a given row ( e.g. 0.57 for C, N, O). This reduction arose from the electron correlation. From there the idea to use these reduced effective charges Z' to calculate the two-center integrals Jab (9). One obtained in this way a reduction factor lambda_ab=J_ab(Z')/J_ab(Z), depending on the nature of the atoms and on their internuclear distance (lambda being an increasing function of this distance, tending to 1 when the latter tends to infinity). Within an accuracy of some percent I obtained the same values as Parr and Pariser, which justified their empirical calculation procedure known under the name of the uniformly charged sphere approximation.

Using the Landshoff-Löwdin orthogonalization procedure, I showed that for the one- and two-center Coulomb integrals one obtained practically the same results as before orthogonalization and that all the other two-electron repulsion integrals could be neglected. I rediscovered the zero-differential overlap postulated a priori by Parr and Pariser and which has been later employed by the CNDO methods! If I had used this preliminary change of basis in my work on azulene, instead of 4500 integrals to calculate and above all, to handle, only a few dozen integrals would have remained to me!

Concerning the core integrals (A+,b2) where A+ is the potential created by the atom A without its pi-electron, and b the orbital situated on atom B, and whose value is not very different from that of the corresponding Coulomb integral J_ab, I postulated that the classically obtained value has to be reduced by the same factor lambda_ab as the integral J_ab. The same has to hold - this hypothesis being rather daring - for the terms (A+,ab) . In such a way, only a single empirical factor, namely which, in fact, one could expect to obtain via sophisticated calculations on atoms, would have to be introduced. That was the whole difference to the parametrization of Parr and Pariser (11) which referred to molecules selected for the circumstance.

Finally I have shown that the orthogonalization of the atomic orbitals had as a consequence the fact that the elements of the energy matrix corresponding to a pair of bonded atoms practically depend on the nature and on the distance of the atoms only, the other off-diagonal elements being very weak (6). That was the justification of the basic hypothesis of Hückel. Pedagogically, this result was for me very important because it allowed me to present the method with a solid theoretical support.

Furthermore I established a general relationship which connected the pi-bond index with the internuclear distance (12). The iteration of the distances allowed to obtain the geometry of the molecule.

All these hypotheses paid off at last. The obtained results for the charges, the dipole moment and the transition energies proved to be excellent. With my small group of researchers, we studied dozens of conjugated molecules (hydrocarbons of different types: ethylene-like, acetylene-like, aromatics, then carbonyl, nitrogen and sulfur derivates), always with the same success. Unfortunately, in all these years, having no computer at our disposal, we performed the calculations by hand with Frieden electromechanical calculators. US researchers, interested in the performances of our method, asked us for the listings. We could not satisfy their wishes and for a very good reason since we ourselves did not have any. Disappointed, they did not follow up their project of using our method.

On the other hand, I never was a good tradesman who knew how to sell his merchandise and to use good marketing strategies, as one would say nowadays. I ought to have made more publicity for my method and to have published in English and, most important of all, I ought to have presented myself on all the international congresses. But the physical difficulties I had in walking hindered me, let alone the problems I had with the English language. Anyway, if I would have been more clever, I would have found a more attractive name for the method. Instead I only called it plainly "Méthode L.C.A.O. améliorée" - improved LCAO method.

When we finally came into the possession of a small computer and although we undertook immediately to construct a general program, it was too late. In Paris, Strasbourg, Grenoble and Toulouse as well as in foreign countries there were already machines sufficiently capable to do SCF ab initio calculations or at the very least taking all the electrons of the molecule into account (e.g. the extended Hückel method). That tolled the passing bell for the empirical and semiempirical pi-electron methods. Extended CI became practicable, which allowed to obtain good transition energies without requiring the need to reduce the electron integrals (Let us recall that CI is a manner to introduce the electron correlation). From this time forth there was no place for us on the market. It became practically impossible to publish our results.

Thus died out the Méthode L.C.A.O. améliorée which had remained a Marseille specialty. I then turned to other problems (ionicity, color and adsorption power of crystals and minerals) while, in parallel, I became more and more interested in the interpretation of Quantum Mechanics. But does this mean that my researches were in vain? I do not think so. And that for two reasons. On one hand, they really brought valuable information concerning various series of molecules and especially, on the other - and there the conclusions will remain valid - my works showed the actual physical meaning of what one calls zero differential overlap (ZDO), and that the necessity to reduce the electron integrals to obtain good transition energies in the absence of CI Lastly my works brought out the justification for the Hückel method.

The Little Story of the Improved-L.C.A.O. Method. (in English)

Une page d'histoire : La méthode L.C.A.O.-améliorée(en francais)