"We can calculate everything"

“This dogma of modern numerical quantum chemistry (Clementi, 1973) has its own origin in the following famous statement by P.A.M. Dirac (1929a) dating from the pioneer time of quantum mechanics: “The underlying physical laws necessary for the mathematical theory of a larger part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the application of these laws leads to equations much too complicated to be soluble.’‘ As we know today, this claim is not correct in at least two respects. Firstly, the formalism of pioneer quantum mechanics of 1929 is a very special case of modern (generalized) quantum mechanics which we now regard as fundamental for every theory of molecular matter. Secondly, the interpretative problems had not been solved in a satisfactory way in 1929. At that time, the conceptual problems of reducing chemical theories to the epistemologically very differently structured quantum mechanics were not discussed, and Dirac viewed the problem of reduction only as a very complicated mathematical problem.

The discovery of the electric nature of chemical forces by quantum mechanics took the valence problem out of its chemical isolation and made it accessible to an exact mathematical treatment. The last fifty years taught us a lot about the relation between chemistry and the Schrodinger equation, and have led to a penetrating understanding of chemical structures. Since the advent of electronic computers, numerical quantum chemistry has been a tremendous success. Nowadays we have a number of masterful analyses of electronic wave functions. Many calculations have been extremely sophisticated, designed by some of the foremost researchers in this field to extract a maximum amount of insight from quantum theory. For simple molecules, outstanding agreement between calculated and measured data has been obtained. Yet, the concept of a chemical bond could not be found anywhere in these calculations. We can calculate bonding energies without even knowing what a chemical bond is!

There is a danger to be sidetracked into purely numerical problems and to forget the original impetus of our enterprise: understanding the behavior of matter. We should not confuse a useful theoretical tool with theory. Numerical quantum mechanics is a most important tool for chemistry but it cannot replace thinking. The final explanation of empirical facts is not achieved by merely calculating measurable quantities from first principles. The ultimate objective of a theory is not to determine numbers but to create a large, consistent abstract structure that mirrors the observable phenomena. We have understood a phenomenon only when we can show that it is an immediately obvious and necessary part of a larger context. The vision of some theoreticians has been narrowed down to problems that can be formulated numerically. Some even take no notice of genuine chemical and biological patterns or deny them scientific significance since they are not computable by their methods. Such a one-sided view of numerical quantum chemistry is by no means the inevitable penalty for the attempt to reduce chemistry to physics. Rather, it is the result of the utilitarian character of contemporary research which lost all philosophical ambitions and has only a very restricted insight into its own limitations.

The important concepts of chemistry have never been well-treated by ab-initio quantum chemistry so that quantum mechanics has not become the primary tool in the chemist’s understanding of matter. Brute-force numerical quantum chemistry can hardly do justice to the qualitative features of chemistry. But without insight into the qualitative concepts we are losing chemistry. The allegedly basic methods often fail to illuminate the essential function of a molecule or a reaction that is evident to the experimental scientists. As a result practical chemists had to look for inspiration elsewhere and generated the ad-hoc semiempirical methods of quantum chemistry. This approach “has become a part of the chemical structure theory, which has an essentially empirical (inductive) basis; it was suggested by quantum mechanics, but it is no longer just a branch of quantum mechanics’’ (Linus Pauling, 1959, p.388). Despite the erudition, imagination and common sense used to create the semiempirical methods of quantum chemistry, the success of this craft remains a central enigma for the theoreticians. The models of semiempirical quantum chemistry are built upon an inadequate conceptual basis, and their mathematical foundation is so wobbly that they are a source of frustration. Moreover, they give us an image of matter that does not conform to what we are led to expect from the first principles of quantum mechanics. But experimentalists are not at all impressed by such scruples. And properly so.

Some contemporary theoreticians have attempted to narrow the scope of scientific inquiry by requiring operational definitions and first-principle underpinnings for all concepts. In theoretical chemistry, there is a distinct tendency to throw out typically chemical variables, admitting that they have served a noble purpose in the past but asserting that they are now obsolete. The premise underlying such a view is that the only valid meaning of any chemical concept is one which can be unequivocally defined in terms of present-day ab-initio quantum chemistry. This method of problem solving by rejection has been proposed for such concepts as valence, bond, structure, localized orbitals, aromaticity, acidity, color, smell, water repellence etc. A particularly powerful variant is the method of problem solving by dissolving definitions. Using this procedure we can easily solve even the “problem of life’’ by claiming that the distinction between living and non-living entities is a pre-scientific idea, obliterated by modern research. But some people consider such a line of action as unfair and shallow. We need a creative approach to the rich field of chemistry, not just a critical one that bids us to dismiss most problems of chemistry as meaningless. The task of theoretical chemistry is to sharpen and explain chemical concepts and not to reject a whole area of inquiry.”

– Hans Primas, Chemistry, Quantum Mechanics and Reductionism (1983) [emphasis mine]

Over thirty years old, but Primas’ critique of theoretical chemistry remains relevant.