Molecular Conformation and Electronic Structure of Biomolecules

ELECTROWEAK QUANTUM CHEMISTRY AND THE DYNAMICS OF PARITY VIOLATION IN CHIRAL MOLECULES

Martin Quack ETH Zürich, Laboratory for Physical Chemistry, Wolfgang-Pauli-Str. 10, CH-8093 Zürich Switzerland

1 INTRODUCTION

In the introduction to his famous paper "Quantum Mechanics of Many Electron Systems" Paul Adrien Maurice Dirac wrote one of the most cited sentences in quantum chemistry:

"The underlying physical laws for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of complex atomic systems without too much computation".

It is remarkable that the second part of this statement, which forms a reasonable starting point for modern, approximate numerical quantum chemistry and computational chemistry is only rarely cited. The more frequently cited first sentence with the strong statement about understanding "the whole of chemistry" and the small restriction "the difficulty is only", which claims that the quantum physics of the first half of the 20th century contains all basic knowledge about chemistry, is the one that seems to be liked by many theoretical chemists and physicists. It turns out, however, that this statement is incorrect. There is at least one important part of chemistry, namely stereochemistry and molecular chirality, which can be understood properly only when including the parity violating weak nuclear force in our quantum chemical theory in the framework of what we have termed "electroweak quantum chemistry, completely and fundamentally unknown at the time of Dirac's statement.

Figure 1 summarizes the modern view of the origin of the fundamental interactions as publicized on the website of a large accelerator facility (CERN) According to this view, the electromagnetic force, which is included in the "Dirac-like" ordinary quantum chemistry, leads to the Coulomb repulsion, say, between two electrons in a molecule by exchange of virtual photons. In the picture the two electrons exchanging photons are compared to the ladies on two boats throwing a ball. If we do not see the exchange of the ball, we will observe only the motion of the boats resulting from the transfer of momentum in throwing the ball, and we could interpret this as resulting from a repulsive "force" between the two ladies on the boats. Similarly, we interpret the motion of the electrons resulting from "throwing photons as field particles" as arising from the Coulomb law, which forms the basis of ordinary quantum chemistry. The Coulomb force with the 1/r potential energy law is of long range. The other forces arise similarly. The strong force with very short range (0.1 to 1 fm) mediated by the gluons is important in nuclear physics but has only indirect influence in chemistry by providing the structures of the nuclei, which enter as parameters in chemistry, but there is otherwise usually no need to retain the strong force explicitly in chemistry. The weak force, on the other hand, is mediated by the W± and Z0 Bosons of very high mass (80 to 90 Daltons, of the order of the mass of a bromine nucleus!) and short lifetime (0.26 yoctoseconds = 0.26 x 10-24 s).

This force is thus very weak and of very short range (< 0.1 fm) and one might therefore think that similar to the even weaker gravitational force (mediated by the still hypothetical graviton of spin 2) it should not contribute significantly to the...