Can Quantum Mechanics Account for Chemical Structures?

  • Anton Amann


In quantum mechanics, there is no fundamental understanding of chemical structure: though chemical structures can be imposed on quantum-chemical calculations, there are many “strange” quantum states which do not fit at all into the world of chemical structure formulas. Such “strange” quantum states are usually notated as superpositions of states having chemical structure, e. g., as superpositions of two different isomers.

Most molecular species can be expected to possess a nuclear structure, whereas for some, e. g. ammonia or monodeuteroanlinine, the issue is not so obvious. The ammonia-MASER transition, for example, is thought to be a transition between “strange” molecular (pure) states not admitting a nuclear structure. Since one cannot sharply distinguish between molecular species “admitting strange (pure) states” and such which do not, it is plausible that all molecules can in principle be prepared in such strange (pure) states, but that the latter do not play an important role for most molecular species (with exceptions such as ammonia, for example). This suggests that chemical classical concepts-e. g. chirality, knot type and nuclear structure of molecules-are not strictly classical in the sense that superpositions between different structures are strictly forbidden. Such superpositions may still arise but are unstable under external perturbations and therefore usually not observed. Instability of “strange” states is thought to increase with increasing nuclear masses or with decreasing level splitting between the low lying eigenstates of the molecular hamiltonian, as, for example, in the sequence of species {monodeuteroaniline → ammonia → naphthazarin → ... → sugar/amino acid}. In other words: chemical classical structures are fuzzy, because “strange” superpositions-not compatible with classicality-are still admitted. But the fuzzyness of such classical structures decreases with increasing nuclear masses (because strange states “die out”).

It is quite hard to substantiate these heuristic ideas by rigorous conceptual and mathematical reasoning. The most important conceptual problem in this respect is that a density operator (non-pure state) cannot uniquely be decomposed into pure states. Hence in traditional statistical quantum mechanics different decompositions of, say, a thermal density operator D β are considered as being equivalent. Nevertheless different decompositions of a given thermal density operator can refer to entirely different physical situations, as, for example, to molecules with or without nuclear structure.

This implies that there is no fundamental understanding of chemical classical concepts. In particular, the fascinating idea of a chemical molecular structure, invented in traditional chemistry and taken over in the Born-Oppenheimer scheme of quantum chemistry, is not fully understood.

Here an attempt is made to adapt the quantum-mechanical formalism for these problems: A canonical decomposition of thermal density operators-stable under external perturbations-is introduced opening a way
  • to understand the concept of chemical structure,

  • to derive and study deviations from chemical structures in the sense that “strange” quantum-mechanical superpositions of different chemical structures appear for certain molecules like ammonia,

  • to get a deeper understanding of the Born-Oppenheimer approximation,

  • to make first steps towards a fully quantum-mechanical explanation of the stochastic aspects in single-molecule spectroscopy.

It is enormously interesting to understand the traditional chemical concepts in the light of quantum mechanics. Such an understanding inevitably leads to studying the “fuzzy” quantum deviations from classical chemical behavior. These quantum deviations are described here by large-deviation techniques and by stochastic dynamics on the set of pure states of a quantum system. A relatively simple example for such a stochastic dynamics is discussed in detail. Furthermore a large-deviations entropy is presented, describing the quantum fluctuations of a Curie-Weiss magnet around classical behavior. For molecules it is not yet possible to calculate large-deviation entropies describing quantum fluctuations around the classical behavior (the latter arising in the limit of infinite nuclear masses), but the Curie-Weiss example discussed here gives a good idea about the similar conceptual problems with molecules.


Thermal State Pure State Density Operator Stochastic Dynamic Chiral Molecule 
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© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Anton Amann
    • 1
  1. 1.Laboratorium für Physikalische ChemieETH ZentrumZürichSwitzerland

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