Deterministic quantum mechanics: The role of nuclear motion


According to classical mechanics, objects exist in a specific place at a specific time. Conversely, in quantum mechanics, objects exist in a haze of probability. In relation to this, the application of the Schrödinger equation to the electronic structure in a molecule has led to the chemists’ picture of electronic energy surfaces on which nuclear vibration and rotation occurs and among which electronic transitions take place. To date, the Schrödinger equation has been incredibly successful in describing any kind of matter by treating the electronic structure quantum mechanically. The application of the Schrödinger equation to molecular motion was way less successful. Consequently, researchers have hypothesized on the probability that nuclear motion could be described classically. This notion has been triggered by the current development of highly sensitive modern experimental techniques that have enabled scientists comprehend better various molecular systems by observing them on the nanometer scale. In addition, noteworthy publications have shown that approaches such as ab initio molecular dynamics (AIMD) can be used to describe chemical reactions successfully. When one determines both nuclear motion and the electron cloud using differential equations, they obtain a purely deterministic model. Since the nuclear positions move classically, tunneling is always tunneling of the electron cloud.

The inversion of ammonia is often viewed as a typical example of nuclear tunneling. Another example of such phenomena are heat capacities, in particular those of the very light hydrogen molecule and of liquid water. By considering the above, German scientists from the University of Hanover: Stefanie Genuit, Florian Matz and Hedda Oschinski and led by Professor Irmgard Frank investigated the inversion of ammonia and the heat capacities of water and hydrogen. Their aim was to use conventional ab initio molecular dynamics (AIMD), which describes nuclear motion classically and the electron cloud using density functional theory. Their work is currently published in the research journal, International Journal of Quantum Chemistry.

The main focus of the research team in the study was to examine the phenomena that have traditionally been considered to be proofs that all phenomena are described by the Schrödinger equation. To achieve this, simulations of ammonia and a sample of 32 hydrogen molecules were undertaken. Simulations of water, where hexagonal ice structure was utilized, were also undertaken.

The authors reported that ammonia inversion was described perfectly by the tunneling of the p orbital through the molecular plane. Nuclear tunneling was not needed to describe this phenomenon. The team also pointed out that while the investigation of heat capacities was hampered by the brief simulation times and limited system sizes, they could nevertheless make some qualitative statements.

In summary, the study by University of Hanover researchers successfully described the simulation of ammonia inversion from first principles using a code that described nuclear motion classically. Fundamentally, they used AIMD as a powerful tool for asking the question of whether a classical treatment of nuclear motion is sufficient. Their simulation results showed electron tunneling through a wavefunction node while the hydrogen atoms followed this motion. In a statement to Advances in Engineering, Professor Irmgard Frank pointed out that indeed, based on their approach, the heat capacity can be frozen out in molecular dynamics simulations of solids, and hence, a quantized description is not required. As a result of treating the electronic cloud quantum mechanically and nuclear motion classically, a perfectly deterministic picture is obtained. From slightly different reaction conditions, different reaction products may result due to classical chaos. As Einstein claimed: God does not play dice.


Irmgard Frank, Stefanie Genuit, Florian Matz, Hedda Oschinski. Ammonia, water, and hydrogen: Can nuclear motion be described classically? International Journal of Quantum Chemistry 2020; volume 120:26142.

Go To International Journal of Quantum Chemistry

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