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Revisiting the Schrödinger Equation in Molecular Reaction Dynamics and a New Perspective of Quantum Chemistry

Hiroyuki Nohira, Toshiyuki Nohira

Published Jun 30, 2025• 0 citations

Abstract

The applicability of the time-dependent Schrödinger equation to molecular reaction dynamics is discussed from several perspectives. First, with reference to Schrödinger's original paper, we point out that he himself stated that what is now called the time-dependent Schrödinger equation is insufficient to solve the problems of non-conservative systems like chemical reactions. Second, the detonation velocity of some explosives has been demonstrated as a new parameter that directly illustrates the timescales of elementary chemical reactions. The calculated values of ~30 fs are in good agreement with the timescale of 10–100 fs for chemical reactions, as experimentally demonstrated by the Nobel laureate Zewail. Third, we consider the state of an electron in a box when the length of the box suddenly increases from L to 2L, which is often found in textbooks as the simplest example of the application of the time-dependent Schrödinger equation to chemical reactions, and highlight the inconsistency between this model and an actual chemical reaction. Finally, we re-iterate that only quantum steady states can be accurately described by the Schrödinger equation and that it is the most natural to connect changes between adjacent quantum steady states by the variational principle.

DOI: 10.26434/chemrxiv-2025-1mjtr

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