Revisiting the von Neumann–Wigner noncrossing rule and validity of a dynamic correlation diagram method

Hiroyuki Nohira,Toshiyuki Nohira

doi:10.1142/s0219633619500135

Hiroyuki Nohira, Toshiyuki Nohira

Open Access

https://doi.org/10.1142/s0219633619500135

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Abstract

The noncrossing rule for potential energy surfaces can be applied only, as originally postulated by von Neumann and Wigner, to slowly occurring changes; it has, however, over many years, been widely used to rationalize fast chemical reactions. Taking the conversion of Dewar benzene to benzene as an example, we demonstrate a reaction that has a timescale for which crossings are allowed. Since it is now established that elementary chemical reactions proceed over ca. 10–100[Formula: see text]fs, as revealed experimentally by Zewail, the noncrossing rule cannot any longer be said to be valid for most chemical reactions. We further demonstrate that the mechanism of the chemiluminescent conversion of Dewar benzene to benzene is explained by an electronic state diagram derived using a dynamic correlation diagram method which allows crossings, whereas the reaction is not explained by a conventional approach, applying the noncrossing rule using a static correlation diagram method.

Highlights

In our previous study,[1,2] we demonstrated that Fukui's frontier orbital (FO)theory[3,4] and Woodward–Ho®mann's orbital symmetry conservation theory (W–H theory)[5,6,7] can be unied consistently by using the dynamic correlation diagram method which is not restricted by the noncrossing rule
It has been long unheeded that von Neumann and Wigner themselves pointed out that the noncrossing rule is not applicable for changes occurring within very short times
We have demonstrated, taking the conversion of Dewar benzene to benzene as an example, that the timescale for this reaction exactly corresponds to the case in which the crossing is allowed

Summary

Introduction

Theory[3,4] and Woodward–Ho®mann's orbital symmetry conservation theory (W–H theory)[5,6,7] can be unied consistently by using the dynamic correlation diagram method which is not restricted by the noncrossing rule. This is an Open Access article published by World Scientic Publishing Company. For many researchers in theeld of theoretical chemistry, it would be very di±cult to accept that the noncrossing rule is invalid in the theory of quantum molecular dynamics. It is not widely known, von Neumann and Wigner provided a very important discussion on the applicability of the noncrossing rule in their paper; they clearly stated: \the wave function has no time to change in the case that the electron state changes very fast".8. We demonstrate that the mechanism of this reaction including chemiluminescence is explained clearly using an electronic state diagram derived from the dynamic correlation diagram method; whereas, an explanation of the reaction is not possible by conventional approaches such as using potential energy surface analysis or via a static correlation diagram method in which the noncrossing rule is applied

Theoretical Basis

Verication of the criteria: A case of reaction from Dewar benzene to benzene

Previous studies on the correlation diagrams

Comparison between the static and dynamic correlation diagrams

Potential energy prole

Conclusion