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The London Edinburgh and Dublin Philosophical Magazine and Journal of Science

III. An unsolved problem in the application of the quantum theory to chemical reactions

William C. Lewis

Published Jan 1, 1920• 17 citations
Publisher

Abstract

  1. 1.On applying the quantum theory to a unimolecutar chemical reaction, it is shown that very different results are obtained according as we assume the continuous or discontinuous view of the abso...
DOI
10.1080/14786440108636014

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Finding optimal pathways in chemical reaction networks is essential for elucidating and designing chemical processes, with significant applications such as synthesis planning and metabolic pathway analysis. Such a chemical pathway-finding problem can be formulated as a constrained combinatorial optimization problem, aiming to find an optimal combination of chemical reactions connecting starting materials to target materials in a given network. Due to combinatorial explosion, the computation time required to find an optimal pathway increases exponentially with the network size. Ising machines, including quantum and simulated annealing devices, are promising novel computers dedicated to such hard combinatorial optimization. However, to the best of our knowledge, there has yet to be an attempt to apply Ising machines to chemical pathway-finding problems. In this article, we present the Ising/quantum computing application for chemical pathway-finding problems. The Ising model, translated from a chemical pathway-finding problem, involves several types of penalty terms for violating constraints. It is not obvious how to set appropriate penalty strengths of different types. To address this challenge, we employ Bayesian optimization for parameter tuning. Furthermore, we introduce a technique that enhances tuning performance by grouping penalty terms according to the underlying problem structure. The performance evaluation and analysis of the proposed algorithm were conducted using a D-Wave Advantage system and simulated annealing. The benchmark results reveal challenges in finding exact optimal pathways. Concurrently, the results indicate the feasibility of finding approximate optimal pathways, provided that a certain degree of relative error in cost value is acceptable. Published by the American Physical Society 2024
Abstract It has been shown in a previous paper that classical mechanics are not adequate to treat the transition of a hydrogen atom or proton across an energy barrier of the dimensions commonly met with in chemical reaction. The treatment given was based on an exact solution of the Schrödinger equation and a type of potential curve having no discontinuities in slope, but owing to the laborious nature of the computations involved, no attempt was made to investigate quantitatively the effect of variations in the heat of activation, the width of the barrier, or the mass of the particle. The present paper describes an approximate treatment leading to simple equations which can be applied directly to investigate these points. In a recent paper, Wigner has given a method of treatment applicable to any form of potential curve. His final equations are, however, only valid for the case in which the difference between the quantum mechanical and classical results can be expressed as a small correction term, and cannot be applied when there are large deviations from classical behaviour.
A continuing and important problem in modeling physical processes deals with creating optimum calculation algorithms. These algorithms should provide the necessary precision yet not demand a lot of storage and time for evaluations. In the present paper the numerical integration of the non-stationary Schrödinger equation (NSSE) is considered. There are many numerical methods of integration of this equation to the present moment. In this paper, we explore the split-operator method (SOM) and consider a way of lessening time computing expenses in view of specificity of the given method. We also consider the choice of optimum discretization steps in coordinate and momentum space. The computer application that we outline is applicable, in method and preparation, to the solution more difficult problems, and it has been applied to simple chemical reactions. We use standard atomic units to simplify equations in the analysis that follows.