An exceedingly effective and inexpensive two-step, fourteenth-order phase-fitting method for solving quantum chemical issues

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-01-10 DOI:10.1007/s10910-023-01560-x

Marina A. Medvedeva, T. E. Simos

引用次数: 0

Abstract

In order to get rid of the phase-lag and its first, second, third, fourth, and fifth derivatives, a phase-fitting method might be applied. The new strategy, called the economical method, maximizes algebraic order (AOR) while minimizing function evaluations (FEvs). Equation PF5DPFN142SPS describes the unique method. An infinitely periodic P-Stable technique is suggested. The proposed method is applicable to numerous problems with periodic and/or oscillatory solutions. In quantum chemistry, this novel approach was used to address the challenging problem of Schrödinger-type coupled differential equations. It is an economic algorithm because each step of the new method only costs 5FEvs to carry out. This helps us to improve our existing condition significantly by achieving an AOR of 14.

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解决量子化学问题的极为有效且成本低廉的两步十四阶相位拟合方法

为了消除相位滞后及其第一、第二、第三、第四和第五次导数，可以采用相位拟合方法。这种新策略被称为 "经济法"，在最大化代数阶（AOR）的同时，最小化函数求值（FEvs）。公式 PF5DPFN142SPS 描述了这种独特的方法。提出了一种无限周期的 P-Stable 技术。所提出的方法适用于许多具有周期性和/或振荡解的问题。在量子化学中，这种新方法被用于解决薛定谔型耦合微分方程这一具有挑战性的问题。这是一种经济算法，因为新方法的每一步执行成本仅为 5FE。这有助于我们显著改善现有条件，使 AOR 达到 14。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Chemistry 化学-化学综合

CiteScore

3.70

自引率

17.60%

发文量

105

审稿时长

6 months

期刊介绍： The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches. Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.