{"title":"An exceedingly effective and inexpensive two-step, fourteenth-order phase-fitting method for solving quantum chemical issues","authors":"Marina A. Medvedeva, T. E. Simos","doi":"10.1007/s10910-023-01560-x","DOIUrl":null,"url":null,"abstract":"<div><p>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 <b>economical method</b>, maximizes algebraic order (<i>AOR</i>) while minimizing function evaluations (<i>FEvs</i>). Equation <i>PF</i>5<i>DPFN</i>142<i>SPS</i> describes the unique method. An infinitely periodic <b>P-Stable</b> 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 <i>economic algorithm</i> because each step of the new method only costs 5<i>FEvs</i> to carry out. This helps us to improve our existing condition significantly by achieving an <i>AOR</i> of 14.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"62 3","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Chemistry","FirstCategoryId":"92","ListUrlMain":"https://link.springer.com/article/10.1007/s10910-023-01560-x","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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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.
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.
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