{"title":"解决化学问题的高效、复杂的十四阶相位拟合方法","authors":"Marina A. Medvedeva, T. E. Simos","doi":"10.1007/s10910-024-01636-2","DOIUrl":null,"url":null,"abstract":"<div><p>Applying a method with vanished phase–lag might potentially eliminate the phase–lag and its first, second, and third derivatives. Improving algebraic order (<i>AOR</i>) and decreasing function evaluations (<i>FEvs</i>) are the goals of the new strategy called the <b>cost–efficient approach</b>. Equation <i>PF</i>3<i>DPHFITN</i>142<i>SPS</i> demonstrates the unique method. The suggested approach is <b>P–Stable</b>, meaning it is indefinitely periodic. The suggested approach is applicable to a wide variety of periodic and/or oscillatory issues. The challenging problem of Schrödinger-type coupled differential equations was solved in quantum chemistry by using this novel approach. Since the new method only needs 5<i>FEvs</i> to run each stage, it may be considered a <i>cost–efficient approach</i>. With an AOR of 14, we can significantly improve our present predicament.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A very efficient and sophisticated fourteenth-order phase-fitting method for addressing chemical issues\",\"authors\":\"Marina A. Medvedeva, T. E. Simos\",\"doi\":\"10.1007/s10910-024-01636-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Applying a method with vanished phase–lag might potentially eliminate the phase–lag and its first, second, and third derivatives. Improving algebraic order (<i>AOR</i>) and decreasing function evaluations (<i>FEvs</i>) are the goals of the new strategy called the <b>cost–efficient approach</b>. Equation <i>PF</i>3<i>DPHFITN</i>142<i>SPS</i> demonstrates the unique method. The suggested approach is <b>P–Stable</b>, meaning it is indefinitely periodic. The suggested approach is applicable to a wide variety of periodic and/or oscillatory issues. The challenging problem of Schrödinger-type coupled differential equations was solved in quantum chemistry by using this novel approach. Since the new method only needs 5<i>FEvs</i> to run each stage, it may be considered a <i>cost–efficient approach</i>. With an AOR of 14, we can significantly improve our present predicament.</p></div>\",\"PeriodicalId\":648,\"journal\":{\"name\":\"Journal of Mathematical Chemistry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-07-03\",\"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/s10910-024-01636-2\",\"RegionNum\":3,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Chemistry","FirstCategoryId":"92","ListUrlMain":"https://link.springer.com/article/10.1007/s10910-024-01636-2","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
A very efficient and sophisticated fourteenth-order phase-fitting method for addressing chemical issues
Applying a method with vanished phase–lag might potentially eliminate the phase–lag and its first, second, and third derivatives. Improving algebraic order (AOR) and decreasing function evaluations (FEvs) are the goals of the new strategy called the cost–efficient approach. Equation PF3DPHFITN142SPS demonstrates the unique method. The suggested approach is P–Stable, meaning it is indefinitely periodic. The suggested approach is applicable to a wide variety of periodic and/or oscillatory issues. The challenging problem of Schrödinger-type coupled differential equations was solved in quantum chemistry by using this novel approach. Since the new method only needs 5FEvs to run each stage, it may be considered a cost–efficient approach. With an AOR of 14, we can significantly improve our present predicament.
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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