On the application of the Rayleigh–Ritz method to a projected Hamiltonian

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2025-04-10 DOI:10.1007/s10910-025-01725-w

Francisco M. Fernández

引用次数: 0

Abstract

We apply the well known Rayleigh–Ritz method (RRM) to the projection of a Hamiltonian operator chosen recently for the extension of the Rayleigh–Ritz variational principle to ensemble states. By means of a toy model we show that the RRM eigenvalues approach to those of the projected Hamiltonian from below in most cases. We also discuss the effect of an energy shift and the projection of the identity operator.

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Rayleigh-Ritz方法在投影哈密顿量中的应用

我们将众所周知的瑞利-里兹方法（RRM）应用于最近为将瑞利-里兹变分原理扩展到综态而选择的哈密顿算子的投影。通过一个玩具模型，我们证明了在大多数情况下，RRM特征值接近于从下面投影的哈密顿量的特征值。我们还讨论了能量偏移和单位算子投影的影响。

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.