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首页> 外文期刊>The journal of physical chemistry, A. Molecules, spectroscopy, kinetics, environment, & general theory >The Utilitiy of Constraining Basis Function Indices When Using the Lanczos Algorithm to Calculate Vibrational Energy Levels
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The Utilitiy of Constraining Basis Function Indices When Using the Lanczos Algorithm to Calculate Vibrational Energy Levels

机译：使用Lanczos算法计算振动能级时约束基函数指数的效用

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摘要

Direct product basis sets are frequently used to calculate vibrational energy levels of small polyatomic molecules. They have the important advantage of simplicity. However, they have the important disadvantage that a very large number of direct product functions is necessary to obtain converged energy levels. By using an iterative, rather than ean explicit. method to calculate eigenvalues of the Hamiltonian matrix, it is possible to calculate energy levels despite the huge size of the direct product basis. Nonetheless, it is natural to attempt to reduce the size of the direct product basis by excluding functions that do not contibute to the wave functions associated with the energy levels of interest. In this paper we present a variational basis representation (VBR) example and a discrete variable representation (DVR) example demonstrating that it is possible to use the Lanczos method and exclude direct product basis functions by restricting basis function indices while maintaining the favorable n~(f+1) scaling relation for the cost of direct product basis matrix-vector products.
机译：直接乘积基集经常用于计算多原子小分子的振动能级。它们具有简单性的重要优势。然而，它们具有重要的缺点，即需要大量的直接乘积函数来获得会聚的能量水平。通过使用迭代而不是ean显式。通过计算哈密顿矩阵特征值的方法，尽管直接乘积基数很大，但仍可以计算能级。尽管如此，通过排除不影响与感兴趣能级相关的波动函数的函数来尝试减小直接乘积的大小是很自然的。在本文中，我们提供一个变分基础表示（VBR）示例和一个离散变量表示（DVR）示例，证明可以使用Lanczos方法并通过限制基础函数索引同时排除n乘以n来排除直接乘积基础函数。 f + 1）直接乘积基矩阵向量乘积的成本的比例关系。

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