关于被不可穿透的球形空腔限制的原子氢的波函数截止因子

IF 2.3 3区 化学 Q3 CHEMISTRY, PHYSICAL International Journal of Quantum Chemistry Pub Date : 2024-06-24 DOI:10.1002/qua.27441
Roberto Reyes-García, Salvador A. Cruz, Remigio Cabrera-Trujillo
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引用次数: 0

摘要

通过有限差分方法求解了被坚不可摧的球形空腔包围的氢原子的薛定谔方程,从而深入了解了在相应的变分计算中为符合迪里夏特边界条件而临时广泛使用的安萨特波函数截止因子的实际性质和结构。这项工作的结果为选择满足边界条件的适当解析截止函数提供了理论基础。我们发现截止函数的行为有三个不同的区域。小空腔半径区域的截止函数是抛物线行为,中间区域的截止函数是准线性行为,大空腔区域的截止函数是阶梯状行为。我们推导出文献中使用的传统线性和二次方截止函数,以及其对约束半径的有效区域。最后,我们根据自由氢化波函数的节点结构和拉盖尔多项式与某些空腔半径的关系,对自由原子能级与约束能级重合时的精确截止函数进行了数学推导。我们发现,当系统被压缩时,截止函数会根据其节点结构在几个非约束解上发生转换。
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On the wavefunction cutoff factors of atomic hydrogen confined by an impenetrable spherical cavity

The Schrödinger equation for the hydrogen atom enclosed by an impenetrable spherical cavity is solved through a Finite-Differences approach to gain an insight on the actual nature and structure of the ansatz wavefunction cutoff factor widely used in an ad hoc manner in corresponding variational calculations to comply with the Dirichlet boundary conditions. The results of this work provide a theoretical foundation for the choice of the appropriate analytical cutoff functions that fulfill the boundary conditions. We find three different regions for the behavior of the cutoff functions. Small cavity radius where the cutoff function has a parabolic behavior, an intermediate region where the cutoff function is quasi-linear, and a large cavity region where the cutoff function is a step-like function. We deduce the traditional linear and quadratic cutoff functions used in the literature as well as its validity region for the confining radius. Finally, we provide a mathematical deduction of the exact cutoff function in terms of the nodal structure of the free hydrogenic wavefunctions and a relation to the Laguerre polynomials for some cavity radii where the free atomic energy level coincides with a confined energy level. We find that the cutoff function transit over several unconfined solutions in terms of its nodal structure as the system is compressed.

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来源期刊
International Journal of Quantum Chemistry
International Journal of Quantum Chemistry 化学-数学跨学科应用
CiteScore
4.70
自引率
4.50%
发文量
185
审稿时长
2 months
期刊介绍: Since its first formulation quantum chemistry has provided the conceptual and terminological framework necessary to understand atoms, molecules and the condensed matter. Over the past decades synergistic advances in the methodological developments, software and hardware have transformed quantum chemistry in a truly interdisciplinary science that has expanded beyond its traditional core of molecular sciences to fields as diverse as chemistry and catalysis, biophysics, nanotechnology and material science.
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