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Commun. Comput. Phys., 18 (2015), pp. 125-146.
Published online: 2018-04
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Numerical atomic orbitals have been successfully used in molecular simulations as a basis set, which provides a nature, physical description of the electronic states and is suitable for $\mathcal{O}$($N$) calculations based on the strictly localized property. This paper presents a numerical analysis for some simplified atomic orbitals, with polynomial-type and confined Hydrogen-like radial basis functions respectively. We give some a priori error estimates to understand why numerical atomic orbitals are computationally efficient in electronic structure calculations.
}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.170414.231214a}, url = {http://global-sci.org/intro/article_detail/cicp/11021.html} }Numerical atomic orbitals have been successfully used in molecular simulations as a basis set, which provides a nature, physical description of the electronic states and is suitable for $\mathcal{O}$($N$) calculations based on the strictly localized property. This paper presents a numerical analysis for some simplified atomic orbitals, with polynomial-type and confined Hydrogen-like radial basis functions respectively. We give some a priori error estimates to understand why numerical atomic orbitals are computationally efficient in electronic structure calculations.