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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク STO-nG basis sets ： ウィキペディア英語版 STO-nG basis sets STO-nG basis sets are minimal basis sets, where $n$ primitive Gaussian orbitals are fitted to a single Slater-type orbital (STO). $n$ originally took the values 2 - 6. They were first proposed by John Pople. A minimum basis set is where only sufficient orbitals are used to contain all the electrons in the neutral atom. Thus for the hydrogen atom, only a single 1s orbital is needed, while for a carbon atoms, 1s, 2s and three 2p orbitals are needed. The core and valence orbitals are represented by the same number of primitive Gaussian functions $\backslash mathbf\; \backslash phi\_i$. For example, an STO-3G basis set for the 1s, 2s and 2p orbital of the carbon atom are all linear combination of 3 primitive Gaussian functions. For example, a STO-3G s orbital is given by: :$\backslash mathbf\; \backslash psi\_(s)=c\_1\backslash phi\_1\; +\; c\_2\backslash phi\_2\; +\; c\_3\backslash phi\_3$ where ::$\backslash mathbf\; \backslash phi\_1\; =\; \backslash left\; (\backslash frac\; \backslash right\; )\; ^e^$ ::$\backslash mathbf\; \backslash phi\_2\; =\; \backslash left\; (\backslash frac\; \backslash right\; )\; ^e^$ ::$\backslash mathbf\; \backslash phi\_3\; =\; \backslash left\; (\backslash frac\; \backslash right\; )\; ^e^$ The values of c1, c2, c3, α1, α2 and α3 have to be determined. For the STO-nG basis sets, they are obtained by making a least squares fit of the three Gaussian orbitals to the single Slater-type orbitals. This differs from the more common procedure where the criteria often used is to choose the coefficients (c's) and exponents (α's) to give the lowest energy with some appropriate method for some appropriate molecule. A special feature of this basis set is that common exponents are used for orbitals in the same shell (e.g. 2s and 2p) as this allows more efficient computation. The fit between the Gaussian orbitals and the Slater orbital is good for all values of r, except for very small values near to the nucleus. The Slater orbital has a cusp at the nucleus, while Gaussian orbitals are flat at the nucleus.〔''Chemical Modeling From Atoms to Liquids'', Alan Hinchliffe, John Wiley & Sons, Ltd., 1999. pg 294.〕〔''Molecular Modelling'', Andrew R. Leach, Longman, 1996. pg 68 - 73.〕 ==Use of STO-nG basis sets== The most widely used basis set of this group is STO-3G, which is used for large systems and for preliminary geometry determinations. This basis set is available for all atoms from Hydrogen up to Xenon.〔''Computational Chemistry'', David Young, Wiley-Interscience, 2001. pg 86.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「STO-nG basis sets」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.