basis_sets
Differences
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basis_sets [2014/03/31 13:19] – created oschuett | basis_sets [2020/11/07 12:57] (current) – oschuett | ||
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Where $R(r)$ denotes the radial part and $Y_{lm}(\theta, | Where $R(r)$ denotes the radial part and $Y_{lm}(\theta, | ||
- | \[ R_i(r) = \sum_{j=1}^N c_{ij}\cdot \exp(\alpha_j\cdot r) \] | + | \[ R_i(r) = r^{l_i} |
===== File Format ===== | ===== File Format ===== | ||
- | We explain the file-format using the following example from the file '' | + | We explain the file-format using the following example from the file '' |
< | < | ||
| | ||
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* The second number specifies the minimal angular quantum number $l_\text{min}$ (here: 0). | * The second number specifies the minimal angular quantum number $l_\text{min}$ (here: 0). | ||
* The third number specifies the maximal angular quantum number $l_\text{max}$ | * The third number specifies the maximal angular quantum number $l_\text{max}$ | ||
- | * The fourth number specifies the number of exponents (here: 4). | + | * The fourth number specifies the number of exponents |
- | The following | + | The following |
- | * The fifth number specifies the number of contractions for $l=0$ or s-functions (here: | + | * The fifth number specifies the number of contractions for $l=0$ or s-functions (here: 2). |
- | * The sixth number specifies the number of contractions for $l=1$ or p-functions (here: | + | * The sixth number specifies the number of contractions for $l=1$ or p-functions (here: 2). |
**Line 10-13** specify the coefficients of the first set. | **Line 10-13** specify the coefficients of the first set. | ||
- | Each line consists of an exponent $\alpha_j$, followed by contraction coefficients $c_{ij}$. For example, line 10 starts with the exponent (1.182), followed by the two contraction coefficients for s-functions (0.321 and 0.0), followed by the two contraction coefficients for p-functions (0.046 and 0.0). | + | Each line consists of an exponent $\alpha_j$, followed by contraction coefficients $c_{ij}$. For example, line 10 starts with the exponent (1.181), followed by the two contraction coefficients for s-functions (0.321 and 0.0), followed by the two contraction coefficients for p-functions (0.046 and 0.0). |
+ | |||
+ | The entire set consists of $\sum_{l=l_\text{min}}^{l_\text{max}} n_l \cdot (l+1)$ basis functions. Each basis function consists of $N$ terms - one for every exponent. | ||
The entire first set consists of the following 8 basis functions: | The entire first set consists of the following 8 basis functions: | ||
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\begin{align} | \begin{align} | ||
- | \varphi_1(\vec r) & | + | \varphi_1(\vec r) & |
- | \varphi_2(\vec r) & | + | \varphi_2(\vec r) & |
- | \varphi_3(\vec r) & | + | \varphi_3(\vec r) & |
- | \varphi_4(\vec r) & | + | \varphi_4(\vec r) & |
- | \varphi_5(\vec r) & | + | \varphi_5(\vec r) & |
- | \varphi_6(\vec r) & | + | \varphi_6(\vec r) & |
- | \varphi_7(\vec r) & | + | \varphi_7(\vec r) & |
- | \varphi_8(\vec r) & | + | \varphi_8(\vec r) & |
\end{align} | \end{align} | ||
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\begin{align} | \begin{align} | ||
- | \varphi_9(\vec r) & | + | \varphi_9(\vec r) & |
- | \varphi_{10}(\vec r) & | + | \varphi_{10}(\vec r) & |
- | \varphi_{11}(\vec r) & | + | \varphi_{11}(\vec r) & |
- | \varphi_{12}(\vec r) & | + | \varphi_{12}(\vec r) & |
- | \varphi_{13}(\vec r) & | + | \varphi_{13}(\vec r) & |
\end{align} | \end{align} | ||
basis_sets.1396271987.txt.gz · Last modified: 2020/08/21 10:15 (external edit)