CP2K Open Source Molecular Dynamics

User Tools

Site Tools

Trace: • index • index • index • printkey • index
basis_sets

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision		Previous revision
basis_sets [2015/03/23 15:08] – [Construction] 129.132.210.65basis_sets [2020/11/07 12:57] (current) – oschuett
Line 9: Line 9:
 ===== File Format ===== ===== File Format =====
  
-We explain the file-format using the following example from the file ''$CP2K_HOME/tests/QS/BASIS_SET'':+We explain the file-format using the following example from the file ''$CP2K_HOME/data/BASIS_SET'':
 <code> <code>
  1   # Silicon  1   # Silicon
Line 40: Line 40:
   * 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 $l_\text{max}$  (here: 1).   * The third number specifies the maximal angular quantum number $l_\text{max}$  (here: 1).
-  * The fourth number specifies the number of exponents (here: 4).+  * The fourth number specifies the number of exponents $N$ (here: 4).
  
-The following number specify the number of contracted basis functions for each angular momentum value. +The following numbers specify the number of contracted basis functions for each angular momentum value  $n_l$.
   * The fifth number specifies the number of contractions for $l=0$ or s-functions (here: 2).   * 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: 2).   * 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:
Line 57: Line 59:
 \varphi_2(\vec r) &=  Y_{0,0} \cdot e^{-0.056 r^2} \\ \varphi_2(\vec r) &=  Y_{0,0} \cdot e^{-0.056 r^2} \\
  
-\varphi_3(\vec r) &=  Y_{1,-1}\left [0.046 \cdot e^{-1.181r^2}  -0.263 \cdot e^{-0.445r^2} -0.543 \cdot e^{-0.164r^2} - 0.543 \cdot e^{-0.056 r^2} \right ] \\+\varphi_3(\vec r) &=  Y_{1,-1}\cdot r \left [0.046 \cdot e^{-1.181r^2}  -0.263 \cdot e^{-0.445r^2} -0.543 \cdot e^{-0.164r^2} - 0.356 \cdot e^{-0.056 r^2} \right ] \\
  
-\varphi_4(\vec r) &=  Y_{1,0}\left [0.046 \cdot e^{-1.181r^2}  -0.263 \cdot e^{-0.445r^2} -0.543 \cdot e^{-0.164r^2} - 0.543 \cdot e^{-0.056 r^2} \right ] \\+\varphi_4(\vec r) &=  Y_{1,0}\cdot r \left [0.046 \cdot e^{-1.181r^2}  -0.263 \cdot e^{-0.445r^2} -0.543 \cdot e^{-0.164r^2} - 0.356 \cdot e^{-0.056 r^2} \right ] \\
  
-\varphi_5(\vec r) &=  Y_{1, +1}\left [0.046 \cdot e^{-1.181r^2}  -0.263 \cdot e^{-0.445r^2} -0.543 \cdot e^{-0.164r^2} - 0.543 \cdot e^{-0.056 r^2} \right ] \\+\varphi_5(\vec r) &=  Y_{1, +1}\cdot r \left [0.046 \cdot e^{-1.181r^2}  -0.263 \cdot e^{-0.445r^2} -0.543 \cdot e^{-0.164r^2} - 0.356 \cdot e^{-0.056 r^2} \right ] \\
  
-\varphi_6(\vec r) &=  Y_{1,-1} \cdot e^{-0.056 r^2} \\+\varphi_6(\vec r) &=  Y_{1,-1} \cdot r \cdot e^{-0.056 r^2} \\
  
-\varphi_7(\vec r) &=  Y_{1,0} \cdot e^{-0.056 r^2}  \\+\varphi_7(\vec r) &=  Y_{1,0} \cdot r \cdot e^{-0.056 r^2}  \\
  
-\varphi_8(\vec r) &=  Y_{1, +1} \cdot e^{-0.056 r^2}+\varphi_8(\vec r) &=  Y_{1, +1} \cdot r \cdot e^{-0.056 r^2}
  
 \end{align} \end{align}
Line 78: Line 80:
  
 \begin{align} \begin{align}
-\varphi_9(\vec r) &=  Y_{2,-2} \cdot e^{-0.45 r^2}  \\ +\varphi_9(\vec r) &=  Y_{2,-2} \cdot r^2 \cdot e^{-0.45 r^2}  \\ 
-\varphi_{10}(\vec r) &=  Y_{2,-1} \cdot e^{-0.45 r^2}  \\ +\varphi_{10}(\vec r) &=  Y_{2,-1} \cdot r^2 \cdot e^{-0.45 r^2}  \\ 
-\varphi_{11}(\vec r) &=  Y_{2,0} \cdot e^{-0.45 r^2}  \\ +\varphi_{11}(\vec r) &=  Y_{2,0} \cdot r^2 \cdot e^{-0.45 r^2}  \\ 
-\varphi_{12}(\vec r) &=  Y_{2, +1} \cdot e^{-0.45 r^2}  \\ +\varphi_{12}(\vec r) &=  Y_{2, +1} \cdot r^2 \cdot e^{-0.45 r^2}  \\ 
-\varphi_{13}(\vec r) &=  Y_{2, +2} \cdot e^{-0.45 r^2} +\varphi_{13}(\vec r) &=  Y_{2, +2} \cdot r^2 \cdot e^{-0.45 r^2} 
 \end{align} \end{align}
  
basis_sets.1427123317.txt.gz · Last modified: (external edit)