diff --git a/trex.org b/trex.org
index 54bc2b6..9a406f6 100644
--- a/trex.org
+++ b/trex.org
@@ -215,17 +215,18 @@ arrays are 0-based. Hence, we introduce the ~index~ type which is an
   All the basis set parameters are stored in one-dimensional arrays:
 
   #+NAME: basis
-  | Variable        | Type    | Dimensions    | Description                                                      |
-  |-----------------+---------+---------------+------------------------------------------------------------------|
-  | ~type~          | ~str~   |               | Type of basis set: "Gaussian" or "Slater"                        |
-  | ~num~           | ~dim~   |               | Total number of primitives                                       |
-  | ~nucleus_index~ | ~index~ | ~(basis.num)~ | One-to-one correspondence between primitives and atomic indices  |
-  | ~ang_mom~       | ~int~   | ~(basis.num)~ | One-to-one correspondence between primitives and angular momenta |
-  | ~shell_index~   | ~index~ | ~(basis.num)~ | One-to-one correspondence between primitives and atomic shells   |
-  | ~shell_factor~  | ~float~ | ~(basis.num)~ | Normalization factor of the shell ($\mathcal{N}_s$)              |
-  | ~exponent~      | ~float~ | ~(basis.num)~ | Exponents of the primitives ($\gamma_{ks}$)                      |
-  | ~coefficient~   | ~float~ | ~(basis.num)~ | Coefficients of the primitives ($a_{ks}$)                        |
-  | ~prim_factor~   | ~float~ | ~(basis.num)~ | Normalization coefficients for the primitives ($f_{ks}$)         |
+  | Variable        | Type    | Dimensions          | Description                                                  |
+  |-----------------+---------+---------------------+--------------------------------------------------------------|
+  | ~type~          | ~str~   |                     | Type of basis set: "Gaussian" or "Slater"                    |
+  | ~prim_num~      | ~dim~   |                     | Total number of primitives                                   |
+  | ~shell_num~     | ~dim~   |                     | Total number of shells                                       |
+  | ~nucleus_index~ | ~index~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and atomic indices  |
+  | ~ang_mom~       | ~int~   | ~(basis.shell_num)~ | One-to-one correspondence between shells and angular momenta |
+  | ~shell_factor~  | ~float~ | ~(basis.shell_num)~ | Normalization factor of each shell ($\mathcal{N}_s$)         |
+  | ~shell_index~   | ~index~ | ~(basis.prim_num)~  | One-to-one correspondence between primitives and shell index |
+  | ~exponent~      | ~float~ | ~(basis.prim_num)~  | Exponents of the primitives ($\gamma_{ks}$)                  |
+  | ~coefficient~   | ~float~ | ~(basis.prim_num)~  | Coefficients of the primitives ($a_{ks}$)                    |
+  | ~prim_factor~   | ~float~ | ~(basis.prim_num)~  | Normalization coefficients for the primitives ($f_{ks}$)     |
 
   #+CALL: json(data=basis, title="basis")
 
@@ -233,15 +234,16 @@ arrays are 0-based. Hence, we introduce the ~index~ type which is an
   :RESULTS:
   #+begin_src python :tangle trex.json
       "basis": {
-		   "type" : [ "str"  , []              ]
-	,           "num" : [ "dim"  , []              ]
-	, "nucleus_index" : [ "index", [ "basis.num" ] ]
-	,       "ang_mom" : [ "int"  , [ "basis.num" ] ]
-	,   "shell_index" : [ "index", [ "basis.num" ] ]
-	,  "shell_factor" : [ "float", [ "basis.num" ] ]
-	,      "exponent" : [ "float", [ "basis.num" ] ]
-	,   "coefficient" : [ "float", [ "basis.num" ] ]
-	,   "prim_factor" : [ "float", [ "basis.num" ] ]
+		   "type" : [ "str"  , []                    ]
+	,      "prim_num" : [ "dim"  , []                    ]
+	,     "shell_num" : [ "dim"  , []                    ]
+	, "nucleus_index" : [ "index", [ "basis.shell_num" ] ]
+	,       "ang_mom" : [ "int"  , [ "basis.shell_num" ] ]
+	,  "shell_factor" : [ "float", [ "basis.shell_num" ] ]
+	,   "shell_index" : [ "index", [ "basis.prim_num" ]  ]
+	,      "exponent" : [ "float", [ "basis.prim_num" ]  ]
+	,   "coefficient" : [ "float", [ "basis.prim_num" ]  ]
+	,   "prim_factor" : [ "float", [ "basis.prim_num" ]  ]
       } ,
   #+end_src
   :END:
@@ -275,27 +277,28 @@ D   1
 
    #+BEGIN_EXAMPLE
 type  = "Gaussian"
-num   = 20
+prim_num   = 20
+shell_num   = 12
 
-# 10 primitives per H atom
+# 6 shells per H atom
 nucleus_index = 
-[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
-  1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
+[ 0, 0, 0, 0, 0, 0,  
+  1, 1, 1, 1, 1, 1 ] 
 
-# 7 primitives for S (l=0), 2 primitives for P (l=1), 1 primitive for D (l=2) shells
+# 3 shells in S (l=0), 2 in P (l=1), 1 in D (l=2)
 ang_mom =
-[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 
-  0, 0, 0, 0, 0, 0, 0, 1, 1, 2 ]
-
-# 5 primitives for first S shell and then 1 primitive per remaining shells
-shell_index = 
-[ 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 
-  0, 0, 0, 0, 0, 1, 2, 3, 4, 5 ]
+[ 0, 0, 0, 1, 1, 2, 
+  0, 0, 0, 1, 1, 2 ]
 
 # no need to renormalize shells 
 shell_factor = 
-[ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 
-  1., 1., 1., 1., 1., 1., 1., 1., 1., 1. ]
+[ 1., 1., 1., 1., 1., 1.,  
+  1., 1., 1., 1., 1., 1. ] 
+
+# 5 primitives for the first S shell and then 1 primitive per remaining shells in each H atom
+shell_index = 
+[ 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 
+  6, 6, 6, 6, 6, 7, 8, 9, 10, 11 ]
 
 # parameters of the primitives (10 per H atom)
 exponent =