Going from the atomic basis set to AOs implies a systematic
@@ -1005,13 +1005,13 @@ shell, as in the GAMESS convention where
In such a case, one should set the normalization of the shell (in
-the Basis set section) to \(\mathcal{N}_{z^2}\), which is the
+the Basis set section) to \(\mathcal{N}_{z^2}\), which is the
normalization factor of the atomic orbitals in spherical coordinates.
The normalization factor of the \(xy\) function which should be
introduced here should be \(\frac{\mathcal{N}_{xy}}{\mathcal{N}_{z^2}}\).
-
+
@@ -1063,8 +1063,8 @@ introduced here should be \(\frac{\mathcal{N}_{xy}}{\mathcal{N}_{z^2}}\).
-
-
6.1 One-electron integrals (ao_1e_int
group)
+
+
6.1 One-electron integrals (ao_1e_int
group)
- \[ \hat{V}_{\text{ne}} = \sum_{A=1}^{N_\text{nucl}}
@@ -1082,7 +1082,7 @@ The one-electron integrals for a one-electron operator \(\hat{O}\) are
over atomic orbitals.
-
+
@@ -1149,8 +1149,8 @@ over atomic orbitals.
-
-
6.2 Two-electron integrals (ao_2e_int
group)
+
+
6.2 Two-electron integrals (ao_2e_int
group)
The two-electron integrals for a two-electron operator \(\hat{O}\) are
@@ -1171,7 +1171,7 @@ notation.
\mathbf{r}_j \vert)}{\vert \mathbf{r}_i - \mathbf{r}_j \vert} \] : electron-electron long range potential
-
+
@@ -1211,10 +1211,10 @@ notation.
-
-
7 Molecular orbitals (mo group)
+
+
7 Molecular orbitals (mo group)
-
+
@@ -1280,8 +1280,8 @@ notation.
-
-
7.1 One-electron integrals (mo_1e_int
group)
+
+
7.1 One-electron integrals (mo_1e_int
group)
The operators as the same as those defined in the
@@ -1289,7 +1289,7 @@ The operators as the same as those defined in the
the basis of molecular orbitals.
-
+
@@ -1356,8 +1356,8 @@ the basis of molecular orbitals.
-
-
7.2 Two-electron integrals (mo_2e_int
group)
+
+
7.2 Two-electron integrals (mo_2e_int
group)
The operators as the same as those defined in the
@@ -1365,7 +1365,7 @@ The operators as the same as those defined in the
the basis of molecular orbitals.
-
+
@@ -1405,13 +1405,13 @@ the basis of molecular orbitals.
-
-
8 TODO Slater determinants
+
+
8 TODO Slater determinants
-
-
9 TODO Reduced density matrices (rdm group)
+
+
9 TODO Reduced density matrices (rdm group)
-
+
@@ -1464,15 +1464,15 @@ the basis of molecular orbitals.
-
-
10 Appendix
+
+
10 Appendix
-
-
10.1 Python script from table to json
+
+
10.1 Python script from table to json
-
print("""#+begin_src python :tangle trex.json""")
+print("""#+begin_src python :tangle trex.json""")
print(""" "%s": {"""%(title))
indent = " "
f1 = 0 ; f2 = 0 ; f3 = 0
@@ -1525,7 +1525,7 @@ the basis of molecular orbitals.
Author: TREX-CoE
-
Created: 2021-10-07 Thu 07:56
+
Created: 2021-10-08 Fri 11:57
Validate