feat: add orbital mapping constants for ABACUS, DeePTB, and OPENMX (#25)

* feat: add orbital mapping constants for ABACUS, DeePTB, and OPENMX

Add orbital number mappings and transformation matrices for ABACUS, DeePTB, and OPENMX DFT codes. These constants define the magnetic quantum number ordering and provide conversion matrices between different code conventions, enabling proper orbital basis transformations.

* refactor: rename OPENMX2DeePTB to OPENMX2DFTIO for consistency

Updated variable name in constants.py to align with the project's naming
convention and reflect the transition from DeePTB to DFTIO. This change
improves code clarity and maintains consistency across the codebase.

Author: QG-phy

dftio/constants.py

@@ -12,6 +12,24 @@
 norb_dict = {'s':1,'e':2,'p':3,'q':4,'d':5,'j':6,'f':7,'o':8,'g':9,'h':11, "i":15, "k":21, "l": 25, "m": 35}
 norb_dict_r = {1:'s', 2:'e', 3:'p', 4:'q', 5:'d', 6:'j', 7:'f', 8:'o', 9:'g', 11:'h', 15:"i", 21:"k", 25:"l", 35:"m"}
 
+ABACUS_orbital_number_m = {
+    "s": [0],
+    "p": [0, 1, -1],
+    "d": [0, 1, -1, 2, -2],
+    "f": [0, 1, -1, 2, -2, 3, -3],
+    "g": [0, 1, -1, 2, -2, 3, -3, 4, -4],
+    "h": [0, 1, -1, 2, -2, 3, -3, 4, -4, 5, -5]
+}
+
+DeePTB_orbital_number_m = {
+    "s": [0],
+    "p": [-1, 0, 1],
+    "d": [-2, -1, 0, 1, 2],
+    "f": [-3, -2, -1, 0, 1, 2, 3],
+    "g": [-4, -3, -2, -1, 0, 1, 2, 3, 4],
+    "h": [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]
+}
+
 ABACUS2DFTIO = {
             0: np.eye(1, dtype=np.float32),
             1: np.eye(3, dtype=np.float32)[[2, 0, 1]],
@@ -57,4 +75,18 @@
 SIESTA2DFTIO[2][[1, 3]] *= -1
 SIESTA2DFTIO[3][[0, 6, 2, 4]] *= -1
 SIESTA2DFTIO[4][[1, 7, 3, 5]] *= -1
-SIESTA2DFTIO[5][[0, 10, 8, 2, 6, 4]] *= -1
+SIESTA2DFTIO[5][[0, 10, 8, 2, 6, 4]] *= -1
+
+OPENMX_orbital_number_m = {
+    "s": [0],
+    "p": [1, -1, 0],
+    "d": [0, 2, -2, 1, -1],
+    "f": [0, 1, -1, 2, -2, 3, -3]
+}
+
+OPENMX2DFTIO = {
+            0: np.eye(1, dtype=np.float32),
+            1: np.eye(3, dtype=np.float32)[[1, 2, 0]],
+            2: np.eye(5, dtype=np.float32)[[2, 4, 0, 3, 1]],
+            3: np.eye(7, dtype=np.float32)[[6, 4, 2, 0, 1, 3, 5]]
+        }