diff --git a/src/nomad_simulations/schema_packages/basis_set.py b/src/nomad_simulations/schema_packages/basis_set.py
index d6e0875d..51f302a0 100644
--- a/src/nomad_simulations/schema_packages/basis_set.py
+++ b/src/nomad_simulations/schema_packages/basis_set.py
@@ -212,10 +212,43 @@ class APWBaseOrbital(ArchiveSection):
         """,
     )  # TODO: add check non-negative # ? to remove
 
+    def _get_lengths(self, quantities: set[str]) -> list[int]:
+        """Extract the lengths of the `quantities` contained in the set."""
+        present_quantities = set(quantities) & self.m_quantities
+        lengths: list[int] = []
+        for quant in present_quantities:
+            length = len(getattr(self, quant))
+            if length > 0:  # empty lists are exempt
+                lengths.append(length)
+        return lengths
+
+    def _of_equal_length(lengths: list[int]) -> bool:
+        """Check if all elements in the list are of equal length."""
+        if len(lengths) == 0:
+            return True
+        else:
+            ref_length = lengths[0]
+            return all(length == ref_length for length in lengths)
+
+    def get_n_terms(self) -> Optional[int]:
+        """Determine the value of `n_terms` based on the lengths of the representative quantities."""
+        rep_quant = {'energy_parameter', 'energy_parameter_n', 'differential_order'}
+        lengths = self._get_lengths(rep_quant)
+        if not self._of_equal_length(lengths) or len(lengths) == 0:
+            return None
+        else:
+            return lengths[0]
+
     def normalize(self, archive: EntryArchive, logger: BoundLogger) -> None:
         super().normalize(archive, logger)
-        if (self.differential_order < 0).any():
-            logger.error('`APWBaseOrbital.differential_order` must be non-negative.')
+        new_n_terms = self.get_n_terms()
+        if self.n_terms is None:
+            self.n_terms = new_n_terms
+        elif self.n_terms != new_n_terms:
+            logger.error(
+                f'Inconsistent lengths of `APWBaseOrbital` quantities: {self.m_quantities}. Setting back to `None`.'
+            )
+            self.n_terms = None
 
 
 class APWOrbital(APWBaseOrbital):
@@ -228,7 +261,7 @@ class APWOrbital(APWBaseOrbital):
     """
 
     type = Quantity(
-        type=MEnum('apw', 'lapw', 'slapw', 'spherical_dirac'),
+        type=MEnum('apw', 'lapw', 'slapw'),  # ? where to put 'spherical_dirac'
         description="""
         Type of augmentation contribution. Abbreviations stand for:
         | name | description | radial product |
@@ -242,6 +275,25 @@ class APWOrbital(APWBaseOrbital):
         """,
     )
 
+    def get_type(self, logger: BoundLogger) -> Optional[str]:
+        """
+        Set the type of the APW orbital based on the differential order.
+        """
+        if self.n_terms is None:
+            logger.error('`APWOrbital.n_terms` must be defined before setting the type.')
+            return None
+        if self.n_terms == 0:
+            return 'apw'
+        elif self.n_terms == 1:
+            return 'lapw'
+        else:
+            return 'slapw'
+
+    def normalize(self, archive: EntryArchive, logger: BoundLogger) -> None:
+        super().normalize(archive, logger)
+        if self.type is None:
+            self.type = self.get_type(logger)
+
 
 class APWLocalOrbital(APWBaseOrbital):
     """
@@ -274,6 +326,7 @@ class APWLocalOrbital(APWBaseOrbital):
         """,
     )
 
+
     def normalize(self, archive: 'EntryArchive', logger: 'BoundLogger') -> None:
         super().normalize(archive, logger)
         if np.any(np.isneginf(self.differential_orders)):
@@ -310,19 +363,19 @@ def _determine_apw(self, logger: BoundLogger) -> dict[str, int]:
         Produce a count of the APW components in the l-channel.
         """
         count = {'apw': 0, 'lapw': 0, 'slapw': 0, 'lo': 0, 'other': 0}
-        order_map = {0: 'apw', 1: 'lapw', 2: 'slapw'}  # TODO: add dirac?
+        order_map = {0: 'apw', 1: 'lapw'}  # TODO: add dirac?
 
         for orb in self.orbitals:
             err_msg = f'Unknown APW orbital type {orb.type} and order {orb.differential_order}.'
             if isinstance(orb, APWOrbital):
-                if orb.type in order_map.values():
+                if orb.type.lower() in order_map.values():
                     count[orb.type] += 1
-                elif orb.differential_order in order_map:
+                elif orb.n_terms in order_map:
                     count[order_map[orb.differential_order]] += 1
-                elif orb.differential_order > 2:
+                elif orb.n_terms > 2:
                     count['slapw'] += 1
                 else:
-                    logger.warning(err_msg)
+                    logger.warning(err_msg)  # TODO: rewrite using `type normalization`
             elif isinstance(orb, APWLocalOrbital):
                 count['lo'] += 1
             else: