diff --git a/src/openfermion/chem/molecular_data.py b/src/openfermion/chem/molecular_data.py
index 64dc376b6..bc79e3e28 100644
--- a/src/openfermion/chem/molecular_data.py
+++ b/src/openfermion/chem/molecular_data.py
@@ -33,7 +33,9 @@
 
 
 # Define error objects which inherit from Exception.
-class MoleculeNameError(Exception):
+class MoleculeNameError(ValueError):
+    """Exception raised when a molecule name is invalid or cannot be generated."""
+
     pass
 
 
@@ -273,10 +275,12 @@ def name_molecule(geometry, basis, multiplicity, charge, description):
         11: 'undectet',
         12: 'duodectet',
     }
-    if multiplicity not in multiplicity_dict:
-        raise MoleculeNameError('Invalid spin multiplicity provided.')
-    else:
+    if multiplicity in multiplicity_dict:
         name += '_{}'.format(multiplicity_dict[multiplicity])
+    elif multiplicity > 0:
+        name += '_{}-multiplet'.format(multiplicity)
+    else:
+        raise MoleculeNameError('Invalid spin multiplicity provided.')
 
     # Add charge.
     if charge > 0:
@@ -491,7 +495,12 @@ def __init__(
         # Metadata fields which must be provided.
         self.geometry = geometry
         self.basis = basis
-        self.multiplicity = multiplicity
+        if isinstance(
+            multiplicity, (int, float, numpy.integer, numpy.floating)
+        ) and multiplicity == int(multiplicity):
+            self.multiplicity = int(multiplicity)
+        else:
+            raise MoleculeNameError('Invalid spin multiplicity provided.')
 
         # Metadata fields with default values.
         self.charge = charge
@@ -500,7 +509,7 @@ def __init__(
         self.description = description
 
         # Name molecule and get associated filename
-        self.name = name_molecule(geometry, basis, multiplicity, charge, description)
+        self.name = name_molecule(geometry, basis, self.multiplicity, charge, description)
         if filename:
             if filename[-5:] == '.hdf5':
                 filename = filename[: (len(filename) - 5)]
diff --git a/src/openfermion/chem/molecular_data_test.py b/src/openfermion/chem/molecular_data_test.py
index d51e6937c..c640f3303 100644
--- a/src/openfermion/chem/molecular_data_test.py
+++ b/src/openfermion/chem/molecular_data_test.py
@@ -104,6 +104,34 @@ def test_invalid_multiplicity(self):
         with self.assertRaises(MoleculeNameError):
             MolecularData(geometry, basis, multiplicity)
 
+        # Test non-integer multiplicity
+        with self.assertRaises(MoleculeNameError):
+            MolecularData(geometry, basis, multiplicity=1.5)
+
+        # Test zero multiplicity
+        with self.assertRaises(MoleculeNameError):
+            MolecularData(geometry, basis, multiplicity=0)
+
+    def test_high_multiplicity(self):
+        # 12 hydrogens can support multiplicity 13
+        geometry = [('H', (0.0, 0.0, i * 1.3)) for i in range(12)]
+        basis = 'sto-3g'
+        molecule = MolecularData(geometry, basis, multiplicity=13)
+        self.assertEqual(molecule.name, 'H12_sto-3g_13-multiplet')
+
+    def test_float_multiplicity(self):
+        geometry = [('H', (0.0, 0.0, 0.0)), ('H', (0.0, 0.0, 0.7414))]
+        basis = 'sto-3g'
+
+        # Float multiplicity <= 12 should work and use name
+        molecule = MolecularData(geometry, basis, multiplicity=2.0)
+        self.assertEqual(molecule.name, 'H2_sto-3g_doublet')
+
+        # Float multiplicity > 12 should work and use number
+        geometry_high = [('H', (0.0, 0.0, i * 1.3)) for i in range(12)]
+        molecule_high = MolecularData(geometry_high, basis, multiplicity=13.0)
+        self.assertEqual(molecule_high.name, 'H12_sto-3g_13-multiplet')
+
     def test_geometry_from_file(self):
         water_geometry = [
             ('O', (0.0, 0.0, 0.0)),