diff --git a/automol/vmat.py b/automol/vmat.py
index 3b29a74b..f83fb876 100644
--- a/automol/vmat.py
+++ b/automol/vmat.py
@@ -12,7 +12,7 @@
 from .util import ZmatConv, dict_, zmat_conv
 
 Symbol = str
-Key = str | None
+Key = int | None
 Name = str | None
 KeyRow = tuple[Key, Key, Key]
 NameRow = tuple[Name, Name, Name]
@@ -218,7 +218,7 @@ def coordinates(
     return coo_dct
 
 
-def distance_coordinates(vma: VMatrix) -> dict[str, tuple[int, ...]]:
+def distance_coordinates(vma: VMatrix) -> dict[Name, CoordinateKey]:
     """Get the distance coordinates by coordinate name.
 
     :param vma: V-Matrix
@@ -227,7 +227,7 @@ def distance_coordinates(vma: VMatrix) -> dict[str, tuple[int, ...]]:
     return dict_.by_key(coordinates(vma, multi=False), distance_names(vma))
 
 
-def central_angle_coordinates(vma: VMatrix) -> dict[str, tuple[int, ...]]:
+def central_angle_coordinates(vma: VMatrix) -> dict[Name, CoordinateKey]:
     """Get the central angle coordinates by coordinate name.
 
     :param vma: V-Matrix
@@ -236,7 +236,7 @@ def central_angle_coordinates(vma: VMatrix) -> dict[str, tuple[int, ...]]:
     return dict_.by_key(coordinates(vma, multi=False), central_angle_names(vma))
 
 
-def dihedral_angle_coordinates(vma: VMatrix) -> dict[str, tuple[int, ...]]:
+def dihedral_angle_coordinates(vma: VMatrix) -> dict[Name, CoordinateKey]:
     """Get the dihedral angle coordinates by coordinate name.
 
     :param vma: V-Matrix
@@ -293,7 +293,7 @@ def distance_names(vma: VMatrix) -> tuple[str]:
     return tuple(more_itertools.unique_everseen(name_mat[1:, 0]))
 
 
-def central_angle_names(vma: VMatrix) -> tuple[str]:
+def central_angle_names(vma: VMatrix) -> tuple[Name, ...]:
     """Obtain names of all central-angle coordinates defined in the V-Matrix.
 
     :param vma: V-Matrix
@@ -304,7 +304,7 @@ def central_angle_names(vma: VMatrix) -> tuple[str]:
     return tuple(more_itertools.unique_everseen(name_mat[2:, 1]))
 
 
-def dihedral_angle_names(vma: VMatrix) -> tuple[str]:
+def dihedral_angle_names(vma: VMatrix) -> tuple[Name, ...]:
     """Obtain names of all dihedral angle coordinates defined in the V-Matrix.
 
     :param vma: V-Matrix
@@ -315,7 +315,7 @@ def dihedral_angle_names(vma: VMatrix) -> tuple[str]:
     return tuple(more_itertools.unique_everseen(name_mat[3:, 2]))
 
 
-def angle_names(vma: VMatrix) -> tuple[str]:
+def angle_names(vma: VMatrix) -> tuple[Name, ...]:
     """Obtain names of all angle coordinates defined in the V-Matrix.
 
     :param vma: V-Matrix
@@ -358,7 +358,7 @@ def standard_names(vma: VMatrix, shift: int = 0) -> dict[Name, Name]:
     return name_dct
 
 
-def standard_name_matrix(vma: VMatrix, shift: int = 0) -> tuple[tuple[str]]:
+def standard_name_matrix(vma: VMatrix, shift: int = 0) -> NameMatrix:
     """Build a name matrix of the V-Matrix where all of the
     coordinate names have been standardized:
         RN: (1<=N<=Ncoords)
@@ -366,10 +366,8 @@ def standard_name_matrix(vma: VMatrix, shift: int = 0) -> tuple[tuple[str]]:
         DN: (1<=N<=Ncoords).
 
     :param vma: V-Matrix
-    :type vma: automol V-Matrix data structure
     :param shift: value to shift the keys by when obtaining the keys
-    :type shift: int
-    :rtype: tuple(tuple(str))
+    :return: Name matrix
     """
     natms = count(vma)
 
@@ -383,7 +381,7 @@ def standard_name_matrix(vma: VMatrix, shift: int = 0) -> tuple[tuple[str]]:
     return name_mat
 
 
-def distance_coordinate_name(zma: VMatrix, key1: int, key2: int) -> str:
+def distance_coordinate_name(zma: VMatrix, key1: int, key2: int) -> Name:
     """Get the name of a distance coordinate for a given bond.
 
     :param zma: the z-matrix
@@ -402,7 +400,9 @@ def distance_coordinate_name(zma: VMatrix, key1: int, key2: int) -> str:
     return name
 
 
-def central_angle_coordinate_name(zma: VMatrix, key1: int, key2: int, key3: int) -> str:
+def central_angle_coordinate_name(
+    zma: VMatrix, key1: int, key2: int, key3: int
+) -> Name:
     """Get the name of angle coordinate for a set of 3 atoms.
 
     :param zma: The z-matrix
@@ -424,7 +424,7 @@ def central_angle_coordinate_name(zma: VMatrix, key1: int, key2: int, key3: int)
 
 def dihedral_angle_coordinate_name(
     zma: VMatrix, key1: int, key2: int, key3: int, key4: int
-):
+) -> Name:
     """Get the name of dihedral coordinate for a set of 4 atoms.
 
     :param zma: The z-matrix
@@ -451,7 +451,7 @@ def dihedral_angle_coordinate_name(
 
 
 # # dummy atom functions
-def dummy_keys(zma: VMatrix) -> tuple[int]:
+def dummy_keys(zma: VMatrix) -> tuple[Key, ...]:
     """Obtain keys to dummy atoms in the Z-Matrix.
 
     :param zma: Z-Matrix
@@ -461,7 +461,7 @@ def dummy_keys(zma: VMatrix) -> tuple[int]:
     return keys
 
 
-def dummy_coordinate_names(vma: VMatrix) -> tuple[str]:
+def dummy_coordinate_names(vma: VMatrix) -> tuple[Name, ...]:
     """Obtain names of all coordinates associated with dummy atoms
     defined in the V-Matrix.
 
@@ -484,16 +484,15 @@ def dummy_coordinate_names(vma: VMatrix) -> tuple[str]:
     return dummy_names
 
 
-def dummy_source_dict(zma, dir_: bool = True):
+def dummy_source_dict(
+    zma: VMatrix, dir_: bool = True
+) -> dict[int, int] | tuple[int, int]:
     """Obtain keys to dummy atoms in the Z-Matrix, along with their
     parent atoms.
 
     :param zma: Z-Matrix
-    :type zma: automol Z-Matrix data structure
     :param dir_: Include linear direction atoms? defaults to True
-    :type dir_: bool, optional
     :returns: A dictionary mapping dummy atoms onto their parent atoms
-    :rtype: dict[int: int]
     """
     key_mat = key_matrix(zma)
     dum_keys = dummy_keys(zma)
@@ -513,14 +512,12 @@ def dummy_source_dict(zma, dir_: bool = True):
     return src_dct
 
 
-def conversion_info(zma) -> ZmatConv:
+def conversion_info(zma: VMatrix) -> ZmatConv:
     """Get the conversion information for this z-matrix, relative to geometry following
     the same atom order.
 
     :param zma: Z-Matrix
-    :type zma: automol Z-Matrix data structure
     :return: The z-matrix conversion
-    :rtype: ZmatConv
     """
     zcount = count(zma)
     src_zkeys_dct = dummy_source_dict(zma)
@@ -529,14 +526,12 @@ def conversion_info(zma) -> ZmatConv:
 
 # # V-Matrix-specific functions
 # # # setters
-def set_key_matrix(vma, key_mat):
+def set_key_matrix(vma: VMatrix, key_mat: KeyMatrix) -> VMatrix:
     """Re-set the key matrix of a V-Matrix using the input key matrix.
 
     :param vma: V-Matrix
-    :type vma: automol V-Matrix data structure
-    :param key_mat: key matrix of V-Matrix coordinate keys
-    :type key_mat: tuple(tuple(int))
-    :rtype: tuple(str)
+    :param key_mat: Key matrix of V-Matrix coordinate keys
+    :return: VMatrix with input keys
     """
     symbs = symbols(vma)
     name_mat = name_matrix(vma)
@@ -545,14 +540,12 @@ def set_key_matrix(vma, key_mat):
     return vma
 
 
-def set_name_matrix(vma, name_mat):
+def set_name_matrix(vma: VMatrix, name_mat: NameMatrix) -> VMatrix:
     """Re-set the name matrix of a V-Matrix using the input name matrix.
 
     :param vma: V-Matrix
-    :type vma: automol V-Matrix data structure
     :param name_mat: name matrix of V-Matrix coordinate names
-    :type name_mat: tuple(tuple(int))
-    :rtype: tuple(str)
+    :return: V-Matrix reset
     """
     symbs = symbols(vma)
     key_mat = key_matrix(vma)
@@ -562,14 +555,12 @@ def set_name_matrix(vma, name_mat):
 
 
 # # # names and naming
-def rename(vma, name_dct):
+def rename(vma: VMatrix, name_dct: dict[str, str]) -> VMatrix:
     """Rename a subset of the coordinates of a V-Matrix.
 
     :param vma: V-Matrix
-    :type vma: automol V-Matrix data structure
-    :param name_dct: mapping from old coordinate names to new ones
-    :type name_dct: dict[str: str]
-    :rtype: automol V-Matrix data strucutre
+    :param name_dct: Mapping from old coordinate names to new ones
+    :return: VMatrix with new names
     """
     orig_name_mat = numpy.array(name_matrix(vma))
     tril_idxs = numpy.tril_indices(orig_name_mat.shape[0], -1, m=3)
@@ -586,7 +577,7 @@ def rename(vma, name_dct):
     return from_data(symbols(vma), key_matrix(vma), name_mat)
 
 
-def standard_form(vma, shift=0):
+def standard_form(vma: VMatrix, shift: int = 0) -> VMatrix:
     """Build a V-Matrix where all of the coordinate names of an input V-Matrix
     have been put into standard form:
         RN: (1<=N<=Ncoords)
@@ -594,30 +585,29 @@ def standard_form(vma, shift=0):
         DN: (1<=N<=Ncoords).
 
     :param vma: V-Matrix
-    :type vma: automol V-Matrix data structure
     :param shift: value to shift the keys by when obtaining the keys
-    :type shift: int
-    :rtype: automol V-Matrix data strucutre
+    :return: V-Matrix of coordinate names
     """
     name_mat = standard_name_matrix(vma, shift=shift)
     return set_name_matrix(vma, name_mat)
 
 
 # # # add/remove atoms
-def add_atom(vma, symb, key_row, name_row=None, one_indexed=False):
+def add_atom(
+    vma: VMatrix,
+    symb: str,
+    key_row: KeyRow,
+    name_row: NameRow = None,
+    one_indexed: bool = False,
+) -> VMatrix:
     """Add an atom to a V-Matrix.
 
     :param vma: V-Matrix
-    :type vma: automol V-Matrix data structure
-    :param symb: symbol of atom to add
-    :type symb: str
-    :param key_row: row of keys to define new atom added to key matrix
-    :type key_row: tuple(int)
-    :param name_row: row of names to define new atom added to name matrix
-    :type name_row: tuple(str)
-    :param one_indexed: parameter to store keys in one-indexing
-    :type one_indexed: bool
-    :rtype: automol V-Matrix data structure
+    :param symb: Symbol of atom to add
+    :param key_row: Row of keys to define new atom added to key matrix
+    :param name_row: Row of names to define new atom added to name matrix
+    :param one_indexed: Parameter to store keys in one-indexing
+    :return: V-Matrix with new atom
     """
     symbs = symbols(vma)
     symbs += (symb,)
@@ -632,15 +622,13 @@ def add_atom(vma, symb, key_row, name_row=None, one_indexed=False):
     return vma
 
 
-def remove_atom(vma, key):
+def remove_atom(vma: VMatrix, key: Key) -> VMatrix:
     """Remove an atom from a V-Matrix. Error raised if attempting
     to remove atom other atoms depend on.
 
     :param vma: V-Matrix
-    :type vma: automol V-Matrix data structure
     :param key: key of atom to remove
-    :type key: str
-    :rtype: automol V-Matrix data structure
+    :return: V-Matrix without atom
     """
     symbs = list(symbols(vma))
     symbs.pop(key)
@@ -664,12 +652,11 @@ def remove_atom(vma, key):
 
 
 # # # validation
-def is_valid(vma):
+def is_valid(vma: VMatrix) -> bool:
     """Assess if a V-Matrix has proper structure.
 
     :param vma: V-Matrix
-    :type vma: automol V-Matrix data structure
-    :rtype: bool
+    :return: True, if V-Matrix has proper structure; False otherwise
     """
     ret = True
     try:
@@ -682,28 +669,25 @@ def is_valid(vma):
     return ret
 
 
-def is_standard_form(vma):
+def is_standard_form(vma: VMatrix) -> bool:
     """Assesses if the names of the V-Matrix are in standard form:
         RN: (1<=N<=Ncoords)
         AN: (2<=N<=Ncoords)
         DN: (1<=N<=Ncoords).
 
     :param vma: V-Matrix
-    :type vma: automol V-Matrix data structure
-    :rtype: bool
+    :return: True if V-Matrix is in standard form, False if not
     """
     return names(vma) == names(standard_form(vma))
 
 
 # # # I/O
-def string(vma, one_indexed=False):
+def string(vma: VMatrix, one_indexed: bool = False) -> str:
     """Write a V-Matrix object to a string.
 
     :param vma: V-Matrix
-    :type vma: automol V-Matrix data structure
-    :param one_indexed: parameter to write keys in one-indexing
-    :type one_indexed: bool
-    :rtype: str
+    :param one_indexed: Parameter to write keys in one-indexing
+    :return: String
     """
     shift = 1 if one_indexed else 0
     symbs = symbols(vma)
@@ -728,14 +712,12 @@ def _line_string(row_idx):
     return vma_str
 
 
-def from_string(vma_str, one_indexed=None):
+def from_string(vma_str: str, one_indexed: bool | None = None) -> VMatrix:
     """Parse a V-Matrix object from a string.
 
     :param vma_str: string containing a V-Matrix
-    :type vma_str: str
     :param one_indexed: Read a one-indexed string?
-    :type one_indexed: bool
-    :rtype: automol V-Matrix data structure
+    :return: V-Matrix of string
     """
     rows = VMAT_LINES.parseString(vma_str).asList()
     symbs = [r.pop(0) for r in rows]
@@ -748,17 +730,16 @@ def from_string(vma_str, one_indexed=None):
 
 
 # # helpers
-def _key_matrix(key_mat, natms, one_indexed=None):
+def _key_matrix(
+    key_mat: KeyMatrix, natms: int, one_indexed: bool | None = None
+) -> KeyMatrix:
     """Build name matrix of the V-Matrix that contains the
     coordinate keys by row and column.
 
     :param key_mat: key matrix of V-Matrix coordinate keys
-    :type key_mat: tuple(tuple(int))
     :param natms: number of atoms
-    :type natms: int
     :param one_indexed: parameter to write keys in one-indexing
-    :type one_indexed: bool
-    :rtype: tuple(tuple(str))
+    :return: Name matrix of V-Matrix
     """
     if natms == 1:
         return ((None, None, None),)
@@ -780,15 +761,13 @@ def _key_matrix(key_mat, natms, one_indexed=None):
     return tuple(map(tuple, key_mat))
 
 
-def _name_matrix(name_mat, natms):
+def _name_matrix(name_mat: NameMatrix, natms: int) -> NameMatrix:
     """Build name matrix of the V-Matrix that contains the
     coordinate names by row and column.
 
     :param name_mat: key matrix of V-Matrix coordinate keys
-    :type name_mat: tuple(tuple(int))
     :param natms: number of atoms
-    :type natms: int
-    :rtype: tuple(tuple(str))
+    :return: Name matrix of Vmatrix
     """
     if name_mat is None:
         name_mat = numpy.empty((natms, 3), dtype=object)
@@ -815,12 +794,11 @@ def _name_matrix(name_mat, natms):
     return tuple(map(tuple, name_mat))
 
 
-def _is_sequence_of_triples(obj):
+def _is_sequence_of_triples(obj) -> bool:
     """Assess if input object sequence has length of three.
 
-    :param obj: object with __len__ attribute
-    :type obj: list, tuple, dict
-    :rtype: bool
+    :param obj: Object with __len__ attribute
+    :return: True if object is less than len=3, False if not
     """
     ret = hasattr(obj, "__len__")
     if ret: