Generate the electronic configuration of neutral atoms

AtomicShells.py

# Possible names of this ordering rule :
# * Madelung rule (after Erwin Madelung)
# * Janet rule (after Charles Janet)
# * Klechkowsky rule (after Vsevolod Klechkovsky)
# * aufbau approximation
# * Uncle Wiggly path or
# * diagonal rule
def aufbau():
    i = 0
    while True:
        subshell = i // 2
        shell = i - subshell
        while (subshell >= 0):
            yield (subshell,shell)
            subshell -= 1
            shell += 1
        i += 1

# Returns the size of the subshell of index i
# It is the sequence 2, 6, 10, 14, ...
subshell_size = lambda i: 4 * i + 2

# Returns the theorical electronic configuration of the neutral atom
# with _atomic_number_ protons in its neucleus
def electronic_configuration(atomic_number):
    result = []
    electrons = atomic_number
    for subshell, shell in aufbau():
        current = min(electrons, subshell_size(subshell))
        while len(result) <= shell:
            result += [list()]
        result[shell] += [current]
        electrons -= current
        if not electrons:
            break
    return result

for n in range(1, 119):
    print("{:3}: {}".format(n, electronic_configuration(n)))

Sample output:

  1: [[1]]
  2: [[2]]
  3: [[2], [1]]
  4: [[2], [2]]
  5: [[2], [2, 1]]
  6: [[2], [2, 2]]
  7: [[2], [2, 3]]
  8: [[2], [2, 4]]
  9: [[2], [2, 5]]
 10: [[2], [2, 6]]
 11: [[2], [2, 6], [1]]
 12: [[2], [2, 6], [2]]
 13: [[2], [2, 6], [2, 1]]
 14: [[2], [2, 6], [2, 2]]
 15: [[2], [2, 6], [2, 3]]
 16: [[2], [2, 6], [2, 4]]
 17: [[2], [2, 6], [2, 5]]
 18: [[2], [2, 6], [2, 6]]
 19: [[2], [2, 6], [2, 6], [1]]
 20: [[2], [2, 6], [2, 6], [2]]
 21: [[2], [2, 6], [2, 6, 1], [2]]
 22: [[2], [2, 6], [2, 6, 2], [2]]

by replacing the break with

offset = (0 if len(result[shell]) == 1 else 34 - 2 * len(result[shell]) ** 2)
return (offset + current, len(result))

one can have the position (starting from (1,1) to (32,7)) of the element on the Mendeliev table