Periodic Table Notation
I decided to define the notation based on the periodic table, which is ordered according to the atomic number.
Definition
The notation has the format using capital letters first. Digraphs use a capital letter followed by a small letter. The expressions in this notation are of this form:
(HHeLiBeBVNOFNeNaMgAl ...)
Here "HHeLiBeBVNOFNeNaMgAl ..." are a sequence of actual letters in the Latin alphabet. Wrapping p{} are simply to distinguish the expressions from actual words. p{} is also a valid expression. An example of a valid expression is p{HHeLi}.
Here is the set of the symbols to represent the number:
(H, He, Li, Be, B, C, N, O, F, Ne, Na, Mg, Al, Si, P, S, Cl, Ar, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Br, Kr, Rb, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Sb, Te, I, Xe, Cs, Ba, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Ly, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, Po, At, Rn, Fr, Ra, Ac, Th, Pa, U, Np, Pu, Am, Cm, Bk, Cf, Es, Fm, Md, No, Lr, Rf, Db, Sg, Bh, Hs, Mt, Ds, Rg, Cn, Nh, Fl, Mc, Lv, Ts, Og)
where:
H = 1
He = 2
Li = 3
Be = 4
B = 5
C = 6
N = 7
O = 8
F = 9
Ne = 10
Na = 11
Mg = 12
Al = 13
Si = 14
P = 15
S = 16
Cl = 17
Ar = 18
K = 19
Ca = 20
Sc = 21
Ti = 22
V = 23
Cr = 24
Mn = 25
Fe = 26
Co = 27
Ni = 28
Cu = 29
Zn = 30
Ga = 31
Ge = 32
As = 33
Se = 34
Br = 35
Kr = 36
Rb = 37
Sr = 38
Y = 39
Zr = 40
Nb = 41
Mo = 42
Tc = 43
Ru = 44
Rh = 45
Pd = 46
Ag = 47
Cd = 48
In = 49
Sn = 50
Sb = 51
Te = 52
I = 53
Xe = 54
Cs = 55
Ba = 56
La = 57
Ce = 58
Pr = 59
Nd = 60
Pm = 61
Sm = 62
Eu = 63
Gd = 64
Tb = 65
Dy = 66
Ho = 67
Er = 68
Tm = 69
Yb = 70
Ly = 71
Hf = 72
Ta = 73
W = 74
Re = 75
Os = 76
Ir = 77
Pt = 78
Au = 79
Hg = 80
Tl = 81
Pb = 82
Bi = 83
Po = 84
At = 85
Rn = 86
Fr = 87
Ra = 88
Ac = 89
Th = 90
Pa = 81
U = 92
Np = 93
Pu = 94
Am = 95
Cm = 96
Bk = 97
Cf = 98
Es = 99
Fm = 100
Md = 101
No = 102
Lr = 103
Rf = 104
Db = 105
Sg = 106
Bh = 107
Hs = 108
Mt = 109
Ds = 110
Rg = 111
Cn = 112
Nh = 113
Fl = 114
Mc = 115
Lv = 116
Ts = 117
Og = 118
Rules
p{} = 0
p{#$%} = #*$*% where #, $, % represents an element.
p{#_{n}} = p{### ... ###} (n #'s) where # represents an element and n ≥ 1.
p{#_{1}} = p{#}
Examples
p{CO_{2}} = p{COO} = 6*8*8 = 384
p{H_{2}O} = p{HHO} = 1*1*8 = 8
p{C_{6}H_{12}O_{6}} = p{CCCCCCHHHHHHHHHHHHOOOOOO} = 6*6*6*6*6*6*1*1*1*1*1*1*1*1*1*1*1*1*8*8*8*8*8*8 = 12,230,590,464
p{O_{2}} = p{OO} = 8*8 = 64