Under construction.
I plan to create the notation based on molar mass of the chemical substance.
I propose the notation for the number named "hydrogen" to be 2^1 = 2, "helium" to be 2^4 = 16, "carbon" to be 2^12 = 4096, "oxygen" to be 2^16 = 65536, etc. With compounds such as "carbon dioxide", this would be equal to 2^44 = 17,592,186,044,416.
I decided that the notation will be the power of 2 with the exponent based on the molar mass rounded to the nearest integer.