DESIGN OF COSMETIC SUN SCREENS 103 ,P = 6.9 X 10ae .... /]•V X a = 1.15 X 10 -3ø X e .... /a (6) where N = the Avogadro number, 6.06 X 102a, and a = the chrornophore area, centimeters squared. The chromophore area is that part of the molecule within which a given photon must strike in order that interaction and absorption shall occur. In complex molecules this area is generally much smaller than the total cross-sectional area, and includes only those atoms and bonds which are concerned in the transition. The values of emax. for high intensity electronic bands are of the order of 10 4 to 10 5, and chromophore areas of the order of 10 -•5 to 10 -'6 cm. 2, or 1 to 10 square Angstrom units. This corresponds to transition prob- abilities of approximately unity. In such a case it is said that the transi- tion is allowed and occurs whenever a photon of the proper energy strikes the appropriate part of the molecule. In order to use these generalizations in the design of new sun screening compounds, it would be necessary to predict the transition energies associated with specific atomic and molecular groupings. An approach to this can be made through our knowledge of the electronic structures of organic compounds. Mineral oils have from time to time been used as sun screens. These oils are predominantly saturated para•n hydrocarbons. The electronic bonds in such compounds are formed by pairs of electrons in covalent bonds. For example in butane: H H H H The absorption of energy in the erythemal range is known to involve electronic shifts. The most probable shifts in saturated compounds involve the complete ionization of the molecule, brought about through bond rupture: --C : C-- • --C: + C-- The probability of such an ionization is extremely small, and we find that extinction coe•cients •or hydrocarbons in the near ultraviolet and the visible range are close to zero. These transitions are not allowed by the molecular structure. This class of compounds does not absorb in the erythemal range, and whatever doubtful value they may have cannot be due to their sun screening activity. For unsaturated compounds, another type of electronic transition is possible. One pair of the two pairs of electrons forming the double bond may resonate between two possible structures:

104 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS /.C. :C k •- •C : : C( • /C: ..C• This type of transition requires about 170 kcal./gm.-mole for a single olefinic group, and corresponds to an absorption at 170 m/•, in the far ultraviolet. At this point the emax. iS high and the transition probability is about 1.0. As the unsaturated structures increase in length, i.e., there are greater numbers of unsaturated bonds in the molecule, the ionic and homopolar resonance structures contribute more and more to both the ground state and excited states of the molecule. This results in the lowering of the potential energy levels of both the ground and the excited states with respect to the unconjugated system. But since the contribution of res- onance structures is greater in the excited than in the ground state, the energy level of the former is lowered more than that of the latter. The transition energy therefore is reduced and the absorption bands are dis- placed to longer wavelengths (bathochromic shift). e ß ß e C C•C C • C=C C•C • --C--C----C--C-- ß . .. As the number of conjugated double bonds in the resonating system in- creases, this shift of em=x. to longer wavelengths continues, as shown in Table 1. TABLE 1--ABSORPTION MAXIMA OF CONJUGATED UNSATURATES OF THE SERIES (--C=C )n kmax. ½max. Color 1 170.0 15,000 Colorless 2 217.0 21,000 Colorless 3 258.0 35,000 Colorless 4 310.0 42,000 Pale Yellow 5 328.0 51,000 Yellow (Vitamin A) 11 472.0 170,000 Red 15 528.0 150,000 Violet 0 Kekul• structures 0:0 • :0• Dipolaf structures Homopolar structures