102 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Braude (1) points out that the absorption maximum for a given molecule corresponds to the most probable transition, and the value of X,•x. is one of the most characteristic parts of the absorption curve. For a cosmetic sun screen, the location of the absorption maximum should therefore correspond to those wavelengths of sunlight which have a major erythemal effect on human skin. Solar radiation is known to extend in a continuous band throughout the entire electromagnetic spectrum. Were it not for the absorption of the lower wavelengths by our atmosphere, which absorbs virtually all radiation of wavelengths shorter than 290 millimicrons (mu), it is doubtful that life, at least as we know it, would have been possible on Earth. At any rate, the major erythemal wave- lengths penetrating the atmosphere to sea level extend from about 290 to 315 mu. From equation 1 it is calculable that these wavelengths correspond to transition energies of 91.4 to 99.4 kcal./gm.-mole. At the wavelength of maximum erythemal effectiveness, 297.5 m/•, the corre- sponding transition energy is 96.9 kcal./gm.-mole. A transition with zXE of 90.4 kcal./gm.-mole will have an absorption maximum at 320 mu, a region where absorption is undesirable because it impedes tanning. At the other end of the erythemal range, a transition energy of 103.2 kcal./gm.-mole results in an absorption maximum at 280 mu, too low to be cosmetically useful. It becomes apparent from these figures that the allowable transitions that will result in a useful cosmetic sun screening fall within an exceedingly narrow range of energy requirements. It is not surprising then that few molecular species have been found which will serve satisfactorily as screens for human use. The extent of the absorption of any particular wavelength depends further on the molecular geometry of the molecules. The quantitative measure of completeness of absorption is given by the molecular extinction coefficient, e,•x., which is defined by the equation: • .... = (O.D./cl)= (100f%T)/cl) (5) where O.D. = optical density -- log (100/%T) %T = per cent transmission c = concentration of the screen, gm.-moles/liter, and l = thickness of the absorbing layer, in centimeters. The value of ema, x ' iS as characteristic of a molecular species as is the value of The absorption coefficient, e .... , is determined by the transition prob- ability, in the statistical sense. That is: when a photon of radiant energy strikes a molecule, what is the statistical probability of absorption of the photon? This transition probability is given approximately by Braude (1) as

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: