Quantum mechanical and classical aspects are of equal importance in chemistry, and theoretical chemistry must be able to deal with this situation. Classical quantities with which a chemist has to deal include, for example, the temperature and the chemical potential of a substance, and chirality, knot-type and tertiary structures of molecules. Classical concepts of this type are no more consequences of traditional quantum chemistry than is the theory of complex chemical processes (for example adsorption, heterogeneous catalysis) and macroscopic systems. Algebraic quantum mechanics affords a general framework for the discussion of classical quantities and large systems. There are other independent approaches for the theoretical treatment of chemical problems; these can be summarized by using the keywords "fractals", "chaotic motion", "quasicrystals" and "knot theory". The relationships between these four research topics and their connection with algebraic quantum mechanics, as well as their importance for theoretical chemistry, were discussed at a NATO Workshop in 1987 (see Ref. 111). In an extended theoretical chemistry, the notion of "molecules" will not play a role as central as it does in quantum chemistry. In the theory of large systems in particular, the introduction of complementary approaches appears to be appropriate; the term "molecule" as used by the chemist does not appear either in the description of disordered systems by means of fractals or in the thermodynamic limit of algebraic statistical mechanics.

Socitte suisse de chimie, BLle -Societa svizzera di chimica, Basilea Nachdruck verboten -Tous droits rCservts -Printed by Birkhauser AG, Basel, Switzerland Erscheint 9mal jahrlich -Parait 9 fois par an ISSN 0018-019X SummaryAll-valence electron calculations on the chiroptic properties of oligopeptides rapidly become intractable, as the size of the molecule increases. A Frozen Core procedure is here proposed, which is inspired by the PPP method. It takes explicitly into account only the (pseudo) 7c electrons and oxygen n electrons of the amide moieties, as well as the 7c electrons of eventual long-wavelength absorbing sidegroups. Local n-71 interaction is taken into account by an adjustable parameter. Other parameters are calibrated on the isolated amide and carbonyl chromophores. The method then follows the usual SCF-CI procedure. Rotatory strengths and f-values for the transitions are computed without further approximations, as previously described. Comparisons with results from exciton calculations and experimental data on polypeptides show the computed quantities to have a consistent and satisfactory order of magnitude. General introduction. -Twenty years ago M o f j t t [ 11 [3] and Fittscomputed by the exciton model the optical activity of the z-n* bands of a-helical polypeptides. Mofitt, using periodic boundary conditions, arrived at definite selection rules and clearcut predictions: If one considers the electric dipoleelectric dipole interaction (,ui-,uj mechanism) of the individual long-wavelength z-z* transitions (A-190 nm) in each amide chromophore, the composite system, i.e. the helix, shows two transitions: One transition at longer wavelength (A-210 nm) polarized parallel to the axis of the helix, another degenerate one at shorter wavelength (A -190 nm) polarized perpendicularly. In the righthanded helix the rotatory strength of the former is negative, that of the latter positive (see Fig. I ) . It was then shown that Moflitt's approach contained an inconsistency [3]: namely, that of assuming periodic boundary conditions -suited for quasi-infinite helices -, while at the same time using the nonretarded spatially averaged expression for the rotatory strength applicable to randomly oriented molecules of much smaller size than the wavelength of light. Later investigations have dealt with this question in detail [4-61. Mofjtt's original predictions, however, appeared to agree essentially ') 2, 120a

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