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Electronic Structures of Cephalosporin and Penicillin Moieties Donald B. Boyd Contribution f r o m The Lilly Research Laboratories, Eli Lilly and Company, Indianapolis, Indiana 46206. Received January 4, 1972 Abstract: The electronic energy levels and charge distributions of the cephem and penam nuclei and their analogs are obtained by extended Huckel molecular orbital calculations. Oscillator strengths for the uv transitions are computed from rigorously evaluated dipole length integrals, and excitation energies are obtained in the virtual orbital approximation. Qualitative agreement with experimental spectral properties across a range of related molecules indicates an adequacy of the theory to describe the general nature of the chromophores involved, even though quantitative agreement is expectedly mediocre. In agreement with deductions from experimental data, the 260-nm band of the 3-cephems is due to the excitation of an electron from an enamine R MO to one with both C=O K* and C=C K* character, and the 230-nm band arises from a transition from an amide lone-pair MO to the C=O, C = C R* MO. In the P-lactams where no chromophore mixes strongly with the MO's localized on the plactam ring, the principal transition is of amide n K* character.
-
ephalosporins and penicillins constitute an important class of therapeutically useful antibiotics. The molecular nuclei of these compounds, namely, a P-lactam ring fused to a dihydrothiazine or thiazolidine ring, have been shown t o be responsible for the biological activity of these compounds, although, of course, the variety of side chains present may enhance or mitigate the activity. In this paper the electronic structures of these molecular nuclei are explored by quantum mechanical calculations. In particular, the uv spectral transitions are studied in order to make assignments and to gain a description of the chromophores. If the calculations are reasonably successful in correlating with experimental data, and we will see that they are, then the computed molecular orbitals may be regarded as a correspondingly reliable description of the electronic structures. Utilizing the proposed2 mechanism of action of these antibiotics and the knowledge of the electronic structure, it should be possible to rationally devise modifications of the cephalosporins and penicillins which will enhance their biological activity. Our initial goal then is t o learn about the electronic structures of the cephalosporin and penicillin nuclei by a comparison of experimental and theoretical findings on the spectra of these moieties. The approach will be to investigate the model compounds depicted schematically below which are appropriate for the analysis of the chromophores of the cephem and penam nuclei. Experimental uv and C D spectral data are not available for these models, but by abstracting information from the most appropriate compounds which have been observed spectroscopically, it will be possible to make qualitative comparisons between theory and experiment. Model 1, 7-amino-3-cephem, is, of course, the fundamental nucleus of the biologically active cephalosporins. A detailed analysis of 3-cephem spectra has recently been p ~ b l i s h e d ,and ~ it is of primary concern t o study this species. Model 2, 7-aminocepham, lacks the carbon-carbon double bond of 1, but still contains the
C
(1) C. Hansch and A . R. Steward, J . Med. Chem., 7, 691 (1964); C. Hansch and E. W. Deutsch, ibid., 8, 705 (1965); G. L. Biagi, M. C. Guerra, A. M . Barbaro, and M. F. Gamba, ibid., 13, 511 (1970). (2: D. J. Tipper and J. L. Strominger, J . Bid. Chem., 243, 3169 (1968); B. Lee, J . Mol. B i d , 61, 463 (1971); R. Hartmann, J.-V. Holtje, and U. Schwarz, Nature (London), 235, 426 (1972).
(3) R. B. Hermann, to be published. (4) R. Nagarajan and D. 0. Spry, J . Amer. Chem. Soc., 93, 2310 (1971).
A,
011
a
3
H,,
/3-lactam and sulfide chromophores. The P-lactam chromophore is also investigated in the simple P-lactam model compound 3 and in the decarboxylated, 4, and carboxylated, 5, penams. Calculations on the known compound 6-aminopenicillanic acid (6-APA), which is 5 with geminal dimethyl substituents on Cs, are not included because the methyl groups are expected t o have only a small perturbing effect and would lengthen the calculations considerably. The P,y-unsaturated sulfide portion of 1 is modeled by compound 6, propylallyl sulfide. A closer analog of 1 is the dihydrothiazine ring without, 7, and with, 8, the carboxyl group. Calculations on the dihydrothiazine ring systems can elucidate the combined effects of the enamine and sulfide chromoBoyd / Electronic Structures of Cephalosporins and Penicillins
6514
phores. Comparison of 7 and 8 allows some assessment of the effect of the carboxyl group. The 3-acetoxymethyl-4-carboxyl form of 1 (giving 7-aminocephalosporanic acid, 7-ACA) was not calculated, again because of the computer times involved and because the smaller analogs should suffice. Experimentally, the effect of 7-methoxylation of a 3-cephem is known,5 so calculations are included on 9 which will be compared to 1. Finally, 7-amino-2-cephem, 10, is studied both because it is an interesting a,P-unsaturated sulfide and because it affords an example of a cephem nucleus without antibiotic activity. The relevant uv and C D spectral data for all the model compounds will be given later along with the presentation of the calculational results.
Methodology The extended Huckel (EH) method6 of molecular orbital theory is especially well suited for the compounds of interest here because their nonplanarity necessitates the simultaneous treatment of all valence electrons. Moreover, the fact that the secular equation for each molecule needs t o be solved only once (as contrasted with several times in an iterative, self-consistent MO method) means that the wave functions are rapidly evaluated on a computer. The main question to ask in regard to selection of the EH method is whether such a simple method is adequate to describe the ground and excited state wave functions. There are an increasing number of that the E H method is adequate for making spectral assignments, if judiciously applied to compounds spanning a sufficiently narrow domain of chemical types. Hence we proceeded cautiously, not expecting quantitative agreement with experimental spectra, but aiming at obtaining qualitatively useful results. One type of data entering into the calculation of an EH wave function includes the orbital exponents and the negative of the valence state ionization potentials (VSIP’s). These were taken at the commonly accepted values for carbon, nitrogen, and hydrogen.6 Several sets of sulfur parameters were tested before settling on the following VSIP’sl’: 20.0 (S 3s), 13.3 ( S 3p), 4.0 eV (S 3d). The energy assigned the S 3d orbitals is such that they are not highly occupied in divalent sulfur compounds (total occupation number of d orbitals is considerably less than O.l), but such that the MO’s formed of d orbitals are accessible by uv excitations. Exponents for sulfur atomic orbitals are the best atom values, l 2 except for the S 3d exponent which is taken as 1.708, the optimized value in a molecular environment.I3 ( 5 ) R . Nagarajan, L. D . Boeck, M. Gorman, R. L. Hamill, C. E. Higgens, M. M. Hoehn, W. M. Stark, and J. G. Whitney, J . Amer. Chem. Soc., 93, 2308 (1971). See, also, E. H. Flynn, “Cephalosporins and Penicillins: Chemistry and Biology,” Academic Press, New York, N . Y . , 1972. (6) D. B. Boyd and W. N. Lipscomb, J. Theor. Biol., 25, 403 (19691, and references therein. (7) R . Hoffmann, Tetrahedron, 22, 539 (1966); Accounts Chem. Res,, 4. . ,1 .(1971) ~
(8) L. Burnelle and M . J. Kranepool, J . Mol. Spectrosc., 37, 383 (1971). (9) D. L. Coffen, J. Q. Chambers, D. R . Williams, P. E. Garrett, and N. D. Canfield, J . Amer. Chem. Soc., 93, 2258 (1971). (10) J. Hinze and H . H . Jaffe, ibid., 84, 540 (1962); T. Jordan, H. W. Smith, L. L. Lohr, Jr., and W. N. Lipscomb, ibid., 85, 846 (1963); J. A. Kapechi and J. E. Baldwin, ibid., 91, 1120 (1969). (1 1) R. Gleiter and R . Hoffmann, Tetrahedron, 24, 5899 (1968). (12) E. Clementi and D. L. Raimondi, J. Chem. Phys., 38, 2686 (1963). (13) F. P. Boer and W. N. Lipscomb, ibid., 50, 989 (1969).
This exponent for the 3d Slater-type basis functions is in line with a proposed ruleI4 on the size of the d orbitals of second-row atoms. Our sulfur parameters provided the most reasonable charge distribution (in terms of net atomic charges) and excitation energies for not only the compounds treated here, but also for other compounds of divalent sulfur.’j Turning to the oxygen orbital parameters, we again tried several sets.6t16 A set consisting of Slater exponents and VSIP’s of 29.0 (0 2s) and 14.5 eV (0 2p) proved to give the least excessive charge separations. These VSIP’s are based on an extrapolation of quadratic functions fitted, respectively, to the 2s and 2p VSIP’s of boron,” carbon,6 and nitrogen6 The values are considerably less negative than those used by previous authors. As is recognized, a common fault of the E H method is to give exaggerated charge separations, so that our set of orbital parameters compensates in the right direction. In addition, our standard usage6~1s~19 of a Wolfsberg-Helmholz constant of 2.0 also diminishes charge separations somewhat. The second type of data entering into EH calculations is the geometry of the molecules specified in terms of atomic coordinates. The tabulation of coordinates for all atoms in compounds 1-10 would be too voluminous to include here, and hence we settle for the following descriptions. The crystal-structure determination2Oasb of cephaloridine. HC1. HaO is the best available source of the nonhydrogenic atomic positions of 1. The preferred conformation of 6 is not known experimentally, so in order to be useful in the analysis of the spectra of 1, the geometry of 6 is based on the SCC=C portion of 1 with the addition of a staggered propyl side chain oriented not to sterically interfere with the allyl portion of the molecule. Similarly, the geometry of 9 is derived from that of 1 with atoms added at standard bond lengths and angles as described below. TWOconformations of 7 and 8 were investigated: one, a distorted half-chair, taken directly from the dihydrothiazine coordinates of 1, and the other, a boat conformation,21based on Dreiding models. The positions of the nonhydrogenic atoms of 10 were obtained from the sole X-ray determined structure of a 2-cephem, phenoxymethyl-A*-desacetoxyl cephalosporin. Since it was expected that the hybridization at the @lactam nitrogen of 2 and 3 would be nearly planar as in 10, the atomic coordinates of 2 and 3 were taken from 10 with the additional assumption that the tetrahydrothiazine ring in 2 exists in a chair conformation. The 4 and 5 penam geometries were taken from the refined crystal structure of potassium benzylpenicillin. * Hy(14) D. B. Boyd, ibid., 52, 4846 (1970). (15) D. B. Boyd, J . Amer. Chem. Soc., in press. (16) R . Hoffmann, G. D. Zeiss, and G. W. Van Dine, ibid., 90, 1485 (1968). (17) R. Hoffmann,J . Chem. P h j , ~ .40, , 2474 (1964). (18) R. A. Archer, D. B. Boyd, P. V. Demarco, I . J. Tyminski, and N. L . Allinger, J . Amer. Chem. Soc., 92, 5200 (1970). (19) D. B. Boyd and R. Hoffmann, ibid., 93, 1064 (1971). (20) (a) R. M. Sweet and L. F. Dahl, ibid., 92, 5489 (1970). (b) Our coordinate system for 1 has N5 at the origin, C6 on the z axis, C3 in the xz plane, and the 01 face of the molecule projecting in the +J direction. (c) Coordinates for 10 were put in a right-handed Cartesian system (as used for the other molecules) with a n arrangement analogous to that described for 1. (21) The coordinate system for the boat forms of 7 and 8 is such that Na is at the origin, C z is on the + z axis, SI is in the xz plane, and CI and CSproject toward the p face of the molecule in the - y direction. (22) G . J. Pitt, Acta Crj.sta/logr.,5, 770 (1952); D. Crowfoot, C . W. B u m , B. W. Rogers-Low, and A. Turner-Jones in “The Chemistry of Penicillin,” H . T. Clarke, J. R . Johnson, and R. Robinson, Ed., Prince-
Journal of the American Chemical Society / 94:18 / September 6 , 1972
+
6515
drogens and other atoms necessary t o complete structures 1-10 were added with the following bond lengths, 1.10 (C-H), 1.00 (N-H), 0.95 (0-H), 1.54 (C-C), and 1.43 8, (C-0), and the following bond angles, 109.4712’ at nitrogens and saturated carbons, 120’ at other carbons, 105’ for C-0-H, and 110’ for C-0-C. In cases where several conformers or rotamers were studied, structural details are described further in the Results. Once the E H MO’s are obtained, then the excitation energies and oscillator strengths may be computed. To reduce the computations to manageable proportions, it is common t o employ the necessarily crude virtual orbital approximation. In this approximation a singletsinglet excitation is assumed to occur by the promotion of an electron from one of the ground-state filled MO’s t o one of the previously empty virtual orbitals (which also come from the solution of the secular equation). Thus, the excitation energy is the gap between the MO eigenvalues, A E = e, - en, and the oscillator strength is evaluated from the transition moment integral between MO’s and $+,. When an electron is excited from to +,, in an N-electron molecule, the transition moment integral (in atomic units and using the dipole length formalism) between the ground and excited state singlet wave functions is
+,
~
m
= n
+,
((N!)+Z(-
1)7~,[+~(1)a(1). ..
r +m(j)dA+m(j
+n(j)a(j)$m(j
+ 1)P(j + 1). . .
+ 1)P(j + 1).
’
+A~/~(”3(WI -
(N!)-’/~C( - 1)7~~[+ 1 1) ~( ( 1 ) . r +n(j)p(j)+m(j
+ 1)a(j + 1).
’
+.~/*(WD(WI})
Here P, is the usual electron permutation operatorz3 with the index Y going over all permutations of the N electrons among the one-electron orbitals, which are given as a product of a MO and a spin function, cy or p. With the aid of the orthonormality of the MO’s, the above expression reduces to Rmn = .\/Z($mirl$n). Since the MO’s are expressed as linear combinations of atomic orbitals, $, = 2,CBmxP,we evaluate Rmn = ~ / z ~ p ~ , C , , C , n ( x p ’ r ~where x p ) , the procedure for the exact evaluation of the dipole moment integrals over the Slater-type basis functions, xp, has been discussed. 2 4 , 2 3 If the transition moment integral is in atomic units and the excitation energy, AE, in electron volts, then the oscillator strength, which is proportional to the area under a uv absorption band, is givenz6 by f = 0.0245AEiRmnjz. For molecules of interest here, symmetry is of little use in deciding on the allowedness of a ton University Press, Princeton, N. J., 1949, p 310. The coordinate system for models 4 and 5 is defined by N Pbeing at the origin, C Sbeing on the +r axis, CZbeing in the xz plane, and the LY face of the molecule projecting in the + y direction. (23) A. Messiah, “Quantum Mechanics,” Vol. 2, Wiley, New York, N. Y., 1962, p 599. (24) D. B. Boyd in “Purines: Theory and Experiment,” E. D. Bergmann and B. Pullman, Ed., Academic Press, New York, N. Y., 1972. (25) D. B. Boyd, J . Amer. Chem. SOC.,94, 64(1972). (26) G . Herzberg, “Molecular Spectra and Molecular Structure,” Vol. 3, D. Van Nostrand Co., Princeton, N. J., 1967, p 417.
transition, and, consequently, Rmn is evaluated exactly with all one- and two-center integrals. N o attempt is made t o compute optical rotatory strengths because of the inadequacy of EH wave functions found in previous studies. 27 Nevertheless, experimental C D data can be useful to our analysis. Frequently, bands occurring in the uv region can be identified in C D spectra because of their optical activity. Results and Discussion 7-Amino-3-cephem. The 3-cephem moiety is observed experimentally to have two well-defined transitions in the uv region: a strong band (extinction coefficient 7000-10,000) near 260 nm which is seen in both uv and C D spectra, and a weaker band (extinction coefficient
