F. S. Richardson, R.
248
Strickland, and D. D. Shiilady
Optical Activity of Simple Cyclic Amides. INDO Molecular Orbital Model1 F. S. Richardson,* R. Strickland, and D. D. Shiilady Department of Chemistry, University of Virginia, Charlottesville, Virginia 22901
(Received June 14, 1972)
Publication costs assisted by the Petroleum Research Fund
An INDO molecular orbital model is used to compute the oscillator strengths, rotatory strengths, and anisotropy factors for the lowest-lying singlet singlet transitions in several dissymmetric pyrrolidin-2one and 2,5-diketopiperazine systems. The chemical compounds included in the study are (1) 5methylpyrrolidin-2-one, (2) 3-methylpyrrolidin-2-one, (3) 3-aminopyrrolidin-2-one, (4) 3-ammoniumpyrrolidin-2-one, (5) 3-methyl-2,5-diketopiperazine, and (6) 3,6-dimethyl-2,5-diketopiperazine. Both planar and nonplanar ring structures are examined for each of the compounds in an attempt to assess the relative importance of inherent ring chirality and asymmetric ring substitution in determining the signs and magnitudes of the molecular rotatory strengths. For the amide n — ir* transition, the calculated rotatory strengths are in qualitative agreement with experiment for all systems except the 3-aminopyrrolidin-2one structures where the computed values differ in sign from the experimentally determined ones. The * rotatory strengths receive significant contributions from all three components of the electric and magnetic transition dipoles. This result is in sharp disagreement with the assumption made on the oneelectron perturbation model that only the z-polarized component (where the z direction is coincident with the carbonyl, C=0, bond axis) of the magnetic transition dipole makes a significant contribution. Irhplicit in this result is the suggestion that the “effective” symmetry which determines the nodal pattern of the * state is not C2V, but rather Cs. It is found that inherent ring chirality does have a profound influence on the computed rotatory strengths; but how this is manifested in the solution CD spectra of actual systems is not clear, since solvent effects and conformational equilibria appear to be so closely related.
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—*
I. Introduction
Small cyclic amide and diamide molecules are of special interest in theoretical studies concerned with the optical rotatory properties of the peptide chromophore in a chiral environment. In general, the amide group (CaCONH) is planar in these systems and the ring structures restrict conformational mobility. The optical rotatory properties of molecular systems exhibit extreme sensitivity to very small structural changes. For this reason it is of some practical importance to study, as model systems, molecules whose structural variables are well defined or restricted to a small range of values. Furthermore, the inherent symmetry of the chromophoric group, in the cyclic amides (planar or C„) permits application of perturbation methods in calculating the optical rotatory properties of the peptide transitions. Although there is considerable inherent interest in the optical properties of small amide molecules, the principal objective for many of the spectroscopic studies carried out on these systems is a more complete understanding of protein and polypeptide spectra. In the 185-230-nm spectral region, the optical properties of proteins and polypeptides are determined almost entirely by electronic states derived from localized peptide excitations.2-3 Extensive theoretical studies have been conducted on the structurespectra relationships which exist for amide systems in various states of aggregation.4"19 However, a prerequisite for the successful application of these theories to proteins and polypeptides is a detailed knowledge of the spectroscopic properties of single peptide chromophores. The ultraviolet absorption spectrum of the peptide chromophore has been intensively studied over the past 15 years18"24 and the electronic structure and spectra of several of the simpler amide molecules have been calculated by ab initio The Journal of Physical Chemistry, Vol. 77, No. 2, 1973
quantum mechanical methods.24"26 These studies have yielded considerable information about the identities, frequencies, polarizations, and absorption intensities of
(1) This work was supported by the Petroleum Research Fund (PRF No. 2022-G2), administered by the American Chemical Society. (2) W. B. Gratzer, “Poly-a-Amino Acids,” G. D. Fasman, Ed., Marcel Dekker, New York, N. Y„ 1967. (3) J. A. Schellman and C. Schellman, "The Proteins,” 2nd ed, H. Neurath, Ed., Academic Press, New York, N. Y., 1964, pp 1-137. (4) D. D. Fitts and J. G. Kirkwood, Proc. Natl. Acad. Sci. U. S., 42, 33
(1956).
(5) W. Moffitt, J. Chem. Phys., 25,467 (1956). (6) W. Moffitt, Proc. Natl. Acad. Sci. U. S„ 42, 736 (1956). (7) W. Moffitt, D. D. Fitts, and J. G. Kirkwood, Proc. Natl. Acad. Sci. U. S., 43, 723 (1957). (8) I. Tinoco and R. W. Woody, J. Chem. Phys., 32, 461 (1960). (9) J. Schellman and P. Oriel, J. Chem. Phys., 37, 2114 (1962). (10) I. Tinoco, R. W. Woody, and D. F. Bradley, J. Chem. Phys., 38, 1317 (1963). (11) D. F. Bradley, I. Tinoco, and R. W. Woody, Biopolymers, 1, 239
(1963). (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23)
E. S. Pysh, Proc. Natl. Acad. Sci. U. S., 56, 825 (1966). R. W. Woody and I. Tinoco, J. Chem. Phys., 46, 532 (1967). K. Rosenheck and B. Sommer, J. Chem. Phys., 46, 532 (1967). D. W. Urry, Proc. Natl. Acad. Sci. U. S„ 60, 394 (1967). R. W. Woody, J. Chem. Phys., 49, 4797 (1968). D. W. Urry, Proc. Natl. Acad. Sci. U. S„ 60, 1114 (1968). W. Rhodes and D. G. Barnes, J. Chem. Phys., 48, 817 (1968). W. Rhodes and D. G. Barnes, J. Chim. Phys., 65, 78 (1968). H. D. Hunt and W. T. Simpson, J. Amer. Chem. Soc., 75,
4540 (1953). E. E. Barnes and W. T. Simpson, J. Chem. Phys., 39, 670 (1963). D. L Peterson and W. T. Simpson, J. Amer Chem. Soc., 77, 3929 (1955); 79, 2375 (1957). E. B. Nielson and J. A. Schellman, J. Phys. Chem., 71, 2297 (1967) H. Basch, . B. Robin, and N. A. Kuebler, J. Chem. Phys., 47, 1201 (1967); 49, 5007 (1968). . A. Robb and I G. Csizmadia, Theor. Chim. Acta, 10, 269 (1968) . A. Robb and I G. Csizmadia, J. Chem. Phys., 50, 1819 (1969). .
(24)
(25)
.
(26)
Optical Activity of Simple Cyclic Amides
249
the amide transitions lying in the 170-230-nm region, although it can be accurately stated that a great deal of ambiguity still exists, even with respect to assignments of
individual bands.18'19·24 The information that can be obtained about the electronic transitions of a chromophore from absorption spectra is, in general, not sufficient for predicting the chiroptical properties of the chromophore in a dissymmetric molecule. The observed intensities are attributable almost entirely to electric-dipole absorption processes, and polarization directions refer to the orientations of the electric transition dipoles in the molecule. These studies give no information about the magnitudes or polarizations of the magnetic transition dipoles associated with the electronic excitation processes. In isotropic media, the optical activity associated with a particular electronic transition (i j) —*·
in a dissymmetric molecule is conveniently measured by the rotatory strength.
Rij
=
Im((V,i|m|V'j>-(V'y|/tl^')
=
Im«m)íy(p)j¡)
(1)
where Im the imaginary part of, m is the electric-dipole operator, and µ is the magnetic-dipole operator. To evaluate Rtj, the directions and magnitudes of both the electric transition dipole (m>y (a polar vector quantity) and the magnetic transition dipole (µ)µ (an axial vector quantity) must be known. In principle, (m)y is obtainable from absorption spectra. However, (µ)µ can only be obtained by direct calculation of the matrix element or by deducing its value from the experimentally determined optical rotatory parameters of the i —* j transition. In fact, the polarization direction of only one amide transition, =
the presumedly N-Vi (r- *) transition in myristamide,22 has been determined with any degree of certainty. If one’s objective, therefore, is to predict optical rotatory properties, his only recourse is direct calculation of both (µ) and (m), since empirical information on these quantities is incomplete. Extensive literature exists on the problem of calculating the rotatory strengths of coupled amide transitions in polypeptides with ordered structures.4-19·27"29 More germane to the present study, however, are the very thorough and extensive studies of Schellman and coworkers on the theoretical basis of optical activity in small amide and diamide systems.30-35 Schellman’s general approach has been to (1) choose a set of electronic state functions which approximate the true eigenstates of a symmetric (Cs), isolated amide chromophore; (2) define a perturbation operator which represents the interaction potential energy between the amide group and the extrachromophoric moeities of the molecule; (3) construct approximations to, the true spectroscopic states of the molecule by first-order perturbation methods; and (4) calculate the rotatory strengths using the first-order perturbed spectroscopic state functions. In his studies of the * transition in l-3aminopyrrolidin-2-one,30·34 Schellman employed the oneelectron theory of optical rotation, wherein the interaction potential between the symmetric amide chromophore and the remaining groups of the molecule is assumed to be electrostatic in nature. In a recent study35 of dipeptide systems, however, he has formulated a very elegant and general perturbation treatment which includes both electrostatic interactions (as in the one-electron theory of Condon, Altar, and Eyring36) and electrodynamic interac-
tions (as included, for example, in the theoretical work of Kirkwood,37 Moffitt,5 Tinoco,38·39 and Weigang40). Although numerical accuracy has, in general, eluded these perturbation treatments of molecular optical activity, the perturbation models have been proved enormously successful for eliciting useful stereochemical information from circular dichroism (CD) and optical rotatory dispersion (ORD) spectra. If reasonably accurate representations of the zero-order chromophoric electronic states and of the perturbation potential function are chosen, the perturbation models frequently provide reliable predictive relationships between specific stereochemical variables and the signs and, in some cases, the relative magnitudes of observed optical rotatory parameters. These predictive relationships, called sector or regional rules, have been examined in considerable detail by Schellman,41 Moscowitz,42'43 Weigang,40 Mason,44 and Richardson45·46 and have been applied successfully to several different classes of dissymmetric chemical systems. Urry47 has made a systematic study of the rotatory strength of the - * transition in a series of model amide and diamide systems under various solvent and pH conditions. His model compounds consisted of substituted pyrrolidinones and diketopiperazines. He developed a semiempirical method for relating the magnitude and sign of the * rotatory strength to the positions and electrical properties (e.g., polar or nonpolar, charged or uncharged) of the substituent groups. The theoretical basis of his method is provided by the work of Tinoco,38 Caldwell and Eyring,48 and Schellman.41 His procedure is to assign various perturber functional groups (substituents on the symmetric peptide chromophore) one or two magnitudes which he calls partial molar rotatory powers, [Pj. Each [P], when multiplied by an assumed distance dependence (r~3, r~4, or r~s, where r = radial distance between a perturber group and an origin located on the peptide chromophore), and by an angular dependence (based on either a quadrant or octant sector rule), represents the contribution of the perturber group to the nr* rotatory strength. In principle, once the appropriate angular, distance, and [P] factors have been determined for a series of frequently encountered peptide substituent groups, Urry’s method should make the * rotatory strength a reliable structure
C. W. Deutsche, J. Chem. Phys., 52, 3703 (1970). W. Rhodes, J. Chem. Phys., 53, 3650 (1970). E. S. Pysh, J. Chem. Phys., 52, 4723 (1970). B. J. Lltman and J. Schellman, J. Phys. Chem., 69, 978 (1965). J. Schellman and E. B. Nielson, “Conformation of Biopolymers," Vol. 1, G. N. Ramachandran, Ed., Academic Press, New York, N. Y., 1967, p 109. (32) J. A. Schellman, Accounts Chem. Res., 1, 144 (1968). (33) J. A. Schellman and E. B. Nielson, J. Phys. Chem., 71, 3914
(27) (28) (29) (30) (31)
(1967).
(34) D. Stlgter and J. A. Schellman, J. Chem. Phys., 51, 3397 (1969). (35) P. M. Bayley, E. B. Nielson, and J. A. Schellman, J. Phys. Chem., 73, 228 (1969). (36) E. U. Condon, W. Altar, and H. Eyring, J. Chem. Phys., 5, 753
(1937).
(37) (38) (39) (40) (41) (42) (43) (44) (45) (46) (47) (48)
J. G. Kirkwood, J. Chem. Phys., 5, 479 (1937). I. Tinoco, Advan. Chem. Phys., 4, 113 (1962). W. C. Johnson, Jr., and I. Tinoco, Jr., Biopolymers, 7, 727 (1969). E. G. Hohn and O. E. Weigang, J. Chem. Phys., 48, 1127 (1968). J. A, Schellman, J. Chem. Phys., 44, 55 (1966). A. Moscowitz, Advan. Chem. Phys., 4, 67 (1962). T. D. Bouman and A. Moscowitz, J. Chem. Phys., 48, 3115 (1968). S. F. Mason, J. Chem. Soc. A, 867 (1971). F. S. Richardson, J. Chem. Phys., 54, 2453 (1971). F. S. Richardson, Inorg. Phys. Chem., 10, 2121 (1971). D. W. Urry, Annu. Rev. Phys. Chem., 19, 477 (1968). D. J. Caldwell and H. Eyring, Rev. Mod. Phys., 35, 577 (1963). The
Journal of Physical Chemistry, Vol. 77, No.
2, 1973
F. S.
250
indicator. That is, * should provide information about stereochemical features in the immediate environment of the peptide group. Although some success is apparent in Urry’s application of this method to small peptide systems,47 it is uncertain whether the method can be reliably, or appropriately, extended to polypeptide and protein structures.49 The present study is an attempt to compute the rotatory strengths of the lowest energy transitions in several dissymmetric pyrrolidone and diketopiperazine derivatives using the all-valence-shell electronic wave functions calculated on an INDO molecular orbital model. That is, we abandon the perturbation approach employed by Schellman and calculate the Rij quantities directly, using the ground-state and virtual-orbital excited state wave functions of the total molecule as obtained from INDO molecular orbital calculations. Similar calculations of molecular rotatory strengths using wave functions obtained from semiempirical, all-valence-shell molecular orbital models have been reported previously.50-56 It is clear that this method of calculating rotatory strengths is not expected to be inherently more accurate or reliable than the perturbation method; nor does it represent a refinement in approach. The most serious sources of error in the perturbation approach can generally be found in the approximations made in constructing the interaction potential between the chromophoric and extrachromophoric parts of the molecule. Inaccuracies in the transition dipoles and rotatory strengths computed directly from molecular allvalence-shell electron wave functions derive entirely from the approximations employed in calculating the wave functions and in evaluating the multicenter transition integrals. The quality of molecular electronic wave functions calculated by the INDO molecular orbital method is, for physical properties other than ground-state energies, unpaired spin distributions and, in some cases, ground state geometries, uncertain. Modifications to the original method, as developed by Pople and coworkers,87’58 have led to some success in providing theoretical estimates of groundstate dipole moments,59 heats of formation,60"63 and electronic excitation energies.64-65 A reparameterization of the model to permit reliable calculations of electronic transition probabilities has, as yet, not been reported. In view of the subtitles and difficulties involved in achieving even modest quantitative success in calculating electronic transition integrals from the “best” variationally determined wave functions,66 reparameterizing the very approximate INDO-MO model for this purpose would appear to have dubious merit. Despite the obvious and well-documented shortcomings of most semiempirical, all-valence-electron molecular orbital models, their application is calculating the optical rotatory properties of a number of molecular systems has been proved useful.50·56 In particular, application of the INDO-MO model to the optical rotatory properties of dissymmetric cyclcpentanone derivatives resulted in several findings not revealed by previous perturbation treatments.56 The primary objective of the present INDO-MO study is to augment our understanding of the optical rotatory properties of the amide transitions in dissymmetric pyrrol id inone and diketopiperazine molecules. The spectroscopic properties of these systems have been thoroughly studied by experiment and, as previously noted, the rotatory strengths have been calculated by Schellman30"35 using perturbation methods. The Journal of Physical Chemistry, Vo/. 77, No. 2, 1973
Richardson, R. Strickland, and D. D. Shillady
II. Methods of Calculation The methods of calculation used here are essentially the as those described in a previous study.56 The computer programs employed in the previous study were, in part, translated from Algol (for use on a Burroughs B-5500 system) to Fortran (for use on a CDC-6400 system). The SCF-MO computations were carried out in the INDO approximation57 utilizing “standard” parameters.58 Excited state wave functions were constructed from linear combinations of determinantal wave functions formed by the replacement of one occupied molecular orbital in the ground-state determinant with a virtual orbital. Basis sets for the configuration interaction calculations were limited to just 15 singly excited configurational wave functions. The oscillator strengths, rotatory strengths, and dissymmetry factors were computed by the same methods used previously.56 The computer program (AMGMOMT) employed in the present study, however, does not provide for singlet-triplet mixing via spin-orbit perturbations. Only the spectroscopic properties of singlet-singlet transitions are calculated. The properties calculated and reported in the present study are defined as follows: (a) reduced rotatory strength same
[J?y]
100/ß ) Im[< |m|·( /'j|/x|i/'j)]
=
(2)
where ß is the Bohr magneton, D is the Debye unit, µ is the magnetic dipole operator, and m is the electric dipole operator
µ
=
(eh/2mci)Xl(v)x vij/3he2)Dij
(6)
(c) oscillator strength
fij where vtj
=
(Ej
-
=
Ei)¡h; (d) dissymmetry factor 8tj
=
4
Rtj/Dij
(7)
(49) C. W. Deutsche, D. A. Ughtner, R. W. Woody, and A. Moscowltz, Annu. Rev. Phys. Chem., 20, 407 (1969). (50) Y. Pao and D. P. Santry, J. Amer. Chem. Soc., 88, 4157 (1966). (51) R. Gould and R. Hoffmann, J. Amer, Chem. Soc., 92, 1813 (1970). (52) R. M. Lyndon-Bell and V. R. Saunders, J. Chem. Soc. A, 2061 (1967) (53) W. Hug and G. Wagnlere, Theor. Chim. Acta., 18, 57 (1970). J. (54) Llnderberg and J. Mlchl, J. Amer. Chem. Soc., 92, 2619 (1970). (55) M. Yaris, A. Moscowltz, and R. S. Berry, J. Chem. Phys., 49, 3150 (1968) (56) F. S. Richardson, D. D. Shillady, and J. E. Bloor, J. Phys. Chem., 75, 2466 (1971). (57) J. A. Pople, D. L. Beveridge, and P. Dobosh, J. Chem. Phys., 47, 2026 (1967). (58) J. A. Pople and D. L. Beveridge, “Approximate Molecular Orbital Theory," McGraw-Hill, New York, N. Y., 1970. (59) D. D. Shillady, F. Billingsley, and J. E. Bloor, Theor. Chim. Acta., .
.
21,1 (1971).
(60) N. C. Baird and M. J. S. Dewar, J. Chem. Phys., 50, 1262 (1969). (61) N. C. Baird and M. J. S. Dewar, J. Amer. Chem. Soc., 91, 352 (1969) (62) M. J. S. Dewar and S. D. Worley, J. Chem. Phys., 50, 654 (1969). (63) M. J. S. Dewar and E. Haselbach, J. Amer. Chem. Soc., 92, 590 (1970) (64) C. Giessner-Prettre and A. Pullman, Theor. Chim. Acta, 13, 265 .
.
(1969).
(65) K. Yamaguchi and T. Fueno, Bull. Chem. Soc. Jap., 44, 43 (1971). (66) A. Hansen and E. N. Svendsen, Theor. Chim. Acta, 20, 303 (1971).
Optical Activity of Simple Cyclic Amides
III. Structure Variables Six different chemical species were included in this study. They are 5-methylpyrrolidin-2-one (5-MP), 3methylpyrrolidin-2-one (3-MP), 3-aminopyrrolidin-2-one 3(3-AP), 3-ammoniumpyrrolidin-2-one (3-AH+P), methyl-2,5-diketopiperazine (3-MDKP), and 3,6-dimethyl- 2 ,5-·diketopiperazine (3,6-DMDKP). In addition to the optical isomerism which exists for each of these chemical compounds, it is expected that limited conformeric and rotameric isomerism might also be of some importance, especially for properties such as optical activity. Crystal structure determination studies by X-ray diffraction techniques on the compounds, L-5-iodomethylpyrrolidin-2-one and L-pyrrolidin-2-one-5-carboxamide, reveal that the five-membered ring is nonplanar.67 In crystalline form 2,5-diketopiperazine has a near planar six-membered ring structure,88·89 whereas the six-membered ring of lc¿s-3,6-dimethyl-2,5-diketopiperazine has a nonplanar conformation in the crystal.70 It is believed that diketopiperazine and its substituted derivatives form highly flexible rings in noncrystalline media.71"73 The possibility of inherent chirality in the ring systems due to conformational preferences cannot be ignored for the molecules included in this study. Schellman34 demonstrated that the one-electron calculations of Rnr, for L-3-aminopyrrolidin-2-one are very sensitive to the rotameric state of the C/si-NHz group. Not only the magnitude, but also the sign of Rnr, varies as the amino group is rotated about the Co)-N bond. In the present study, two Cis)-NH2 rotameric isomers of the 3-AP molecule were studied and three C(3)-NH3+ rotameric isomers of the 3-AH+P compound were considered. Calculations were performed on 15 different structures. These structures are listed as follows: (I) 5-MP, planar ring; (II) 5-MP, nonplanar ring; (III) 3-MP, planar ring; (IV) 3-AP, planar ring, = 60°; (V) 3-AP, planar ring, = = 240°; (VI) 3-AP, nonplanar ring, 60°; (VII) 3-AH+P, planar ring, a = 60°; (VIII) 3-AH+P, nonplanar ring, a = 60°; (IX) 3-AH+P, planar ring, a = 30°; (X) 3-AH+P, nonplanar ring, a = 30°; (XI) 3-AH+P, planar ring, a = 0°; (XII) 3-AH+P, nonplanar ring, a = 0°; (XIII) 3MDKP, nonplanar ring; (XIV) 3,6-DMDKP, planar ring; (XV) 3,6-DMDKP, nonplanar ring. Only one planar ring geometry and one nonplanar ring geometry are used for the pyrrolidin-2-one structures. The atomic coordinates for the nonplanar five-membered ring structure are listed in Table I. In Figure 1, a coordinate system and an atomic numbering system are specified for the pyrrolidinone ring. The angle a for the C(3)-HN3+ rotamers of the 3-AH+P structures is defined in Figure 2. In the 3-AP structures, the angle measures the rotation of the amino group with respect to the ring, in clockwise direction when looking = from the ring toward the amino group. For 0°, the amino group hydrogens eclipse the carbonyl carbon atom C. This rotameric form of structure IV cor60° rotamer of 3-AP studied by Stigter responds to the and Schellman.34 In structure V, the lone pair of electrons on the amino nitrogen atom are directed away from the ring and eclipse the Coi-H bond. Only a single Coi-CHg rotamer, the staggered (or a = 60°) form, is considered for 3-MP. ~
251
TABLE I: Atomic Coordinates for Nonplanar Pyrrolidinone Ring (A)° Atom 0
X
Y
0
0
1.1217
1
2
0
3 4
-1.1916 -0.6725
5
0.8701
“See Figure
1
0 0
0.0068 0.1751
-0.0602
z
1.2403
-0.7568 0
-0.8466 -2.2633 -2.1815
for atomic numbering system and coordinate system.
TA
5'
z Figure 1. Numbering system for pyrrolidinone ring atoms.
Figure 2. Definition of angle a for the C(3)-NH3+ rotamers of the 3-AH + P structures. C3 and C* are pyrrolidinone ring atoms and the C(3)-N bond is perpendicular to plane of the figure.
Just
one nonplanar six-membered ring conformation considered in the present study. The rings of structures XIII and XV have identical conformations. The geometrical parameters for the rings of XIII and XV are those reported by Benedetti, et al.,70 for crystalline l-cis-3,6was
dimethyl-2,5-diketopiperazine. In this conformation, both methyl groups of 3,6-DMDKP occupy positions equatorial to the ring and are directed away from one another. The structural parameters for the planar ring of XIV were obtained from the crystal data reported by Degeilh and Marsh69 for 2,5-diketopiperazine. The absolute configurations at the asymmetric centers in the six chemical compounds considered in this study can be seen from Figures 3a-f.
IV. Results and Discussion A. Lowest Energy Singlet-Singlet Transitions. Calculated properties for the lowest energy singlet transitions in structures I-XV are displayed in Table II. For those structures in which the first two lowest lying transitions are close in energy, the calculated properties of both transi(67) J. A. Molin-Case, E. Fleischer, and D. W. Urry, J. Amer. Chem. Soc., 92, 4728 (1970). (68) R. B. Corey, J. Amer. Chem. Soc., 60, 1598 (1938). (69) R. Degeilh and R. E. Marsh, Acta Crystallogr., 12, 1007 (1959). (70) E. Benedetti, P. Corradlnl, and C. Redone, Biopolymers, 7, 751
(1969). (71) E. Benedetti, P. Corradlnl, M. Goodman, and C. Redone, Proc. Natl. Acad. Sc/'. U. S„ 62, 650 (1969). (72) F. Nalder, E. Benedetti, and M. Goodman, Proc. Natl. Acad. Sci. U. S„ 68, 1195 (1971). (73) K. D. Kopple and D. Marr, J. Amer. Chem. Soc., 89, 6193 (1967).
The
Journal of Physical Chemistry, Vol. 77, No.
2, 1973
252
Strickland, and D. D. Shillady
F. S. Richardson, R.
X
5%-
¡
\ ,NK
/ K2C
\ / CH3^C\c/NH H2N^C\c/NH O
i
O
c.
o
o
H2C--CH2
/
\
II
HN\r/C^CH3 HNXr/C^
II
d.
°
V^nh
/i~\xnh h-CT
H3Qx
'h3n^C\c/nh
TABLE II: Calculated Properties for the Lowest Energy Singlet Transitions
\
/
b.
o
a,
h2c—CH2
II
II
h2c—CH2
e·
f
s
&
Figure 3. Absolute configurations at the asymmetric centers of (a) 5-MP, (b) 3-MP, (c) 3-AP, (d) 3-AH+P, (e) l,l-3,6DMDKP, and (f) L-3-MDKP.
tions are given. The lowest lying singlet excited state of structures I--VI can be characterized on our model as an amide * state. That is, the dominant configurational contribution to the lowest energy singlet excited state function can be described approximately as a promotion of an electron from a nonbonding orbital localized on the carbonyl oxygen atom to an antibonding orbital delocalized over the OCN amide group. The two lowest lying excited states of structures VII-XII are best described asn~* NH3+ and r -*· NHa+ charge-transfer states formed by electron transfer from amide-localized molecular orbitals to the ammonium substituent group. The two lowest lying excited states of structures XIII-XV are computed to be essentially * amide states, although there is significant *, and * configurational funcscrambling of the *, tions for the nonplanai structures XIII and XV. We concentrate our attention first on structures I-VI for which the first singlet excited state can be described almost entirely in terms of an amide * electronic configuration. An unsubstituted pyrrolidin-2-one molecule with a planar ring structure and a planar amide moiety has Cs -*· * transition is y polarized in symmetry and the electric dipole absorption and x, z polarized in magnetic dipole absorption. If the plane of symmetry is destroyed, either by ring distortions or by asymmetric ring substitution, the electric transition dipole of the —* * transition will also have nonvanishing x- and z-polarized components and the -*· * magnetic transition dipole will include a y component. The values computed for the x, y, * electric and magnetic diand z components of the pole transition moments are listed in Table III. These values, computed for the six dissymmetric structures I-VI, can be compared with the transition dipoles computed for the n —* * transition of the nondissymmetric, unsubstituted pyrrolidin-2-one molecule (planar ring structure). The transition dipoles computed for the latter system are (µ ) = 0.28, (ß ) = 0, (ß ) = 0.78 (Bohr magnetons): (mx> = 0, (my) = 1.48, (mz) = 0 (Debye). In the simplest application of the one-electron model to the optical activity of dissymmetric amide compounds it is assumed, to zero order, that the n — * transition is localized in the carbonyl group and that the magnetic transition dipole is z polarized (i.e., directed along the C=0 bond axis). To first order in this perturbation model, the extrachromophoric groups induce a small z-polarized component into the n —»· * electric transition dipole which, when coupled with the magnetic transition dipole, produces a nonvanishing rotatory strength. Therefore, both
1038D,
Structure
£, eV
(i) (II) (III)
6.56 6.79 6.87 6.63 6.45 6.77 8.37 8.88 8.39 8.90 8.38 8.94
(IV) (V)
(VI)
(VII)
(VIII) (IX)
8.97 8.33 8.93 8.36 8.95 7.95 8.32 6.68 9.79 8.84 9.35
(XI)
(XII)
(XIII) (XIV) (XV)
“[R]
226 326 356 659 286 306 39 128
8.41
(X)
= ;
g, cgs
cgs units
10+
268 349 375 737 324
41
331 12 38 13
147
43
31
11
160 32 184 25 167 24 188 1185
45 10 47 9
46 8
331
48 403 105
412 1674 669 1170
45 30 33
11
unit
[R]=
0.0020
-11.4
+0.44
0.0001
+ 84.1 -58.7 -109 -125 -11.4 -7.91 -13.3 -7.93 -11.4 -13.9 -13.5 -14.4 -9.85 -15.6
0.0088 0.0032 0.0136 0.0152 0.040 0.009 0.041
0.008 0.041
0.010 0.052 0.010 0.047 0.010 0.053 0.010
-10.6 -15.9 +8.87 -9.32 + 76.0
0.001
0.004 0.281
+ 137 + 114 -44.2
0.123 0.152 0.052
reduced rotatory strength at 1.08 X 104°R(cgs units). R
=
lm[(^i|m I )·( )\ß\ )]· TABLE III: Components of the Transition Dipoles
ture
X
(l) (II)
-0.35 "0.32 "0.57 0.13 0.48 0.74
(IV) (V)
(VI) “Values
—*
* Electric and Magnetic
Electric transition dipole“
Struc-
(III)
n
In
y
z
1.58 1.84
-1.82 2.68 -1.50
-1.26
Debye units.
b
0.01 0.01
-0.34 -0.14 0.87 1.08
Magnetic transition dipole" X y Z
0.39 0.39
-0.19 0.36 -0.14 -0.16
0.01
0.07 -0.26
-0.19 0.15 0.10
0.73 0.77 -0.75 0.88
-0.93 -0.94
Values In Bohr magneton units.
—
The
Journal of Physical Chemistry, Vol. 77, No.
2,
1973
the sign and the magnitude of the * rotatory strength are determined entirely by the quantity ( )(ß ). Neglect of the x polarized component of the n — * magnetic dipole transition moment is based on the assumption that the electronic orbitals involved in the transition have a higher effective symmetry (Civ) than the amide group (Cs).32 The “quadrant rule” for the CD of amide systems rests on the assumption that the local CiV symmetry of the carbonyl group determines the nodal structure of the * excited state, to zero order. If the symmetry is exactly Civ, then of course the —> * transition is entirely z polarized in magnetic dipole radiation. The results displayed in Table III show that the %-polarized components of the magnetic dipole transition moments are not negligible compared with the z-polarized components. Additionally, the y component of the magnetic dipole transition moment in structures -VI (the structures with ring substituents adjacent to the carbonyl
Optical Activity of Simple Cyclic Amides TABLE IV: Components of the Structure
(l) (II)
(III) (IV) (V)
(VI) °
n
—*
253
ir* Rotatory Strength"
µ)
¡(my){py)
i(mz)(pz)
-13.65
1.58 12.2 46.8
0.73 1.03 25.9 -12.7 -80.7
-12.7 11.2 4.65
-6.86 -11.5
-50.1 -22.2 -12.5
-100
Values In 1040 cgs units.
group) also is computed to have a nonnegligible magnitude. In fact, in the present computational model, only for structures V and VI does the ( )(µ ) contribution to the rotatory strength predominate over the contributions from i( µ ). The computed values for these quantities are listed in Table IV, The net charges computed for selected atoms and groups of atoms in. structures I-VI are given in Table V. The net atomic charges were obtained by first computing the gross electron population for each atom and then subtracting this number from the core charge. The net charges on the methyl and amino substituent groups were obtained by adding up the net charges on the constituent atoms of each group. The methyl carbon atom in each of the structures carries a net positive charge (~0.06) and the methyl hydrogen atoms in these structures each carry a net negative charge. The amino nitrogen atom in each of the structures IV-VI carries a net negative charge (~0.25) and the amino group hydrogen atoms each carry a net positive charge (—0.10). Urry47 has reported a value of -6.5 X 10"40 cgs unit for the nir* rotatory strength of L-5-methyIpyrroIidin-2-one in trifluoroethanol solvent. Our computed values for the nr* rotatory strength of l-5-MP are —10.6 x 10"40 cgs unit for the structure with ring planarity I and 0.41 X 10~4° for the nonplanar structure II. The conformation of the ring in structure II is such that the methyl substituent group is equatorial to the ring. The structural parameters for the ring of II are precisely those determined from X-ray diffraction studies for crystalline L-5-iodomethylpyrrolidín2-one. Note, from the data given in Table I, that the ring atom C(5) is distorted out of the plane defined by the amide group OCN by only |0.06|Á, whereas the ring atom C(4) deviates by |0.18|A from the plane of the amide group and ring atom C(3) lies in this plane. Warshel, Levitt, and Life on74 have suggested that the most stable ring
conformation in unsubstituted pyrrolidin-2-one is a nonplanar one which is very similar to one we adopt for structure II. However, they further suggest that the barrier to inversion of this ring conformation into its mirror image is very small; they estimate a barrier of 100 cal, considerably smaller than kT at 300°K. Ring substitution at C(5) might be expected to result in a preference for one nonplanar ring conformation over the other due to steric repulsion factors. However, considering the very small deviation of C(5) from coplanarity with OCN, the distinction between axial and equatorial substitution is very small in terms of the relative spatial dispositions of the substituent groups. Consequently, it is likely that considerable conformational mobility will exist even for substituted pyrrolidin-2-one systems, especially if the substituent is relatively small and neutral (e.g., a methyl group). ~
The computed values of R(nr*) reported for l-5-MP in trifluoroethanol solvent suggest that, in solution, the pyrrolidinone ring of l-5-MP is not rigidly fixed in the conformation specified by structure II. These data are, with a model in which it is ashowever, in consonance sumed that equilibria exist between several conformational isomers which, when superimposed on one another, yield an “average” planar structure. Greenfield and Fasman75 studied the circular dichroism of 3-methylpyrrolidin-2-one in various solvents. The compound resolved and studied by them had the same absolute configuration at ring atom C(3) as does structure III of the present study (see Figure 3b). This compound exhibits a positive CD band at 210-220 nm, which is red shifted upon going from water and other hydroxylic solvents to solvents with lower polarity and negligible hydrogen bonding properties. Greenfield and Fasman assigned this band to the amide n * transition. From the experimental CD spectra they calculated the following values for the mr* rotatory strength: 6.1 X 10"40 (water as solvent), 4.2 X 10"40 (trifluoroethanol as solvent), and 2.7 X 10"40 cgs unit (acetonitrile as solvent). Our computed value of R(nir*) = 77.9 X 10"40 cgs unit for structure III agrees in sign with the experimentally determined values for 3-MP, but is an order of magnitude too large. Litman and Schellman30 carried out the first study of the optical rotatory properties of L-3-aminopyrrolidin-2one using optical rotatory dispersion. They found that, in the solvents acetonitrile and dioxane, l-3-AP exhibits a positive Cotton effect around 230 nm, but that in water this Cotton effect either disappears or is blue shifted so that its presence is obscured by a very intense Cotton effect centered around 190-195 nm. They assigned the longr* transition wavelength Cotton effect to the amide n -» and the one at shorter wavelengths to an amide tt* transition. More recently Greenfield and Fasman76 have measured the CD of l-3-AP in several different solvents. The sign of the lowest frequency CD band is positive for l-3-AP in every solvent except trifluoroethanol (the other solvents included water, methanol, ethanol, isopropyl alcohol, and acetonitrile). This band is centered near 220 nm in water and is red shifted and increases in magnitude with decreasing solvent polarity. In trifluoroethanol the first CD band is negative in sign and of relatively low intensity. In all the solvents studied, a second, intense negative CD band was observed at around 190 nm. Additionally, in acetonitrile a third CD band (negative in sign) —
observed at around 200 nm. Greenfield and Fasman76 assigned the low-energy CD band to an amide n -*· ir* transition and the CD band at 190 nm to an amide ir was
·* transition. The values computed for the mr* rotatory strengths of structures IV, V, and VI are -54.3 X 10"40, -101 x 10"40, and —116 X 10"40 cgs unit, respectively. Except for the CD spectrum of l-3-AP in trifluoroethanol solvent, these computed values are in obvious disagreement with the experimental results. Stigter and Schellman34 have calculated the mr* rotatory strength of l-3-AP using a one-electron perturbation model. They assumed a planar
(74) A. Warshel, M. Levitt, and S. Lilson, J. Mol. Spectrosc., 33, 84 (1970). (75) N. J. Greenfield and G. D. Fasman, J. Amer. Chem. Soc., 92, 177 (1970). (76) N. J. Greenfield and G. D. Fasman, Biopolymers, 7, 595 (1969). The
Journal of Physical Chemistry, Vol. 77, No.
2, 1973
254
F. S. Richardson, R.
Strickland, and D. D. Shillady
TABLE V: Net Charges Computed for Atoms and Groups of Atoms (in Electron Units) 0
Structure
-0.43 -0.43 -0.42 -0.42 -0.41 -0.42
(l) (II)
(III) (iv) (V)
(VI)
(N)“
C(2)
N(1)
C(3)
C (4)
C(5)
H
0.42 0.42 0.42
-0.22 -0.22 -0.22 -0.21 -0.22 -0.22
-0.02 -0.02 -0.02
0.04 0.04 0.05
0.18 0.18 0.17 0.17 0.18 0.17
0.11 0.11 0.11 0.11
0.41
0.40 0.41
0.10 0.10 0.10
0.01 0.01
0.02
0.12 0.11
H(S)6
-NH2c
-0.05 -0.06
0.02 0.01
0.04
0
-0.03 -0.02 -0.03
-CH3d
-0.05 -0.06 -0.05
6 on same ring atom as the substituent amino or methyl group. “Sum of net atomic charges “Hydrogen atom on amide nitrogen. Hydrogen atom d computed for the atoms in the -NH2 substituent group. Sum of net atomic charges computed for the atoms in the -CH3 substituent group.
ring conformation and calculated the rotatory strength as a function of the angle (see section III for the definition of angle ). On their model the sign and magnitude of the rotatory strength are, in large part, determined by the sign and magnitude of the interaction energy between the amino substituent group and the chromophoric electron. To calculate this interaction term, one must first adopt some explicit representation of the perturber group (amino group in this case) with respect to its overall charge distribution. Generally, this representation of the perturber group charge distribution is the most difficult and least satisfactory step in any one-electron calculation of optical rotatory properties. Stigter and Schellman chose three different representations of the amino group in l-3-AP and made three different sets of calculations of f?(mr*) vs. . In each calculation they found that R( *) < 0 for 240°, a result identical with our own. For > 0 for two of the amino 60°, they calculated ( *) and R(nir*) < 0 for the third. Our group representations 60° is ·
*
X
nz
—
n
—*·
X*
x* *
polarization in-plane out-of-plane in-plane out-of-plane in-plane
The transitons listed in Table VI of the present work
must be characterized in terms of the filled SCF molecu-
lar orbitals and unfilled virtual orbitals obtained from semiempirical all-valence-shell SCF calculations in the INDO approximation. For each of the structures I-VI, transition A can be characterized approximately as a charge-transfer transition in which an electron is promoted out of the delocalized amide to orbital to the amide NH group. This transiton is strongly polarized perpendic-
TABLE VI: Calculated Properties for Higher Energy (Singlet) Transitions Transition
Structure (1) E, eV
f
m (II)
E, eV
f
W (III)
E, eV
f
[R] (IV) E, eV f [R] (V) £, eV f [R] (VI) E, eV f [R]
A
8.64 0.523 3.16 8.70 0.524
-20.4 8.87 0.488
-26.7 8.83 0.533 18.4 8.87
0.503 16.3 8.83 0.504 19.8
C
B
10.44 0.019 2.90
D
11.94 0.165 4.11 11.90 0.183 23.3 11.86 0.144 18.80 10.76 0.204 60.6 11.12 0.081
10.41
0.026 -22.3 10.51
0.046 -14.8 10.39 0.109 39.4 10.35 0.118 39.3 10.38 0.088 35.3
12.38 0.002 2.91
12.07 0.071 -22.7 12.75 0.068 54.0 11.29 0.094 -87.4 11.79 0.151 -64.2 11.86 0.174
-91.8 11.14 0.028 -82.0
-62.7
ular to the plane of the amide group. Transitions B and C are strongly polarized in-plane and they each contain apt* and n NH charproximately equal amounts of x acter, where the latter transition can be characterized as a charge-transfer process in which a nonbonding electron on the carbonyl oxygen atom is transferred to the amide NH group. For structures IV-VI, transition D primarily involves charge transfer from the lone pair of the amino substituent group to the amide x* orbital, and is almost entirely in-plane polarized. Transition D for structures I—III cannot be clearly assigned to any one or two orbital excitations. Transitions B and C can be correlated with the transix* and n * by Rhodes and Barnes19 tions labeled x for simple amide systems. Under the influence of ring nonplanarity and asymmetric ring substitution it is exx* and *) willpected that these transitions (i.e., x be somewhat scrambled in structures I-VI. As pointed out x* above, transitions B and C each have considerable x NH is and NH character. The virtual orbital of n localized primarily on the amide NH group, but it also has a significant amount of antibonding character between NH and the carbonyl carbon atom. The polarization of transition A suggests that it be correlated with the mystery band listed by Rhodes and Barnes. However, the oscillator strengths we compute for A are much too high to permit such an assignment without extensive qualification. The ah initio all-electron molecular orbital calculations of Basch, Robin, and Kuebler24 and of Robb and Csizmadia25,26 using extended basis sets demonstrate the inadequacy of valence-shell-only, minimum basis set molecular orbital calculations of amide spectra. Although the amide n —*· x* transition is probably well represented on the model employed in the present study, the model is expected to be less reliable in representing higher energy transitions. —*
-*
—
—
—»
—1
—
—>
Acknowledgments. We express our gratitude to the doof the Petroleum Research Fund, administered by the American Chemical Society, for financial support of this research. nors
The Journal of Physical Chemistry, Vol. 77, No. 2, 1973
