3975
SEMIEMPIRICAL CALCULATIONS ON SULFUR-CONTAINING HETEROCYCLES
Semiempirical Calculations on Sulfur-Containing Heterocycles by J. Fabian, A. Mehlhorn, Institute of Organic Chemistry, Technical University, Dresden, Germany
and R. Zahradnik Institute of Physical Chemistry, Czechoslovak Academy of Sciences, Prague, Czechoslovakia (Received February 6 , 1968)
The PPP procedure (neglect of the penetration integrals, constant parameters, idealized geometry, p model for the sulfur, and limited number of singly excited states in the configuration interaction) provides a satisfactory interpretation of the singlet-singlet absorptions of heterocyclic sulfur-containing compounds in the ultraviolet and visible spectral regions. The authors suggest the values US = 20 eV, PCS = 0.7Pc0, and 7 5 s = ycc as parameters for u-bivalent sulfur and employ the Mataga-Nishimoto relation for the two-center repulsion integrals. A reliable evaluation of the calculated charge distribution in the ground state would require additional experimental data.
Introduction Quantum-chemical calculations of sulfur-containing heterocycles by the Hiickel MO-LCAO method have contributed to a systematic classification and understanding of certain physical and chemical properties.’ However, since this simple theoretical method can be employed only to a very limited extent for calculations of optical electronic excitations, the interpretation of electronic spectra is still very incomplete. On the other hand, it has already been shown2 that the Pariser-Parr-Pople (PPP) method, which has made fundamental contributions to the theory of hydrocarbon spectra, is better suited to provide information on the electronic structure of sulfur-containing heterocycles. The number of PPP-type calculations on the spectra of these compounds published so far is very limited, however, and they are mostly limited to thiophene. 3-12 Today numerous electronic spectra of heterocyclic sulfur-containing compounds are known. The spectra of these substances, unlike those of the analogous oxygen compounds, are remarkably similar to those of the isoelectronic hydrocarbons.1a-19 The aim of the present paper therefore is: (1) to find optimum empirical values for the quantities Us (valence state ionization potential of sulfur), PCS (core-resonance integral of the C-S bond), and YSS (monocentric electronic repulsion integral) and their influence on the calculated physical characteristics of the heterocycle; (2) to perform calculations for a representative set of diverse sulfur-containing heterocycles with optimum parameters; (3) to correlate the results with as many physical properties as possible, such as electronic spectra, ionization potentials, dipole moments, bond distances, etc.; (4) to indicate the limits of applicability of the simple MO method. The compounds examined are formally derived by
substituting a sulfur atom for a CH-CH group in the alternant hydrocarbons benzene (HC-1)) the acenes (HC-2 and HC-3), and the phenes (HC-4-HC-7), while for nonalternant hydrocarbons the iso-a-electronic reference systems are represented by azulenes (HC-8-HC-11), heptalene (HC-12), cyclohepta[d,e]naphthalene (HC-13), cyclopenta[e,f]heptalene (HC14), acenaphtho [1,2-j]fluoranthene (HC-15), and the tropylium cations (HC-16-HC-19). (1) R. Zahradnik in “Physical Methods in Heterocyclic Chemistry,” Vol. 5, A. R. Katritaky, Ed., Academic Press, New York, N. Y., 1965. (2) R. Zahradnik, J. Fabian, A. Mehlhorn, and V. KvasniEka in “Organosulfur Chemistry,” M. J. Janssen, Ed., Interscience Publishers, New York, N. Y., 1967. (3) M. Solony, F.W. Birss, and J. B. Greenshield, Can. J . Chem., 43,
1569 (1965). (4) A. J. H. Wachters and D. W. Davies, Tetrahedron, 20, 2841 (1964). (5) D. S. Sappenfield and M. Kreevoy, ibid., 19, 157 (1963). (6) A. Zweig and A. K. Hoffmann, J. Org. Chem., 30, 3997 (1965). (7) M. J. Bielefeld and D. D. Fitts, J. Amer. Chem. Soc., 88, 4804 (1966). (8) V. Santhamma, Proc. Nat. Inst. Sci. India, A22, 204 (1956). (9) F.Dorr, G. Hohlneicher, and S. Schneider, Ber. Bunsenges Phys. Chem., 70, 803 (1966). (10) F. Momicchioli and A. Rastelli, J. Mol. Spectrosc., 22, 310 (1967). (11) L. Bonscasse, E. J. Vincent, and J. Metager, BUZZ. SOC.Chim. Fr., 1182 (1967). (12) N. Trinajstih and A. Hinchliffe, Croat. Chem. Acta, 39, 119 (1967). (13) G. M. Badger and B. J. Christie, J . Chem. SOC.,3438 (1956). (14) W. Carruthers and J. R. Crowder, ibid., 1932 (1957). (15) 0.Dann, M. Kokorudz, and R. Coopper, Chem. Ber., 87, 140 (1954). (16) A. G.Anderson, Jr., W. F. Harrison, R. G. Anderson, and A. G. Osborne9 J. Amer. 818 1255 (lg5’). (17) M. R. Padhye and J. C. Patel, Trans. Faraday SOC.,49, 1119 (1963). (18) 0. Dann and H. Distler, Chem. Ber., 87, 365 (1954). (19)G. v. Boyd, J. Chem. SOC., 55 (1959). Volume 7.9, Number 18 November 1968
3976
J. FABIAN, A. MEHLHORN, AND R. Z A H R A D N f K
nc 43
IiC 16
SH 23
SH 22
SH 25
SH 26
HC17
SH 27
SH 24
HC 15
SH 28
SH 29
SH 30
SH 32
Calculations Since the PPP method has been sufficiently explained elsewhere,20~21 few comments are needed. Interaction between the monoexcited configurations which were set up from SCF-310 functions was investigated. As a rule, those configurations were selected which are derived by electron excitation between the four highest occupied ( n = 1-4) and the lowest four virtual molecular orbitals (n’ = 1’--4’). In the case of thiophene (SH-1), the thienothiophenes (SH-4-SH-6), and the 1,3-dithiolium cation (SH-26)) configuration interaction was restricted to four ( n = 1 and 2 and n’ = 1’ and 2’)) and in the case of the thiopyrylium cation (SH-25) to nine (n = 1-3 and n’ = 1’-3’) configurations. For comparison, the results of the HMO and the corresponding LCI-HMO calculations were at our disposal. The Journal of Physical Chemistry
According to the Rlataga-Nishimoto relation22twocenter electronic repulsion integrals are defined by Y~~ and yssas well as byJhe molecular geometry (RCS= 1.7 8 and RCC= 1.4 A). If not otherwise indicated, the parameters for the hydrocarbon parts of molecules under study were selected as UC = 11.42 eV, PCC = -2.318 eV, and ~ C = C 10.84 eV. For the sulfur atom, the p model was employed exclusively.
Discussion Parameter Study. Figure 1 presents the results of (20) R. G. Parr, “Quantum Theory of Molecular Electronic Structure,” W. A. Benjamin, Inc., New York, N. Y., 1964. (21) P. Hoohmann, R. Zahradnik, and V. KvasniOka, Collect. Czech. Chem. Commun., in press. (22) N. Mataga and K. Nishimoto, 2. Phys. Chem. (Frankfurt am Main), 13, 140 (1957).
3977
SEMIEMPIRICAL CALCULATIONS ON SULFUR-CONTAINING HETEROCYCLES Varlable parameter
Constant parameter
'-dipoh nomen!
Spectral data
'-dip011 iomen
Spectral data
10.51
17,98
90,75
79
$85
7b69
Us -7OeV
-
zSs 7484eV Res-
Pcs--7,3eV
I
pcs--2,3 e V
II
1.401 pcs--3,3eV
I
III Ill
pcS--2,3eV
Us -10eV
& -70,84eV
Us =20e V
Res-
I......,s
I I
J
Ill I
IJJ
f
I
I
,J ...........
i
74 57 7031
-
..i I
..................I
1 . .I :i i
7Z09
,f
i:
II II I .....!
t 4 0 1 US =30eV
)
:
10.57
7698
3,09
5,77
493
j j
3,99
12,24
Ib48 72,29
-
1
I /-
Experiment
\
LL60
50
40
30
20
I
I
I
50
40
30
I
10
-
Figure 1. Parameter study on benzo[b]thiophen and cyclopenta[b]thiopyran. The lengths of the vertical lines correspond to the intensities (log B = log f 4 ) up to logf = -2; transitions with smaller intensities are indicated by circles.
+
the parameter study on benzo [blthiophene (SH-2) and cyclopenta [b]thiopyran (SH-15). The comparison with the measured spectral curves and the T moments calculated from the experimental dipole moments suggests a value of about 20 eV for US and a value less than -2.3 eV for pes. The influence of ~ S Sand of the molecular geometry upon the spectral transitions proved to be small. (The only exception is SH-6, whose calculated excitation energies proved especially sensitive to small variations in the assumed geometry.) The slightly different values of the parameters (UC = 11.22 eV, PCC = -2.388 eV, and ycc = 10.53 eV) did not lead to significant differences from the other calculations. After the preliminary rough parameter study, we subjected four parameter combinations, models A-D, Table I to a more profound examination, which now also includes the systems SH-3-SH-3, SH-22, SH-23,
SH-25, and SH-26. (The values used by the other are not included in this table because they are mutually comparable to a limited extent only. This is due to the various approximations and parameters used for carbon. The list of these values is available upon request from the authors.) Figure 2 shows that the monocyclic representatives are very sensitive to changes in the parameters. Models A and B failed completely in describing their spectra. It must be pointed out, however, that model B, which leads to a strong localization of electrons on sulfur, (23) G. Leroy, Bull. SOC.Chim. Belges, 73, 166 (1964). (24) G. Klose, Habilitationsschrift Universitat Leipzig, 1966. (25) K. Nishimoto, Theor. Chim. Acta, 7, 207 (1967). (26) L. Paolini, Nuovo Cimento, 4, 410 (1956). (27) P. J. Zandstra and J. D. Michaelsen, J. Chem. Phys., 39, 933 (1963). volume 78, Number 19 November 1968
3978
J. FABIAN, A. n/IEHLHORN,
AND
R. Z A H R A D N i K
Figure 2. Spectral curves and calculated transition energies as well as intensities for the sulfur-containing heterocycles SH-1, SH-2, SH-8, SH-15, SH-16, SH-22, SH-23, SH-25, and SH-26 according to the models A-D. (For the parameters see Table I; for the intensities see Figure 1.) The Journal of Physical Chemistry
SEMIEMPIRICAL CALCULATIONS ON SULFUR-CONTAINING HETEROCYCLES gives dipole moments closely approaching the experimental values. The use of model C leads to an essential improvement of the calculation of the spectral transitions; the strong charge flow from sulfur, giving very high dipole moments, seems to be unrealistic. Table I : The Parameters Employed
us,
-ocs,
YSS,
Model
eV
eV
eV
A B
22.9 21 18 20
2.46 1.159 1.623 1.623
11.9 10.84 10.84 10.84
c
D
For this reason, we sought another set of parameters, preserving good agreement with the experimental spectral data but avoiding excessive polarity. This set of parameters (model D) was employed for final calculations on the systems under study. Their spectral characteristics are known, with the exception of SH-20 and SH-21. Electronic Spectra. The results of the LCI-HMO calculations, in the case of some derivatives of nonalternant hydrocarbons, differ considerably from the LCI-SCF results. Figure 3 presents a comparison of the theoretical and experimental results. As far as possible, the spectra of the iso-.rr-electronic hydrocarbons are also recorded. The agreement between theory and experiment is as satisfactory as for hydrocarbons. The only difficulties are in the interpretation of the spectrum of the recently prepared thieno [3,4-b]thiophene (SH-6),28owing to the strong dependence of the calculated transition energies on the assumed molecular geometry. A recalculation of SH-6 with a geometry adjusted to the experimental result for thiophenez9 gave a good agreement with experiments (33.11 kcm-I (log f = -0.46), 35.11 kcm-l (log f = -1.06), 43.10 kcm-I (log f = -9.09)) and 46.06 kcm-l (log f = - 1.42)). This change in the assumed geometry, however, had practically no influence on the results for systems SH-4 and SH-5. The thiophene band in the nearultraviolet region contains two .rr-.rr* transitions, whose transition moments are perpendicular to each other. Similar results were obtained by the SCF,aLCI-HM0,5 and VB (valence bond) methods.30 Also the inclusion of the 3d orbitals of sulfur in the SCF calculation7 results in no qualitative change of this interpretation. The existence of two or three transitions in the near-ultraviolet region was already deduced by Milazzo from the analysis of the vapor spectrum31 and was found to be in agreement with substituent effects.82 The second transition, however, has not been established experimen tall^.^^-^^ The presumed third .rr-.rr* transition between 200 and 220 mpp3lwhich Milazzo and co-
3979
workerss6endeavored to prove by simple ” I O calculations, is not confirmed by the SCF-CI calculations and might be explained by the presence of impurities.87 The calculated oscillator strength is too high. Whereas the theoretical values aref 0.19 (band at 43.3 kcm-9 and f = 0.32 (band at 44.3 kcm-I), the experimental value amounts to 0.11 in solution and 0.096 in vapor34 for the observed absorption in the near-ultraviolet region. For the far-ultraviolet region, the theory predicts a system of mutually overlapping bands at about 7.4 eV. Absorption regions were found experimentally a t 6.59-8.8538and 6.59-7.75 eV.31 The condensed thiophenes have been investigated in less detail. Vapor-phase spectra extending into the far-ultraviolet region are a ~ a i l a b l e . ~ The ~ ~ ~agree~-~~ ment is good, except that the calculated frequency of the second band is too low by about 3 kcm-’. Fluorescence polarization measurements recently performed on SH-842show, in agreement with the calculation, that the longest wavelength band is polarized perpendicularly to the second band. The absorption spectrum of the thiopyrylium cation and of the derived condensed ring systems is very well reproduced by the theory. The oscillator strengths of SH-25, as estimated from the maximum extinction coefficient and half-widths, however, are too high by a factor of approximately 3 (fi(expt1) = 0.05, fl(theor) = 0.15, fZ(expt1) = 0.1, andfz(theor)= 0.32). Special spectra features of the cyclopentathiopyranes are also reproduced by the theory, and the considerable differences from the isomeric benzothiophenes are thus rationalized. For cyclopenta [blthiopyrane (SH15), owing to the smaller band overlap, it is possible to estimate the oscillator strengths of two lowest energy bands. As above, these strengths are smaller than the theoretical values dfi(expt1) = 0.02, fi(theor) = 0.05, fZ(expt1) = 0.11, andf2(theor)= 0.34). Similar relations apply also to the oscillator strengths (28) H. Wynberg and D. J. Zwannenburg, Tetrahedron Lett., 761 (1967). (29) B. Bak, D. Christensen, L. Hansen-Nygaard, and J. RastrupAndersen, J. Mol. Spectrosc., 7 , 58 (1961). (30) A. Mangini and C. Zauli, J. C h m . SOC.,2210 (1960). (31) G. Milazzo, h’xperbntia, 3 , 1 (1947); Spectrochim. Acta, 2, 245 (1944); Rend. Ist. Super. Sunita, 11, 383 (1948); Guzz. Chim. Ital., 78,835 (1948); 83, 392 (1963). (32) 8. Gronowitz, Advan. Heterocyclic Chem., 1, 14 (1963). (33) C. Zauli, Ann. Chim., 53, 702 (1963). (34) A. Trombetti and C. Zauli, ibid., 53, 805 (1963). (35) L.Verbit, E.Pfeil, and W. Becker, TetrahedronLett., 2169 (1967). (36) G.Milazzo and G . De Alti, Rend. Ist. Super. Sanita, 2 2 , 787 (1959). (37) G.Horvath and A. I. Kiss, Spectrochim. Acta, A23, 921 (1967). (38) W. C. Price and A. D. Walsh, PTOC. Roy. Sac., A179, 201 (1941). (39) 0.P. Kharitonova, Opt. Spektrosk., 14, 214 (1963). (40) J. M. Hollas, Spectrochim. Acta, 19, 753 (1963). (41) J. Platt, “Systematics of the Electronic Spectra of Conjugated Molecules,” John Wiley & Sons, Inc., New York, N. Y.,1964. (42) F. Darr, Angew. Chem., 78, 473 (1966). Volume 73, Number 18 November 1868
3980
J. FABIAN, A. JIEHLHORN,
AND
R. ZAHRADNfK
?[hem.']
Figure 3. Comparison of the calculated excitation energies of the sulfur-containing heterocycles SH-1-SH-19 and SH-22-SH-32 according to model D with the experimental absorption curves (full lines). The dotted curves are the spectral absorptions of the iso-r-electronic hydrocarbons. Vertical lines indicate the theoretical energies and intensities (log f ) ; weak transitions (log f < - 1.50) are marked by dots. As far as the absorption curves themselves were not a t our disposal but numerical data were available, the arrows indicate the absorption maxima. Literature for the represented spectral curves with the solvents employed (A, acetic acid; AN, acetonitrile; B, benzene; C, cyclohexane; CH, chloroform; D, dioxane; E, ethanol; HX, hexane; HP, heptane; I, isooctane; M, methanol; P, perchloric acid; S, sulfuric acid; V, vapor; W, water): SH-1: V (J. Platt, “Systematics of the Electronic Spectra of Conjugated Molecules,” John Wiley & Sons, Inc., New York, N. Y., 1964), C (S. F. Mason in “UV Atlas of Organic Compounds,” Vol. 11, Butterworth and Co. Ltd., London, 1966); SH-2: V (J. Platt, “Systematics of the Electronic Spectra of Conjugated Molecules,” John Wiley & Sons, Inc., New York, N. Y., 1964), E (L. Lang, “Absorption Spectra in the Ultraviolet and Visible Region,” Vol. I, Publishing House of the Academy of Science, Budapest, 1959); SH-3: C (R. Mayer, unpublished data); SH-4: solvent not given (M. R. Padhye and J. C. Patel, J . Sci. Znd. Res., 15b, 49 (1956)); SH-5: (for the reference see SH-4); SH-6: E (H. Wynberg and D. J. Zwanenburg, Tetrahedron Lett., 761 (1967)); SH-7: E (W. Carruthers, private communication; cf. ref 14); SH-8: E (L. Lang, “Absorption Spectra in the Ultraviolet and Visible Region,” Vol. 11, Publishing House of the Academy of Science, Budapest, 1961); SH-9, SH-10: E (for references see SH-7); 1,3-dimethyl-SH-l1: E,18 numerical data of SH-11 in M (M. P. Cava and N. N. Pollak, J . Amer. Chem. SOC., 88, 4112 (1966)); SH-12: CH;16 SH-13: D (M. Zander in “UV Atlas of Organic Compounds,” Vol. I, Butterworth Inc., New York, N. Y., 1966); SH-14: I (0.Kruber and G. Grigoleit, Chem. Bey., 87, 1895 (1954)); SH-15: C, (for the reference see SH-3); SH-16: HX (for the reference see SH-3); c. SH-17, SH-18: CH (for the reference see SH-3); SH-19: D (for the reference see SH-3); SH-22: E (S. O’Brien and D. Smith, J. Chem. Soc., 2907 (1963)); 2-phenyl-6-isopropyl-8-methyl-SH-23:solvent not given (L. L. Replogle, K. Katsumoto, and T. C. Morrill, Tetrahedron Lett., 1877 (1965)); SH-24: B (for the reference see SH-13); SH-25: P,AN (I. Degani, R. Fochi, and C. Vincenzi, Gazz. Chim. Ztal., 94, 203 (1964)); SH-26: P, E (D. Leaver, W. A. H. Robertson, and D. M. McKinnon, J . Chim. Ind. Bologna, 23, 151 (1965)); Chem. Soc., 5104 (1962)); SH-27: S (I. Degani, R. Fochi, and G. Spunta, Boll. Scient. FUC. SH-28: A (A. Luttringhaus and N. Engelhardt, Chem. Ber., 93, 1525 (1960)); SH-9: W (D. Sullivan and R. Pettit, Tetrahedron Lett., 401 (1963)); SH-30: P, W (R. Zahradnik and C. P&rk&nyi,Collect. Czech. Chem. Commun., 30, 3016 (1965)); SH-31: s (for the reference see SH-27); SH-32: P,W (I. Degani, R. Fochi, and C. Vincenzi, Boll. Scient. Fac. Chim. Znd. Bologna, 23, 21 (1965)); HC-1: H P (J. Petruska, J. Chem. Phys., 34, 1120 (1961)); HC-2: V (L. C. Jones, Jr., and L. W. Taylor, Anal. Chem., 27, 228 (1965)), E (H. H. Jaffe and M. Orchin, “Theory and Application of Ultraviolet Spectroscopy,” John Wiley & Sons, Inc., New York, N. Y., 1962), C (for the reference see HC-2, E ) ; HC-3, HC-4, HC-6, HC-7: H P (for the reference see HC-2, v); HC-5: E (for the reference see HC-2: E ) ; HC-8: E (H. Zimmermann and N. Joop, 2. Elektrochem., 64, 1219 (1960)); HC-9: c (E. Kloster-Jensen, E. Kovats, A. Eschenmoser, and E. Heilbronner, Helv. Chim. Acta, 39, 1051 (1956)); HC-10: (cf. E. Heilbronner and J. N. Murrell, Mol. Phys., 6 , 1 (1963)); HC-13: E. (J. Boeckelheide and G. K. Vick, J . Amer. Chem. SOC.,78, 653 (1956)); HC-14: solvent not given (K. Hafner, private communication); “2-1: B, E (K. F. Lang and ill. Zander, Chem. Ber., 94, 1871 (1961)); HC-16-HC-19: S (for the reference see HC-10).
c.
The Journal of Physical Chemistry
3981
SEMIEMPIRICAL CALCULATIONS ON SULFUR-CONTAINING HETEROCYCLES ii [kcm-;] 5
50
40
30
40
60
30 1
40.
30
30
20
I
4
t
w
3
8 2
1-I' 1-2
7-3 1-4 2-1 2 -2
2-3 2-4
2-4'
3-7
3-1'
3-2
3-2' 7
5
4
[
3
-1 O
9
9 2
cf
-2
7-4
7 -?'
7-2
? -2'
7-3
r -4
r -3' r -+'
2- 7
2-7'
2-2
2-2'
2-3
2-3'
2-4
2-4'
3-7
3-1'
3-2
3-2'
Figure 4. Comparison of experimental and calculated spectral characteristics of four sulfur-containing heterocycles with the iso-r-electronic hydrocarbons. (The arem of the circles indicate the proportions of the individual configurations.)
of the longest wavelength bands of the previously examined cyclopenta [c l t h i ~ p y r a n e s(SH-16 ~~ : fcexptl) = 0.02 and f(theor) = 0.09, SH-17: j(exptl) = 0.02 and f(theor) = 0.07, SH-18: f(expt1) = 0.04 and f(theor) 0.12, and SH-19: f(exptl) = 0.06 andf(theor)= 0.16). The absorption band calculated for SH-23 at the unusually low wave number Of 12*3 kcm-' has been convincingly confirmed e~perirnentally.~~ On the other
hand, the agreement in the region of shorter wavelengths is less convincing, because the compound investigated experimentally was phenyl substituted. Satisfactory agreement between the experimental (43) R. Mayer, unpublished data. (44) L. L. Replogle, K. Katsumoto, and T. C. Morrill, Tetrahedron Lett., 1877 (196s). Volume 7.9 Number 18 November 1068
3982 and theoretical results in the interpretation of the absorption spectra of 30 sulfur heterocycles (cf. Figure 3) encourages us to attempt a prediction of the spectral characteristics of the unknown cycloheptathiopyrans SH-20 and SH-21. Both compounds, which, owing to the energetically rich occupied frontier orbital, will not be very stable,l are characterized by an absorption band of weak to medium intensity in the near-infrared region, followed by a more intense band at a shorter wavelength (assuming planar structure). This prediction could be rendered more reliable by taking bond alternation into account. The singlet-triplet transition energies are not tabulated, since it is known from an investigation of hydrocarbons that the repulsion integrals employed for calculations of the singlet-singlet transition overestimate the singlet-triplet splitting; furthermore, reliable experimental data on the singlet-triplet excitation energies are only available for a very few sulfurcontaining heterocycles. In the case of thiophenea7 the results often quoted in theoretical papers45were not r e p r o d ~ c i b l e . ~A~remark concerning SH-2 and SH-8 was made previously.2 Figure 3 further emphasizes the spectral relations between the sulfur-containing heterocycles and the iso-a-electronic hydrocarbons. Besides the condensed [blthiophens and cyclopentathiopyrans, remarkable analogies are exhibited by the thiopyrylium salts. These spectral analogies are characterized not only by the common absorption region but also by the shape of the absorption curves. This similarity results from the specific properties of sulfur: relatively easy ionization of its valency electron and rather small overlap of its 3pz orbital with the pz orbitals of the carbon atoms. Both factors are responsible, for example, for the fact that benzothiophene absorbs at longer wavelengths than benzofuran ( U O > US and lpcol > ~PcsI, cf. Figure 1) and absorbs in the same region as napht halene. A special absorption characteristic of benzenoid hydrocarbons is the occurrence of a, p, and fl bands,47 which are theoretically described by configurational interaction.48 It is hardly fortuitous that just where the similarity is particularly strong between the sulfurcontaining heterocycles and the iso-a-electronic compounds, we find far-reaching parallels in the weights of individual configurations contributing to the wave functions of the excited states (cf. Figure 4). On this basis it seems possible to extend Clar’s classification to the thiophenes. On the other hand, a comparison of the configuration weights of the transitions of greatest wavelength of SH-15, SH23, and SH-27 with those of the spectrally very similar iso-a-electronic hydrocarbons HC-8, HC-14, and HC-17 (cf. the theoretical investigation of HC-14 in ref 21) shows clearly that the band of greatest wavelength of medium intensity is always of the The Journal of Physical Chemistry
J. FABIAN, A. MEHLHORN, AND R. Z A H R A D N f K p type, followed at shorter wavelength by the a or p bands (cf. Figure 4). In the case of heterocyclic compounds, the expansion coefficients of the configuration wave function are more limited in significance than for hydrocarbons, since they depend strongly on the selection of parameters, particularly for small a-electron systems. There are examples where a variation of the parameters leads to an essential change of the configuration mixture of all spectral transitions without a material change in the transition energies (cf. Table 11). The SCF-CI calculations also offer the possibility of answering this question: To what extent can the simple Huckel method correctly describe a long-wave intense absorption? If we plot the SCF-CI energy of the transition representing the 1 + 1’excitation against the smallest HMO transition energies, we find no relation for SH-1-SH-32. I n agreement with the previous HMO investigation^,^^^^^ a linear relation is indicated only for thiophenes and thiopyrylium cations (cf. Figure 5). Outside of these classes of compounds it is not possible to estimate the transition energies by means of the HMO method. Ionization Potentials and Electron Afinities. According to the Koopmans theorem it is possible to identify the energy of the highest occupied molecular orbital with the first ionization p ~ t e n t i a l . ~Since ~ the energy scale for U employed here was not adjusted experimentally, the calculated values must be corrected by a constant value. For comparison, the data for iso-nelectronic hydrocarbons calculated by a corresponding approximation are also summarized. According to the calculations, the corresponding sulfur compounds should be more readily ionizable throughout. The theoretical values for the hydrocarbons are near the experimental results, while considerable discrepancies are encountered for the sulfur compounds. An experimental ionization potential is unfortunately known for thiophene only, so that the missing values had to be estimated from CT (charge transfer) band frequen~ies.5~The cyclopenta [blthiopyran and cyclopenta [clthiopyran should be still more readily subject to ionization than thionaphthene. A similar picture is presented by the comparison of (45) M. R. Padhye and B. R. Desai, Proc. Phys. Soc., 65, 298 (1952). (46) D.F. Evans, J . Chem. Soc., 3885 (1957). (47) E. Clar, “Polycyclic Hydrocarbons,” Vol. 1, Academic Press, New York, N. Y., 1964. (48) M. J. 8. Dewar and H. C. LonguetrHiggins, Proc. Phys. SOC., A67, 95 (1954). (49) R. ZahradnIk and C. P4rk&nyi,Collect. Czech. Chem. Commun., 30, 195 (1965). (50) T. E. Young and C. J. Ohnmaoht, J . Org. Chem., 32, 444 (1967). (51) T. Koopmans, Physica, 1, 104 (1933). (62) A. R. Cooper, C. W. P. Crowne, and P. G . Farrell, Trans. Faraday SOC.,62,18 (1966).
SEMIEMPIRICAL CALCULATIONS ON SULFUR-CONTAINING HETEROCYCLES
Figure 5. Comparison of HMO and SCF-GI transition energies of true or predominant l+l' character. The straight lines define corresponding correlations for benzenoid hydrocarbons (upper line) and tropylium salts; circles indicate thiophenes; squares indicate thiopyrylium salts. SH-8 and SH-31 deviate significantly unless the second SCF-GI transition energies are employed (arrow). The dotted lines correspond to the regression lines for benzenoid hydrocarbons (the upper line) and for the tropylium cations.
the polarographic oxidation potentials with the highest occupied molecular orbitals. The values determined in anhydrous dimethylformamide, containing 0.2 m Mg(C10& as the supporting electrolyte and with a rotating platinum electrode against sce, represent correctly not only the theoretically expected essential difference in the oxidation behavior of SH-1 and SH-2 (EHBMO = -9.53 and -9.15 eV, respectively, and el/? = 1.15 and 0.95 V, respectively) but also the almost equal oxidizability of the cyclopentathiopyrans SH-15 (EHBMO = -8.56 eV and BI/,OX = 0.78 V), SH-16 (EHBMO = -8.36 eV and = 0.93 V), SH-17 (EHBMO = -8.53 eV and el/:* = 0.89 V), and SH-18 (EHBMO = -8.35 eV and el/? = 0.83 V). As a measure of the electron affinity, one may take the polarographic reduction potentials (cf. ref 53; in this paper the preceding papers are cited). While thiophene was not reducible under the experimental conditions (dimethylfonnamide, 0.1 m tetrabutylammonium iodide as the supporting electrolyte, and a dropping mercury electrode with a drop interval of 3 sec against sce), a parallelism appears between the reduction half-wave potentials and the energies of the lowest free molecular orbitals of the other examined
3983
representatives. Thus it becomes clear that, in agreement with theory, the cyclopenta[b]thiopyrans SH-15 (ELFMO = -3.10 eV and tl/,Ted = -1.20 V), SH-17 (ELFMO = -3.39 eV and = -1.10 V), and SH-18 (ELFMO = -2.90 eV and = -1.17 V) are readily reducible and are classed before cyclopenta [clthiopyran SH-16 (ELFMO = -2.78 eV and = -1.61 V) and the thiophenes SH-2 (ELFMO = -1.71 eV and = -2.27 V) and SH-24 (ELFMO = -3.30 eV and = -2.14 V). The good linear proportionality is somewhat affected only by a slight inversion between SH-17 and SH-18 and by the too-high electron affinity calculated for SH-24. Dipole Moment and Charge Distribution. The T dipole moments calculated according to model D are higher than could be estimated from the experimental data with the use of incremental u moments. On the other hand, the decreasing tendency of the a moments in the sequence SH-1-SH-2-SH-8 is independent of the selection of the parameters. Since the experimentally determined dipole m o m e n t ~ exhibit ~ ~ r ~ ~a decrease in the opposite sequency, the overcompensation of the a component by an almost constant u vector within these types becomes obvious. A change of the parameters to U S = 22 eV and pcs = -1.391 eV leads to a close agreement between the calculated a components and the ?r moments estimated from the experiment, without a considerable change in the calculated transition energies. In this case we obtain for SH-1, SH-2, and SH-8 the total moments of 0.56, 0.81, and 0.98 D, respectively, which are very near the experimental values 0.54,s40.62, and 0.83 D,55 respectively. For SH-16 a total moment of 2.25 D has been predicted, which is in reasonable relation to the polarity of the cy~lopentapyrans.~~ The SCF charge distribution exhibits a distinct relation to the HMO calculations. In the a position of the sulfur-containing heterocycles, the a-electron density calculated by HMO is always smaller than that obtained by the SCF procedure, so that the inductive auxiliary parameter formerly employed within the Huckel model for the a-C atom brings the two closer together. Contrary to the HMO method, a higher electron density is obtained for the a position than for p position. This is not in contradiction to the experience based upon the molecular structure and the dipole m ~ m e n t . ~It~was , ~ ~only Vincent, et al.,5awho have (53) R. Zahradnfk and C. Pdrkbnyi, Talanta, 12, 1289 (1965). (54) H. Lumbroso and C. Carpanelli, Bull. Chim. SOC.Fr., 3198 (1964); H. V. Robles, Rec. Trav. Chim. Pays-Bas, 58, 111 (1959). (55) R. G. Charles and H. Freiser, J . Amer. Chem. Soc., 72, 2233 (1950). (56) R. Borsdorf, Habilitationsschrift, Universitilt Leipzig, 1966. (57) T. Shimozowa, Bull. Chem. SOC.Jap., 38, 1047 (1965). (58) B. Bak, Boll. Sci. Fac. Chim. Ind. Bologna, 21, 8 (1963). (59) E. J. Vincent, R. Phan-Tan Luu, and J. Metzger, Bull. SOC. Chim. Fr., 3537 (1966).
Volume 7.2, Number 12 Nosember 1068
J. FABIAN, A. MEHLHORN, A N D R. ZAHRADNfK
3984
Table I1 : Experimental and Theoretical Values and Mixture of Configurations of the Spectral Transitions for the Thiopyrylium Ion E , kcm-1 (j)-----
Parameter
D C a
7
Mixture of configurations, %-----
Polarity direction
7---
Theor
Exptl
*(l --c 1')
V(1 -L 2')
34.2 (0.15) 41.2 (0.32) 34.4 (0.04) 41.7 (0.36)
35.2" (0.05) 40.8" (0.1)
83.7
...
...
i
11.1 31.1
86.9 68.3
i
...
...
q ( 2 + 1')
...
86.8
II i1
...
According to I. Degani, R. Fochi, and C. Vincenzi, Boll. Sci. Fac. Chim. Ind. Bologna, 23,21 (1965).
Table I11 : SCF Calculations on Some S-Containing Heterocycles (D) and Iso-n-electronic Hydrocarbons and Physical Properties (Electron density)/
Compd
SH-1
Vertical ionization ---potential, eV-Themd Exptl
8.41
9.32" 9.35"
-=-dipole Theor
2.72
moment, uDExptP
1.40'
-T-s
C-C bond length ( E p 8 ) 8-7 , Theore Exptl
2-3
1.420
3-4
1.374 1,397
1.4239 1.41gP 1.370 1.370
_-__ (chemical shift)---T
Pr
1.09
2.70'
3
1.07
2.90
1.00
2. 73z
2 3 4 5 6 7
1.05 1.07 1.00 1.02 1.01 1.03
2 . 67k 2.78 2.28 2.74 2.76 2.21
1 2
1.00 1.00
2.201 2.55
1 2 3 4
1.00 1.02 1.00 1.04
1.397
HC-1
9.54
9.52" 9. 56b
0
0
SH-2
8.03
8.47"
2.55
1.65'
2-3 3-3a 3a-4 4-5 3a-7a 5-6 6-7 7-7a
1.366 1.436 1.413 1.389 1.412 1.405 1.390 1.408
HC-2
8.42
8.26'
0
0
1-2 1-8a 2-3 4a-8a
1.384 1.420 1.411 1.419
SH-8
8.03
8.35"
2.01
1.13i
1-2 1-9b 2-3 3 4 4-4a 4a-9b
1.392 1.408 1,402 1.393 1.406 1.410
HC-4
8.33
8.03'
0
0
1-2 1-loa
1.388 1.414
1.381' 1.457
1 2
1.00 1.00
2-3 3-4 4-4a 8a-9 9-10
1.406 1.389 1.412 1.423 1.372
1.398 1.383 1.425 1.390 1.372
3 4 9
1.00 1.00 1.00
2-3 3-4 44a 4a-5 4a-7a 5-6 6-7 7-7a
1.381 1.414 1.394 1.428 1.449 1.381 1.419 1.385
2 3 4 5 6
0.97 1.06 0.90 1.13 1.03 1.15
SH-15
7.44
The Journal of Physical Chemistry
5.09
1.368h 1.422 1.414 1.419
r , ppm
2
2.01-
2.581
7
1.30 2.30
3985
SEMIEMPIRICAL CALCULATIONS ON SULFUR-CONTAINING HETEROCYCLES
Table 111 (Continued)
Compd
(Electron density)/ -(chemical shift)--
Vertioal ionization --potential, eV-Tbeord Exptl
SH-16
7.24
HC-8
7.75
cr-dipole moment, pDTheor Exptl”
6.33
7.72”
3.13
0.796’
YC-C r-8
bond length (Ria), A-Theor* Exptl
la-1 3-4 44a 4a-5 5-6 6-7 7-7a
1,385 1.369 1.431 1,392 1.414 1.383 1.429
1-2 1-8a 3a4 4-5 5-6 3a-8a
1.399 1.407 1.408 1.399 1.401 1.462
1.399’ 1.418 1.383 1.406 1.403 1.501
91
7,
ppm
1 3 4 5 6 7
0.93 1.08 0.99 1.10 1.03 1.12
1 . 65f 3.15 2.02 3.15 2.58 3.15
1 2 4 5 6
1.11 1.00 0.89 1.02 0.93
2.54‘ 2.05 1.61 2.74 2.36
a H. Baba, I. Omura, and K. Higashi, Bull. Chem. SOC. Jap., 26,521 (1956). * G. F. Grable and G. L. Kvans, J. Phys. Chem., 66 436 (1962). R. J. van Brunt and M. E. Wacks, J . Chem. Phys., 41, 3195 (1964); M. E. Wacks and V. H. Dibeler, ibid., 31,1557 = 9.54 - ACB, where ACBis the difference of the energies of the highest molecular orbitals between benzene and the (1959). IE(DI) compound under examination. ’ E,, = 1.517 - 0.18Oprs(see C. A. Coulson and A. Golebiewski, Proc. Phys. Soc., 78, 1310 (1961))‘ A. G. Anderson, Jr., and W. F. Harrison, Tetrahedron Lett., 11 (1960). ‘ 0 . Bastiansen and J. L. Berissen, Acta Chem. Scand., 20, 1319 (1966). Experimental mean values according to G. V. Boyd and N. Singer, Tetrahedron, 22, 3383 (1966). ’ Separation of the c moment according to the increment method (see A. Mehlhorn, Ph.D. Dissertation, Technical University, Dresden, 1967). H. J. Tobler, A. Bauder, and H. H. Gunthard, J . Mol. Spectrosc., 18,239 (1965). K. Takanashi, I. Ito, and Y . Matsuki, Bull. Chem. SOC. Jap., 39,2316 (1966). H. Suhr, “Anwendung der kernmagnetischen Resonanz in der organischen Chemie,” Springer-Verlag, Berlin, 1965, SH-1 in CDCls, HC-1 in CCl4, HC-2 and HC-4 in ccl4 or CSZ,HC-8 in CHzC12. E. Keupp, Ph.D. Dissertation, Universitat Frankfurt, 1962. Estimated from C T with tetracyanoethylene (TCE) (see G. Troger, Diplomarbeit Technical University, Dresden, R. A. Bonham and F. A. 1967) according to IE(EII) = 1.16hv 5.74. ” Calculated from experimental values (cf. ref 54 and 55). Momany, J. Phys. Chem., 67, 2474 (1963). Reference 29. J. Trotter, Acta Crystallogr., 16, 605 (1963).
’
’
J
+
calculated, by a quantitative analysis of the chemical shifts, that the p position of thiophene carries a charge higher by 0.005, It must be pointed out not only that there is an uncertainty in the correction of the nmr data but also that it is not clear whether the chemical shift in heterocyclic compounds should not be more appropriately regarded as a function of the total electron density.60*61 Calculations by the extended Huckel method according to HoffmannB2carried out for fivering heterocycles show that the a position in the u system is rendered noticeably positive,63so that the proton shift can reflect a smaller *-electron density. In any case it is hardly possible to compare the chemical shifts directly with the *-electron densities (cf. Table 111). Bond Distances. The calculated bond distances64 are very well reproduced not only for the hydrocarbons but also for the only compound of our series so far investigated in the vapor state, SH-12g,e6(cf. Table 111). For SH-5, a crystallographic investigation is availablens6 The experimental and theoretical lengths, respectively, in hngstroms, of the bonds are: bond 2-3, 1.36 and 1.37; bond 3-3a, 1.41 and 1.43; and bond 3a-6a, 1.36 and 1.40. (Cf.ref 67.) We intend to discuss the chemical reactivity and some
other properties connected with the electron distribution in a subsequent paper. Acknowledgment. We are indebted to Professor Dr. R. Mayer, Institute of Organic Chemistry, Technical University, Dresden, for the support of our work. The spectra of the naphthothiophenes were kindly put at our disposal by Professor Dr. W. Carruthers, University of Exeter, and samples of the cyclopenta [blthiopyrans by Dr. J. Franke. The polarographic half-wave potentials were measured by Mr. D. Kunz. The calculations by means of an Elliott 503b computer were carried out by Mr. V. Simon in the Computation Center for Data Processing in Dresden using a program written by Mr. V. Kvasni6ka. (60) T.F.Page, Jr., T. Alger, and D. M. Grant, J . Amer. Chem. SOC., 87, 5333 (1965).
(61) W.Adam and A. Grimison, Tetrahedron, 21, 3417 (1965); 22, 835 (1966). (62) R. Hoffmann, J . Chem. Phys., 39, 1397 (1963). (63) W.Adam and A. Grimison, Theor. Chim. Acta, 7, 342 (1967). (64) C. A. Coulson and A. Golebiewski, Proc. Phys. Soc., 78, 1310 (1961). (65) R. A. Bonham and F. A. Momany, J . Phys. Chem., 67, 2474 (1963). (66) E.G. Cox, R. J. J. H. Gillot, and G. A. Jeffrey, Acta Crystallogr., 2, 356 (1949). (67) D.T.Clark, Tetrahedron Lett., 2889 (1967).
Volume 7.2, Number 1.2 November 1968
