J . Phys. Chem. 1988, 92,4591-4594
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Molecular Structure and Conformational Stability of Ethyl Methyl Disulfide: A Model of Cystine+ Masaru Ohsaku* Department of Chemistry, Faculty of Science, Hiroshima University, Higashisenda 1-1-89, Hiroshima 730, Japan
and Norman L. Allinger Department of Chemistry, School of Chemical Sciences, The University of Georgia, Athens, Georgia 30602 (Received: October 12, 1987; In Final Form: February 16, 1988)
The results of ab initio self-consistent field molecular orbital (SCF MO) calculations on ethyl methyl disulfide using several basis sets are presented. The geometrical parameters were reproduced very well by the 3-21G+d(0.8C+0.6) set as was previously found for ethyl methyl sulfide. With this basis set, the MP2 and MP3 perturbation procedure was applied to include electron correlation. The calculated results are consistent with the observed molecular geometry and the relative conformational stabilities as estimated by a variety of spectroscopic techniques. The calculated results also correspond very well with earlier molecular mechanics estimations and STO-3G calculations but not with the results of CNDO/2 calculations.
Introduction Ethyl methyl disulfide is important as a model molecule of cystine. Figure 1 shows a schematic structure of the “zwitterionic” form of the cystine. Cystine is well-known as an amino acid that imparts very peculiar and important characteristics to a protein unit. For example, this unit connects two polymer chains via the S-S bond that leads to a relatively rigid and very different threedimensional structure than the protein would otherwise have. The roles of cystine and cystein have been examined extensively on the basis of a variety of procedures and analyzed from many viewpoints, e.g., ref 1-6. It would be desirable to know the molecular geometry of ethyl methyl disulfide exactly as an aid in understanding the role of the sulfur-containing amino acid in proteins. Theoretical calculations have previously been carried out to determine the conformational stability of this m ~ l e c u l e . ~ Ex~* perimental studies on this molecule have also been reported, e.g., vibrational spectra, Raman and infrared,+14 and electron diff r a ~ t i 0 n . l ~The experimental work does not report, however, complete and unambiguous geometrical parameters. Additional theoretical calculation^^"^^ have focused on the structures and reactions of compounds that contain the S-S bond. In the present paper, we have investigated ethyl methyl disulfide using an ab initio S C F MO procedure to obtain a reasonable molecular geometry and a full conformational analysis. All calculations were performed by using the GAUSSIAN 82 program package;25the geometry optimization was performed by using the energy gradient method.26 Optimized Geometry The optimized geometries are summarized in Table I, together with those observed.15 The atom numbering and the notations of the geometrical parameters are shown in Figure 2. The semiempirical C N D 0 / 2 method produced arl S-S bond length that was too short.22 The ab initio calculation overcame this difficulty. It is of interest that the geometry is well reproduced by even the smallest basis set, STO-3G. The largest differences in the bond lengths between the STO-3G and 3-21G+d(C,S) basis sets are seen in the differences in R1, R3, and R4 (0.012 A each). All of these bonds are between the heavy atoms. There are only small differences in the valence angles calculated by the STO-3G and 3-21G+d(C,S) sets (less than 2O). The 3-21G set gave rather longer r(C-S) and r(S-S) bonds than those from the other sets. The bond lengths r(C-S) were calculated to have different lengths +Part of this work was presented at the 54th Annual Meeting of the Chemical Society of Japan, Tokyo, April 1-4, 1987.
0022-365418812092-4591$01.50/0
for Et-S and Me-S by the present calculations, and r(Et-S) is longer than the r ( M e S ) except for the case of the 3-21G set. The electron diffraction experiment could not resolve these bonds and forced us to assume they were identical. In examining the dependency of the geometry on the basis set, if we accept that the 3-21G+d(C,S) geometry is most nearly correct, the STO-3G geometry is really quite close to it. The same is true in the previous papers that treated some sulfur-containing molecule^.^^^^*
(1) (2) (3) (4)
Boyd, R. J.; Perkyns, J. S.; Ramani, R. Can. J. Chem. 1983,61, 1082. Ravi, A,; Balaram P. Tetrahedron 1984, 40, 2577. Walters, D. W.; Gilbert, H. F. J. Biol. Chem. 1986, 261, 13135. MacPhee-Quigley, K.; Vedvick, T. S.; Taylor, P.; Taylor, S. S. J. B i d .
Chem. 1986, 261, 13565. ( 5 ) Packard, B.; Edidin, M.; Komoriya, A. Biochemistry 1986,25, 3548. (6) Snyder, G. H. Biochemistry 1987, 26, 688. (7) Van Wart, H. E.; Shipman, L. L.; Scheraga, H. A. J . Phys. Chem. 1975, 79, 1428, 1436. (8) Allinger, N. L.; Kao, J.; Chang, H.-M.; Boyd, D. B. Tetrahedron 1976, 32, 2867. (9) Sugeta, H.; Go, A,; Miyazawa, T. Chem. Lett. 1972, 83. (10) Sugeta, H.; Go, A.; Miyazawa, T. Bull Chem. SOC.Jpn. 1973, 46, 3407. (11) Sugeta, H. Spectrochim. Acta, Part A 1975, 31A, 1729. (12) Van Wart, H. E.; Cardinaux, F.; Scheraga, H. A. J . Phys. Chem. 1976, 80,625. (13) Van Wart, H. E.; Scheraga, H. A. J. Phys. Chem. 1976,80, 1812. (14) Van Wart, H. E.; Scheraga, H. A. J . Phys. Chem. 1976,80, 1823. (15) Yokozeki, A.; Bauer, S. H. J. Phys. Chem. 1976.80, 618. (16) Rauk, A. J . Am. Chem. SOC.1984, 106, 6517. (17) Grein, F. Chem. Phys. Lett. 1985, 116, 323. (18) Ha, T.-K. THEOCHEM 1985, 122, 225. (19) Baird, N . C . THEOCHEM 1986, 137, 1. (20) Magnusson, E. Aust. J . Chem. 1986, 39, 735. (21) Tyblewski, T.; Ha, T.-K.; Bauder, A. J. Mol. Spectrosc. 1986,115, 353. (22) Van Wart, H. E.; Shipman L. L.; Scheraga, H. A. J . Phys. Chem. 1974, 78, 1848. (23) Allinger, N. L.; Hickey, M. J.; Kao, J. J. Am. Chem. SOC.1976, 98, 2741. (24) Aida, M.; Nagata, C. Chem. Phys. Lett. 1984, 112, 129. (25),Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Raghavachari, K.; Whiteside, R. A,; Schlegel, H. B.; Fluder, E. M.; Pople, J. A. Program GAUSSIAN 82, Carnegie-Mellon University, Washington, DC, 1982. (26) Schlegel, H. B. J. Comput. Chem. 1982, 3, 214. Pulay, P. In Applications of Efectronic Structure Theory; Schaefer, H. F., 111, Ed.; Plenum: New York, 1977.
0 1988 American Chemical Society
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The Journal of Physical Chemistry, Vol. 92, No. 16, 1988
TABLE I: Optimized Structural Parameters of Ethyl Methyl Disulfide (Bond Lengths Are in angstroms, Angles Are in degrees) obsd” STO-3G 3-21G STO-3G* 3-21G+d(C,S) Trans, T, Form R1 R2 R3 R4 R5 R6 R7 R8 R9 A1 A2 A3 A4 A5 A6 A7 A8 B2 B3
1.540 1.817* 2.031 1.817 l.lllc 1.111 1.111 1.111 1.111 112.4 103.2d 103.2
R1 R2 R3 R4 R5 R6 R7 R8 R9 A1 A2 A3 A4 A5 A6 A7 A8 B2 B3
1.540 1.817b 2.031 1.817 1.11lC 1.111 1.111 1.111 1.111 112.4 103.2d 103.2
111.5e 111.5
1.541 1.815 2.064 1.803 1.086 1.086 1.089 1.085 1.087 109.40 100.27 100.33 110.48 110.74 109.67 108.83 1 11.93 (180) 90.58
1.533 1.889 2.245 1.890 1.084 1.083 1.079 1.079 1.077 109.29 99.91 99.43 109.61 110.79 111.19 106.41 108.94 (180) 89.54
1.545 1.807 1.948 1.796 1.086 1.086 1.090 1.088 1.089 109.08 103.28 103.29 110.54 110.74 109.63 108.78 111.94 (180) 87.08
1.528 1.822 2.052 1.815 1.088 1.088 1.085 1.086 1.084 109.13 102.21 101.73 109.88 110.85 110.62 107.37 110.31 (180) 86.82
1.544 1.808 1.948 1.796 1.087 1.086 1.090 1.088 1.089 113.64 103.46 103.25 110.61 110.58 109.75 108.81 111.93 66.00 86.85
1.524 1.825 2.052 1.815 1.089 1.087 1.086 1.086 1.084 113.21 102.08 101.62 110.16 110.49 111.07 107.37 110.31 70.86 87.00
1.544 1.808 1.949 1.798 1.087 1.085 1.090 1.088 1.088 115.00 104.08 103.72 110.38 110.76 109.54 108.65 112.10 291.b9 97.99
1.523 1.825 2.055 1.816 1.089 1.087 1.086 1.086 1.084 114.37 102.52 102.42 110.22 110.54 110.96 107.06 110.45 291.43 100.04
H-N+-C-C
H H-C-H
S
I \ I T 7-7 -7 +-H H-C-H
Gauche, G, Form
111.5e 111.5 66.8 84.4
1.542 1.815 2.064 1.803 1.087 1.086 1.088 1.085 1.087 113.53 100.50 100.24 110.49 110.66 109.69 108.81 111.94 69.12 90.75
1.527 1.891 2.245 1.890 1.085 1.082 1.081 1.079 1.077 112.92 99.65 99.29 109.86 110.48 11 1.61 106.41 108.94 69.87 89.37
Gauche, G’, Form R1 R2 R3 R4 R5 R6 R7 R8 R9 A1 A2 A3 A4 A5 A6 A7 A8 B2
1.540 1.817b 2.031 1.817 1.11lC 1.111 1.111 1.111 1.111 112.4 103.2d 103.2
111.Y 111.5
83
1.542 1.816 2.067 1.803 1.086 1.086 1.088 1.085 1.087 114.34 100.68 100.37 110.43 110.76 109.57 108.71 111.99 291.53 105.97
1.527 1.891 2.249 1.891 1.085 1.083 1.080 1.079 1.077 113.61 99.80 99.85 109.98 110.48 11 1.58 106.20 108.99 291.47 104.20
From ref 15. Both r(C-S) are assumed identical. CAll of the r(C-H) are assumed identical. d Both $(SSC) are assumed identical. e
Assumed.
Conformational Stability of the Rotational Isomers In earlier papers, Raman spectral analysis suggested that the gauche forms G (or G’) were ca. 0.90 kcal/mol more stable than the T form in the liquid state, and the G form alone remained in the solid state.”’ Normal coordinate analysis showed that the (27) Ohsaku, M.; Imamura, A. Mol. Phps. 1985, 55, 331 (28) Ohsaku, M. THEOCHEM 1986, 138, 283.
-0
H
H
Figure 1. Cystine in the “zwitterionic”form.
Figure 2. Schematic structure, atom numberings, and notation of geometrical parameters in ethyl methyl disulfide: B2, T(clc2-S3s4); B3, T(c2s3-s4c5).
TABLE I 1 Conformational Energy Differences (kcal/mol) for Ethyl Methyl Disulfide” calcd STO-3G 3-21G STO-3G* 3-21G+d(C,S) trans (T) 0.08 0.44 0.08 0.18 gauche (G) 0 0 0 0 gauche (G’) 0.66 0.41 1.04 0.73
“The actual calculated energies of the gauche conformation for the four different sets were -566 803.63, -570 245.82, -566 865.76, and -570 320.62 kcal/mol. distinction between GG and GG’ forms (the first letter relates to the C2-S3 bond and the second S3-S4) is difficult,” and the temperature dependency of the Raman spectra was interpreted as indicating the coexistence of the three forms around the CC-SS bond.12 Among these, two forms have similar energy, and the other was less stable by ca. 0.3kcal/mol. It was concluded that this other form was not T. The gas-phase electron diffraction studyI5 concluded that more than one rotamer existed at room temperature, and that the trans population was on the order of 36-45%. The experiment did not offer any further conformational information. The calculated total H F energies are summarized in Table 11. From our calculations, the G form is always the most stable conformation, and, except with the 3-21Gbasis, the gauche’ is always least stable. The most stable form agreed very well with the conformation of L-cystine in 2 N hydrochloric acid solution.’ Generally speaking, the stability order G > T 1 G’ or G 1 T > G’ can be deduced by the present Hartree-Fock (HF) treatment. These results agree well with those of molecular mechanics
The Journal of Physical Chemistry, Vol. 92, No. 16, 1988 4593
Ethyl Methyl Disulfide as a Model of Cystine TABLE I11 Conformational Energies (kcal/mol) of Ethyl Methyl Disulfide (3-21G+d(C,S)) corr (MP2/MP3) total re1 -570721.42/-570755.29 0.77/0.71 trans (T) -401.02/-33.86 gauche (G) -401.57/-33.81 -570722.19/-570756.00 0/0 gauche (G') -401.65/-33.86 -570721.55/-570755.40 0.64/0.60
0
60
120
180
240
300
360
Dihedral a n g l e (deq)
Figure 4. Total energy as a function of the rotational angle around the S3-S4 bond. The case where the conformation around the bond C2-S3 is fixed as the T form (rigid rotation): ( 0 )STO-3G; (A) 3-21G. The case where the conformation around the bond C2-S3 is fixed as the G form (rigid rotation): (0) STO-3G; (m) 3-21G.
I
I
I
I
I
I
I
0
60
120
180
240
300
360
Dihedral angle ( d e g )
Figure 3. Total energy as a function of the rotational angle around the C2-S3 bond. All of the energy is for the fully geometry optimized case (flexible rotation): ( 0 )STO-3G; (0)STO-3G*; (A) 3-21G.
calculations8and with earlier STO-3G calculations using molecular mechanics geometries.8 Including Electron Correlation
To include electron correlation, the Mdler-Plessett (MP2 and MP3) perturbation calculations29~30 were performed using the 3-21G+d(C,S) basis set, and the fixed geometry optimized with this basis set at the H F level. The results of the calculations are shown in Table 111. After the MP2 calculations, the order of the total energy between the T and G' forms was reversed. The MP3 calculations did not change the tendency. At any rate, the energy difference between the T and G' forms is very small in the case that includes the electron correlation. It is possible to overestimate the correlation energy by the MP2 and/or MP3 calculation. Therefore, while it seems likely that the gauche form is the most stable, the difference between the other two forms is small and of uncertain direction. Rotational Barrier Height
For the molecules HSSH, CH3SSCH3, and CH3SSH, the barrier heights for rotations around the S-S bonds were estimated; for example, see ref 1, 16-18, 20, and 21. We are not aware of any reported calculations on the barrier height around the CS-SC bond for the EtSSMe at any level. We have calculated the rotational barrier heights for the molecule around the C2-S3 and the S3-S4 bonds using different basis sets. Figure 3 shows the total energy as a function of the rotational angle around the C2-S3 bond. We have examined six molecular conformations, and the geometry was fully optimized at every point except B2 in the following three cases. In the cases where B2 = ,'O 120', and 240°, this angle was fixed during the geometry optimization. The figure shows that the barriers for the rotation from the G to the T form and from the T to the G' form are ca. 1.5 and 1.O-1.5 kcal/mol, respectively. These values are quite low, and are in good agreement with earlier calculations.8 From the G' form to the T form the height is ca. 1 kcal/mol or less. Examining these values, we can conclude that the rotation from the form G to the G' form via the T form is not actually so difficult. The barrier ~~~
(29) Meller, C.; Plessett, M. S.Phys. Reu. 1934, 46, 618. (30) Binkley, J. S.; Popie, J. S. Int. J . Qunnt. Chem. 1975, 9, 229.
heights from the G to the cis form or from the G' to the cis form are ca. 3.5 and ca. 2-3 kcal/mol, respectively. These values are in good agreement with earlier ab initio and molecular mechanics calculations,8 but they do not agree at all with the C N D 0 / 2 calc~lations.~ They can be compared to those of CH3CH2-SCH3, 2.05 and 1.7 1 kcal/m01.~'*~~ Figure 4 shows the total energy as a function of the rotational angle around the S3-S4 bond. The rotation was carried out twice, assuming two different conformations around the C2-S3 bond. The first one was the rotation around the S3-S4 bond, assuming that the C2-S3 bond was the T form, and the second one assumed that the conformation around the C2-S3 bond was in the G form. In each case the rotation was performed by a rigid rotation with the geometry optimized in each set for the T and G forms, respectively. The barrier height in going from the B3 = 90' to B3 = 240' or = 270' is ca. 3.5-4.0 kcal/mol. The curvature for the T form around the C2-S3 form is symmetric around B3 = 180'. However, the one for the G form around the C2-S3 bond is not symmetric around B3 = 180°, and the energy minimum around 270' that was obtained for the T form is shifted to around 240'. The envelopes of the curvatures are also different below 60' and above 270'. Now the barrier around the S-S bond may be compared with the same barrier in other molecules. Rauk's values (using a split valence basis) of the cis and trans barriers to the hindered rigid rotation for HSSH are 8.98 and 5.17 kcal/mol, respectively.I6 Grein reported the cis and trans barriers for HSSH using 4-31G+d (fully optimized) to be 8.0 and 5.52 kcal/mol, respectively." Ha reported the barriers for HSSH, CH3SSH, and CH3SSCH3in the 3-21G, 3-21G*, and 3-21G+d basis sets;'* the cis and trans barriers are (fully optimized by using 3-21G+d basis set) 8.13 and 5.67, 8.60 and 5.79, and 11.66 and 5.55 kcal/mol for HSSH, CH,SSH, and CH3SSCH3,respectively. Generally the cis barrier increases in the order HSSH, CH3SSH, CH3SSCH3,while the trans barrier is nearly constant. Our values (rigid rotation) are, e.g. (3-21G), cis and trans barriers ca. 12 and 3.5 kcal/mol, respectively. Thus the tendency is the same. The STO-3G set produced much higher barriers for this bond than did the 3-21G set. The same tendency is reported for the molecules containing the C,:-S bond.33 In the case of rotation around the S3-S4 bond for the G form, the barrier is very high below 60' or above 270'. These very high values are partly an
(31) Durig, J. R.; Compton, D. A. C.; Jalilian, 83, 511.
M.-R.J. Phys. Chem. 1979,
(32) Adachi, M.; Nakagawa, J.; Hayashi, M. J . Mol. Spectrosc. 1982, 91, 381. (33) Kao, J.; Eyermann, C.; Southwick, E.; Leister, D. J . Am. Chem. SOC. 1985, 107, 5323.
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The Journal of Physical Chemistry, Vol. 92, No. 16, 1988
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TABLE I V Variation for the Bond Angle A1 and Torsional Anele B3 (in degrees) B2' 3Gb 0 69.12 120 180 240 291.53
AI
3-21
3G*
3-21d
69.87
66.00
70.86
291.47
291.09
291.43
3G 116.71 113.53 111.73 109.40 111.94 114.34
3-21 116.08 112.92 111.39 109.29 111.69 113.61
B3 3G* 116.49 113.64 111.53 109.08 111.86 115.00
3-21d 113.21 109.13 114.37
3G 95.14 90.75 89.64 90.58 90.56 105.97
3-21 92.37 89.37 90.00 89.54 89.64 104.20
3G* 91.31 86.85 86.63 87.08 87.16 97.99
3-21d 87.00 86.82 100.04
'See also Figure 2. b3G, STO-3G; 3-21, 3-21G; 3G*, STO-3G*; 3-21d, 3-21G+d(C,S).
TABLE V Total Atomic Charges (3-21G)' b cis G S T c1 c2 S3 S4 H6 H7 H8 H9 H10
6.59 6.67 15.93 15.93 0.78 0.76 0.78 0.74 0.74
6.59 6.68 15.92 15.94 0.79 0.78 0.76 0.74 0.75
6.58 6.68 15.92 15.93 0.78 0.78 0.77 0.75 0.72
6.60 6.67 15.92 15.93 0.78 0.78 0.77 0.75 0.73
S' 6.58 6.68 15.92 15.93 0.78 0.78 0.78 0.72 0.74
G' 6.59 6.67 15.92 15.94 0.78 0.77 0.78 0.73 0.74
'Other atoms; C5, 6.83; H11, 0.75; H12, 0.74; H13, 0.75. bNotations from ref 15.
artifact resulting from the rigid rotation approximation. Variation of the Valence Angles and the Torsional Angles It is interesting to examine the variation of the valence angles and the torsional angles under the change of the internal rotation angle around the C2-S3 bond. The results are summarized in Table IV. This table shows only the A1 and B3 angles. These two angles exhibit typical behavior. The A1 angles are most open in the cis form, then narrow in going from the cis to the T form, and again open in going from the T to the cis form. The tendency is almost the same in every basis set. This is understood: In the cis form the terminal groups become very close to each other and A1 widens, while in the T form they are far apart and A1 narrows. The behavior of the B3 angle is different from that of the A1 angle. This angle narrows drastically in going from the cis form (B2 = Oo) to the G form, and then it stays around ca. 90' in going from 60° to the B2 = 240' form, and then it increases the B2 abruptly in the G' form. As a result, even if the torsional angle
B2 varies in going from 70' (G) to 290' (G') via the S, T, S' forms, the B3 angle still remains near 90'. This is in good agreement with the theoretically calculated resultz4that during the thio-disulfide reaction, the geometry does not vary very much. In the case of B3, no clear basis set dependency is seen. Electronic Charges If the cis form were to be stabilized as previously suggested by Scheraga,' the attractive interaction between S4 and H7 or H8 might be stronger in this form than in the others. To check this possibility, we have made a list of the atomic charges for the molecule (Table V) where the results of the 3-21G calculation are summarized. Examining this table, one sees substantial variation in only three atoms, H8, H9, and H10. Thus there appears to be no evidence from these calculations for strong hydrogen bonding between S4 and H7 and/or H8. Conclusions From S C F M O calculations on ethyl methyl disulfide, it is concluded that the 3-21G+d(C,S) basis set gives a good geometry, which is in agreement with the limited experimental data. Conformationally, the gauche (G) form is most stable, with the T and G' forms being 0.5-1.0 kcal/mol higher in energy. These conformations are separated by low barriers, in agreement with previous molecular mechanics and a b initio calculations. In contrast, rotation around the S3-S4 bond meets with barriers of about 4 (trans) and 12 (cis) kcal/mol.
Acknowledgment. Thanks are due to the Computer Center of the Institue for Molecular Science for use of the GAUSSIAN 82 program library for the HITAC-810 system. Registry No. H3CCH2SCH3,20333-39-5; @)-cystine, 56-89-3.
