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J . Phys. Chem. 1985, 89, 5334-5336
The Molecular Structure of H,S, and Barriers to Internal Rotation David A. Dixon,* Daniel Zeroka,+ John J. Wendoloski, and Zelda R. Wasserman Central Research and Development Department,$ E. I . Du Pont de Nemours and Co., Inc., Wilmington, Delaware I9898 (Received: August 27, 1985)
The molecular structure of H2S2has been determined by ab initio molecular theory at the SCF and CI-SD levels. The SCF and CI-SD results are in good agreement with each other for all parameters and are in agreement with experiment except for the value of B(HSS). The calculated value for 0 is 98.4O as compared to an experimental value of 91.3O. It is suggested that the experimental value is too low. The vibrational frequencies for the optimum skew structure and the cis ( 7 = 0') and trans ( T = 180') structures have been calculated at the SCF level. The cis and trans structures have one imaginary frequency and are true transition states on the internal rotation energy surface. The barriers to internal rotation were calculated at the SCF and CI-SD levels and were corrected for the difference in zero-point energies; this correction is 0.6-0.7 kcal/mol. The trans barrier is 5.0 f 0.15 kcal/mol and the cis barrier is 7.5 f 0.15 kcal/mol.
Introduction Ab initio molecular orbital theory has been used extensively to investigate' barriers to internal rotation since the pioneering work of Pitzer and Lipscomb on the ethane barrier.2 There is ample demonstration that a b initio calculations can reproduce rotation barriers at the Hartree-Fock level if a large enough basis set is employed; this is consistent with the predictions of Freed.3 One of the early challenges for ab initio molecular orbital theory was the prediction of the rotation barrier and equilibrium structure of H202.4-7 Accurate barrier heights are found at the Hartree-Fock level if a large enough basis set (including polarization functions) is employed and if geometry optimization is performed at the optimum skew structure and for the cis and trans structures. It has been suggested that correlation corrections are required for obtaining good geometric parameters for H202.596 Although there is a large amount of data available for the peroxide, much less information is available for the disulfide HzS2, even though this compound serves as a model for the S-S linkage in proteins and provides a starting point for understanding the structure of S, systems. The structure of HzS2was initially determined by Winnewisser and Haase8 with the electron diffraction technique. They found r(S-S) = 2.055 f 0.001 A and B(SSH) = 91'57' f 30'. In a subsequent study, Winnewisser et aL9 studied the millimeter-wave spectrum of H2S2and from the microwave spectrum obtained the geometric parameters r ( S H ) = 1.327 f 0.007 A, B(SSH) = 91'20' f 30', and torsion angle r(HSSH) = 90'36' f 3'. A number of theoretical studies of the structure of H2S2have been performed. In a study of the chiroptical properties of R2S2, RaukIo calculated the rotation barrier for HzS2at the SCF level with an extended polarized basis set. He assumed the experimental geometry and rigid rotation and found a cis barrier of 9.0 kcal/mol and a trans barrier of 5.2 kcal/mol. Earlier, Veillard and Demuynck" found a cis barrier of 9.3 kcal/mol and a trans barrier of 6.0 kcal/mol at the S C F level with a double [basis set augmented by polarization functions. HinchcliffeI2 optimized the three parameters for H2S2at the S C F level with a polarized double [ (DZ+P) basis set. H e found r(S-S) = 2.081 A, B(SSH) = 98.3O, and r(HSSH) = 91.7' with r(SH) constrained at 1.356 A. There is a surprising difference in the calculated and experimental values for ff. We are interested, in general, in the conformational properties of molecules containing sulfur-sulfur bonds and began this work with a theoretical study of H2S2. We present an ab initio selfconsistent field-configuration interaction (SCF-CI) study of the equilibrium geometry and rotation barrier for H2S2. We have also determined the force field for H2S2at the SCF level at the optimum structure and at the cis and trans structures in order 'Permanent address: Department of Chemistry, Lehigh University, Bethlehem, PA 18015. 'Contribution No. 3840.
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TABLE I: Optimum Geometry Parameters for H2S20 method r(SS) r(SH) B(HSS) 7(HSSH)
SCF/opt SCF/cis SCF/trans CI/opt exptlb
2.067 2.118 2.106 2.074 2.055
1.331 1.329 1.329 1.337 1.327
98.2 97.3 94.3 98.4 91.3
89.7
0 180 89.7' 90.6
Bond distances in A. Bond angles in degrees. References 8 and 9. 'Not optimized. Taken from SCF/opt value. to determine the vibrational correction to the barrier height.
Calculations The calculations were done with the HOND0I3 program package on VAXl1/780 and IBM 3081 computers. The geometries were optimized at the S C F level by using gradient technique^'^ and were pointwise optimized at the C I level. The CI calculations were done with the GUGA f0rma1ism.I~ All single and double excitations from the valence space to the virtual space were included. The sulfur n = 1 and n = 2 shells were kept doubly occupied and the top ten virtual orbitals which correspond to the virtual n = 1 and n = 2 orbitals on the sulfur atoms were excluded. The orbitals for the CI were taken from the SCF single reference configuration. The force field was calculated at the S C F level by finite differencing of the gradient. The basis set for these calculations is a DZ+P basis set of the form (1 ls7pld/4slp)/
( I ) Payne, P. W.; Allen, L. C. In "Applications of Electronic Structure Theory", Schaefer, H. F., Ed.; Plenum Press: New York, 1977; p 29. (2) Pitzer, R. M.; Lipscomb, W. N. J . Chem. Phys. 1963, 39, 1995. (3) Freed, K. Chem. Phys. Lett. 1968, 2, 255. (4) Dunning, T. H., Jr.; Winter, N. W. J . Chem. Phys. 1975, 63, 1847. (5) Cremer, D. J . Chem. Phys. 1978, 69, 4440. (6) Bair, R. A,; Goddard, W. A., 111 J . A m . Chem. SOC.1982, 104, 2719. (7) Block, R.; Jansen, L. J . Chem. Phys. 1985, 82, 3322. (8) Winnewisser, M.; Haase, J. Z. Naturforsch. 1958, 231, 56. (9) Winnewisser, G.; Winnewisser, M.; Gordy, W. J . Chem. Phys. 1968, 49, 3465. ( I O ) Rauk, A. J . Am. Chem. SOC.1984, 106, 6517. (11) Veillard, A,; Demuynck, J. Chem. Phys. Lett. 1970, 4 , 476. (12) Hinchcliffe, A. J . Mol. Struct. 1979, 55, 127. (13) (a) Dupuis, M.; Rys, J.; King, H. F. J . Chem. Phys. 1976, 65, 111. (b) King, H. F.; Dupis, M.; Rys, J., "National Resource for Computer Chemistry Software Catalog", Vol. 1, Program QH02 (HONDO), 1980. (14) (a) Komornicki, A.; Ishida, K.; Morokuma, K.; Ditchfield, R.; Conrad, M. Chem. Phys. Lett. 1977, 45, 595. McIver, J. A.; Komornicki, A., Jr. Ibid. 1971, 10, 303. (b) h l a y , P. In "Methods of Electronic Structure Theory", Schaefer, H. F., Ed.; Plenum: New York, 1977; p 153. (c) Komornicki, A.; Pauzat, F., Ellinger, Y. J . Phys. Chem. 1983, 87, 3847. (15) (a) Brooks, B.; Schaefer, H. F. J . Chem. Phys. 1979, 70, 5092. (b) Brooks, B.; Laidig, W.; Saxe, P.; Handy, N.; Schaefer, H. F. Phys. Scr. 1980, 21, 312.
0 1985 American Chemical Society
Letters
The Journal of Physical Chemistry, Vol. 89, No. 25, 1985 5335
TABLE 11: Vibrational Frequencies for H,S, in opt
freq 445 (a) 562 (a) 1000 (a) 1006 (b) 2849 (a) 2850 (b) a
(7
cis
= 90)b
assignment
freq
torsion S-S str HSS bend sym HSS bend asym HS str sym HS s t r asym
494i (b,) 540 (a,) 911 (a,) 1044 (b,)
2844 (b,) 2860 (a,)
(7
= O)c
assignment torsion S-S str HSS bend sym HSS bend asym HS str asym HS str sym
trans (7 = 1 8 0 ) ~ freq 363i (a,) 545 (ag) 838 (b,) 1122 (ag) 2850 (b,) 2859 (ag)
exptle (7 = 9 1)
assignment torsion
freq
S-S str HSS bend asym HSS bend sym HS str sym HS str asym
assignment torsion
s-s str HSS bend sym HSS bend asym HS str HS str
417 (a) 510 (a) 882 (a) 886 (b)
2577 2577
str = stretch, sym = symmetric combination, asym = asymmetric combination. bAssigned in C, point group. Assigned in Czh point group. e Reference 20 except for torsion from ref 21.
Assigned in C, point
group.
[6s4pld/2slp]. The double { exponents and contraction coefficients are from Dunning and Hay.16 The exponents for the polarization functions are a = 0.60 on S and a = 1.0 on H.
Results and Discussion Geometries. The geometric parameters were optimzed at the ' 0 S C F level for the optimum skew structure and the cis (7 = ) and trans (7 = 180') structures (Table I). The optimal S C F values are in excellent agreement with experiment (within 0.01 8, and lo) except for the calculated value of 8 which is 7' larger than the experimental value. This large value for 8 is in agreement with the work of Hinchcliffe.I2 The S C F values for the bond distances are slightly larger than the experimental values. This is in contrast to the case usually observed for first row compounds where the optimized bond distances at the S C F level tend to be shorter than experiment." In order to demonstrate that the difference in the value of 0 between theory and experiment was not due to correlation corrections, we optimized 0, r(SS),and r ( S H ) at the SCF-CI level. The value for 0 did not change at the CI level. This result is consistent with a wide range of ab initio calculations where it has been demonstrated that bond angles are well-determined with polarized double {basis sets at the S C F level.'' We thus suggest that the microwave data for H2S2be reevaluated in order to examine the discrepancy between theory and experiment. We do note that since the experimental measurements give only three rotational constants for the four geometric parameters, one parameter is generally chosen to begin the fitting process. For H2S2, the chosen parameter was 8 taken from the electron diffraction work.8 Our suggestion that 8(HSS) is too small is consistent with the results found for H 2 0 2 . Cremer calculated5 B(HO0) to be -4' larger than experiment and subsequently reanalyzed the microwave data.18 He and Christenla concluded that 6'(HOO) = 99.4' instead of the previously determined experimental value of 94.8' if a value for(0H) of 0.965-0.967 A is employed instead of the canonical 0.950 A. The geometries of the cis and trans structures show some significant differences from the optimum skew structure. The value for r(S-S) is 0.04-0.05 8, longer in the cis and trans structures. The value for 6' shows a significant dependence on the value of 7,being 1' smaller for the cis structure and 4' smaller for the trans structure. The value for r ( S H ) is essentially independent of 7. The change in r(SS) with variation of 7 is typical of what is observed in homocyclic sulfur molecules where SS bonds in a cis orientation are significantly longer than those in a skew orientation.19 Vibrational Spectra. The harmonic force field for the three structures was determined at the S C F level and the frequenices are given in Table 11. The calculated harmonic frequencies for the skew structure are 10% larger than the experimental values20.21due to correlation corrections to the harmonic values and our neglect of anharmonic effects. We see excellent agreement
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(16) Dunning, T. J., Jr.; Hay, P. J. In "Methods of Electronic Structure Theory", Schaefer, H. F., 111, Ed.; Plenum Press: New York, 1977; p I . (17) Pople, J. A. In "Applications of Electronic Structure Theory", Schaefer, H. F., Ed.; Plenum Press: New York, 1977; p 1. (18) Cremer, D.; Christen, D. J . Mol. Spectrosc. 1979, 74, 480. (19) Steudel, R. Top. Curr. Chem. 1982, 102, 149. (20) Wilson, M. K.; Badger, R. M. J. Chem. Phys. 1949, 17, 1232. (21) Redington, R. L. J . Mol Spectrosc. 1962, 9, 469.
TABLE III: Rotation Barriers and ZPE's for H&"
calculation SCFb SCF/ZPEC CI-SD" CI-SD/ZPEC
Rotation Barriers trans 5.78 5.13 5.67
5.02
Zero-Point Energies structure opt (T = 90') CIS (1 =
00)
trans (T = 1 8 0 O ) exptl (T = 91')
cis
8.28 7.61 8.21 7.54
ZPE 12.45 11.71 11.73 11.27
"Energies in kcal/mol. bAt SCF optimum geometry. E(SCF, opt) = -796.17491 1 au. 'Calculated with scaled ZPE. dAt SCF optimum geometry, E(C1-SD, opt) = -796.444 578 au. for the ordering in comparison with experiment and we note that experiment and theory are in good agreement on predicting the asymmetric HSS bend combination to be slightly higher than the symmetric combination. The calculations predict the symmetric and asymmetric HS stretching bands to be essentially identical. We thus agree with the suggestion of Wilson and Badger20 that the infrared band at 2577 cm-' is due to the presence of the two transitions. The band at 2513 cm-' in the Raman spectrum of the liquid is also due to the SH stretches but is shifted to lower frequency because of the change in phase. The force fields for the cis and trans structures have one imaginary frequency and demonstrate that these structures are true transition states. The imaginary frequency for the cis structure is larger than that for the trans structure, consistent with the higher barrier to cis rotation (see below). The S-S stretch decreases for the cis and trans structures, consistent with the increase in the S-S bond length. The symmetric and asymmetric HSS bends split apart in the cis structure with the symmetric combination falling below the asymmetric combination. A larger split is found for the trans structure and the order is reversed with the asymmetric bend being much lower than the symmetric bend. The two HS stretching frequencies are also split for the cis and trans structures, but to a much smaller extent. For the cis structure, the asymmetric combination is below the symmetric combination while the order is reversed for the trans structure. The splitting of the bends and stretches shows that there is some coupling of the individual stretches and bends at the cis and trans structures in comparison with the near zero coupling found in the optimum structure where the S-H bonds are essentially orthogonal. Barriers to Rotation. The barriers to internal rotation are given in Table I11 at the S C F and CI-SD levels. As noted above, the cis and trans structures are true transition states and thus the energies for the cis and trans structures can be used to determine the barrier heights. The S C F barrier heights are similar to those of Rauklo and Veillard and Demuynck." Our cis barrier is lower than the other calculated values presumably because of our use of optimum geometries. The trans barrier is in good agreement with the Veillard and Demuynckll value but Rauk's valuelo is somewhat low. This difference is probably due to differences in geometries. As expected, the inclusion of correlation effects does
J . Phys. Chem. 1985, 89, 5336-5343
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not change the barrier heights.22 We have determined the barrier heights at the CI-SD level with the optimum S C F .geometries for consistency. This should not introduce more than 0.1-0.2 kcal/mol of error in the barrier heights. In order to compare with an experimental value, zero-point corrections to the barrier height must be included since the cis and trans structures have one less active mode than the skew structure. The zero-point energies (ZPE) are given in Table 111. To a good approximation, the difference in zero-point energies is due to the loss of the torsional mode. Subtraction of this mode from the ZPE for the optimum structure gives 11.8 1 kcal/mol, in good agreement with the ZPE's for the cis and trans structures. In order to account for the effects of correlation and anharmonicity on the ZPE, we have scaled the difference in ZPE's by the ratio ZPE,,,,I/ZPE,Id for the skew structure which is 0.900. The final barriers including the scaled barrier heights are 5.02 and 7.54 kcal/mol for trans and cis, respectively. We suggest that a good estimate for the trans barrier is 5.0 & 0.15 kcal/mol and for the cis barrier it is 7.5 f 0.15 kcal/mol. Redington2' analyzed the torsional band in the far-infrared (22) The effeot of higher-order excitations can be included with the use of Davidson's formula for unlinked clusters (Langhoff, S. R.; Davidson, E. R. Int. J . Quantum Chem. 1974,8, 61). These effects are again small, -0.1 kcal/mol, lowering the trans barrier to 5.55 kcal/mol and the cis barrier to 8.08 kcal/mol (E(C1-SDQ, S C F opt) = -796.472 548 kcal/mol). Since the formula is only approximate, we are probably overestimating the effect of higher-order excitations since the size of the correction is the same as the CI-SD correction.
spectrum. Using a model potential, he estimated a barrier of 6.9 kcal/mol. This barrier could be considered as the average of the cis and trans barrier. Our average value is 6.25 kcal/mol which is slightly lower. This agreement is quite good considering the approximate form of the potential used in interpreting the experimental results and the fact that the experimental result is extrapolated from the low-lying modes. We have examined the dependence of the dipole moment, p, and the ionization potential, IP, on T . For the optimum structure, the value of p is 1.44 D at the CI-SD level (p(SCF) = 1.51 D). The S-H bonds are aligned at T = 0' giving p(C1-SD) = 2.02 D (p(SCF) = 2.12 D) while at T = 180°, there is no dipole moment since the S-H bonds are aligned in opposite directions. The ionization potential from Koopmanns' theorem is predicted to be 10.43 eV at the optimum value of T with the NHOMO (next highest occupied molecular orbital) slightly more stable at 10.52 eV. At T = O', these orbitals split apart with the IP decreasing to 9.17 eV and the N H O M O stabilized at 12.44 eV. A similar splitting is found at T = 180' with the IP = 9.13 eV and the NHOMO at 12.32 eV. In conclusion, we have determined the structure for H2S2and found it to be in good agreement except for the value for B(HSS). We suggest that the experimental value is too small. We have also determined the cis and trans rotation barriers and have shown that the correction for zero-point energy effects is not negligible. The barriers to internal notation are of a reasonable enough size that splitting of the higher vibrational levels of the torsional band could be observed experimentally.
FEATURE ARTICLE The F -t H, Potential Energy Surface: The Ecstasy and the Agony Henry F. Schaefer I11 Department of Chemistry and Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 (Received: June 13, 1985)
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This account surveys 14 years of more or less continuing theoretical research on the FH2potential energy hypersurface. Early encouragement concerning the ability of theory to reliably characterize the entrance barrier for F + H2 FH + H has more recently been sobered by the realization that very high levels of theory are required for this task. The importance of zero-point vibrational corrections and tunneling corrections in reliable predictions of the same activation energy is discussed. In contrast, the barrier height of H + FH HF + H three-center exchange stands as a prominent early success of ab initio molecular electronic structure theory
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Introduction It is possible to make a strong case that the elementary molecular process F + H2 ---* F H + H (1) is now the best understood of all chemical reactions.',* It may be stated with confidence that the only serious competitor is the simpler reaction3 H H,+H2 + H (2)
+
(1) D. E. Neumark, A. M. Wcdtke, G. N. Robinson, C. C. Hayden, and Y . T. Lee, Phys. Reu. Left.,53,226 (1984); J. Chem. Phys., 82,3045 (1985). (2) D. M. Neumark, A. M. Wcdtke, G. N. Robinson, C. C. Hayden, K. Shobatake, R. K. Sparks, T. P. Schafer, and Y . T. Lee, J . Chem. Phys., 82, 3067 (1985).
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The F + H2 reaction (1) has been studied many times over the past 15 years by using the traditional methods of by (3) See, for example, D. P. Gerrity and J. J. Valentini, J . Chem. Phys., 82, 1323 (1985). (4) K. Homann, W. C. Soloman, J. Warnatz, H. G. Wagner, and C. Zetzsch, Ber. Bunsenges. Phys. Chem., 74, 585 (1970). ( 5 ) A. F. Dodonov, G . K. Lavrovskaya, I. I. Morozov, and V. L. Tal'roze, Dokl. A k a d . Nauk SSSR, 198, 622 (1971) (p 440 in English edition). (6) R. Foon and G. R. Reid, Trans. Faraday SOC.,67, 3573 (1971). (7) R. L. Williams and F. S. Rowland, J . Phys. Chem., 75,2709 (1971); 77, 301 (1973). (8) K. H. Homann and D. I. MacLean, Ber. Bunsenges. Phys. Chem., 75, 945 (1971). (9) R. Foon, G. P. Reid, and K. B. Tait, Trans. Faraday SOC.,68, 113 1 (1972). (10) K. L. Kompa and J. Wanner, Chem. Phys. Lett., 12, 560 (1972).
0 1985 American Chemical Society
