Jean Demaison*^{a},
Natalja Vogt^{ab},
Rizalina Tama Saragi^{c},
Marcos Juanes^{c},
Heinz Dieter Rudolph^{a} and
Alberto Lesarri*^{c}
^{a}Section of Chemical Information Systems, University of Ulm, 89069 Ulm, Germany. E-mail: jean.demaison@gmail.com
^{b}Department of Chemistry, Lomonosov Moscow State University, 119992 Moscow, Russia
^{c}Departamento de Química Física y Química Inorgánica – IU CINQUIMA, Facultad de Ciencias, Universidad de Valladolid, 47011 Valladolid, Spain. E-mail: lesarri@qf.uva.es; Web: http://www.uva.es/lesarri
First published on 3rd June 2019
The symmetrically substituted diallyl disulfide adopts a non-symmetric conformation in the gas-phase, as observed with supersonic-jet rotational spectroscopy. The determination of the equilibrium structure with a predicate mixed regression illustrates both the benefits of the mass-dependent method for moderately large molecules and the structural peculiarities of the disulfide bridge.
DADS contains the disulfide bridge, a weaker (40–70% dissociation energies of a C–C or C–H bond) but important linker in the folding and stability of biological and industrial molecules such as proteins and vulcanized rubber.^{2} The disulfide bridge forms links between different parts of a molecule, stabilizing folded topologies^{3} on which biomolecules such as insulin or immunoglobulin rely on.
The disulfide bond is also considerably longer (ca. 2.05 Å) than a C–C bond and subject to a relatively low torsional barrier around the S–S axis. The torsional geometry of the disulfide affects its stability and reactivity, with most disulfides showing preference for dihedral angles close to 90°. In order to obtain specific structure–function relationships, an accurate description of reference equilibrium geometries is needed, locating the molecule in the minimum of its potential energy surface. However, equilibrium structures are not directly accessible to experiments, so their determination is far more complicated than resolving (vibrationally-averaged) ground-state structures. We attack this structural investigation with an integrated experiment–theory approach, using high-resolution rotational spectroscopy and high-level quantum chemical (QC) ab initio and density-functional theory (DFT) calculations. This work is part of a systematic study which has also examined diphenyl and dicyclohexyl homodisulfides,^{4} complementing the few equilibrium structures for this class of compounds.
We advocate a methodology based on independent semiexperimental (SE) structures.^{5,6} For this investigation we combine experimental data of the ground-state rotational constants of the parent species and all heavy-atom isotopologues, obtained by broadband (chirped-pulse) high-resolution microwave spectroscopy,^{7} and supporting QC calculations. In the SE method, equilibrium rotational constants are derived from experimental ground-state rotational constants and rovibrational corrections deduced from a QC anharmonic force field.^{6} However, we anticipated that, in the present case, low-frequency vibrations are present so predictions based on a cubic force field might be unreliable. For this reason, we decided to use the mass-dependent method^{8} combined with the method of predicate observations (or mixed regression),^{9,10} as previously investigated for diphenyldisulfide^{4} and ethynylcyclohexane.^{11} In order to use the mixed regression method, auxiliary information data points called predicates are added with appropriate weights to the data matrix during the least-squares fitting. Estimates of the predicates, bond lengths and bond angles are obtained from QC calculations at an accessible level of theory, and corrected, if necessary, by comparisons between QC predictions at this level and known equilibrium structures for various types of bonds. The second objective of this paper is thus to check the accuracy of this mass-dependent method by comparing its results with those of high-level ab initio calculations. With this information, we will finally be able to examine comparable equilibrium data for the aliphatic C–C and C–H bonds, drawing conclusions on the similitudes and differences between DADS and other persulfides. No previous gas-phase spectroscopic investigations of DADS were available. Specific details of the experimental and computational methods are given in the ESI.†
The prediction of the rotational spectrum started with a conformational search using a fast and computationally effective DFT method (B3LYP-D3(BJ)/6-311++G(d,p)). The goal was to determine the number of low-lying conformers, rotational constants and electric dipole moments. Six stable conformations were predicted within 4 kJ mol^{−1} in Table S1 (ESI†), with the two most stable structures predicted, either asymmetric (isomer 1) or C_{2}-symmetric (isomer 2, see 3D models in Fig. S1 and S2, ESI†). Finally, only one conformer was observed in the (2–8 GHz) microwave spectrum of Fig. 1. Moreover, the extreme (kHz) frequency resolution of our experiment allowed recording the independent spectra of all monosubstituted ^{34}S and ^{13}C isotopic species in natural abundance, as exemplified in Fig. 1 and Fig. S3 (ESI†). Noticeably, different transitions were observed for the two sulfur atoms and for each of the carbon positions, unequivocally confirming the non-symmetric (C_{1}) conformation of this homodisulfide. This fact contrasts with the C_{2} symmetric conformation observed for diphenyl disulfide,^{4} where the paired sulphur and carbon atoms are rendered equivalent, producing degenerate transitions. The observed transitions in Tables S2–S10 (ESI†) were analysed with a semirigid-rotor model with Watson's S-reduced Hamiltonian.^{12} The experimental rotational constants and quartic centrifugal distortion parameters are collected in Table 1 and Table S11 (ESI†) (isotopologues). Comparison with the predictions confirmed that the observed conformation corresponds to the global minimum of Fig. 2 and Fig. S1 (ESI†).
Fig. 1 A typical rotational transition of DADS showing the isotopic satellites corresponding to all ^{13}C and ^{34}S isotopologues in natural abundance. |
Experiment | Theory^{d} | ||
---|---|---|---|
Isomer 1 (C_{1}) | Isomer 2 (C_{2}) | ||
a Rotational constants (A, B, C), Watson's S-reduction centrifugal distortion constants (D_{J}, D_{JK}, D_{K}, d_{1}, d_{2}) and electric dipole moments (μ_{α}, α = a, b, c).b Number of transitions (N) and rms deviation (σ) of the fit.c Standard errors in units of the last digit.d B3LYP-D3(BJ)/6-311++G(d,p) (harmonic vibrational frequencies). | |||
A/MHz^{a} | 1784.34618(81)^{c} | 1749.4 | 2486.5 |
B/MHz | 981.02970(50) | 972.8 | 785.8 |
C/MHz | 879.83311(48) | 877.2 | 726.0 |
D_{J}/kHz | 0.6173(69) | 0.57 | 0.45 |
D_{JK}/kHz | −1.9591(55) | −1.78 | −4.44 |
D_{K}/kHz | 4.050(19) | 3.56 | 16.3 |
d_{1}/kHz | −0.13453(89) | −0.12 | 0.02 |
d_{2}/kHz | −0.00959(31) | −0.01 | 0.00 |
|μ_{a}|/D | 0.6 | 0.0 | |
|μ_{b}|/D | 1.8 | 0.0 | |
|μ_{c}|/D | 0.0 | 1.8 | |
N^{b} | 109 | ||
σ/kHz | 11.5 |
A Born–Oppenheimer (BO) ab initio structure was then calculated for the observed conformation, as detailed in the ESI.† For this purpose, the structure of DADS was calculated using the coupled-cluster method CCSD(T) with a V(T+d)Z basis set of triple-ζ quality, in the frozen core (FC) approximation. The small structural effects of further triple-quadruple basis set improvement (V(T+d)Z → V(Q+d)Z) were estimated with the Møller–Plesset MP2(FC) method. The largest differences were found for the SS bond, which decreases by 0.009 Å when going from V(T+d)Z to V(Q+d)Z. A decrease of 0.004 Å is also observed for the CS bond lengths. The convergence might not be fully achieved for these bond lengths. On the other hand, the convergence seems to be achieved for the valence angles, with the largest difference being a decrease of 0.29° for the dihedral angle τ(C2C1SS′). Finally, for the treatment of the inner-shell correlation effects, the wCVTZ basis set was used together with the MP2 method. This choice might seem disputable because the wCVTZ basis set is too small to recover all the electronic correlation,^{13} but, on the other hand, the MP2 method overestimates this correction.^{14} In consequence, the errors might compensate each other. To check this assumption, we calculated the core correlation of the smaller molecule dimethyldisulfide, CH_{3}SSCH_{3}, at both the CCSD(T)/wCVQZ and MP2/wCVTZ levels of theory. This is nicely confirmed by the results given in Table S12 (ESI†). Likewise, the core correlations computed at the MP2/wCVTZ level of theory for the C–C and CC bond lengths are −0.0032 Å and −0.0028 Å, respectively. This is in perfect agreement with the results found at the CCSD(T)/wCVQZ level for ethylene^{14} and ethane.^{15} The final BO structure is given in Table 2, with full details of the calculations in Tables S13 and S14 (ESI†). The equilibrium BO structure of DADS is expected to be very accurate, although the computed S–S bond length is probably slightly too large. This uncertainty will be confirmed below.
r^{BO}_{e}^{}^{a} | r^{(1)}_{m}^{}^{b} | |
---|---|---|
a Born–Oppeheimer computational structure, r^{BO}_{e} = CCSD(T)_FC/V(T+d)Z + MP2/[V(Q+d)Z(FC) – V(T+d)Z(FC) + wCVTZ(AE) – wCVTZ(FC)].b Mass-dependent structure. | ||
C2C3/Å | 1.3341 | 1.3337(15) |
C2C1/Å | 1.4891 | 1.4870(14) |
C1S/Å | 1.8298 | 1.8325(10) |
SS′/Å | 2.0328 | 2.0282(13) |
S′C1′/Å | 1.8322 | 1.8332(15) |
C1′C2′/Å | 1.4883 | 1.4851(16) |
C3′C2′/Å | 1.3336 | 1.3314(12) |
C3C2C1/deg | 123.3974 | 123.50(16) |
C2C1S/deg | 113.0249 | 112.92(10) |
C1SS′/deg | 102.5641 | 102.284(92) |
SS′C1′/deg | 103.4401 | 103.910(35) |
S′C1′C2′/deg | 112.2558 | 112.24(15) |
C1′C2′C3′/deg | 123.2486 | 123.268(51) |
SC1C2C3/deg | −113.2476 | −114.43(14) |
S'SC1C2/deg | 67.7303 | 68.93(27) |
C1SS′C1′/deg | −92.9469 | −93.63(14) |
SS′C1′C2′/deg | −64.41 | −63.44(16) |
S′C1′C2′C3′/deg | 113.0231 | 115.05(24) |
DADS behaves as a floppy molecule, experiencing large-amplitude vibrations. Indeed, it has four fundamental vibrations below 100 cm^{−1}, and the difference between the computed harmonic and anharmonic frequencies is too large to be reasonably estimated. At the MP2/V(T+d)Z level, the harmonic frequencies (in cm^{−1}) are 39.5, 71.9, 89.5 and 98.3. The consequence is that the anharmonic force field is probably not reliable and cannot be used to calculate the small variations of the rovibrational corrections upon isotopic substitution. For this reason, a near-equilibrium structure was calculated using the mass-dependent or r_{m} method, where the moments of inertia along the principal inertial axes (g = a, b, c) are approximated as
(1) |
The weak point of the mass-dependent method is that it requires the determination of three to six additional parameters, which may be considerably difficult to fit. For this reason, the r_{m} method was rarely successful for a moderately large molecule, restricting the determination of equilibrium structures to small molecular sizes. However, it was shown in the cases of diphenyldisulfide,^{4} ethynylcyclohexane,^{11} and other moderately large molecules such as fructose^{17} that the predicate or mixed estimation method gives a structure whose quality is comparable to that of the traditional semiexperimental method. For this purpose, predicate observations are required, as already discussed in previous papers for common bonds.^{11,18}
The specifics of the calculations of predicates, which used MP2 and the cc-pVTZ and cc-pV(T+d)Z basis sets, are provided in the ESI† and collected in Table S13 (ESI†). Predicates were given appropriate uncertainties, i.e., 0.0015 Å for the CH bond lengths, 0.0020 Å for the other bonds, 0.3° for the bond angles, and 0.7° for most dihedral angles (the weight of some dihedral angles involving the sulfur atom was lowered, with their uncertainty being increased up to 2°). Then, different fits were made using the r_{0}, r^{(1)}_{m} and r^{(2)}_{m} approximations. When going from r_{0} to r^{(1)}_{m}, the standard deviation of the fit decreased by almost a factor of 2, which is an indication of the stability of the fits. However, for the r^{(2)}_{m} fit, the three d_{g} parameters (g = a, b, c) are not determined. For this reason, the best determinable structure is the r^{(1)}_{m} one. The final r^{(1)}_{m}-structure is given in Table 2 and Table S13 (ESI†). The comparison with the computed r^{BO}_{e} parameters (in the same tables) gives a median absolute deviation (MAD) of 0.0004 Å for the bond lengths, with the largest deviation being 0.0045 Å for the S–S bond. However, as noted previously, the r^{BO}_{e} value of this bond is probably slightly too long. For the bond angles, the MAD is only 0.04°, with the mean absolute error being 0.10°. This result is a significant improvement compared to the predicate values. The comparison of the dihedral angles is quite interesting. For the angles involving heavy atoms, the improvement is significant. For instance, for the angle τ(SC1C2C3) the difference between r^{BO}_{e} and r^{(1)}_{m} is 1.1°, whereas it is more than twice larger between r^{BO}_{e} and MP2/V(T+d)Z. A similar result is obtained for the angle τ(S′SC1C2). The comparison for the dihedral angles specifying the positions of the hydrogen atoms is less meaningful because they are mostly determined by the predicate values.
In conclusion, DADS adopts a characteristic non-symmetric C_{1} conformation in the gas phase for which we determined the equilibrium structure using two independent methods: high-level ab initio optimizations and mass-dependent fits to the experimental rotational data. The agreement between the results is very satisfactory, confirming that the mass-dependent method can give reliable results, provided it is used with the help of the mixed estimation method in order to avoid ill-conditioning problems. This procedure opens the field for the determination of equilibrium structures in other sulphides and larger molecules. The validity of this approach is emphasized by comparison in Table S15 (ESI†) with the common Kraitchman substitution structure (r_{s}), showing considerable deviations (up to 0.014 Å and 1.3°), which confirm the limitations of this purely empirical method.^{4,11,19}
DADS raises two chemical questions concerning the higher stability of the non-symmetric isomer and the specific structural features of the disulfide link. Among the homodisulfides already studied, DADS is the only one whose most stable conformer does not possess C_{2} symmetry. However, the structures of the two allyl groups are extremely close and they are also quite close from the structure of propene.^{20} As an example, the difference between r(SC1) and r(S′C1′) is only 0.002 Å (i.e., the order of magnitude of the accuracy), while the C–S bond length (1.833 Å) is significantly longer than those in dimethyl disulfide (1.808 Å) and diphenyl disulfide (1.776 Å). Intramolecular stabilization forces can be invoked to justify the lack of symmetry. However, stereoelectronic hyperconjugative effects are to be excluded, since natural-bond-orbital^{21} calculations in Tables S16 and S17 (ESI†) did not reveal significant differences between the two most stable isomers. Alternatively, it can be argued that a weak non-covalent C–H···π intramolecular hydrogen bond in the asymmetric isomer (B3LYP-D3(BJ): r_{H···π} = 2.81 Å) would benefit the C_{1} compact structure against the stretched geometry of the C_{2}-symmetric conformation, justifying the observations.
A precise assessment of the conformational energy of the C_{2} isomer was obtained with the CBS-QB3 method of Petersson et al.,^{22} giving a Gibbs energy of 1.4 kJ mol^{−1}. Since this small energy would allow the observation of the second conformation under equilibrium conditions, the presence of a single isomer confirms the conformational relaxation^{23} of isomer 2 to the global minimum in the jet expansion.
Relevant structural features of the persulfides are also noticeable, though still the number of comparable molecules with high precision data is scarce. The S–S bond length in DADS (2.028 Å) is intermediate and relatively similar to the values found for dimethyl disulfide (2.033 Å) and diphenyl disulfide (2.020 Å). However, we previously noticed a considerable dispersion of the persulfide dihedral angles τ(C–S–S–C), ranging from 77.7°(21) in (CF_{3}COS)_{2} to 104.4°(40) in (CF_{3}S)_{2} (Table 7 in ref. 4). For DADS the torsional angle of 93.6° is 6–8° larger than those in both dimethyl disulfide (84.8°) and diphenyl disulfide (87.2°). This fact points to a considerable flexibility in the disulfide link, which, added to the long bond length, justifies the particular role played by the persulfide bond as an adaptive linker in intramolecular chemical unions.
The relevance of computationally effective methods for accurate equilibrium structure determination and the synergy of rotational data and ab initio calculations should be emphasized. Other persulfides are under study for a better understanding of this chemically important bond.
Footnote |
† Electronic supplementary information (ESI) available: Experimental methods, ab initio calculations and rotational transitions. See DOI: 10.1039/c9cp02508a |
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