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On the thermal stability of the branched hexasulfane isomers. A DFT molecular dynamics study of H2S6 conformers
Chemical Physics Letters 607 (2014) 64–69
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
On the thermal stability of the branched hexasulfane isomers. A DFT molecular dynamics study of H2S6 conformers A. Ramírez-Solís ⇑,1, L. Maron Laboratoire de Physicochimie de Nano-objets, INSA-Université de Toulouse, 135, Av. de Rangueil, Toulouse F-31065, France
a r t i c l e
i n f o
Article history: Received 9 April 2014 In final form 7 May 2014 Available online 27 May 2014
a b s t r a c t Using Born–Oppenheimer DFT molecular dynamics we address the stability and non-harmonic vibrational effects of the three isomers of hexasulfane at 300 K and 700 K. Both branched structures are stable and dynamic effects introduce large changes to the SAS distances due to the oscillating behavior between ASAS@SASA and ASASAS@SA structures. The largest non-harmonic effects (40%) are found for isomer B in the low frequency region corresponding to the torsional mode coupling the two HS3–S3H moieties. The simultaneous detection of the peaks shifts in the 250 and 800 cm 1 regions could be used to unequivocally characterize these branched hexasulfane isomers in sulfur melts. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Sulfur is known for having many allotropic forms. From the molecular point of view, sulfur chains and rings have been found to be the dominant structures. The latter have been known to exist since the early 1930s when the crown structure of cyclo S8 was found by X-ray crystallography [1] and determined to have D4d point group symmetry. Forty years later Meyer [2] made the general observation that elemental sulfur exists mainly as sulfur rings, Sn. The stability of these sulfur rings is attested by the fact that the most important commercial source of sulfur is elemental sulfur. Although S8 rings dominate in natural elemental sulfur, more than a dozen additional sulfur rings have been synthesized [3–5]. Already more than century ago Engel [6] prepared a stable rhombohedral form, called e-sulfur, which was much later established to be composed of cyclo-S6 rings [4]. Note that S8 and S6 possess structures which make all sulfur atoms equivalent. While S7 is also a known ring having four distinct distances ranging from 1.98 to 2.18 A with Cs point symmetry [7], S9, S11 and S13 have been synthesized and (from spectroscopic studies) appear to be cyclic [3,8] but no crystal structures have been reported so far. Cyclic S10 has SAS distances ranging from 2.03 to 2.08 Å [9] with D2 point symmetry. On the other hand, the isomerization of cyclic to chain radical structures in sulfur melts have been studied by various techniques like ESR [10] and magnetic measurements [11] at high ⇑ Corresponding author. E-mail address: [email protected] (A. Ramírez-Solís). On sabbatical leave from Facultad de Ciencias, Universidad Autónoma del Estado de Morelos. 1
http://dx.doi.org/10.1016/j.cplett.2014.05.028 0009-2614/Ó 2014 Elsevier B.V. All rights reserved.
temperatures. In this direction, using the G3X(MP2) approach Wong et al. [12] studied the stability of possible octasulfur isomers other than cyclo-S8 which are lower in energy than the chain diradical. In that study they also proposed the existence of hexasulfane (H2S6) as model chain species in high-temperature sulfur melts. That study led to the discovery that two branched H2S6 stable isomers exist (A and B shown in Figure 1) whose Gibbs free energy differences are only 12.1 and 13.4 kcal/mol with respect to the unbranched helical hexasulfane at 298 K. A natural question that arises at this point is whether these branched isomers are stable when finite temperature effects are considered. Here we report Born–Oppenheimer DFT molecular dynamics studies of the three isomers of hexasulfane in order to study their stability at high temperature. In particular, given the unusual coordination pattern we address the non-harmonic vibrational effects of the branched isomers at high temperature. The goal of this study is twofold. First, we wish to explore the possibility of interconversion between these three low-lying structures and, secondly, we aim to provide an answer to the question as to whether it is possible to distinguish these isomers using spectroscopic information. If they exist, large enough differences in the vibrational spectra at high temperature could help experimentalists in the search of these branched hexasulfane isomers. 2. Method and computational details We start from the detailed information of Ref. [12] where the optimized structures of the branched hexasulfane isomers are given at the B3LYP/6-311G(2df,p) level. These isomers were found by these authors to lie in energy slightly above the helical isomer.
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A. Ramírez-Solís, L. Maron / Chemical Physics Letters 607 (2014) 64–69
(a)
Table 2 Harmonic vibrational frequencies (cm 311G(d,p) level.
(c)
(b)
Figure 1. Geometries of the three hexasulfane isomers: (a) helical, (b) isomer A, (c) isomer B.
Since the calibration of the method has already been done in [12] for this type of molecules, we shall use the same type of basis sets and electronic structure approach. In order to obtain the nonharmonic vibrational contributions it is necessary to refer to the harmonic spectra of each species, therefore we have calculated them for the three hexasulfane isomers (see next section). The thermal stability of the optimized structures was verified using Born–Oppenheimer (BO) molecular dynamics at the DFT level. The BO-DFT molecular dynamics simulations were carried out with the Geraldyn2.1 code [13], which has been coupled to the electronic structure modules of GAUSSIAN09 [14]. The BODFT-MD algorithm in Geraldyn uses the velocity-Verlet integration scheme [15]. The BO-MD simulations were done with a time step of 0.5 fs. A chain of four Nosé–Hoover thermostats [16,17] was used to control the temperature at 300 K and 700 K. Electronic structure and energy gradient calculations were performed at the B3LYP level of theory with the 6-311G(d,p) basis sets, since these yield a good compromise between accuracy and computational efficiency (see below for a comparison with previous results using the 6-311G(2df,p) basis sets). The simulations started from the optimized equilibrium structure of each isomer without any preferred velocity vector other than the thermal energy. The MD simulations for the three isomers (all singlet electronic states) took 76 days on 32 processors running the Linux versions of Geraldyn2.1-G09. The production run was started following an initial thermalization period which was achieved after 3 ps, so that data were extracted from the last 10 ps of each simulation. In order to obtain the vibrational spectra, the Fourier-transform of the velocity autocorrelation functions (FT-VACF) were built from
1
) of the hexasulfane isomers at the B3LYP/6-
Helical
A
B
33, 41, 75, 107, 193, 227, 253, 322, 340, 364, 412, 427, 450, 453, 859, 860, 2637,2638
26, 44, 99, 112, 120, 208, 231, 257, 294, 387, 414, 514, 519, 619, 894, 899, 2611, 2612,
50, 55, 89, 104, 184, 207, 215, 226, 237, 276, 389, 409, 546, 594, 793, 802, 2655, 2656,
the trajectories. We recall that the vibrational spectrum obtained from the velocity autocorrelation functions does not require the knowledge of the dipole moment, therefore, the calculated vibrational amplitudes yield an accurate description of the relative infrared intensities as well as of the Raman intensities. This FT-VACF approach to obtain dynamic vibrational spectra has been successfully used on many other small molecules (see for instance, [18–20]). 3. Results and discussion 3.1. Static geometries and vibrational frequencies In agreement with the G3X(MP2) results of Ref. [12], using Gibbs free energy differences at the B3LYP/6-311G(d,p) level we find that the helical conformer is the most stable structure and that isomers A and B lie 17.7 and 19.5 kcal/mol above this structure, respectively. The optimized geometries and the corresponding vibrational frequencies for the three isomers are given in Tables 1 and 2, respectively. The optimized geometries of the branched isomers A and B are in good agreement with those reported at the B3LYP level using the larger 6-31G(2df) basis sets [12]. As pointed out in Ref. [12], isomer B exhibits a non-conventional bonding pattern between two HS3 units, where two S atoms (labeled 2 and 3 in Figure 1) appear hypercoordinated. We find here that the largest deviation (ca. 0.17 Å) from the previously optimized geometry corresponds precisely to the 2–3 SAS bond of this isomer. As shown in Table 2, all the vibrational frequencies of the three isomers are real, in agreement with the previous results. 3.2. Born–Oppenheimer molecular dynamics Since we are interested in the thermal stability of the hexasulfane isomers, we used the optimized geometries of all isomers as starting points for BO-MD simulations at room temperature (300 K) and at 700 K. We found that all isomers are stable at both
Table 1 Geometrical parameters of the hexasulfane isomers at the B3LYP/6-311G(d,p) level. Distances in Å, angles in degrees. Atom numbering as given in Figure 1. Previous values in parentheses from Ref. [12] at the B3LYP/6-311G(2df,p) level. Isomer
SAS distances
Helical
1-2: 2.106 3-4: 2.112 2-6: 2.106
A
1-2, 2-4: 2.401 (2.327) 1-3, 4-5: 2.035 (2.015) 2-6: 1.938 (1.926) 2-3: 2.591 (2.435) 2-1: 1.953 (1.934) 3-4: 1.982 (1.986) 1-7: 2.160 (2.110) 3-5: 2.194 (2.162)
B
2-3: 2.108 4-5: 2.108
SASAS angles
SASASAS dihedrals
1-2-3:108.3 2-3-4:108.6 3-4-5:108.6 4-5-6:108.3 2-1-3, 2-4-5: 101.9 1-2-6, 4-2-6: 105.9 1-2-4: 102.4 2-1-7: 112.0 2-1-4: 110.2 4-3-5: 112.0 2-3-4:99.1 7-1-4:96.7
1-2-3-4: 82.3 2-3-4-5: 77.1 3-4-5-6: 82.3 3-1-2-6, 5-4-2-6:14.6
3-4-1-2:1.49 7-1-4-3:108.3 1-4-3-5: 96.9
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A. Ramírez-Solís, L. Maron / Chemical Physics Letters 607 (2014) 64–69
Figure 2. Temporal evolution of the SAS distances (Å) for the helical isomer.
Figure 3. Temporal evolution of the SAS distances (Å) for isomer A.
Figure 4. Temporal evolution of the SAS distances (Å) for isomer B. Note the very slow oscillation regime for the bond connecting the two S3H units in this hypercoordinated isomer.
A. Ramírez-Solís, L. Maron / Chemical Physics Letters 607 (2014) 64–69
Figure 5. Temporal evolution of the SASAS angles (degrees) for the helical isomer.
Figure 6. Temporal evolution of the SASAS angles (degrees) for isomer A.
Figure 7. Temporal evolution of the SASAS angles (degrees) for isomer B.
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A. Ramírez-Solís, L. Maron / Chemical Physics Letters 607 (2014) 64–69
Table 3 Static harmonic frequencies, dynamically derived vibrational frequencies (cm 1) and non-harmonicities (in parentheses) for the branched hexasulfane isomers at 300 and 700 K. Isomer A
Isomer B
xstat, (300 K), x(700 K),
xstat, (300 K), x(700 K),
NH(300 K,700 K) 26, 27, 33 (1, 6) 44, 40, 39 ( 4, 5) 99, 98, 93 ( 1, 6) 112, 108, 109 ( 4, 5) 120, 121, 123 (1, 3) 208, 201, 200 ( 7, 8) 231, 236, 229 (5, 3) 257, 246, 237 ( 9, 20) 294, 295, 297 (1, 3) 387, 383, 383 ( 4, 5) 414, 407, 403 ( 7, 11) 514, 508, 503 ( 6, 11) 519, 517, 523 ( 2, 4) 619, 603, 597 ( 16, 22) 894, 873, 870 ( 21, 24) 899, 887, 880 ( 12, 19) 2611, 2623, 2633 (12, 22) 2612, 2631, 2650 (19, 38)
NH(300 K,700 K) 50, 35, 30 ( 15, 20) 55, 43, 41 ( 12, 14) 89, 83, 76 ( 6, 13) 104, 106, 113 (2, 9) 184, 182, 180 ( 2, 4) 207, 199, 190 ( 8, 17) 215, 214, 209 ( 1, 6) 226, 222, 219 ( 4, 7) 237, 236, 227 ( 1, 10) 276, 275, 275 ( 1, 1) 389, 380, 378 ( 9, 11) 409, 402, 408 ( 7, 1) 546, 549, 550 (3, 4) 594, 592, 596 ( 2, 2) 793, 786, 783 ( 7, 10) 802, 800, 793 ( 2, 9) 2655, 2658, 2670 (3, 15) 2656, 2664, 2676 (8, 20)
temperatures. Figures 2–4 show the temporal evolution of the SAS distances for each isomer at 700 K; the corresponding curves at 300 K are not shown since they are qualitatively equivalent to those presented and do not provide any relevant information. Figures 2–4 show that the bonding patterns remain unaltered throughout the simulations for the three isomers. While for the helical isomer small dynamical changes of the SAS bonds (2.13 Å dynamical average) and angles have been found around its equilibrium geometry, for the branched isomers these changes are considerably larger. For isomer A there are two long, two intermediate and one short SAS distances that reflect the symmetry of the static optimized structure (Figure 1a); their dynamical averages at 700 K are d12 = 2.373 Å, d24 = 2.433 Å, d13 = 2.053 Å, d45 = 2.038 Å, d26 = 1.948 Å, which can be compared with the static values given in Table 1. For isomer B there is only one very long SAS distance, two intermediate and two short SAS distances, their dynamical averages being also larger than the static values: d23 = 2.945 Å, d17 = 2.192 Å, d35 = 2.185 Å, d12 = 1.969 Å, d34 = 1.975 Å. However, a particularly interesting result is that the dynamical average of
the weak SAS bond (2.945 Å) linking the two HS3 moities in the hypercoordinated isomer B is substantially longer (more than 0.5 Å) than the static optimized distance (2.43 Å) at 0 K, a fact associated to the rather long oscillation period (varying from 0.8 to 1.1 fs) of this bond. The temporal evolution of the SASAS angles in Figures 5–7 confirm that no qualitative structural changes occur for any of the hexasulfane isomers, all of them oscillating around their equilibrium geometries. Thus, no structural interconversion has been detected between these stable isomers during these BO-MD simulations. The dynamic non-harmonicities (NH) have been obtained using the usual definition (see, for instance, Ref. [16]). If mj stands for the number of vibrational quanta in the j-th mode, the NH are determined by the difference of the dynamically derived frequency xAIMD(m1, m2, m3, . . .., m18) minus a m-weighted linear combination of the corresponding static purely harmonic B3LYP frequencies (x1, x2, ..., x18). We report in Table 3 the NH effects for the eighteen fundamental modes, where mi = dij stands for a single vibrational quantum in mode i and none in all the other modes, so that NH(i) simply becomes xAIMD(i)–xi.) of the A and B isomers. While in absolute value the largest non-harmonic contribution is found for the most energetic SAH stretching mode of isomer A (38 cm 1), we focus on the relative dynamic changes with respect to the static frequencies in each case. In this direction, while the largest non-harmonic effects are only 7.8% for the central-unit SASASAS stretching mode (257 cm 1) of isomer A at 700 K., for isomer B they attain up to 40% in the very low frequency region (around 50 wavenumbers) corresponding to the torsional mode coupling the two HS3–S3H moieties. The main feature of this mode is that it elongates (shortens) the shortest (longest) SAS bonds of the trapezoid formed by S1AS2AS3AS4. A couple of figures showing the vectors of these low frequency highly anharmonic modes are given as Supplementary material. Figure 10 shows the dynamics-derived vibrational spectra of the three isomers at 700 K. For comparison purposes, the intensities have been normalized to unity with respect to the largest peak of each spectrum. The numerical data of these spectra at both temperatures is available upon request from the authors. The vibrational spectra at 300 K do not differ significantly from the ones shown at 700 K. Some interesting facts can be drawn from these spectra at high temperature. Using the spectrum of the
Figure 10. Vibrational spectra (cm 1) of the helical (blue), A (red) and B (green) isomers at 700 K. Intensities are normalized to unity with respect to the largest peak of each spectrum. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
A. Ramírez-Solís, L. Maron / Chemical Physics Letters 607 (2014) 64–69
helical isomer as the reference, it can be seem that the most intense peaks for the branched isomers in the low (below 400 cm 1), medium (700–950 cm 1) and high (above 2500 cm 1) are shifted from the reference helical peaks. Clearly, the largest differences are found for the most intense peaks in the low frequency region for both isomers so that the branched isomers can be identified using these peak shifts. For the A species the strongest peak is blue shifted (407 vs. 292 cm 1), while for the B isomer we find a red-shifted peak (217 vs. 292 cm 1). We also stress that, using the above mentioned spectral normalization, the relative (A:B) intensity of the strongest low-frequency peaks is 0.48:0.89. Also, quite remarkably, the spectrum of the B isomer shows 12 peaks whose intensity is at least five times larger than that of the A isomer in the 80–270 cm 1 region. Since the same type of peak shift occurs for the A (blue shift) and B (red shift) isomers with respect to the helical isomer around 700–900 cm 1, the simultaneous detection of these peaks shifts could be used to unequivocally characterize these branched hexasulfane isomers. 4. Conclusions We have performed a series of DFT Born–Oppenheimer molecular dynamics simulations for the three hexasulfane isomers at room temperature and at 700 K. We have found that all the isomers are stable even at the highest temperature and no interconversion between these low-lying isomers was observed. The dynamically derived structural parameters are in good agreement with the static optimized values and, as expected, the average SAS– distances are slightly longer than the 0 K values. The dynamical behavior of the B isomer is the most interesting one since the SAS bond connecting the two HS3 moieties shows rather large variations, going from 2.4 to 3.8 Å. These large amplitude oscillations arise due to the rather weak p⁄–p⁄ interactions of the four nearly-flat trapezoidal S atoms in the B isomer. We also found that both H atoms rotate freely around the terminal SAS bond of each HS3 moiety in the B isomer. The dynamic vibrational spectra for the three isomers have been obtained at room temperature and at 700 K. Moderate (8%) and very large non-harmonic effects (up to 40%) were found at the low frequency region for the A and B isomers at 700 K, respectively. The large NH effects are due to the weak p⁄–p⁄ interactions of the four trapezoidal S atoms in the B isomer. We conclude that, although the largest differences in the vibrational spectra of the branched isomers with respect to the helical isomer appear in the low-frequency region (below 400 cm 1), the detailed information concerning the strongest peak shifts and the relative
69
amplitudes of the largest peaks might be of help to experimentalists to achieve detection of these uncommon but rather stable hypercoordinated hexasulfane species in the gas phase. Acknowledgments The authors thank support from the ECOS-ANUIES/CONACYT Mexican–French cooperation program through project M10-P02. L.M. is grateful to the A. von Humboldt foundation. A.R.S. thanks CONACYT through the Basic Science project No. 130931, for support from the CONACYT 2013-Sabbatical Program and from the Professeur Invité program at INSA-Toulouse. This work was also supported by Programme Investissements d’Avenir under the program ANR-11-IDEX-0002-02, reference ANR-10-LABX-0037-NEXT. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cplett.2014.05. 028. References [1] B.E. Warren, J.T. Bursell, J. Chem. Phys. 3 (1935) 6. [2] B. Meyer, Sulfur, energy and environment, Elsevier, Amsterdam, 1977. [3] N.N. Greenwood, A. Earnshaw, Chemistry of the elements, Pergamon, Oxford, 1984. [4] J. Donohue, The structures of the elements, Wiley, New York, 1974. [5] M. Schmidt, New uses of sulfur, in: D.J. Bourne (Ed.), Advances in chemistry, Ser. No. 165, Vol. II, American Chemical Society, Washington DC, 1978, pp. 1– 12. [6] M.R. Engel, C. R. Acad. Sci. Paris 112 (1891) 866. [7] R. Steudel, R. Reinhardt, F. Schuster, Angew. Chem. Int. Ed. Engl. 16 (1977) 715; J. Donohue, J. Cryst. Mol. Struct. 8 (1978) 141. [8] T. Sandow, J. Steidel, R. Stuedel, Angew. Chem. Int. Ed. Engl. 21 (1982) 794. [9] R. Reinhardt, R. Steudel, F. Schuster, Angew. Chem. Int. Ed. Engl. 17 (1978) 57. [10] D.C. Koningsberger, Doctoral dissertation, Technische Hogeschool Eindhoven, Netherlands, 1971; H. Radscheit, J.A. Gardner, J. Non-Cryst. Solids 35 & 36 (1980) 1263. [11] J.A. Poulis, C.H. Massen, P.v.d. Leiden, Trans. Faraday Soc. 58 (1962) 474; J.A. Poulis, W. Derbyshire, Trans. Faraday Soc. 59 (1963) 559. [12] M.W. Wong, Y. Steudel, R. Steudel, Chem. Phys. Lett. 364 (2002) 387. [13] C. Raynaud, L. Maron, J.P. Daudey, F. Jolibois, Phys. Chem. Chem. Phys. 6 (2004) 4226. [14] Frisch, M.J. ; Trucks, G.W.; Schlegel, H.B. et al., GAUSSIAN 09, (2009) Pittsburg, USA. [15] L. Verlet, Phys. Rev. 159 (1967) 98. [16] S. Nosé, J. Chem. Phys. 81 (1981) 511. [17] W.G. Hoover, Phys. Rev. A 31 (1985) 1695. [18] L. Maron, A. Ramírez-Solís, J. Phys. Chem. A 111 (2007) 3173. [19] F. Jolibois, L. Maron, A. Ramírez-Solís, J. Mol. Struct. Theochem. 899 (2009) 9. [20] A. Ramírez-Solís, F. Jolibois, L. Maron, J. Phys. Chem. A 114 (2010) 12378.
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
On the thermal stability of the branched hexasulfane isomers. A DFT molecular dynamics study of H2S6 conformers A. Ramírez-Solís ⇑,1, L. Maron Laboratoire de Physicochimie de Nano-objets, INSA-Université de Toulouse, 135, Av. de Rangueil, Toulouse F-31065, France
a r t i c l e
i n f o
Article history: Received 9 April 2014 In final form 7 May 2014 Available online 27 May 2014
a b s t r a c t Using Born–Oppenheimer DFT molecular dynamics we address the stability and non-harmonic vibrational effects of the three isomers of hexasulfane at 300 K and 700 K. Both branched structures are stable and dynamic effects introduce large changes to the SAS distances due to the oscillating behavior between ASAS@SASA and ASASAS@SA structures. The largest non-harmonic effects (40%) are found for isomer B in the low frequency region corresponding to the torsional mode coupling the two HS3–S3H moieties. The simultaneous detection of the peaks shifts in the 250 and 800 cm 1 regions could be used to unequivocally characterize these branched hexasulfane isomers in sulfur melts. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Sulfur is known for having many allotropic forms. From the molecular point of view, sulfur chains and rings have been found to be the dominant structures. The latter have been known to exist since the early 1930s when the crown structure of cyclo S8 was found by X-ray crystallography [1] and determined to have D4d point group symmetry. Forty years later Meyer [2] made the general observation that elemental sulfur exists mainly as sulfur rings, Sn. The stability of these sulfur rings is attested by the fact that the most important commercial source of sulfur is elemental sulfur. Although S8 rings dominate in natural elemental sulfur, more than a dozen additional sulfur rings have been synthesized [3–5]. Already more than century ago Engel [6] prepared a stable rhombohedral form, called e-sulfur, which was much later established to be composed of cyclo-S6 rings [4]. Note that S8 and S6 possess structures which make all sulfur atoms equivalent. While S7 is also a known ring having four distinct distances ranging from 1.98 to 2.18 A with Cs point symmetry [7], S9, S11 and S13 have been synthesized and (from spectroscopic studies) appear to be cyclic [3,8] but no crystal structures have been reported so far. Cyclic S10 has SAS distances ranging from 2.03 to 2.08 Å [9] with D2 point symmetry. On the other hand, the isomerization of cyclic to chain radical structures in sulfur melts have been studied by various techniques like ESR [10] and magnetic measurements [11] at high ⇑ Corresponding author. E-mail address: [email protected] (A. Ramírez-Solís). On sabbatical leave from Facultad de Ciencias, Universidad Autónoma del Estado de Morelos. 1
http://dx.doi.org/10.1016/j.cplett.2014.05.028 0009-2614/Ó 2014 Elsevier B.V. All rights reserved.
temperatures. In this direction, using the G3X(MP2) approach Wong et al. [12] studied the stability of possible octasulfur isomers other than cyclo-S8 which are lower in energy than the chain diradical. In that study they also proposed the existence of hexasulfane (H2S6) as model chain species in high-temperature sulfur melts. That study led to the discovery that two branched H2S6 stable isomers exist (A and B shown in Figure 1) whose Gibbs free energy differences are only 12.1 and 13.4 kcal/mol with respect to the unbranched helical hexasulfane at 298 K. A natural question that arises at this point is whether these branched isomers are stable when finite temperature effects are considered. Here we report Born–Oppenheimer DFT molecular dynamics studies of the three isomers of hexasulfane in order to study their stability at high temperature. In particular, given the unusual coordination pattern we address the non-harmonic vibrational effects of the branched isomers at high temperature. The goal of this study is twofold. First, we wish to explore the possibility of interconversion between these three low-lying structures and, secondly, we aim to provide an answer to the question as to whether it is possible to distinguish these isomers using spectroscopic information. If they exist, large enough differences in the vibrational spectra at high temperature could help experimentalists in the search of these branched hexasulfane isomers. 2. Method and computational details We start from the detailed information of Ref. [12] where the optimized structures of the branched hexasulfane isomers are given at the B3LYP/6-311G(2df,p) level. These isomers were found by these authors to lie in energy slightly above the helical isomer.
65
A. Ramírez-Solís, L. Maron / Chemical Physics Letters 607 (2014) 64–69
(a)
Table 2 Harmonic vibrational frequencies (cm 311G(d,p) level.
(c)
(b)
Figure 1. Geometries of the three hexasulfane isomers: (a) helical, (b) isomer A, (c) isomer B.
Since the calibration of the method has already been done in [12] for this type of molecules, we shall use the same type of basis sets and electronic structure approach. In order to obtain the nonharmonic vibrational contributions it is necessary to refer to the harmonic spectra of each species, therefore we have calculated them for the three hexasulfane isomers (see next section). The thermal stability of the optimized structures was verified using Born–Oppenheimer (BO) molecular dynamics at the DFT level. The BO-DFT molecular dynamics simulations were carried out with the Geraldyn2.1 code [13], which has been coupled to the electronic structure modules of GAUSSIAN09 [14]. The BODFT-MD algorithm in Geraldyn uses the velocity-Verlet integration scheme [15]. The BO-MD simulations were done with a time step of 0.5 fs. A chain of four Nosé–Hoover thermostats [16,17] was used to control the temperature at 300 K and 700 K. Electronic structure and energy gradient calculations were performed at the B3LYP level of theory with the 6-311G(d,p) basis sets, since these yield a good compromise between accuracy and computational efficiency (see below for a comparison with previous results using the 6-311G(2df,p) basis sets). The simulations started from the optimized equilibrium structure of each isomer without any preferred velocity vector other than the thermal energy. The MD simulations for the three isomers (all singlet electronic states) took 76 days on 32 processors running the Linux versions of Geraldyn2.1-G09. The production run was started following an initial thermalization period which was achieved after 3 ps, so that data were extracted from the last 10 ps of each simulation. In order to obtain the vibrational spectra, the Fourier-transform of the velocity autocorrelation functions (FT-VACF) were built from
1
) of the hexasulfane isomers at the B3LYP/6-
Helical
A
B
33, 41, 75, 107, 193, 227, 253, 322, 340, 364, 412, 427, 450, 453, 859, 860, 2637,2638
26, 44, 99, 112, 120, 208, 231, 257, 294, 387, 414, 514, 519, 619, 894, 899, 2611, 2612,
50, 55, 89, 104, 184, 207, 215, 226, 237, 276, 389, 409, 546, 594, 793, 802, 2655, 2656,
the trajectories. We recall that the vibrational spectrum obtained from the velocity autocorrelation functions does not require the knowledge of the dipole moment, therefore, the calculated vibrational amplitudes yield an accurate description of the relative infrared intensities as well as of the Raman intensities. This FT-VACF approach to obtain dynamic vibrational spectra has been successfully used on many other small molecules (see for instance, [18–20]). 3. Results and discussion 3.1. Static geometries and vibrational frequencies In agreement with the G3X(MP2) results of Ref. [12], using Gibbs free energy differences at the B3LYP/6-311G(d,p) level we find that the helical conformer is the most stable structure and that isomers A and B lie 17.7 and 19.5 kcal/mol above this structure, respectively. The optimized geometries and the corresponding vibrational frequencies for the three isomers are given in Tables 1 and 2, respectively. The optimized geometries of the branched isomers A and B are in good agreement with those reported at the B3LYP level using the larger 6-31G(2df) basis sets [12]. As pointed out in Ref. [12], isomer B exhibits a non-conventional bonding pattern between two HS3 units, where two S atoms (labeled 2 and 3 in Figure 1) appear hypercoordinated. We find here that the largest deviation (ca. 0.17 Å) from the previously optimized geometry corresponds precisely to the 2–3 SAS bond of this isomer. As shown in Table 2, all the vibrational frequencies of the three isomers are real, in agreement with the previous results. 3.2. Born–Oppenheimer molecular dynamics Since we are interested in the thermal stability of the hexasulfane isomers, we used the optimized geometries of all isomers as starting points for BO-MD simulations at room temperature (300 K) and at 700 K. We found that all isomers are stable at both
Table 1 Geometrical parameters of the hexasulfane isomers at the B3LYP/6-311G(d,p) level. Distances in Å, angles in degrees. Atom numbering as given in Figure 1. Previous values in parentheses from Ref. [12] at the B3LYP/6-311G(2df,p) level. Isomer
SAS distances
Helical
1-2: 2.106 3-4: 2.112 2-6: 2.106
A
1-2, 2-4: 2.401 (2.327) 1-3, 4-5: 2.035 (2.015) 2-6: 1.938 (1.926) 2-3: 2.591 (2.435) 2-1: 1.953 (1.934) 3-4: 1.982 (1.986) 1-7: 2.160 (2.110) 3-5: 2.194 (2.162)
B
2-3: 2.108 4-5: 2.108
SASAS angles
SASASAS dihedrals
1-2-3:108.3 2-3-4:108.6 3-4-5:108.6 4-5-6:108.3 2-1-3, 2-4-5: 101.9 1-2-6, 4-2-6: 105.9 1-2-4: 102.4 2-1-7: 112.0 2-1-4: 110.2 4-3-5: 112.0 2-3-4:99.1 7-1-4:96.7
1-2-3-4: 82.3 2-3-4-5: 77.1 3-4-5-6: 82.3 3-1-2-6, 5-4-2-6:14.6
3-4-1-2:1.49 7-1-4-3:108.3 1-4-3-5: 96.9
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Figure 2. Temporal evolution of the SAS distances (Å) for the helical isomer.
Figure 3. Temporal evolution of the SAS distances (Å) for isomer A.
Figure 4. Temporal evolution of the SAS distances (Å) for isomer B. Note the very slow oscillation regime for the bond connecting the two S3H units in this hypercoordinated isomer.
A. Ramírez-Solís, L. Maron / Chemical Physics Letters 607 (2014) 64–69
Figure 5. Temporal evolution of the SASAS angles (degrees) for the helical isomer.
Figure 6. Temporal evolution of the SASAS angles (degrees) for isomer A.
Figure 7. Temporal evolution of the SASAS angles (degrees) for isomer B.
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Table 3 Static harmonic frequencies, dynamically derived vibrational frequencies (cm 1) and non-harmonicities (in parentheses) for the branched hexasulfane isomers at 300 and 700 K. Isomer A
Isomer B
xstat, (300 K), x(700 K),
xstat, (300 K), x(700 K),
NH(300 K,700 K) 26, 27, 33 (1, 6) 44, 40, 39 ( 4, 5) 99, 98, 93 ( 1, 6) 112, 108, 109 ( 4, 5) 120, 121, 123 (1, 3) 208, 201, 200 ( 7, 8) 231, 236, 229 (5, 3) 257, 246, 237 ( 9, 20) 294, 295, 297 (1, 3) 387, 383, 383 ( 4, 5) 414, 407, 403 ( 7, 11) 514, 508, 503 ( 6, 11) 519, 517, 523 ( 2, 4) 619, 603, 597 ( 16, 22) 894, 873, 870 ( 21, 24) 899, 887, 880 ( 12, 19) 2611, 2623, 2633 (12, 22) 2612, 2631, 2650 (19, 38)
NH(300 K,700 K) 50, 35, 30 ( 15, 20) 55, 43, 41 ( 12, 14) 89, 83, 76 ( 6, 13) 104, 106, 113 (2, 9) 184, 182, 180 ( 2, 4) 207, 199, 190 ( 8, 17) 215, 214, 209 ( 1, 6) 226, 222, 219 ( 4, 7) 237, 236, 227 ( 1, 10) 276, 275, 275 ( 1, 1) 389, 380, 378 ( 9, 11) 409, 402, 408 ( 7, 1) 546, 549, 550 (3, 4) 594, 592, 596 ( 2, 2) 793, 786, 783 ( 7, 10) 802, 800, 793 ( 2, 9) 2655, 2658, 2670 (3, 15) 2656, 2664, 2676 (8, 20)
temperatures. Figures 2–4 show the temporal evolution of the SAS distances for each isomer at 700 K; the corresponding curves at 300 K are not shown since they are qualitatively equivalent to those presented and do not provide any relevant information. Figures 2–4 show that the bonding patterns remain unaltered throughout the simulations for the three isomers. While for the helical isomer small dynamical changes of the SAS bonds (2.13 Å dynamical average) and angles have been found around its equilibrium geometry, for the branched isomers these changes are considerably larger. For isomer A there are two long, two intermediate and one short SAS distances that reflect the symmetry of the static optimized structure (Figure 1a); their dynamical averages at 700 K are d12 = 2.373 Å, d24 = 2.433 Å, d13 = 2.053 Å, d45 = 2.038 Å, d26 = 1.948 Å, which can be compared with the static values given in Table 1. For isomer B there is only one very long SAS distance, two intermediate and two short SAS distances, their dynamical averages being also larger than the static values: d23 = 2.945 Å, d17 = 2.192 Å, d35 = 2.185 Å, d12 = 1.969 Å, d34 = 1.975 Å. However, a particularly interesting result is that the dynamical average of
the weak SAS bond (2.945 Å) linking the two HS3 moities in the hypercoordinated isomer B is substantially longer (more than 0.5 Å) than the static optimized distance (2.43 Å) at 0 K, a fact associated to the rather long oscillation period (varying from 0.8 to 1.1 fs) of this bond. The temporal evolution of the SASAS angles in Figures 5–7 confirm that no qualitative structural changes occur for any of the hexasulfane isomers, all of them oscillating around their equilibrium geometries. Thus, no structural interconversion has been detected between these stable isomers during these BO-MD simulations. The dynamic non-harmonicities (NH) have been obtained using the usual definition (see, for instance, Ref. [16]). If mj stands for the number of vibrational quanta in the j-th mode, the NH are determined by the difference of the dynamically derived frequency xAIMD(m1, m2, m3, . . .., m18) minus a m-weighted linear combination of the corresponding static purely harmonic B3LYP frequencies (x1, x2, ..., x18). We report in Table 3 the NH effects for the eighteen fundamental modes, where mi = dij stands for a single vibrational quantum in mode i and none in all the other modes, so that NH(i) simply becomes xAIMD(i)–xi.) of the A and B isomers. While in absolute value the largest non-harmonic contribution is found for the most energetic SAH stretching mode of isomer A (38 cm 1), we focus on the relative dynamic changes with respect to the static frequencies in each case. In this direction, while the largest non-harmonic effects are only 7.8% for the central-unit SASASAS stretching mode (257 cm 1) of isomer A at 700 K., for isomer B they attain up to 40% in the very low frequency region (around 50 wavenumbers) corresponding to the torsional mode coupling the two HS3–S3H moieties. The main feature of this mode is that it elongates (shortens) the shortest (longest) SAS bonds of the trapezoid formed by S1AS2AS3AS4. A couple of figures showing the vectors of these low frequency highly anharmonic modes are given as Supplementary material. Figure 10 shows the dynamics-derived vibrational spectra of the three isomers at 700 K. For comparison purposes, the intensities have been normalized to unity with respect to the largest peak of each spectrum. The numerical data of these spectra at both temperatures is available upon request from the authors. The vibrational spectra at 300 K do not differ significantly from the ones shown at 700 K. Some interesting facts can be drawn from these spectra at high temperature. Using the spectrum of the
Figure 10. Vibrational spectra (cm 1) of the helical (blue), A (red) and B (green) isomers at 700 K. Intensities are normalized to unity with respect to the largest peak of each spectrum. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
A. Ramírez-Solís, L. Maron / Chemical Physics Letters 607 (2014) 64–69
helical isomer as the reference, it can be seem that the most intense peaks for the branched isomers in the low (below 400 cm 1), medium (700–950 cm 1) and high (above 2500 cm 1) are shifted from the reference helical peaks. Clearly, the largest differences are found for the most intense peaks in the low frequency region for both isomers so that the branched isomers can be identified using these peak shifts. For the A species the strongest peak is blue shifted (407 vs. 292 cm 1), while for the B isomer we find a red-shifted peak (217 vs. 292 cm 1). We also stress that, using the above mentioned spectral normalization, the relative (A:B) intensity of the strongest low-frequency peaks is 0.48:0.89. Also, quite remarkably, the spectrum of the B isomer shows 12 peaks whose intensity is at least five times larger than that of the A isomer in the 80–270 cm 1 region. Since the same type of peak shift occurs for the A (blue shift) and B (red shift) isomers with respect to the helical isomer around 700–900 cm 1, the simultaneous detection of these peaks shifts could be used to unequivocally characterize these branched hexasulfane isomers. 4. Conclusions We have performed a series of DFT Born–Oppenheimer molecular dynamics simulations for the three hexasulfane isomers at room temperature and at 700 K. We have found that all the isomers are stable even at the highest temperature and no interconversion between these low-lying isomers was observed. The dynamically derived structural parameters are in good agreement with the static optimized values and, as expected, the average SAS– distances are slightly longer than the 0 K values. The dynamical behavior of the B isomer is the most interesting one since the SAS bond connecting the two HS3 moieties shows rather large variations, going from 2.4 to 3.8 Å. These large amplitude oscillations arise due to the rather weak p⁄–p⁄ interactions of the four nearly-flat trapezoidal S atoms in the B isomer. We also found that both H atoms rotate freely around the terminal SAS bond of each HS3 moiety in the B isomer. The dynamic vibrational spectra for the three isomers have been obtained at room temperature and at 700 K. Moderate (8%) and very large non-harmonic effects (up to 40%) were found at the low frequency region for the A and B isomers at 700 K, respectively. The large NH effects are due to the weak p⁄–p⁄ interactions of the four trapezoidal S atoms in the B isomer. We conclude that, although the largest differences in the vibrational spectra of the branched isomers with respect to the helical isomer appear in the low-frequency region (below 400 cm 1), the detailed information concerning the strongest peak shifts and the relative
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amplitudes of the largest peaks might be of help to experimentalists to achieve detection of these uncommon but rather stable hypercoordinated hexasulfane species in the gas phase. Acknowledgments The authors thank support from the ECOS-ANUIES/CONACYT Mexican–French cooperation program through project M10-P02. L.M. is grateful to the A. von Humboldt foundation. A.R.S. thanks CONACYT through the Basic Science project No. 130931, for support from the CONACYT 2013-Sabbatical Program and from the Professeur Invité program at INSA-Toulouse. This work was also supported by Programme Investissements d’Avenir under the program ANR-11-IDEX-0002-02, reference ANR-10-LABX-0037-NEXT. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cplett.2014.05. 028. References [1] B.E. Warren, J.T. Bursell, J. Chem. Phys. 3 (1935) 6. [2] B. Meyer, Sulfur, energy and environment, Elsevier, Amsterdam, 1977. [3] N.N. Greenwood, A. Earnshaw, Chemistry of the elements, Pergamon, Oxford, 1984. [4] J. Donohue, The structures of the elements, Wiley, New York, 1974. [5] M. Schmidt, New uses of sulfur, in: D.J. Bourne (Ed.), Advances in chemistry, Ser. No. 165, Vol. II, American Chemical Society, Washington DC, 1978, pp. 1– 12. [6] M.R. Engel, C. R. Acad. Sci. Paris 112 (1891) 866. [7] R. Steudel, R. Reinhardt, F. Schuster, Angew. Chem. Int. Ed. Engl. 16 (1977) 715; J. Donohue, J. Cryst. Mol. Struct. 8 (1978) 141. [8] T. Sandow, J. Steidel, R. Stuedel, Angew. Chem. Int. Ed. Engl. 21 (1982) 794. [9] R. Reinhardt, R. Steudel, F. Schuster, Angew. Chem. Int. Ed. Engl. 17 (1978) 57. [10] D.C. Koningsberger, Doctoral dissertation, Technische Hogeschool Eindhoven, Netherlands, 1971; H. Radscheit, J.A. Gardner, J. Non-Cryst. Solids 35 & 36 (1980) 1263. [11] J.A. Poulis, C.H. Massen, P.v.d. Leiden, Trans. Faraday Soc. 58 (1962) 474; J.A. Poulis, W. Derbyshire, Trans. Faraday Soc. 59 (1963) 559. [12] M.W. Wong, Y. Steudel, R. Steudel, Chem. Phys. Lett. 364 (2002) 387. [13] C. Raynaud, L. Maron, J.P. Daudey, F. Jolibois, Phys. Chem. Chem. Phys. 6 (2004) 4226. [14] Frisch, M.J. ; Trucks, G.W.; Schlegel, H.B. et al., GAUSSIAN 09, (2009) Pittsburg, USA. [15] L. Verlet, Phys. Rev. 159 (1967) 98. [16] S. Nosé, J. Chem. Phys. 81 (1981) 511. [17] W.G. Hoover, Phys. Rev. A 31 (1985) 1695. [18] L. Maron, A. Ramírez-Solís, J. Phys. Chem. A 111 (2007) 3173. [19] F. Jolibois, L. Maron, A. Ramírez-Solís, J. Mol. Struct. Theochem. 899 (2009) 9. [20] A. Ramírez-Solís, F. Jolibois, L. Maron, J. Phys. Chem. A 114 (2010) 12378.