1,4-DithiineâPuckered in the Gas Phase but Planar in Crystals: Role

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1,4-Dithiine – Puckered in Gas - Phase but Planar in Crystal: Role of Cooperativity Saied Md Pratik, and Ayan Datta J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b04908 • Publication Date (Web): 11 Jun 2015 Downloaded from http://pubs.acs.org on June 16, 2015

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The Journal of Physical Chemistry

1,4-dithiine – Puckered in Gas - Phase but Planar in Crystal: Role of Cooperativity Saied Md Pratik, Ayan Datta* Department of Spectroscopy, Indian Association for the Cultivation of Science, Jadavpur-700032,West Bengal (India).

Email: [email protected]

Abstract Tricyclic C6S8 is known to exist in two different polymorphic phases namely, alpha (α) and beta (β) forms with planar and puckered conformations, respectively. Recently, it has been shown that the individual molecule undergoes spontaneous symmetry breaking due to Pseudo Jahn-Teller (PJT) distortion resulting in puckered conformation at the ground state. Here, based on solid state dispersion corrected DFT, DFT-D2 as well as the localized Gaussian basis calculations, on periodic systems we have compared the relative stabilities and structural preferences for α and β polymorphs in a systematic way, starting from the monomers to different forms of higher aggregates in both alpha and beta crystals. From the molecular viewpoint, puckered conformations of the β form are found to be more stable compared to that of planar ones in the α form. Nevertheless, it is shown that PJT distortion can be suppressed by increasing the π-stacking interactions in its aggregates along crystallographic c-axis and therefore, eventually in the α crystal form. The same general principle is also shown to occur in the Form-II of the dithianon polymorph. Unlike C6S8 molecule of α form, dithianon molecules require only a dimer aggregate to suppress PJT distortion due to shorter π-stacking distance. It has been shown that environmental or cooperativity effect as found in crystalline phases, play a crucial role to quench the PJT distortion in the molecule. The computed IR spectra for both the molecular conformations as well as crystalline phases show good agreement with the experimental spectra.

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KETWORDS: Polymorphism; Solid-state dispersion corrected DFT (DFT-D); Molecular Packing; Cooperativity; Molecular Vibrations; THz spectroscopy; Suppression of PJT.

Introduction The aggregation of molecules into the crystal is mainly governed by the weak interactions.1,2 Depending upon the strength and directionality of the weak interactions, one molecule can adopt more than one different crystal structures within different or sometimes similar crystallizing conditions, called polymorphs.3–7 Polymorphism which is of paramount importance in solid state chemistry, occurs frequently in molecules having the dynamically flexible side chains even though it might also occur in the rigid molecules.8 Understanding the mechanism of aggregation of molecules into the polymorphic crystal is important for a variety of applications in the field of pharmaceutical and materials science because of their distinct physicochemical properties including thermodynamic, spectroscopic, kinetic and bioavailability.3,6 In this context, we have studied an interesting polymorphic form of tricyclic carbon sulfide molecule. The binary tricyclic C6S8 (3H,7H-bis[1,2]dithiolo[3,4-b:3' ,4' -e][1,4]dithiine-3,7-dithione) is found to exist in two different crystallographic forms i.e alpha (α) and beta (β). The α form, reported by Rauchfuss et. al. in 1993 has been synthesized through the dimerization of β-C3S5H2. It is an air stable monoclinic structure with reddish brown color (space group: P21/c) where the individual molecules are planar.9 After a decade Michel Dolg et. al. has reported the second polymorph which has puckered molecules and forms a black, insoluble and tetragonal crystal structure with 𝑃42! 𝑐 space group by following the same synthesis procedure.10 The building block of both crystals is tricyclic carbon-sulphide, C6S8 molecule which accommodates two sulphur units in the 1,4 position of the central six member ring and two five members rings in either side contain one disulphide (S-S) and one thione (C=S) bond. 1,4-dithiine ring is found to have non-planar aromatic stability with C2v


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symmetry.11,12 Based on DFT calculations Vessally has studied a series of 1,4-dithiine and their Soxygenated molecules and in most of the cases, the molecules become puckered from the conformational point of view.13 Based on theoretical calculations, recently we have proposed that the individual 1,4-dithiine substituted tricyclic carbon sulphide molecule has a puckered shadow boat like conformation and the corresponding planar form has an expectedly first order saddle point that shows a butterfly flapping type instability.14 We have also reported that the origin of the distortion in case of tricyclic carbon sulfide is a (1Ag+1Au+2Au+3Au) × au PJT problem and the planar molecule deforms to a bent form by lowering the symmetry from C2h to C2. The suppression of PJT, that is recovering the planar conformation from the deformed bent structures, is a well-known phenomenon.15–17 The quenching of PJT distortion maybe attained by increasing the energy gap between active ground and excited states or/and by populating the excited states via substitution of atom or group with more electronegative analogues, coordinating with cations and by applying external pressure or electric field.18–21 PJT and suppression of PJT has significant influence in structural chemistry and magnetic properties of materials through tuning of band gap.22–24 In the present case of tricyclic carbon sulfide molecule, it is shown that, PJT is suppressed due to increasing π-stacking along parallel direction. As a consequence of PJT distortion the individual molecule has bent conformation in gas phase but PJT distortion is totally suppressed in α polymorph and the molecules within this crystal has planar configuration. Apart from tricyclic carbon sulphide polymorphs, we have also studied another 1,4-dithiine substituted pesticide molecule, dithianon (5,10-dihydro-5,10-dioxonaphtho[2,3-b]-1,4-dithiine-2,3dicarbonitrile), C14H4N2O2S2, which have four conformational polymorphic forms.25 Except one polymorph (Form-II, triclinic, space group 𝑃1) all the other forms have bent molecular conformation whereas Form-II is found to exist in planar conformation inside crystal. Here again, the individual molecule of Form-II has puckered conformation. On π-stacking aggregation along the crystallographic ACS Paragon Plus Environment

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c-axis, PJT distortion is suppressed in the dimer and eventually in the crystal. In this article, based on plane wave dispersion-corrected DFT as well as localized Gaussian basis set calculations on periodic crystals, we have investigated the relative stabilities of α and β polymorphs of C6S6 along-with their molecular aggressions in a systematic way starting from dimer to tetramer. It has been shown that the PJT distortion can be suppressed progressively with the increase of the π-stacked aggregations along crystallographic c-axis and hence in α crystal of C6S8 as well as in crystal of Form-II of C14H4N2O2S2. Calculated numerical frequencies of the α C6S8 crystal also conform that the first order saddle point for monomer and dimer conformations due to instability, disappear in the crystalline phase. Apart from this, we have also calculated the THz spectra at periodic dispersion corrected DFT level for monomer along with the crystalline polymorph of C6S8 which has a good agreement with the experimental IR-spectra.

Computational Details Both the, α and β monomer of tricyclic carbon sulphide, C6S8, have 14 atoms and the unit cell consists of 4 monomeric units. We have used plane wave based DFT method as well as localized Gaussian basis. For Gaussian calculations, 6-31G split basis has been used. We have used the hybrid functional HSEh1PBE26 for the crystal structures along with the Gaussian basis.

Periodic DFT

calculations for the polymorphic crystal were performed using the PWSCF (Plane-Wave Self Consistent Field) code with generalized gradient approximation (GGA) and Perdew-Burke-Ernzerhof (PBE) functional27 and compared with Becke-Lee-Yang-Parr (BLYP)28 and Perdew-Wang-91 functional29 as implemented in QUANTUM ESPRESSO Package.30 The ionic cores are taken care of by ultrasoft pseudopotential.31 The crystals are fully relaxed until all the forces became less than 10-3 a.u by taking a 6×6×6 k-point mesh. The monomer, dimer and trimer forms of both planar and bent molecules were optimized by immersing them in a 20×20×20 cubic box to create gas phase like


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environment with a 4×4×4 k-point mesh. In both cases a kinetic energy cutoff of 30 Ry was used. Dispersion interactions were taken into account by using Grimme's DFT-D2 empirical formalism.32 The vibrational IR-spectra for the crystals were calculated at Γ-point by taking 4×4×4 k-point mesh through the PHONON30 code, implemented in QUANTUM ESPRESSO. We have also performed plane wave DFT-D3 calculation as implemented in VASP code to calculate the relative energies.33 The core-valence interactions were taken into account by projected augmented wave (PAW) approach along with generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) functional which is well demonstrated for carbon-sulphur system. The k-point mesh and energy cut off were chosen to be 6×6×6 and 500 eV respectively. The relative energies for the crystals were calculated as ∆E=(Eα-crystal – Eβ-crystal). Using localized Gaussian basis we have also obtained the optimized ground states geometry for the individual monomers and their higher order aggregates in gas phase. Further, harmonic vibrational frequencies were calculated to ensure that obtained structure is not a saddle point. Truhlar's M06-2X hybrid meta-GGA functional34 has been used as they are able to consider middle range electron correlations which are required to describe intramolecular dispersion forces like non-bonded interactions between closed shell atoms and also provide a reasonable balance between accuracy and computation resources. The Pople's 6-31+G(d,p) were used.35 Binding energies of the higher order aggregates with respect to monomer were also calculated with Basis Set Superposition Error (BSSE) by using the Counterpoise Correction (CP).36 The BSSE corrected binding energies of the higher order aggregates were calculated as ∆E = (Ehigher

order aggregates

-n.Emonomer). The relative energies of the

molecules were calculated as ∆E=(Eα-form-Eβ-form). All localized Gaussian basis calculations were carried out by using the Gaussian 09 suite of programs.37 Form-II of the Dithianon polymorph contains 2 monomeric units and the monomer is build up by 24 atoms. Here we have only used GGA-PBE functional for periodic calculations by taking a 5×5×5 k-point mesh for the crystal structure and all other calculations were performed similarly as in tricyclic carbon sulphide.


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Results and Discussions

Figure 1. Optimized crystal structures for (a) α and (b) β polymorphs of tricyclic C6S8 (3H,7Hbis[1,2]dithiolo[3,4-b:3' ,4' -e][1,4]dithiine-3,7-dithione) are shown. On the right, the corresponding optimized trimers of (c) α and (d) β are shown where A,B,Aʹ represents the types of crystal packing.

The optimized crystal structures of α and β tricyclic carbon sulphide are shown in Figure 1 along with their trimeric conformations to visualize the crystal packing. The conformational variation of the individual molecules inside the α and β crystal leads to form the conformational polymorphs of C6S8 molecule. The initial crystal structures are taken from the experimental CIF (Crystallographic Information Files) of the α and β forms and change in the unit cell volume on optimization is less than 1%. The α form of the crystal is planar and contains ABA' type of stacking where the A and A' are slipped parallel but B is not only slipped parallel but also rotated about 65° w.r.t A as shown Figure 1(c).10 On the other hand, the β form which has the bent conformation is build up by ABA type parallel stacking where B is about 180° rotated as in Figure 1 (d). Apart from the structural diversity of the


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crystal, individual molecules also show considerable differences in bonding and bond angles. Both the computed and experimental non-bonded S(k)...S(k') distances for the central 1,4-dithiine moiety are 3.60 Å for α form where as it is 3.36 Å and 3.33 Å respectively for the β form. Based on the Gaussian localized basis as well as Plane-wave DFT-D2 and DFT-D3 calculations we have compared the relative energies difference between the α and β crystals and the results are assembled in Table 1. According to Gaussian localized basis calculations with HSEh1PBE/6-31G functional β crystal is more stable over α crystal by 7.5 kcal/mol. But based on DFT-D2 plane wave calculations by using PBE and PW91 functional α crystal is more stable over β by 5.6 and 6.0 kcal/mol respectively whereas according to BLYP α is marginally stable over β by a factor of 0.7 kcal/mol. Plane-Wave DFT-D3 calculations also led to the similar result as DFT-D2 and α crystal is stable over β crystal. Dolg and coworkers have reported that even after several attempts they could only isolated the bent, β crystal structure of C6S8 and concluded that the β form is thermodynamically more favorable than the α form. So, the α form, reported by Rauchfuss et. al., might be a disappearing polymorph. Unfortunately, based on the electronic energy calculations at 0 K we cannot directly correlate with their relative stability at room temperature. Gibbs free energy calculations using QHA (quasi harmonic approximation) are intractable for crystals with large number atoms in the unit cell as in the present case.


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Table 1. Relavite energies (in kcal/mol) of the fully optimized crystals at different level of theory. Type of Calculation

Functional

α-form

β-form

PBE

0

5.6

BLYP

0

0.7

PW91

0

6.0

PBE

0

3.9

HSEh1PBE/6-31G

7.5

0

Plane Wave Basis DFT-D2 Plane Wave Basis DFT-D2 Plane Wave Basis DFT-D2 Plane Wave Basis DFT-D3 Localized Gaussian Basis

For details understanding of the stability order, we have also followed the bottom up approach. For the individual molecules the bent form with C2 point group, is the most stable. On gradually decreasing of the dihedral angle φ(C(i)-C(j)-S(k)-C(j')) (see Figure S1 in Supp. Info. File), the α form with C2h point group symmetry is retrieved which is unstable with a first-order saddle point according to our calculations. As reported previously is, the computed barrier for the planarization (∆E‡) at M062X/6-31+G(d,p) level of theory is 2.42 kcal/mol.14


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Table 2. ∆E1 and ∆E2 are the BSSE corrected binding energies of α and β form. ∆E3 is the relative energies of the corresponding molecular forms. All reported energies are calculated at M06-2X/631+G(d,p) level of theory.

∆E1

∆E2

∆E3

(kcal/mol)

(kcal/mol)

(kcal/mol)

Monomer

--

--

2.4

Dimer

-15.6

-17.6

7.1

Trimer

-31.4

-35.6

10.7

Energy

Figure 2. Radial distribution functions of (a) α and (b) β form of C6S8 crystals upto a distance of 15Å by taking 3×3×3 supercells. In case of π-stacked dimer (Figure S2, see in Supp. Info. File), α form still has a first order saddle point and it tends to form a puckered structure with lower degree of puckering. The dimeric α form forms a stable ground state conformation with dihedral in between ~2-5°. But the β remain as puckered one with a dihedral angle of ~38.5°. The BSSE corrected binding energies (∆E1) of the α and ACS Paragon Plus Environment

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β stacked dimers are -15.6 and -17.6 kcal/mol respectively calculated at M06-2X/6-31+G(d,p) which is good agreement with previously reported data at RI-MP2/aug-cc-pVQZ level.10 Further, increasing the associations along crystallographic c-axis in case of both α and β forms leads to an interesting result. The π-stacked trimer of the α form has a dihedral of 0° and again π-stacked trimer of the β has an average dihedral of 38.5° which is almost similar to the monomer of β form. As a consequence, πstacked trimer of α form becomes planar and that for β remain puckered. Our calculated BSSE corrected binding energies (∆E1) for α and β π-stacked trimers are -31.4 and -35.6 kcal/mol respectively at same level of theory as reported in Table 2. On the basis of the Plane-wave DFT-D2 calculations, performed with PBE functional, the binding energies of the π-stacked dimer and trimer are -11.5 and 23.4 kcal/mol respectively which becomes -12.4 and -25.2 kcal/mol respectively for the β form as shown in Table 3. Again from the Table 2 and Table 3, it is clear that based on both Gaussian localized basis as well as Plane-wave DFT-D2 calculations, the relative stabilities of stacked dimer and trimer of the β form is much higher compared to corresponding α form. Though the relative order of stability remain consistent for both method but Plane-Wave DFT-D2 calculations seem to underestimate the binding as well as relative energies. So, in comparison with the previously reported data, the localized Gaussian basis DFT calculations for the isolated molecules are much more reliable than that of PlaneWave DFT calculations. We have also considered the linear arrangement of both planar α and bent β in dimeric and tetrameric assemblies (see Figure S2 and S3 in Supp. Info file). For the planar linear conformations both the dimeric and tetrameric forms are not ground state structures and tends to form puckered structures. The larger relative gain in stability by the higher order aggregates of β form over α arises due to their ABA type parallel ordered crystal packing. In order to understand the fact, we have calculated the radial distribution functions, g(r)38 of the molecular centre of masses for both α and β polymorph by taking a 3x3x3 supercell upto a distance of 15 Å. This provides us an estimate of the environment of the molecule in each crystal. Figure 2, shows that the major contributions are coming at a distance of 3.81 Å and 4.02 Å for β and α polymorph and these distance correspond to π-stacked and ACS Paragon Plus Environment

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rotated π-stacked respectively. So, because of comparatively larger stacking distance and also the rotation of the monomer with respect to one another in higher order aggregates there is a weakening of the π stacking interactions for the α-polymorph.

Table 3. ∆E1 and ∆E2 are the binding energies of α and β form of α and β form. ∆E3 is the relative energies of the corresponding molecular forms. All reported energies are calculated at DFT-D2 level of theory. ∆E1

∆E2

∆E3

(kcal/mol)

(kcal/mol)

(kcal/mol)

Monomer

--

--

0.5

Dimer

-11.5

-12.4

1.1

Trimer

-23.4

-25.2

3.3

Energy


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Figure 3. (a) Planar-bent-planar hybrid trimer (left panel) and its optimized structure (right panel). (b) Bent-planar-bent hybrid trimer (left panel) and its optimized structure (right panel).

As shown previously, the lowest electronic state (1Ag) for the planar conformation shows instability at q(au)=0 calculated at the EOM-CCSD/def2-SVP level of theory which is a (1Ag+1Au+2Au+3Au)×au PJT problem where the high symmetric unstable planar molecule goes to considerably low symmetric stable bent conformer by breaking the symmetry. But on increasing the association along the crystallographic c-axis, the dihedral angles of ground state stable dimer decreases and becomes completely planar in π-stacked trimer of the α form. As a consequence, the PJT distortion gets reduced in the dimer and is completely quenched for the trimer in α form. Again if we look back at the radial distribution functions, g(r) in Figure 2, most of the contributions are coming from π-stacked and slipped parallel rotated π-stacked aggregates in β and α form respectively. So, one might expect ACS Paragon Plus Environment

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that the suppression of the PJT distortion is arising due the π-stacking type aggregations. To verify the postulate, we retrieve trimers from both β and α form and replace the central unit with the opposite conformation by keeping the orientation and centre of mass fixed as shown in Figure 3 and optimize the structures. Interestingly, as shown in Figure 3(a), the puckered molecule incorporated α trimer (hybrid α) becomes completely planar and planar molecule incorporated β trimer (hybrid β) becomes bent (see Fig. 3(b)) depending upon the environment of the substituted monomer. In case of hybrid α and β trimer, the conformation of the central unit is mainly affected and governed by two other updown monomeric units which are basically planar for hybrid α and bent for hybrid β respectively. It is rather well-known that cooperativity has significant influence in aggregation of molecules and the formation of crystal.39 However, planarization of an otherwise PJT distorted molecule due intermolecular interactions in aggregates is a rare phenomenon which this tricyclic C6S8 molecule exhibits. It is indeed interesting to note that even though 1,4-dithiine moieties are generally puckered, we show that PJT distortions might be suppressed by non-covalent molecular packing.


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Figure 4. Optimized (a) monomer, (b) dimer at M06-2X/6-31+G(d,p) level of theory and (c) Optimized crystal structures at plane wave DFT-D2 level of theory of the Dithianon molecule.

The optimized crystal of Form-II and corresponding optimized single molecule containing 1,4dithiine substituted pesticide molecule, dithianon (5,10-dihydro-5,10-dioxonaphtho[2,3-b]-1,4-dithiine2,3-dicarbonitrile), C14H4N2O2S2 have been shown in Figure 4. The individual molecules of Form-II inside the crystal have almost planar conformation with an experimental dihedral angle, φ(C(i)-C(j)S(k)-C(j')), of 2.8°. Interestingly this planar monomer having C2v symmetry is not the ground state structure but a first order saddle point. Hence, it distorts to a more stable, puckered structure (dihedral, φ(C(i)-C(j)-S(k)-C(j')) = 37.2° at M06-2X/6-31+G(d,p) level). Further, increasing the aggregations along crystallographic c-axis led to the formation of dimers which on optimization becomes almost planar with a dihedral angle of 3.5° with the binding energy, ∆E=(Edimer-2Emonomer)= -12.7 kcal/mol calculated at same level of theory. Similar to the tricyclic C6S8 monomer, this monomer of the dithianon is also unstable towards distortion along the a2 vibrational mode due to PJT distortion. As reported previously19,20,40, this distortion can arise from a PJT mixing of the relevant OMO and UMO having an overall product of A2 symmetry between them. Figure 5 shows the important OMO and UMO in C14H4N2O2S2. The lowest energy gap between OMO (HOMO + 3) and UMO (LUMO) is 4.92 eV which is sufficiently small to indicate a possibility of strong vibronic mixing along the a2 puckering mode to result in a distorted structure as expected from the general PJT theory. The centre to centre distance between two monomers is 3.96 Å in the dimer which indicates a strong π-stacking interactions. As a consequence, the PJT distortion gets suppressed for the dimer and eventually in the crystal of Form-II.


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Figure 5. Possible combinations of the occupied molecular orbitals (OMO) and unoccupied molecular orbitals (UMO) with small OMO-UMO gaps. H, H–3, H–4, L, L+1, L+4, L+5 indicate the HOMO, HOMO – 3, HOMO – 4, LUMO, LUMO + 1, LUMO + 4, LUMO + 5 respectively. Apart from the explicit structure determinations and explaining their stability, we have also calculated the vibrational spectroscopy and numerical frequencies of the C6S8 polymorphs. Recently, THz spectroscopy has been receiving significant attention from the research communities as a sophisticated tool to distinguish between various polymorphic forms.4,41–44 According to localized Gaussian basis calculations, the single monomer of α form shows lowest frequency at 62.2i cm-1 which is a first order saddle point with butterfly flapping type instability. In order to check the stability of the α crystal we have also calculated the numerical frequencies at HSEh1PBE/6-31G level of theory and find that the structure is vibrational stable. This also confirms that though the monomer of α form is unstable but inside the crystal the monomers are stable. We have also performed DFT-D2 plane wave calculation to find out the IR spectra for both α and β crystals and their corresponding monomers. The spectra are shown in Figure 6. From the Figure 6 (a) and (b), we see that the most of the intense bands are coming from the region of 1400 cm-1 to 1450 cm-1 due to C=C asymmetric stretching (asym str), 1256 to 1283 cm-1 due to C-C asym str. and 1002 to 1040 cm-1 due to C=S asym str. Comparatively


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less intense spectra in the region of 890 to 916 cm-1 due to C-S asym str. On close examination around the region of 890 to 916 cm-1, the asym str. due to C-S bond, it is clear that there is small blue shift from the molecule to crystal. The lower region spectra arise due to asym ring deformation. The computed spectra of the β form have a reasonable agreement with the experimentally available IRspectra of the β crystal.

Figure 6. (a) The computed infrared spectra for the α form and (b) the computed and experimental infrared spectra for β form of C6S8 crystals. The infrared spectra of the corresponding α and β monomers are also shown. A Lorentzian broadening is used for smoothening the delta functions at the peak positions.

Conclusion To summarize, our calculations at plane-wave DFT-D2 as well as DFT-D3 levels suggest that α polymorph of C6S8 is more stable than its β form. However, an unambiguous determination of ACS Paragon Plus Environment

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the most stable form is not possible. Therefore, further experimental or high level free energy calculations for the crystals would be required to assess the most stable crystal form. We have also studied the Form-II polymorph of dithianon molecule, C14H4N2O2S2, alongwith its monomer and dimer. Interestingly the planar monomeric conformation has ground state instability due to PJT distortion. The monomers of both planar C6S8 and C14H4N2O2S2 readily form puckered conformation by breaking the symmetry due to PJT distortion. We have demonstrated the PJT distortion can be suppressed by increasing the aggregations along crystallographic c-axis. Due to shorter π-stacking distance, dithianon molecules need to have only dimeric aggregations whereas the tricyclic C6S8 molecules of the planar α form require at least a trimeric aggregations in the parallel direction to suppress the PJT distortion. We have also calculated the THz-spectra based on plane-wave DFT-D2 for α and β crystals as well as their corresponding monomers and the calculated spectra of the β crystal is in a good agreement with the experimentally available spectra of the crystal. We believe that the unambiguous demonstration of suppression of the PJT in molecules on crystallization due to π-stacking can be effective design principle to planarize otherwise vibrationally unstable molecules. We realize that many of these π-rich cyclic molecules have advanced field-effect transistor (FET) applications and therefore, isolating their planar polymorphs is expected to boost their applications in organic electronics. AUTHOR INFORMATIONS Corresponding Auther: [email protected] ACKNOWLEDGMENT We thank CRAY supercomputer and IBM P7 cluster for computational facilities. SMP thanks CSIR India for financial assistance for SRF. AD thanks DST, BRNS and INSA for partial funding. We thank Dr. Sumantra Bhattacharya for fruitful discussions. ACS Paragon Plus Environment

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Supporting Information: Schematic diagram of the C6S8 molecule, Figure of monomer, dimer and tetramer of α and β conformations, Optimized coordinates of crystals and molecules, complete Gaussian 09 reference. This material is available free of charge via the Internet at http://pubs.acs.org.

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1,4-DithiineâPuckered in the Gas Phase but Planar in Crystals: Role

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