Molecular orbital description of the polythiazyl polymer

Journal of Molecular Structure (Theochem), 139 (1986) 321-332 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

MOLECULAR ORBITAL DESCRIPTION OF THE POLYTHIAZYL POLYMER Part 1. MNDO calculations of models of (SN),

A. J. A. AQUINOa, L. A. SOARES II, A. B. F. DA SILVA and M. TRSIC* Znstituto de Fisica e Q&mica de S&o Carlos, University of Sao Paula, P.O. Box 369, 13560-Sdo Carlos, SP (Brazil) (Received 3 June 1985)

ABSTRACT Semiempirical MNDO calculations are performed on various models for the polythiazyl polymer with increasing chain sizes. Population analysis, geometry optimization and the evolution of the frontier orbital energies are discussed. A low-lying broken symmetry structure with (SN), repeating units is detected. INTRODUCTION

The polythiazyl polymer, (SN),, is a unique material being the only example of an intrinsic electric polymeric conductor at room temperature and superconductor at temperatures close to absolute zero. It also exhibits the behaviour of a quasi one-dimensional metal with the conductivity along the polymeric chain three orders of magnitude greater than in the transverse direction [ 11. While there are a number of calculations on (SN), at the band-theory level, the results do not seem to clearly explain the conduction mechanism, nor to completely recover the experimental molecular structure [ 21. It is not known what makes (SN), different from other polymers which are insulators or semi-conductors. A bridge between the understanding at the molecular level of sulphur nitrides, “n-electron rich” compounds [ 31 and (SN), at the solid state level seems desirable. Our approach, at the molecular level, attempts to gain an understanding of how the electronic structures of fragments of the polymer relate to its prop erties. The procedure consists of studying fragments with an increasing number of atoms until a periodic behaviour in properties such as atomic charge distribution and bond indexes is reached. The geometry of this fragment is then optimized. aPermanent address: Conselho National de Desenvolvimento Cientffico CNPq, Av. W/3 Norte, Quadra 511, 70750-Brasflia, DF, Brasil. 0166-1280/86/$03.50

0 1986 Elsevier Science Publishers B.V.

e TecnoMgico,

328

For this study we have chosen the MNDO (Modified Neglect of Differential Overlap) method [ 41. This well-calibrated procedure is more reliable for properties such as molecular geometry and ionization potentials than ab initio procedures at the single-determinant minimal-basis level [ 51. We should emphasize that the interest in materials such as (SN), is not merely academic. There is reasonable expectation that polymeric conductors may have a technological impact within a decade [6] (already projects are starting on the industrial production of polymer-based batteries). For accounts of the properties and band-theory calculations on (SN),, see refs. 1 and 2, respectively. At the MO level we refer to the work of S&hub and Messmer [7] and Yanabe et al. [8], who discuss the polymerization of SzNz to give (SN),, the calculations of Deutsch and Curtiss [9] of SN, (SN), and (SN), and the recent paper of Palmer and Findlay [lo]. CALCULATIONS

The evolution of the properties of fragments of polythiazyl was followed by adding SzN2 units, corresponding to each single chain in the crystallographic unit cell [ 111. It is not clear what the terminal atoms are in the real polymer and these may well be hydrogen atoms [12]. Thus we opted for two representations for the end of the chains: (1) H-atoms as terminators, the fragments being H*N(SN),SH, n = 2, 4,. . . , 12. The geometrical parameters for the H-atoms were optimized, the results being as expected for -NH2 and -SH groupings. The sustantiation for H-atoms as terminators is the presence of 5-10 mol percent hydrogen impurities in the polymer [ 121. (2) S-atoms as terminators, the fragments being (SN),S chains, n = 2, 4,. . . , 10. This structure has the unique feature of minimizing end effects. Indeed, each N and S atom have an image around a central S atom, which is not the case for (SN), calculations reported in the literature. The series (1) and (2) were calculated by using the x-ray diffraction geometry [ 131. The geometry of the (SN)JJ fragment was then fully optimized. Both H,N(SN),SH and (SN),S showed a clear tendency to periodicity in the atomic charges and bond indexes, but of a broken symmetry (BS) character, and this induced us to repeat the geometry optimization of (SNh,S, relaxing the crystal structure geometry. A lower energy BS solution was found giving rise to a third series: (3) (SN),S-[BS] chains, n = 2, 4,. . . , 10. RESULTS

AND DISCUSSION

The geometry

optimization

of the (SN)&3 fragment

Table 1 shows the three geometries considered and dard heats of formation (AH;), as provided by the MNDO-optimized structure, with the same symmetry reported X-ray structures [ 131, i.e., SN repeating units

their respective stanMNDO routine. The restriction as in the (symmetry adapted,

329 TABLE 1 Three geometries for the (SN),,S Structure

fragment

Geometry

AW (kcal mol-I)

Distances (A)

Angles (“)

X-ray

SN = 1.593 NS = 1.628

SNS = 119.9 NSN = 106.2

552.3

MNDO optimized-SAa

SN = 1.573 NS = 1.584

SNS = 127.1 NSN = 105.5

538.6

MNDO optimized-BSb

SN NS SN NS

same as in MNDO-SA

523.3

= = = =

1.535 1.549 1.617 1.623

%A: symmetry adapted, i.e., repeating SN units. bBS: broken symmetry, S,N, units.

i.e., repeating

SA), appears as being somewhat more stable than the X-ray structure; actually the MNDO-SA resembles remarkably the neutron diffraction structure [ 111. If the SA restriction is relaxed during the optimization procedure, an even lower energy value is obtained, with (SN), repeating units and a short-shortlong-long sequence for the distances (BS). The calculations of Yanabe et al. [8 ] and Palmer and Findlay [lo] also show a BS character, although the authors do not elaborate on this point. It is not obvious whether this pattern is a result of a Hartree-Fock instability or of a close to 0 K transition of (SN),; the latter case would have implications in the superconductivity mechanism. As a matter of fact, the low-lying BS solution for polythiazyl is not that unexpected. Low-lying BS states have also been found for the S3N; and &NY ions and were attributed to the n-electron richness of these systems [ 141; obviously, end effects cannot be at the origin of the appearance of BS in these ring compounds. Further to our results, Laidlaw and BCnard [15] initiated calculations on the model “polymer” 1 with SNS and NSN angles equal to 90” and found low-lying BS states. N-

S -N-

S

1

330

Charge distributions

and bond indexes

Figure 1 shows the net atomic charges and bond indexes for (SN),,S-[CS] (crystal structure), (SN),,S-[SA] , (SN),,S-[BS] and H2N(SN@H. The charge alternation for all cases for the S atoms is apparent in all the structures, although it is somewhat more enhanced in the BS case. The fact that the symmetry is found to break at the S centre in our work may not be crucial since it may also happen for the N centres, corresponding to another low-lying BS state [ 10, 14, 151. The bond indexes also show a BS character with (SN), repeating units. For instance in H,N(SN)&JH, two larger values of the bond indexes, ca. 1.35-1.25 a are followed by two lower values, ca. 1.05 8. Again this BS character is enhanced for (SN),,S-[BS] . The evolution

of the frontier

orbital eigenvalues

with chain size

Figure 2a shows the evolution of enoMo, eLuMo and Ae (HOMO-LUMO energy gap) for (SN),S-[CS] and (SN),S-[BS] , and Figure 2b shows the linear dependence of Ae with l/n; for the latter case, the regression coefficients are 0.9993 and 1.0000, respectively. The Ae values are not meant to represent the electronic transition energies. We compared the MNDO calculated Ae values for a series of sulphur nitrides [16], and found that this Ae-MNDO value was above the experimental

(dl

Fig. 1. Net atomic charges and bond indexes for (SN),,S with: (a) X-ray geometry (b) MNDO optimized geometry (SA); (c) MNDO optimized geometry with broken metry (BS); and (d) H,N(SN),,SH.

(CS); sym-

331

100

5: Y :50

00

I

0.1

I

0.2

I

I

03

04

I

0.5

I/n Fig. 2. Evolution of eHOMO, cLUMO and EWE in (SN),S crystal structure; (BS) broken symmetry geometry.

with: (a) n and (b) l/n. (CS)

by a surprizingly constant 4.2 eV. In a similar comparison for polyenes, Melo and Melo [ 171 found the same value. The implication is that for the CS case Ae, -.+m vanishes while for the BS case Ae n-+cc - 0.4 eV, a small but finite band gap.

values

CONCLUSIONS

MNDO calculations were performed on several models of (SN), of increasing size. Charges and bond indices indicated a BS wave function with (SN), repeating units. Energy optimization indicated that the BS solution was lower in energy than structures with SN repeating units. For (SN),S chains, a linear connection between l/n and Ae (the band gap) was found. This allows the extrapolation for n --f 00, although a discontinuity for some larger and finite n value cannot be ruled out. ACKNOWLEDGEMENTS

We acknowledge support from the Brazilian agencies CAPES (fellowship to A. J. A. A.) and CNPq (fellowship to L. A. S. and operating grants and financial assistance to M. T.). We are grateful to CNPq for allowing A. J. A. A. to develop M.Sc. studies in Sao Carlos. We acknowledge useful comments from Drs. W. G. Laidlaw, J. R. Lechat, R. H. de A. Santos and T. Chivers. REFERENCES 1 M. M. Labes, P. Love and L. F. Nichols, Chem. Rev., 79 (1979) 1. 2 J. L. Bredas, Ann. Sot. Sci. Bruxelles, 94 (1980) 83. 3 T. Chivers, Chem. Rev., 85 (1985) 341. W. G. Laidlaw and T. Trsic, in V. H. Smith (Ed.), Proceedings of the Applied Quantum Chemistry Symposium, D. ReideI, Dordrecht, in press. 4 M. J. S. Dewar and W. Thiel, J. Am. Chem. Sot., 99 (1977) 4899,4907. M. J. S. Dewar and M. L. McKee, J. Comput. Chem., 4 (1983) 84.

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