The Journal of Physical Chemistry, Vol. 82, No. 12, 1978
Communications to the Editor
1453
COMMUNICATIONS TO THE EDITOR Orbital Interaction in the Dimerization of Disulfur Dinitride to Tetrasulfur Tetranitride
Sir: In recent years, disulfur dinitride, S2N2, and tetrasulfur tetranitride, S4N4,shown in Figure 1, have been of much interest in that they are the precursors of polymeric sulfur nitride, (SN),,’ which is a low-dimensional metallic conductor and even becomes a superconductor a t 0.3 K.2 On t h e other hand, it has been also reported t h a t SzNz rapidly dimerizes, in certain organic solvents with a trace of alkali, to S4N4,3which is known to have a geometry with coplanar N atoms from X-ray diffraction analysis.? I t is a n interesting problem to explain the process of the formation of S4N4from S2Nzby considering orbital interaction~.~ From the atomic arrangement of S4N4and the principle of maximum overlap of the highest occupied (HO) MO and the lowest unoccupied (LU) MO between two S2N2molecules, two kinds of SzN2stacking interaction models A and B are considered as shown in Figure 2. They are of essentially different stacking configurations when S2Nz approaches each other. Several spectroscopic and MO theoretical studies have been performed as to the assignment of orbital patterns in S2N2.6,iThe HOMO and the LUMO of SzNzemployed here are t h e same as those obtained previously by the present authors with the use of the ASMO-SCF method.s T h e shape of the HOMO is consistent with that analyzed by photoelectron spectroscopic study6a and that of the LUMO is the same with those obtained by others with various MO calculations.7bf The HOMO-LUMO interactions of S1-N,j and N2-S4 are “bonding” in model A, and thereby two new PCTtype bonds are ready to be formed between them, accordingly as the T bonds of S1-Nz and N3-S4 are weakened. On the c o n t r a r y , interactions of N,-S:, a n d S2-N4 a r e “antibonding” and, therefore, do not contribute to form new bonds. T h e intermediate-range interaction of S2-S3, which is favorable for bonding, should be taken into account as well even though the interaction is weak, since the T A 0 of S stretches considerably, and the overlap between Szand S3 is not then negligible. On the other hand, the stacking interaction in model B merely favors the S&4 bond formation. This type of orbital interaction is disadvantageous in bringing about the subsequent process of dimerization; model B should be discarded. It should be noted that the stacking in model B coincides with that in the S2Nzcrystal along the b axis.IC One can explain the process of the formation of S4N4 with coplanar N atoms with the use of model A as follows: the main bonds to be formed are S1-N:, and Nz-S4 p a bonds while the previous S1-N2 and Ns-S4 cleave simultaneously with the formation of new bonds as shown in Figure 2A. In the framework of this dimerization model, the reaction proceeds quite easily only through bond interchange without large dislocation among nuclei and, therefore, without going over a large potential barrier. A slight deformation then takes place until the most stable geometry in Figure 1 is accomplished along the S2-S3bond which plays t h e role of a fulcrum as illustrated in Figure 3. T h e most stable geometry is then expected t o be completed when the weak S1-S4 bond is formed. T h e existence of these transannular S-S bonds has also been 0022-3654/78/2082-1453$01 .OO/O
Figure 2. Two stacking interaction models A and B to form S4N4by the dimerization of S2Nz. The absolute value of A 0 coefficient on S in the HOMO is 0.707, and those on S and N in the LUMO are 0.412 and 0.511, respectively. The contributions from 3d AO’s of S to those MO’s are small and neglected here.
Figure 3. Topological mode of deformation from the SzNz stacking model A to S4N,. White circles represent S atoms and black ones N atoms.
suggested by the MO calculations for the S4N3molecule itself,7b,7cv9 Another geometry of S4N, with coplanar S atoms which had been proposed by IR and Raman spectroscopic analyses” is ruled out a t least in the present orbital interaction treatment on the direct dimerization of S2N2to S,N4. T h e extended Huckel MOScand the CNDO/BW M09g calculations have also supported a geometry with coplanar N atoms from the viewpoint of the total energy of S4N4. However, there still may be a possibility for the interconversion of S4N4 between the geometries with coplanar N atoms and with coplanar S atoms making use of some appropriate vibrational modes each other. In this @ 1978 American Chemical Society
1454
The Journal of Physical Chemistry, Vol. 82, No. 12, 1978
Additions and Corrections
point, further investigation on these geometries taking also vibrational analysis into account would be desirable.
Duke, and G. P. Ceasar, Phys. Rev. B , 13, 4517 (1976); (d) M. KertBsz, S. Suhai, A. Aiman, D. Kocjan. and A. I. Kiss, Chem. Phys. Lett., 44, 53 (1976); (e) J. A. Jafri, M. D. Newton, T. A. Pakkanen, and J. L.Whitten, J . Chem. Phys., 66, 5167 (1977); (1) I. P. Batra, S. Ciraci, and W. E. Rudge, Phys. Rev. 8,15, 5858 (1977); (9) W. Y. Ching, J. G. Harrison, and C. C. Lin, ibid., 15, 5975 (1977); (h) P. W. Deutsch and L. A. Curtiss, Chem. Phys. Left., 51, 125 (1977). T. Yamabe, K. Tanaka, K. Fukui, and H. Kato, J . Phys. Chem., 81, 727 (1977). (a) D. Chapman and T. C. Waddington, Trans. Faraday Soc., 58, 1679 (1962); (b) F. S. Braterman, J. Chem. SOC.A , 2297 (1965); (c) A. G. Turner and F. S. Mortimer, Inorg. Chem., 5, 906 (1966); (d) J. B. Mason, J. Chem. Soc. A, 1567 (1969); (e) R. Gleiter, ibid., 3174 (1970); (1) P. Cassoux, J. F. Labarre, 0. Glemser, and W. Koch, J . Mol. Struct., 13, 405 (1972); (9) M. S. Gopinathan and M. A. Whitehead, Can. J . Chem., 53, 1343 (1974). E. R. Lippincott and M. C. Tobin, J . Chem. Phys., 21, 1559 (1953).
Acknouiledgment. This work was partly supported by Grants-in-Aid for Scientific Research from the Ministry of Education of Japan (No. 065101 and No. 255315). R e f e r e n c e s a n d Notes (a) A. G. MacDiarmid, C. M. Mikulski, P. J. Russo, M. S. Saran, A. F. Garko, and A. J. Heeger, J. Chem. Soc., Chem. Commun., 476 (1975); (b) C. M. Mikulski, P. J. Russo, M. S. Saran, A. G. MacDermid, A. F. Garito, and A. J. Heeger, J. Am. Chem. Soc., 97, 6358 (1975); (c) M. J. Cohen. A. F. Garito, A. J. Heeger, A. G. MacDiarmid, C. M. Mikulski, M. S. Saran, and J. Kleppinger, ibid., 98, 3844 (1976). R. L. Greene, G. B. Street, and L. J. Suter, Phys. Rev. Lett., 35, 1799 (1975). H. J. EmelBus, Endeavour, 32, 76 (1973). B. D. Sharma and J. Donohue, Acta Crystallogr., 16, 891 (1963). K. Fukui, “Theory of Orientation and Stereoselection”. Springer-Verbg, Berlin, 1975. (a) D. C. Frost, M. R. LeGeyt, N. L. Paddock, and N. P. C. Westwocd, J . Chem. Soc., Chem. Commun., 217 (1977); (b) J. Sharma, D. S . Downs, 2. Iqbal, and F. J. Owens, J . Chem. Phys., 67, 3045 (1977). (a) M. P. S. Collins and B. J. Duke, J. Chem. Soc., C k m . Commun., 701 (1976); (b) D. R. Salahub and R. P. Messmer, J . Chem. Phys., 64, 2039 (1976); (c) W. R. Salaneck, J. W-p Lin, A. Paton, C. B.
Department of Hydrocarbon Chemistry Faculty of Engineering Kyoto University Kyoto 606,Japan College of General Education Nagoya University Nagoya 464, Japan Received January 16, 1978
ADDITIONS AND CORRECTIONS 1976. Volume 80
K. W. Hipps, G. A. Merrell, a n d G. A. Crosby*: Determination of Geometrical Parameters of Excited States. Application to d6 Transition Metal Complexes of 0 and D4 Symmetry. Page 2239. Equations B9, B10, B12, and B13 are wrong, as are their reproductions in the text (eq 15 and 16). In the limit where h2 = 1, the equations are correct, as are the table entries which were computed in this approximation. T h e correct expressions are as follows:
+
1)I(0’In 1)I’ = &-A (TI - 1)KO’ In - 2) l 2 [ a t An - a.aOz]I(O’In - 1)12 [ a +ao2 -
C U + ~t( ~
+
a_a+’n] l(0’ In) I’
+ (B9)
+ A)nl(O‘ln)I2 = a - A ( n - 2)1(0’1n - 3)12 t [CY+ A(n - 1)I(O’In - 2)12 +
a+(l
CY.-CX~’]
[a+ao2
- a.a,’(n
-
-
l)] KO‘In - 1)I’ b2
n + 2 A ( A + 1 ) +7 2k - n3 = n2[Z + (1- 2/k2)(k’ - 1!] -n 7 - (bz/2)(kz - 1)+ n2
=-2
1%
cyo
=
(B10)
kb/dT
-G. A. Crosby
+ 2E’ + + 3A(3h2 -
($)[;
Karuyoshl Tanaka Tokio Yamabe Akinori Noda Kenichi Fukul’ Hiroshl Kat0
