The electronic structure of the tetrasulphur tetranitride dication, S4N42+:an ab initio
molecular orbital study
MILANTRSIC
Itlstituto de Fisicn e Quitnicn de S i o Cnrlos, Utliuersidnde de S i o Pnulo, C.P. 369,13560,Sdo Corlos, S.P., Brnzil
AND
WILLIAM
G. LAIDLAW
A N D RICHARD
T. OAKLEY'
Departtnet~tof Chemistry, University of Cnignry, Cnlgnry, Alm, Catzndc~T2N I N4
Received March 4. 1982
G. LAIDLAW,
and RICHARD
T . OAKLEY.
Can. J. Chem. 60, 2281 (1982).
MILANTRSIC,WILLIAM
Ab itlirio Hartree-Fock-Slater molecular orbital calculations on the planar tetrasulphur tetranitride dication S4Nd2+reveal that it
can be described as a fully delocalised 10 rc-electron system. Overlap populations for the NS bonds suggest a bond order
at 346 and 262 nm are assigned to
substantially stronger than in neutral S4N4.The strong uvlvisible absorptions observed for S4NdZ+
nrc, + rc * and nrc, + rc * excitations. The Hartree-Fock-Slater rc-molecular orbital manifold is discussed in relation to simple HMO
concepts.
G. LAIDLAW
et RICHARD
T. OAKLEY.
Can. J. Chem. 60, 2281 (1982).
MILANTRSIC,WILLIAM
Des calculs crb initio d'orbitales molCculaires de Hartree-Fock-Slater sur les dications planaires de tktraazoture de soufre,
S4NdZ+,
rCvelent qu'on peut dCcrire ce cation comme Ctant un systeme pleinement dClocalisC a 10 Clectrons rc . Le recouvrement de
populations des liaisons NS suggkre un ordre de liaison substantiellement plus fort que dans le compost5 neutre S4N4.On attribue les
fortes absorptions uvlvisible observCes pour le S4N42+a 346 et 262 nm a des excitations nrc, + rc * et nrc, + rc *. On discute des
multiples d'orbitales molCculaires rc de Hartree-Fock-Slater en relation avec des concepts simples de OMH.
[Traduit par le journal]
Introduction
The unusual cage-like structure of tetrasulphur
tetranitride 1 has long been of central interest in the
study of binary SN species. A little over a decade
ago Gleiter presented an intuitively appealing rationalization of its molecular structure by considering the n-system of an idealised planar S4N4ring 2
/\-?\
\x/
N
N N
S-S
S N ~ \ S
N
I
N
\S
\
7
S
'N'
1
2
system, with 10 n-electrons, would be stable. In
1978, Michl recognized the spectroscopic consequences of such a n-electron distribution, and
predicted the appearance of the MCD spectrum of
S4N4,+ (3). Very recently Sharma, Aubke, and
Paddock have provided a specific and quantitative
molecular orbital analysis of the S4N4,+species (4).
Their extended Hiickel and CNDO calculations
yield orbital eigenvalues and Mulliken overlap
populations which are crucial to the understanding
of the system. Although these studies have enhanced our knowledge of the electronic make-up of
S4N4,+,it nevertheless has seemed appropriate to
us to undertake an investigation of the species at
the ab initio level. Our Hartree-Fock-Slater
(HFS) calculations not only provide a confirmation, within the ab initio context, of many of the
concepts developed by previous workers, but also
allow the prediction of electronic excitation and
total energies. In addition, a more detailed analysis
of the charge density distribution and overlap
populations permits a discussion of the HFS results
in terms of elementary considerations of electronegativity and simple Hiickel MO theory.
(1). In this view the 12 n-electron ground state of 2
would be orbitally degenerate and, as such, unstable with respect to Jahn-Teller distortion. Of the
several possible symmetry changes that will break
the orbital degeneracy of the ground state, the D,,
conformation is the most attractive since, in the
extended Hiickel description, two antibonding
n-MO's of 2 would be converted into cross-ring
S-S o-interactions. With the discovery of the
planar S4N4,+ dication in 1977 by Gillespie and
Theoretical method
co-workers (2), the structure/bonding relationships
The Hartree-Fock-Slater method has been well
of Gleiter were strengthened. Implicit in his origidocumented in the literature, and efficient procenal analysis was the concept that a planar S,N4,+ dures for its implementation have been outlined
and tested extensively by Baerends and co'To whom all correspondence should be addressed.
0008-40421821172281-05$01.OOIO
01982 National Research Council of CanadaIConseil national de recherches du Canada
CAN. I. CHEM. VOL. 60, 1982
TABLE1. Eigenvalues and Mulliken population analysis of S4Nd2+
Overlap and self-atom populations
Orbital
20 2,
2e,(LUMO)
26,,(HOMO)
lb,u
4e~
162"
262,
30 I,
3eu
lefi
la2,
20 1,
102,
leu
lbzfi
161,
leu
la,,
Eigenvalue
(au)
SN
-0.4537
-0.5399
-0.6612
-0.6618
-0.6627
-0.6992
-0.7001
-0.7404
-0.7859
-0.7880
-0.8300
-0.8430
-0.9863
-1.0745
-1.1923
-1.2234
- 1.3142
- 1.3580
-0.042
-0.019
0.010
0.000
-0.027
0.013
-0.007
-0.043
0.005
0.017
0.019
-0.003
0.023
0.019
0.022
0.023
0.024
0.023
SIS,
SISS
0.001
0.008
-0.003 -0.001
0.000
0.000
-0.014
0.002
0.005
0.000
0.001
0.000
-0.006
0.003
0.011
0.002
0.001 -0.001
0.001 -0.001
0.003
0.000
0.001
0.000
-0.004
0.000
0.000
-0.005
0.001
-0.008
0.002
0.000
0.000
0.003
0.000
0.002
N
0.183
0.128
0.214
0.000
0.209
0.196
0.034
0.227
0.072
0.094
0.083
0.062
0.106
0.104
0.040
0.139
0.082
0.080
S
Designation
0.217
0.202
0.014
0.276
0.138
0.010
0.252
0.168
0.161
0.088
0.079
0.183
0.067
0.089
0.134
0.029
0.068
0.062
n*
n*
IlrS N
IIRS
o*
~ K N
nos
o*
nos
n
7~
nos
0
0
0
(3
0
0
Ground state overlap and self-atom populations
n-Contribution
(3-Contribution
Total
0.26
0.35
0.61
-0.03
0.01
-0.02
0.00
0.02
0.02
0.93
3.67
4.60
1.08
3.64
4.72
-0.19
0.00
-0.19
0.69
0.00
0.69
Ground state charges
n-Contribution
o-Contribution
Total
workers (5). Our application of the method to a
variety of S,N,"* cages (6), rings (7), and chains (8)
has provided satisfactory results. The calculations
reported here were carried out using a single
determinant closed shell state function and the
double { basis of Clementi and Roetti (9) augmented with a sulphur 3d orbital with exponent
1.68 (10). Throughout the SCF calculations the
core electrons were kept "frozen" in the manner
described by Baerends and co-workers (11). An
idealized planar D, geometry with d(S-N) =
1.545 A, 5 = 120", and N = 150" was assumed for
S4N42+.These parameters represent an average of
those observed in a variety of S4N4,+ salts (2b).
(0.69) and nitrogen (-0.19) indicate that the positive charge resides primarily on sulphur, as expected on electronegativity grounds. However, an
analysis of the a- and K-electron distributions of
S4N4,+ shows that the transfer of electrons is
entirely within the K-system; in the o-system psu =
pNu= 4.0, while for the K-MO'SpsX= 1.3 1 and pNn
= 1.21.2 Thus if one arbitrarily assumes that 0.5
electron is lost from each sulphur atom in the
ionization process S4N4-. S4N4,+ 2e (l,2), then
an additional transfer of -0.2 K-electron occurs
during the formation of the S4N4,+ K-bonding
network.
The total NS overlap population of 0.61 is significantly larger than in S4N4(0.49) and illustrates
the strengthening of the skeletal bonds caused by
oxidation of the neutral molecule (cf. NS -.NS+
e effects the removal of a K *-electron and increases
the net NS bond order from 2.5 to 3 (12)). Analysis
of the orbital overlap populations reveals a K-contribution of 0.26 (approximately of a K-bond),
which is clearly larger than in S3N3- (0.16). By
contrast, the o-contributions for both species (0.35
in S4N4,+ vs. 0.36 in S3N3-) are almost identical.
+
Results and discussion
Orbital energy leuels
The HFS molecular orbital energies (eigenvalues), atomic charges, and Mulliken overlap
populations calculated for S4N4,+ are shown in
Table 1. Figure 1 illustrates the upper energy levels
of the valence shell of S4N4,+ along with the
corresponding levels for the neutral S4N4molecule
(6). Since the representations a,,, b b,,, and e,
are antisymmetric with respect to the molecular
plane, it is clear that the ground state of the S4N4,+
2Thelack of polarity in theo-framework imparts to it a pseudo
dication is a 10 K-system in our a b initio calcula- D m symmetry. Thus several energy levels (e.g., lb,, and lb2J
tions. The calculated atomic charges on sulphur are approximately degenerate.
+
+
,,
2283
TRSIC ET AL.
I
1
I
I
(2a2,)
-
I
au
I
-
I
(6e)
--0.5
I
-,
,
1
,
''11
"1
I
I
I
1
I
I
'-
(Zed
-
I
I
-
I
I
- -0.6
FIG.1. Correlation diagram between the upper part of the
energy level stack of S4N4(D,) and planar S,N4Z+(D,). Virtual
orbitals are indicated by parentheses.
Thus the stronger bond in S4N4,+ (d(S-N) =
1.53-1.57 A) compared to S3N3- (d(S-N)
=
1.58-1.62 A) can be attributed to the strengthened
n-network of the former, i.e. there are fewer
occupied anti-bonding levels. Gillespie and coworkers (2b) have suggested the presence of a
partial n-bond between nearest neighbour
sulphurs, but little or no cross-ring interaction.
However, our calculations indicate that there is
essentially zero overlap between adjacent and
remote pairs of sulphur atoms. Indeed, the highest
occupied n -orbital lb ,, which would presumably
be a candidate for 1,3-SS-overlap in a valence bond
approach, is strongly localised on sulphur, and the
very weak overlap population that it has is antibonding in character.
Comparison of the HFS energy levels with the
CNDO results of Paddock and co-workers reveals
major similarities. In both cases there is a sulphur
lone pair orbital l b at the Fermi surface (because
of the choice of axes their subscripts 1 and 2 on the
b, and b, representations are interchanged with
ours), and at somewhat lower energy lies a nitrogen
lone pair orbital lb,,. The remaining occupied
n-orbitals la,, and leg are well buried in the upper
o-levels and the two lowest unoccupied levels are
,
,
the n-orbitals 2e, and 2a2,. Perhaps the major
distinction between the CNDO results and ours is
the accumulation of several energy levels near the
Fermi surface in the HFS case. This grouping of
lone pair and antibonding orbitals at the top of the
filled energy level stack seems typical of a b initio
calculations on SN compound^.^ This difference in
the position of the o-energy levels is reflected in
a somewhat different characterization of the oorbitals themselves. We find a total of eight obondingorbitals la,,, la,,, lb,,, lb,,, le,, and2eu,
with the eight remainingo-orbitals divided between
five lone pairs (2a ,, 2bIg,2b2,, and 3eu) and three
anti-bonding orbitals (3a ,,and 4eu). This description is reminiscent of Gillespie's characterization
(2b) of the o-system into eight bonding pairs and
eight lone pairs (valence bond parlance does not
recognize anti-bonding orbitals), but is in contrast
to the CNDO picture of a dozen o-bonding orbitals
(4)
Ab initio us. Hiickel MO description
Partitioning of the electrons of planar ring systems into o- and x-networks, as we have done
above, has a long history in carbocyclic systems,
and retains its appeal in the present context.
Indeed, the implications of simple Hiickel molecular orbital (HMO) theory pervade much of the
current understanding of the n-structure of cyclic
SN systems. In any HMO treatment of the n-system of a cyclic molecule of general formula (AB), ,
the energy levels of the system are given by the
roots of the secular determinant (14):
I :,
i:ln,n
2P cos ln/n
a. -
1
=o
(n odd)
where 1 = 0, f 1, f 2, . .. f (n - 1)/2
l=O.fl.f2,-..fn/2
(neven)
However, the form of the MO's will depend
critically on the values of the Coulomb parameters
a, and a,, their relative magnitudes reflecting the
electronegativity difference between the A and B
sites. In sulphur-nitrogen rings, the choice of a,
and a, is not obvious. Gleiter (1, 15) has proposed
"a higher electronegativity of nitrogen compared
to sulphur" (i.e. a, < a,) and refers to the atomic
electronegativity scale of Pauling (16). By contrast,
Gimarc and TrinajstiC. (17) have pointed out the
potential applicability of the orbital electronegativities proposed by Streitweiser (18) (i.e. a, > a,).
From our ab initio calculations (and from Paddock's CNDO work) it is apparent that the sulphur
3See, for example, our own results (6) and those of Palmer et
al. (13) for S,N4.
2284
CAN. J. CHEM. VOL. 60, 1982
lone pair n-orbital lb,,lies above the corresponding nitrogen-based orb~tallb,,. From this energy
level ordering one would conclude that nitrogen is
more electronegative than sulphur (aN < a,).
However, upon examination of the HFS n-electron
density distribution, one finds (as mentioned earlier) a greater n-charge on sulphur (pSn= 1.31) than
on nitrogen (pNn= 1.21). At the HMO level such a
result can only be reproduced by choosing Coulomb parameters such that as < w,, i.e. a sulphur
which is more electronegative than nitrogen.
It is therefore apparent that the n-MO's of
S4N4,+respond to a potential field that cannot be
modelled by a single Hiickel parameterization.
This is not really surprising insofar as the lower
n-levels are well buried in the stack and consequently sense a potential more characteristic of the
'ontrast the higher lying and more diffuse
core.
levels
frontier orbitals l b 2 ~
and lb1, and the
charac2e, and 2 a 2 ~ see a potential which is
teristic of a complete nitrogen and sulphur valence
shell, for which the atomic electronegativity scale
(i-e. @ N < a,) is more appropriate. Simple Hiickel
concepts must therefore be used with caution.
bearing this caveat in
information can be obtained by a suitable choice of
parameters. If properties such as n-charge densities are desired, the ab initio charge distribution is
best described at the Hiickel level by setting 8s <
C ~ N -However, if inf~rmationconcerning the cornposition and ordering of the frontier orbitals is
required, as would be the case in the study of
pericyclic reactions, the ratio a, > a Nwill provide
more meaningful results.
Ionization of S4N4
Before leaving the discussion of the molecular
of S4N42+ we
'Omment
On the
pro~osition(1, 4, 15) that ionization of S4N4 to
S4N42+
the 2 a 2 ~orbital. Certainly this
orbital has SS-bonding character in S4N4;removal
of electrons from it would weaken the cross-ring
interaction and could lead to the formation of a
planar S4N42+.This concept is consistent with Fig.
1, which shows that the 2a2. orbital of S4N4,+, to
is
of S4N4 has
which the 4b2
noticeably destabilized. However, such a description has certain shortcomings. For example, upon
oxidation of S4N4with chlorine to give S4N4C12,3,
one of the S-S bonds of S4N4 is retained (19). As
we have already noted, S4N4 itself has several
orbitals located very near the surface which could
be involved in the attack of electrophiles (e.g. C1+),
and the retention of the cage shape in S,N,CI,
implicates the use of orbitals other than the 462 in
the formation of the S-Cl o-bonds. The structures
of the Lewis acid adducts of S4N4,e.g. S4N4.L(4,
L = BF, (20), SbC1, (21), FeCI, (22), AsFS(23), SO,
(24)) also pose an interesting question. Adduct
formation through nitrogen effects structural
changes similar to those caused by ionization, i.e.
both cross-ring S-S bonds are lost, but it is hard to
conceive of the 46, orbital being significantly
perturbed by the N + L interaction. Instead the
nitrogen lone pairs 2b, and 4e seem more likely
candidates for adduct formation.
s2'
N
I'
N
'S-N
3
F
,Cl
Lh
S-N--s/
N'
N
/
S
's-N'
4
In order to understand better the thermodynamics of the structural change which occurs upon the
ionization of S4N4,we have calculated the energy
of the S4N42+cage (D,) formed by removing the
two electrons from one of the three uppermost
orbitals of S4N4: 2a2, 4a,, and 4b2. Although we
have had difficulty in obtaining a fully converged
state in the case of an empty 4b2 orbital, the energy
of all of these cage dications is over
kcallmol
above that of the planar form. This rather
cant stabilization of the latter reflectsthe energetic
found
importance of the well developed
in it. The high n-bond energy achieved in the planar
structure is more than sufficientto offset the loss of
cross-ring SS-bonding (25).
Electronic spectrum of S4N4,+
The uvlvisible spectrum of S4N4,+contains two
major peaks with La,at 346 and 262 nm (4). There
is also a small shoulder near 300nm on the latter
peak. In order to assign the electronic excitations
responsible for these absorptions we have calculated the oscillator strengths4 of all symmetryallowed transitions which correspond to a &, >
200nm.
Of these the
lb,,
(nn,)
2e, (n*) and lb,, (nn,) + 2e,(n*) are dominant
(see Table 2). There is in addition another allowed
transition 4eu
has an
+ 2eg (n *)
oscillator strength of about 1% of the two major
absorptions. The calculated energies5 for the two
intense transitions are 334nm (lb,, + 2e,) and
+
4The dipole length - dipole velocity formula was employed
for the calculation of transition moments. See ref. 26.
5Excitation energies have been obtained by adding 0.4eV to
the corresponding one-electron energy differences; this correction reproduces well the total energy differences calculated by
the more expensive, and exact, transition state method (27) we
used in refs. 7 , s . Theoretical and numericaljustification for this
correction will be published elsewhere.
TRSIC ET AL.
TABLE2. Electronic spectrum of S,N,'+
Observed"
Calculated
Calculated
oscillator
strength (au)
346
300
262
334
33 1
262
2 x 10
1 x lo-'
1 x 10
L a x
Transition
Polarization
Molecular plane
C , axis
Molecular plane
l b , , -t 2e,
4 e , + 2e,
l b , , -t 2e,
(nm)
"From ref. 4
262 nm (lb,,, + 2e3, both of which compare 3 . J. MICHL.J. Am. Chem. Soc. 100,6801 (1978).
remarkably-iell wi& the observed La, vaiues.4 . R. J. SHARMA,F. AUBKE,and N. L. PADDOCK.Can. J.
Chem. 59, 3157 (1981).
The weak transition 4eu
2eg has a
5 . ( a ) E. J. BAERENDS
and P. Ros. Intl. J. Quantum Chem.
energy
331 nm, and we presume that the weak
Symp. 12, 169 (1978); ( 6 ) T . ZIEGLERand A. RAUK.
absorption near 300 nm corresponds to this excitaTheoret. Chim. Acta. 46, 1 ( 1 9 7 3 .
6 . T. CHIVERS,
L. FIELDING,
W. G. LAID LAW,^^^ M. TRSIC.
tion.
Inorg. Chem. 18, 3379 (1979).
The above assignments provide theoretical conW. G. LAIDLAW,
and M. TRSIC.
) J . BOJES,T. CHIVERS,
firmation of Michl's prediction for the MCD spec- 7 . (J.a Am.
Chem. Soc. 101, 4517 (1979);( b ) N. BURFORD,
T.
trum of S4N42+(3). Treating S4N42+as an &atom 10
CHIVERS,
A. W. CORDES,W. G. LAIDLAW,
M. C. NOBLE,
x-electron perimeter one would expect two x +n *
J. Am. Chem. Soc.
R. T. OAKLEY,
and P. N. SWEPSTON.
104, 1282 (1982); T . CHIVERS,P. W. CODDING,W. G.
transitions to be symmetry-allowed. These are
LAIDLAW,
S. W. LIBLONG,
R. T. O A K L E YM.
, ~TRSIC.
~ ~ J.
indeed the two excitations which, according to our
Am. Chem. Soc. To be published.
calculations, dominate the electronic spectrum. 8 . ( a ) T . CHIVERS,W. G. LAIDLAW,R. T . OAKLEY,and M.
Both transitions give rise to a degenerate excited
TRSIC.J. Am. Chem. Soc. 102,5773 (1980);( 6 )J. BOJES,T.
CHIVERS,
W. G. LAIDLAW,
and M. TRSIC.Inorg. Chem. T o
state and, according to the perimeter model (3),
be published.
should give rise to a pair of positive A-terms in the
9 . E. CLEMENTI
and C. ROETTI.At. Data Nucl. Data Tables,
MCD spectrum.
14. 177 (1974).
10. W: G. ~ a l ~ ~ a w M.
a nTRSIC.
d
Chem. Phys. 36,323 (1979).
Summary
1 1 . E . J. BAERENDS,
D. E. ELLIS,and P. Ros. Chem. Phys. 2 ,
Ab initio Hartree-Fock-Slater molecular orbital
41 (1973).
calculations on the S4N42+dication confirm the 12. J . M. DYKE,A. MORRIS,and I. R. TRICKLE.
J. Chem. Soc.
Faraday Trans. 11, 147 (1977).
description of its electronic structure in terms of a
fully delocalised 10 n-electron system. The prefer- 13. R. H . FINDLAY,M. H. PALMER,A. J. DOWNS,R. G.
and R. EVANS.Inorg. Chem. 19, 1307 (1980).
ence for the planar form of S4N42+over a cage 14. EGDELL,
Chem. Rev. 69, 157 (1969);( 6 ) D .
( a ) K. A. R. MITCHELL.
structure can be rationalized in terms of the strong
P. CRAIG.J. Chem. Soc. 997 (1959); (c) D. P. CRAIG.I n
x-network of the former, which is more than
Theoretical organic chemistry. Kekule Symposium.
Butterworth and Co., Ltd. London. 1959. p. 20.
sufficient to counterbalance the loss of cross-ring
sulphur-sulphur bonding in the cage. The elec- 15. R. GLEITER.Ang. Chem. Int. Ed. Engl. 20,444 (1981).
L. PAULING.
The nature of the chemical bond. Cornell
tronic spectrum of S4N42+provides a classic exam- 16. University
Press, Ithaca. 1960.
ple of an &atom 10 x-electron perimeter, the two 17. B. M. GIMARCand N. TRINAJSTIC.Pure Appl. Chem. 5 2 ,
1443 (1980).
intense uvlvisible absorptions being assigned to
18. A. STREITWEISER.
Molecular orbital theory for organic
nns + n * and nn, + x * transitions.
+
Acknowledgements
We thank the Natural Sciences and Engineering
Research Council of Canada and FINEP of Brazil
for financial support and for an NSERC University
Research Fellowship (to R.T.O.). The use of a set
of X, programs provided by Dr. T. Ziegler is
acknowledged, as are several stimulating conversations with Dr. T. Chivers.
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