A New Look at the Chemical Bonding in S2N2 and S4N4


Tetrasulfur tetranitride is the earliest known sulfur–nitrogen compound , having been first prepared in 1835 . Disulfur dinitride was discovered as an unstable intermediate in 1910 during the purification of a sample of S4N4 by vacuum sublimation ; it spontaneously polymerized to a golden , metallic material , poly(sulfur nitride) , having the formula (SN)x . These three compounds are the tetramer , dimer , and polymer respectively of the thiazyl radical , S–N .

The unusual formulas of these sulfur–nitrogen compounds have been both puzzling and intriguing . The sulfur valence –S– is normal for sulfur(II) compounds , such as in hydrogen sulfide , mercaptans (thiols) , sulfides (thioethers) , disulfides , and in elemental “octosulfur” S8 . The sulfur atoms in these substances all have a tetrahedral coordination , in which the six valence electrons (3s2 3p4) have a sp3 configuration . Two electrons are shared in two sigma covalent bonds with neighbouring atoms , and four electrons are in two nonbonding lone pairs . The –S– atoms in S2N2 , S4N4 , and (SN)x seem to be ordinary divalent sulfur , and have a similar tetrahedral sp3 configuration .

The problem arises with the peculiar electronic state of the nitrogen atoms in these compounds . The –N– type of valence implies trigonal planar nitrogen , sp2 + pz , such as is found in the nitrogen atom of the pyridine molecule , for example . Two of the five nitrogen valence electrons , 2s2 2p3 , are shared in sigma covalent bonds with neighbouring carbon atoms , two are in a nonbonding lone pair in the x-y plane , and the fifth valence electron is in an axial native (unhybridized) 2pz orbital . In pyridine this latter orbital with its singlet electron can overlap with the five carbon 2pz1 orbitals to form a hexagonal ring in which the six 2pz electrons have a stabilizing aromatic resonance .

A similar resonance has been proposed in various electronic structures for S2N2 and S4N4 [the references are presented at the end of the text , below] . The nitrogen atoms are trigonal , while half of the sulfur atoms are divalent –S– and the other half are tetravalent =S= . These two sulfur valences are reproportionated into trigonal –S= by resonance with the nitrogens : –S–N=S=N– -----> –S=N–S=N– . This works well for the nitrogens , but a problem arises with the sulfurs in that they have six valence electrons , but only five can be accomodated in the pi resonance system . Where does the sixth one go ? Some of these resonance schemes become quite complicated as they attempt to provide rational Lewis covalent bond structures for the compounds .

The objective of this essay is to describe the chemical bonds in S2N2 and S4N4 in a simple , elementary manner . Several guidelines have been followed in this study :

* The sulfur atoms have a tetrahedral sp3 configuration , and are electronically inert linking atoms ;

* The nitrogen atoms have a trigonal planar sp2 + pz configuration , and are the electronically active components of S2N2 and S4N4 ; and ,

* There is no transfer or resonance of valence electrons between the sulfur and nitrogen atoms in S2N2 and S4N4 . An unusual sort of resonance will be proposed for the nitrogen 2pz1 valence electrons in tetrasulfur tetranitride .

The electronic structure of poly(sulfur nitride) is discussed in another web page , “Three Models of the Metallic Bond in Poly(sulfur nitride)” [Underlined blue hyperlinks can be clicked when online to download the PDF or HTML file , which will open in a new window] . As with S2N2 and S4N4 , the sulfur atoms in (SN)x are again considered to have the electronically inert tetrahedral configuration . However , instead of being trigonal planar sp2 + pz , the nitrogen atoms are considered to have the trigonal pyramid s + p3 configuration . The s orbital in this case is the 2s1 native (unhybridized) orbital , which can overlap continuously in the polymer chains to form the metallic bond in them .

The consequences of the sp2 + pz configuration of the nitrogens , and how the electronic state of the chemical bonds in S2N2 and S4N4 are correlated with their known physical and chemical properties , are discussed in the following sections of this web page .


Disulfur Dinitride , S2N2


Brauer (pp. 409-410) describes S2N2 as ...........

“Well-formed , colorless crystals ; very volatile ; unpleasant iodine-like odor ; stable only at low temperatures ; becomes dark after a short exposure to 20 C ; sublimes at 10-2 mm even at room temperature ; polymerizes readily to (SN)x ; in the presence of moisture , about 67% of the S2N2 polymerizes to (SN)x , while 33% dimerizes to S4N4 .......”. The addition of even trace amounts of various salts (NaOH , KCN , Na2CO3) to S2N2 “causes instantaneous and complete dimerization”. “To purify the S2N2 it can be sublimed at room temperature in high vacuum . Beautiful , large , colorless crystals are obtained”. “The material detonates violently at 30 C , or when under high mechanical pressure”.

S2N2 is diamagnetic ; as it polymerizes to (SN)x it darkens and becomes paramagnetic :

“As polymerization proceeds the colorless diamagnetic S2N2 crystals turn intense blue-black and become paramagnetic giving a weak free radical signal at g = 2.005 . As the blue-black color fades , the crystals become a metallic golden color and the free radical signal gradually decreases to zero” (Mikulski and co-workers , p. 6361) . They also note ,

“It should be stressed that S2N2 , which is a slightly volatile colorless solid , has been reported to be extremely explosive and sensitive to slight mechanical shock” (p. 6360) .

Mikulski et al. determined the molecular structure and physical constants of S2N2 by X-ray diffraction . They found it had a nearly perfect square , flat shape :

Sulfur(II)–sulfur(IV) resonance was thought to average the S–N bond lengths in S2N2 to 1.654 :

“........ suggesting a bond order of approximately 1.5 for all of the equivalent S–N bonds . The S–N single bond length is expected to be approximately 1.74 and that for the S–N double bond is approximately 1.54 . Their average , 1.64 , expected for a bond order of ca. 1.5 , is remarkably close to that found experimentally (1.654 )” [Mikulski et al. , p. 6361 ; Gritsan and co-workers] .

This resonance structure of S2N2 is sketched as follows :

It certainly is an attractive model in many ways . The almost perfectly square , planar shape of the S2N2 molecule is explained . There is an aromatic type of p bonding over the sigma bonds , consisting of six p electrons in the four pz orbitals , which would stabilize the molecule . Resonance of the two singlet nitrogen electrons in this pi cloud would result in diamagnetism in S2N2 , which is observed . The nitrogen atoms unquestionably have a trigonal planar configuration ; this is shown in the stable , crystalline adduct S2N2(SbCl5)2 , which X-ray diffraction demonstrates has a linear shape :

In this compound the nucleophilic nitrogen sp2 lone pairs form coordinate covalent bonds with the electrophilic antimony atoms of the SbCl5 .

As attractive as it is , there are three problems with the resonance-stabilized model of S2N2 . First , there probably isn't any aromatic p stabilzation in the molecule , as it is well known to be very unstable , exploding at only a few degrees above room temperature . Second , the six electrons resonating in the four p bonds would result in a total bond order in the molecule of 2.5 [1.0 S–N sigma + 1.5 S–N pi] . This 2.5 bond order would result in a much shorter S–N bond length , possibly ~ 1.5 , than is actually observed in S2N2 (1.654 ) .

Third , the 90 bond angles are much too small for the usual trigonal planar coordination , whose ideal bond angle is 120 . The well-known Valence Bond octahedral hybrid orbital has 90 angles , but would be inapplicable to the nitrogen atoms in all molecules , and to the sulfur atoms in S2N2 . The composite hybrid orbital [comprised of two simpler hybrids] sp+p2 would have 90 angles . If all four atoms in S2N2 had such a sp+p2 hybridization , a perfectly square molecule could be constructed from their combination :

However , this model is unsatifactory , as the sp lobes of the nitrogen atoms are pointing in the wrong direction with respect to forming coordinate covalent bonds with electrophilic acceptor molecules such as SbCl5 . The nitrogens must have a “standard” trigonal planar sp2 + pz configuration , but with a “non-standard” type of orbital overlap with the sulfur atoms .

One possibility is that the nitrogen and sulfur bonds could have a bent “banana” orbital overlap , thereby forming slightly curved sigma covalent bonds . To examine this idea more closely I constructed a model of S2N2 using the Framework Molecular Model kit (Prentice-Hall , Englewood Cliffs , NJ) from my college chemistry days back in the mid 1960s . The kit is equipped with three types of small metal “jacks” with tetrahedral (109) , trigonal bipyramid (120 , equatorial) and octahedral (90/180) angles . It also has many thin plastic tubes in various colors , for constructing the interatomic bonds .

I tried making the model directly with trigonal jacks for the nitrogens and tetrahedral ones for the sulfurs , but ring closure was impossible . Then I tried a bent “banana” orbital overlap , which was more successful , but there was still considerable ring strain when any sort of jack was used to connect the overlap . Finally , I used adhesive tape to join the ends of the tubes together , and this provided the required flexibility for the “banana” orbital overlap , whose connection angle is comfortably between trigonal and linear (probably ~ 160) :

The resulting S2N2 molecule , while rather crude , was approximately square . A similar result was obtained when using trigonal planar jacks for the sulfur atoms . However , a tetrahedral sp3 sulfur configuration is more realistic , occurring in a great majority of organosulfur molecules . Trigonal planar sulfur is found in some heterocyclic compounds , the best known of which is undoubtedly thiophene . A possible reason for the minority of trigonal planar sulfur compounds compared to tetrahedral sulfur ones is that the former configuration is probably less energetically stable than the latter when completely filled with six electrons (as in thiophene's sulfur) . There is more steric repulsion between the two lone pairs (one axial , the other equatorial , 90) than in tetrahedral sulfur , in which the two lone pairs are more widely spaced apart (109) [see the model above] . In the case of thiophene , the aromatic stabilization energy it gains when its sulfur atom is trigonal exceeds the energy stabilization it would have with a tetrahedral configuration compared to being trigonal .

In the above model the singlet electrons in the nitrogen 2pz1 orbitals are shown with opposite spins . This could result in an overall zero magnetic moment for S2N2 , thereby making the compound diamagnetic , which is observed experimentally .

The slightly curved S–N “banana bonds” in the above model are weaker than conventional sigma covalent bonds ; these attenuated bonds would cause S2N2 to be thermally unstable , which is very much the case .

The concise overview by Evans and co-workers (2011) of various models of the electronic structure of S2N2 deserves to be quoted at some length :

“There is ........ the question of the bonding in S2N2 . It was first described with four localized s-bonds and six delocalized p-electrons , in accordance with the Hckel 4n+2 rule . Numerous theoretical studies seeking to elucidate the structure have found difficulty , however , in arriving at a clear consensus . Thus , the aromaticity implicit in the earliest models has been countered by the resemblance of the primary Lewis-type valence bond (VB) structure to a spin-paired diradical with a long transannular N–N bond . Yet , while favoring a singlet diradical description , spin-coupled VB theory calculations lend weight to the contrary view that the diradical character is associated solely with two coupled p-electrons , one from each of the S atoms . More recently , though , various ab initio and DFT calculations have been used to re-establish the case for aromaticity . In common with the currently unknown analogues Se2N2 and SeSN2 , S2N2 should now be described , according to the most recent analysis , as a 2-electron aromatic with minor singlet diradical character of 6–8% that can be attributed solely to the N atoms . High-level quantum chemical calculations have then been used to reproduce molecular properties for the S2N2 molecule close to those determined experimentally for the crystalline solid” (p. 5127) .

Evans et al. refer to a “long transannular N–N bond” ; a simple trigonometric calculation (sketch of the physical structure of S2N2 , above) shows that the N–N distance in the molecule is 2.33 . The N–N bond length in hydrazine , H2N–NH2 , is 1.45 ; in the nitrogen molecule , it's 1.0976 . The N=N double bond length is approximately the average of the hydrazine single bond and nitrogen triple bond lengths , i.e. 1.27 . The hypothetical N=N bond in S2N2 would therefore have to be almost double that , which is very doubtful . Similarly , a 2.33 long S=S bond , as hypothesized by Gerratt and McNicholas (mentioned by Evans et al.) , would be equally dubious .

It's also puzzling as to why sulfur atoms would transfer a valence electron to the nitrogens , so as to have 3pz1 for the p bond . Given that the Pauling electronegativities of sulfur and nitrogen are 2.58 and 3.04 respectively , the S–N bond shouldn't even be very polar . The nearly similar electronegativities of sulfur and nitrogen don't support the concept of electron transfer from S to N , or vice versa . Of course , they don't rule out a pi bond , but given the 2.33 N–N (or S–S) distance , that scenario seems unrealistic in S2N2 .

The overlapping of empty , higher energy level sulfur 4pz0 orbitals with the nitrogen 2pz1 orbitals could form a pi MO cloud over the S–N sigma bond framework :

Two-electron resonance over the four atoms would produce a pseudo-aromatic pi MO in the S2N2 molecule . It would result in diamagnetism in the compound , and would add half a bond order to the single S–N bond order . The 1.5 bond order would result in a contraction of the S–N bond length to the observed 1.654 , as noted above by Mikulski and co-workers . The question must be posed , though : how realistic is the use of the relatively high energy sulfur 4pz orbitals in the pi MO ?

It would be interesting to experimentally confirm the configuration of the sulfur atoms : are they tetrahedral (my model) or trigonal planar (resonance model) ? If a sulfur-selective electrophile could be found to complex with S2N2 as SbCl5 did with its nitrogens , an X-ray analysis of the adduct's crystal structure could shed some light on this question . For example , iron is known to bond strongly with sulfur but weakly to nitrogen in forming coordinate covalent compounds . Possibly iron pentacarbonyl would selectively bond to the sulfur atoms in S2N2 , forming an adduct somewhat similar to the known compound S2N2(SbCl5)2 :

In the above sketch the S2N2 has combined with two equivalents of Fe(CO)5 , displacing a CO ligand from each one to form the hypothetical compound S2N2[Fe(CO)4]2 . The iron(0) atoms have a trigonal bipyramid coordination , as in the Fe(CO)5 reagent . The adduct is shown with a non-linear (“chair”) structure , which might be observed if the sulfur atoms had a tetrahedral configuration , and retained it in the formation of the adduct .

Update (added February 10th , 2012) : a revised electronic structure for S2N2 combines features from both the resonance model with the 6 p electrons resonating in the four atom ring , and from the sp + p2 model discussed (and rejected) above . In this latest version both the sulfur and nitrogen atoms have a s + p2 + pz electronic configuration , as shown in the following sketch :

In this picture the sulfur 3pz lone pairs don't participate in the resonance ; rather , the nitrogen 2pz1 singlet electrons use their 3pz orbitals as a conduit to complete the “electrical circuit”, so to speak , around the ring . As mentioned above , the S–N bond order is 1.5 , with the 4 S–N s covalent bonds providing a single order , and the two resonating nitrogen singlet electrons in the p MO providing the 0.5 bond order . If the sulfur 3pz lone pairs participated in the p MO , an additional full bond order would have to be added to the structure , shortening the S–N bond lengths to ~ 1.5 , which isn't observed in S2N2 . The nitrogen singlet electrons are thus only “piggybacking” over the sulfur 3pz orbitals , which are energetically accessible and have the correct shape , symmetry , and orientation for MO formation with the nitrogen 2pz orbitals .

Positive attributes of this model are a rationalization of the square , flat structure of the S2N2 molecule , of its diamagnetism , of the bond angles and bond lengths / bond order , and of the possible pseudoaromatic 2p electron resonance . A negative aspect of the model is the somewhat nondirectional nature of the sulfur and nitrogen 3s2 and 2s2 lone pairs , respectively . The linear structure of the S2N2(SbCl5)2 coordinate covalent adduct is difficult to reconcile with the spherical shape of the the nitrogen 2s orbitals that would have to be used in forming the N–Sb bonds . Synthesis of a well-defined sulfur-selective S–X coordinate covalent complex of S2N2 , and the determination of its molecular structure by X-ray crystallography , might provide some clues in the resolution of this question .

A final possibility for the electronic structure of S2N2 is presented in the following sketch . There is no hybridization of the sulfur and nitrogen native p orbitals in this scheme :

A sigma overlapping of the unhybridized p orbitals would produce only feeble covalent S–N bonds ; an important benefit of the hybridization of native orbitals is a “concentration” of electron probability density , leading to the formation of strong covalent bonds between atoms . This non-hybridization model of S2N2 would actually be consistent with its highly unstable nature , detonating at ~ 30 C .


Tetrasulfur Tetranitride , S4N4


Brauer (pp. 406-408) describes S4N4 as a ..........

“light yellow-orange solid at ordinary temperatures ; becomes light yellow at –30 C ; on heating to 100 C , orange-red ...... m.p. 178 C , b.p. ~ 185 C ; explodes at > 185 C ....... readily soluble in benzene , CS2 , dioxane ; insoluble in water”. The Wikipedia article on S4N4 describes it as a “vivid orange” or “golden-poppy colored solid” which melts at 187 C (this latter melting point is more applicable to highly purified material) . Tetrasulfur tetranitride is thermally unstable , exploding at its melting point , and is also mechanically unstable ; highly pure S4N4 crystals are shock sensitive and will detonate if ground in a mortar . It's an insulator with an electrical conductivity of sRT = 10-14 ohm-1-cm-1 (Labes , Love , and Nichols , p. 2) . It's also diamagnetic , with a magnetic susceptibility of cmol = –102 x 10-6 cgsu (Allen , Table 1 , p. 38) . S4N4 has an asymmetrical shape and a small dipole moment of p = 0.52 D resulting from its relatively nonpolar S–N bonds .

Because of its unstable , explosive nature S4N4 isn't offered commercially , but must be prepared by the researcher following a published synthesis procedure . The preparations generally involve the reaction of sulfur monochloride or dichloride with ammonia or ammonium chloride .

Tetrasulfur tetranitride has an remarkable folded molecular structure , usually described as a “cradle” conformation :

This sketch was adapted from Fig. 1 , “Bond Distances and Angles”, by Sharma and Donohue (p. 894) . My thanks to the copyright holder .

The N–S–N bond angles of 105 indicate that the sulfur atoms in S4N4 are tetrahedral sp3, and are therefore electronically inert linking atoms in the molecule . The S–N–S bond angles , at 113, are suggestive of a compressed trigonal planar configuration for the nitrogen atoms . The arithmetic average of the eight S–N bond lengths in Sharma and Donohue's sketch is 1.616 .

The S4N4 molecule seems to be “curled up”, so to speak . In its hydrogen-reduced analogue , tetrasulfur tetraimide [S4(NH)4] , the N–S–N bond angles = 109 , the S–N–S bond angles = 123 , and the S–N bond length averages ~ 1.673 . While still somewhat puckered , the S4(NH)4 ring is flatter than the more rounded , folded shape of S4N4 . Clearly , hydrogenation of the latter's nitrogens has broken some bonds and has permitted a relaxation in the curled-up S4N4 form . The tetrahedral and trigonal planar configurations of the sulfur and nitrogen atoms , respectively , are now very obvious in S4(NH)4 , and imply they are the same in S4N4 , while being somewhat compressed in it because of its cradle shape .

As with S2N2 , I once again deployed my Framework Molecular Model kit and began making various models of S4N4 . Despite the simplicity of these little models – or maybe because of it – I was able to study the nitrogen atoms' 2pz orbital overlap in various molecular configurations , with revealing results . In the first model , the sulfurs are tetrahedral and the nitrogens are trigonal planar :

A top view of the molecule shows the neat symmetry of the “banana bonds” and the square shape of the S–N ring :

When the nitrogens are trigonal planar , their 2pz orbitals with the singlet “fifth” electrons can overlap in a rather odd manner . The positive and negative symmetry lobes can overlap tip-to-tip with corresponding orbital lobes on adjacent nitrogen atoms , but in an alternating pattern above and below the molecular “equator” . This 2pz orbital overlap should thus produce N–N “banana bonds” around the periphery of the molecule . There are four nitrogen 2pz valence electrons resonating in the four sigma bonds ; therefore they could be considered as one-electron bonds . These peculiar N–N resonating one-electron bonds could have five effects on the S4N4 molecule :

First , while they are expected to be very weak , they could nevertheless add a small stabilizing secondary 0.5 bond order to it (the normal S–N sigma covalent bonds being the primary 1.0 bond order) . Note that while the nitrogen 2pz1 orbitals' overlap is sigma and not pi in nature , the continuous –N–N–N–N– “daisy-chain” nature of of the overlap would permit a delocalization of the four 2pz1 electrons around the perimeter of the molecule . This resonance could provide some stabilization to S4N4 , if only of a partial bond order .

Second , this secondary bond order to S4N4 would result in a contraction of the observed S–N bond length from that in S4(NH)4 [1.673 , considered to be a single S–N bond] to that in S4N4 [1.616 , considered to be of a 1.5 S–N bond order ; see comments by Mikulski et al. , quoted above in the S2N2 section below the S(II)S(IV) resonance sketch , and in the Gritsan and co-workers reference below] .

Third , the resonance would pair up the nitrogen atoms' singlet “fifth” electrons , thus resulting in diamagnetism in the compound , which has been observed experimentally .

Fourth , these weak N–N one-electron bonds would “freeze” the molecule into its characteristic cradle shape . They could therefore be responsible for the peculiar folded conformation of S4N4 ; and ,

Fifth , they might also be responsible for the observed thermochromism in the material [as described by Brauer , quoted above] . Because the 2pz orbitals are overlapping tip-to-tip , the resulting molecular orbital is sigma and will have nodes around the nitrogen kernels . These nodal sigma MOs will impose a thermal dependence on the electron resonance in them . An analogous situation occurs in the semiconductors , whose electrical conductivity is similarly temperature dependent , and which also have nodal metallic bonds . As S4N4 is cooled down , the 2pz1 electrons become more and more localized between the nitrogen kernels . The color fades to a pale yellow . As it is heated , more and more of the energetic electrons are able to tunnel through the nodes , and their resonance around the ring increases . As the electron resonance strengthens , the solid's color intensifies to a deep red at 100 C . As is well known in organic compounds , the stronger the electron resonance is in the molecule , the more intense is its color . For example , such an increase in color is noted in the series of aromatic compounds , from benzene and napthalene (colorless) through to tetracene (orange) and pentacene (purple) . An extreme example of this phenomenon is provided by polyacetylene , which has a bright silvery appearance and a metallic luster .

The addition of hydrogen atoms to S4N4 to form S4(NH)4 breaks these N–N bonds and permits the molecule to unfold into a flatter , if still puckered , eight-atom ring . Pritchina and co-workers found evidence of a transitory cyclic eight-atom compound corresponding to an unfolded form of S4N4 when its solution in hexane is irradiated with UV light . S4N4 strongly absorbs the energetic UV energy at 254 nm , apparently resulting in a cleavage of the N–N bonds .

Gopinathan and Whitehead [cited in various electronic structures] noted the existence of a diamagnetic ring current in S4N4 , but attributed it to a S–N p-p p resonance :

“The diamagnetic ring current in S4N4 suggests electron delocalization around the SN ring . From the LMOs the diamagnetic ring current is obviously due to the p-orbital lone pair electrons on nitrogen delocalizing into the p-orbitals on the sulfur atoms to which it is directly bonded” (p. 1347) .

In my model of S4N4 the diamagnetic ring current , originally observed by Mason , would be produced by the N–N one-electron bonds resonating around the molecule's perimeter . In the proposed model of the electronic structure of poly(sulfur nitride) , there are similarly N–N resonating one-electron bonds , but the nitrogen “fifth” valence electrons are delocalized throughout the polymer chains ; the material is metallic as a result . In this model of S4N4 the N–N one-electron bonds are localized around its circumference , so tetrasulfur tetranitride is an electrical insulator . A comparison can be made to benzene [insulator] , with resonating but localized p bonds , and graphite [metallic solid] , with resonating and delocalized p bonds .

In a second model of tetrasulfur tetranitride both the sulfur and nitrogen atoms have a tetrahedral sp3 configuration :

The dihedral angle made by the N–S–N “peaks” relative to the square plane of the four nitrogen atoms is exactly 90 (unfortunately this structural feature isn't shown above in Sharma and Donohue's sketch of S4N4) . Thus , in this second model the nitrogen axial sigma orbitals are precisely parallel in each of the two sets . If each s orbital has the “fifth” nitrogen singlet electron (the lone pairs are in the less sterically-hindered equatorial s lobes) , it might be possible for these two sets of parallel s lobes to overlap to form a s type of molecular orbital .

Using the trigonometric formula a2 = b2 + c2 – 2bc cos A , with a = the N–N distance across the sulfur atom , b = c = 1.616 , and A = N–S–N = 105 , the value for a = 2.5459 . As mentioned above , a typical N–N single bond length (as in hydrazine) would be ~ 1.45 , so the hypothetical N–N sigma bond would seem to be ruled out . If there actually were such bonds between the two sets of nitrogens , they would be very diffuse and weak . Also , in this second model the two N–N bonds would be spatially isolated , and no diamagnetic ring current would be observed in S4N4 .

There are at least five possible conformations for eight-atom rings :

This sketch was adapted from Fig. 3 , “Some Configurations of the Eight Ring”, by Lu and Donohue (p. 821) . My thanks to the copyright holder .

I built Framework Molecular Models for all five of the S4N4 configurations , first with trigonal planar nitrogens , and then again with tetrahedral nitrogen atoms in the ring . The puckered X8 ring was the most interesting , because it's the usual conformation of “octosulfur” S8 , which comprises the common and familiar “flowers of sulfur” :

This image was copied from the Wikipedia web page , “Sulfur”. I thank the author of this sketch , and Wikipedia , for implied permission to reproduce it on this web page .

In a sense , S4N4 can be thought of as a derivative of S8 , with four sulfur atoms replaced by four nitrogens . The molecular model clearly shows that no overlapping of the nitrogens' 2pz orbitals with their singlet electrons are possible when S4N4 is in this conformation :

A top view of the puckered conformation of S4N4 shows the symmetrical ring and the nitrogen 2pz orbitals :

The tub and chair conformations of S4N4 were equally unsuccessful with respect to any possible overlapping of the nitrogen 2pz orbitals . The butterfly conformation permitted a possible overlap of either the + or – lobes of the 2pz orbitals separately , but not both simultaneously .

The curled-up cradle conformation is the only one having the essential four co-planar nitrogen atoms and the correct orientation of those nitrogens so that a complete and proper (if somewhat unusual) overlap of the nitrogen 2pz orbitals is possible . It could be that in the formation of S4N4 the ring undergoes the various conformations examined ; when it curls into the cradle conformation the N–N 2pz1–2pz1 one-electron bonds form and the molecule is “locked” into that configuration .

Sharma and Donohue sketched two models that were then (1963) considered as reasonable candidates for the molecular structure of S4N4 :

This sketch was adapted from the illustration on p. 891 in the article by Sharma and Donohue . My thanks to the copyright holder .

The co-planar sulfur atoms model was appealing because both the sulfurs and the nitrogens had the correct valences , the latter with the familiar three covalent bonds . In the co-planar nitrogen atoms model the sulfurs had the conventional divalent sulfur , but also required the strange and perplexing –N– . Sharma and Donohue's painstakingly careful X-ray analysis of S4N4 (see their sketch above) validated beyond any doubt the co-planar nitrogens model .

Ten years earlier (in 1953) , Lippincott and Tobin had carried out a meticulous infrared and Raman spectroscopic analysis of S4N4 . They assigned the 925 cm-1 IR absorption band , and the 888 and 934 cm-1 Raman bands , to the N–N bond stretching frequency , by analogy with that in hydrazine (at 893 cm-1, Raman) :

This sketch was adapted from Fig. 3B , p. 1560 in the article by Lippincott and Tobin . My thanks to the copyright holder .

The absorption bands assigned to the N–N bond stretching frequency in S4N4 were entirely absent in the IR and Raman spectra of a co-analysed sample of S4(NH)4 . They remarked ,

“We are now in a position to see why the reduction products of nitrogen tetrasulfide never contain N–N bonds . The fact that the infrared spectrum of nitrogen hydrogen sulfide very closely resembles that of nitrogen tetrasulfide in the region 250-1000 cm-1 makes it appear probable that the skeleton is intact and that the N–N bonds of nitrogen tetrasulfide were broken to form N–H bonds . In other words , the N–N bonds were attacked more readily than the N–S bonds” (p. 1563) .

A decade after Lippincott and Tobin's report Sharma and Donohue conclusively solved the molecular structure of S4N4 and thereby completely discredited the co-planar sulfur atoms model , which contained the N–N bonds . Thereafter , any subsequent studies of tetrasulfur tetranitride either didn't mention the possibility of N–N bonds in the compound , or even specifically refuted the concept . For example , Bragin and Evans (1969) studied the Raman and infrared spectra of both S4N4 and S2N2 ; their IR spectrum of S4N4 was quite similar to that of Lippincott and Tobin . While they detected the strong 925 cm-1 band in the solid [Nujol mull] IR spectrum first observed by Lippincott and Tobin , they didn't provide an assignment for it . The the nearby 938 cm-1 band (dioxane solution) was assigned to a S–N stretching mode . Bragin and Evans made no mention at all of N–N bonds in S4N4 . They did suggest the possibility of a non-bonded S–S interaction in the molecule :

“....for the nonbonded S–S interaction a repulsive force constant in the range 1.13-1.36 was obtained . This value is comparable to that of the main force constants of the molecule and supports the view that the nonbonded S–S repulsion plays a significant role in the molecular potential field of S4N4” (pp. 274-275) .

Touzin (1981) also carried out a Raman and infrared spectroscopic analysis of S4N4 ; he reported a band at 937 cm-1 , but assigned it to a ring vibration . He also found absorption bands at 180 and 213 cm-1 , and assigned them to S–S bond stretching . No mention was made of the 925 cm-1 band observed by previous researchers .

S–S bonds in S4N4 , if only weak and of thin density , are now considered almost conventional . Modern-day sketches of the compound often have a dashed line connecting the opposite pairs of sulfur atoms in the illustrations . As pointed out earlier , the N–S–N bond angles in both S4N4 and its “relaxed , unfolded” analogue , S4(NH)4 , are strongly indicative of a tetrahedral configuration of the sulfur atoms in these compounds . Tetrahedral means sp3 ; sp3 means two covalent S–N bonds plus two lone pairs ; and that means the sulfur atoms are just electronically inert linking atoms in S4N4 and S4(NH)4 . If anything the sulfur lone pairs should produce some repulsion , not bonding (cf. Bragin and Evans' comment above) , between the two opposed pairs of sulfur atoms in the ring .

Unfortunately , when the co-planar sulfur atoms model of S4N4 was discredited by Sharma and Donohue in 1963 , the idea of N–N bonds in the compound was also discarded . Perhaps the concept might be revisited , but within the framework of the correct molecular structure of tetrasulfur tetranitride . The model having N–N 2pz1–2pz1 resonating one-electron bonds with the unusual “banana” type of overlap could be a good starting point for a renewed investigation of the chemical bonds in tetrasulfur tetranitride :

It might be quite difficult , though , to experimentally verify the existence of the four N–N one-electron bonds . They are undoubtedly thin and feeble , and would contribute only half of a bond order to the molecule . Their IR absorption might be minor (or nil) , and could easily be masked by the overwhelming S–N bond frequencies and ring flexing and bending . There is also the unresolved question of the 925 cm-1 band in the IR absorption spectrum of S4N4 . Is it genuine , i.e. reproducible , and can it really be attributed to the N–N bond stretching frequency ? And are there really S–S bonds in the compound ?

In the companion web page to this one , “Three Models of the Metallic Bond in Poly(sulfur nitride)”, the instrumental technique of ARPES/ARPUS (angle-resolved photoelectron/ultraviolet spectroscopy) was suggested as a possible method of determining the nature of the metallic bond orbitals in (SN)x . ARPES might also be used to detect the hypothetical N–N resonating one-electron bonds in tetrasulfur tetranitride . They are expected to be at a higher energy level , and physically outside , the stronger S–N sigma covalent bonds .

Would the somewhat fragile N–N bonds survive in the ARPES/ARPUS experimental environment ? Recall Pritchina and co-workers' photolysis experiments with S4N4 , in which the molecule strongly absorbed the UV light and unfolded into an unstable , puckered eight-atom ring . This transient intermediate in turn rearranged into a six-atom ring with a –SN attachment : a S–N analogue of styrene . The ARPES/ARPUS energy input into the S4N4 test sample might well overstress its delicate chemical stability .

The essence of the scientific method is the experimental testing of models . Those of the chemical bonding in S2N2 and S4N4 discussed above provide a simple , fresh , new approach to understanding the electronic structures of these two compounds . I hope this essay with its admittedly unorthodox ideas will be thought-provoking , and will stimulate more experimental study of S2N2 and S4N4 in the ongoing effort of resolving the long-standing puzzle of their chemical bonding .


References , Notes , and Comments


various electronic structures : A brief summary of various theoretical studies of the electronic structure of S4N4 is provided by W.R. Salaneck et al. , “Direct Determination of the Electronic Structure of S4N4 by X-ray and Ultraviolet Photoemission”, Phys. Rev. B 13 (10) , pp. 4517-4528 (1976) ; p. 4524 . These researchers observed a transfer of electron density from the sulfurs to the nitrogens :

“The X-ray photoemission spectra of the N(1s) and S(2p) core levels , when compared with those of charge neutral atoms in N2 and S8 molecules , respectively , indicate an effective charge transfer of about one-half of an electronic charge from the sulfur atoms to the nitrogen atoms” (p. 4526) ;

A.G. Turner and F.S. Mortimer , “On the Electronic Structure of Tetranitrogen Tetrasulfide”, Inorg. Chem. , 5 (5) , pp. 906-910 (1966) . They emphatically declared :

“Lippincott and Tobin assigned the coplanar sulfur structure on the basis of the occurrence of a Raman line at 888 cm-1 corresponding to an N–N bond (to be compared with a line at 893 cm-1 for N2H4) .The molecular orbital calculations , SCC–MO , show absolutely no tendency for bonding between nitrogen atoms since the calculated overlap population between nitrogen atoms is negative or zero under all parametizations . Hence , both experiment and theory argue against a structure containing a N–N bond” (p. 907) ;

M.S. Gopinathan and M.A. Whitehead , “The Electronic Structure and Localized Molecular Orbitals in S4N4 by the CNDO/BW Theory”, Can. J. Chem. 53 (9) , pp. 1343-1347 (1975) [PDF , 328 KB . Note : this file can be opened only with Adobe Acrobat Reader v. 6 or later . If desired , this application can be downloaded for free from Oldversion.com] . They concluded ,

“S4N4 has a molecular structure with coplanar nitrogen atoms . The electronic formula for the molecule is the polar Lewis structure B [on p. 1344] . There is no s-p hybridization at nitrogen or sulfur . The N–S and S–S bonds are bent single bonds involving pure p-orbitals . There is no N–N bond . Electron delocalization occurs by delocalization of the p-electrons in a nitrogen lone pair to the p-orbitals on the sulfur atoms to which the nitrogen is bonded” (p. 1347) ;

D.R. Salahub and R.P. Messmer , “A Study of the Electronic Structures of SN , S2N2 , S4N4 , NO , and N2O2 and Their Implications for (SN)x”, J. Chem. Phys. 64 (5) , pp. 2039-2047 (1976) ;

R.H. Findlay et al. , “Electronic Structure of the Sulfur Nitrides . Ab Initio Calculations and Photoelectron Spectra”, Inorg. Chem. 19 (5) , pp. 1307-1314 (1980) . These authors concluded that the “localized molecular orbitals”– i.e. roughly corresponding to a Valence Bond description – in S4N4 consists of 8 S–N bonds , 2 S–S bonds , 4 lone pairs on the sulfurs (one pair each) , and 8 lone pairs on the nitrogens (2 pairs each) ; see Table VII , p. 1314 . Their figure 8 on p. 1314 shows an ionic S4N4 molecule , with full positive charges on the sulfurs and full negative charges on the nitrogens . Such a structure would be strongly polar and would have a large dipole moment . However , Rogers and Gross (dipole moment , below) found that S4N4 was relatively nonpolar , with a dipole moment of p = 0.52 D , as mentioned above . Water and many polar organic solvents have dipole moments several times that . The solubility of S4N4 in relatively non-polar solvents such as benzene , dioxane , and CS2 , and its insolubility in water , are consistent with a non-polar , un-ionized molecular structure . These observed polarity properties of S4N4 suggest that resonance structures involving charge transfer from sulfur to nitrogen or vice versa , resulting in partial or full ionic charges on the atoms , are unlikely .

R.D. Harcourt , T.M. Klaptke , A. Schulz , and P. Wolynec , “On the Singlet Diradical Character of S2N2”, J. Phys. Chem. A , 102 (10) , pp. 1850-1853 (1998) . Resonance structures for S2N2 .

Brauer : G. Brauer (ed.) , Handbook of Preparative Inorganic Chemistry , 2nd edition , vol. 1 , Academic Press , New York , 1963 ; S2N2 , pp. 409-410 ; S4N4 , pp. 406-408 . This exhaustive inorganic chemistry synthesis compendium (Vols. 1 & 2 combined) can be downloaded for free from the Sciencemadness.org library resources web page [PDF , 19,090 KB] . Note : this PDF file can be opened only with Adobe Acrobat Reader v. 6 or later . If desired , a suitable version of this application can be downloaded for free from Oldversion.com .

Mikulski and co-workers : C.M. Mikulski et al. , “Synthesis and Structure of Metallic Polymeric Sulfur Nitride , (SN)x , and Its Precursor , Disulfur Dinitride , S2N2”, J. Amer. Chem. Soc. 97 (22) , pp. 6358-6363 (1975) .

Gritsan and co-workers : N.P. Gritsan et al. , “Matrix Isolation and Computational Study of the Photochemistry of 1,3,2,4-Benzodithiadiazine”, J. Phys. Chem. A 111 (5) , pp. 817-824 (2007) [PDF , 300 KB] . These researchers calculated S–N and S=N bond lengths of 1.71 and 1.56 , respectively , in the title compound (Figure 8 , p. 823) :

X-ray diffraction demonstrates : R.L. Patton and K.N. Raymond , “The Crystal and Molecular Structure of S2N2(SbCl5)2”, Inorg. Chem. 8 (11) , pp. 2426-2431 (1969) .

Evans and co-workers : R. Evans , A.J. Downs , R. Kppe , and S.C. Peake , “Vibrational Properties of the Disulfur Dinitride Molecule , S2N2 : IR and Raman Spectra of the Matrix-Isolated Molecule”, J. Phys. Chem. A 115 (20) , pp. 5127-5137 (2011) .

iron pentacarbonyl : S2N2 could conceivably form a dithiolene type of adduct with iron pentacarbonyl :

Perhaps more effective sulfur-selective candidate electrophiles for preparing S2N2 coordinate covalent adducts might be heavy metal cations such as silver(I) [5s0] and mercury(II) [6s0] . These two cations in particular are well-known for having especially strong affinities for sulfur , certainly much more so than for nitrogen . Both silver(I) perchlorate , AgClO4 , and mercury(II) chloride , HgCl2 , are soluble in various organic solvents (MeOH , EtOH , benzene , and acetone ; possibly also in ethyl ether and THF) . S2N2 is soluble in ethyl ether and maybe it dissolves in the other organic solvents mentioned without reaction or decomposition . Insoluble coordination compounds might precipitate from the combination of Ag1+ and Hg2+ with S2N2 in a suitable anhydrous organic solvent .

mechanically unstable : A.F. Cotton , G. Wilkinson , C.A. Murillo , and M. Bochmann , Advanced Inorganic Chemistry , 6th edition , John Wiley , New York , 1999 :

“The compound [S4N4] must be handled with care , since grinding , percussion , friction , or rapid heating can cause it to explode” (p. 509) . S4N4 is discussed on pp. 509-511 .

Labes , Love , and Nichols : M.M. Labes , P. Love , and L.F. Nichols , “Polysulfur Nitride – A Metallic , Superconducting Polymer”, Chem. Rev. 79 (1) , pp. 1-15 (1979) .

Allen : C.W. Allen , “The Chemistry of Tetrasulfur Tetranitride”, J. Chem. Educ. 44 (1) , pp. 38-44 (1967) .

dipole moment : M.T. Rogers and K.J. Gross , “The Electric Moments of Some Sulfur and Selenium Compounds”, J. Amer. Chem. Soc. 74 (21) , pp. 5294-5296 (1952) .

synthesis procedure : M. Becke-Goehring , “Sulfur Nitrides”, Inorg. Synth. 6 , pp. 123-128 , E.G. Rochow et al. (eds.) , McGraw-Hill , New York , 1960 ; M. Villena-Blanco and W.L. Jolly , “Tetrasulfur Tetranitride”, Inorg. Synth. 9 , pp. 98-102 , L.F. Audrieth et al. (eds.) , McGraw-Hill , New York , 1967 ; W.L. Jolly , Synthetic Inorganic Chemistry , Prentice-Hall , Englewood Cliffs (NJ) , 1960 ; pp. 166-168 ; idem. , The Synthesis and Characterization of Inorganic Compounds , Prentice-Hall , Englewood Cliffs (NJ) , 1970 ; pp. 500-502 . The actual sulfur precursor for S4N4 is sulfur dichloride , SCl2 , a corrosive , lachrymatory , viscous , red liquid , b.p. 60 C . It's somewhat unstable and is difficult to obtain pure , so in practice the sulfur source usually employed in S4N4 syntheses is the stable sulfur monochloride [disulfur dichloride] , S2Cl2 . This latter chemical is a yellow-red , oily liquid , b.p. 137 C , and is also corrosive and lachrymatory like SCl2 . Sulfur monochloride is chlorinated in situ to SCl2 in the initial stages of the S4N4 preparation . S2Cl2 (98% reagent grade) is offered commercially , eg. by the Aldrich Chemical Company .

Sharma and Donohue : B.D. Sharma and J. Donohue , “The Crystal and Molecular Structure of Sulfur Nitride , S4N4”, Acta. Cryst. 16 (9) , pp. 891-897 (1963) .

tetrasulfur tetraimide : D. Gregson , G. Klebe , and H. Fuess , “Charge Density Distribution in Tetrasulfur Tetraimide (S4(NH)4)”, J. Amer. Chem. Soc. 110 (25) , pp. 8488-8893 (1988) . See esp. Figure 5 , p. 8492 for a sketch of S4(NH)4 showing its bond lengths and angles .

one electron bonds : L. Pauling , The Nature of the Chemical Bond and the Structure of Molecules and Crystals , 3rd ed. , Cornell University Press , Ithaca (NY) , 1960 ; p. 340 ; A. Holden , The Nature of Solids , Dover Publications , New York , 1992 [reprint of the Columbia University Press textbook , 1965] ; p. 91 .

Pritchina and co-workers : E.A. Pritchina , N.P. Gritsan , A.V. Zibarev , and T. Bally , “Photochemical Study on the Reactivity of Tetrasulfur Tetranitride , S4N4”, Inorg. Chem. 48 (9) , pp. 4075-4082 (2009) [PDF , 404 KB] .

Mason : J.B. Mason , “Electronic Structure of Tetrasulphur Tetranitride , S4N4”, J. Chem. Soc. A 1969 , pp. 1567-1570 . I've only read the abstract of this paper , and unfortunately have been unable to access its full text .

Lu and Donohue : C-S. Lu and J. Donohue , “An Electron Diffraction Investigation of Sulfur Nitride , Arsenic Disulfide (Realgar) , Arsenic Trisulfide (Orpiment) and Sulfur”, J. Amer. Chem. Soc. 66 (5) , pp. 818-827 (1944) .

various conformations : The SN compounds may be fluxional to a certain extent . One of the best known examples of a fluxional molecule is that of iron pentacarbonyl , mentioned above . Fe(CO)5 flip-flops to and from the trigonal bipyramid and square pyramid structures . In Valence Bond terms these structures correspond respectively to the sp3dz2 and the sp3dx2-y2 hybrid orbitals on the iron atom . Since the iron 3dz2 and 3dx2-y2 orbitals are at the virtually same energy level in the molecule , the hybrid orbitals can readily change to and from sp3dz2 and sp3dx2-y2 . As they change back and forth , the iron pentacarbonyl structure correspondingly flips back and forth (the flip-flopping has the technical name of the Berry mechanism) .

S2N2 , S4N4 , and (SN)x may behave in somewhat the same way , at least in their formative stages . The sulfur atoms are most thermodynamically stable in their tetrahedral sp3 configuration , as mentioned above . The nitrogen atoms may try out several different configurations : sp3 , sp2 + pz , s + p3 , and so on . S4N4 may also try out the various ring conformations , as discussed above . Finally , when the most stable electronic configurations and structural conformations have been achieved , the molecule is frozen into its familar form . When S4N4 folds into its cradle shape , the NN bonds form and the molecule “locks up . When the nitrogens in (SN)x try out the s + p3 configuration , the metallic bond forms along the polymer spines and it's “frozenas a metallic solid .

Lippincott and Tobin : E.R. Lippincott and M.C. Tobin , “The Vibrational Spectra and Structure of Nitrogen Tetrasulfide”, J. Chem. Phys. 21 (9) , pp. 1559-1565 (1953) .

with that in hydrazine : P.A. Gigure and I.D. Liu , On the Infrared Spectrum of Hydrazine”, J. Chem. Phys. 20 (1) , pp. 136-140 (1952) . These researchers stated ,

Finally the N–N fundamental vibration n5 is expected to be weak in infrared since it involves an essentially nonpolar bond . In addition , it falls in a region of strong absorption from the NH wagging modes . No definite evidence of it was observed in the spectrum of the vapor , but in the liquid a remarkably strong maximum at 873 cm-1 corresponds to a Raman line of moderate intensity at 876 cm-1 . This frequency seems a little low compared to the O–O vibration in hydrogen peroxide (877 cm-1) and the C–N vibration in methylamine (1045 cm-1) . From electron diffraction and x-ray data the N–N bond length in hydrazine is known to be 1.46 ; application of Badger's rule yields about 960 cm-1 for the corresponding frequency . Values of 816 and 801 cm-1, respectively , have been found for it in methylhydrazine and sym-dimethylhydrazine , the gradual decrease in frequency being caused by an increase in the reduced mass of the vibrating groups” (p. 140) .

J.C. Decius and D.P. Pearson , “The Infrared Absorption of Crystalline and Liquid Hydrazine Monochloride and Monobromide”, J. Amer. Chem. Soc. 75 (10) , pp. 2436-2439 (1953) . These authors found a somewhat higher value for the N–N bond stretch absorption in hydrazine hydrochloride :

For N2H5Cl , this region may be expected to include the N–N stretch , a torsional vibration and the lattice modes . In agreement with Edsall and Scheinberg , we assign 973 cm-1 (which shifts only to 940 cm-1 in N2D5Cl) as the N–N stretch” (p. 2438) .

Bragin and Evans : J. Bragin and M.V. Evans , “Vibrational Spectra and Structure of S4N4 and S2N2”, J. Chem. Phys. 51 (1) , pp. 268-277 (1969) ; see esp. Table I , p. 270 .

Touzin : J. Touzin , “Vibration Spectra of Sulfur Tetranitride”, Coll. Czech. Chem. Commun. 46 (11) , pp. 2613-2619 (1981) ; see esp. Table 1 , p. 2615 .

S–S bond stretching : R.M. Silverstein , F.X. Webster , and D.J. Kiemle , Spectrometric Identification of Organic Compounds , 7th edition , John Wiley , New York , 2005 :

“Disulfides : The S–S stretching vibration is very weak and falls between 500 and 400 cm-1 ” (p. 106) .

N.B. Colthup , L.H. Daly , and S.E. Wiberly , Introduction to Infrared and Raman Spectroscopy , 3rd edition , Academic Press , Boston (MA) , 1990 . In organic disulfides the S–S stretching frequency exhibits a weak band at 500 cm-1 (p. 371) .

On the web page , Infrared Spectroscopy , the S–S absorption is listed as having a weak band in the 500-540 cm-1 range in the “Other Functional Groups tabulation .

No mention of N–N IR frequencies was made in these three references , nor in any other IR spectroscopy reference I consulted (eg. in the CRC Handbook of Chemistry and Physics) .

tetrahedral configuration : Salaneck and co-workers [various electronic structures above] noted :

“From the chemical perspective , sulfur in S4N4 corresponds to sp3 hybridization . The NSN bond angle is about 105, and thus a small amount of S(3d) mixing is necessary to account for the geometry (p. 4521) . I don't agree with this ; the slight (4)compression of the N–S–N bond angles can be accounted for by the steric compression of the two lone pairs on the sulfurs , and by the curled , compressed geometry of the S4N4 molecule in general . The 3d orbitals in sulfur are rarely , if ever , used in chemical bonding . See my discussion of this in another Chemexplore web page .

In a Valence Bond analysis the sulfur atoms in S4N4 simply have a tetrahedral sp3 configuration . The trigonal planar hybrid orbital is less energetically favorable for sulfur than the tetrahedral one unless it is involved in an aromatic resonance (as in thiophene) , which doesn't occur in S4N4 . Other hybrid orbitals , such as the trigonal bipyramid sp3d hybrid , are also unsatisfactory for the sulfur atoms .

The concept of SS bonding in S4N4 is derived from the Molecular Orbital Theory . In MO analyses the sulfur atoms have higher energy orbitals which can overlap to form weak SS bonds :

“Perhaps the most significant feature of the frontier orbitals is the effect of the weak SS interaction on the wave functions and the corresponding orbital energies . The weak SS (4b2) bonding orbital has the lowest ionization potential of any filled orbital . In particular , this highest occupied MO contains almost 70% of its charge density in the SS bonding portion of the wave function . The lowest unoccupied MO , on the other hand , contains over 80% of its charge density in the corresponding SS antibonding portion of the wave function (Salaneck et al. , p. 4524) .


See also the related web page , “Three Models of the Metallic Bond in Poly(sulfur nitride)


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