An Appreciation of the Classic Valence Bond Theory

8/10/2019 An Appreciation of the Classic Valence Bond Theory

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An Appreciation of the Classic Valence Bond Theory

Chemical bonding in a variety of inorganic compounds will be discussed in thisweb page , using the Valence Bond (VB) theory to describe their electronicstructures . VB is infrequently employed these days by chemists , who generally

prefer the Molecular Orbital (MO) theory for electronic analyses . My objective isto show in the case studies below that VB is still a valuable tool in helping usunderstand chemical bonding in many types of materials .

VB was developed in the late 1920s and early 1930s by several theoreticalchemists . Paulingis usually given most of the credit for the popularization of VB ;indeed , he was awarded the 1954Nobel Prize in Chemistryprimarily for this

accomplishment (thereferencesare listed at the end of this web page .Underlinedblue hyperlinkscan be clicked when online to download the PDF orHTML file , which will open in a new window) . Actually , the peak of VBs

popularity had come and gone by the 1950s , as it had been mostly displaced bytherival MO theory(PDF , 55 KB) by then .

Valence bond theory , as originally developed by Heitler , London , Slater , andPauling (it was originally known asHLSP, after their initials) , was a highlyabstract , mathematical concept in the domain of theoretical chemistry . Indeed ,the physics underlying VB was so abstruse , and its mathematical treatment socomplex , it took Pauling three years to simplify VB theory to the point where itcould be understood by other chemists . I've read Pauling's various theoretical

papers concerning VB , and I must admit I can't follow the math in them ; but Imay be in distinguished company in that aspect . Acharming anecdoteis relatedabout the time when Albert Einstein , while visiting the United States , auditionedone of Pauling's VB lectures :

In 1931 , Albert Einstein , in Pasadena for several months being wooed for afaculty position at Caltech , sat in on a Linus Pauling seminar . Knowing that he

had the world's greatest living scientist in his audience , Pauling worked especiallyhard to explain at length his new ideas about the application of wave mechanics tothe chemical bond . Afterward , Einstein was asked by a reporter what he thoughtof the young chemist's talk . He shrugged his shoulders and smiled . It was toocomplicated for me, he said.

Only in the following years of practical application in the study of small organicmolecules was VB transformed into a familiar , useful implement in the chemist'sintellectual toolbox . A set of hybrid orbitalsemerged that could be used to providea realistic picture of the covalent bonds of small molecules . Mathematically-

inclined theoretical chemists like Pauling could skilfully use VB to calculate bondlengths , angles , and strengths in covalently-bonded molecules (for example ,
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see these articles) . The average chemist , however , usually employed VB ina qualitative, rather than quantitative way to understand the chemical bonding inthe system of interest . I think it's this extraordinary pictorialquality of VB thatmade it so popular among chemists in the 1930s and 1940s , before it was replaced

by the more computational MO theory .MO theory is generally considered to be much more effective than VB (but maybenotmodern VB)as a quantitative analytical tool , especially in fields such asspectroscopy . VBs continuing value to chemists , which we will see amplydemonstrated as this web page unfolds , derives from its ability to portray a simple, clear picture of a covalently-bonded system , whether organic or inorganic , andwhether molecular or nonmolecular . That's why I refer to the original concept ofthe valence bond theoryclassic VBin its non-mathematical form , as pictureVB. Such picture VB is never used in isolation , as some sort of abstraction ; it's

always correlated in a reasonable , rational manner with the known physical andchemical properties of the material studied .

Let's now survey the hybrid orbitals , which are the key elements in classic andpicture VB .

Hybrid Atomic Orbitals

The theory of the covalent bond was first proposed in 1916 by Lewis, whosuggested that pairs of shared valence electrons were located between theirrespective atoms and bonded them together . The actual bonding force waselectrostatic , between the negative electrons and the positive atomic kernels . VBis really a mathematical description of Lewis's covalent bond concept , expressedin quantum (electron wave) terms . Heitler and London first described the covalent

bond in the hydrogen molecule ; Slater and Pauling extended their approach to

small organic molecules such as methane a few years later .The question immediately arises : are hybrid orbitals necessary ? By the late 1920sfour distinct types of atomic orbitals were recognized : s , sharp ; p , principal ; d ,diffuse ; and f , fine ; these names were given to them by spectroscopists . Orbitalsare volumes of space around atomic nuclei in which there is a certain probability oflocating specific electrons ; they are where the electrons are in and around atoms

. Quantum theory treats electrons as particles with wave-like properties , and so theatomic orbitals , with their component electrons , had both spatial and wavefeatures . Here's a simple sketch of the s , p , and d orbitals (I won't be discussing

the f orbitalsin this web page) :
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When Slater and Pauling applied their new quantum theory approach to thechemical bonds in methane , the shapeof the molecule , which has a tetrahedralconfiguration of hydrogen atoms about the central carbon atom , immediately

posed a problem . There was simply no way to reconcile the shapes of the native s

and p carbon orbitals with a tetrahedral structure . Also , theorbital symmetriesclearly forbade any overlap between the carbon and hydrogenorbitals to form the CH covalent bonds . To solve these problems , they

postulated a hybridizationa blending of the carbon 2s and its three 2p nativeatomic orbitals into a singlesp3hybrid atomic orbital . This latter new orbital hadfour prominent positive symmetry lobes in a tetrahedral configuration , with asmaller inner zone of negative symmetry around the atomic kernel . The four

positive symmetry lobes could then readily overlap with the spherical , positivesymmetry , hydrogen 1s orbitals to form the four CH covalent bonds in themethane molecule :
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The promotion of one of the carbon 2s valence electrons into a higher energy level2p orbital , and the subsequent blending of the native orbitals and rearrangement ofthe hybrid orbital lobes , all required energy ; Slater calculated the hybridizationenergyfor promotion of carbon's ground state 2s22p2electrons to

the 2s

1

2p

3

excited state in the hybrid orbital to be about 199 Kcal/mol . However ,this was more than offset by the lowering of the system free energy in the methanesynthesis , so in this case formation of the carbon sp3hybrid atomic orbitals wasfeasible .

The success of VB in the early 1930s with small organic molecules led to itsextension to other more complex compounds and to simple inorganic molecules insubsequent years . Hybridization schemes grew to include a wide range of s , p ,and d (and even f , not discussed here) orbital combinations .

In his later years Pauling statedthat he considered the hybridization concept to behis most important contribution to chemistry (Kauffman and Kauffman, 1996)[from the comprehensiveonline biographyof Pauling by J.D. Dunitz ] .

Various s , p , and d hybrid orbitals are presented in the following tabulation :
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These hybrid atomic orbitals are employed in the picture VB description of thecovalent bonds in a wide variety of compounds . I'll also introduce two importantupgrades for picture VB :composite hybrid orbitals, and the use of hypervalent

native orbitals(lower energy level ones with their electrons , and higher energylevel ones) . Composite hybrid orbitals are formed by the combination of two or
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more simpler hybrid orbitals . For example , the familar d2sp3octahedral hybridorbital can be thought of as a composite of the three simpler linear hybrids , dpx+dpy+ spz. The well-known square planar hybrid orbital dsp

2can similarly becreated by the combination of the linear dpx+ spyhybrids . The combination of

hypervalent orbitals with normal valence orbitals was virtually unknown in classicVB , and is still debated even today . This topic will be explored in several of thecase studies to follow . We'll see that the use of hypervalent orbitals and electronsis essential for obtaining a satisfactory picture VB electronic structure for certainmaterials .

Sulfur Hexafluoride

The picture VB analysis ofsulfur hexafluorideillustrates the use of hypervalentorbitals . SF6is a very dense (five times that of air) , chemically inert , colorless ,odorless gas at room temperature . It resembles carbon dioxide in that its liquid

phase exists only under high pressure . While it freezes at51 C , its solidsublimes without melting , like dry ice . The molecule has an octahedral structure ,with six equal length SF bonds (1.564 ) . Its extraordinary chemical inertnessand resistance to attack by aggressive reagents have been attributed to the sterichindrance of the fluorine atoms around the sulfur atom . Incoming nucleophilesmerely bounce harmlessly off the surrounding protective layer of fluorine atoms : ateflon molecule ! The remarkable chemical stability of sulfur hexafluoride has

led to its main use as a dielectric insulator in electrical equipment to suppresssparking , but in recent years the industrial applications of SF6have been restricted

because it is avery efficient greenhouse gas, far more so than carbon dioxide ,methane , or nitrous oxide .

A variety of chemical bonding schemes have been proposed for sulfur hexafluorideover the past few decades . Sulfur has six valence electrons , 3s23p4, one of which

is used in each of the six SF bonds . Only four3 s-p native orbitals are availableto form sulfur's octahedral hybrid orbital , while sixare required for it . Theoristshave always been very reluctant to use higher energy level hypervalent orbitals inSF6bonding schemes . Can they be used for the hybrid orbital , and if so , whichare the best ones to blend with the 3 s-p valence orbitals ?

Our preferred choice would be to combine two of sulfur's empty 3d native orbitalswith its valence shell 3s and 3p orbitals to form the familiar sp3d2octahedralhybrid orbital . However , as sulfur is a lighter p-block element its 3d orbitals arethought to be unsuitable for hybridization .Maclagancommented ,
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It was discovered that the d orbitals in some states of atoms like sulfur could be so

diffuse that they could not reasonably be expected to participate to a significantextent in bonding (p. 428) .

Reed and Weinholdrather more bluntly state :

Models of SF6requiring sp3d2hybridization should be discarded (p. 3586) .

These latter authors favored an ionic model of bonding in SF6, and suggested thatd orbitals could contribute to its stabilization via a backbonding process . Theycalculated the following contributions to the hybrid orbital by native orbitals in thesulfur atom : 32% by 3s ; 59% by 3p ; 8% by 3d ; and 1% by 4p . Imsurprisedthat no mention of the 4s orbital was made in this analysis , since it's somewhatlower in energy than either the 3d or 4p orbitals . If we agree to retain a small

amount of 3d character in sulfur's hybrid orbital , I would suggest using thefollowing recipe to obtain a suitable octahedral orbital for sulfur hexafluoride :

3s + 3px= spx(x axis) ; 4s + 3py= spy(y axis) ; 3dz2+ 3pz= dz2pz(z axis) ; then thethree simple , linear hybrid orbitals are combined to form the composite octahedralorbital : spx+ spy+ dz2pz= sp

3ds , which has a small percentage of d character (thedz2orbital is the most stereochemically prominent of the d orbitals , and theaddition of the pzorbital to it would greatly increase its volume) .

A purely covalent set of six SF bonds , with no recourse to ionic resonance

structures necessary (or even desirable , given the obviously nonpolar covalentnature of sulfur hexafluoride) can be readily formed from the overlap of this sp 3dshybrid orbital , together with its six sulfur valence electrons , with the fluorineatoms . These latter reactants may have a tetrahedral (sp3) hybridization , with oneof the four lobes containing the seventh (2p5) fluorine valence electron . I like todrawsimple , colorful little picture VB sketches to illustrate these electronicstructures :


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The large energy gap between the 2 s-p and 3 s-p levels normally prevents the useof the latter's empty hypervalent orbitals with the former's valence orbitals to formany sort of hybrid orbitals . As a result , the 2 s-p elements can form only simpler ,

lower-coordination types of hybrid orbitals , usually sp , sp2

, and sp3

. Of course ,the smaller size of the 2 s-p atoms also sterically limits the number of theirattached ligands . Thus , the larger 3 s-p element phosphorus can form PF3, PF5,and the PF6

-anion with fluorine ; but the smaller 2 s-p element nitrogen can formonly NF3, a very stable , inert gas similar to sulfur hexafluoride , with fluorine .

The 3 s-p elements are in a gray area between the energetically isolated 2 s-pelements and the heavier elements of the Periodic Table . The closely spacedenergy levels of the latter elements permit a facile hybridization of both normalvalent and hypervalent orbitals . The larger 4 s-p and heavier elements can also

bond to a greater number of ligands . Not surprisingly , as a rule molecules of the


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heavier elements have higher coordination numbers than those of the lighterelements , and with more complex geometries than theirs .

The 3 s-p elements mayform hypervalent molecules with relatively highcoordination numbers , but probably only as products ofstrongly exoergicreactions , such as fluorinations . For example , the synthesis ofsulfur hexafluoride byburning sulfur in fluorineis quite exothermic(288.9Kcal/mol ; the SF bond energy in SF6is 76 Kcal/mol) , so there should be morethan enough reaction energy available for creating the sp3ds octahedral hybridorbital .

A composite hybrid orbital that has no d character can be readily formed byhybridization of the sulfur 3 s-p orbitals with two hypervalent 4p orbitals to

produce the composite sp5hybrid orbital :

3s + 3pz= spz(linear) ; 3px+ 4py= p2

xy(bent) ; 3py+ 4px= p2

xy(bent) ; spz+p2xy+ p

2xy= sp

5(octahedral) , shown in the following sketch :

From the practical chemistry point of view the hypothetical sp5hybrid orbital

would actually be preferable to the alternate sp3ds octahedral hybrid for use with p-block post-Transition metal elements in which the native d orbitals areenergetically or otherwise inaccessible . The elements of the Periodic Table aredivided into four groups , based on their valence shell orbitals : the s-block (pre-Transition) , d-block (Transition metals) , p-block (post-Transition) , and f-block(lanthanides and actinides) . The hybrid orbitals are formed primarily from thevalence shell native orbitals , plus one or more hypervalent orbitals in some cases .So the p-block elements will , by common chemical sense, use mostly native porbitals when they form hybrid orbitals for covalent bonding . Similarly , the

Transition metal elements will use mainly their native d valence orbitals forhybridization . The voluminous , positive symmetry s orbitals are sort of a


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universal orbital that can participate in hybridization with p and d orbitals across

the Periodic Table .

In the early Transition metal elements mostly d orbitals are involved inhybridization , with virtually no p character ; I have proposed the d5s octahedralhybrid orbital (sketch above) for their covalent bonds . Similarly , the d3stetrahedral hybrid is used for covalent bonding in Transition metal compounds ,compared to the more familar sp3tetrahedral hybrid for pre- and post-Transitionelements . In later Transition metal elements more and more p character enters thehybrids , as more and more d electrons remain sequestered in the electronicallyinactive atomic kernels . Thus , the well-known octahedral d2sp3 octahedral hybridappears in the chemistry of mid-Transition metal coordinate covalent complexes ,while the dsp2square planar hybrid predominates with d8and d9Transition metalcations .

The selection of a proper hybrid orbital for use in the covalent bonding in anygiven compound should therefore be made judiciously , respecting its chemistryand the place of its component atoms in the Periodic Table . Hypervalent orbitalscan be used in the formation of hybrid orbitals where the coordination number ofthe central atom requires them ; however , care must be taken in their selection .The energetics of the hybridization should be reasonable and practical . If at all

possible there should be a minimal energy gap between the normal valent andhypervalent orbitals involved in the hybrid . With larger energy gaps hybridizationcan be supported only by strongly exothermic synthesis conditions (as in most

fluorinations), or by the application of high pressure .

From these considerations I conclude that either the sp3ds or the sp5octahedralhybrid orbital , both of which are chemically practical and energetically accessibleto sulfur atoms , would be satisfactory for use in the SF bonds of sulfurhexafluoride . These are classic Lewis covalent bonds with no ionic characterwhatsoever , in agreement with the completely nonpolar covalent nature of SF 6.

The Metallic Bond and Picture MO

That covalent and metallic bonds are diametrically opposed converses of eachother is nicely illustrated in the examples of diamond and cesium . In a diamondthe carbon atoms are linked by very strong covalent bonds usingtetrahedral sp3hybrid orbitals . A pure diamond weighing 12.011 grams wouldcontain a mole of carbon atoms (Avogadro's Number , NA= 6.022142 x 10

23) with

2NAcarboncarbon covalent bonds , all of which are at essentially the same energylevel .


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In contrast , cesium is held together only by a feeble metallic bond , making it it avery soft , low melting (28.6 C) solid . A mole of cesium weighs 132.905 gramsand contains NAcesium atoms . Asinglemetallic bond , comprised of cesium's 6sorbitals and valence electrons , fills the interatomic space in the metal's lattice .

Cesium's valence electrons are distributed in a vast number of energy levelsthroughout its metallic bond . There are NAenergy levels in the metallic bond of amole of cesium , corresponding to the NA6s orbitals that overlap throughout thesolid to create the sigma XO (crystal orbital= conduction band = metallic bond) init . The Fermi-Dirac distributionpairs most (typically 99%) of the 6s1electrons inthe XO in its lower energy levels . The other ~1% of the unpaired singlet electronsoccupy higher energy levels above the Fermi level , EF. The lower energy levelswith the paired electrons have bonding MO character that provides the strength ofthe metallic bond (such as it is in cesium) . The energy levels above EFwith the

singlet electrons have antibonding MO [ABMO] character . While the singletelectrons don't contribute to the bond strength , they are responsible forthephysical propertiesthat make metallic solids such unique materials : their highelectrical and thermal conductivities , reflectivity (metallic luster) , colors , opacity, and Pauli paramagnetism .

Thus , in a diamond with a mole of carbon atoms there are 2N AcarboncarbonMOs (covalent bonds) at the same energy level , while in a mole of cesium there isa single metallic bond whose NAelectrons are distributed over the NAenergy levelsof its XO . The electrons in the diamond's covalent bonds are essentially

100% localizedlocated between the carbon atomswhile the electrons incesium's metallic bond are effectively 100% delocalized; they can resonatethroughout the entire solid in its XO . In these two extreme examples , at least , thecovalent and metallic bonds are indeed the converse of each other .

VB and MO theories can both provide a good description of the carboncarbonbonds in diamond , but classic VB is incapable of properly describing thedelocalized electrons in metallic bonds . The simple picture I portrayed above ofthe metallic bond in cesium is derived from the MO theory . Pauling introduced a

concept he referred to as the resonating valence bondhis version of the metallicbondbut I've always preferred , and recommend , the MO approach in this regard.

MO theory has a broader and more comprehensive scope than VB theory , withsigma , pi , and delta MOs and their corresponding ABMOs . It's applicable to boththe ground state and excited states of molecules ,which is why MO theory is

preferred by spectroscopists , for example . By comparison , VB theory describesonly sigma covalent bonds , applies just to the ground states of chemical systems ,and makes no reference at all to antibonding orbitals . VB theory's main advantage

is its use of the hybrid atomic orbitals , by which it excels at describing thelocalized sigma bonds that comprise the strong skeletons of covalent molecules
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and solids . Molecular geometry is set by VB's hybrid orbitals , while MO requiresan auxilliary theory , Valence Shell Electron Pair Repulsion (VSEPR) , todetermine the geometry of molecules and covalent solids . Despite its narrowerscope compared to MO theory , the simpler nature of VB , and in particular picture

VB , makes it much easier to use by chemists than MO , providing results that arein most cases remarkably well correlated with the actual physical and chemicalproperties of the materials studied . Wouldn't it be wonderful if some day aningenious theoretical chemist was able to combine the best aspects of VB (thehybrid orbitals) with MO , to create a unifiedorbital bond theory ?

The metallic bond is a very general sort of chemical bond , and can be found inmolecular and infinite lattice solids , in polymers , and in both organic andinorganic compounds . It often occurs together with other types usually covalent

of chemical bonds . KCP [K2Pt(CN)4Br0.3. 3H2O] , briefly discussed below , is

bonded by all five types of chemical bonds(covalent , ionic , van der Waals dipolar, hydrogen , and metallic) . In my studies of metallic solids I use picture VB todescribe the localized covalent bonds in them . Any extra , unused , or leftoverelectrons are assigned to an available empty , higher energy frontier orbital abovethe covalently-bonded skeleton of the structure (molecule or lattice) . I thenusepicture MOto create the polymerized MO the crystal orbital , XOthatconstitutes the metallic bond in the solid and contains the extra electrons .

Picture MO illustrates the metallic bond XO in a qualitative , nonmathematicalmanner using a simple sketch . The crystal orbital is formed by the continuous

overlapping of the native(unhybridized) atomic orbitals of the component atoms inthe solid . There are many possible ways in which s , p, and d native atomicorbitals can overlap , both with themselves and with the other types , to form amolecular orbital . Of particular interest with regard to the creation of a metallic

bond are the ss sigma , pp pi , and dd delta nodelessXOs , which are shown inthe following sketch :


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In the above sketch , the yellow sections refer to the part of the electron wavefunction having a positive symmetry ; the gray sections represent its negativesymmetry parts .

The significance of orbital nodes in superconductivity was first realized by Krebs,who stated :

The rule that superconductivity is only possible if there exists at least one space

direction not intersected by plane or conical nodal surfaces can only be verified fora limited number of superconductors . On the other hand , in no case does anything

point against the validity of this rule . In those cases in which the condition of therule is fulfilled , superconductivity is found with very few exceptions . We can thusassume that the principle condition for the occurrence of superconductivity is in

fact the absence of these nodal surfaces.


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I extended this concept to metallic solids in general (of which superconductors area rather unique subset) , naming it Krebs's Theoremand re-stating it as follows :

True metals have a metallic bond consisting of a nodeless crystal orbital along atleast one crystal axis , while in pseudometals the metallic bond consists of a crystalorbital that is periodically intersected by nodes.

Nodeless sigma XOs occur in the elementary metals , their alloys , and manyintermetallic compounds , since such elements always have valence electrons in sorbitals . The voluminous sigma XO can readily overlap with adjacentenergetically-accessible p orbitals , leaking electron density into them , resulting inthe formation of the s-p XO metallic bond .

Pi XOs can be found in materials with systems of extended bonds , such as in

graphite and doped polyacetylene , both of which are respectable electricalconductors . Delta XOs are undoubtedly found in the Transition metals , whichhave prominent d orbitals and valence electrons . I've discussed the possibilityofdelta TiTi bondsin the metallic solid titanium disulfide , TiS2, which has agolden , lustrous appearance and a lamellar morphology like that of graphite .

The following example will demonstrate how picture VB-MO can describe theelectronic structure of a metallic solid . The coordinate covalent platinumcompound KCP, K2Pt(CN)4Br0.3. 3H2O , is a pseudometal with a nodal metallic

bond . The semiconductors are all pseudometals with very low electrical

conductivities ; however , that of KCP is more substantial , around 830 ohm-1cm-1at room temperature . As a pseudometal KCP exhibits a directtemperatureelectrical conductivity relationship ; it has , in effect , a reversiblemetallic bond ,which strengthens as the material is warmed , and fades away as it is cooled down .The periodic nodes in its sigma XO act as bottlenecks to the flow of electrons ;

as KCP is warmed , more and more electrons can tunnel through the nodes , andconversely fewer as it is cooled down .

The coordinate covalent platinumcyanide bonds in the Pt(CN)4molecules arehighly localized , and don't participate in the metallic bond . They can therefore beaccurately described by picture VB as the donation of the nucleophilic cyanidecarbons' sigma electron pairs into the empty electrophilic lobes of the platinumsquare planar dsp2hybrid orbital . The metallic bond in KCP is formed by thecontinuous overlapping of the platinum 5dz

2AOs throughout the chains ofPt(CN)4molecules , which are stacked on top of each other like dinner plates or

poker chips :
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The interested reader is referred to a related Chemexplore web page , A NewClassification of MetallicSolids, for a more detailed discussion of this topic ,which includes studies of many other remarkable metallic compounds of elementsfrom across the Periodic Table .

The Structural Chemistry of a Tin Can

In this section we'll chemically explore a tin-plated steel can commonly used forpackaging and storing processed foods . We'll look under the shiny outer surface ofthe can , first studying thetinlayer , then the interface of the tinand steel , and

finally analysing the iron component of the steel body . Simple , qualitative pictureVB-MO models of the electronic structures of the tin , iron , and tin-ironcompounds comprising a typical tin can will be presented . These models will becorrelated as closely as possible with the known chemical and physical propertiesof the materials studied .

Tin has a most interestingand surprising !electronic structure. Wells(1)observed that the solution of white and gray tin in hydrochloric acid

produced two different salts :

white Sn (metal) + concentrated HCl (aq) ----------------> SnCl2 . 2H2O + H2(g)

gray Sn (nonmetal) + concentrated HCl (aq) ----------------> SnCl4. 5H2O + H2(g)

Tin(II) is 5s2electronically , while Sn(IV) is 5s0. The heavier atomic weight post-Transition metal elements are well known for displaying inert pairsof electrons intheir compounds . The term inert is a relative one , since these lower-valentelectrons can be removed by oxidizers of varying strengths to leave the higher-valent cation product . The hydrochloric acid reaction of the two tin allotropesseems to show that there's an inert pair of electrons in white tinthe common tinmetalbut not in the less well known gray tin . Chemists are quite familar with thelone pairs of non-bonding electrons in many covalently bonded compounds suchas the water molecule , with two lone pairs on the oxygen , and ammonia , with alone pair on nitrogen at the apex of its pyramid . The presence of a lone or inert

pair of electrons in a structure is a reliable diagnosis for covalent bonding in it .The 5s2inert pair in white tin suggests that underneath its shiny metallic surfacelies a network of covalent bonds . What might that structure consist of ?

First , let's look at gray tin with its simpler diamond crystal structure , whose atoms

utilize the tetrahedral sp3

hybrid orbital :
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Gray tin is a a pseudometal with a directelectrical conductivitytemperaturerelationship :

The electrical conductivity data for this graph were fromEwald and Kohnke.

The metallic bond in gray tin is in the covalent bonds , since all of its valenceelectrons are in them ; there are no leftover electrons in frontier orbitals . Those

covalent bonds are nodal in nature , although the nodes are fairly narrow in heavieratoms such as tin . As mentioned above , the nodes act as periodic bottlenecks tothe flow of the free , mobile electrons , and are thus responsible for gray tin's
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pseudometal behaviour . Gray tin has a respectable (for a pseudometal) electricalconductivity of 2090 ohm-1cm-1 at 273 K .

The electrical conductivity of white tin , on the other hand , is 86,957 ohm-1cm-1 at273 K , and it superconducts at T

c= 3.72 K , which indicates it's a true metal with a

nodeless XO as its metallic bond . The white tin atoms have a distortedoctahedralcoordination . They are in layers , each atom with four short bonds in azig-zag pattern in the horizontal plane , and with two longer vertical bondsconnecting the layers together :

An inert pair of electrons is stereochemically prominent , and will produce anoticeable bulge or elongation in the atomic spacings of a structure (incrystallography the x-rays can see the atomic kernels , but not the electrons orinert pairs in between them) . Unusually long bonds in a crystal structure are oftena good clue to the presence in them of inert pairs of electrons . The 5s2inert pair inwhite tin is undoubtedly located in its long axial bonds , and could actually befunctioning as a sort of coordinate covalent bond , as shown in the following

sketch :


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The above sketch highlights several interesting features of the white tin electronicstructure . First , it shows all sevenSnSn bonds per tin atom : four covalent , two

coordinate covalent , and the actual metallic bond (6 s-p) XO . Second , it showsthe use of two hypervalent 4d orbitals , together with their four electrons , in thecovalent bonds . Note the 4d orbitals and their electrons are at approximately thesame energy level as the normal valence 5 s-p orbitals in tin (see the energy levelsketch of the s , p , and d orbitals , above) , and so are readily accessible for use in

bonding , if required . Third , it reveals the presence in white tin of not one ,but twoinert pairs ! The 5s2valence electrons are located in the axial SnSn bonds; the 6s2pair are in the metallic bond XO . A trickle of electron density from the6s2pair into the adjacent empty 6p orbitals opens up vacancies in the 6s sigma XOand permits it to act as the metallic bond in white tin .

While the four valence electrons in degeneratetin atoms (isolated in space , withno neighbours) are 5s25p2, this VB-MO picture predicts that in solid-statetinmetal the 5p2electrons have been promoted up to the 6 s-p energy level , as the 5porbitals are now occupied by covalent bonds .

The reactive hydrochloric acid can readily oxidize the 6s2inert pair ; when thathappens , the tin structure disintegrates , the 4d electrons retreat back to theirnative orbitals , and the remaining 5s2inert pair surrounds the tin(II) cation , nowan electrophilic sphere that is quickly coordinated by nucleophilic water ligands .


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In the case of gray tin , the four identical covalent bonds per tin atom aresimultaneously oxidized by the HCl , leaving a residual hydrated Sn(IV) cation .

When gray tin is warmed to room temperature and higherthe actual transitiontemperature is 13.2 Cit's transformed into white tin . Only a small amount ofenvironmental thermal energy is required for the hybridization of two of tin'shypervalent 4d and its normal valence 5 s-p orbitals and electrons to create the4(d2) + 5(sp) + 5(p2) hybrid orbital . Conversely , if that environmental energy isremovedi.e. if white tin is cooled below 0 C for a prolonged period of time access to those hypervalent orbitals is lost , and it's slowly converted back into graytin [excellent YouTube video] .

***********************************************************************

Jamiesonreported in 1963 that under high pressure the diamond crystal structureof both silicon and germanium will change into that of white tin . Subsequently, Drickamerdetermined that those white tin phases of silicon and germanium areexcellent metallic electrical conductors . This leads us to a startling conclusion:the application of high pressure to silicon compresses its atoms to such an extentthat its hypervalent 2p orbitals and electrons (from 2s22p6) can be combined withits normal valent 3 s-p orbitals and electrons (3s23p2) to create the 2(p2) + 3(sp) +3(p2) distorted octahedral hybrid orbital , plus the 4 s-p sigma XO metallic bond inthe solid :

As discussed above in the sulfur hexafluoride section , the very large energy gapbetween the 2 s-p and 3 s-p energy levels normally isolates the former orbitals ,preventing them from combining with the higher energy orbitals to form hybridorbitals with more than four positive symmetry lobes . I've indicated a larger thanusual energy gap between the 2 s-p and 3 s-p energy levels in the sketch above formetallic silicon . It seems that tremendous compression of the silicon atoms can

squeeze and narrow that gap sufficiently to permit the hybridization of two of the
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hypervalent 2p orbitals and their four electrons with the normal valence3s23p2orbitals and electrons . The result is an electronic structure for highlycompressed metallic silicon rather like that of tin metal .

The electronic structure of compressed germanium would be similar to that ofsilicon , with its metallic bond located by picture VB-MO in the 5 s-p sigma XO .Since the energy gap in germanium (3 s-p to 4 s-p) is narrower than thecorresponding gap in silicon , we would expect that less pressure would berequired to convert diamond germanium to its white tin form . In Drickamer's Fig.7 , p. 1433 , we see that this is indeed the case , with the transition to the metallic

phase occurring at about 200 kbars in silicon , but significantly lower (~ 120 kbars)in germanium .

Molten silicon (m.p. ca. 14101414 C) is also metallic :

It is noteworthy that the melting of Si at ambient conditions [one atmospherepressure] also displays a transition both from four-fold to sixfold coordination andfrom the semiconducting solid phase to a metallic liquid (R.G. Hennig and co-workers [PDF, 405 KB] , p. 1) .

That silicon near its melting point changes from the diamond to the white tinstructure just before liquifying is significant . This suggests that the huge amountof thermal energy applied to its lattice is sufficient to promote its inner 2p orbitalsand their electrons to a higher excited state , making them accessible to the 3 s-

porbitals for creation of the 2(p2) + 3(sp) + 3(p2) hybrid orbital . The thermalconversions of silicon and gray tin to their distorted octahedral white tin structuresare thus analogous , differing only in the amount of energy required for thetransitions . This example of silicon shows that even the very large 2 s-p to 3 s-penergy gap can be closed , and lower energy level hypervalent orbitals and theirelectrons can be used in covalent bonding , provided enough heat is supplied , or

pressure is applied to the material .

***********************************************************************

It might surprise the reader to learn that there could be intermetallic tin compoundsin his or her kitchen . We are all familiar with the tin-plated steel cans used to

package and store many processed foods ; most kitchens have a few of these ontheir shelves . The chemistry of the tinning and de-tinning of steel is ofconsiderable economic importance , and so has been widely researched . I countedover 300 research papers listed in SciFinder Scholar on this subject ! When steel iscoated with liquid tin , there is a very small but observable mutual diffusion of thetin and iron atoms into each other's phases , with the formation of at least two iron

tin intermetallic compounds . Giefers and Nicoldescribe five well characterizedFeSn intermetallic phases (FeSn2, FeSn , Fe3Sn2, Fe5Sn3, and Fe3Sn) in their
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comprehensive review . Of these , the first two exist at room temperature ; theremaining three are found only at high temperatures (refer to their phase diagramof the FeSn system , Fig. 1 , p. 133) . FeSn and FeSn2have well defined crystalstructures (nicely illustrated in their Fig. 2 , p. 133) that are readily amenable to a

picture VB-MO analysis .FeSn is antiferromagnetic with a Nel temperature of TN= 373 K (CRC Handbookof Chemistry and Physics) , or 368 K (Hggstrm and co-workers) . The centralthesis of several of my Chemexplore web pages , for example ,AntiferromagneticInduction in High Temperature Superconductors, emphasizesthe crucial role of antiferromagnetism in the design of new superconductors . If anantiferromagnetic spin rgime , i.e antiparallelism , can be imposed on the mobile ,free electrons above EFin a metallic solid , they can magnetically couple togetherinto Cooper pairs and the material will be a superconductor . If FeSn is a true metal

, and if it's antiferromagnetic , then it should be superconducting at an elevatedtemperature . However , it apparently never becomes superconducting at all . Whynot ?

Stenstrmcarried out a careful study of the electrical resistivity of FeSn , andfound that a very pure single crystal of the compound had a nearlylinear inversetemperatureelectrical conductivity relationship (his Fig. 2 , p. 215) .The FeSn crystal was anisotropic ; its electrical conductivity was somewhatdifferent when measured along the major crystal axis , compared to across the axis. The ambient electrical conductivity of FeSn was found to be about 12,500 ohm-

1cm-1(parallel) , and ~ 15,400 ohm-1cm-1(perpendicular) . Stenstrmreported aresidual resistivity [in conductivity terms] of FeSn cooled in liquid helium at 4.2K of 833,000 ohm-1cm-1(parallel) and 2.9 million ohm-1cm-1(perpendicular) . Theelectrical conductivity characteristics of FeSn are similar to those of the closelyrelated metallic solid , iron monophosphide, FeP , whose ambient electricalconductivity is also 12,500 ohm-1cm-1, rising to 3.3 million ohm-1cm-1in liquidhelium . FeP similarly doesn't seem to superconduct , and like FeSn it too isantiferromagnetic (TN = 123 K) .

The electrical conductivity behaviour of FeSn indicates it's a true metal with anodeless XO as its metallic bond . It consists of alternating hexagonal layers ofiron-rich Fe2Sn and pure Sn :
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The layer of tin atoms (green spheres) is better viewed in the next sketch , in whichthe structure has been rotated to display its side :

The iron atoms (blue spheres) all have an octahedral coordination by the tin atoms .However , the latter atoms have a hexagonal planarcoordination in the Fe2Snlayers , and a trigonal prismaticcoordination by the iron atoms in the pure tinlayers . The structure of FeSn is quite similar to the well known nickelarsenide crystal structure , in which the metal atoms are in hexagonal layers , withthe nonmetal atoms sandwiched between them . The nickel atoms in NiAs have an

octahedral coordination , while the arsenic atoms have a trigonal prismaticcoordination . In fact , both Wells(2)and Wyckofflist FeSn as having a NiAscrystal structure , although its more recent classification is the hexagonalB35CoSnstructure .

With this essential crystallographic and electrical conductivity information in hand, a reasonable picture VB-MO electronic structure for FeSn can be sketched asfollows :
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The tin atoms , which are basically electronically inert linking atoms (like thearsenics in NiAs) , must use both their 4d10and 6p0hypervalent orbitals in thehexa-coordinate hybrid orbitals . The iron atoms deploy six of their eight (3d64s2)valence electrons in the octahedral covalent FeSn bonds ; the two extra , leftoverelectrons will most likely be located in the energetically accessible , empty 4pfrontier orbitals . These can readily overlap continuously along the lines of ironatoms in the Fe2Sn layers to form a pi XO , which is predicted to be the nodelessmetallic bond in FeSn .

The puzzling question as to why FeSn , an antiferromagnetic metallic solid , shouldnot be a high temperature superconductor , may have been answered

by Yamaguchi and Watanabe, who studied the magnetic structure of the materialby neutron diffraction . They commented ,

....... it is quite evident that the magnetic moments of Fe atoms lie in the c-planeand are coupled ferromagnetically within a c-plane , while they are coupled

antiferromagnetically to those on the adjacent c-planes (p. 1211) .


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Their Fig. 5 , p. 1212 , illustrates the three-dimensional arrangement of the electronspins in the FeSn lattice . The spins are parallel within the horizontal Fe2Sn planes ,

but since the orientation of the iron electrons' spins alternates from plane to plane ,the overall magnetic structure of FeSn is antiparallel , i.e. antiferromagnetic ,

which is experimentally observed in magnetic susceptibility measurements :

Our VB-MO analysis of FeSn indicates its metallic bond is located in the 4p pi XOover the iron atoms in the Fe2Sn layers . However , the electrons in the XO havea ferromagneticordering ; such a parallel spin ordering of the free electrons aboveEFwill effectively prevent them from magnetically coupling into Cooper pairs forsuperconduction (antiparallelismis required !) . That's a simple , straightforwardexplanation of why FeSn , which has a very high electrical conductivity at lowtemperatures and is simultaneously antiferromagnetic , never becomessuperconducting .

As mentioned , FeSn strongly resembles FeP and FeAs , which have the NiAscrystal structure . Iron pnictides such as FeAs form the foundation of a large familyof recently-developed medium temperature (Tc~ 3060 K) superconductors , ofwhich electron-doped derivatives of the layered compound LaOFeAs are typicalexamples . These materials are reviewed in other Chemexplore web pages such astheIronandDopingones , so I won't comment any further on them here . TheFeAs layers are the electronically-active parts , having FeAs covalent bondscoated with a metallic bond in which the electrical conductivity and

superconductivity occur . In those web pages picture VB-MO analyses of typical

LaOFeAs derivatives are presented , and they are all predicted to have a pi XOmetallic bond like that of FeSn above .
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The iron pnictide layers in them , though , no longer have the NiAs crystalstructure ; rather , they have been flattened out into two-dimensional layers whichnow have the anti-lithargestructure . The litharge crystal structure [for PbO ,yellow lead(II) oxide , and the related black tin(II) oxide , SnO] was determined in

1941by Pauling and his post-doc researcher , W.J. Moore (who later wrote one ofmy favourite solid state chemistry textbooks , Seven Solid States , referencedbelow) . They proposed an unusualsquare pyramidcoordination for the leadand tin atoms in these two compounds , which caused the flattening and layeringeffect in them :

We suggest that the orbital arrangement for Pb(II) and Sn(II) in these crystals isthat of a square pyramid , four bond orbitals being directed from the metal atomwithin the pyramid toward the four corners of the base and a fifth orbital , occupied

by a stereochemically-active unshared electron pair [inert pair], being directed

toward the apex (p. 1394) .

As mentioned above , the presence of the inert pairs on the metal atoms indicatescovalent bonding in the structure , so PbO and SnO are really inorganic

polymershaving metaloxygen covalent (notionic) bonds . The oxygens aretetrahedrally-coordinated linking atoms in these two compounds :

The picture VB analysis of litharge is fairly simple , as shown in the followingsketch :


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The lead atoms in PbO must involve one of their hypervalent orbitals , in this casean empty 6dx2-y2orbital , in order to create a hybrid orbital with fivelobes (sp

3dx2-y2, the usual square pyramid hybrid) , the axial one being reserved for the inert pairof electrons . The sp4composite orbital (sp2+ p2) , sketched above in theSF6section , might also be used by the lead atoms in PbO . In this case , theywould have to involve one of their empty 7p hypervalent orbitals in the hybrid .

The similarity of FeSn to FeAs suggests it might be used as the metallic substrate

in the design and synthesis of new superconductor candidate compounds related toLaOFeAs . As recommended in theDopingweb page , ionicfluoridereducinglayers should be more efficient at electron-doping than the corresponding ionicoxide layers . Also , blends of reducers adding a non-integralnumber of electronsto the substrate are desirable , which should prevent the inevitable spin densitywave (SDW) from forming in the doped composite at lower temperatures . Such anSDW effectively inhibits the appearance of superconductivity in the compound bylocalizing electron pairs in FeFe covalent bonds , rather than creating Cooper

pairs with them . When FeSn is layered with the ionic fluorides , its three-dimensional crystal structure should be flattened into the two dimensionallitharge/anti-litharge structure , as with FeAs .

A stock of FeSn could be prepared , for example by the simultaneous co-reductionof equimolar quantities of Fe2+or Fe3+and Sn2+by aqueous borohydridereduction (Zhang and co-workers) , or possibly by a direct combination (shake-'n-

bake) of equimolar quantities of pure ,finely-divided iron and tin powders. AnFeSn composite for electrical and superconductivity testing might be compoundedas follows using the fluoride reducers AlF and TiF :

2/3 Al

0

+ 1/3 AlF3+ FeSn ----- (argon atm.) -----> AlFFeSn , i.e. [AlF]

2+

[FeSn]

2-

;
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2/3 Ti0+ 1/3 TiF3+ FeSn ----- (argon atm.) -----> TiFFeSn , i.e. [TiF]3+[FeSn]3-;

then ,

x [AlF]2+[FeSn]2-+ (1-x) [TiF]3+[FeSn]3------ (argon atm.) -----> [AlxTi1-xF](3-

x)+[FeSn](3-x)-.

The mole ratio x would be taken experimentially between 0 and 1 , to synthesize asmany of the electron-doped composites as the researcher considers necessary .Here's a sketch of the picture VB-MO analysis of the doped composites :

In the layered composites the FeSn component is expected to have the lithargestructure (sketched above) , its iron atoms with a tetrahedral (d3s) configuration ,while that of the tin atoms is now the square pyramid (dsp3) . Note that in atetrahedral ligand environment the d orbitals' energy levels are split into a lowerenergy level (dx2-y2and dz2) , and a higher energy level (dxy,xz,yz) . The d

3s hybridorbital is created using the three higher energy level dxy,xz,yznative orbitals ,combined with the 4s native orbital . The added electrons from the AlF and TiFreducers must then be located in the empty and energetically accessible 4p frontierorbitals on the iron atoms . These will form the predicted pi XO metallic bond inthe solids . Our picture VB-MO sketch is thus very useful in helping us understandthe electronic situation both in FeSn and in its possible layered derivatives insimple , qualitative terms . We might reasonably expect to observesuperconductivity in these latter materials at a modest (Tc~ 3060 K) temperature .

Returning to the irontin intermetallic compounds found in tin-plated steel ,themore common one, FeSn2, is also antiferromagnetic (TN= 378 K , Venturini
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and co-workers) . Tin-plating processes involving molten tin often produce a wastematerial , a dross commonly referred to as hartling. Hartling consists mostly ofFeSn2crystals , cemented together by tin metal . A modern practical application forthe otherwise unremarkable FeSn2involves its use as an anode material in lithium

ion secondary (rechargeable) batteries (Zhang and co-workers) . Inthe chargecycle it reacts with lithium cations and electrons to form the transientcompound Li4.4Sn , plus Fe

0. This unstable LiSn intermediate decomposes inthedischargecycle to Sn0+ 4.4 Li1++ 4.4 electrons . The Fe0recombines with theSn0to regenerate the FeSn2anode , continuing the electrochemical cycling .

As shown in the following sketch , the tin atoms in FeSn2have a square pyramidcoordination (dsp3) to the iron atoms , which in turn have a square antiprismcoordination (d5p3) to the tin atoms . When tin atoms predominate in a compoundand so are in a lower valence state , their 5s2inert pairs of electrons appear in non-

bonding lobes of their hybrid orbitals . In compounds where they aren't as plentifulas their partner atoms and are thus in a higher valence state , they are obliged touse them in covalent bonding , as was observed with FeSn . Tin's inert pairs arestereochemically prominent in the lattice of FeSn2, which formally hastheCuAl2(C16)(or Fe2B , Wyckoff) crystal structure :

A picture VB sketch of a possible electronic structure of FeSn2is presented below :
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In this model all of the tin and iron valence electrons are involved in the eight FeSn covalent bonds , per formula unit . There are no unused , extra electrons locatedin empty frontier orbitals on the iron atoms , as was the case with FeSn . Thus ,FeSn2is predicted to be apseudometalwith a direct temperatureelectricalconductivity relationship . The tin atoms act asspacers, which spread out the ironatoms and place gaps in between them . The metallic bond would most likely be in

the FeSn covalent bonds , which have periodic nodes around the iron and tinkernels . However , these nodes are expected to be quite narrow , as is the casegenerally with larger , heavier atoms . The electrical conductivity of FeSn2couldthus be quite respectable , as with gray tin (graph above) . Since the 4s nativeorbitals on the iron atoms are at approximately the same energy level as its 3d and4p orbitals forming the d5p3square antiprism hybrid orbital , some electron densitycould leak from the FeSn covalent bonds into them , resulting in an augmentationof the electrical conductivity of the material and some leveling of its temperatureconductivity curve .

Marchal and co-workersstudied the electrical resistivity of amorphous thinfilmsof irontin compounds , FexSn1-x, on inert surfaces . They discovered radicaldifferences in the electrical resistivity of the films based on a dividing line of x ~0.37 :

A value of x ~ 0.37 seems to correspond to a border composition between two

very different types of resistivity behaviour(p. 12) . And two very different iron-tin compounds , as we now know.

Their electrical resistivity data , graphically displayed in their Fig. 1 , p. 12 , arecomplicated by the crystallization of the irontin compounds at elevated


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temperatures . The crystalline films provided completely different traces than theiramorphous counterparts . An extract of their data (at 77 K , in liquid nitrogen , andat room temperature , 295 K) is presented in the Table below :

The traces for the amorphous films look very strange and irregular , but those forthe crystalline films are fairly linear , and are almost level , with a slight inclinationto the inverse . At x = 0.35 , the irontin compound involved is essentiallyFeSn2(Fe0.33Sn0.67) , while the x = 0.625 material is mostly FeSn (Fe0.5Sn0.5) . Theremarkably linear trace for Marchal and co-workers' crystalline FeSn agrees verywell with Stenstrm's resistivity measurements , mentioned above . The magnitudeof the electrical conductivities reported for crystalline FeSn2films by Marchal andco-workers well exceeds that of gray tin . Its slight inverse nature suggests , inaccordance with Krebs's Theorem , that substantial leakage of electron densityfrom the FeSn covalent bonds into the empty 4s orbitals could be occurring .

Researchers (Havinga , Damsma , and Kanis) at Philips Electronics , Eindhoven ,Holland , reported on the low temperature conductivities of 46 CuAl2typeintermetallics , including FeSn2, in 1972 . They noted (in their Table 1 , p. 285) ,that FeSn2showed an antiferromagnetic transition and had Tc< 0.07 K , whichcould be interpreted as meaning that no superconducting Tcwas observed forFeSn2down to their lower experimental limit of 0.07 K . A careful study of thetemperatureelectrical conductivity relationship of a single crystal of pure FeSn2,as Stenstrm did with FeSn , would be instrumental in resolving the uncertainty

surrounding the electrical behaviour of FeSn2, and thereby either verifying orrefuting the picture VB electronic structure of the compound presented above .

Returning again to the tin cans , their steel bodies are a mixture of phases , withvery complex physical and chemical natures . I would refer the interested reader tothe descriptions of steel by Mooreand Wells(3), and in the KOECT. However ,we could take a look at the electron organization in pure iron , the principalcomponent of steel . Pauling was interested in the electronic structure of iron (andof tin, too , by the way) , suggesting that several readily accessible excited statesin it could lead to the creation of suitable hybrid orbitals for the body-centered

cubic phases of iron . However , his proposed hybrid orbitals for iron (and for tin)don't have enough electrons to satisfy the covalent bond requirements (eightper


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iron atom) , plus the twoextra ones for the conventional s-p metallic bond XO ,plus the twounpaired singlet electrons in each iron atom . Of course , we all knowthat iron metal is strongly ferromagnetic , and can be readily magnetized by theimposition on it of an external magnetic field . Iron atoms in the metal have a Curie

magnetism of 2.22 BM(Bohr magnetons) , indicating the presence in them of twounpaired singlet electrons per atom . The electronic configuration for degenerateiron(0) is 3d64s2, so there simply aren't enough valence shell electrons in it for theelectronic structure of solid state iron , which requires twelve.

Pauling was reluctant to invoke the use of any sort of hypervalent orbitals orelectrons in the creation of hybrid orbitals , for example in his electronic structureofphosphorus pentachloride. However , in the case of bcc iron [and with white tinmetal , discussed above] , we absolutelymustinvolve hypervalent orbitals andelectrons (and empty outer frontier orbitals) in the description of an electronic

structure for iron which is in a reasonable agreement with its known chemical andphysical properties . With this latter requirement foremost in mind , the followingpicture VB-MO electronic structure for iron metal is brought forward :

Interestingly , the d5sp2square prism hybrid orbital is one of the excited states

proposed by Pauling for iron ; but while he preferred to use normal valence shellorbitals for it (and as a result didn't have enough electrons) , I've used


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an innerd5sp2square prism hybrid orbital , involving two hypervalent 3p orbitals ,including their four electrons , in the electronic structure . Now there are just theright number of electrons (12) for the bcc structure , with eight FeFe covalent

bonds per iron atom , plus two unpaired singlet electrons in the 4p native orbitals

(which cause the ferromagnetism in iron) , plus the usual two electrons in the s-pmetallic bond XO .

The 4px,yorbitals can overlap end-to-end between the iron atoms in the x-y planeto form p-p sigmaMOs, each of which can form a one-electron bond, which canalso contribute to the overall bond strength in iron . Their singlet electrons have a

parallel spin orientation , and produce the strong ferromagnetism in the bulk metal. The 4pzorbitals perpendicular to the planes of atoms can overlap side-to-side toform a continuouspi XOover the planes . However , since the individual4pzorbitals have two electrons each , the XO is completely filled , and must leak

some its electron density into an adjacent empty frontier orbital if it is to functionas a metallic bond . This leakage likely occurs from the 4pzinto the 5s orbitals ,thereby producing the typical s-p metallic bond XO in iron .

The question will naturally be posed : how practical is the use of the twohypervalent 3p orbitals and their electrons in this scheme ? Are they energeticallyaccessible ? The 3d , 4s , and 4p orbitals in iron are all at roughly the same energylevelsee the sketch further up this web page showing the relative energy levelsof the s , p, and d orbitalsbut there is a significant energy gap separating the 3 s-

p and 4 s-p levels . Considerable energy will be required to create a d5sp2square

prism hybrid orbital which includes two of the 3p native orbitals . Again , we mustconsider thepracticalchemistry of iron , and even its metallurgy , in pondering thisquestion . The agglomeration of iron atoms into a macroscopic sample of ironmetal requires a large amount of energy . Pure iron melts at 1536 C , and it'smanufactured (as pig iron) in vast amounts worldwide in blast furnaces .Undoubtedly there is more than enough heat energy in a blast furnace to promotethe four hypervalent 3p electrons into the d5sp2square prism hybrid orbital ! Aswith sulfur hexafluoride and metallic silicon discussed above , the creation ofhybrid orbitals should be possible even in extraordinary or unusual systems by the

provision of considerable thermal energy and/or high pressure , both of which canclose forbiddingly wide energy gaps between the s-p energy levels .

Picture VBthe simple , qualitative version of the classic valence bond theoryhas been shown in this example of iron and in the other case studies presented inthis web page to be a surprisingly effective and revealing technique in the analysisof the electronic structures of many types of materials . Picture VB is anindispensible model-making tool in my chemistry studies . I hope I'vedemonstrated how useful and informative it can be in helping us understand thechemical bonding in molecules and crystalline solids .


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References , Notes , and Further Reading

Acknowledgement : I would like to thank Dr. Antonio G. De Crisci , Departmentof Chemistry , Stanford University , Stanford , CA , for providing me with severalof the references below .

Pauling: L. Pauling , The Nature of the Chemical Bond Application of ResultsObtained from the Quantum Mechanics and from a Theory of ParamagneticSusceptibility to the Structure of Molecules,J. Amer. Chem. Soc. 53 (4) , pp.1367-1400 (1931) . This first exposition of the VB theory was later incorporatedinto Paulings textbook ,The Nature of the Chemical Bond and the Structure ofMolecules and Crystals , 3rded. , Cornell University Press , Ithaca (NY) , 1960 ;

Ch. 4 , The Directed Covalent Bond : Bond Strengths and Bond Angles, pp. 108 -144 .

these articles: L. Pauling and Z.S. Herman , Valence-Bond Concepts inCoordination Chemistry and the Nature of MetalMetal Bonds,J. Chem.Educ. 61 (7) , pp. 582- 587 (1984) ; L. Pauling , Valence-Bond Theory ofCompounds of Transition Metals,Proc. Nat. Acad. Sci. USA 72 (11) , pp. 4200-4202 (1975) [PDF, 615 KB] ; idem. , Bond Angles in Transition-MetalTricarbonyl Compounds : A Test of the Theory of Hybrid Bond Orbitals,Proc.

Nat. Acad. Sci. USA 75 (1) , pp. 12-15 (1978) [PDF, 869 KB] ; idem. , BondAngles in Transition Metal Tetracarbonyl Compounds : A Further Test of theTheory of Hybrid Bond Orbitals,Proc. Nat. Acad. Sci. USA 75 (2) , pp. 569-572(1978) [PDF, 709 KB] .

Lewis: G.N. Lewis , The Atom and the Molecule,J. Amer. Chem. Soc. 38 (4) ,pp. 762-785 (1916) . Pauling remained faithful to Lewis's concept of localizedelectron pairs in the covalent bond (and deferential to Lewis personally)throughout his lifetime : L. Pauling , G.N. Lewis and the Chemical Bond,J.Chem. Educ. 61 (3) , pp. 201-203 (1984) ; idem. ,Pauling on G.N. Lewis,

Chemtech 13 (6) , pp. 334-337 (1983) ; idem. , The Origins of BondingConcepts,J. Chem. Educ. 62 (4) , p. 362 (1985) .
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f orbitals: O. Kikuchi and K. Suzuki , Orbital Shape Representations,J. Chem.Educ. 62 (3) , pp. 206-209 (1985) ; see Figure 2 , the 7 4f atomic orbitals , p. 207.

single: Some writers refer to the individual positive symmetry lobes of the hybridorbitals as orbitals; my practice throughout this and other Chemexplore web

pages is to consider the entire combination of lobes as one single orbital . Forexample , the tetrahedral sp3orbital has four positive symmetry lobes . Suchterminology is purely a matter of personal inclination , of course .

hybridization energy: L. Pauling , The Nature of the Chemical Bond (op. cit.) , pp.118-120 .

Kauffman and Kauffman: G. B. Kauffman and L. M. Kauffman , An InterviewWith Linus Pauling,J. Chem. Educ. 73 (1) , pp. 29-32 (1996) . For anotherilluminating Pauling interview , see : E. Garfield , Linus Pauling : An

Appreciation of a World Citizen-Scientist and Citation Laureate,CurrentContents , no. 34 , pp. 3-11 (August 21 , 1989) [PDF, 713 KB] .

Maclagan: R.G.A.R. Maclagan , Symmetry , Ionic Structures and d Orbitals inSF6,J. Chem. Educ. 57 (6) , pp. 428-429 (1980) .

Reed and Weinhold: A.E. Reed and F. Weinhold , On the Role of d Orbitals inSF6,J. Amer. Chem. Soc. 108 (13) , pp. 3586-3593 (1986) . See also E.Magnusson , Hypercoordinate Molecules of Second-Row Elements : d Functionsor d Orbitals ? ,J. Amer. Chem. Soc. 112 (22) , pp. 7940-7951 (1990) ; P.G.

Nelson , Modified Lewis Theory , Part 1 . Polar Covalent Bonds and
http://www.garfield.library.upenn.edu/essays/v12p229y1989.pdfhttp://www.garfield.library.upenn.edu/essays/v12p229y1989.pdfhttp://www.garfield.library.upenn.edu/essays/v12p229y1989.pdfhttp://www.chemexplore.net/valence-bond.htmhttp://www.garfield.library.upenn.edu/essays/v12p229y1989.pdf


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The Resonating-Valence-Bond Theory of Superconductivity : CrestSuperconductors and Trough Superconductors,Proc. Natl. Acad. Sci. 60 (1) , pp.59-65 (1968) [PDF, 716 KB] ; idem. , The Nature of Metals,Pure & Appl.Chem. 61 (12) , pp. 1271-1274 (1989) [PDF, 384 KB] ; also in Pauling's textbook

, The Nature of the Chemical Bond (op. cit.) , Ch. 11 , The Metallic Bond, pp.393-448 .

all five types of chemical bonds: S.T. Matsuo , J.S. Miller , E. Gebert , and A.H.Reis , Jr. , One-Dimensional K2Pt(CN)4Br0.3. 3 H2O , A Structure ContainingFive Different Types of Bonding,J. Chem. Educ. 59 (5) , pp. 361-362 (1982) .

Krebs: H. Krebs , Superconductivity in Metals , Alloys , Semiconductors , andGlasses as a Result of Particular Bond Systems,Prog. Solid State Chem. 9 , pp.269-296 , Pergamon Press , Oxford , UK , 1975 ; pp. 294-295 . Also in Krebs's

textbook : idem , Fundamentals of Inorganic Crystal Chemistry , transl. by P.H.L.Walter , McGraw-Hill , London , UK , 1968 ; pp. 231-232 .

KCP: J.M. Williams and A.J. Schultz , One-Dimensional Partially OxidizedTetracyanoplatinate Metals : New Results and Summary, pp. 337-368in Molecular Metals , W.E. Hatfield (ed.) , Plenum Press , New York , 1979 ; J.S.Miller and A.J. Epstein , One Dimensional Inorganic Complexes, Prog. Inorg.Chem. 20 , pp. 1-151 , S.J. Lippard (ed.) , John Wiley , New York , 1976 ; A.J.Epstein and J.S. Miller , Linear Chain Conductors,Scientific American 241 (4) ,

pp. 52-61 (October , 1979) ; a color photograph of K1.75Pt(CN)4.1.5 H2O is on p.

54 .

Wells(1): A.F. Wells , Structural Inorganic Chemistry , 3rdedition , ClarendonPress , Oxford (UK) , 1962 ; p. 976 .

tin: Alicia O'Reardon Overbeck , Tin , the Cinderalla Metal,NationalGeographic 78 (5) , pp. 659-684 (November , 1940) [this article is mostly about tinmining in Bolivia] ; Tin : From Ore to Ingot, International Tin Research Institute, 5 pp. , undated (PDF, 4375 KB) .
http://www.pnas.org/content/60/1/59.full.pdfhttp://www.pnas.org/content/60/1/59.full.pdfhttp://www.pnas.org/content/60/1/59.full.pdfhttp://media.iupac.org/publications/pac/1989/pdf/6112x2171.pdfhttp://media.iupac.org/publications/pac/1989/pdf/6112x2171.pdfhttp://media.iupac.org/publications/pac/1989/pdf/6112x2171.pdfhttp://www.itri.co.uk/POOLED/DOCUMENTS/a230527/Tin-From%20ore%20to%20ingot.pdfhttp://www.itri.co.uk/POOLED/DOCUMENTS/a230527/Tin-From%20ore%20to%20ingot.pdfhttp://www.itri.co.uk/POOLED/DOCUMENTS/a230527/Tin-From%20ore%20to%20ingot.pdfhttp://www.itri.co.uk/POOLED/DOCUMENTS/a230527/Tin-From%20ore%20to%20ingot.pdfhttp://media.iupac.org/publications/pac/1989/pdf/6112x2171.pdfhttp://www.pnas.org/content/60/1/59.full.pdf


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Scan of a toy soldier , cast from pure reagent mossytin by the author when ca.12 years old .

Ewald and Kohnke: A.W. Ewald and E.E. Kohnke, Measurements ofElectricalConductivity and Magnetoresistance of Gray Tin Filaments,Phys. Rev. 97 (3) ,

pp. 607-613 (1955) ; see Figure 2 , p. 609 for the graph of the electrical

conductivity of gray tin over a range of temperatures .

Jamieson: J.C. Jamieson ,Crystal Structures at High Pressures of MetallicModifications of Silicon and Germanium,Science 139 (3556) , pp. 762-764(1963) .

Drickamer: H.G. Drickamer , Pressure and ElectronicStructure,Science 142 (3598) , pp. 1429-1435 (1963) .

Giefers and Nicol: H. Giefers and M. Nicol , High Pressure X-ray DiffractionStudy of All FeSn Intermetallic Compounds and One FeSn Solid Solution,J.Alloys & Compounds422 (1-2) , pp. 132-144 (2006) .

Hggstrm and co-workers: L. Hggstrm , T. Ericsson , R. Wppling , and K.Chandra , Studies of the Magnetic Structure of FeSn Using the MossbauerEffect,Physica Scripta 11(1) , pp. 47-54 (1975) .

Stenstrm: B. Stenstrm , The Electrical Resistivity of FeSn SingleCrystals,Physica Scripta 6 (4) , pp. 214-216 (1972) .


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iron monophosphide: D. Bellavance , M. Vlasse , B. Morris , and A. Wold ,Preparation and Properties of Iron Monophosphide,J. Solid State Chem. 1 (1) ,

pp. 82-87 (1969) ; D. Bellavance and A. Wold , Single Crystals of IronMonophosphide,Inorg. Synth. 14 , pp. 176-182 , A. Wold and J.K. Ruff (eds.) ,

McGraw-Hill , New York , 1973 .Wells(2): A.F. Wells , Structural Inorganic Chemistry (op. cit.) , Table 156 , p.1013 (NiAs sketch : Fig. 168 , p. 514) .

Wyckoff: R.W.G. Wyckoff , Crystal Structures , 2ndedition , vol. 1 , Interscience(John Wiley) , New York (1963) ; Table III,7 , p.124 (ref. on p. 190) . FeSn2hasthe Fe2B crystal structure : Table IV,22 , p. 363 (ref. on p. 398) ; illustrated in Fig.IV,70a,b , p. 363 .

Yamaguchi and Watanabe: K. Yamaguchi and H. Watanabe , NeutronDiffraction Study of FeSn, J. Phys. Soc. Jpn. 22 (5) , pp. 1210-1213 (1967) .

determined in 1941: W.J. Moore Jr. and L. Pauling , The Crystal Structures of theTetragonal Monoxides of Lead , Tin , Palladium , and Platinum,J. Amer Chem.Soc. 63 (5) , pp. 1392-1394 (1941) .

Zhang and co-workers: C.Q. Zhang et al. , Preparation and ElectrochemicalPerformances of Nanoscale FeSn2as Anode Material for Lithium Ion Batteries,J.Alloys Compd. 457 (1-2) , pp. 81-85 (2008) . Schaak and co-workers have

described the preparations of numerous intermetallic compounds , includingFeSn2, in organic solvents . By adjusting the FeSn stoichiometry to equimolar , itmight be possible to synthesize pure FeSn : N.H. Chou and R.E. Schaak , Shape-Controlled Conversion of -Sn Nanocrystals into Intermetallic M-Sn (M = Fe , Co, Ni , Pd) Nanocrystals,J. Amer Chem. Soc. 129 (23) , pp. 7339-7345 (2007) ; the

procedure for FeSn2is described on p. 7340 ; R.E. Cable and R.E. Schaak , Low-Temperature Solution Synthesis of Nanocrystalline Binary IntermetallicCompounds Using the Polyol Process,Chem. Mater. 17 (26) , pp. 6835-6841(2005) ; N.L. Henderson and R.E. Schaak , Low-Temperature Solution-MediatedSynthesis of Polycrystalline Intermetallic Compounds from Bulk MetalPowders,Chem. Mater. 20 (9) , pp. 3212-3217 (2008) ; N.L. Henderson et al. ,Toward Green Metallurgy : Low-Temperature Solution Synthesis of Bulk-ScaleIntermetallic Compounds in Edible Plant and Seed Oils,Green Chem. 11 (7) , pp.974-978 (2009) .

Venturini and co-workers: G. Venturini et al. , Low-Temperature Structure ofFeSn2,Phys. Rev. B 35 (13) , pp. 7038-7045 (1987) ; see also K. Kanematsu , K.Yasukochi and T. Ohoyama , Antiferromagnetism of FeSn2 ,J. Phys. Soc.Jpn. 15 (12) , p. 2358 (1960) . These latter authors described the synthesis of pure

FeSn2by the direct combination of iron and tin metal reagents .


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hartling: V. V. Pokrovskii , Yu. S. Arzamastsev , and O. F. Purvinskii ,Preparation of a Pure TinIron Intermetallic Compound,Uch. Zap. Tsentr.

Nauchn.-Issled. Inst. Olovyan. Prom. 2 , pp. 44-45 (1964) [from SciFinderScholar ; hartling was used to electrolytically prepare pure FeSn2] .

Marchal and co-workers: G. Marchal et al. , Composition and TemperatureRanges for Amorphous FexSn1-xAlloy Stability,Mater. Sci. Eng. 36 (1) , pp. 11-15 (1978) .

Havinga , Damsma , and Kanis: E.E. Havinga , H. Damsma , and J.M. Kanis, Compounds and Pseudo-Binary Alloys with the CuAl2(C16)-Type Structure IV.Superconductivity,J. Less-Common Metals 27 (3) , pp. 281-291 (1972) .

Moore: W.J. Moore , Seven Solid States (op. cit.) , Ch. 4 , Steel, pp. 100-132 .

Wells(3): A.F. Wells , Structural Inorganic Chemistry (op. cit.) , pp. 1026-1028 .

KOECT: W.A. Knepper , Iron, pp. 735-753 in the Kirk-Othmer Encyclopedia ofChemical Technology , 3rdedition , Vol. 13 , M. Grayson and D. Eckroth (eds.) ,John Wiley , New York (1981) ; R.J. King , Steel, ibid.21 , pp. 552-625 (1983) .

Pauling was interested: L. Pauling , The Nature of the Chemical Bond (op. cit.) ,pp. 415-416 .

and of tin: L. Pauling , The Nature of the Chemical Bond (op. cit.) , pp. 401-404 .See also L. Pauling , The Nature of the Interatomic Forces in Metals,PhysicalReview 54 (11) , pp. 899-904 (1938) ; possible valence bond descriptions of grayand white tin are discussed on p. 904 . Pauling suggested the4d15s15p35d1configuration for the distorted octahedral hybrid orbitals tin metal ,

but this electronic structure makes no allowance for any inert pair or pairs in itslattice . Full credit must be given to Pauling for introducing the novel concept ofcovalent bonding in metals (using s-p-d hybrid orbitals) , which he discussed atlength in his 1938 Physical Review article .

Curie magnetism of 2.22 BM: W.J. Moore , Seven Solid States (op. cit.) , p. 104 .Moore mentions Pauling's valence bond approach to describing the electronicstructure of bcc iron on pp. 103-104 . Pauling's explanation of ferromagnetism : L.Pauling , A Theory of Ferromagnetism,Proc. Nat. Acad. Sci. USA 39 (6) , pp.551-560 (1953) [PDF, 1122 KB] .

phosphorus pentachloride: L. Pauling , The Nature of the Chemical Bond (op. cit.), pp. 177-179 . He suggested that PCl5consisted of [PCl4]

+Cl-having severalelectronic resonance forms , using conventional s-p hybrid orbitals withoutrecourse to any hypervalent 3d orbitals . Actually , it's now known that solidPCl5consists of the two ionic molecules , [PCl4]+[PCl6]-, the former with
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tetrahedral PCl bonds , and the latter with octahedrally coordinated phosphorus .Pauling's ionic resonance forms would be difficult to reconcile with the known

physical properties of phosphorus pentafluoride , PF5, which is a colorless gas(b.p.75 C) somewhat like SF6.

one-electron bond: L. Pauling , The Nature of the Chemical Bond (op. cit.) , p.340 ; A. Holden , The Nature of Solids , Dover Publications , New York , 1992[reprint of the Columbia University Press textbook , 1965] ; p. 91 .

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An Appreciation of the Classic Valence Bond Theory

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