An Appreciation of the Classic Valence Bond Theory


Chemical bonding in a variety of inorganic compounds will be discussed in this web page , using the Valence Bond (VB) theory to describe their electronic structures . VB is infrequently employed these days by chemists , who generally prefer the Molecular Orbital (MO) theory for electronic analyses . My objective is to show in the case studies below that VB is still a valuable tool in helping us understand chemical bonding in many types of materials .

VB was developed in the late 1920s and early 1930s by several theoretical chemists . Pauling is usually given most of the credit for the popularization of VB ; indeed , he was awarded the 1954 Nobel Prize in Chemistry primarily for this accomplishment (the references are listed at the end of this web page . Underlined blue hyperlinks can be clicked when online to download the PDF or HTML 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 by the rival MO theory by then .

Valence bond theory , as originally developed by Heitler , London , Slater , and Pauling (it was originally known as HLSP , after their initials) , was a highly abstract , mathematical concept in the domain of theoretical chemistry . Indeed , the physics underlying VB was so abstruse , and its mathematical treatment so complex , it took Pauling three years to simplify VB theory to the point where it could 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 I may be in distinguished company in that aspect . A charming anecdote is related about the time when Albert Einstein , while visiting the United States , auditioned one of Pauling's VB lectures :

“In 1931 , Albert Einstein , in Pasadena for several months being wooed for a faculty 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 especially hard to explain at length his new ideas about the application of wave mechanics to the chemical bond . Afterward , Einstein was asked by a reporter what he thought of the young chemist's talk . He shrugged his shoulders and smiled . “It was too complicated for me”, he said”.

Only in the following years of practical application in the study of small organic molecules was VB transformed into a familiar , useful implement in the chemist's intellectual toolbox . A set of hybrid orbitals emerged that could be used to provide a realistic picture of the covalent bonds of small molecules . Mathematically-inclined theoretical chemists like Pauling could skilfully use VB to calculate bond lengths , angles , and strengths in covalently-bonded molecules (for example , see these articles) . The average chemist , however , usually employed VB in a qualitative , rather than quantitative way to understand the chemical bonding in the system of interest . I think it's this extraordinary pictorial quality of VB that made 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 maybe not modern VB) as a quantitative analytical tool , especially in fields such as spectroscopy . VBs continuing value to chemists , which we will see amply demonstrated as this web page unfolds , derives from its ability to portray a simple , clear picture of a covalently-bonded system , whether organic or inorganic , and whether molecular or nonmolecular . That's why I refer to the original concept of the valence bond theory classic VB in its non-mathematical form , as picture VB . 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 and chemical properties of the material studied .

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


Hybrid Atomic Orbitals


The theory of the covalent bond was first proposed in 1916 by Lewis , who suggested that pairs of shared valence electrons were located between their respective atoms and bonded them together . The actual bonding force was electrostatic , between the negative electrons and the positive atomic kernels . VB is really a mathematical description of Lewis's covalent bond concept , expressed in 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 1920s four distinct types of atomic orbitals were recognized : s , sharp ; p , principal ; d , diffuse ; and f , fine ; these names were given to them by spectroscopists . Orbitals are volumes of space around atomic nuclei in which there is a certain probability of locating specific electrons ; they are “where the electrons are” in and around atoms . Quantum theory treats electrons as particles with wave-like properties , and so the atomic orbitals , with their component electrons , had both spatial and wave features . Here's a simple sketch of the s , p , and d orbitals (I won't be discussing the f orbitals in this web page) :

When Slater and Pauling applied their new quantum theory approach to the chemical bonds in methane , the shape of the molecule , which has a tetrahedral configuration 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 , the orbital symmetries clearly forbade any overlap between the carbon and hydrogen orbitals to form the C–H covalent bonds . To solve these problems , they postulated a hybridization – a “blending” – of the carbon 2s and its three 2p native atomic orbitals into a single sp3 hybrid atomic orbital . This latter new orbital had four prominent positive symmetry lobes in a tetrahedral configuration , with a smaller inner zone of negative symmetry around the atomic kernel . The four positive symmetry lobes could then readily overlap with the spherical , positive symmetry , hydrogen 1s orbitals to form the four C–H covalent bonds in the methane molecule :

An excellent YouTube video nicely illustrating the formation of sp , sp2 , and sp3 hybrid orbitals from native s and p orbitals can be viewed at : (flash video format , 1:36 runtime , 1531 KB) .

The promotion of one of the carbon 2s valence electrons into a higher energy level 2p orbital , and the subsequent blending of the native orbitals and rearrangement of the hybrid orbital lobes , all required energy ; Slater calculated the hybridization energy for promotion of carbon's ground state 2s2 2p2 electrons to the 2s1 2p3 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 methane synthesis , so in this case formation of the carbon sp3 hybrid atomic orbitals was feasible .

The success of VB in the early 1930s with small organic molecules led to its extension to other more complex compounds and to simple inorganic molecules in subsequent 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 stated that he considered the hybridization concept to be his most important contribution to chemistry (Kauffman and Kauffman , 1996)” [from the comprehensive online biography of Pauling by J.D. Dunitz ] .

Various s , p , and d hybrid orbitals are presented in the following tabulation :

These hybrid atomic orbitals are employed in the picture VB description of the covalent bonds in a wide variety of compounds . I'll also introduce two important “upgrades” for picture VB : composite hybrid orbitals , and the use of hypervalent native orbitals (lower energy level ones with their electrons , and higher energy level ones) . Composite hybrid orbitals are formed by the combination of two or more simpler hybrid orbitals . For example , the familar d2sp3 octahedral hybrid orbital can be thought of as a composite of the three simpler linear hybrids , dpx + dpy + spz . The well-known square planar hybrid orbital dsp2 can similarly be created by the combination of the linear dpx + spy hybrids . The combination of hypervalent orbitals with normal valence orbitals was virtually unknown in classic VB , and is still debated even today . This topic will be explored in several of the case studies to follow . We'll see that the use of hypervalent orbitals and electrons is essential for obtaining a satisfactory picture VB electronic structure for certain materials .


Sulfur Hexafluoride


The picture VB analysis of sulfur hexafluoride illustrates the use of hypervalent orbitals . SF6 is 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 at 51 ºC , its solid sublimes without melting , like dry ice . The molecule has an octahedral structure , with six equal length S–F bonds (1.564 Å) . Its extraordinary chemical inertness and resistance to attack by aggressive reagents have been attributed to the steric hindrance of the fluorine atoms around the sulfur atom . Incoming nucleophiles merely bounce harmlessly off the surrounding protective layer of fluorine atoms : a “teflon” molecule ! The remarkable chemical stability of sulfur hexafluoride has led to its main use as a dielectric insulator in electrical equipment to suppress sparking , but in recent years the industrial applications of SF6 have been restricted because it is a very efficient greenhouse gas , far more so than carbon dioxide , methane , or nitrous oxide .

A variety of chemical bonding schemes have been proposed for sulfur hexafluoride over the past few decades . Sulfur has six valence electrons , 3s2 3p4 , one of which is used in each of the six S–F bonds . Only four 3 s-p native orbitals are available to form sulfur's octahedral hybrid orbital , while six are required for it . Theorists have always been very reluctant to use higher energy level hypervalent orbitals in SF6 bonding schemes . Can they be used for the hybrid orbital , and if so , which are 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 orbitals with its valence shell 3s and 3p orbitals to form the familiar sp3d2 octahedral hybrid orbital . However , as sulfur is a lighter p-block element its 3d orbitals are thought to be unsuitable for hybridization . Maclagan commented ,

“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 significant extent in bonding” (p. 428) .

Reed and Weinhold rather more bluntly state :

“Models of SF6 requiring sp3d2 hybridization should be discarded” (p. 3586) .

These latter authors favored an ionic model of bonding in SF6 , and suggested that d orbitals could contribute to its stabilization via a backbonding process . They calculated the following contributions to the hybrid orbital by native orbitals in the sulfur atom : 32% by 3s ; 59% by 3p ; 8% by 3d ; and 1% by 4p . I’m surprised that no mention of the 4s orbital was made in this analysis , since it's somewhat lower 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 the following “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 the three simple , linear hybrid orbitals are combined to form the composite octahedral orbital : spx + spy + dz2pz = sp3ds , which has a small percentage of d character (the dz2 orbital is the most stereochemically prominent of the d orbitals , and the addition of the pz orbital to it would greatly increase its volume) .

A purely covalent set of six S–F bonds , with no recourse to ionic resonance structures necessary (or even desirable , given the obviously nonpolar covalent nature of sulfur hexafluoride) can be readily formed from the overlap of this sp3ds hybrid orbital , together with its six sulfur valence electrons , with the fluorine atoms . These latter reactants may have a tetrahedral (sp3) hybridization , with one of the four lobes containing the seventh (2p5) fluorine valence electron . I like to draw simple , colorful little picture VB sketches to illustrate these electronic structures :

The turquoise squares represent classic Lewis covalent bonds with shared electron pairs (xo) , while the green squares represent non-bonding lone pairs of electrons (oo) .

The 4s , 4p , and 3d orbitals are substantially higher in energy than sulfur's 3 s-p valence orbitals :

The large energy gap between the 2 s-p and 3 s-p levels normally prevents the use of the latter's empty hypervalent orbitals with the former's valence orbitals to form any 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 their attached 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 form only 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-p elements and the heavier elements of the Periodic Table . The closely spaced energy levels of the latter elements permit a facile hybridization of both normal valent 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 heavier elements have higher coordination numbers than those of the lighter elements , and with more complex geometries than theirs .

The 3 s-p elements may form hypervalent molecules with relatively high coordination numbers , but probably only as products of strongly exoergic reactions , such as fluorinations . For example , the synthesis of sulfur hexafluoride by burning sulfur in fluorine is quite exothermic (288.9 Kcal/mol ; the S–F bond energy in SF6 is 76 Kcal/mol) , so there should be more than enough reaction energy available for creating the sp3ds octahedral hybrid orbital .

A composite hybrid orbital that has no d character can be readily formed by hybridization of the sulfur 3 s-p orbitals with two hypervalent 4p orbitals to produce the composite sp5 hybrid orbital :

3s + 3pz = spz (linear) ; 3px + 4py = p2xy (bent) ; 3py + 4px = p2xy (bent) ; spz + p2xy + p2xy = sp5 (octahedral) , shown in the following sketch :

From the “practical chemistry” point of view the hypothetical sp5 hybrid 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 are energetically or otherwise inaccessible . The elements of the Periodic Table are divided 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 the valence 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 p orbitals when they form hybrid orbitals for covalent bonding . Similarly , the Transition metal elements will use mainly their native d valence orbitals for hybridization . The voluminous , positive symmetry s orbitals are sort of a “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 in hybridization , with virtually no p character ; I have proposed the d5s octahedral hybrid orbital (sketch above) for their covalent bonds . Similarly , the d3s tetrahedral hybrid is used for covalent bonding in Transition metal compounds , compared to the more familar sp3 tetrahedral hybrid for pre- and post-Transition elements . In later Transition metal elements more and more p character enters the hybrids , as more and more d electrons remain sequestered in the electronically inactive atomic kernels . Thus , the well-known octahedral d2sp3 octahedral hybrid appears in the chemistry of mid-Transition metal coordinate covalent complexes , while the dsp2 square planar hybrid predominates with d8 and d9 Transition metal cations .

The selection of a proper hybrid orbital for use in the covalent bonding in any given compound should therefore be made judiciously , respecting its chemistry and the place of its component atoms in the Periodic Table . Hypervalent orbitals can be used in the formation of hybrid orbitals where the coordination number of the 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 and hypervalent orbitals involved in the hybrid . With larger energy gaps hybridization can 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 sp5 octahedral hybrid orbital , both of which are chemically practical and energetically accessible to sulfur atoms , would be satisfactory for use in the S–F bonds of sulfur hexafluoride . These are classic Lewis covalent bonds with no ionic character whatsoever , in agreement with the completely nonpolar covalent nature of SF6 .


The Metallic Bond and Picture MO


That covalent and metallic bonds are diametrically opposed converses of each other is nicely illustrated in the examples of diamond and cesium . In a diamond the carbon atoms are linked by very strong covalent bonds using tetrahedral sp3 hybrid orbitals . A pure diamond weighing 12.011 grams would contain a mole of carbon atoms (Avogadro's Number , NA = 6.022142 x 1023 ) with 2NA carbon–carbon covalent bonds , all of which are at essentially the same energy level .

In contrast , cesium is held together only by a feeble metallic bond , making it it a very soft , low melting (28.6 ºC) solid . A mole of cesium weighs 132.905 grams and contains NA cesium atoms . A single metallic bond , comprised of cesium's 6s orbitals and valence electrons , fills the interatomic space in the metal's lattice .

Cesium's valence electrons are distributed in a vast number of energy levels throughout its metallic bond . There are NA energy levels in the metallic bond of a mole of cesium , corresponding to the NA 6s orbitals that overlap throughout the solid to create the sigma XO (crystal orbital = conduction band = metallic bond) in it . The Fermi-Dirac distribution pairs most (typically 99%) of the 6s1 electrons in the XO in its lower energy levels . The other ~1% of the unpaired singlet electrons occupy higher energy levels above the Fermi level , EF . The lower energy levels with the paired electrons have bonding MO character that provides the strength of the metallic bond (such as it is in cesium) . The energy levels above EF with the singlet electrons have antibonding MO [ABMO] character . While the singlet electrons don't contribute to the bond strength , they are responsible for the physical properties that make metallic solids such unique materials : their high electrical and thermal conductivities , reflectivity (metallic luster) , colors , opacity , and Pauli paramagnetism .

Thus , in a diamond with a mole of carbon atoms there are 2NA carbon–carbon MOs (covalent bonds) at the same energy level , while in a mole of cesium there is a single metallic bond whose NA electrons are distributed over the NA energy levels of its XO . The electrons in the diamond's covalent bonds are essentially 100% localized – located between the carbon atoms – while the electrons in cesium's metallic bond are effectively 100% delocalized ; they can resonate throughout the entire solid in its XO . In these two extreme examples , at least , the covalent and metallic bonds are indeed the converse of each other .

VB and MO theories can both provide a good description of the carbon–carbon bonds in diamond , but classic VB is incapable of properly describing the delocalized electrons in metallic bonds . The simple picture I portrayed above of the metallic bond in cesium is derived from the MO theory . Pauling introduced a concept he referred to as the resonating valence bond – his version of the metallic bond – but I've always preferred , and recommend , the MO approach in this regard .

MO theory has a broader and more comprehensive scope than VB theory , with sigma , pi , and delta MOs and their corresponding ABMOs . It's applicable to both the ground state and excited states of molecules , which is why MO theory is preferred by spectroscopists , for example . By comparison , VB theory describes only 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 the localized sigma bonds that comprise the strong “skeletons” of covalent molecules and solids . Molecular geometry is set by VB's hybrid orbitals , while MO requires an auxilliary theory , Valence Shell Electron Pair Repulsion (VSEPR) , to determine the geometry of molecules and covalent solids . Despite its narrower scope 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 are in most cases remarkably well correlated with the actual physical and chemical properties of the materials studied . Wouldn't it be wonderful if some day an ingenious theoretical chemist was able to combine the best aspects of VB (the hybrid orbitals) with MO , to create a unified orbital bond theory ?

The metallic bond is a very general sort of chemical bond , and can be found in molecular and infinite lattice solids , in polymers , and in both organic and inorganic 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 to describe the localized covalent bonds in them . Any extra , unused , or “leftover” electrons are assigned to an available empty , higher energy frontier orbital above the covalently-bonded skeleton of the structure (molecule or lattice) . I then use picture MO to create the “polymerized MO” – the crystal orbital , XO – that constitutes the metallic bond in the solid and contains the extra electrons .

Picture MO illustrates the metallic bond XO in a qualitative , nonmathematical manner using a simple sketch . The crystal orbital is formed by the continuous overlapping of the native (unhybridized) atomic orbitals of the component atoms in the solid . There are many possible ways in which s , p, and d native atomic orbitals can overlap , both with themselves and with the other types , to form a molecular orbital . Of particular interest with regard to the creation of a metallic bond are the s–s sigma , p–p pi , and d–d delta nodeless XOs , which are shown in the following sketch :

In the above sketch , the yellow sections refer to the part of the electron wave function having a positive symmetry ; the gray sections represent its negative symmetry 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 for a 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 the rule is fulfilled , superconductivity is found with very few exceptions . We can thus assume that the principle condition for the occurrence of superconductivity is in fact the absence of these nodal surfaces”.

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

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

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

Pi XOs can be found in materials with systems of extended p bonds , such as in graphite and doped polyacetylene , both of which are respectable electrical conductors . Delta XOs are undoubtedly found in the Transition metals , which have prominent d orbitals and valence electrons . I've discussed the possibility of delta Ti–Ti bonds in the metallic solid titanium disulfide , TiS2 , which has a golden , lustrous appearance and a lamellar morphology like that of graphite .

The following example will demonstrate how picture VB-MO can describe the electronic structure of a metallic solid . The coordinate covalent platinum compound 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-1 at room temperature . As a pseudometal KCP exhibits a direct temperature–electrical conductivity relationship ; it has , in effect , a reversible metallic 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 , and conversely fewer as it is cooled down .

The coordinate covalent platinum–cyanide bonds in the Pt(CN)4 molecules are highly localized , and don't participate in the metallic bond . They can therefore be accurately described by picture VB as the donation of the nucleophilic cyanide carbons' sigma electron pairs into the empty electrophilic lobes of the platinum square planar dsp2 hybrid orbital . The metallic bond in KCP is formed by the continuous overlapping of the platinum 5dz2 AOs throughout the chains of Pt(CN)4 molecules , which are stacked on top of each other like dinner plates or poker chips :

The VB-MO electronic picture of KCP's platinum atoms can now be sketched as follows :

The metallic bond in KCP is made possible by the mixed-valent nature of the platinum atoms , which consist of approximately 80% Pt(II) and 20% Pt(IV) , with an overall NIOS (non-integral oxidation state) valence of Pt(2.3+) . The resulting sigma XO has orbital vacancies that permit the flow of the free , mobile electrons through the crystal lattice . Unoxidized K2Pt(CN)4 . 3H2O with IOS Pt(II) is a rather ordinary colorless , water-soluble salt , quite unlike KCP , whose insoluble crystals have the form of long , slender , shiny , copper-coloured needles .

The interested reader is referred to a related Chemexplore web page , “A New Classification of Metallic Solids”, for a more detailed discussion of this topic , which includes studies of many other remarkable metallic compounds of elements from 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 for packaging and storing processed foods . We'll look under the shiny outer surface of the can , first studying the tin layer , then the interface of the tin and steel , and finally analysing the iron component of the steel body . Simple , qualitative picture VB-MO models of the electronic structures of the tin , iron , and tin-iron compounds comprising a typical tin can will be presented . These models will be correlated as closely as possible with the known chemical and physical properties of the materials studied .

Tin has a most interesting – and 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 5s2 electronically , while Sn(IV) is 5s0 . The heavier atomic weight post-Transition metal elements are well known for displaying inert pairs of electrons in their compounds . The term “inert” is a relative one , since these lower-valent electrons can be removed by oxidizers of varying strengths to leave the higher-valent cation product . The hydrochloric acid reaction of the two tin allotropes seems to show that there's an inert pair of electrons in white tin – the common tin metal – but not in the less well known gray tin . Chemists are quite familar with the “lone pairs” of non-bonding electrons in many covalently bonded compounds such as the water molecule , with two lone pairs on the oxygen , and ammonia , with a lone 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 5s2 inert pair in white tin suggests that underneath its shiny metallic surface lies 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 :

Gray tin is a a pseudometal with a direct electrical conductivity–temperature relationship :

The electrical conductivity data for this graph were from Ewald and Kohnke .

The metallic bond in gray tin is in the covalent bonds , since all of its valence electrons 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 heavier atoms such as tin . As mentioned above , the nodes act as periodic bottlenecks to the flow of the free , mobile electrons , and are thus responsible for gray tin's pseudometal behaviour . Gray tin has a respectable (for a pseudometal) electrical conductivity of 2090 ohm-1cm-1 at 273 K .

The electrical conductivity of white tin , on the other hand , is 86,957 ohm-1cm-1 at 273 K , and it superconducts at Tc = 3.72 K , which indicates it's a true metal with a nodeless XO as its metallic bond . The white tin atoms have a distorted octahedral coordination . They are in layers , each atom with four short bonds in a zig-zag pattern in the horizontal plane , and with two longer vertical bonds connecting the layers together :

An inert pair of electrons is stereochemically prominent , and will produce a noticeable bulge or elongation in the atomic spacings of a structure (in crystallography the x-rays can “see” the atomic kernels , but not the electrons or inert pairs in between them) . Unusually long bonds in a crystal structure are often a good clue to the presence in them of inert pairs of electrons . The 5s2 inert pair in white tin is undoubtedly located in its long axial bonds , and could actually be functioning as a sort of coordinate covalent bond , as shown in the following sketch :

The above sketch highlights several interesting features of the white tin electronic structure . First , it shows all seven Sn–Sn bonds per tin atom : four covalent , two coordinate covalent , and the actual metallic bond (6 s-p) XO . Second , it shows the use of two hypervalent 4d orbitals , together with their four electrons , in the covalent bonds . Note the 4d orbitals and their electrons are at approximately the same energy level as the normal valence 5 s-p orbitals in tin (see the energy level sketch 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 two inert pairs ! The 5s2 valence electrons are located in the axial Sn–Sn bonds ; the 6s2 pair are in the metallic bond XO . A trickle of electron density from the 6s2 pair into the adjacent empty 6p orbitals opens up vacancies in the 6s sigma XO and permits it to act as the metallic bond in white tin .

While the four valence electrons in degenerate tin atoms (isolated in space , with no neighbours) are 5s2 5p2 , this VB-MO picture predicts that in solid-state tin metal the 5p2 electrons have been promoted up to the 6 s-p energy level , as the 5p orbitals are now occupied by covalent bonds .

The reactive hydrochloric acid can readily oxidize the 6s2 inert pair ; when that happens , the tin structure disintegrates , the 4d electrons retreat back to their native orbitals , and the remaining 5s2 inert pair surrounds the tin(II) cation , now an electrophilic sphere that is quickly coordinated by nucleophilic water ligands . In the case of gray tin , the four identical covalent bonds per tin atom are simultaneously oxidized by the HCl , leaving a residual hydrated Sn(IV) cation .

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


Jamieson reported in 1963 that under high pressure the diamond crystal structure of both silicon and germanium will change into that of white tin . Subsequently , Drickamer determined that those white tin phases of silicon and germanium are excellent metallic electrical conductors . This leads us to a startling conclusion : the application of high pressure to silicon compresses its atoms to such an extent that its hypervalent 2p orbitals and electrons (from 2s2 2p6) can be combined with its normal valent 3 s-p orbitals and electrons (3s2 3p2) to create the 2(p2) + 3(sp) + 3(p2) distorted octahedral hybrid orbital , plus the 4 s-p sigma XO metallic bond in the solid :

As discussed above in the sulfur hexafluoride section , the very large energy gap between 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 hybrid orbitals with more than four positive symmetry lobes . I've indicated a larger than usual energy gap between the 2 s-p and 3 s-p energy levels in the sketch above for metallic 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 hypervalent 2p orbitals and their four electrons with the normal valence 3s2 3p2 orbitals and electrons . The result is an electronic structure for highly compressed metallic silicon rather like that of tin metal .

The electronic structure of compressed germanium would be similar to that of silicon , 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 the corresponding gap in silicon , we would expect that less pressure would be required 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. 1410–1414 ºC) is also metallic :

“It is noteworthy that the melting of Si at ambient conditions [one atmosphere pressure] also displays a transition both from four-fold to sixfold coordination and from 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 tin structure just before liquifying is significant . This suggests that the huge amount of thermal energy applied to its lattice is sufficient to promote its inner 2p orbitals and their electrons to a higher excited state , making them accessible to the 3 s-p orbitals for creation of the 2(p2) + 3(sp) + 3(p2) hybrid orbital . The thermal conversions of silicon and gray tin to their distorted octahedral white tin structures are thus analogous , differing only in the amount of energy required for the transitions . This example of silicon shows that even the very large 2 s-p to 3 s-p energy gap can be closed , and lower energy level hypervalent orbitals and their electrons 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 compounds in 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 on their shelves . The chemistry of the tinning and de-tinning of steel is of considerable economic importance , and so has been widely researched . I counted over 300 research papers listed in SciFinder Scholar on this subject ! When steel is coated with liquid tin , there is a very small but observable mutual diffusion of the tin and iron atoms into each other's phases , with the formation of at least two iron–tin intermetallic compounds . Giefers and Nicol describe five well characterized Fe–Sn intermetallic phases (FeSn2 , FeSn , Fe3Sn2 , Fe5Sn3 , and Fe3Sn) in their comprehensive review . Of these , the first two exist at room temperature ; the remaining three are found only at high temperatures (refer to their phase diagram of the Fe–Sn system , Fig. 1 , p. 133) . FeSn and FeSn2 have well defined crystal structures (nicely illustrated in their Fig. 2 , p. 133) that are readily amenable to a picture VB-MO analysis .

FeSn is antiferromagnetic with a Néel temperature of TN = 373 K (CRC Handbook of Chemistry and Physics) , or 368 K (Häggström and co-workers) . The central thesis of several of my Chemexplore web pages , for example , “Antiferromagnetic Induction in High Temperature Superconductors”, emphasizes the crucial role of antiferromagnetism in the design of new superconductors . If an antiferromagnetic spin régime , i.e antiparallelism , can be imposed on the mobile , free electrons above EF in a metallic solid , they can magnetically couple together into 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 elevated temperature . However , it apparently never becomes superconducting at all . Why not ?

Stenström carried out a careful study of the electrical resistivity of FeSn , and found that a very pure single crystal of the compound had a nearly linear inverse temperature–electrical conductivity relationship (his Fig. 2 , p. 215) . The FeSn crystal was anisotropic ; its electrical conductivity was somewhat different 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) . Stenström reported a “residual resistivity” [in conductivity terms] of FeSn cooled in liquid helium at 4.2 K of 833,000 ohm-1cm-1 (parallel) and 2.9 million ohm-1cm-1 (perpendicular) . The electrical conductivity characteristics of FeSn are similar to those of the closely related metallic solid , iron monophosphide , FeP , whose ambient electrical conductivity is also 12,500 ohm-1cm-1, rising to 3.3 million ohm-1cm-1 in liquid helium . FeP similarly doesn't seem to superconduct , and like FeSn it too is antiferromagnetic (TN = 123 K) .

The electrical conductivity behaviour of FeSn indicates it's a true metal with a nodeless XO as its metallic bond . It consists of alternating hexagonal layers of iron-rich Fe2Sn and pure Sn :

The layer of tin atoms (green spheres) is better viewed in the next sketch , in which the 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 planar coordination in the Fe2Sn layers , and a trigonal prismatic coordination by the iron atoms in the pure tin layers . The structure of FeSn is quite similar to the well known nickel arsenide crystal structure , in which the metal atoms are in hexagonal layers , with the nonmetal atoms sandwiched between them . The nickel atoms in NiAs have an octahedral coordination , while the arsenic atoms have a trigonal prismatic coordination . In fact , both Wells(2) and Wyckoff list FeSn as having a NiAs crystal structure , although its more recent classification is the hexagonal B35 CoSn structure .

With this essential crystallographic and electrical conductivity information in hand , a reasonable picture VB-MO electronic structure for FeSn can be sketched as follows :

The tin atoms , which are basically electronically inert linking atoms (like the arsenics in NiAs) , must use both their 4d10 and 6p0 hypervalent orbitals in the hexa-coordinate hybrid orbitals . The iron atoms deploy six of their eight (3d6 4s2) valence electrons in the octahedral covalent Fe–Sn bonds ; the two extra , leftover electrons will most likely be located in the energetically accessible , empty 4p frontier orbitals . These can readily overlap continuously along the lines of iron atoms in the Fe2Sn layers to form a pi XO , which is predicted to be the nodeless metallic bond in FeSn .

The puzzling question as to why FeSn , an antiferromagnetic metallic solid , should not be a high temperature superconductor , may have been answered by Yamaguchi and Watanabe , who studied the magnetic structure of the material by neutron diffraction . They commented ,

“....... it is quite evident that the magnetic moments of Fe atoms lie in the c-plane and are coupled ferromagnetically within a c-plane , while they are coupled antiferromagnetically to those on the adjacent c-planes” (p. 1211) .

Their Fig. 5 , p. 1212 , illustrates the three-dimensional arrangement of the electron spins 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 XO over the iron atoms in the Fe2Sn layers . However , the electrons in the XO have a ferromagnetic ordering ; such a parallel spin ordering of the free electrons above EF will effectively prevent them from magnetically coupling into Cooper pairs for superconduction (antiparallelism is required !) . That's a simple , straightforward explanation of why FeSn , which has a very high electrical conductivity at low temperatures and is simultaneously antiferromagnetic , never becomes superconducting .

As mentioned , FeSn strongly resembles FeP and FeAs , which have the NiAs crystal structure . Iron pnictides such as FeAs form the foundation of a large family of recently-developed medium temperature (Tc ~ 30–60 K) superconductors , of which electron-doped derivatives of the layered compound LaOFeAs are typical examples . These materials are reviewed in other Chemexplore web pages such as the Iron and Doping ones , so I won't comment any further on them here . The FeAs layers are the electronically-active parts , having Fe–As covalent bonds “coated” 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 XO metallic bond like that of FeSn above .

The iron pnictide layers in them , though , no longer have the NiAs crystal structure ; rather , they have been flattened out into two-dimensional layers which now have the anti-litharge structure . The litharge crystal structure [for PbO , yellow lead(II) oxide , and the related black tin(II) oxide , SnO] was determined in 1941 by Pauling and his post-doc researcher , W.J. Moore (who later wrote one of my favourite solid state chemistry textbooks , Seven Solid States , referenced below) . They proposed an unusual – square pyramid – coordination for the lead and tin atoms in these two compounds , which caused the flattening and layering effect in them :

“We suggest that the orbital arrangement for Pb(II) and Sn(II) in these crystals is that of a square pyramid , four bond orbitals being directed from the metal atom within 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 indicates covalent bonding in the structure , so PbO and SnO are really inorganic polymers having metal–oxygen covalent (not ionic) bonds . The oxygens are tetrahedrally-coordinated linking atoms in these two compounds :

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

The lead atoms in PbO must involve one of their hypervalent orbitals , in this case an empty 6dx2-y2 orbital , in order to create a hybrid orbital with five lobes (sp3dx2-y2 , the usual square pyramid hybrid) , the axial one being reserved for the inert pair of electrons . The sp4 composite orbital (sp2 + p2) , sketched above in the SF6 section , might also be used by the lead atoms in PbO . In this case , they would 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 to LaOFeAs . As recommended in the Doping web page , ionic fluoride reducing layers should be more efficient at electron-doping than the corresponding ionic oxide layers . Also , blends of reducers adding a non-integral number of electrons to the substrate are desirable , which should prevent the inevitable spin density wave (SDW) from forming in the doped composite at lower temperatures . Such an SDW effectively inhibits the appearance of superconductivity in the compound by localizing electron pairs in Fe–Fe 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 dimensional litharge/anti-litharge structure , as with FeAs .

An FeSn composite for electrical and superconductivity testing might be compounded as follows using the fluoride reducers “AlF” and “TiF” :

2/3 Al0 + 1/3 AlF3 + FeSn ----- (argon atm.) -----> AlFFeSn , i.e. [AlF]2+ [FeSn]2- ;

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.) -----> [Alx Ti1-x F](3-x)+ [FeSn](3-x)-.

The mole ratio x would be taken experimentially between 0 and 1 , to synthesize as many 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 litharge structure (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 a tetrahedral ligand environment the d orbitals' energy levels are split into a lower energy level (dx2-y2 and dz2) , and a higher energy level (dxy,xz,yz) . The d3s hybrid orbital is created using the three higher energy level dxy,xz,yz native orbitals , combined with the 4s native orbital . The added electrons from the AlF and TiF reducers must then be located in the empty and energetically accessible 4p frontier orbitals on the iron atoms . These will form the predicted pi XO metallic bond in the solids . Our picture VB-MO sketch is thus very useful in helping us understand the electronic situation both in FeSn and in its possible layered derivatives in simple , qualitative terms . We might reasonably expect to observe superconductivity in these latter materials at a modest (Tc ~ 3060 K) temperature .

Returning to the irontin intermetallic compounds found in tin-plated steel , the more common one , FeSn2 , is also antiferromagnetic (TN = 378 K , Venturini and co-workers) . Tin-plating processes involving molten tin often produce a waste material , a dross commonly referred to as hartling . Hartling consists mostly of FeSn2 crystals , cemented together by tin metal . A modern practical application for the otherwise unremarkable FeSn2 involves its use as an anode material in lithium ion secondary (rechargeable) batteries (Zhang and co-workers) . In the charge cycle it reacts with lithium cations and electrons to form the transient compound Li4.4Sn , plus Fe0 . This unstable LiSn intermediate decomposes in the discharge cycle to Sn0 + 4.4 Li1+ + 4.4 electrons . The Fe0 recombines with the Sn0 to regenerate the FeSn2 anode , continuing the electrochemical cycling .

As shown in the following sketch , the tin atoms in FeSn2 have a square pyramid coordination (dsp3) to the iron atoms , which in turn have a square antiprism coordination (d5p3) to the tin atoms . When tin atoms predominate in a compound and so are in a lower valence state , their 5s2 inert pairs of electrons appear in non-bonding lobes of their hybrid orbitals . In compounds where they aren't as plentiful as their partner atoms and are thus in a higher valence state , they are obliged to use them in covalent bonding , as was observed with FeSn . Tin's inert pairs are stereochemically prominent in the lattice of FeSn2 , which formally has the CuAl2 (C16) (or Fe2B , Wyckoff) crystal structure :

A picture VB sketch of a possible electronic structure of FeSn2 is presented below :

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 located in empty frontier orbitals on the iron atoms , as was the case with FeSn . Thus , FeSn2 is predicted to be a pseudometal with a direct temperatureelectrical conductivity relationship . The tin atoms act as spacers, which spread out the iron atoms 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 tin kernels . However , these nodes are expected to be quite narrow , as is the case generally with larger , heavier atoms . The electrical conductivity of FeSn2 could thus be quite respectable , as with gray tin (graph above) . Since the 4s native orbitals on the iron atoms are at approximately the same energy level as its 3d and 4p orbitals forming the d5p3 square antiprism hybrid orbital , some electron density could leak from the FeSn covalent bonds into them , resulting in an augmentation of the electrical conductivity of the material and some leveling of its temperatureconductivity curve .

Marchal and co-workers studied the electrical resistivity of amorphous thin films of irontin compounds , FexSn1-x , on inert surfaces . They discovered radical differences 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 , are complicated by the crystallization of the irontin compounds at elevated temperatures . The crystalline films provided completely different traces than their amorphous counterparts . An extract of their data (at 77 K , in liquid nitrogen , and at room temperature , 295 K) is presented in the Table below :

The traces for the amorphous films look very strange and irregular , but those for the crystalline films are fairly linear , and are almost level , with a slight inclination to the inverse . At x = 0.35 , the irontin compound involved is essentially FeSn2 (Fe0.33Sn0.67) , while the x = 0.625 material is mostly FeSn (Fe0.5Sn0.5) . The remarkably linear trace for Marchal and co-workers' crystalline FeSn agrees very well with Stenström's resistivity measurements , mentioned above . The magnitude of the electrical conductivities reported for crystalline FeSn2 films by Marchal and co-workers well exceeds that of gray tin . Its slight inverse nature suggests , in accordance with Krebs's Theorem , that substantial leakage of electron density from 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 CuAl2 type intermetallics , including FeSn2 , in 1972 . They noted (in their Table 1 , p. 285) , that FeSn2 showed an antiferromagnetic transition and had Tc < 0.07 K , which could be interpreted as meaning that no superconducting Tc was observed for FeSn2 down to their lower experimental limit of 0.07 K . A careful study of the temperatureelectrical conductivity relationship of a single crystal of pure FeSn2 , as Stenström did with FeSn , would be instrumental in resolving the uncertainty surrounding the electrical behaviour of FeSn2 , and thereby either verifying or refuting the picture VB electronic structure of the compound presented above .

Returning again to the tin cans , their steel bodies are a mixture of phases , with very complex physical and chemical natures . I would refer the interested reader to the descriptions of steel by Moore and Wells(3) , and in the KOECT . However , we could take a look at the electron organization in pure iron , the principal component of steel . Pauling was interested in the electronic structure of iron (and of tin , too , by the way) , suggesting that several readily accessible excited states in 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 (eight per iron atom) , plus the two extra ones for the conventional s-p metallic bond XO , plus the two unpaired singlet electrons in each iron atom . Of course , we all know that iron metal is strongly ferromagnetic , and can be readily magnetized by the imposition 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 two unpaired singlet electrons per atom . The electronic configuration for degenerate iron(0) is 3d6 4s2 , so there simply aren't enough valence shell electrons in it for the electronic structure of solid state iron , which requires twelve .

Pauling was reluctant to invoke the use of any sort of hypervalent orbitals or electrons in the creation of hybrid orbitals , for example in his electronic structure of phosphorus pentachloride . However , in the case of bcc iron [and with white tin metal , discussed above] , we absolutely must involve hypervalent orbitals and electrons (and empty outer frontier orbitals) in the description of an electronic structure for iron which is in a reasonable agreement with its known chemical and physical properties . With this latter requirement foremost in mind , the following picture VB-MO electronic structure for iron metal is brought forward :

Interestingly , the d5sp2 square prism hybrid orbital is one of the excited states proposed by Pauling for iron ; but while he preferred to use normal valence shell orbitals for it (and as a result didn't have enough electrons) , I've used an inner d5sp2 square prism hybrid orbital , involving two hypervalent 3p orbitals , including their four electrons , in the electronic structure . Now there are just the right number of electrons (12) for the bcc structure , with eight Fe–Fe 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-p metallic bond XO .

The 4px,y orbitals can overlap end-to-end between the iron atoms in the x-y plane to form p-p sigma MOs , each of which can form a one-electron bond , which can also 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 4pz orbitals perpendicular to the planes of atoms can overlap side-to-side to form a continuous pi XO over the planes . However , since the individual 4pz orbitals 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 function as a metallic bond . This leakage likely occurs from the 4pz into 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 two hypervalent 3p orbitals and their electrons in this scheme ? Are they energetically accessible ? The 3d , 4s , and 4p orbitals in iron are all at roughly the same energy level – see the sketch further up this web page showing the relative energy levels of the s , p, and d orbitals – but there is a significant energy gap separating the 3 s-p and 4 s-p levels . Considerable energy will be required to create a d5sp2 square prism hybrid orbital which includes two of the 3p native orbitals . Again , we must consider the practical chemistry of iron , and even its metallurgy , in pondering this question . The agglomeration of iron atoms into a macroscopic sample of iron metal requires a large amount of energy . Pure iron melts at 1536 ºC , and it's manufactured (as pig iron) in vast amounts worldwide in blast furnaces . Undoubtedly there is more than enough heat energy in a blast furnace to promote the four hypervalent 3p electrons into the d5sp2 square prism hybrid orbital ! As with sulfur hexafluoride and metallic silicon discussed above , the creation of hybrid orbitals should be possible even in extraordinary or unusual systems by the provision of considerable thermal energy and/or high pressure , both of which can close forbiddingly wide energy gaps between the s-p energy levels .

Picture VB – the simple , qualitative version of the classic valence bond theory – has been shown in this example of iron and in the other case studies presented in this web page to be a surprisingly effective and revealing technique in the analysis of the electronic structures of many types of materials . Picture VB is an indispensible model-making tool in my chemistry studies . I hope I've demonstrated how useful and informative it can be in helping us understand the chemical bonding in molecules and crystalline solids .


References , Notes , and Further Reading


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

Pauling : L. Pauling , “The Nature of the Chemical Bond – Application of  Results Obtained from the Quantum Mechanics and from a Theory of Paramagnetic Susceptibility to the Structure of Molecules”, J. Amer. Chem. Soc. 53 (4) , pp. 1367-1400 (1931) . This first exposition of the VB theory was later incorporated into Pauling’s textbook , The Nature of the Chemical Bond and the Structure of Molecules and Crystals , 3rd ed. , 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 in Coordination Chemistry and the Nature of MetalMetal Bonds, J. Chem. Educ. 61 (7) , pp. 582- 587 (1984) ; L. Pauling , “Valence-Bond Theory of Compounds of Transition Metals”, Proc. Nat. Acad. Sci. USA 72 (11) , pp. 4200-4202 (1975) [PDF , 615 KB] ; idem. , “Bond Angles in Transition-Metal Tricarbonyl 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. , “Bond Angles in Transition Metal Tetracarbonyl Compounds : A Further Test of the Theory 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 localized electron 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 Bonding Concepts, J. Chem. Educ. 62 (4) , p. 362 (1985) .

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 hybrid orbitals asorbitals ; my practice throughout this and other Chemexplore web pages is to consider the entire combination of lobes as one single orbital . For example , the tetrahedral sp3 orbital has four positive symmetry lobes . Such terminology 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 Interview With Linus Pauling”, J. Chem. Educ. 73 (1) , pp. 29-32 (1996) . For another illuminating Pauling interview , see : E. Garfield , “Linus Pauling : An Appreciation of a World Citizen-Scientist and Citation Laureate”, Current Contents , no. 34 , pp. 3-11 (August 21 , 1989) [PDF , 713 KB] .

Maclagan : R.G.A.R. Maclagan , “Symmetry , Ionic Structures and d Orbitals in SF6”, J. Chem. Educ. 57 (6) , pp. 428-429 (1980) .

Reed and Weinhold : A.E. Reed and F. Weinhold , “On the Role of d Orbitals in SF6”, J. Amer. Chem. Soc. 108 (13) , pp. 3586-3593 (1986) . See also E. Magnusson , “Hypercoordinate Molecules of Second-Row Elements : d Functions or d Orbitals ? ”, J. Amer. Chem. Soc. 112 (22) , pp. 7940-7951 (1990) ; P.G. Nelson , “Modified Lewis Theory , Part 1 . Polar Covalent Bonds and Hypervalency”, Chemistry Education : Research and Practice in Europe 2 (2) , pp. 67-72 (2001) [PDF , 161 KB] ; SF6 is discussed on pp. 70-71 .

to draw : The sketches and non-structure illustrations in this web page were produced using the ACD/ChemSketch software program . A full-featured commercial version is available , and the software publisher , Advanced Chemistry Development Inc. , Toronto , Ontario , Canada , has graciously made the previous-to-commercial version available as freeware . Highly recommended !

burning sulfur in fluorine : J.R. Partington , A Textbook of Inorganic Chemistry , 6th edition , Macmillan , London (UK) 1957 ; p. 460 :

“Sulphur burns spontaneously in fluorine producing colourless gaseous sulphur hexafluoride , SF6 (Moissan and Lebeau , 1900)” .

exothermic : H.L. Roberts , The Chemistry of Compounds Containing SulfurFluorine Bonds, Quart. Rev. 15 (1) , pp. 30-55 (1961) ; p. 38 .

crystal orbital : I use the term crystal orbital to mean a polymerized molecular orbital, spanning the entire crystal dimensions . Thus , crystal orbital is synonymous with the terms metallic bond (chemistry) and conduction band (physics) . I abbreviate crystal orbital as XO , since Xal is sometimes used as an abbreviation for crystal (and I don't want to use CO , the formula of carbon monoxide !) . Crystal orbitals are discussed in two excellent solid state chemistry textbooks : P.A. Cox , The Electronic Structure and Chemistry of Solids , Oxford University Press , Oxford (UK) , 1987 ; Ch. 4 , pp. 79-133 ; R. Hoffmann , Solids and Surfaces , A Chemist’s View of Bonding in Extended Structures , VCH Publishers , New York , 1988 ; pp. 43-55 .

Fermi-Dirac distribution : A.R. Mackintosh , “The Fermi Surface of Metals”, Scientific American 209 (1) , pp. 110-120 (July , 1963) . The electron theory of metals is reviewed by W.J. Moore , Seven Solid States , An Introduction to the Chemistry and Physics of Solids , W.A. Benjamin , New York , 1967 ; Ch. 2 , “Gold”, pp. 41-72 ; see Fig. 2.4 , p. 49 for a sketch of a typical Fermi-Dirac distribution curve .

typically 99% : A.B. Ellis et al. , Teaching General Chemistry , A Materials Science Companion , American Chemical Society , Washington , D.C. , 1993 ; pp. 191-192 (example of sodium metal) .

resonating valence bond : L. Pauling , “The Nature of the Interatomic Forces in Metals”, Phys. Rev. 54 (11) , pp. 899-904 (1938) ; idem. , “The Resonating-Valence-Bond Theory of Metals”, Physica 15 (1-2) , pp. 23-28 (1949) ; idem. , “The Resonating Valence-Bond Theory of Metals and Intermetallic Compounds”, Proc. Roy. Soc. Lond. A196 (1046) , pp. 343-362 (1949) ; idem. , “The Resonating-Valence-Bond Theory of Superconductivity : Crest Superconductors 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 Containing Five Different Types of Bonding”, J. Chem. Educ. 59 (5) , pp. 361-362 (1982) .

Krebs : H. Krebs , “Superconductivity in Metals , Alloys , Semiconductors , and Glasses 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 Oxidized Tetracyanoplatinate Metals : New Results and Summary”, pp. 337-368 in 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 , 3rd edition , Clarendon Press , Oxford (UK) , 1962 ; p. 976 .

tin : Alicia O'Reardon Overbeck , Tin , the Cinderalla Metal, National Geographic 78 (5) , pp. 659-684 (November , 1940) [this article is mostly about tin mining in Bolivia] ; Tin : From Ore to Ingot, International Tin Research Institute , 5 pp. , undated (PDF , 4375 KB) .

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

Ewald and Kohnke : A.W. Ewald and E.E. Kohnke, “Measurements of Electrical Conductivity 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 Metallic Modifications of Silicon and Germanium”, Science 139 (3556) , pp. 762-764 (1963) .

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

Giefers and Nicol : H. Giefers and M. Nicol , “High Pressure X-ray Diffraction Study of All Fe–Sn Intermetallic Compounds and One Fe–Sn Solid Solution”, J. Alloys & Compounds 422 (1-2) , pp. 132-144 (2006) .

Häggström and co-workers : L. Häggström , T. Ericsson , R. Wäppling , and K. Chandra , “Studies of the Magnetic Structure of FeSn Using the Mossbauer Effect”, Physica Scripta 11 (1) , pp. 47-54 (1975) .

Stenström : B. Stenström , “The Electrical Resistivity of FeSn Single Crystals”, Physica Scripta 6 (4) , pp. 214-216 (1972) .

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 Iron Monophosphide”, 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 , 2nd edition , vol. 1 , Interscience (John Wiley) , New York (1963) ; Table III,7 , p.124 (ref. on p. 190) . FeSn2 has the 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 , Neutron Diffraction 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 the Tetragonal 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 Electrochemical Performances of Nanoscale FeSn2 as 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 , including FeSn2 , in organic solvents . By adjusting the Fe–Sn stoichiometry to equimolar , it might be possible to synthesize pure FeSn : N.H. Chou and R.E. Schaak , “Shape-Controlled Conversion of b-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 FeSn2 is described on p. 7340 ; R.E. Cable and R.E. Schaak , “Low-Temperature Solution Synthesis of Nanocrystalline Binary Intermetallic Compounds Using the Polyol Process”, Chem. Mater. 17 (26) , pp. 6835-6841 (2005) ; N.L. Henderson and R.E. Schaak , “Low-Temperature Solution-Mediated Synthesis of Polycrystalline Intermetallic Compounds from Bulk Metal Powders”, Chem. Mater. 20 (9) , pp. 3212-3217 (2008) ; N.L. Henderson et al. , “Toward Green Metallurgy : Low-Temperature Solution Synthesis of Bulk-Scale Intermetallic 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 of FeSn2”, 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 FeSn2 by the direct combination of iron and tin metal reagents .

hartling : V. V. Pokrovskii , Yu. S. Arzamastsev , and O. F. Purvinskii , “Preparation of a Pure Tin–Iron Intermetallic Compound”, Uch. Zap. Tsentr. Nauchn.-Issled. Inst. Olovyan. Prom. 2 , pp. 44-45 (1964) [from SciFinder Scholar ; hartling was used to electrolytically prepare pure FeSn2] .

Marchal and co-workers : G. Marchal et al. , Composition and Temperature Ranges for Amorphous FexSn1-x Alloy 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 of Chemical Technology , 3rd edition , 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”, Physical Review 54 (11) , pp. 899-904 (1938) ; possible valence bond descriptions of gray and white tin are discussed on p. 904 . Pauling suggested the 4d1 5s1 5p3 5d1 configuration for the distorted octahedral hybrid orbitals tin metal , but this electronic structure makes no allowance for any inert pair or pairs in its lattice . Full credit must be given to Pauling for introducing the novel concept of covalent bonding in metals (using s-p-d hybrid orbitals) , which he discussed at length 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 electronic structure 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 PCl5 consisted of [PCl4]+ Cl- having several electronic resonance forms , using conventional s-p hybrid orbitals without recourse to any hypervalent 3d orbitals . Actually , it's now known that solid PCl5 consists of the two ionic molecules , [PCl4]+ [PCl6]-, the former with tetrahedral P–Cl 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 ºC) 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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