Editing William Lipscomb (section)

===Boron chemistry and the nature of the chemical bond===

In this area Lipscomb originally intended a more ambitious project: "My original intention in the late 1940s was to spend a few years understanding the [[borane]]s, and then to discover a systematic [[Valence (chemistry)|valence]] description of the vast numbers of electron deficient [[intermetallics|intermetallic]] compounds. I have made little progress toward this latter objective. Instead, the field of [[boron]] chemistry has grown enormously, and a systematic understanding of some of its complexities has now begun."<ref name=Lipscomb1977PrixNobel/>
Examples of these intermetallic compounds are KHg<sub>13</sub> and Cu<sub>5</sub>Zn<sub>7</sub>.  Of perhaps 24,000 of such compounds the structures of only 4,000 are known (in 2005) and we cannot predict structures for the others, because we do not sufficiently understand the nature of the chemical bond.
This study was not successful, in part because the calculation time required for intermetallic compounds was out of reach in the 1960s, but intermediate goals involving boron bonding were achieved, sufficient to be awarded a Nobel Prize.

[[File:lipscomb diborane b2h6 atomic diagram.png|thumb|right|Atomic diagram of [[diborane]] (B<sub>2</sub>H<sub>6</sub>).]]
[[File:Diborane 02.svg|thumb|right|Bonding diagram of [[diborane]] (B<sub>2</sub>H<sub>6</sub>) showing with curved lines a pair of [[three-center two-electron bond]]s, each of which consists of a pair of electrons bonding three atoms, two boron atoms and a hydrogen atom in the middle.]]

The three-center two-electron bond is illustrated in [[diborane]] (diagrams at right).
In an ordinary covalent bond a pair of electrons bonds two atoms together, one at either end of the bond, the diboare B-H bonds for example at the left and right in the illustrations.
In three-center two-electron bond a pair of electrons bonds three atoms (a boron atom at either end and a hydrogen atom in the middle), the diborane B-H-B bonds for example at the top and bottom of the illustrations.

Lipscomb's group did not propose or discover the three-center two-electron bond,
nor did they develop formulas that give the proposed mechanism.
In 1943, [[H. Christopher Longuet-Higgins|Longuet-Higgins]], while still an undergraduate at Oxford, was the first to explain
the structure and bonding of the boron hydrides. The paper reporting the work, written with his tutor R. P. Bell,
<ref>{{Cite journal | last1 = Longuet-Higgins | first1 = H. C. | last2 = Bell            | first2 = R. P. | author-link = H. Christopher Longuet-Higgins | title   = 64. The Structure of the Boron Hydrides | journal = Journal of the Chemical Society (Resumed) | year    = 1943 | volume  = 1943 | pages   = 250–255 | doi     = 10.1039/JR9430000250 }}</ref> also reviews the history of the subject beginning with the work of Dilthey.
<ref name=Dilthey1921/> Shortly after, in 1947 and 1948, experimental spectroscopic work was performed by Price<ref name=Price1947/><ref name=Price1948/>
that confirmed Longuet-Higgins' structure for diborane. The structure was re-confirmed by electron diffraction measurement in 1951 by K. Hedberg and V. Schomaker, with the confirmation of the structure shown in the schemes on this page.<ref>{{ cite journal |author1=Hedberg, K. |author2=Schomaker, V. | title = A Reinvestigation of the Structures of Diborane and Ethane by Electron Diffraction | journal = [[Journal of the American Chemical Society]] | year = 1951 | volume = 73 | issue = 4 | pages = 1482–1487 | doi = 10.1021/ja01148a022 }}</ref> Lipscomb and his graduate students further determined the [[molecular structure]] of [[borane]]s (compounds of boron and hydrogen) using [[X-ray crystallography]] in the 1950s and developed theories to explain their [[chemical bond|bond]]s. Later he applied the same methods to related problems, including the structure of [[carborane]]s (compounds of carbon, boron, and hydrogen). [[H. Christopher Longuet-Higgins|Longuet-Higgins]]
and Roberts<ref name=Longuet-Higgins1954/><ref name=Longuet-Higgins1955/>
discussed the electronic structure of an icosahedron of boron atoms and of the borides MB<sub>6</sub>. The mechanism of the three-center two-electron bond was also discussed in a later paper by Longuet-Higgins,<ref>{{cite journal | author1 = H. C. Longuet-Higgins | title = title unknown | journal =  J. Roy. Inst. Chem.| year = 1953 | volume = 77 | page = 197}}</ref> and an essentially equivalent mechanism was proposed by Eberhardt, Crawford, and Lipscomb.<ref name=Eberhardt1954ThreeCenter/>
Lipscomb's group also achieved an understanding of it through electron orbital calculations using formulas by Edmiston and Ruedenberg and by Boys.<ref name=Kleir1974Rudenberg/>

The Eberhardt, Crawford, and Lipscomb paper<ref name=Eberhardt1954ThreeCenter/> discussed above  also devised the "[[styx rule]]" method to catalog certain kinds of boron-hydride bonding configurations.

[[File:lipscomb diamond-square-diamond-horizontal.png|thumb|left|Diamond-square-diamond (DSD) rearrangement. At each vertex is a boron atom and (not shown) a hydrogen atom. A bond joining two triangular faces breaks to form a square, and then a new bond forms across opposite vertices of the square.]]

Wandering atoms was a puzzle solved by Lipscomb<ref name=Lipscomb1966DSD/> in one of his few papers with no co-authors.
Compounds of boron and hydrogen tend to form closed cage structures.
Sometimes the atoms at the vertices of these cages move substantial distances with respect to each other.
The diamond-square-diamond mechanism (diagram at left) was suggested by Lipscomb to explain this rearrangement of vertices.
Following along in the diagram at left for example in the faces shaded in blue,
a pair of triangular faces has a left-right diamond shape.
First, the bond common to these adjacent triangles breaks, forming a square,
and then the square collapses back to an up-down diamond shape
by bonding the atoms that were not bonded before.
Other researchers have discovered more about these rearrangements.<ref>{{cite journal|last=Hutton|first=Brian W. |author2=MacIntosh, Fraser |author3=Ellis, David |author4=Herisse, Fabien |author5=Macgregor, Stuart A. |author6=McKay, David |author7=Petrie-Armstrong, Victoria |author8=Rosair, Georgina M. |author9=Perekalin, Dmitry S. |author10=Tricas, Hugo |author11=Welch, Alan J. |title=Unprecedented steric deformation of ortho-carborane|journal=Chemical Communications |date=2008|issue=42|pages=5345–5347|doi=10.1039/B810702E|pmid=18985205 |url=http://pubs.rsc.org/en/Content/ArticleLanding/2008/CC/b810702e}}</ref>
<ref name=Hosmane1996DSD/>

[[File:Lipscomb b10-h16-horizontal.png|thumb|right|B<sub>10</sub>H<sub>16</sub> showing in the middle a bond directly between two boron atoms without terminal hydrogens, a feature not previously seen in other boron hydrides.]]

The B<sub>10</sub>H<sub>16</sub> structure (diagram at right) determined by Grimes, Wang, Lewin, and Lipscomb found a bond directly between two boron atoms without terminal hydrogens, a feature not previously seen in other boron hydrides.<ref name=Grimes1961/>

Lipscomb's group developed calculation methods, both empirical<ref name=Eaton1969/> and from quantum mechanical theory.<ref name=Pitzer1962/><ref name=Stevens1963/>
Calculations by these methods produced accurate [[Hartree–Fock method|Hartree–Fock self-consistent field (SCF)]] [[molecular orbital]]s and were used to study boranes and carboranes.

[[File:Lilpscomb-ethane-barrier.png|thumb|left|Ethane barrier to rotation about the carbon-carbon bond, first accurately calculated by Pitzer and Lipscomb.]]

The [[ethane]] barrier to rotation (diagram at left) was first calculated accurately by [[Russell M. Pitzer|Pitzer]] and Lipscomb<ref name=Pitzer1963Ethane/> using the [[Hartree–Fock method|Hartree–Fock (SCF)]] method.

Lipscomb's calculations continued to a detailed examination of partial bonding through "... theoretical studies of multicentered chemical bonds including both delocalized and [[localized molecular orbitals]]."<ref name=Lipscomb1977/>
This included "... proposed molecular orbital descriptions in which the bonding electrons are delocalized over the whole molecule."<ref name="autogenerated1">{{cite journal | doi = 10.1036/1097-8542.109100| title = Carborane |journal=AccessScience |last=Getman |first=Thomas D. |year=2014}}</ref>

"Lipscomb and his coworkers developed the idea of transferability of atomic properties, by which approximate theories for complex molecules are developed from more exact calculations for simpler but chemically related molecules,..."<ref name="autogenerated1"/>

Subsequent [[Nobel Prize in Chemistry|Nobel Prize]] winner [[Roald Hoffmann]] was a doctoral student
<ref name=Hoffmann1962TheoryIII/>
<ref name=Hoffmann1962TheoryI/>
<ref name=Hoffmann1962LCAO/>
<ref name=Hoffmann1962Sequential/>
<ref name=Hoffmann1963Carboranes/>
in Lipscomb's laboratory.
Under Lipscomb's direction the [[Extended Hückel method]] of molecular orbital calculation was developed by Lawrence Lohr<ref name=Lipscomb1977PrixNobel/> and by Roald Hoffmann.<ref name=Hoffmann1962TheoryI/><ref name=Lipscomb1963/>  This method was later extended by Hoffman.<ref name=Hoffmann1963/>
In Lipscomb's laboratory this method was reconciled with [[Hartree–Fock method|self-consistent field (SCF)]] theory by Newton<ref name=Newton1966/> and by Boer.<ref name=Boer1966/>

Noted boron chemist [[M. Frederick Hawthorne]] conducted early<ref name=LipscombHawthorne1959/><ref name=PitochelliHawthorne1962/> and continuing<ref name=LipscombHawthorne1972/><ref name=PaxtonHawthorne1974/> research with Lipscomb.

Much of this work is summarized in a book by Lipscomb, ''Boron Hydrides'',<ref name=Lipscomb1963/> one of Lipscomb's two books.

The 1976 [[Nobel Prize in Chemistry]] was awarded to Lipscomb "for his studies on the structure of boranes illuminating problems of chemical bonding".<ref>{{cite web|url=http://nobelprize.org/nobel_prizes/chemistry/laureates/1976/ |title=The Nobel Prize in Chemistry 1976 |publisher=Nobelprize.org |access-date=2012-02-01}}</ref>
In a way this continued work on the nature of the chemical bond by his doctoral advisor at the California Institute of Technology, [[Linus Pauling]], who was awarded the 1954 Nobel Prize in Chemistry "for his research into the nature of the chemical bond and its application to the elucidation of the structure of complex substances."<ref>{{cite web|url=http://nobelprize.org/nobel_prizes/chemistry/laureates/1954/ |title=The Nobel Prize in Chemistry 1954 |publisher=Nobelprize.org |access-date=2012-02-01}}</ref>

The source for about half of this section is Lipscomb's Nobel Lecture.<ref name=Lipscomb1977/><ref name=Lipscomb1977PrixNobel/>