Modern Structural Chemistry Nobel Lecture —- December 1954 by Linus Pauling A century ago the structural theory of organic chemistry was developed. Frankland in 1852 suggested that an atom of an element has a definite capacity for combining with atoms of other elements - a definite valencee Six years later Kekulé and Couper, independently, introduced the idea of valence bonds between atoms, including the formation of bonds between two carbon atoms, and suggested that carbon is quadri- valent. In 1861 Butlerov, making use for the first time of the term of a compound “chemical structure’, stated clearly that the properties/are determined by its molecmlar structure and reflect the way in which atoms are bonded to one another in the molecules of the compound. The development of the structure theory of organic chemistry then progressed rapidly, and this theory has been of inestimable value in aiding organic chemists to Pow interpret their experimental results and to new experiments. n ~2— A most important early addition to organic structure theory was made by the first Nobel Laureate in Chemistry, van't Hoff, who in 1874 recognized that the optical activity of carbon compounds can be ex= plained by the postulate that the four valence bonds of the carbon atom are directed in space toward the corners of a tetrahedrone The structure theory of inorganic chemistry may be said to have been born only fifty years ago, when Werner, Nobel Laureate in Chemistry in 1913, found that the chemical composition and properties of complex inorganic substances could be explained by assuming thet metal atoms often coordinate about themselves a number of atoms different wy from their valence, usually four atoms at the corners, of a tetrahedron ora square coplanar with the central atom, or six atoms at the corners of an octahedron. His ideas about the geometry of inorganic complexes were completely verified twenty years later, through the application of the technique of x-ray diffraction. After the discovery of the electron many efforts were made an electronic to develop theory of the chemical bond. A great contribution was made in 1916 Gilbert by @éivewt Newton Lewis, who proposed that the chemical bond, such as 3- the single bond between two carbon atoms or a carbon atom and a hydrogen atom represented by a line in the customary structural formula for ethane, consists of a pair of electrons held jointly by the two atoms that are bonded together. Lewis also suggested that +he—keaview atoms tend to assume the electronic configuration of a noble gas, through the sharing of electrons with other atonaf ox through electron transfer, and that the eight outermost electrons in an atom with a noble-gas electronic structure are pranged tetrahedrally in pairsf about the atom. Applica- tions of the theory and additional contributions were made by many chemists, including Irving Langmuir and Nevil Vincent Sidgwick. stter- After the discovery of quantum mechanics in 1025 fst became eo" nee ence srw ee SIN corer M, UL a reliable evident that the ‘equations quentum mechani cg fonstitute thé basis f a emcee nro for uw the theory of molecular structure. It also soon became evident that these equations, such as the Schridinger wave equation, cannot be solved rigorously for any but the simplest molecules. The development of the theory of molecular structure and the nature of the chemical bond during the past twenty-five years has been in considerable part empirical - based upon the facts of chemistry - but with the interpretation of these ~L= facts greatly influenced by quantum mechanical principles and concepts. The solution of the wave equrtion for the hydrogen molecule= ion by J» Burrau (Det Kgl. Danske Vide Selsk. Math.-fys. Meddelel$ser, 7, 14 (1927)) completely clarified the question of the nature of the Tao one-electron bond in this molecule~ion. / ZYlluminating quantum mechanical discussions of the shared-electron-pair bond in the hydrogen molecules then simultaneously were eeem published, oney—-seonstituting—the—fivet—example-—of—a by Heitler and London (Z. ®y Physik, 44, 455 (1927)), and the other by E. Ue Condon (Proc. Nate AcadScie U.S., 13, 466 (1927)). In the preat- ment-ef ts approximate solution of the wave equation for the hydrogen molecule by Heitler and London a wave function is used that voqures requires Sect to be separated, each being close to one of the two nuclei. The treatment by Condon permits the electrons to be dis= tributed between the two nuclei indevendently of one another, each occupying a wave function similar to Burrau's function for the hydrogen- molecule ione Condon's treatment is the prototype of the molecular-— orbital treatment that has been extensively applied in the discussion of aromatic and conjugated molecules, and Heitler and London's trestment is the prototype of the valence-bond methods When the effort is made to -5< refine the two treatments they tend to become identical. wy These early applications of quantum mechanics to the peoblem of a) the nature of the chemical bond made it evident that in general a cpp vetent bond, involving the sharing of a pair of electrons between two atoms, can be formed if & two electrons are available (their spins must be opposed, in order that the bond be formed), and if each atom has avail- able a stable electronic orbital for occupancy by the electrons. The equivalence of the four bonds formed by a carbon atom, which had become a part of chemical theory, was not at first easily reconciled with the suantunf ant et description of the carbon stony as having one 2s orbital and three 2p orbitals in its outer shell. The solution to this difficulty was obtained when it was recognized that as @ result of the resonance phenomenon of quantum mechanics a tetrahedral arrangement of the fmx four bonds of the quedpiveten’s carbon atom is { f achieved. The carbon atom can be described as having four equivalent le Linus Pauling, The Shared~Electron Chemical Bond, Proce Nat. Acade Sele UsS., 14, 359-362 (1928). -b= tetrahedral /oond orbitals, which are hybrids of the s and p orbitals. Further study of this problem led to the discovery of many sets of hybrid bond orbitals, which could be correlated with bond angles, magnetic moments, and other 2 molecular propertiese In particular it was found that sp’ hybrid 2. Linus 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, ta.J. Ame Cheme Soce, $8 53, 1367 -1400 (1931). ovbiteisy dsp’, and d@sp3 hybrid orbitals correspond respectively to the tetrahedral, square planar, and octahedral configurations of Qed) he Wanner ‘ inorganic complexes that -hewre been discovered, Conclusions as to the A. utilization of atomic orbitals in bond formation can be drawn from Try eonpfo j experimental values of magnetic moments. the theory of the dsp2 square complexes of bipositive nickel, palladium, and platinum requires that these substances be diamagnetic. The square complexes of bipositive -7— palladium and platinum had been recognized by Wermer and their struc= ture verified by Dickinson (J. Am. Chem. Soc., 44, 2404 (1922)); but the assignment of the square configuration to the complexes of nickel which are diamagnetic had not been made until the development of the new theory. Further detailed information about the chemical bond fesulted ; from a consideration of the energy of single bonds in relation to relative 3 the/electronegativity of the bonded atoms. It was found that the 3+ Iinus Pauling, The Nature of the Chemical Bond. IV. The Energy of Single Bonds and the lKelative Electronegativity of Atoms, Je Ame Cheme Soce, 54, 3570-82 (1932). elements can be assigned electronegativity values such as to permit the rough prediction of the heats of formation of compounds to which chemical structures involving only single bonds are conventionally assigned, and that meny of the properties of substances can be discussed in a simple way with the use oi the electronegetivity values of the elements e Ban The idea that the properties of many organic compounds, especially the aromatic compounds, cannot be simply correlated with a & somewhat more complex single valence-bond structure, but required the assignment of an/electronic structure was developed during the period 1923 to 1926 by man- a number of chemists, including lowry, latworth, kobinson, and Ingold in bngland, Lucas in the United States, and Arndt and Eistert in Germany. It was recognized that the properties of aromatic and conjugated molecules can be described by the use of two or more valence=bond structures, Mis as reflected in the names, the theory of mesomerism and the theory of intermediate eteses states, proposed for the new chemical theory. In 1931 Slater, E. Hiickel, and others recognized that these theories can be given a quantum mechanical interpretation: an approximate wave the sum of function for a molecule of this sort can be set up as/e~dineex-funetion ef wave functions representing the etter corresponding to the individual valence-bond structures. The-nesmed~siete-ef-she The /molecule can then be described as e—hybridy having a structure that is a hybrid of the individual valence-bond structures, or as resonating among Ja these structures, and the theory itself is now usually called the resonance theory of chemical structuree Vey many quantitative calculations, approximate solutions of the wave equation, for aromatic and conjugated molecules have been made, with results that are in general in good agreement with experiment. Perhaps mre important than the quantitative calculations is the possibility of prediction by simple chemical arguments. For example, the amide group, an important structural feature of proteins, can be described as resonating between two structures*#one with the $f double bond between the carbon atom and the oxygen atom, and the other with the aouble bond between the carbon atom and the nitrogen ston:t @ % Y \ / \ / C—N == N J \e Y Se linus Pauling, Interatomic Distances in Covalent Molecules and Resonance between Iwo or More Lewis Electronic Structures, Proc. Nat. Acade Scie UeSe,y 18, 2934297 (1932). -10- buperi-enee-with-ethor—substanceey-and-seneral-—chenieal-sereumente General arguments about a the stability of alternative structures indi- catef that the structure with the double bond between carbon and oxygen should contribute somewhat more to the normal state of the amide group ; acquaintance than the other structure; experience with other substances and/with the results of quantum mechanical calculations suggests the ratio 60%: 40% for the respective contributions of these structurese A 40% contribution of the structure with the double bond between the carbon atom and the nitrogen atom would confer upon this bond the property of planarity of the group of six atoms; the resistance to deformation from the phanar configuration would be expected to be 40% as great as for a molecule such as ethylene, containing a pure double bond, and it can be calculated 3° that rotation of one end by # dagmmee relative to the other end would in- AN troduce a strain energy of 100 coVmoles The estimate of 40% double-bond character for the C-N bond is supported by the experimental value of o the bond win length, 1.32 A. interpreted with the aid of the empirical relation between double-bond character and interatomic dietance.o a & linus Pauling and L. 0. Brockway, and J. Y. Beach, The Dependence of Interatomic Distance on Singte-Bend Single Bond-Double Bond Resonance, Js Am. Chame Soce, 57, 2705 (1935). Knowledge of the structure of amides, and also of the amino acids, provided by the theory of resonance and verified by extensive careful experimental studies made by R. B. Corey and his coworkers, has been of much value in the determination of the structure of proteinse tn the description of the theory of resonance in chemistry [neve has been a perhaps unnecessarily strong emphasis on its arbitrary \ Ne character. Joumenuumpizn, Wy & -12- It is true, of course, that a description of the benzene molecule can be given, in quantum mechanical language, without any reference to the two Kekulé structures, in which double bonds and single bonds alternate in the ring. An approximate wave function for the benzene molecule may be formulated by adding together two functions, representing the two Kekulé structures, and adding other terms, to make the wave function epproximate the true wave function for the molecule more closely, or it may be constructed without explicit introduction of the wave functions two 7 representing the/Kekule structures. It might be possible to develop a simple way of discussing the structure of the amide group, for example, that would have permitted chemists to predict its properties, such as planarity; but in fact no simple way of discussing tire=emite a other than the way given above, involving resonance between two alternative valence-bond structures, has been discovered, and it seems likely that the discussion of complex molecules in terms of resonance among two or more valence-bond structures will continue x in the future to be useful to chemists, as it has been during the past twenty years. 13 The convenience and usefulness of the concept of resonance in the discussion of chemical problems are so great ad to make the dis- advantage of the element of arbitrariness of little significance. Also, occurs it must not be forgotten that the element of arbitrariness entexs in essentially the same way in the simple structure theory of organic chemistry as in the theory of resonance - ttere is the same use of resonance idealized, hypothetical structural elements. In the/discussion of the benzene molecule the two Kekulé structures have to be described as hypothetical: it is not possible to synthesize molecules with Wh< one or the other of the two Kekulé structures. In the same way, however, the concept of the carbon-carbon single bond or—the-T. cabeni eg is an idealizatione The benzene molecule has its own structure, which cannot be exactly composed of structural elements from other moleculese The propane wrec et is own structure, which cannot be eenetzuete composed of structural elements from other molecules the-eaxben-earben bende it is not possible to isolate a portion of the propane molecule, involving parts of two carbon atoms and perhaps two electrons in between them, and say that this pext of the propane molecule is the carbon-carbon -l1- Single bond, identical with a pems of the ethane molecule. ‘The description of the propane moleculef as involving carbon-carbon single bonds and carbon-hydrogen single bonds is arbitrary; the concepts themselves are ideqlizations, in the same way as the concepts of the Kekulé structures that are described as contributing to the normal state of the benzene (molectles For nearly a century organic chemists have found that them idealizations of carbon-carbon single bonds, double bonds, etc. are useful, and thet the simple structural theory of organic chemistry is valuable despite its arbitrariness. The resonance ———" b Kex mengegerrs’ Chemists have found that the simple structursé theory of organic chemistry and also the resonance theor; are valuable, despite their use of idealizations and their arbitrary character. Other extensions of the theory of the chemical bond made in recent years involve the concept of fractional bonds. Twenty-five years a simple theory of ago it was discovered that/complex crystals with largely ionic struc- tures, such as the silicate minerals, can be developed on the basis of the assumption that each cation or metal atom divides its charge or valence equally among the anions that are coordinated about ite For example, in a crystal of topaz, Al,Si0,F., - ob linus Pauling, The Principles Determining the Structure of Complex Ionic Crystals, J. Ame Cheme Soce, 51, 1010-1026 (1929). -15- (tng silicon each aluminum atom is surrounded by a tetrahedron of four oxygen atoms, -_ oxygen and each aluminum atom is surrounéed by an octahedrfon of four adweblmam atoms and two fluorine atomse The valence of silicon, 4, is assumed to be divided among four bonds, which then have the bond number 1 - they are @iea- single bondse The valence of aluminum, 3, is divided among six bonds, each of which is a half bond. A stable structure results when the atoms are arranged in such a way that each anion, oxygen or fluorine, forms bonds equal to its valence. In topaz each oxygen atom forms one single bond with siliconf and two half bonds with aluminun, whereas each fluorine ston forms only two half bonds with aluminum. The distribution of the valences hence then corresponds to the bivalence of oxygen and the univalence of fluorine. It was pointed cathe W. Le Bragg that if the metal atoms are idealized as cations dein t-and-Abs-- (sat*** and a8? it) and the oxygen and fluorine atoms as anions (O~ and F"), this distribution corresponds to having kimm the shortest possible lines of force between the cations and the anions - the lines -16- of force need to reach only from a cation to an immediately adjacent anion, which forms part of its coordination polyhedron. Occasionally ionic crystals are found in which there are smsll deviations from sete aN te nie ark this requirement, but newereiy | the deviations gume=mt larger than one quarter of a valence unit. Another application of the concept of fractional valence bonds has been made in the field of metals and alloyse In the usual quantum mechanical diséussion of metals, initiated by We Pauli (4. Physik, 41, 81 (1927)) and Sommerfeld (Naturwiss., 15, 825 (1927)), the assumption was made b that only a small number of electrons contribute significantly to the binding together of the metal atoms. For example, it was cuse significantly tomary to assume that only one electron, occupying a 4s orbital, is / the involved in the copper-copper bonds in/metalike copper. Sixteen years an ago/analysis of the magnetic properties of the transition metals was made that indicated that the number of bonding electrons in the transition metals is much larger, of the order of magnitude of aix.? fp Linus Pauling, Ihe Nature of the Interatomic Forces in Metals, Phys. Rev., 54, 899-904 (1938). -17= Iron, for example, can be described as having six ef-kte valence electrons, which occupy hybrid a ap* orbitals. the six bonds, corresponding to theese these six valence electrons, resonate among the fourteen positions connecting an iron atom with its fourteen nearest neighbors. the bonds to the eight nearest neighbors have bond number approximately 5/8, and those to the six slightly more distant neighbors have hes number 1/66 In gamma iron, where each atom is surrounded by twelve ecually distant neighbors, the bonds are half bonds. The concept that the velenee bende structure of metals and intermetallic comoounds can be described in terms of valence bonds that resonate among alternative positions, aidec by an extra orbital on most or all of the atoms (the metallic orbital) has been found of value in the discussion of the properties of these “Th substances © @rtP-coneopt-was-deyeleped resonsating-bond theory of - linus Pauling, A kesonating-Bond Theory of hetals and Intermetallic Compounds, Proce Roy. Soce London, A 196, 343-362 (1949). metals is supported especially strongly by the consideration of inter atomic distances in metals and intermetallic compounds. . Linus Pauling, Atomic Radii and Interatomic Distances in Metals, de « Chem. DCey 69, 5ShA2 (1947). ~18- The iron atom has eight electrons outside of the argon shell of eighteen. Six of these electrons are assumed, in the resonating= valence=bond theory, to be valence electrons, and the remaining two are atomic electrons, Occupying xe 3d orbitals, and contributing two Bohr magnetons to the megnetic moment of the atom. A theory of the ferro- magnetism of iron has recently been developed, in which, as suggested by aeneryxthmx (Phys. keve, 81, 440 (1951)), the interaction producing the Weiss field in the ferromagnetic metal is an interaction of the I ' spin moments of the atomic electrone/ and uncoupled spins of some of the valence electrons. It has been found nossible to use spectroscopic energy values to predict the smount-ef-—uneouptinge number of uncoupled valence electrons, and hence the xx saturation magnetic moment for iron: 0.26 the calculation leads to @e20 uncoupled valence electrons per aton, and saturation magnetic moment 2.26 Bohr mapnetons, which might be sub- ject to correction by two or three percent because of the contribution of orbital moment. The experimental value is 2.22. A calculated value of the Curie temperature in rough agreement with experiment is slso ob- tainede 19. Linus Feuling, a theory of Ferromagnetism, Proce Net. Acade Scie UsSe, 39, 551-560 (1953). ~19- ‘ihe valence theory of metals and intermetallic compounds is still in a wey unsatisfactory state. It is not yet possible to make pre= A dictions about the composition and properties of intermetallic compounds with even a small fraction of the assurance with which they can be made about organic compounds and ordinary inorganic compoundse We may, however, thy 2 O89 hope that, significant progress Wéetiebeuwmie in the attack on this prob= Lem during the next few yearse Let us now return to the subject of the structural chemistry of organic substances, especially the complex substances that occur in living organisms, such as protéins. kecent work in this rieralk has 4. linus Pauling and Robert B. Corey, Two Hydrogen-Bonded Spiral Configurations of the Folypeptide Chain, J. Am. Cheme Soc. ,x¥ky 5349 (1950) ; Linus Pauling, Kobert B. Corey, and H. R. Branson; 725 fo