UNSOLVED PROBLEMS OF STRUCTURAL CHEMISTRY

By Linus Pauling

Theodore William Richards Medal Address. Cambridge, Massachusetts.

May 8, 1947.

It is difficult for me to find words to express my appreciation at having been selected by the Northeastern Section of the American Chemical Society to receive the Theodore William Richards Medal. My pleasure at being the recipient of this honor is especially great not only because of my admiration for Professor Theodore William Richards himself, but also because of the facts that Professor Arthur Amos Noyes, to whom I am deeply indebted for support and encouragement during my early years of work in science, was the first recipient of the Theodore William Richards Medal (after Professor Richards himself) and that also the fourth Theodore William Richards Medal was given to Professor Gilbert Newton Lewis, in whose footsteps I hare endeavored to follow throughout my scientific career.

The subject of my talk tonight is "Unsolved Problems of Structural Chemistry." As I consider our present knowledge of structural chemistry, and compare it with that of twenty-five years ago, I am astonished at the progress that has been made, and almost tempted to feel that the major problems have been solved, and that the future developments of structural chemistry may be far less interesting than this developments which we have watched during the past quarter century. Twenty-five years ago we had no precise knowledge of interatomic distances and bond angles in molecules, and the understanding of the nature of the forces responsible for chemical combination was very vague. Sow the detailed atomic structures of many hundreds of molecules and thousands of crystals are known, and the theory of valence and the chemical bond, with its basis in Quantum mechanics, has developed far enough to permit reliable predictions to be made in many cases.

Nevertheless, despite this progress, there remain many unsolved problems. I shall take this opportunity to discuss soma of these problems, dividing them into four successive categories.

Problems Presented in Advertisements

In our present atomic age everyone is continually made aware of the existence of atoms nd molecules. Atomic fission and other atomic phenomena are presented to the younger generation in the comic papers, and molecules and their own properties are introduced to us in advertisements. The school boy now accepts the existence of atoms and molecules without question, and he is apt to have a reasonably good understanding of their properties and significance before undertaking the study of science in school. I myself have noticed, however, that the advertisements in our national magazines sometimes present problems, and some of these problems have, so far as my knowledge goes, remained unsolved. One of the problems which has interested me is the nature of "pin-point carbonation.” I have been given the impression that this phenomenon is interesting and valuable, but I have not been able to discover its nature. Another phenomenon of which I have tried, without success, to obtain an understanding is the "activation" of chlorophyll in the household deodorizer “Airwick.” The selection of chlorophyll to be used in this preparation is no doubt to be attributed to Its well-known ability to purify the air by converting carbon dioxide to oxygen. I have been interested in the properties of chlorophyll for some time, and I had not heard from other sources about the activation of chlorophyll. By obtaining a copy of a patent I learned that chlorophyll is activated by formaldehyde. This type of activation seems to differ somewhat from ordinary types, because a great many molecules of formaldehyde are required for the activation of each molecule of chlorophyll. The thought has occurred to me that the significant phenomenon may really be one of deactivation, rather than activation, and that the formaldehyde may be acting in a way similar to that effective when it is used in embalming fluid.

Some Puzzling Small Problems

There are many molecules, even rather simple ones, whose structures have not yet been determined reliably, or about which there exists a difference of opinion. One of these molecules is the ozone molecule. Spectroscopic data have been interpreted in recent years as showing that the ozone molecule consist a of two oxygen atone very close together, and a third one much farther away, and equidistant from the first two. This structure would be described as an oxygen molecule with a third oxygen atom only loosely bonded to it. The alternative structure of ozone (analogous to the structure of sulfur dioxide) is that in which a central oxygen atom is attached to two equidistant oxygen atoms, with a bond angle of about 125°, corresponding to the presence of a double bond and a single bond, in resonance. I believe that this structure, originally suggested by G.N. Lewis and substantiated by the electron-diffraction investigation by W. Shand, Jr. and R.A. Spurr, is the correct one, but it is difficult to understand the contradictory conclusions reached by the spectroscopic investigators.

Another molecule about which there has been a difference of opinion is diborane, B₂H₆. The alternative structures for this molecule are a structure similar to ethane, and a structure in which two hydrogen atoms are shared between the two boron atoms. The experimental evidence now favors the second of these structures. In particular, an electron-diffraction investigation of tetramethyldiborane carried out by V. Schomaker and W. Shand, Jr., and not yet published, provide strong support for these structures. These investigators have found that the four methyl groups are essentially coplanar with the two boron atoms, with bond angles of approximately 120° and boron-carbon distance of 1.59 Å. The boron-boron distance is about 1.85 Å. I think that this structure may be described in various ways, as, for example, by saying that there is a protonated double bond (E. Wiberg, K.S. Pitzer). My own inclination is to describe the molecule in terms of resonating bonds. If it is assumed that the bonds between the methyl carbon atoms and the boron atoms are single covalent bonds, then there are enough electrons for two additional electron-pair hoods to be formed, and there are five positions available for these bonds, one between two boron atoms, and four between boron and hydrogen atoms. If these bonds resonate equally among these positions, each position would be occupied by a bond with bond number O.4. With the relation which I have recently suggested between interatomic distance and bond number, we then predict the distances B-B = 1.85 Å, exactly the value re¬ported from the electron diffraction investigation, and B-H = 1.35 Å.

A problem of a different sort In the field of inorganic chemistry is that of explaining the nonexistence of perbromic acid. It might be suggested that bromine lies just in the middle of the transition from a stable acid with coordination number 4 such as perchloric acid, HClO₄, to a stable acid with coordination number 6, such as paraperiodic acid, H₅IO₆. However, the existence of salts of periodic acid with coordination number 4, such as KIO₄, renders this explanation unsatisfactory.

Another interesting problem in inorganic chemistry is that of the structure of uninegative rhenium. The discovery by G.E.F. Lundell that perrhenate ion in sulfuric solution is reduced by passage through a Jones, reductor by eight stages, to rhenium with oxidation number -1, carries great interest because this is the only known occurrence of a metal with negative coordination number, although compounds of meals with oxidation number 0, such as the nickel cyanide complex Ni(CN)₄ ^4-, have been made. The only explanation which I have been able to formulate for the existence of rhenium in this negative oxidation state is that the rhenium ion exists in this system with an electronic structure similar to that of bipositive platinum, which is isoelectronic with uninegative rhenium. Bipositive platinum exists only in complexes in which it forms four covalent bonds, with four groups arranged in a coplanar square about it. Accordingly it seems likely that uninegative rhenium exists in the same state, and it may be that the four groups which it coordinates about itself at the corners of a square are four water molecules. Experimental verification of this suggestion has, however, not yet been obtained; the problem is now being attacked by Mr. E. Maun.

Some Larger Problems

There ere a number of problems dealing with the structural chemistry of groups of substances which merit mention.

First, there is the question of the observed increase in coordination number of atoms which do not have a sufficiently large complement of electrons to permit the formation of electron-pair bonds In number permitted by the available bond orbitals. The boron hydrides, if we assume the new structures to be correct, are examples of this situation. Boron in BH₃ has only three valence electrons, permitting it to form three single covalent bonds. However, as a first row element it has available for bond formation four bond orbitals. It might be expected that a polymer would be formed, diborane, in which all four bonds are used with the available electron pairs resonating among the bond positions; this description applies to the ehtane-like structure for diborane. However, the alternative and presumably correct structure is one in which the bonds resonate among five bond positions about each boron atom. Similarly, in calcium hexaboride, in which there are enough electrons (assuming the presence of calcium ion) for 3 1/3 electron bonds per boron atom, the configuration of the boron framework is such that each boron atom is bonded to five boron neighbors instead of the four expected from the four available bond orbitals. Also, in boron carbide, B₄C, which is an electron-deficient structure with 3 1/5 electrons for every four atomic bond orbitals, each boron atom is surrounded by six atoms (either five boron atoms and a carbon atom or six boron atoms), and the carbon atoms are present as ketene groups C=C=C, with, however, the end carbon atoms having three boron neighbors apiece instead of the two that would be expected for the ketene bond structure. Similarly the molecules of platinum tetramethyl, Pt₄(Ch₃)₁₆, in which there are electron pairs enough for quadrivalent platinum to form four single bonds, whereas the platinum atom has six stable d²sp³ bond orbitals, have been found by R.E. Rundle and J.H. Sturdivant to have a resonating-bond structure in which each carbon atoms has increased its coordination number to 5, with platinum having its normal coordination number of 6. The metals and intermetallic compounds, of course, provide an extremely large number of examples of structures of this sort, in which bonds resonate among a number of positions considerably greater than the number of bond orbitals available. A few years ago the general principle was expressed to me by Professor V. Schomaker that when the number of electron pairs is less than the number of available bond orbitals resonance of the electron pairs among several alternative positions occurs with an increase in the number of bond positions above the number of bond orbitals. This interesting general principle has not yet been given quantitative formulation (of the amount of increase in coordination number in relation to the amount of electron deficiency) or theoretical justification.

Another question in the field of inorganic chemistry about which little is known at present is that of the extent to which covalent bonds be¬tween metal atoms occur in non-metallic compounds. I had thought that every chemist was familiar with one of the substances in which these bonds occur, but a year or so ago I was astonished to learn, while telling a young man who had recently received his doctor's degree in chemistry about the enneachloroditungsten complex ion, that he could not think of any common representative of this class of substances and, moreover, that he did not know what calomel is or what metals appear in the first group of the scheme of qualitative analysis. The existence of the mercury-mercury bond in the mercurous ion, Hg₂ ⁺⁺, and in molecules such as Cl-Hg-Hg-Cl has been recognized for many years, but until recently other examples of such bonds had bot been reported. The complex ion W₂Cl₉ --- was discovered to have such a structure a few years ago by Cyril Brosset, when he determined the crystal structure of K₃W₂Cl₉ and isomorphous substances. This complex ion has a configuration obtained by sharing a face between two W₂Cl₆ octahedra. The triangular face held in common by the two octahedra is large enough to permit the two tungsten atoms to approach one another to the small distance 2.46 Å, is only slightly larger than that expected for a single covalent bond.

The structure reported for crystals of molybdenum dioxide and tungsten dioxide by Arné Magnéli also shows the presence of bonds between the metal atoms. These crystals have a distorted rutile structure, in which each metal atom is surrounded by an octahedron of oxygen atoms. The distortion from the ideal structure is of such a nature as to bring two molybdenum or tungsten atoms very close together, to form a pair of atoms 2.48 Å apart, the corresponding edge shared by the two octahedra being greatly lengthened. The bond number calculated from this interatomic distance is 1.47, suggesting that there is an effort by each quadrivalent molybdenum or tungsten atom to use its two remaining valence electrons for the formation of a double bond with another atom of molybdenum or tungsten. The distance from the metal atom to the oxygen atom suggests resonance of about four covalent bonds among the six positions, causing the total valence of the molybdenum or tungsten atom to be approximately 6.

In the corresponding crystals molybdenite, MoS₂, and tungstenite, WS₂, however, the metal atoms are so far apart that there is no bond formed between them.

There are many essentially non-metallic crystals known in which metal atoms approach one another to within such distances as to correspond to significantly large fractional bond numbers, and there is little doubt that many of the physical and optical properties of the crystals are determined essentially by this closeness of approach. For example, the oxygen compounds containing iron seem to have a color which is correlated with the distance between iron atoms: pseudobrookite, (Fe₂TiO₅), and hematite, with iron-iron distance 2.88 Å, are red, whereas hydrated iron oxides such as lepidocrocite, goethite, limonit, and xanthosiderite tend to be lighter in color. The mineral cubanite, CuFe₂S₃, contains pairs of iron-sulfur tetrahedra in which the iron-iron distance, approximate 2.5 Å, corresponds to a bond number 0.3. It was suggested by the investigator of the crystal, M.J. Buerger, that this closeness of approach of iron atoms might be related to the unusual ferromagnetism shown by this sulfide mineral.

The theory of the color of dyes and other complex organic molecules has been rather well developed in recent years, and in general it may be said that the color of these substances is reasonably well understood. However, very little progress has been made in the development of a systematizing or correlating theory of the color of inorganic complexes. Moreover, there is one set of substances which shows especially striking coloration. This is the set of substances containing the same element in two different valence states. Substances of this sort have been recognized for many years as having abnormally deep and intense coloration, for example, the complexes of cuprous copper with chloride ion, in solution in concentrated hydrochloric acid, are colorless, as is cuprous chloride itself, and the complexes of cuprous copper with chloride ion are green. However, if cuprous and cupric solutions are mixed an intensely colored brown or black solution is obtained, apparently due to complexes containing both cuprous and cupric copper. Similarly, trivalent antimony chloride and quinquevalent antimony chloride are colorless, but a mixture of the two has a deep brown or black color. Crystals of (NH₄)₂SbCl₆, a black substance, have been investigated by x-rays by N. Elliott and shown to have a structure indistinguishable from that of potassium chlorostannate. Moreover, the crystals are diamagnetic, so that the complexes cannot be SbCl₆ ^{- -}, which would necessarily be paramagnetic because of the presence of an odd number of electrons, but must be alternately SbCl₆ ^{- - -} and SbCl₆ ^-. Crystals of cesium auric chloride, Cs₂AuAuCl₆, which are also intensely black in color, have been studied with x-rays, and shown to contain the aurous complex AuCl₂ ^-, with linear configuration, and the square coplanar auric chloride complex AuCl₄ ^-. The existence of these two distinct complexes rules out the obvious suggestion that the intense color is due to the resonance of electrons among the atoms of the metal, in such a way as to give each atom a resonating structure in which it is a hybrid of two covalent states.

Another example of the phenomenon is observed often in the chemical laboratory when a solution containing ferrous ion is precipitated with alkali. Ferrous hydroxide is white, and ferric hydroxide is brown. When a ferrous solution is precipitated, however, the initially white precipitate is immediately partially oxidized by atmospheric oxygen, to form a ferrous ferric hydroxide, which is black in color (or deep green when finely divided).

A few years ago it was pointed out to me by Dr. Sterling Hendricks that ordinary black mica, biotite, which has an intensely black color, owes this color to the presence of iron in both the ferrous and ferric oxidation state. Black tourmalines also usually contain both ferrous and ferric iron. Another intensely black mineral, with black streak, is ilvaite, with composition Ca(Fe⁺⁺)₂Fe⁺⁺⁺(SiO₄)₂OH.

Molybdenum blue and tungsten blue, which have intense deep blue coloration, have the formulas MoO_2.5-3 and WoO_2.5-3. The tungsten bronzes also contain tungsten in an intermediate valence state; their formulas lie between the limits Na₃W₂O₆ and Na₂W₃O₉. Many metal oxides, such as Fe₃O₄, U₃O₈, and Pr₄O₁₁, may owe their black color to this phenomenon. However, it is interesting that the intermediate oxide Sb₂O₄ is white, although the halogen complexes of antimony with mixed valence are intensely colored. The consideration of the color and other properties of ordinary complexes (not involving intermediate oxidation states) has recently led me to formulate a new rule, to the effect that half-full and full electronic shells in an atom are closely similar in properties. This rule applies not only to the ordinary shells such as the 3d subgroup of 5 orbitals in an isolated atom, but also to special subgroups of orbitals in atoms which form covalent bonds. For example, it applies to the set of three 3d orbitals available for unshared electrons in an atom of the first transition period which forms six octahedral d²sp₃ covalent bonds.

Examples of the similarity of half-full and full shells for isolated atoms or ions are not hard to find. The tripositive gadolinium ion, with seven 4f electrons, is colorless, and in this and other properties. A striking phenomenon is the abnormally large atomic volume shown by metallic europium and metallic ytterbium, and by no other rare-earth metal. This large atomic volume of these two metals is due to their acceptance of metallic valence 2, instead of the normal value of about 3 shown by the other rare-earth metals. The metallic valence 2 is correlated for europium with the achievement of a half-full 4f subshell and for ytterbium with the achievement of a full 4f subshell.

In transition elements forming six covalent bonds there are three 3d orbitals not sued in bond formation. For example, in the complexes of tripositive cobalt these three 3d orbitals contain their full complement of six electrons, whereas in the complexes of tripositive chromium they contain three electrons. The extraordinarily close similarity in properties of the cobaltic complexes and chromic complexes is well known.

The same close similarity in properties is shown also by the corresponding complexes of heavier transition elements. Thus both potassium hexachlororhodiate, K₃RhCl₆, and potassium hexachloromolybdite, K₃MoCl₆, form red crystals.

There are many striking examples of the existence of stable polynuclear inorganic complexes which deserve explanation. The existence of anions such as orthosilicate, (SiO₄)^-4, disilicate, Si₂O₇)^6-, trisilicate (Si₃O₁₀)^8-, etc., ultimately leading by continued condensation to rings, infinite chains, and sheets of silicate tetrahedra, offers no significant problems at the present time. This process of condensation of simple acids to complex acids, with sharing of polyhedral elements, is well understood. Often, however, it is found that an element forms certain very complex polynuclear anions which show a striking stability, and clearly do not simply fit into a series of polymers of increasing complexity. One et of examples is the duodecimolybdic acid. Nearly twenty years ago I suggested a structure for these duodeci complexes in which a roughly spherical cage of twelve condensed octahedra was formed about a central phosphate ion or similar tetrahedral ion. It was then shown by Keggin that these duodeci complexes do possess a structure of this general sort, but with the twelve molybdenum or tungsten octahedra arranged in a somewhat different way from that which I had proposed. I believe that many of the surprisingly complex stable anions formed by elements such as molybdenum, tungsten, vanadium, columbium, and tantalum have similar compact structures of condensed polyhedra.

An example of the complications which are introduced into inorganic chemistry by the stability of these unusual complexes can be seen by reading about the chemistry of molybdenum dichloride, MoCl₂. When this substance is dissolved in water only one-third of the chlorine is precipitable by silver ion. the electrolytic properties of the aqueous solution are also abnormal, and show the presence of an ion with large electrical charge. It was suggested long ago that eh substance contains the complex Mo₃Cl₄ ⁺⁺. However, the difficulties of assigning a reasonable electronic structure to this complex caused me a few years ago to assume that the complex is Mo₆Cl₈ ⁺⁺⁺⁺, and that molybdenum dichloride itself is to be assigned the formula [Mo₆Cl₈]++++Cl₄ ^-. The ionic chlorine is easily replaced by other anions, such as bromide ion, hydroxide ion, and sulfate ion. In order to verify this suggestion Mr. Philip Vaughan in our laboratories has been making an x-ray investigation of two crystals thought to contain this complex, (NH₄)₃[Mo₆Cl₈]Cl₆•2H₂O and H₂[Mo₆Cl₈]Cl₆•6H₂O. In the meantime, however, crystal structure determinations of two other substances, [Mo₆Cl₈](OH)₄•14H₂O and >[Mo₆Cl₈]Cl₄•8H₂O, have been reported by Cyril Brosset. These crystals have been found to contain complexes with the expected structure. This structure is a very interesting one. The eight chlorine atoms are at the corners of a cube, and the six molybdenum atoms are a little displaced outward from the centers of the six faces of the cube. Presumably each molybdenum atom forms bonds with the four chlorine atoms which surround it in a square, nearly coplanar configuration, each chlorine atom thus being bonded to three molybdenum atoms. Inasmuch as bivalent molybdenum has two unshared electron pairs, the configuration suggests that the molybdenum atoms in this complex have an octahedral configuration with the unshared pairs at two opposite corners of the octahedron, one directed toward the center of the complex and one directed outward. This arrangement accordingly conforms to the general rule that an atom with some unshared pairs of electrons tends to form a coordination polyhedron, with some corners occupied by bonded atoms and other by unshared pairs.

I think that the compound Ta₆Br₁₄, studied by W.H. Chapin, may be somewhat similar in structure. This substance, in which tantalum has average oxidation number of 2 1/3 (the color of the compound is deep green, corresponding to the intermediate oxidation state), contains the complex ion Ta₆Br₁₂ ⁺⁺and the related emerald-green substance Ta₆Cl₁₄ contains the complex ion Ta₆Cl₁₂ ⁺⁺. The two remaining halide ions are easily replaced by hydroxide ions or other anions. A reasonable structure for the complex is that in which the six tantalum atoms occupy the six corners of a regular octahedron, with the twelve halogen atoms near the centers of the twelve edges of the octahedron. With such a structure each tantalum atom is bonded to four halogen atoms, which lie at the corners of a square which may be nearly coplanar with the tantalum atom, and each halogen atom is bonded to two tantalum atoms. There are not two unshared electron pairs (four electrons) per tantalum atom to occupy the other two corners of an octahedral coordination polyhedron about tantalum, but only an average of 2 2/3 electrons. The significance of this electron number is not clear.

Vanadium, columbium, and tantalum form many compounds which can be represented as salts of oxygen acids containing six metal atoms. An example of a hexavanadate is sodium hexavanadate, Na₂V₆O₁₆•3H₂O. A possible structure for the hexavanadate complex ion may be assigned by writing this formula Na₂V₆O₁₃(OH)₆. If six vanadium atoms are placed at the corners of an octahedron and twelve oxygen atoms are placed out from the centers of the twelve edges of the octahedron, a thirteenth oxygen atom may then be located at the center of the octahedron, being thus bonded to all six vanadium atoms, and six hydroxyl groups may be placed directly out from the six vanadium atoms, completing the six octahedra. Hexacolumbates and hexatantalates also occur with similar formulas, such as K₂Cb₆O₁₃(OH)₆•2H₂O, Na₂Ta₆O₁₃-(OH)₆•2H₂O, and (NH₄)₂Ta₆O₁₃(OH)₆•2H₂O. Most of the salts of these acids, however, have formulas corresponding to the replacement of eight hydrogen atoms. Examples are K₈CbO₁₉•16H₂O, Na₂K₆CbO₁₉•9H₂O, Na₈Ta₆O₁₉•24H₂O, K₈Ta₆O₁₉•16H₂O, Ag₈Ta₆O₁₉•3H₂O, and Mg₄Ta₆O₁₉•9H₂O. It seems likely that the hexacolumbate and hexatantalate ions in these crystals have the structure described above, with the hydrogen ions of the six hydroxyl groups replaced by metal.

Another structural problem of somewhat different sort is that presented by the complex ion Pb₉ ^----, which exists in liquid ammonia solutions containing sodium and lead, as was shown by C.A. Kraus. A possible structure for this complex is again a cubic structure, with eight lead atoms at the corners of the cube and one in the center of the cube. The lead atoms at the corners of the cube might be considered to be uninegative, analogous to bismuth, and with the power of forming three covalent bonds, extending along edges of the cube. A quadripositive lead atom at the center of the cube would then cause the resultant charge on the complex to be correct. There would, of course, be bonds formed between the central lead atom and the surrounding atoms.

Some Great Problems

One great problem in structural chemistry which still awaits satisfactory solution is that of the structure of metals and intermetallic compounds. A small amount of progress has been made in correlating the composition of alloys such as the gamma alloys (Cu₅Zn₈, Cu₃₁Sn₈, Al₄Cu₉, Fe₅Zn₂₁, etc.) with the Hume-Rothery ratio of valence electrons to atoms, and with the electron numbers of Brillouin zones as calculated by quantum mechanical methods. Nevertheless, progress has not yet been great enough to permit confident predictions to be made about intermetallic compounds, nor to provide a satisfactory general theory of their composition, structure, and properties.

Another great problem is that of the structure of activated complexes. The general quantum mechanical concept involving resonating bonds, as developed by Eyring and Polyani, is, of course, satisfying, but a general chemical theory of the structure and stability of activated complexes still awaits formulation.

It may turn out that the problem of the structure of atomic nuclei may be considered a problem of structural chemistry. I do not know to what extent the available facts about the properties of nuclei indicate that the structure is a dynamic one, in which the nucleons cannot be assigned average positions relative to one another. It seems to me, however, that it is conceivable that the forces between nucleons involve attractive terms and repulsive terms in such a way as to cause the nucleons to assume average equilibrium positions relative to one another in the same way that atoms do in molecules and crystals, and that in the course of time the geometrical structures of atomic nuclei may be determined. A great contribution towards the solution could be made by obtaining diffraction data from atomic nuclei (starting with the deuteron, tritium nucleus, and alpha particles) by bombarding them with essentially monochromatic neutrons of high energy, approximately 30,000,000 electron volts.

In the field of organic and biological chemistry, it is my opinion that the structure of proteins and the origin of the specific properties of biological substances are the most important problems at the present time. The specificity of antigens and antibodies, of enzymes, and of genes will, I think, all be found to be due to the same modes of physical-chemical interaction between molecules. The evidence from the field of immunochemistry supports very strongly the concept that this biological specificity is due to a complementariness in structure of large molecules, and that the specific forces operate only when the complementary structures are in close contact with one another, with the surface atoms of the two structures approaching to within an Ångstrom or a few Ångstroms before the forces become large. It is true that this theory cannot explain the experiments reported by A. Rothen, who has published experimental results interpreted as showing that under certain circumstances enzymes are able to exert their specific action through a film of polymer as much as 200 Å thick. I do not have any explanation to offer for these experiments, except the obvious one that the polymer film may not be completely intact and impenetrable, but I feel that the evidence for the theory that specific biological forces result from complementariness in structure and require very close approximation of the complementary structures for their operation is extremely strong, and I think it highly likely that this is the only mechanism of biological specificity which has been developed in living organisms.

The progress of science in recent years is bringing biology and medicine into closer and closer contact with the basic sciences, and I am confident that the next few decades will bring to us a detailed understanding of the molecular structure of biological systems like that which we now have of simpler substances, and that this understanding will help in the rapid general progress of biology and medicine.