Linus Pauling (1983) - Structures of Compounds of Transition Metals

I have been dividing my time about equally among three activities, one has been work in chemistry, especially structural chemistry. Second, has been work for world peace and against nuclear weapons, or against war in general. And the third has been work in the field of nutrition, in relation to health, especially the vitamins and in particular vitamin C in relation to cancer, especially. Well, a month or two ago there was some article in a magazine called Hospital Medicine, it was an interview with me. And it ended with a question that the interviewer had put to me, he said “Are you hopeful that the world will not be destroyed in a nuclear war?”, and I said “Well, of course I'm hopeful, you can see that I have hope, otherwise I wouldn't be wasting my time talking about nuclear war, nuclear weapons and destruction of civilization, but I would be enjoying myself”. He said “How would you be enjoying yourself?”, and I said “By making quantum mechanical calculations about nuclear structure”. So I put down that here I would enjoy myself by talking about the structure of compounds of the transition metals. The sort of thing that interests me, that I like to do. But of course this problem of world peace or of possible destruction of civilization or even bringing the human race to an end is such an important one that I feel that I need to say something about it. In fact I'm vowed to do so. In December 1947, my wife and children and I were on our way to Europe, on the Queen Mary. And I got out a sheet of cardboard which was an announcement of a speech that I was to give or had given in Cornell or Princeton, I’ve forgotten where, and on the back of it I wrote a vow that in every lecture that I gave from then on, I would say something about world peace. Well, you know I didn’t really live up to the vow, sometimes I would forget to say anything about world peace. But I remember it now, it’s been impressed on me by circumstances, by our having president Reagan in the White House, for example. Things are worse now than they were even a few years ago! the 15th June a revised edition, the 25th anniversary edition of this book No More War!. When the publisher asked me to revise it, I looked over the ten chapters, I thought here things haven’t changed very much. The world has become more dangerous, the situation has become more dangerous, but the arguments are essentially just what they were 25 years ago. So I don’t see that I can improve it. I thought the writing was pretty good, too. I don’t see anything wrong with the English. So what can I do? Well, the ten chapters are reprinted just the way they were printed 25 years ago, but then there is an addendum of five pages, roughly at the end of each of the chapters, and a couple of additional appendices at the end of the book. I was astonished when I looked at this book and looked at the present accounts of lectures that I was giving around 25 years ago at the fact that the stock piles of nuclear weapons have not increased in magnitude. and with a little contribution from Britain and France, have 60,000 megatons of nuclear weapons. And my estimate now is 60,000 megatons. There’s been a great increase in the number of individual nuclear weapons, almost everybody sells some, various authorities at the United States now has 30,000 war heads, Soviet Union 20,000. President Reagan’s policy is that we build 17,000 more in the next few years. But the warheads are smaller now than they were 25 years ago. We had a few thousand 20 megaton warheads then. Now we have, United States and Soviet Union 50,000 which run around one megaton each. What happened? Well, what happened is that somebody in the bureau of the budget said “Here you have these thousands of 20 megaton bombs”, one 20 megaton bomb exploded over New York, it is estimated, would kill at least 10 million people. How many targets are there in the Soviet Union that justify exploding a 20 megaton bomb? Why not save money by tailoring them to the size of the target. And so the morph system was introduced and we began with these multiple warheads carrying smaller, these rockets that would carry smaller war heads and be independently directed towards various targets suited to one megaton or even a 500 kiloton bomb. I got pretty worried the other day when I saw an advertisement by an oil company. I can’t remember why the advertisement was what it was, but it showed a picture of a small city devastated by an explosion with ordinary explosives. Perhaps, well, you know, the advertisement said that 457 tons of dynamite exploded with megaton might. I thought here the officers of this oil company are pretty smart people, the people who work for the advertising agency, no doubt, are pretty smart people and yet they make an error of more than 2,000 fold in the magnitude of a megaton. A megaton is not 457 tons of dynamite or TNT. It’s a million tons, more than 2,000 times as much as 457 tons. And if these people, these smart people are off by 2,000 fold in understanding what nuclear war is about, then the people as a whole are off by that much in understanding what nuclear war is about, including the people in Germany. Now, in 1958 Joseph Rotblat, professor of physics in the University of London and General Secretary for the Pugwash conferences for many years discussed his estimate of what a nuclear war would be like. He said that the initial attack would involve 10,000 or 15,000 megatons and the counter attack would involve 10,000 or 15,000 megatons, a total of 20,000 or 30,000 megatons. The other people who have analyzed the effects of nuclear war have almost also said, also discussed attacks by 10,000 megatons by each side on the other side. So we can expect that a nuclear war would involve 20,000 or 30,000 megatons. This means, well, what does that mean? The Second World War was a 6 megaton war. The whole of the Second World War involved 6 million tons of high explosives. So if a nuclear war, if it were fought, would involve between 3,000 and 5,000, is that right, ... between 3,000 and 5,000 times the destructive power of the whole of the Second World War. And condensed into a single day, not spread out over five years. You can understand why scholars, scientists who investigate these matters try to make predictions feel that almost certainly civilisation would be destroyed. And perhaps the human race would cease to exist. And most other species of animals, perhaps the smoke and dust would obscure the surface of the earth from the sun light in the same way that the dust from the meteorite that struck the world 65 million years ago led to the great extinction when all the dinosaurs died, all species of dinosaurs, all 18 species and most species of animals and plants that were in existence ceased to exist. Most living organisms on earth ceased to exist. Well, life continued after that great extinction. But the dinosaurs didn’t continue. Human beings might well not continue to exist. And what have we done in the last 25 years? We have made these systems more and more complicated. So that there is a greater and greater probability that some accident would occur that would initiate this ultimate catastrophe. I find it hard to believe that the world is in this insane state that it is in now. And that the United States would continue to spend the hundreds of billions of dollars per year in this really irrational manner. I think that it’s a good thing that nuclear weapons were developed; we had the First World War with 20 or 30 million people killed and the Second World War with 40 or 50 million people killed. If we had just continued - and the Second World War began 20 years after the end of the first world war – we can then extrapolate, if the nuclear weapons hadn’t come into existence by this time, we would have had the conflict between the United States and the Soviet Union, capitalism against communism. With perhaps 60 or 80 million people killed. It’s good that we have had this nuclear deterrent. But it has reached an insane size. This development has gone on, already 25 years ago it had gone far too far. As professor Philip Morrison at MIT said: If it were 1% as big as it is now, it would still involve 100 times the destructive power of the Second World War. What we need to do is to get it under control. To make sure that these nuclear weapons will not be used. Of course that means we have to start to cooperate. It is really unworthy of the human race that the great nations of the world should not be cooperating with one another and with all the other nations in solving the other great problems that exist in the world. Of malnutrition, starvation and the fact that we have a world in which most people are not able to lead good lives. We should, as intelligent beings, be working to achieve a world in which every human being has the opportunity to lead a good life. Even with cooperation it will be difficult enough to solve the great world problems. Well, the greatest of all, of course, is militarism. So we need to do something about that. One commentator wrote, you know,“President Reagan has said what their policy is, he didn’t initiate it for 25 years or more.” There have been two groups of people in the state department of the United States. One group saying “Time has come when we need to cooperate to solve world problems”. And the other group has said “The United States has twice the wealth, twice the gross national product of the Soviet Union, we can stand having a big military budget and the Soviet Union is forced to try to keep up with us”. And that means military burden, this is a much greater one for them. So sooner or later they will break. One commentator wrote in order to bankrupt the Soviet Union has already in its first year brought to the United States to the verge of bankruptcy. Not only economically but also spiritually and morally”. You know, I believe that human beings are good, I believe in morality. And I deplore that the world is being run now in the way that it is being run. I think that it is the duty of every human being to do what he can to eliminate this great evil. To do anything that it is possible for him to do. To start the world moving in the direction of peace and cooperation and morality. Well, I think one reason for doing this is that it will permit human beings to enjoy themselves making quantum mechanical calculations. And I have enjoyed myself over all of the years. Back in 1928, I published a paper in the proceedings of a national academy of sciences on the nature of the chemical bond. In it I said “The resonance theory in quantum mechanics shows that the carbon atom should form four equivalent bonds directed towards the corners of a regular tetrahedral”. And it was only about one sentence, perhaps two on that subject that discussed a number of aspects of molecular structure and chemical bond formation. I think it perhaps ended with a statement that detailed account of this work will be published later. Well, three years went by without a detailed account of the work being published, and as I think back 2 ½years anyway, and as I think back, I think I understand why. The calculations that I had made were just so complicated because the radio part of the wave functions for the carbon atom, they are relatively simple functions,of course, but they’re complicated enough so that these calculations that I had made, that I had interpreted as showing that the tetrahedral carbon, providing a theoretical base for the tetrahedral carbon seemed to me not to be convincing enough to the reader to justify publication. They weren’t even convincing to me. Because they were so complicated. So time went by. In, I think, December of 1930, one day I had an idea. It’s astonishing how hard it is to have ideas, new ideas. But I had this idea, the idea was this: I had published back in 1927 a drawing showing the radial distribution of the wave functions in various atoms, and here the S function, the 2S function and 2P functions of carbon, they are somewhat different functions. The 2S has a node and the 2P doesn’t have a node. But in fact, as you get a little way away from the carbon nucleus, they are pretty much the same. The idea was a very simple one, why not assume that the radial functions are the same for 2S and 2P, and then you just look at the angular functions. Well, the angular function for 2S is just a constant over the surface of a sphere. Independent of faith and fee. And the angular function for 2P is just a cosine function oriented, there are three of them oriented and three different directions. Very easy, the mathematics is very easy to handle a constant plus a simple trigonometric function, cosine or sine. So for several hours, until early morning the next day I was hard at work, I was hard at work making these simple calculations and getting a whole lot of results, a whole series of results which within three months had been published in a 35 page paper on the nature of the chemical bond in the Journal of the American Chemical Society. The first thing about it was to combine this S function and the P functions into a normalised function and determine the nature of this hybrid function that would give the strongest chemical bond. This means it projected to the greatest extent in the direction of the other atom, the hydrogen atom, say in methane. Having got that function, I asked what's the next best function? Or tie them all to the first one. It turned out to be equivalent to the first one and off at the angle of 109.47°. That’s just the tetrahedral angle. And you could make a third equivalent function in the fourth one, so that the 2S function and the 2P functions could be rewritten as four equivalent best bond forming tetrahedral functions directed towards, which were directed, in fact came out from this simple calculation to be directed towards the corners of irregular tetrahedral. So there is the basis of quantum mechanical basis, very simple. It’s in the Freshman, probably in the high school text books of chemistry now. Very simple theory of the tetrahedral carbon atom, pretty much the basis of organic chemistry. I don’t go so far as Dirac went in saying that the Schrödinger equation is the basis of a large part of physics and the whole of chemistry, there’s more to chemistry than just calculation of the sort. But it’s pretty satisfying to know that this simple theory leads to the explanation of the tetrahedral carbon atom. Well, I'm talking now about bonds formed by the transition metals. How much, 40 years went by before I got around to thinking really seriously about bonds formed by the transition metals. Perhaps 15 years ago I suggested to a student working for his PhD degree with me that he tried to find for the transition metals the best hybrid SPD orbitals. The best bond orbitals, the best set of mine that you could form. Normalised and mutually octagonal. A pretty difficult problem and he solved it. And he got his doctor’s degree and I even read his thesis. But it still took me a few years to get really excited about it. And then I thought, can’t we make progress in understanding the transition metals by using this simple technique of just looking at the wave functions. You have an S function, 4S for the iron group, 5S, 6S for the palladium platinum transition sequences. And that gives a total of 9. We would expect that transition metals might well be able to form 9 single covalent bonds. Well, let me have the slides, I want to show those slides anyway having got them all the way from California and if they are here, they will remind me about what to say next! G.N. Lewis was a Californian, a great chemist who came from Massachusetts Institute of Technology in 1910 I think to this school in Berkeley that had a few chemists not doing very much. And he built up what might well be considered to be the greatest department of chemistry in the world. In 1916 he wrote a paper on the chemical bond in which he said the chemical bond is at all times and in all molecules merely a pair of electrons held jointly by two atoms. This was essentially the start of modern electronic structural theory of molecules. Langmuir wrote a number of papers in 1919, 1920, 1921, in which he made really significant contributions to the electronic structure theory. Next slide, please. Here, probably few of you have ever seen a picture of G. N. Lewis. I went to Pasadena to be a graduate student in chemistry, physics and mathematics in 1922. This picture was taken in Pasadena a few years earlier. G. N. Lewis is the man sitting on the running board of the car. The car belonged to Arthur Amos Noyes who had been at MIT and moved to Pasadena was the head of the division of chemistry and chemical engineering in California Institute of Technology. He is at the wheel. I went in this car to the desert with A. A. Noyes and a couple of others, just on an outing a few years later. Next slide, please. Here there was a discussion going on, an argument about the static atom and dynamic atom. And Lewis said: then we may think of each electron orbit as having a fixed position in space. The average position of the electron in the orbit may be called the position of the electron as in the static atom.” Of course this is worked out. This is essentially the basis of the calculation that I mentioned. Here is a figure that appeared in my 1931 paper. I think for the first time. Up at the top we have a sphere that means that an S orbital has a constant value, the same value in all directions. And the 3P orbital’s are shown below, they extent farther out in space but only in certain directions. John Slater was the first person to say in 1930 that an atom such as sulphur combining with hydrogen forms hydrogen sulphide should form P bonds which would be at 90° to one another. The bond angle in H2S is in fact 92.5° and similarly in Arsine AsH3. Well, if we combine these functions, the P functions have a positive slope and a negative slope, so they add onto S in one direction and subtract in the other. We get a tetrahedral function which has twice the extent of the S orbital in the bond direction. And it has a nodal cone of 109.47°, a tetrahedral direction. There’s a simple theorem in quantum mechanics that you can form a second best bond orbital in the direction in which the first one has a node, has zero value. This is what leads to the tetrahedral carbon atom. And it is the basis of the tetrahedral structure of methane. In 1926 and 1927, while I was a post-doctoral fellow in Munich in Sommerfelds Institut für theoretische Physik, there was a man who got his PhD degree by interpreting the band spectrum of methane to show that the methane molecule is flat, a square, the four hydrogen atoms around the carbon corners of a square. Well, you know, in 1927 science was in a primitive, very primitive stage. The structure of the water molecule wasn’t even known. The hydrogen oxygen distance of 0.965 Å or the bond angle of 96°, these things weren’t known in 1927. And of course the tetrahedral carbon atom gives a simple explanation of the existence of system trance, You just assume bent bonds, two bent single bonds equals a double bond, three bent single bonds equals a triple bond. Very simple. In fact it even tells the bond length, the carbon-carbon distance. If you assume that the bonds are bent around the arcs of circles, starting out at the tetrahedral angle, and have the same standard, the normal length 1.54 Å, then the calculated distance between the carbon atoms agrees within a hundredth of an Å for both the double bond and the triple bond with the experimental value. It’s a very good representation, a very good theory of organic compounds, this chemical bond theory. I deplore that students beginning the study of chemistry are taught a lot of complex, largely meaningless material about molecular orbitals. It just confuses them, turns them away from chemistry. I'm not saying molecular orbital calculations aren’t worth making, but it’s pretty poor judgment on the part of text book writers and teachers to talk about molecular orbitals to beginning students of chemistry. Well, here’s the periodic table, the S and P hybrid orbitals account for a good bit of the chemistry of the short period elements. When we come to the long periods, each of them involves 18 elements. Argon, then potassium, calcium, scandium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, copper, zinc, gallium, germanium, arsenic, selenium, bromine. So I'm going to be talking about the transition metals chromium, manganese,iron, cobalt, nickel. Well, in my 1931 paper there was already a discussion of SPD octahedral orbitals and of the square plainer orbitals formed by bipositive palladium and platinum and also nickel, they weren’t known for nickel yet but that was the prediction. And here we have a slide showing on the left side the ionic view of cobalt hexamine, tripositive cation in which the cobalt atom has a charge of +3. And on the right side is the normal covalent or pure covalent view in which you transfer 6 electrons to cobalt, so it has the charge of -3. Well, each of these structures violates a principle that Irving Langmuir proposed 53 years ago, the principle of electro-neutrality, that in every stable molecule or crystal all of the atoms are electrically neutral or nearly electrically neutral. In fact the bonds here are covalent bonds with about 50% ionic character. Here we are, showing bonds that are 50% covalent and 50% ionic. But the cobalt atom has zero resulting charge, each nitrogen atom would have a charge of +1 ½ except that the nitrogen hydrogen bonds are also partially ionic, so that the nitrogen atoms turn out to have essentially zero charge. Each hydrogen atom, and there are 18 of those, has a charge of +1/6. And, of course, in a solution, this charge is partially transferred to the surrounding water molecules so that the hydrated complex is like a metallic sphere, charged metallic sphere, and the electric charge is on the surface. This diagram shows the levels constant…

Linus Pauling (1983)

Structures of Compounds of Transition Metals

Linus Pauling (1983)

Structures of Compounds of Transition Metals

Comment

The chemist Linus Pauling was one of the few recipients of two Nobel Prizes, the Chemistry Prize in 1954 and the Peace Prize in 1962. He was also the only person so far receiving two Nobel Prizes without having any co-recipients. When the Peace Prize was announced, however, some thought that he should have shared it with his wife. She had initiated his activities for nuclear disarmament and always backed him up during his protest marches. Pauling came to Lindau four times and gave four lectures. Two of the lectures concerned his disputed thesis that very large intakes of vitamin C could act as a treatment against cancer. It seems that these two lectures were not recorded, possibly because Pauling thought that the subject was too controversial. The other two lectures have chemistry titles but are, interestingly enough, more than chemistry lectures. Actually, the present 1983 lecture has an extended introduction where Pauling talks about nuclear weapons and world peace. It seems that he once made the decision always to say something on this subject when he gave a lecture. In his characteristically loud and clear voice, he argues in a logical way that the two major players, the US and the USSR, should agree on diminishing their stocks of nuclear warheads. At the time, they represented about 3-5000 times more explosive power than the bombs which exploded during the whole of World War II. According to Pauling, if this amount was to be blown up, the result could cause the extinction of the human race, similar to the extinction of the dinosaurs 60 million years ago! But eventually Pauling turns to the subject of chemistry and tells an interesting story, which began in 1930, when he got an idea about the structure of the bonds formed by a carbon atom, thereby introducing the so-called tetrahedral carbon atom. In his lecture, Pauling reports on the application of this idea to the bonds formed by transition metals and comes to analogous conclusions.

Anders Bárány

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