00:00:00 I'm very pleased to have the opportunity to introduce this year's recipient of the ACS Award in Inorganic Chemistry, sponsored by the Monsanto Company.

00:00:14 Professor Henry Taube from Stanford University is the recipient.

00:00:18 And for over three decades now, Henry has been providing, year after year, work which has given us great insight into inorganic reactions in solution.

00:00:42 Today, Henry will tell us about recent work, but I'd like to go back almost three decades to cite some of the work that he did in the early 50s that really laid the foundations for much of the solution chemistry that's gone on in the last 25 years or so.

00:01:07 This is the classic Chem Review article in which Henry correlated the rates of substitution reactions in inorganic complexes with the electronic structure of the metal ion.

00:01:24 You have to remember that at the time of this paper, a lot of papers in this field involved discussion at sort of this level of sophistication.

00:01:36 Ionic reactions are fast and covalent reactions are slow.

00:01:41 So this paper was a real trailblazer, and it's in this paper that the terms labile and inert were introduced, and we use them with facility now.

00:01:57 But the points that Henry made in this paper really did a lot for inorganic solution chemistry.

00:02:06 The establishment of the composition of the solvation shell around metal ions in solution had been a very elusive goal, and one found values all over the place, many obtained by rather ill-defined transference experiments.

00:02:31 Well, Henry Talby with his students John Hunt and Bob Plain exploited the inertness of chromium-3 and using O-18 demonstrated that chromium-3 ion in aqueous solution was hexa aqua chromium-3, a well-defined inert chemical species.

00:02:58 And by demonstrating this, I think they clarified thinking about all metal ions in solution.

00:03:12 The mechanisms of oxidation-reduction reactions involving metal ions wasn't very well understood in the early 50s.

00:03:22 By exploiting the lability of chromium-2 and the inertness of chromium-3, Henry Talby was able to show that certain oxidations of chromium-2 went by ligand-bridge transition states.

00:03:43 And I think by having a system in which there was an unambiguous answer on the type of transition state involved, I think these papers really provided the basis for discussing all types of redox reactions,

00:04:09 both those involving inner-sphere transition states and outer-sphere transition states.

00:04:16 Henry, I think the whole chemical community is grateful to you for the insights you've provided over these last 30 years, and at this time I'd like to introduce your talk, which is electron delocalization in mixed valence molecules.

00:04:40 Thank you.

00:04:55 Ed, thank you very much for your warm introduction.

00:04:58 If Ed had continued this subject, he would have mentioned an experiment in which we worked in collaboration, one of the most enjoyable experiences I've had, partly because of the science and partly because of the kind of person that Ed King is.

00:05:12 Thank you very much.

00:05:15 For the last 10 years, a little bit more than 10 years, a portion of my research group has paid attention to the field of mixed valence compounds, and I want to deal with some aspects of this work, especially introducing some fairly recent work.

00:05:36 May I have the first slide, please?

00:05:39 The kind of system that we've been concerned with, ruthenium mixed valence species bridged by 4,4'-bipyridine.

00:05:47 A stands for ammonia.

00:05:50 And we've chosen to work with substitution inert molecular entities.

00:06:00 Prussian blue is a mixed valence compound.

00:06:03 But Prussian blue doesn't lend itself as readily to systematic variations in structure.

00:06:09 It's important for us to be able to vary the communication between the metal centers, and it's obviously very difficult to do this for a three-dimensional solid.

00:06:18 Furthermore, one can't do chemistry of the same kind, at least, with the solids that one can do with species in solution.

00:06:28 And the chemistry, the possible chemistry, one hoped that some of it might be novel, was the thing that first attracted me to this subject.

00:06:38 Mixed valence molecules had been known, of course.

00:06:42 Many of them were labile species.

00:06:45 If one mixes a solution of copper 1 and copper 2 in a strong chloride medium, a species is formed which has been shown to contain one copper 1 and one copper 2.

00:06:57 But that's really all you know about its composition.

00:06:59 We don't know how many chlorides are there.

00:07:01 We know nothing about the structure.

00:07:03 This is a labile species, and with all the attempt and difficulties in characterization.

00:07:09 Here, the species retain their integrity whether the molecule carries a charge of 4+, 5+, or 6+.

00:07:19 And that's a great advantage for us.

00:07:21 We know the structure.

00:07:23 A great advantage if we want to interpret the observations in terms of fundamental properties.

00:07:29 May I have the next slide, please?

00:07:32 A photograph of a model of the 4, 4-prime bipyridine molecule is shown here to give you an idea of what it looks like, at least when it's blown up.

00:07:44 The distance between the ruthenium atoms is something like 11 angstroms.

00:07:54 And at this distance, one can be certain that there is virtually no communication resulting from direct overlap of the orbitals on the ruthenium atoms.

00:08:04 The metals communicate through the bridging group.

00:08:09 I'd like to turn now to the properties that we're interested in, studying first, measuring, and then interpreting.

00:08:17 May I have the next slide, please?

00:08:20 We can do electrochemistry on these species in solution, and the couples are nicely reversible.

00:08:28 This stands for the system in the fully oxidized state, this in the fully reduced state, and this then is the mixed valence system.

00:08:37 And a quantity of great interest to us is the free energy associated with this particular reaction,

00:08:46 the comproportional, the comproportionation equilibrium.

00:08:50 How much more stable is the mixed oxidation state than the isovalence state?

00:08:55 We have delocalization between the two centers in the mixed valence state, and we'd like to assess the energy that's associated with this delocalization.

00:09:03 And this gives us at least a measure, and as it turns out, an upper limit.

00:09:08 It'll turn out to be, in fact, a very generous upper limit on the stability that's gained from delocalization in the mixed valence state.

00:09:15 These comproportionation constants, as we've measured them, have ranged all the way from something like 4,

00:09:21 which is the statistical value, if there were no communication, the comproportionation constant would be 4,

00:09:29 to as high as 10 to the 16th in a molecule which Roy Magnuson studied.

00:09:37 For all of the cases I'm going to be talking about here, where the communication is weak,

00:09:41 the comproportionation constant, in fact, lies below 100.

00:09:45 And this is simply the equation that relates the free energy change here to the measured values for the first and second stages of reduction.

00:09:54 May I have the next slide, please?

00:10:05 Important among the observations that we make are the spectra for the species.

00:10:10 We show here the spectrum of the fully reduced molecule, here the spectrum for the fully oxidized molecule,

00:10:20 and then this one is a spectrum for the mixed valence molecule.

00:10:25 And if you look at these, you can see that the mixed valence molecule in the visible region features both of the 3 and the 2.

00:10:33 And from this standpoint, it's not very interesting,

00:10:35 because we simply have a mixture of ruthenium-3 and ruthenium-2 linked in some peculiar way.

00:10:41 There are subtle differences which we're trying to understand,

00:10:44 and I'm sure they'll be very important, but we don't understand them yet.

00:10:48 The next slide, please.

00:10:52 However, in the near-infrared, things get to be more interesting.

00:10:55 The mixed valence molecule shows an absorption, in this case with a maximum at 100 nanometers,

00:11:01 and this absorption is not shown by either the fully reduced or the fully oxidized.

00:11:07 And this absorption band is analogous to that band which gives the blue color to Prussian blue.

00:11:14 And understanding or studying the properties of this band gives us a great deal of insight

00:11:19 into the electronic coupling between the metal centers.

00:11:24 May I have the next slide, please?

00:11:25 Please.

00:11:28 The goals that we've set are indicated on this slide.

00:11:35 We'd like to be able to understand the factors that contribute to the stability of the mixed valence state

00:11:41 compared to the isovalence state.

00:11:43 And it isn't only the electron delocalization that contributes, as we'll see.

00:11:47 There are other factors which, in the cases that I'm going to be talking about,

00:11:51 turn out to be much more important than the part that I'm particularly interested in,

00:11:55 which is stability gained by delocalization.

00:11:59 And it turns out that the free energy associated with the comproportionation equilibrium

00:12:05 sets an upper limit on the stabilization from delocalization.

00:12:10 And then the second thing to understand the electronic coupling mechanisms

00:12:15 is the function of the properties of the bridging loops.

00:12:18 May I have the next slide, please?

00:12:21 Those in my group who have, those co-workers who have contributed

00:12:26 to the subject of mixed valence molecules, it started with Carol Kreutz,

00:12:31 who synthesized an ion which is called the Kreutz ion now,

00:12:34 with, what is the molecule? It's a bridging group that I used.

00:12:39 Well, pyrazine, with pyrazine as a bridging group.

00:12:44 Roy Magnuson, Glenn Tom, Krentzian, Von Kamecki, Stein, Sutton.

00:12:49 And the work that I'm going to talk about is mainly that of James Sutton and Dave Richardson.

00:12:55 Tommy Meyer at the University of North Carolina and his group

00:12:59 have also worked with mixed valence molecules of this type

00:13:02 and have made many important contributions,

00:13:04 both to the experimental observations and to their interpretations.

00:13:09 We've relied heavily on the theoretical ideas of Hush

00:13:15 and on a paper by Mayo and Day

00:13:20 in which they introduced second-order perturbation theory

00:13:23 in order to try to account for the extent of delocalization.

00:13:28 And Richardson simply extended their treatment to a new class of molecules.

00:13:34 And I also want to acknowledge generous support over the years

00:13:37 by the National Institutes of Health and the National Science Foundation.

00:13:42 Needless to say, the success that we've had

00:13:46 has depended on the efforts also of others of my graduate students

00:13:50 and whose names I simply wouldn't be able to get on this slide.

00:13:54 May I have the next slide, please?

00:13:59 Now, let's consider the factors that contribute

00:14:02 to the stability of the mixed oxidation state.

00:14:06 One of them which can be very important when the coordination spheres interlock

00:14:09 is simply steric.

00:14:11 Now, this is a very important factor

00:14:14 and it's perhaps the dominant one in many enzymes

00:14:20 where you have two metals or perhaps even four metals closely coupled.

00:14:24 But it isn't my present concern.

00:14:26 I want to be concerned mainly with the electronic factor.

00:14:30 There is a simple electrostatic factor

00:14:33 which arises from the fact that the repulsions in the isovalent state

00:14:37 are greater than they are in the mixed valence state.

00:14:41 And we've attempted to estimate the contribution by this electrostatic factor

00:14:46 by dusting off the Kirkwood-Westheimer theory dealing with these interactions.

00:14:52 It's still valid, I'm sure.

00:14:55 It has been refined by Aronson to allow for the fact

00:14:59 that a real molecule isn't really a nice ellipsoid of revolution

00:15:04 allowing the charges to move apart,

00:15:06 not being constrained to the focus of the ellipse.

00:15:09 In fact, Sutton had done this independently.

00:15:11 We were gratified to find that...

00:15:13 Well, we were disappointed to find that Aronson had published

00:15:15 but gratified to find that his conclusions and ours were in agreement.

00:15:19 May I have the next slide, please?

00:15:23 And then there's the electronic factor

00:15:24 which I'm particularly interested in

00:15:28 under A1 electron delocalization between the metal centers.

00:15:32 Just how much does the delocalization change the properties of the reactants?

00:15:38 As you will see presently, this is an extremely small number.

00:15:41 It doesn't change them very much at all.

00:15:44 There is a factor that we haven't been able to allow for quantitatively

00:15:49 which is an inductive effect.

00:15:51 Resinium-2 interacts with a bridging ligand by backbonding.

00:15:55 If you put any positive charge on the ligand

00:15:59 that interacts with resinium-2,

00:16:01 you're going to increase that backbonding.

00:16:04 In the mixed oxidation state,

00:16:06 you have put a plus-3 ion in place of a plus-2 ion

00:16:10 so this inductive effect is increased

00:16:12 and this enhances the stability of the mixed oxidation state.

00:16:16 We think we'll be able to assess this contribution

00:16:20 by replacing resinium-3 by rhodium-3.

00:16:23 Rhodium-3 has the same charge.

00:16:25 It doesn't have the electron hole

00:16:27 but this will require some very careful electrochemical measurements.

00:16:32 I'm not sure it'll be worth doing in a number of cases

00:16:34 but it'll be worth doing at least in one case

00:16:36 to get an idea of how big this effect is.

00:16:40 Now, since we're comparing the stability of products to reactants,

00:16:44 we also have to worry about special electronic effects in the reactants.

00:16:48 Now, we're certain that in the 3-3 state,

00:16:51 the interactions are minor

00:16:53 if you allow for the electrostatic one that I've already mentioned.

00:16:59 But in the 2-2, because we have two metal ions,

00:17:02 both dumping electrons into a common pi-star orbital,

00:17:05 there will be a destabilization.

00:17:09 And we don't quite know how to handle this particular one.

00:17:13 May I have the next slide, please?

00:17:17 I've introduced this slide to show you

00:17:19 just how important the steric constraints can be.

00:17:23 This is work done by Cooper and Calvin

00:17:26 where we have a manganese-3 and manganese-4

00:17:29 bridged by two oxide ions.

00:17:32 There's no reason whatever to believe

00:17:34 that there is strong electron delocalization

00:17:36 between the two centers.

00:17:38 The shape of the coordination sphere around manganese-3 and manganese-4

00:17:41 are quite different.

00:17:43 And I believe that the stability of the mixed oxidation state

00:17:46 is attributable largely to the steric constraints

00:17:51 imposed by the interlocking coordination spheres.

00:17:54 And I think this is the case with many binuclear complexes

00:17:57 which have copper closely linked by this kind of arrangement.

00:18:02 May I have the next slide, please?

00:18:05 Let's turn now to the question of measuring

00:18:08 the stability of the mixed valence

00:18:10 relative to the isovalent state.

00:18:14 And in principle, one can use electrochemistry,

00:18:17 but when the two stages of reduction

00:18:20 are governed by almost the same value of potential,

00:18:23 it's quite difficult to use the data

00:18:26 to get the equilibrium quotient.

00:18:28 And when Pat and Jim Sutton

00:18:32 first thought about this problem,

00:18:35 they decided that they wouldn't be competent

00:18:37 to handle the electrochemistry,

00:18:39 but they devised a spectrophotometric way of doing it.

00:18:42 What one does is to start with a fully oxidized species,

00:18:46 and one chooses a wavelength in the near-infrared region

00:18:50 where only the mixed valence compound absorbs.

00:18:53 And then as you reduce,

00:18:55 the light absorption reaches a maximum

00:18:57 precisely when you have half reduced it,

00:19:00 and then when you pass through the maximum,

00:19:03 again, the solution becomes colorless

00:19:05 in this region of the spectrum.

00:19:07 Now, if the mixed oxidation state

00:19:10 were very stable with respect to the isovalent state,

00:19:15 the profile would look something like this.

00:19:17 You'd have a very sharp break at this point.

00:19:20 And in such a case,

00:19:21 you couldn't use a spectrophotometric method.

00:19:23 All you could say is that the contraportionation equilibrium

00:19:26 is greater than, say, 200.

00:19:28 But for the cases of present interest,

00:19:31 it turns out that you get a nice curvature,

00:19:33 and one can analyze the shape of this curve

00:19:36 and obtain a value for the contraportionation constant.

00:19:39 And this was the first way that we were able to do it.

00:19:44 May I have the next slide, please?

00:19:48 Now, Dave Richardson was somewhat bolder

00:19:50 than either of the Suttons,

00:19:52 and he decided that he should be able

00:19:54 to handle the electrochemical problem,

00:19:56 and, in fact, he did.

00:19:59 He handled both the cyclic voltammetry problem

00:20:02 and differential pulse voltammetry.

00:20:05 And in the case of cyclic voltammetry,

00:20:07 it was simply a matter of extending the treatment

00:20:09 by pulsine and chain to the region of present interest,

00:20:13 but the equations were written down by then.

00:20:16 It took a little bit more work

00:20:18 to handle the differential pulse data,

00:20:21 relying on the work of Ruzic.

00:20:24 It's important to appreciate

00:20:25 that one simply doesn't get the addition of two different ways,

00:20:31 because the system,

00:20:34 the distribution between the isovalent

00:20:36 and the mixed valence state changes

00:20:38 as it goes through the oxidation region.

00:20:41 So it wasn't really a trivial exercise.

00:20:45 May I have the next slide, please?

00:20:49 This shows the fit for the case of the 4-4 prime bipyridine

00:20:55 to the cyclic voltammetry data obtained by Richardson.

00:20:59 I'll put the value down on a slide presently.

00:21:02 The deviation here is nothing to be alarmed about.

00:21:05 The theoretical equations require one

00:21:08 to be able to handle the diffusion problem completely,

00:21:11 and one often, in drawing the theoretical curve,

00:21:15 assumes ideal diffusion behavior.

00:21:19 The fit is good enough

00:21:21 so we can assign a comproportionation constant

00:21:23 within about 10%.

00:21:25 And the next slide, please.

00:21:29 Illustrates what one sees with differential pulse voltammetry.

00:21:34 If the values of E1 and E2 were well separated,

00:21:37 one would see something like this.

00:21:39 When they run together, this is the kind of thing you have.

00:21:41 But again, one can find a value of the equilibrium quotient,

00:21:48 if you like, or values of E1 and E2

00:21:50 that reproduce the experimental data.

00:21:52 And again, I think we can fix the comproportionation constant

00:21:55 within about 10%.

00:21:58 May I have the next slide, please?

00:22:01 This is a summary of the cyclic voltammetry data

00:22:05 compared to the titration data.

00:22:08 For the 4-4 prime bipyridine,

00:22:09 a comproportionation constant of something of the order of 20.

00:22:13 The agreement is really quite good.

00:22:15 And the cyclic voltammetry and differential pulse data

00:22:18 agree easily within 10%.

00:22:22 The electrochemical method is to be preferred.

00:22:25 The titration method depends on the system being nice and stable.

00:22:29 And some of these compounds, it turns out,

00:22:31 decompose in ways that are mysterious to us,

00:22:34 so that Sutton's values, I don't think,

00:22:36 are as good as the more recent values by Richardson.

00:22:39 But at any rate, we can get these comproportionation constants.

00:22:41 Now, it's important for us not simply as something to do.

00:22:45 We want to know the extinction coefficients

00:22:48 for the mixed valence molecule.

00:22:50 And if the equilibrium quotient is 4,

00:22:53 then half of the material is stored in the isovalent state,

00:22:55 and you make an error of 2 in the extinction coefficient.

00:22:59 So we wanted these for very practical reasons,

00:23:01 not just as an exercise.

00:23:04 May I have the next slide, please?

00:23:08 This summarizes the conclusions.

00:23:10 Unfortunately, this is a slide made up a couple of years ago,

00:23:13 and we thought that this value was 24 rather than 20,

00:23:16 but it doesn't really materially affect the number.

00:23:21 We gain, in comparing the stability of the 3, 2

00:23:26 to the isovalent state per molecule,

00:23:28 we gain only 500 calories per mole, not kilocalories,

00:23:32 a very small quantity indeed.

00:23:34 And as I've mentioned earlier,

00:23:36 this is an upper limit on the stabilization from delocalization.

00:23:40 The factor 4 simply is a statistical value

00:23:43 which is not interesting to us.

00:23:45 It's simply a way of counting.

00:23:49 The extinction coefficient for this case,

00:23:53 roughly 900 in these particular units.

00:23:58 I might say that we've measured extinction coefficients

00:24:01 ranging all the way from 1 up to 10 to the 4th

00:24:03 for these mixed valence molecules.

00:24:05 May I have the next slide, please?

00:24:09 Now, we can extract a value

00:24:14 for the energy associated with delocalization

00:24:17 from the absorption spectrum.

00:24:20 And in doing this, we follow simply the treatment

00:24:23 developed by Mulliken and Person

00:24:25 and published in their book, Molecular Complexes, 1969.

00:24:30 This is simply a special case of charge transfer.

00:24:33 In their cases, they transfer charge

00:24:36 from, let's say, a metal to a ligand

00:24:38 or between two organic molecules which are associated here

00:24:41 with transferring charge between two metal centers

00:24:43 mediated by a bridging group.

00:24:45 But the quantum mechanics is the same.

00:24:47 This treatment is approximate,

00:24:49 but I think it gives you a ballpark figure

00:24:51 of how much you gain from delocalization.

00:24:56 And we take the wave functions for the unperturbed states.

00:24:59 That is the states.

00:25:01 This is the ground state.

00:25:03 This is the state after you transfer the electron

00:25:06 under the influence of light to the other center

00:25:10 with energies E1 and E2.

00:25:13 And then you allow delocalization to set in.

00:25:16 And you represent this then by writing two new wave functions

00:25:20 with mixing coefficients where the wave functions

00:25:24 for the ground and this state are mixed.

00:25:26 And it's the value of A that we're interested in.

00:25:29 And for our cases, A is so small that this coefficient is unity.

00:25:34 May I have the next slide, please?

00:25:39 This slide is introduced to show some of the parameters

00:25:42 that we're interested in getting.

00:25:44 The intervalence band that I've been talking about

00:25:47 is this particular one.

00:25:49 The dotted lines are the potential energies

00:25:55 without delocalization.

00:25:57 And then when you allow for delocalization,

00:25:59 you get a big splitting at the crossover point

00:26:01 between the bonding and antibonding level.

00:26:04 This is an extremely important number to extract

00:26:07 because it allows you to assess how important delocalization is

00:26:12 completely freed of the front quantum factor.

00:26:14 In this configuration, the coordination spheres

00:26:18 around the two complexes are identical.

00:26:21 So delocalization is at its maximum.

00:26:24 And so beta gives you a measure of what the organic group does

00:26:27 in bringing the electron from one center to another.

00:26:31 So beta is something that we want to extract from the data.

00:26:34 And we also want to extract the stabilization of the ground state

00:26:37 because this is what would be reflected then

00:26:40 in the value of the free energy associated

00:26:43 with the comproportionation equilibrium.

00:26:45 And then this is the quantity that we measure experimentally.

00:26:49 I might mention that the theory that we're applying

00:26:54 depends on this energy being large compared to beta

00:26:57 and being large compared to delta EG.

00:27:00 And this is, in fact, true.

00:27:02 This slide doesn't pretend to be quantitative.

00:27:04 I just wanted to stress the point that beta will be larger than delta EG.

00:27:09 May I have the next slide, please?

00:27:13 Well, the quantity delta EG is related to beta by this equation.

00:27:19 Beta multiplied by beta.

00:27:21 And this is simply the energy difference between E0 and E1.

00:27:26 Beta itself, in terms of the fundamental equations,

00:27:29 the resonance integral, the overlap integral.

00:27:32 But the important thing for us is that beta is related to A

00:27:36 by the energy of the transition in the near infrared.

00:27:41 And we can get A from the experimental data

00:27:44 by looking at the intensity and the energy of the intervalence band.

00:27:52 And again, this equation is approximate,

00:27:55 but at least it's a good beginning.

00:27:57 R is the site-to-site separation.

00:28:00 This is the band width at half height for the intervalence band.

00:28:06 And later on, I'm going to be talking about dipole strengths of transitions,

00:28:10 and it simply is the mixing coefficient

00:28:12 multiplied by the distance between the two metal centers.

00:28:15 May I have the next slide?

00:28:19 Well, this summarizes the experimental observations made by Jim Sutton.

00:28:25 Some of his work was a refinement of earlier work.

00:28:29 At least it got us to the point that we're able to write values

00:28:33 for the comproportionation equilibrium constant.

00:28:37 And the numbers of particular interest to us, I think,

00:28:40 are the values of the extinction coefficient.

00:28:45 Comparing these two cases, the electronic coupling obviously goes down

00:28:49 when you put these hysterically demanding groups in

00:28:53 and constrain the rings to be almost perpendicular.

00:28:56 It goes down still further when you insert saturated material between the two rings.

00:29:04 But comparing these two, we now have a lone pair of electrons

00:29:08 and the communication is dramatically increased over this particular molecule.

00:29:15 We thought we'd learn something from the comparison here,

00:29:18 and we may have, but neither Jim nor I are quite sure what it is.

00:29:23 It turns out that the values of the extinction coefficient are virtually the same.

00:29:28 There is another point.

00:29:30 If the coordination spheres around the two metals are the same,

00:29:34 and if the reaction coordinate, if the movement of the nuclei

00:29:39 that promote the coupling is the same in both cases,

00:29:43 and if then the distances are the same,

00:29:46 then the energy should be the same, according to simple theory.

00:29:49 And there is only a slight difference here.

00:29:51 There is a large difference in this case.

00:29:53 The dimensions are the same, and each molecule has the same coordination sphere.

00:29:58 And I think it reflects the fact that the reaction coordinate is different in this case than in this case,

00:30:04 and perhaps suggests that the molecule has to bend.

00:30:08 The two rings have to, the angle between the two rings has to be changed in order to promote the interaction.

00:30:18 May I have the next slide, please?

00:30:21 Now, to summarize Jim Sutton's work, these are the same molecules that we had before.

00:30:29 These are the distances between the metal centers as determined from models, if you like.

00:30:37 And then we're considering the stabilization of the mixed oxidation state relative to the isovalent state per molecule now.

00:30:48 That which we calculate using the oscillator strengths for the intervalence transition is indicated in the last column.

00:30:57 The experimental values are here.

00:30:59 Now, these are good, at least as good as our electrochemistry.

00:31:03 This is, of course, softer. I'm not enough of a theoretician to know whether we're off here by a factor of two.

00:31:10 I hope it's not a factor of five. I'm sure it's not a factor of 10 because this number has to be bigger than this number.

00:31:20 The electrostatic contribution is probably handled reasonably well by the Kirkwood-Westheimer treatment as modified by Aronson.

00:31:31 I mean, I can't congratulate myself about the agreement here.

00:31:36 We simply use this molecule in which the electronic interaction is small as a way of assigning an effective dielectric constant.

00:31:45 And I think we can really, I think, to assume that the electronic interaction is small in any oxidation state is in accord with the fact that this number is very small.

00:31:58 Well, the point is that the stabilization of the ground state by delocalization is indeed virtually trivial.

00:32:08 There is a fairly important electrostatic factor.

00:32:12 The most important of the remaining ones is the inductive effect that I've mentioned.

00:32:16 And as I say, there is an experimental strategy for assessing it, which is to replace ruthenium-3 by rhodium-3 and then comparing the electrochemical behavior.

00:32:25 One such comparison was made by Carol Kreutz on the Kreutz ion.

00:32:30 And it, in fact, shows that this is a very important contribution to the stability of the mixed oxidation state.

00:32:36 But for me, it has been important to get an idea of what this number is.

00:32:41 And now I know that it's not very big.

00:32:45 And I can't expect any dramatic chemical effects from this class of molecules, let's say.

00:32:51 It simply is a molecule that bears one ruthenium-2 and one ruthenium-3.

00:32:58 I'd like to turn now to, no, I still have one other point I want to make in connection with Jim Sutton's work.

00:33:04 May I have the next slide, please?

00:33:08 I didn't develop the connection between this intervalence band and thermal electron transfer in an earlier slide.

00:33:16 But, in fact, one can, in principle, use the spectroscopic observations to estimate the rate of thermal electron transfer.

00:33:25 And in doing it from the intervalence absorption, you can apply the Eyring equation.

00:33:32 And for our systems, which we believe, at least for the particular system that I'm describing here, which is that bridged by 4, 4 prime by pyridine,

00:33:42 we believe that electron transfer is adiabatic.

00:33:46 And we believe that on one count is an experimental one.

00:33:52 We've done a number of experiments in which we've taken a molecule which has cobalt-3 at one end and ruthenium-2 at the other

00:34:00 with the same kinds of bridging groups and measured the net rate of electron transfer.

00:34:05 And it turns out that you can fiddle with the communication between the pyridine rings quite a bit before the rate begins to go down.

00:34:11 And this suggests that we are in the adiabatic regime.

00:34:14 Furthermore, for these reactions, the entropy of activation for electron transfer is about zero.

00:34:21 So we think that kappa in the Eyring equation is unity.

00:34:26 Kappa is, of course, ordinarily incorporated into the entropy change associated with the reaction.

00:34:35 So we're simply going to set delta S of activation equal to zero.

00:34:41 Now, to get at the entropy change for the activation, if the potential energy curves that I showed earlier were simple harmonic,

00:34:53 then the energy associated with the intervalence band is four times the energy that it takes to get from the minimum to the crossover point for the unperturbed levels.

00:35:07 So we simply take this energy and divide it by four.

00:35:11 But it turns out that the stabilization at the crossover point is about two kilocalories.

00:35:16 It's two beta, so we have to subtract beta from this.

00:35:19 This then gives us the entropy of activation.

00:35:22 And we calculate then for the rate of intramolecular electron transfer, something like three times ten to the eighth mole to the minus one and second to the minus one.

00:35:30 Now, before we had done the experiment, had done the calculations,

00:35:33 an estimate of rate of intramolecular electron transfer for closely related systems had been made and published, Brown, et cetera.

00:35:43 This is measuring, if you like, a pseudo self-exchange process.

00:35:46 We take ruthenium-3 with a pyridine-like ligand on it, ruthenium-2 with a pyridine-like ligand on it.

00:35:54 We make them different because we don't want to use isotopic tracers.

00:35:58 We simply want to do spectrophotometry.

00:36:00 And we can measure the second order rate for electron transfer in this system.

00:36:07 Now, to convert the second order specific rate into a specific rate for intramolecular electron transfer,

00:36:14 we have to be able to estimate the concentration of, if you like, the collision complex,

00:36:19 the oxidant and reductant in equilibrium with a separate species.

00:36:24 And people think they can do this.

00:36:25 And obviously, I thought I could do it, too, because I'm also on this paper.

00:36:31 But again, I think that you can only do this within a factor of something like two or three.

00:36:37 And anyway, the value that we had published prior to doing this calculation was something like two times ten to the eighth.

00:36:43 It suggests at least that one can get a fair idea from measuring the properties of these intervalence molecules,

00:36:51 simply the spectrophotometric properties of the rate of thermal electron transfer.

00:36:57 Well, I'd like to turn now to the second goal, which I announced in the introduction,

00:37:02 which is to see if we can do anything about understanding the magnitude of the coupling in terms of fundamental properties of the groups connecting the metal ions.

00:37:11 So may I have the next slide, please?

00:37:15 And in talking about mechanisms for electron transfer, if you like, we have talked, for example,

00:37:22 about possible charge transfer from the reduced member to the bridging group.

00:37:30 And I think a molecule such as cyanogen, which was studied as a bridging group by Glenn Tom,

00:37:38 in this molecule as bridging group, this provides the principal mechanism for delocalization.

00:37:45 This is a very strong pi acid.

00:37:47 Pi star level lies quite low, and it produces strong communication between the two centers,

00:37:53 chiefly through pi-d-pi star interactions.

00:37:58 Then in another class of organic molecules, we have those that are easily oxidizable.

00:38:03 This is the anion from melanonitrile.

00:38:08 And here a very important interaction is taking an electron from the bridging group and depositing it then on the metal ion.

00:38:17 Metal to ligand, and here ligand to metal.

00:38:21 Now, these qualitative ideas have been put into a more quantitative form by Mayo and Day.

00:38:28 They have applied them to the Kreutz ion, and they've applied them also to Prussian blues.

00:38:34 May I have the next slide, please?

00:38:37 And to give you an idea of the kind of quantities that go into these calculations,

00:38:43 it is an application of second-order perturbation theory, but of course it's not a priori.

00:38:48 You use experimental measurements as much as possible.

00:38:52 We have the ground state.

00:38:54 We have the excited state, which arises when you leave the nuclei fixed and simply deposit the electron,

00:39:01 take it from the reducing agent and put it on the oxidizing agent.

00:39:05 And then you find the energies of the states that result,

00:39:09 A, when you take an electron from ruthenium-2 and put it into a pi-star level,

00:39:15 B, if you take an electron from a filled pi level on the ligand and put it onto ruthenium-3.

00:39:22 And we know what these energies are from the spectra in the visible.

00:39:28 I didn't go through the earlier slide in great detail to point out the transitions for the ruthenium-2 and ruthenium-3

00:39:36 in mononuclear complexes that allow us to say what these energies are.

00:39:41 But then you need the whole hierarchy of pi-star and pi levels.

00:39:45 And here you rely on endocalculations, which you then adjust using experimental data,

00:39:53 such as photoelectron spectroscopy, wherever possible.

00:39:56 But the important states that contribute to the mixing are the pi and pi-star.

00:40:00 They become less important as you go up.

00:40:02 And these you get reasonably accurately simply from the visible absorption bands.

00:40:09 May I have the next slide, please?

00:40:12 Now, the formal statement of how you calculate the mixing coefficient is given here.

00:40:18 The two rutheniums and the two nitrogen atoms, this is not nearly as bad as it looks.

00:40:22 This is the energy difference between a chosen, excited pi-star level and the ground state.

00:40:30 And as I say, for the first pi-star state that interacts with metals, we get this experimentally.

00:40:37 And then for the others, the contribution becomes less, but we rely on calculations to locate the other levels.

00:40:43 These are the coefficients for the molecular orbitals on the nitrogen atoms.

00:40:49 And here again we rely on calculations, but one can't fiddle with these very much.

00:40:55 And then these are resonance integrals,

00:40:58 which we can get by analyzing the spectrophotometric data in the visible.

00:41:05 We look now at the intensity, or at the oscillator strength,

00:41:08 and this allows us then to assign values to these quantities.

00:41:13 The important factor I want to point out is the one in the denominator.

00:41:17 If you really want to increase the interaction through the ligand,

00:41:21 what you want to do is to make these numbers small,

00:41:24 either by having the metal level so that it's close to the pi-star or close to the pi.

00:41:29 If you're smack in the middle, the interaction isn't going to be very great.

00:41:33 You want to maximize one term or the other by adjusting the levels,

00:41:39 and I'll mention some experimental strategies for doing this.

00:41:42 May I have the next slide, please?

00:41:45 To give you an idea of how this point of view applies,

00:41:51 let's take a case of a ruthenium-2 and a ruthenium-3,

00:41:54 each with a pyridine on them and with variable coupling between the pyridines.

00:42:00 And again, this is our ground state.

00:42:02 This is the state that arises when you transfer the electron leaving the nuclei fixed.

00:42:08 And in the case when the interaction is very weak,

00:42:12 you have, of course, a symmetric and anti-symmetric combination of levels here.

00:42:18 The splitting is very small, and one of these contributes negatively.

00:42:23 The other contributes in a positive fashion so that the net interaction is zero.

00:42:28 It's only when there is a reasonable interaction so that these levels are split

00:42:33 that you will get a contribution to the mixing coefficient.

00:42:37 May I have the next slide, please?

00:42:41 Well, Dave Richardson's contributions took various forms.

00:42:47 I think the work that he did on the electrochemical problem was very nice.

00:42:52 He also is a very good experimentalist,

00:42:55 and he decided that he would try to extend the Mayo Day treatment to a class of molecules.

00:43:00 And we want rigid molecules because we want the distance between the metals to be fixed and known.

00:43:06 And he chose, well, these are among the ones.

00:43:10 This is a molecule that Carol Kreutz used

00:43:14 when she synthesized the first of this series of mixed valence molecules.

00:43:18 Dave Richardson managed also to construct the molecule

00:43:21 in which we have the nitrogens in the meta position and so on.

00:43:27 And here I've shown the values of the distance between the metals,

00:43:34 one nitrogen, one on the other.

00:43:38 Here are the dipole strengths of the transition observed and calculated.

00:43:46 This agreement is much too good.

00:43:48 In fact, one should be suspicious of it

00:43:50 because in the Kreutz ion the delocalization is very strong

00:43:54 and the calculations have no reason at all for working.

00:43:59 So rather than the agreement inspiring confidence,

00:44:02 it should make you suspicious that not everything is fully understood.

00:44:06 I don't think that it's important to compare the absolute values.

00:44:10 The important thing is to compare trends.

00:44:13 And I think this point of view does at least,

00:44:16 in cases where the observations tell you the number gets smaller,

00:44:20 the treatment tells you that the number gets smaller.

00:44:22 And in this sense it can be used.

00:44:24 There are some ad hoc assumptions made in getting an absolute value.

00:44:28 And I think the proper way is to take some case and then adjust it

00:44:32 and then, in other words, take an experimental parameter.

00:44:37 But I think on the whole, the Mayo and Day point of view

00:44:42 accounts reasonably well for the trends,

00:44:44 the trends themselves reflecting differences in extinction coefficient.

00:44:49 Beta is this quantity that I mentioned earlier.

00:44:52 The stabilization at the crossover point,

00:44:55 the splitting between the bonding and antibonding levels,

00:44:58 a direct reflection of the extent of delocalization.

00:45:01 And you can see that in the case of the Kreutz ion,

00:45:03 this turns out to be nine kilocalories,

00:45:05 so that some of the assumptions on which this treatment is based

00:45:08 simply do not obtain.

00:45:13 In the other cases, these values of beta are quite a bit less.

00:45:21 I think there's one more slide.

00:45:25 Yes, he also synthesized the dinitriles based on naphthalene.

00:45:30 And again, with fairly reasonable trends, looking at it this way,

00:45:35 these numbers usually are a factor of two to four less than the observed values

00:45:39 and with corresponding values of beta.

00:45:41 We had difficulty extracting the intervalence band in some of these cases

00:45:44 because it overlapped with the pi D pi star absorption.

00:45:48 Well, I feel that the stage that Richardson and Sutton has brought us to

00:45:56 is that we have sort of a semi-quantitative understanding

00:45:59 of at least the extent of electron delocalization

00:46:02 in certain classes of these molecules.

00:46:05 But of course, organic chemistry is a very rich field

00:46:08 and there are always molecules that one hasn't thought of.

00:46:11 I was going to say that we can handle the cases

00:46:15 in which we have a conjugated organic molecule bridging the two metal ions.

00:46:19 We can handle this case without even doing the experiments.

00:46:22 But then I want to call off that by saying that there are always molecules

00:46:26 that have some unexpected electronic features

00:46:29 that one simply hasn't thought of.

00:46:31 But I think at least the Mayo and Dave treatment

00:46:34 allows you to reject a number of experiments

00:46:36 that one might otherwise do out of sort of idle curiosity

00:46:39 or in the hope that it might teach you something

00:46:41 and can then turn to systems that are more likely

00:46:44 to produce some novel and significant effects.

00:46:50 Now, as I mentioned earlier,

00:46:53 if you want to increase the communication between the two metals,

00:46:59 if you want a completely delocalized system,

00:47:01 the best factor to work with is the energy difference.

00:47:04 Now, if you want to use the pi star levels,

00:47:07 then an obvious thing that you can do is to use osmium in place of ruthenium

00:47:12 because osmium amines are easier to reduce

00:47:16 than ruthenium amines by almost a volt.

00:47:19 And we've done enough work to know that there's very strong mixing

00:47:23 of the pi star levels in an osmium pyridine complex with the pi d levels.

00:47:28 But the preparative problem there is much more difficult

00:47:31 than it is for the ruthenium,

00:47:33 and we're only slowly learning how to handle the osmium complexes.

00:47:39 The other direction, of course,

00:47:43 would be to improve the interaction with the filled pi levels.

00:47:48 And there is, in fact, one more slide, which I think it's there.

00:47:54 And this is work done by Crensian using, again, a melanonitrile as a bridging group

00:48:01 where we get a whopping big extinction coefficient for the intervalence band,

00:48:06 a comproportionation constant of 10 to the 10th.

00:48:09 And here the communication is largely attributable to taking an electron

00:48:14 from the ligand and depositing it on the electron hole.

00:48:17 Unfortunately, this does not lend itself to systematic development.

00:48:20 These molecules are all quite unstable

00:48:23 and undergo various kinds of decomposition reactions,

00:48:27 which we don't understand.

00:48:28 I'm sure they're interesting.

00:48:30 At least they do give pretty colors.

00:48:32 And what we'd really like is a rugged bridging ligand of this kind.

00:48:38 And then an area in which the experimentalists, I think, still must take the lead

00:48:45 is the area where we don't have conjugated molecules bridging the two metal centers.

00:48:52 We have saturated ligands.

00:48:54 Cy Stein made a beginning in this work.

00:48:57 And for this field, a theoretical framework that I've sort of introduced

00:49:01 and illustrated with some examples simply does not apply.

00:49:04 And I think it is a field for further investigation

00:49:07 and one that I'm really very much interested in.

00:49:11 Well, I think this concludes what I wanted to say in the way of formal remarks.

00:49:16 I also want to add my thanks to those voiced by Herb to the Monsanto Company

00:49:20 for their support of an extremely important part of science, of chemistry.

00:49:27 And thank you for your attention.