I. OPTICAL AND MAGNETIC PROPERTIES INTRODUCTORY PAPER PHYSICAL PROPERTIES OF TRANSITION IONS BY M. H. L. PRYCE Received 2nd October, 1958 In recent years the ions of transition elements have been attracting the attention of many workers in different fields, publishing, often unknown to one lanother in a wide variety of journals. Chemists, inorganic and physical, naturaly have, had an interest in transition ions fur a long time, not necessarily restricted to what may be termed more obviously chemical properties, but also including physical properties which may be used diagnostically to gain insight into chemical struc- tures, such as magnetism and spectra. Physicists might have been expected thirty years ago to have taken an interest in transition-ion spectra, at the time when spectroscopy appeared to be one of the most powerful tools of physics. And to some extent this happened,l-lo but the time was not then ripe for a proper under- standing.More recently, through magnetism, and particularly magnetic ieson- ance phenomena, physicists have been induced to study these very interesting systems, and this has led them to fields on the borders of chemistry and physics similar to those investigated by the chemists. This meeting serves a valuable dual purpose; first, in linking up the efforts of various groups of researchers by bringing their members together in one place, so that each may learn from the others what has been achieved in related fields; and secondly, in giving us all an opportunity to take stock of the situation in a subject which has reached a particularly interesting stage in its development, and of formulating the outstanding problems for future study.It should become clear by the end of this meeting that each aspect of the properties of transition ions is capable of throwing light on all the others, and that many apparently different properties are intimately interrelated. It is particularly fitting that the Faraday Society should be the sponsor of this synthesis of chemistry and physics. My task in this introductory talk is to try to convey the background of the physicists’ view of the nature of the problems, in as intelligible a way as possible. A good place to start, it seems to me, is to ask in what essential way the ions of transition elements differ from other ions, particularly other metallic ions.For it is not without reason that a whole meeting has been devoted to transition ions, to the exclusion of the more law-abiding cations. When we have identified the essential feature we shall then wish to study how it is responsible for the properties that we find interesting, such as the stability of their complexes, their colour (which is a direct visual manifestation of their interesting optical spectra), their magnetism, etc. I would say that the distinguishing feature lies in the arrangement of the elec- trons in the ion. Ions of the ordinary, non-transition, elements have their elec- trons in completed shells of energy levels. In the transition ions, however, the topmost shell of energy levels, or more precisely, orbitals, is incompletely filled. Before going any further, let me remind you that the language of orbitals which I have used-and which I propose to continue using-expresses an ap- proximation to the proper description of the electronic structure.It has the great merit of giving a simple mental picture: electrons are packed into the available energy states or orbitals, one orbital per electron. (I assume that the 2122 INTRODUCTORY PAPER specification of the orbital includes spin-otherwise each orbital can hold two electrons.) The real state of affairs is of course more complicated than is de- scribed by saying n electrons, n orbitals. But it often seems to be a rather good approximation-and one which readily forms the starting point for further re- finements when these are necessary.For my present purpose it is quite adequate. The orbitals of electrons in an ion fall into groups, or shells. In each shell the energies of the orbitals are rather close together; but Werent shells differ widely in energy. In a closed-shell ion the orbitals in the lowest shells are all filled, and those in the higher shells are all empty. Such an electron configuration has certain notable features. The charge distribution is spherically symmetrical ; there is no net angular momentum of the electrons, because to each occupied orbital which might contribute to electron rotation there corresponds one with rotation in the opposite sense, and there is full compensation; similarly there is no net magnetic moment, because the circulating currents all compensate, and the spins are all paired.Furthermore, it takes considerable energy to excite an ion from this configuration to its next highest energy level, since this requires the transfer of an electron from an orbital in the topmost occupied shell to one in a higher shell. Also, it generally requires considerable energy to detach an electron from such an ion, since even the topmost orbital is relatively tightly bound ; while at the same time the affinity for a further electron is relatively low, as only orbitals in the higher shells are available. Such ions therefore exhibit no paramagnetism; and are unable to absorb quanta of visible light, which have too little energy to excite them. Their compounds are therefore colourless and diamagnetic, while their stereochemistry tends to be dominated by their spherically symmetric charge distribution.When the topmost shell of orbitals is incomplete, however, the situation is radically different in all the respects just mentioned. Before going on to analyze in greater detail how this comes about it is well to remark on one important feature of the transition ions, namely, their degeneracy in the ground state. That is to say, there is more than one quantum state with the same lowest energy. In fact there is a whole infinity of states, whose wave-functions are made up by linear combination from a limited number of independent wave-functions. Consequently there is a great variety of charge configurations, each corresponding to the same lowest energy. It may be instructive to give an example.The Fez+ ion has six 3d-electrons in addition to those occupying closed shells. Now the 3d-shell contains ten independent orbitals, so that there are as many independent states of the ion made up in this way as there are ways in which one can arrange six objects in ten boxes, namely, 210. It is true that not all these states have pre- cisely the same energy, because although there are always six electrons in 3d- orbitals, their correlation in space is different, so that their mutual energy, arising from their electrical repulsion, is different. Nevertheless, a good deal of degeneracy remains, and in any case, the energy differences of the 210 levels are relatively small. In the example quoted, there is a lowest group of 25 levels within an energy span of 2,000 cm-1, the ground state being ninefold degenerate ; and the majority of the remaining levels lie within 40,OOO cm-1 (5 ev) of the ground state.That the ion now possesses magnetic moment is a natural consequence of the fact that with an incomplete shell the magnetic effects of circulating electric currents, or of electron spins, no longer necessarily cancel. The degeneracy we have just described is a manifestation of the different “ directions ” in which the magnetic moment can point, which are governed by the socalled ‘‘space quantization ”. What has just been said applies to the free ion, uninfluenced by external sur- roundings, and needs modifying for ions in combination-as in complexes or in inorganic crystals. The fact that in the free ion there are many different charge distributions for the same energy means that in an external force field Werent states will behave differently and have different energies.In other words theM. H. L. PRYCB 23 external surroundings remove the degeneracy-or partly. One may visualize this as follows. Some states have electron distributions which point strongly towards negatively charged regions in the surroundings (e.g. the ligands of a complex)- they will have a relatively high energy because of the mutual repulsion of negative charges. Others will have electron distributions avoiding the negative charges, and will consequently have a lower energy. This splitting of degenerate levels by the surroundings is the most important factor in determining the optical absorption of transition metal compounds, and hence their colour.The fact that the lowest energy level corresponds to a charge distribution adapted to fit snugly into the interstices between surrounding negative charges implies that a transition ion compares favourably with an ordinary ion of the same radius, which cannot so adapt itself.11-13 Its compounds and complexes are therefore stabilized in comparison. In most compounds the stabilization energy increases sharply with decreasing cation-anion (or cation-ligand) distance, and this results in the configuration of overall minimum energy being achieved for a shorter cation-anion distance than would happen for a simple cation.14-16 In other words, the effective ionic radius of a transition ion is decreased by its powers of adaptation to its surroundings.Similarly, since the stabilization energy also depends on the shape of the framework of surrounding ligands or ions, the requirement of minimum energy influences this shape. In complex ions where the Jahn-Teller effect is strong, this can be very important.12.17-21 A well-known example is Cu2+6H2O, in which the octahedron of water molecules is so distorted that four are much closer to the central ion and the other two are further from it, than would be expected for an aquo-complex in this part of the periodic table (Ni2+6H20 by contrast is quite regular.)13. 199 20 This state of affairs, which I have described in qualitative terms, can be given a quantitative expression. Energy differences, magnetic moments and spectro- scopic splitting factors such as are related to paramagnetic resonance observations, can all be related to models of the field set up by the ligands.ll.22-42 Relations between observable quantities are deduced, which are independent of the details of the model, and can be tested.If the ion is only loosely associated with its ligands, the orbitals for the electrons fall into two distinct classes : those localized on the ion ; and those localized on the ligands. And the orbitals on the ion are very little different from the orbitals of the free ion. Calculations based on the approximation that the ionic orbitals are unchanged by bonding are often referred to as “crystal field theory” or ‘‘ ligand field theory ”. They have the merit of being often quite simple and straightforward, and so of giving an insight into the outlines of the situation.For so-called “ ionic ” compounds, where the orbitals are reasonably well localized, ligand field theory gives a very good account of magnetic, optical and energetic properties. Even in ‘‘ covalent ” complexes, where the orbitals spread strongly from the central core to the ligand atoms, it makes a useful first approximation. One may see qualitatively how bonding affects the orbitals. Those orbitals originally localized on the ligands, which are directed towards the central ion, acquire a certain amplitude in the region of the ion, particularly where the 3d wave-function is important. If the ligand atoms are oxygen or nitrogen, the 2p-orbitals are the ones most affected in this way. Their energy is lowered, so that they become bonding orbitals.They are always completely filled in transition- ion complexes. The orbitals which in the free ion are pure 3d, and are directed toward the ligands, similarly overspill on to them. Their energy tends to be raised, as they correspond to anti-bonding hybrid orbitals. Such considerations of course apply to closed-shell ions as well as to transition ions, and to some extent modify the statement that the former’s stereochemistry is dominated by their spherical shape. It remains true, nevertheless, that closed-shell ions are less adaptable to their surroundings.24 INTRODUCTORY PAPER Since the magnetic properties and the optical absorption are connected with the orbitals of the unfilled shell, such aspects of them as are determined by the behaviour of the electrons close to the central nucleus will be reduced if the orbitals overspill on to the ligands.This provides a quantitative measure of the overspill, and in a certain sense may be taken as one measure of the covalent, as opposed to ionic, character of the complex. Effects which can be used in this way are the hyperfine coupling, and the effective spin-orbit coupling as revealed by g-values, in paramagnetic resonance ; and the wavelengths of the sharp lines in the optical absorption spectra. The former two arise from the interaction of electrons with either the nucleus of the ion, or with the electric field in its immediate vicinity, and are therefore reduced from the free-ion values proportionately to the electron probability- density.27.38s 439 44 The latter comes from the mutual repulsion between pairs of electrons in the unfilled shell, which again comes mainly from the probability density close to the nucleus.27.45 Jn relation to the sharp lines in the spectra it is worth making a few comments. They correspond to transitions between states which have, on the orbital ap- proximation, the same charge density, but in which the electrons are differently correlated. Since the charge density is the same in the two states, the energy difference is unaffected by variations in the ligand field. In particular the equilib- rium configuration of the ligand-framework in the excited state is the same as in the ground state. Consequently no vibrations are excited by the electronic transi- tions, and the energy required is just the electronic energy-difference.37 These sharp lines are always very weak, because they correspond to a rearrangement of the spin orientation, without change of orbital state, and such " intersystem combinations " as they are called in atomic spectroscopy, are weak.The main absorption of light, by contrast, is spread over a broad band of frequencies. The main reason for this is that, since the charge distribution in the upper state reached by the electronic transition when light is absorbed is different from that in the ground state, the ligands, which are near their equilibrium position in the ground state, are no longer in equilibrium in the upper state, and vibrations are set up. Since there are very many vibration modes in a crystal or in a solution, there is a wide spread in the energy going into vibration.The quantum energy of the light is the sum of the electronic energy-difference and the energy of vibration-so one sees that it is spread over a wide spectral region. Thermal agitation, which causes fluctuation in the crystal field, also contributes to the width, though not so importantly. The experimental approach has been along three main lines : thermodynamic, spectroscopic and magnetic. By thermodynamic I mean the broad approach towards measuring energies or heats of formation and reaction, stabilities of complexes.12* 46 Many complexing agents and most of the ions of the 3d group have been investigated.34-36.47148 Spectra have been studied in the solid state for simple hydrated com- pounds,l-9*49-53 and more extensively in solution for a wide variety of com- plexes.8-10s 54-58 The solid-state spectra show some fine structure if taken at low temperatures (14°K or below), which is smeared out at higher temperatures.Of recent years, measurements of oscillator strengths and band widths have proved interesting, in view of developments in the theory which enable calculations to be made.59-64 In solution spectroscopy the establishment of spectrochemical series of complexing agents has proved fruitful, throwing light on the mechanism Magnetic studies have dealt with many aspects. Susceptibility measurements have provided chemists with a tool for probing stereochemistry and the electronic structure of the complexes.22r 24.25.67.68 More recently, paramagnetic reson- ance has complemented this approach, and in favourable cases given information of a very detailed nature concerning the electronic structure.26127.38.39. 69-71 of bonding.65.66.34,35. 36.48M. H. L . PRYCE 25 The following list of references is far from complete. The reader is referred to the bibliographies at the end of the specialized papers of this Discussion, for a more comprehensiv: sirvey. 1 du Bois and Elias, Ann. Physik, 1908, (4), 27, 233. 2 Sauer, Ann. Physik, 1928 (4), 87, 197. 3 Snow and Rawlins, Proc. Camb. Phil. SOC., 1932, 28, 522. 4Deutschbein, Ann. Physik, 1932 (5), 14, 712, 729; 1934 (5), 20, 828; 2. Physik, 5 Joos and Schnetzler, 2. physik. Chem By 1933, 20, 1. 6 Spedding and Nutting, J. Chem. Physics, 1934, 2, 421 ; 1935, 3, 369.7 Gielessen, Ann. 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