The Future

In this final chapter, an attempt is made to provide an overview of the capabilities of quantum-mechanical methods at the present time, and to highlight the needs for future development and possible future applications of these methods, particularly in areas related to mineral structures, energetics, and spectroscopy. There is also a brief account of some new areas of application, specific directions for future research, and possible developments in the perception and use of quantum-mechanical approaches. The book ends with an epilog on the overall role of “theoretical geochemistry” in the earth and environmental sciences. The local structural characteristics of minerals such as Mg2SiO4, which contain only main-group elements, are reasonably well reproduced by ab initio Hartree-Fock-Roothaan (SCF) cluster calculations at the mediumbasis- set level. Calculations incorporating configuration interaction will inevitably follow and probably lead to somewhat better agreement with experiment. The most pressing needs in this area of study are for the development of systematic procedures for cluster selection and embedding, for a greater understanding of the results at a qualitative level, and for more widespread efficient application of the quantum-chemical results currently available. In the last area, substantial progress has already been made by Lasaga and Gibbs (1987), Sanders et al. (1984), Tsuneyuki et al. (1988), and others, who have used ab initio calculations to generate theoretical force fields which can then be used in molecular-dynamics simulations. If the characteristics of the resultant force fields can be understood at a first-principles level, then it may be possible to understand details of the simulated structures at the same level. Unfortunately, as regards a greater qualitative understanding of the quantum-mechanical calculations, little progress has been made. Rather old qualitative theories describe some aspects of bond-angle variation (Tossell, 1986), but no general model to interpret variations in bond lengths has been developed within either chemistry or geochemistry beyond the model of additive atomic (Slater) or ionic (Shannon and Prewitt) radii. Indeed, global theories of bond-length variations within an ab initio framework seem to be nonexistent. Nonetheless, quantum-chemical studies have shown the presence of intriguing systematics in bond lengths (Gibbs et al., 1987), which had been already noted empirically.

Applications to Silicate, Carbonate, and Borate Minerals and Related Species

The most abundant materials making up the crust of the earth (i.e., the “rock-forming minerals”) can be regarded as dominated by oxyanion units; notably, the units that can be formally represented by SiO44- and AlO45- clusters of the silicate minerals, and the CO32- unit of the carbonates. less common, but geochemically interesting, oxyanion units include, for example, BO33-, BeO46- , and PO43-. in this chapter, applications of quantum-mechanical calculations and experimental techniques to such materials are considered. first, the silicates are discussed, commencing with the large amount of work undertaken on the olivines, before considering such work as has so far been done on the other silicate minerals and related materials. second, the most important of the nonsilicate rock-forming mineral groups, the carbonates, are discussed. finally, although of less petrological importance but interesting geochemically and in terms of contrast with the othergroups, the borates and related species are considered. in each case, geometric aspects of structure and the problems of calculating structural properties are considered before going on to consider electronic structures and the factors controlling stabilities and a wider range of physical properties. in all of these materials, there is considerable interest in the, bonding in the oxyanion unit and how this is affected by, and controls, the interaction with counterions or the polymeric units. the building up of the minerals by such interactions exerts the dominant control over their crystal chemistries and properties and thus forms a central theme of this chapter. the silicate minerals are, of course, characterized by the presence of the tetrahedral siO4 cluster unit and the crystal chemistry and classification of silicates dominated by the structures built up by the linking together (polymerization) of these units. in the “simplest” of the silicates, the island silicates such as the olivine minerals (dominated by the forsterite (Mg2 SiO4)-fayalite (Fe2SiO4) solid solution series), the sio4 units are isolated by counterions such as Mg2+, Fe2+, Ca2+.

Theoretical Methods

In this chapter, the most important quantum-mechanical methods that can be applied to geological materials are described briefly. The approach used follows that of modern quantum-chemistry textbooks rather than being a historical account of the development of quantum theory and the derivation of the Schrödinger equation from the classical wave equation. The latter approach may serve as a better introduction to the field for those readers with a more limited theoretical background and has recently been well presented in a chapter by McMillan and Hess (1988), which such readers are advised to study initially. Computational aspects of quantum chemistry are also well treated by Hinchliffe (1988). In the section that follows this introduction, the fundamentals of the quantum mechanics of molecules are presented first; that is, the “localized” side of Fig. 1.1 is examined, basing the discussion on that of Levine (1983), a standard quantum-chemistry text. Details of the calculation of molecular wave functions using the standard Hartree-Fock methods are then discussed, drawing upon Schaefer (1972), Szabo and Ostlund (1989), and Hehre et al. (1986), particularly in the discussion of the agreement between calculated versus experimental properties as a function of the size of the expansion basis set. Improvements on the Hartree-Fock wave function using configuration-interaction (CI) or many-body perturbation theory (MBPT), evaluation of properties from Hartree-Fock wave functions, and approximate Hartree-Fock methods are then discussed. The focus then shifts to the “delocalized” side of Fig. 1.1, first discussing Hartree-Fock band-structure studies, that is, calculations in which the full translational symmetry of a solid is exploited rather than the point-group symmetry of a molecule. A good general reference for such studies is Ashcroft and Mermin (1976). Density-functional theory is then discussed, based on a review by von Barth (1986), and including both the multiple-scattering self-consistent-field Xα method (MS-SCF-Xα) and more accurate basis-function-density-functional approaches. We then describe the success of these methods in calculations on molecules and molecular clusters. Advances in density-functional band theory are then considered, with a presentation based on Srivastava and Weaire (1987). A discussion of the purely theoretical modified electron-gas ionic models is followed by discussion of empirical simulation, and we conclude by mentioning a recent approach incorporating density-functional theory and molecular dynamics (Car and Parrinello, 1985).

Introduction

The early descriptions of chemical bonding in minerals and geological materials utilized purely ionic models. Crystals were regarded as being made up of charged atoms or ions that could be represented by spheres of a particular radius. Based on interatomic distances obtained from the early work on crystal structures, ionic radii were calculated for the alkali halides (Wasastjerna, 1923) and then for many elements of geochemical interest by Goldschmidt (1926). Modifications to these radius values by Pauling (1927), and others took account of such factors as different coordination numbers and their effects on radii. The widespread adoption of ionic models by geochemists resulted both from the simplicity and ease of application of these models and from the success of rules based upon them. Pauling’s rules (1929) enabled the complex crystal structures of mineral groups such as the silicates to be understood and to a limited extent be predicted; Goldschmidt’s rules (1937) to some degree enabled the distribution of elements between mineral phases or mineral and melt to be understood and predicted. Such rules are further discussed in later chapters. Ionic approaches have also been used more recently in attempts to simulate the structures of complex solids, a topic discussed in detail in Chapter 3. Chemical bonding theory has, of course, been an important component of geochemistry and mineralogy since their inception. Any field with a base of experimental data as broad as that of mineralogy is critically dependent upon theory to give order to the data and to suggest priorities for the accumulation of new data. Just as the bond with predominantly ionic character was the first to be quantitatively understood within solidstate science, the ionic bonding model was the first used to interpret mineral properties. Indeed, modern studies described herein indicate that structural and energetic properties of some minerals may be adequately understood using this model. However, there are numerous indications that an ionic model is inadequate to explain many mineral properties. It also appears that some properties that may be rationalized within an ionic model may also be rationalized assuming other limiting bond types.

Application of Bonding Models to Sulfide Minerals

The sulfide minerals are a group of materials dominated by binary and ternary compounds of sulfur with iron, cobalt, nickel, copper, zinc, and lead. Other members of this group of naturally occurring crystalline materials incorporate a variety of cations (e.g., Mn2+, MO4 + , Ag+, Hg2+, Cr3 + , Sn4+, Pt4+) and several other anions (Se2-, Te2-, As2 - , Sb2-). The sulfides are not only the most important group of ore minerals, constituting the raw materials for most of the world’s supplies of nonferrous metals, but also are substances that exhibit a fascinating diversity in structural chemistry and in electrical, magnetic, and other physical properties (Ribbe, 1974; Vaughan and Craig, 1978). The sulfide minerals range in properties from materials that are diamagnetic insulators, forming virtually colorless crystals when pure (e.g., ZnS), to diamagnetic semiconductors (e.g., PbS), to semiconductors or metallic conductors exhibiting various forms of ordered magnetism (e.g., CuFeS2, Fe7S8, CoS2), and to metals exhibiting weak temperature-independent Pauli paramagnetism (e.g., Ni3S4, Co9S8). The diversity of sulfide properties indicates that the valence electrons in these materials can range from extensively delocalized as in metals, to localized on the atoms as in insulators. This has presented problems for those attempting to develop bonding models and has also led to certain misconceptions regarding the kinds of models that may be appropriate. Earlier attempts to develop qualitative bonding models for sulfide minerals have been reviewed by Vaughan and Craig (1978) and include applications of valence-bond theory (Pauling, 1970) and ligand-field theory (Nickel, 1968, 1970), zone theory (Freuh, 1954), and qualitative molecular- orbital/band models (Burns and Vaughan, 1970; Vaughan et al., 1971; Prewitt and Rajamani, 1974). At about the same time, band-structure calculations on some of the binary sulfides of importance in materials science were being performed by physicists, and certain of the data of mineralogical interest have been reviewed by Marfunin (1979). The mid- 1970s saw the first successful attempts to perform MO calculations on metal-sulfide mineral systems, and a substantial number of systems have since been studied (many having been reviewed by Vaughan and Tossell, 1983).

Applications To Geochemical Problems

In this, the last major chapter of the book, we turn our attention to the applications of modern electronic structure models and concepts to more general geochemical problems; namely, those described by Goldschmidt as being concerned with the “distribution of elements in the geochemical spheres and the laws governing the distribution of the elements” (see Preface). The majority of minerals and rocks originally formed by crystallization from melts, and so the first section of this chapter is devoted to considering the nature of melts (and glasses), structure and bonding in melts, and the partitioning of elements (particularly transition elements) between the melt and crystallizing solid phases. The classic work of Bowen (1928) led to the recognition of particular sequences of crystallization and crystal-melt reaction relationships in the silicate melts from which major rock types form, as enshrined in the “Bowen Reaction Series.” Attempts were also made to explain the incorporation of particular elements into particular mineral structures using simple crystal chemical arguments, notably as laid down in “Goldschmidt’s Rules” (Goldschmidt, 1937). Such concepts are reappraised in the light of modern electronic structure theories. The other major realm of formation of minerals and rocks, and the most important medium of transport and redistribution of the chemical elements at the Earth’s surface, is the aqueous solution. The molecular and electronic structures of aqueous solutions, their behavior at elevated temperatures, formation and stabilities of complexes in solution, and the mechanisms of reactions in solution are all considered in the second section of this chapter. The surfaces of minerals (or other crystalline solids) differ from the bulk material in terms of both crystal structure and electronic structure. A great variety of spectroscopic, diffraction, scanning, and other techniques are now available to study the nature of solid surfaces, and models are being developed to interpret and explain the experimental data. These approaches are discussed with reference to a few examples of oxide and sulfide minerals. Although relatively few studies have been undertaken specifically of the surfaces of minerals, many of the reaction phenomena that occur in natural systems take place at mineral surfaces, so that such surface studies represent an important area of future research.

Applications in Mineral Physics and Chemistry

In this book we have concentrated up to this point on the experimental and theoretical methods involved in determining the electronic structure of minerals and related materials, and on the applications of these methods to major groups of compounds such as the oxides, silicates, carbonates, borates, and sulfides. It is now appropriate to turn to more general applications in the study of minerals. Three major areas are addressed in this chapter. The first concerns the general field of crystal chemistry and the extent to which calculations can be used (alongside appropriate experiments) to approach such questions as the ionic versus covalent nature of a particular bond, the understanding and prediction of crystal structure of a material of a particular composition at room temperature and pressure (or other conditions, and hence key elements of the phase relations), and the rules and principles governing the crystal structures of solids. The second concerns the behavior of minerals and related materials at high pressures, of interest because of applications to understanding the physics and chemistry of the Earth’s interior. Theoretical studies of phases at high pressure are discussed with particular reference to attempts to understand the materials that are believed to comprise the core and mantle of the Earth. The third addresses examples of application in areas of direct industrial interest, that is, to mineral materials of importance in ion-exchange and absorption, and in catalysis. These three major areas represent applications of the theoretical (and experimental) methods discussed in earlier chapters to problems of importance in mineral and crystal chemistry, in mineral physics and geophysics, and in industrial mineralogy and materials science. They are illustrative of the value of these methods, but are far from being a comprehensive account. diffraction, has led to intimate links between mineralogy and crystal and structural chemistry. Because crystal structure depends upon bonding character (“electronic” structure), it should be possible accurately to predict the crystal (or “geometric” structure) adopted by a particular composition material using quantum-mechanical methods. The extent to which this is possible is discussed below, with reference to the example of the SiO2 polymorphs.

Application of Quantum-Mechanical Methods to Simple Inorganic “Molecules” of Relevance to Mineralogy, and to Oxide Minerals

As noted in the introduction to this text, much can be learned through the application of both quantum-mechanical calculations and experimental techniques to simple molecules that contain bonds of the type found in the important groups of minerals. One reason for this approach is that calculations at a higher level of quantum-mechanical rigor can be applied to such simple systems. This approach will be illustrated with reference to the SiO, SiO2, Si2O2, Si3O3, and SiF4 molecules. Attention will then be turned to the major oxide minerals MgO, Al2O3, and SiO2 and the binary transition-metal oxides of Ti, Mn, and Fe, with some brief discussion of the series of transition-metal monoxides (MnO, FeO, CoO, NiO) and complex oxides (FeCr2O4, FeTiO3, etc.), and of the problem of the calculation of Mössbauer parameters in iron oxides (and other compounds). Although silicon monoxide, SiO, is not an important component of minerals, it is an important chemical constituent in interstellar and circumstellar space and an important starting material for the gas-phase synthesis of silicates from components of the nebula (Day and Donn, 1978). The structure, energetics, and spectral properties of SiO have been calculated by a number of different methods. The Si-O bond distance calculated using ab initio Hartree-Fock-Roothaan SCF methods at the 6-31G* basis- set level is 1.487 Å (Snyder and Raghavachari, 1984), slightly smaller than the experimental value of 1.5097 Å (Field et al., 1976). A near Hartree- Fock limit basis set and limited configuration-interaction calculation has given the slightly better value of 1.496 Å (Langhoff and Arnold, 1979). This study also gave a bond dissociation energy of 8.10 eV, compared to an experimental value of 8.26 ± 0.13 eV (Hildenbrand, 1972), and a bond stretching frequency of 1248 cm- 1 , compared to an experimental value of 1242 cm-1 (Anderson and Ogden, 1969). Even more highly correlated calculations give a bond distance of 1.515 Å and a stretching frequency of 1242 cm-1 (Werner et al., 1982). The 6-31G* basis-set Hartree-Fock-Roothaan calculation also gives an almost exactly correct bond-stretching frequency after the standard correction factor describing correlation effects is applied (Hehre et al., 1986).

Experimental Methods

An understanding of chemical bonding in a system can be gained through calculations based on the theoretical approaches outlined in the previous chapter, or through experimentation. In a much more limited way, it is also possible to gain some understanding of the bonding in a system by a “phenomenological” application of (qualitative) theory given certain properties of the system (e.g., chemical composition, crystal or molecular structure, magnetic and electrical behavior, etc.). Ideally these approaches should be combined so as to gain a unified understanding of the bonding in a particular system. It is very important that the results of quantum-mechanical calculations are compared with experimental data so as to assess their validity. Conversely, the results of calculations may be used in the interpretation of the data from experiments. In this chapter, the wide range of experimental methods that can provide information on chemical bonding in geochemical systems is reviewed. Following a very brief summary of the principles of each technique, some examples are given of its application to minerals (or other systems of geochemical interest, such as melts, glasses, or aqueous solutions). The objective is to draw attention to techniques of importance and to show their relevance to bonding studies and their relationships both to quantum-mechanical calculations and to other experimental methods. No attempt is made to explain the theoretical background of these techniques fully or the practical problems involved in their application. Indeed, each of them has spawned a substantial literature, including books and review articles, some of which are cited here for the reader requiring further details. The experimental methods to be discussed have been divided into five major categories—diffraction effects, electron and x-ray spectroscopies, optical (uv-visible-near-ir) spectroscopy, vibrational spectroscopy, and nuclear spectroscopy. A number of techniques are also discussed in the sixth category—”other methods.” Nevertheless, the range of techniques discussed is very far from complete, and a fuller listing is given in Appendix B. This Appendix also serves to provide some useful references on each technique and a key to the numerous acronyms and abbreviations used throughout the literature to refer to these techniques.