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This lecture note gives an analysis of electronic structure effects for a new class of molecular solids, i. e. one-dimensional organometal­ lic systems formed by transition-met. l atoms that are embedded in a matrix of macrocyclic organic ligands. These systems as well as orga­ nic metals have focused considerable interest due to the potential formation of high-mobility charge carriers. For the present author it is difficult to participate in this restriction on a single physical property (i. e. high electronic conductivities, technical applications, etc. ). The lecture note is hopefully a small contribution to enhance the general understanding of certain electronic properties in organo­ metallic polymers. Those problems have been considered in the first place that seem to form a theoretical deficit in one specific field of solid-state chemistry. For the reader it will become evident that this contribution is a compromise always guided and limited by boundaries: i) An attempt to present problems to a ·chemical· audience which have their roots in solid-state physics. ii) The model calculations are limited by the currently available computational facilities. This ·boundary· implies that the compu­ tational data a~e subject to severe theoretical approximations. iii) Theorists have often a strong tendency to identify their numeri­ cal results and models with physical effects. Also this lecture note is not free of this almost universal trend. Nevertheless the author hopes that this text leads to some insight into a rather modern research field. M. e. B6hm I.

Inhaltsverzeichnis

Frontmatter

Introduction and Historical Review

I. Introduction and Historical Review

Abstract
Solid-state systems with pronounced one-dimensional (1D) structures and strong anisotropies of electronic interactions have focused considerable experimental and theoretical interest over the past years [I.1–I.13]. 1D materials with building principles that differ from those realized in “classical” solids have been studied in many chemical and physical laboratories. Research fields in chemistry cover the synthesis and determination of crystal structures of new classes of low-dimensional materials with collective properties that are comparable to those of “classical” solids (e.g., metals, alloys, simple semi-conductors and insulators, etc.). Physical experiments concern the quantification of electronic and lattice properties. Relevant topics in this context are e.g. electric conductivities, activation parameters for the charge transfer, drift mobilities, mean free paths of the carriers, and spectroscopic and magnetic properties. These quantities have been measured and classified as a function of structural building principles. Solid-state ensembles that are formed by discrete, well-defined molecular building blocks are suitable model-systems for a transparent analysis of the strength and influence of “ensemble properties” (i.e. modifications in the electronic structure as a result of the formation of a low-dimensional order).
M. C. Böhm

Backmatter

Experimental Results and Global Band Structure Properties

II.1. One-Dimensional Building Principles in Organometallic Solids and General Band (Electronic) Structure Properties

Abstract
Low-dimensional (1D) solids which are formed by organometallic building blocks can be divided into four structure types. The relevant geometric distinctive marks are discussed in the present section. Additionally we give a short review of global electronic structure properties determined for representative model solids. The building principles realized in 1D organometallic materials are discriminated on the basis of the metal and ligand orientation relative to the direction of the stacking axis as well as on the electronic nature of the coupling between adjacent molecular building units. A schematic display of the suggested structure types is shown in fig. II. 1.
M. C. Böhm

II.2. Electric Conductivities of Partially Oxidized Organometallic 1D Systems

Abstract
It had been mentioned that a partial charge transfer is often a necessary condition in organometallic solids to observe high electric conductivities. Detailed experimental investigations of the temperature-dependence of single crystal conductivities are available for metallomacrocycles that crystallize in columnar structures of type I (see section II.1). The subsequent analysis is thus restricted to the conductivities (σ) of these 1D materials. The largest (room temperature) conductivities in this class of compounds are of the order of 2·103 (Ωcm)−1. The maximum conductivities in organometallic solids of type III or IV are ca. 10−4 to 10−3 (Ωcm)−1. The temperature dependence of σ in the latter 1D systems corresponds to a semiconducting behavior. The outline of this section is as follows; the temperature-dependence of the single-crystal conductivity is discussed for representative model systems. Furthermore we give a short comparison of charge carrier parameters (i.e. mean free paths) of organometallic systems with quantities derived for organic metals and “inorganic” 1D conductors (i.e. Krogmann’s salt). Only simple phenomenological relations and qualitative interpretations are employed to classify experimental findings. At the end of this section microscopic approaches to the conductivity problem are shortly mentioned; these schemes go beyond widely used semiphenomenological descriptions.
M. C. Böhm

II.3. Electron Paramagnetic Resonance (EPR) Data of 1D Organometallic Solids of Class I

Abstract
The identification of the nature of the charge carriers in organometallic solids with macrocyclic ligands was an unresolved problem until the late seventies where it was conventionally (frequently) accepted that partial oxidation processes are metal-centered. But this assignment was misguided and lead to the incorrect assumption that metal-metal contacts in columnar structures should be a prerequisite for highly conducting modifications of suitable 1D materials. Subsequent experimental investigations of organometallic solids, that crystallize in the columnar structure of class I, have shown that most of the systems are organic metals with channels for the charge transfer that are provided by the (cyclic) organic ligands. This experimental result was corroborated by (semiempirical) tight-binding calculations which are discussed in section IV. The identification of the transfer channels was possible by several experimental techniques. In the first place one has to mention electron paramagnetic resonance (EPR) spectra where the measured g values have been used to discriminate between organic π radicals and partially oxidized transition-metal centers. Synthetic strategies (i.e. variations in the composition of the stoichiometric units) allowed for empirical assignments. Substitutions of the central nd site (e.g. Ni→Pd→Pt) in a large number of metallomacrocycles were not accompanied by larger changes in the conductivities; i.e, the transfer channels are independent of the nd center.
M. C. Böhm

Backmatter

Theoretical Methods; Crystal Orbital (CO) Approaches

III.1. A (Semiempirical) Crystal Orbital Formalism

Abstract
In the Introduction it has been mentioned that the large unit cell dimensions of organometallic polymers prevent the application of traditional solid state techniques. Published computational results in this field are thus sparse. In the following we give a description of a semiempirical crystal orbital (CO) approach which has been used by the author in a number of electronic structure investigations of organometallic 1D stacks. The basic framework of this CO scheme is of an INDO-type (intermediate neglegt of differential overlap) approximation supplemented by the simpler CNDO (complete neglect of differential overlap) technique. The semiempirical LCAO variants have been designed for atoms up to bromine under the inclusion of the first (i.e. 3d) transition-metal series [III.1,III.2].
M. C. Böhm

III.2. Nonlocal Hartree-Fock Exchange in Narrow-Band Materials

Abstract
One computational problem of CO calculations in the mean-field approximation is connected with the convergence properties of the nonlocal HF exchange which gives rise to a cos(kj) dependence in matrix elements of the Fock operator. The asymptotic behavior of exchange interactions and relevant physical consequences of real-space truncation criteria have been analyzed in simple model solids [III.40–III.45]. Ukrainski investigated exchange phenomena in a one-orbital one-electron system and found a (−1)jj−2 decay of the exchange summation. Furthermore he pointed out that divergent energy gradients, see eq. (III.59), occur at the Fermi surface leading to vanishing density of states (DOS) distributions, N(E).
M. C. Böhm

III.3. Electronic Correlations and “Relaxations” in One-Dimensional (Organometallic) Polymers

Abstract
The strength and influence of corrections beyond the mean-field description (quasi-particle (QP) picture; i.e. electronic correlations and “relaxations”) on the band structures of low-dimensional materials has been the subject of detailed theoretical investigations [III.72–III.86]. The SCF methods that are used as prerequisite for the determination of QP corrections span the range from traditional APW or OPW schemes to CO approaches on the basis of ab initio and semiempirical Hamiltonians. Remarkable shifts of ε(k) curves due to QP interactions and pronounced graduations of these corrections as a function of the localization properties of the one-electron (band) states have been observed in solids that contain transition-metal atoms [III.85, III.86]. Relations between band structure properties, electronic intracell (intrasite) repulsions and the strength of QP corrections have been discussed for simple transition-metal oxides (e.g., Mott insulators, MnO, FeO, CoO, NiO) [III.87–III.92] and transition-metal polymers with organic π ligands [III.85,III.86,III.93,III.94]. The degree of sophistication of any many-body approach is of course determined by the complexity of the studied low-dimensional material (i.e. structural boundaries).
M. C. Böhm

III.4. A Simple Electrostatic Model for Interchain Interactions in Quasi 1D Solids

Abstract
Most of the conducting organometallic solids crystallize in the form of segregated donor and acceptor stacks. The observed metallic conductivities are the result of a partial charge transfer (i.e. incompletely filled bands). For a (semiconducting) exception and the relevant theoretical interpretation see [III.110, III. 111]. Next we present a simple electrostatic model that allows for an approximate computational treatment of segregated donor-acceptor (DA) solids (generally of quasi 1D materials) [III.34, III.112, III.113]. In DA systems with roughly comparable intra- and interchain interactions (i.e. coherent 3D solids) the k-vector must be described by three cartesian components (kx,ky,kz). The k-dependent interchain coupling opens a covalency gap ΔEC. The magnitude of ΔEC is determined by the strength of this interaction. If H is a general hopping element for the interchain interaction we have ΔEC = 2H.
M. C. Böhm

Backmatter

Model Calculations in the Framework of a (Semiempirical) Crystal Orbital Approach

IV.1. Neighborstrand Interactions in One-Dimensional Tight-Binding Models. The (Tetrathiosquarato)nickel(II) System

Abstract
In this chapter we analyze band structure properties of quasi 1D systems under the influence of interchain interactions. The necessary coupling elements are approximated by the electrostatic self-consistent-field (SCEF) formalism derived in section III.4. Two aspects will be discussed in some detail: i) variations of the dispersion curves, charge distributions, etc. as a function of structural building principles realized in the solid and ii) possible formations of symmetry broken solutions of the charge density wave (CDW) or bond-order alternation wave (BOAW) type as response to magnifications of the “field strength” experienced by the 1D reference chain. Experimental investigations have shown that interactions which are higher than 1D (i.e. interchain coupling) or CDW/ BOAW solutions in the donor and acceptor units of a segregated DA stack are often desirable to observe high electric conductivities [IV.1–IV.3]. Recent numerical studies on the significance of higher dimensionalities in donor-acceptor systems are either based on one-electron calculations of the Wolfsberg-Helmholtz (WH) type [IV.4, IV.5] or on physically transparent phenomenological model Hamiltonians which can be treated analytically [IV.6]. It lies in the nature of simple one-electron Hamiltonians that it is not possible to detect any symmetry broken solutions.
M. C. Böhm

IV.2. Band-Structure Properties of One-Dimensional Polydecker Sandwich Systems

Abstract
The one-dimensional polydecker compounds collected in fig. IV.7 are suitable model systems for a transparent investigation of the dependence of band structure porperties on the type of the central 3d atom and the stoichiometry of the organic π ligand [IV.23]. The synthesis, and the physical and chemical characterization of the first infinite 1D model in this class of low-dimensional solids has been reported recently [IV.24]. The polymer is formed by a 13 valence electron fragment of the general stoichiometry Ni(R5C3B2). The band structure and other electronic properties of this 1D system are reviewed in [IV.25].
M. C. Böhm

IV.3. Partially Oxidized Transition-Metal Polymers; Stabilization of Mixed Valence States

Abstract
The theoretical description of spatial hole-state properties in low-dimensional materials is a central problem in electronic structure theories of the solid state [IV.42–IV.45]. Two extreme solutions are in principle accesible in numerical methods that are formulated in any one-determinantal approximation. The removal of an electron can be described in terms of “spatially uncorrelated” Bloch orbitals under the assumption of the validity of Koopman’s theorem [IV.46]. Some time ago it had been suggested by Seitz that the description of hole-states in terms of delocalized Bloch orbitals is a physically reliable approximation in crystalline solids [IV.47]. In the past years the spatial localization properties of holes have been reinvestigated by Kunz and coworkers in simple narrow-band insulators of the Mott-Hubbard type. Energetic consequences of electron removal from localized orbitals of the Heitler-London type have been studied by elaborate computational methods [IV.42,IV.43,IV.48].
M. C. Böhm

IV.4. The Band Structure of One-Dimensional (Tetrazaporphyrinato) - Cobalt(II)

Abstract
In the last paragraph, IV.3, we have used an ensemble averaged tight-binding variant for the analysis of spatial symmetries encountered in crystal orbital wave functions of partially oxidized 1D systems with narrow dispersions. The oxidized states of the considered 1D chains were always characterized by occupation patterns with an uneven electron-number per supposed unit cell. In this section band structure data of (tetrazaporphyrinato)Co(II), Co(tp), are presented. Also the simplest stoichiometric unit of Co(tp) contains an uneven number of electrons. The repeat-unit considered in this analysis is a single Co(tp) fragment. The relative stabilities of insulating (Mott) and metallic configurations are investigated as a function of the widths of the half-filled dispersion.
M. C. Böhm

IV.5. The Band Structure of the One-Dimensional (Bisglyoximato)Ni(II) System

Abstract
(Bisglyoximato)Ni(II), Ni(gly)2 see fig. IV.16, is employed for an analysis of torsional energies in 1D organometallic systems as well as a quantification of intracell and intercell interactions as a function of certain details of the stacking geometry. Ni(gly)2 has been the subject of tight-binding studies on the basis of the semiempirical INDO CO Hamiltonian that has been used as principal computational framework for the present lecture note [IV.74–1V.77]; a simple one-electron approach based on the popular Wolfsberg-Helmholtz Hamiltonian has been published at the same time [IV.78]. Ni(gly)2 and a large number of alkyl or phenyl derivatives belong to a class of organometallic 1D systems that have been studied extensively in the late seventies [IV.79,IV.80]. Experimental studies have shown that partial oxidation with Br or I leads to conductivities and transport properties that are characteristic for semiconducting solids. The relevant experimental quantities are neither a function of the transition-metal center (Ni or Pd) nor a function of the halide sites (Br or I). The predominant halide component in Ni(gly)I is I 5 ; the fractional oxidation state in the 1D column is thus +0.2.
M. C. Böhm

IV.6. Band Structures of 1D (Porphyrinato)Ni(II) Systems

Abstract
In the model calculations reviewed in the last section we have discussed possible interrelations between the stacking geometry of organometallic 1D chains (i.e. intercell separation), on one side, and electronic structure effects (i.e. torsional barriers, magnitude of intra- and intercell energies, charge distribution, etc.), on the other. One-dimensional (porphyrinato)NI(II) systems are suitable materials to quantify correlations between structural parameters and physical or chemical solid-state properties. In fig. IV.21 we have displayed four (prophyrinato)Ni(II), Ni(p), systems that have been the subject of a number of experimental [IV.35,IV.83–1V.85] and theoretical [IV.36,IV.86–IV.89] studies. These 1D solids show significant changes in the nature of injected carriers, paramagnetic susceptibi1ities χP and the temperature dependence of the electric conductivity σ as response to structural changes in the macrocyclic π ligand.
M. C. Böhm

IV.7. The 1D Band Structure of Tetrathiotetracene

Abstract
The analysis in the foregoing sections has shown that most of the organometallic systems belong to the class of the organic metals upon partial electron removal; the transfer paths are ligand-centered. In this section we discuss tetrathiotetracene, TTT, as its solid-state properties are comparable to those of low-dimensional organometallic 1D systems with ligand-centered charge-transfer channels. TTT is schematized in fig. IV.24 where also the stacking pattern is displayed. The angle between the mean molecular plane and the 1D direction differs from 90° (i.e. 41.9°). TTT has been studied in several experimental contributions [IV.102–1V.105]; for a semiempirical tight-binding analysis see [IV.106].
M. C. Böhm

IV.8. The Band Structure of Polyferrocenylene

Abstract
The 1D polyferrocenylene system is employed for an analysis of “hybridization” effects in the HF bands of complex organometal1ic solids. An important physical consequence of this type of hybridization is a strong k-dependence in the character of the CO microstates (i.e. correlation between localized metal-centered and delocalized ligand basis functions) in a given energy band. This is a solid-state phenomenon which is (frequently) not found in the molecular building blocks. Hybridization is enhanced in the case of extended units with closely spaced one-electron energies in the ligand unit and at the transition—metal center. Trans polyferrocenylene, see fig. IV.26, is one member in a larger class of conducting or semiconducting materials that are formed by ferrocene-like units [IV.108–IV.110].
M. C. Böhm

Backmatter

Outlook

V. Outlook

Abstract
It has been the scope of this lecture note to analyze typical electronic structure effects in a new class of one-dimensional molecular conductors and semiconductors; i.e. organometallic solids formed by transition-metal atoms which are embedded in a matrix of (macrocyclic) organic ligands. The chemical flexibility realized in the formal molecular repeat-units allows, at least potentially, for the design of 1D materials with chemical and physical properties which cover a broad spectrum. One motivation for the recent experimental effort is the potential formation of high-mobility charge carriers upon doping (i.e. partial oxidation or reduction). In the author’s opinion this topic (i.e. preparation of highly conducting materials; potential technical applications, etc.) is perhaps overemphasized. Such a “false assessment” can be only explained in terms of efforts at financial support, research grants, etc. The present lecture note had been planned as a general contribution to one rather modern research direction in solid—state chemistry. It should be one of the principal scopes of this discipline to understand those chemical and physical phenomena in low—dimensional materials that are not the result of intramolecular interactions but are determined by the cooperation between molecular building-blocks.
M. C. Böhm

Backmatter

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