Electronic energy transfer processes and charge carrier transport in pi-conjugated polymers

Conjugated polymers have attracted tremendous academical and industrial research interest over the past decades due to the appealing advantages that organic / polymeric materials offer for electronic applications and devices such as organic light emitting diodes (OLED), organic field effect transistors (OFET), organic solar cells (OSC), photodiodes and plastic lasers. The optimization of organic materials for applications in optoelectronic devices requires detailed knowledge of their photophysical properties, for instance energy levels of excited singlet and triplet states, excited state decay mechanisms and charge carrier mobilities. In the present work a variety of different conjugated (co)polymers, mainly polyspirobifluorene- and polyfluorene-type materials, was investigated using time-resolved photoluminescence spectroscopy in the picosecond to second time domain to study their elementary photophysical properties and to get a deeper insight into structure-property relationships. The experiments cover fluorescence spectroscopy using Streak Camera techniques as well as time-delayed gated detection techniques for the investigation of delayed fluorescence and phosphorescence. All measurements were performed on the solid state, i.e. thin polymer films and on diluted solutions. Starting from the elementary photophysical properties of conjugated polymers the experiments were extended to studies of singlet and triplet energy transfer processes in polymer blends, polymer-triplet emitter blends and copolymers. The phenomenon of photonenergy upconversion was investigated in blue light-emitting polymer matrices doped with metallated porphyrin derivatives supposing an bimolecular annihilation upconversion mechanism which could be experimentally verified on a series of copolymers. This mechanism allows for more efficient photonenergy upconversion than previously reported for polyfluorene derivatives. In addition to the above described spectroscopical experiments, amplified spontaneous emission (ASE) in thin film polymer waveguides was studied employing a fully-arylated poly(indenofluorene) as the gain medium. It was found that the material exhibits a very low threshold value for amplification of blue light combined with an excellent oxidative stability, which makes it interesting as active material for organic solid state lasers. Apart from spectroscopical experiments, transient photocurrent measurements on conjugated polymers were performed as well to elucidate the charge carrier mobility in the solid state, which is an important material parameter for device applications. A modified time-of-flight (TOF) technique using a charge carrier generation layer allowed to study hole transport in a series of spirobifluorene copolymers to unravel the structure-mobility relationship by comparison with the homopolymer. Not only the charge carrier mobility could be determined for the series of polymers but also field- and temperature-dependent measurements analyzed in the framework of the Gaussian disorder model showed that results coincide very well with the predictions of the model. Thus, the validity of the disorder concept for charge carrier transport in amorphous glassy materials could be verified for the investigated series of copolymers.

Conjugated semiconducting organic materials for electronic applications

Since conjugated polymers, i.e. polymers with spatially extended pi-bonding system have offered unique physical properties, unobtainable for conventional polymers, significant research efforts directed to better understanding of their chemistry, physics and engineering have been undertaken in the past two and half decades. In this thesis we discuss the synthesis, characterisation and investigation of conjugated semiconducting organic materials for electronic applications. Owing to the versatile properties of metal-organic hybrid materials, there is significant promise that these materials can find use in optical or electronic devices in the future. In addressing this issue, the synthesis of bisthiazol-2-yl-amine (BTA) based polymers is attempted and their metallation is investigated. The focus of this work has been to examine whether the introduction of coordinating metal ions onto the polymer backbone can enhance the conductivity of the material. These studies can provide a basis for understanding the photophysical properties of metal-organic polymers based on BTA. In their neutral (undoped) form conjugated polymers are semiconductors and can be used as active components of plastics electronics such as polymer light-emitting diodes, polymer lasers, photovoltaic cells, field-effect transistors, etc. Toward this goal, it is an objective of the study to synthesize and characterize new classes of luminescent polymeric materials based on anthracene and phenanthrene moieties. A series of materials based on polyphenylenes and poly(phenyleneethynylene)s with 9,10-anthrylene subunits are not only presented but the synthesis and characterization of step-ladder and ladder poly(p-phenylene-alt-anthrylene)s containing 9,10-anthrylene building groups within the main chain are also explored. In a separate work, a series of soluble poly-2,7- and 3,6-phenanthrylenes are synthesized. This can enable us to do a systematic investigation into the optical and electronic properties of PPP-like versus PPV-like. Besides, the self-organization of 3,6-linked macrocyclic triphenanthrylene has been investigated by 2D wide-angle X-ray scattering experiments performed on extruded filaments in solution and in the bulk. Additionally, from the concept that donor-acceptor materials can induce efficient electron transfer, the covalent incorporation of perylene tetracarboxydiimide (PDI) into one block of a poly(2,7-carbazole) (PCz)-based diblock copolymer and 2,5-pyrrole based on push-pull type material are achieved respectively.

Nitrogen-bridged polyphenylene-based materials for electronic applications

Conjugated polymers are macromolecules that possess alternating single and double bonds along the main chain. These polymers combine the optoelectronic properties of semiconductors with the mechanical properties and processing advantages of plastics. In this thesis we discuss the synthesis, characterization and application of polyphenylene-based materials in various electronic devices. Poly(2,7-carbazole)s have the potential to be useful as blue emitters, but also as donor materials in solar cells due to their better hole-accepting properties. However, it is associated with two major drawbacks (1) the emission maximum occurs at 421 nm where the human eye is not very sensitive and (2) the 3- and 6- positions of carbazole are susceptible to chemical or electrochemical degradation. To overcome these problems, the ladder-type nitrogen-bridged polymers are synthesized. The resulting series of polymers, nitrogen-bridged poly(ladder-type tetraphenylene), nitrogen-bridged poly(ladder-type pentaphenylene), nitrogen-bridged poly(ladder-type hexaphenylene) and its derivatives are discussed in the light of photophysical and electrochemical properties and tested in PLEDs, solar cell, and OFETs. A promising trend which has emerged in recent years is the use of well defined oligomers as model compounds for their corresponding polymers. However, the uses of these molecules are many times limited by their solubility and one has to use vapor deposition techniques which require high vacuum and temperature and cannot be used for large area applications. One solution to this problem is the synthesis of small molecules having enough alkyl chain on the backbone so that they can be solution or melt processed and has the ability to form thin films like polymers as well as retain the high ordered structure characteristics of small molecules. Therefore, in the present work soluble ladderized oligomers based on thiophene and carbazole with different end group were made and tested in OFET devices. Carbazole is an attractive raw material for the synthesis of dyes since it is cheap and readily available. Carbazoledioxazine, commercially known as violet 23 is a representative compound of dioxazine pigments. As part of our efforts into developing cheap alternatives to violet 23, the synthesis and characterization of a new series of dyes by Buchwald-type coupling of 3-aminocarbazole with various isomers of chloroanthraquinone are presented.

Photoinduced electronic transitions and leakage correlation to defects/dislocations in GaN heterostructures

III-nitride materials are very promising for high speed electronics/optical applications but still suffer in performance due to problems during high quality epitaxial growth, evolution of dislocation and defects, less understanding of fundamental physics of materials/processing of devices etc. This thesis mainly focus on GaN based heterostructures to understand the metal-semiconductor interface properties, 2DE(H)G influence on electrical and optical properties, and deep level states in GaN and InAlN, InGaN materials. The detailed electrical characterizations have been employed on Schottky diodes at GaN and InAl(Ga)N/GaN heterostructures in order to understand the metal-semiconductor interface related properties in these materials. I have observed the occurrence of Schottky barrier inhomogenity, role of dislocations in terms of leakage and creating electrically active defect states within energy gap of materials. Deep level transient spectroscopy method is employed on GaN, InAlN and InGaN materials and several defect levels have been observed related to majority and minority carriers. In fact, some defects have been found common in characteristics in ternary layers and GaN layer which indicates that those defect levels are from similar origin, most probably due to Ga/N vacancy in GaN/heterostructures. The role of structural defects, roughness has been extensively understood in terms of enhancing the reverse leakage current, suppressing the mobility in InAlN/AlN/GaN based high electron mobility transistor (HEMT) structures which are identified as key issues for GaN technology. Optical spectroscopy methods have been employed to understand materials quality, sub band and defect related transitions and compared with electrical characterizations. The observation of 2DEG sub band related absorption/emission in optical spectra have been identified and proposed for first time in nitride based polar heterostructures, which is well supported with simulation results. In addition, metal-semiconductor-metal (MSM)-InAl(Ga)N/GaN based photodetector structures have been fabricated and proposed for achieving high efficient optoelectronics devices in future.

Ion implantation of organic thin films and electronic devices

Organic semiconductors have great promise in the field of electronics due to their low cost in term of fabrication on large areas and their versatility to new devices, for these reasons they are becoming a great chance in the actual technologic scenery. Some of the most important open issues related to these materials are the effects of surfaces and interfaces between semiconductor and metals, the changes caused by different deposition methods and temperature, the difficulty related to the charge transport modeling and finally a fast aging with time, bias, air and light, that can change the properties very easily. In order to find out some important features of organic semiconductors I fabricated Organic Field Effect Transistors (OFETs), using them as characterization tools. The focus of my research is to investigate the effects of ion implantation on organic semiconductors and on OFETs. Ion implantation is a technique widely used on inorganic semiconductors to modify their electrical properties through the controlled introduction of foreign atomic species in the semiconductor matrix. I pointed my attention on three major novel and interesting effects, that I observed for the first time following ion implantation of OFETs: 1) modification of the electrical conductivity; 2) introduction of stable charged species, electrically active with organic thin films; 3) stabilization of transport parameters (mobility and threshold voltage). I examined 3 different semiconductors: Pentacene, a small molecule constituted by 5 aromatic rings, Pentacene-TIPS, a more complex by-product of the first one, and finally an organic material called Pedot PSS, that belongs to the branch of the conductive polymers. My research started with the analysis of ion implantation of Pentacene films and Pentacene OFETs. Then, I studied totally inkjet printed OFETs made of Pentacene-TIPS or PEDOT-PSS, and the research will continue with the ion implantation on these promising organic devices.

Electronic transport in the heavy fermion superconductors UPd 2 Al 3 and UNi 2 Al 3

This work addresses the electronical properties of the superconductors UPd2Al3 and UNi2Al3 on the basis of thin film experiments. These isotructural compounds are ideal candiates to study the interplay of magnetism and superconductivity due to the differences of their magnetically ordered states, as well as the experimental evidence for a magnetic pairing mechanism in UPd2Al3. Epitaxial thin film samples of UPd2Al3 and UNi2Al3 were prepared using UHV Molecular Beam Epitaxy (MBE). For UPd2Al3, the change of the growth direction from the intrinsic (001) to epitaxial (100) was predicted and sucessfully demonstrated using LaAlO3 substrates cut in (110) direction. With optimized deposition process parameters for UPd2Al3 (100) on LaAlO3 (110) superconducting samples with critical temperatures up to Tc = 1.75K were obtained. UPd2Al3-AlOx-Ag mesa junctions with superconducting base electrode were prepared and shown to be in the tunneling regime. However, no signatures of a superconducting density of states were observed in the tunneling spectra. The resistive superconducting transition was probed for a possible dependence on the current direction. In contrast to UNi2Al3, the existence of such feature was excluded in UPd2Al3 (100) thin films. The second focus of this work is the dependence of the resisitive transition in UNi2Al3 (100) thin films on the current direction. The experimental fact that the resisitive transition occurs at slightly higher temperatures for I║a than for I║c can be explained within a model of two weakly coupled superconducting bands. Evidence is presented for the key assumption of the two-band model, namely that transport in and out of the ab-plane is generated on different, weakly coupled parts of the Fermi surface. Main indications are the angle dependence of the superconducting transition and the dependence of the upper critical field Bc2 on current and field orientation. Additionally, several possible alternative explanations for the directional splitting of the transition are excluded in this work. An origin due to scattering on crystal defects or impurities is ruled out, likewise a relation to ohmic heating or vortex dynamics. The shift of the transition temperature as function of the current density was found to behave as predicted by the Ginzburg-Landau theory for critical current depairing, which plays a significant role in the two-band model. In conclusion, the directional splitting of the resisitive transition has to be regarded an intrinsic and unique property of UNi2Al3 up to now. Therefore, UNi2Al3 is proposed as a role model for weakly coupled multiband superconductivity. Magnetoresistance in the normalconducting state was measured for UPd2Al3 and UNi2Al3. For UNi2Al3, a negative contribution was observed close to the antiferromagnetic ordering temperature TN only for I║a, which can be associated to reduced spin-disorder scattering. In agreement with previous results it is concluded that the magnetic moments have to be attributed to the same part of the Fermi surface which generates transport in the ab-plane.

Thiophene-containing organic semiconducting heteroacenes for electronic applications

Diese Studie verfolgt das Konzept der "Oligomer-Ansatz", die von Müllen angesprochen wurde et.al. vor etwa 10 Jahren. Der Schwerpunkt dieser Arbeit war die Synthese, Charakterisierung und Anwendung von halbleitenden konjugierten heteroacenes für organische Elektronik.rnZur weiteren Entwicklung der Familie von schwefelhaltigen Pentacene, zwei Moleküle (Benzo [1,2 - b :4,5-b '] bis [b] benzodithiophene und dithieno-[2,3-d: 2', 3'-d ']-benzo-[1,2-b :4,5-b'] dithiophene)rnfacilely wurden synthetisiert und charakterisiert durch eine Kombination verschiedener Methoden. Die beiden neue Moleküle weisen hervorragende ökologische Stabilität und angewendet OFETs Geräte als p-Kanal-Material. Die Vorversuche gaben Ladungsträgerbeweglichkeiten von 0,1 cm2 V-1 s-1 undrn1,6 cm2 V-1 s-1 bzw. aus den beiden Molekülen.rnAusgelöst durch die Frage "je länger desto besser?", Eine Reihe von neuen heteroheptacenes wurden synthetisiert und intensiv im Hinblick auf ihre feste Struktur, Selbst-assenbly auf der studierte Oberfläche, opto-elektro-Eigenschaften und Eigenschaften des Orbits Grenze. Einer derrnheteroheptacene Moleküle wurden als die aktiven Kanäle in OFET Geräten angewendet. Jedoch in Trotz der mehr verlängert Konjugationslänge die Geräte auf der Basis zeigten heptacenes viel schlimmer Ladungsträgerbeweglichkeiten als die heteropentacenes. Viele Faktoren können Festlegung der endgültigen Leistung der Produkte und der chemischen Struktur ist nur einer von ihnen.rnIn dieser Hinsicht scheint es, dass es auch sinnvoll, den Einfluss der Heteroatome Studie und Alkylsubstitution auf der soliden und elektronischen Strukturen. Daher mehr heteroheptacenes wurden synthetisiert. Abwechslungsreiches in der Anzahl und Art der heteroatomare Brücke,rndiese Oligoazene ausgestellt dramatisch anders feste Struktur und opto-elektronischernEigenschaften. Darüber hinaus wurde eine kombinierte DFT Berechnung der Molekülorbitale dieser heptacenes darauf hingewiesen, dass die Einführung von Stickstoff Brücken wird die π-Orbitale zu destabilisieren, während stabilisieren den Schwefel Brücken sowohl HOMO und LUMO Energien. Dies ist wichtig, wenn man will hoch π verlängert Oligoazene synthetisieren und dabei eine angemessene Stabilität.

Describing and explaining the foreign expansion of network managing electronic business companies (NM-EBCs)

This study deals with the internationalization behavior of a new and specific type of e-business company, namely the network managing e-business company (NM-EBC). The business model of such e-business companies is based on providing a platform and applications for users to connect and interact, on gathering and channeling the inputs provided by the users, and on organizing and managing the cross-relationships of the various participants. Examples are online communities, matching platforms, and portals. Since NM-EBCs internationalize by replicating their business model in a foreign market and by building up and managing a network of users, who provide input themselves and interact with each other, they have to convince users in foreign markets to join the network and hence to adopt their platform. We draw upon Rogers’ Diffusion of Innovations Theory and Network Theory to explain the internationalization behavior of NM-EBCs. These two theories originate from neighboring disciplines and have not yet been used to explain the internationalization of firms. We combine both theories and formulate hypotheses about which strategies NM-EBCs may choose to expand abroad. To test the applicability of our theory and to gain rich data about the internationalization behavior of these firms, we carried out multiple case studies with internationally active Germany-based NM-EBCs.

Electronic structure and physical properties of Heusler compounds for thermoelectric and spintronic applications

This thesis focuses on synthesis as well as investigations of the electronic structure and properties of Heusler compounds for spintronic and thermoelectric applications.rnThe first part reports on the electronic and crystal structure as well as the mechanical, magnetic, and transport properties of the polycrystalline Heusler compound Co2MnGe. The crystalline structure was examined in detail by extended X-ray absorption fine structure spectroscopy and anomalous X-ray diffraction. The low-temperature magnetic moment agrees well with the Slater-Pauling rule and indicates a half-metallic ferromagnetic state of the compound, as is predicted by ab-initio calculations. Transport measurements and hard X-ray photoelectron spectroscopy (HAXPES) were performed to explain the electronic structure of the compound.rnA major part of the thesis deals with a systematical investigation of Heusler compounds for thermoelectric applications. Few studies have been reported on thermoelectric properties of p-type Heusler compounds. Therefore, this thesis focuses on the search for new p-type Heusler compounds with high thermoelectric efficiency. The substitutional series NiTi1−xMxSn and CoTi1−xMxSb (where M = Sc, V and 0 ≤ x ≤ 0.2) were synthesized and investigated theoretically and experimentally with respect to electronic structure and transport properties. The results show the possibility to create n-type and p-type thermoelectrics within one Heusler compound. The pure compounds showed n-type behavior, while under Sc substitution the system switched to p-type behavior. A maximum Seebeck coefficient of +230 μV/K (at 350 K) was obtained for NiTi0.26Sc0.04Zr0.35Hf0.35Sn, which is one of the highest values for p-type thermoelectric compounds based on Heusler alloys up to now. HAXPES valence band measurement show massive in gap states for the parent compounds NiTiSn, CoTiSb and NiTi0.3Zr0.35Hf0.35Sn. This proves that the electronic states close to the Fermi energy play a key role for the behavior of the transport properties. Furthermore, the electronic structure of the gapless Heusler compounds PtYSb, PtLaBi and PtLuSb were investigated by bulk sensitive HAXPES. The linear behavior of the spectra close to εF proves the bulk origin of Dirac-cone type density of states. Furthermore, a systematic study on the optical and transport properties of PtYSb is presented. The compound exhibits promising thermoelectric properties with a high figure of merit (ZT = 0.2) and a Hall mobility μh of 300 cm2/Vs at 350 K.rnThe last part of this thesis describes the linear dichroism in angular-resolved photoemission from the valence band of NiTi0.9Sc0.1Sn and NiMnSb. High resolution photoelectron spectroscopy was performed with an excitation energy of hν = 7.938 keV. The linear polarization of the photons was changed using an in-vacuum diamond phase retarder. Noticeable linear dichroism is found in the valence bands and this allows for a symmetry analysis of the contributing states. The differences in the spectra are found to be caused by symmetry dependent angular asymmetry parameters, and these occur even in polycrystalline samples without preferential crystallographic orientation.rnIn summary, Heusler compounds with 1:1:1 and 2:1:1 stoichiometry were synthesized and examined by chemical and physical methods. Overall, this thesis shows that the combination of first-principle calculations, transport measurements and high resolution high energy photoelectron spectroscopy analysis is a very powerful tool for the design and development of new materials for a wide range of applications from spintronic applications to thermoelectric applications.rn

Contribution of Non-Covalent Interactions and Electronic Effects on the Conformational Landscape and Tautomeric Equilibria of Molecules and Molecular Complexes: Structural and Dynamical Data from Rotational Spectroscopy

This thesis concerns the study of complex conformational surfaces and tautomeric equilibria of molecules and molecular complexes by quantum chemical methods and rotational spectroscopy techniques. In particular, the focus of this research is on the effects of substitution and noncovalent interactions in determining the energies and geometries of different conformers, tautomers or molecular complexes. The Free-Jet Absorption Millimeter Wave spectroscopy and the Pulsed-Jet Fourier Transform Microwave spectroscopy have been applied to perform these studies and the obtained results showcase the suitability of these techniques for the study of conformational surfaces and intermolecular interactions. The series of investigations of selected medium-size molecules and complexes have shown how different instrumental setups can be used to obtain a variety of results on molecular properties. The systems studied, include molecules of biological interest such as anethole and molecules of astrophysical interest such as N-methylaminoethanol. Moreover halogenation effects have been investigated on halogen substituted tautomeric systems (5-chlorohydroxypyridine and 6-chlorohydroxypyridine), where it has shown that the position of the inserted halogen atom affects the prototropic equilibrium. As for fluorination effects, interesting results have been achieved investigating some small complexes where a molecule of water is used as a probe to reveal the changes on the electrostatic potential of different fluorinated compounds: 2-fluoropyridine, 3-fluoropyridine and penta-fluoropyridine. While in the case of the molecular complex between water and 2-fluoropyridine and 3-fluoropyridine the geometry of the complex with one water molecule is analogous to that of pyridine with the water molecule linked to the pyridine nitrogen, the case of pentafluoropyridine reveals the effect of perfluorination and the water oxygen points towards the positive center of the pyridine ring. Additional molecular adducts with a molecule of water have been analyzed (benzylamine-water and acrylic acid-water) in order to reveal the stabilizing driving forces that characterize these complexes.

Variational Monte Carlo study of the hydrogen electronic structure at ultra-high pressure

Die causa finalis der vorliegenden Arbeit ist das Verständnis des Phasendiagramms von Wasserstoff bei ultrahohen Drücken, welche von nichtleitendem H2 bis hin zu metallischem H reichen. Da die Voraussetzungen für ultrahohen Druck im Labor schwer zu schaffen sind, bilden Computersimulationen ein wichtiges alternatives Untersuchungsinstrument. Allerdings sind solche Berechnungen eine große Herausforderung. Eines der größten Probleme ist die genaue Auswertung des Born-Oppenheimer Potentials, welches sowohl für die nichtleitende als auch für die metallische Phase geeignet sein muss. Außerdem muss es die starken Korrelationen berücksichtigen, die durch die kovalenten H2 Bindungen und die eventuellen Phasenübergänge hervorgerufen werden. Auf dieses Problem haben unsere Anstrengungen abgezielt. Im Kontext von Variationellem Monte Carlo (VMC) ist die Shadow Wave Function (SWF) eine sehr vielversprechende Option. Aufgrund ihrer Flexibilität sowohl lokalisierte als auch delokalisierte Systeme zu beschreiben sowie ihrer Fähigkeit Korrelationen hoher Ordnung zu berücksichtigen, ist sie ein idealer Kandidat für unsere Zwecke. Unglücklicherweise bringt ihre Formulierung ein Vorzeichenproblem mit sich, was die Anwendbarkeit limitiert. Nichtsdestotrotz ist es möglich diese Schwierigkeit zu umgehen indem man die Knotenstruktur a priori festlegt. Durch diesen Formalismus waren wir in der Lage die Beschreibung der Elektronenstruktur von Wasserstoff signifikant zu verbessern, was eine sehr vielversprechende Perspektive bietet. Während dieser Forschung haben wir also die Natur des Vorzeichenproblems untersucht, das sich auf die SWF auswirkt, und dabei ein tieferes Verständnis seines Ursprungs erlangt. Die vorliegende Arbeit ist in vier Kapitel unterteilt. Das erste Kapitel führt VMC und die SWF mit besonderer Ausrichtung auf fermionische Systeme ein. Kapitel 2 skizziert die Literatur über das Phasendiagramm von Wasserstoff bei ultrahohem Druck. Das dritte Kapitel präsentiert die Implementierungen unseres VMC Programms und die erhaltenen Ergebnisse. Zum Abschluss fasst Kapitel 4 unsere Bestrebungen zur Lösung des zur SWF zugehörigen Vorzeichenproblems zusammen.

Novel algorithms for electronic structure based molecular dynamics with linear system-size scaling

Die vorliegende Arbeit behandelt die Entwicklung und Verbesserung von linear skalierenden Algorithmen für Elektronenstruktur basierte Molekulardynamik. Molekulardynamik ist eine Methode zur Computersimulation des komplexen Zusammenspiels zwischen Atomen und Molekülen bei endlicher Temperatur. Ein entscheidender Vorteil dieser Methode ist ihre hohe Genauigkeit und Vorhersagekraft. Allerdings verhindert der Rechenaufwand, welcher grundsätzlich kubisch mit der Anzahl der Atome skaliert, die Anwendung auf große Systeme und lange Zeitskalen. Ausgehend von einem neuen Formalismus, basierend auf dem großkanonischen Potential und einer Faktorisierung der Dichtematrix, wird die Diagonalisierung der entsprechenden Hamiltonmatrix vermieden. Dieser nutzt aus, dass die Hamilton- und die Dichtematrix aufgrund von Lokalisierung dünn besetzt sind. Das reduziert den Rechenaufwand so, dass er linear mit der Systemgröße skaliert. Um seine Effizienz zu demonstrieren, wird der daraus entstehende Algorithmus auf ein System mit flüssigem Methan angewandt, das extremem Druck (etwa 100 GPa) und extremer Temperatur (2000 - 8000 K) ausgesetzt ist. In der Simulation dissoziiert Methan bei Temperaturen oberhalb von 4000 K. Die Bildung von sp²-gebundenem polymerischen Kohlenstoff wird beobachtet. Die Simulationen liefern keinen Hinweis auf die Entstehung von Diamant und wirken sich daher auf die bisherigen Planetenmodelle von Neptun und Uranus aus. Da das Umgehen der Diagonalisierung der Hamiltonmatrix die Inversion von Matrizen mit sich bringt, wird zusätzlich das Problem behandelt, eine (inverse) p-te Wurzel einer gegebenen Matrix zu berechnen. Dies resultiert in einer neuen Formel für symmetrisch positiv definite Matrizen. Sie verallgemeinert die Newton-Schulz Iteration, Altmans Formel für beschränkte und nicht singuläre Operatoren und Newtons Methode zur Berechnung von Nullstellen von Funktionen. Der Nachweis wird erbracht, dass die Konvergenzordnung immer mindestens quadratisch ist und adaptives Anpassen eines Parameters q in allen Fällen zu besseren Ergebnissen führt.